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https://scikit-learn.org/dev/whats_new/v1.1.html	# Version 1.1.0¶ In Development ## Legend for changelogs¶ • Major Feature : something big that you couldn’t do before. • Feature : something that you couldn’t do before. • Efficiency : an existing feature now may not require as much computation or memory. • Enhancement : a miscellaneous minor improvement. • Fix : something that previously didn’t work as documentated – or according to reasonable expectations – should now work. • API Change : you will need to change your code to have the same effect in the future; or a feature will be removed in the future. ## Minimal dependencies¶ Version 1.1.0 of scikit-learn requires python 3.7+, numpy 1.14.6+ and scipy 1.1.0+. Optional minimal dependency is matplotlib 2.2.3+. Put the changes in their relevant module. ## Changed models¶ The following estimators and functions, when fit with the same data and parameters, may produce different models from the previous version. This often occurs due to changes in the modelling logic (bug fixes or enhancements), or in random sampling procedures. • Efficiency cluster.KMeans now defaults to algorithm="lloyd" instead of algorithm="auto", which was equivalent to algorithm="elkan". Lloyd’s algorithm and Elkan’s algorithm converge to the same solution, up to numerical rounding errors, but in general Lloyd’s algorithm uses much less memory, and it is often faster. • Fix The eigenvectors initialization for cluster.SpectralClustering and manifold.SpectralEmbedding now samples from a Gaussian when using the 'amg' or 'lobpcg' solver. This change improves numerical stability of the solver, but may result in a different model. • Fix feature_selection.f_regression and feature_selection.r_regression will now returned finite score by default instead of np.nan and np.inf for some corner case. You can use force_finite=False if you really want to get non-finite values and keep the old behavior. ## Changelog¶ • Enhancement All scikit-learn models now generate a more informative error message when some input contains unexpected NaN or infinite values. In particular the message contains the input name (“X”, “y” or “sample_weight”) and if an unexpected NaN value is found in X, the error message suggests potential solutions. #21219 by Olivier Grisel. • Enhancement All scikit-learn models now generate a more informative error message when setting invalid hyper-parameters with set_params. #21542 by Olivier Grisel. ### sklearn.cluster¶ • Enhancement cluster.SpectralClustering and cluster.spectral now include the new 'cluster_qr' method from cluster.cluster_qr that clusters samples in the embedding space as an alternative to the existing 'kmeans' and 'discrete' methods. See cluster.spectral_clustering for more details. #21148 by Andrew Knyazev • Efficiency In cluster.KMeans, the default algorithm is now "lloyd" which is the full classical EM-style algorithm. Both "auto" and "full" are deprecated and will be removed in version 1.3. They are now aliases for "lloyd". The previous default was "auto", which relied on Elkan’s algorithm. Lloyd’s algorithm uses less memory than Elkan’s, it is faster on many datasets, and its results are identical, hence the change. #21735 by Aurélien Geron. • Enhancement cluster.SpectralClustering now raises consistent error messages when passed invalid values for n_clusters, n_init, gamma, n_neighbors, eigen_tol or degree. #21881 by Hugo Vassard. ### sklearn.feature_extraction¶ • Feature Added auto mode to feature_selection.SequentialFeatureSelection. If the argument n_features_to_select is 'auto', select features until the score improvement does not exceed the argument tol. The default value of n_features_to_select changed from None to ‘warn’ in 1.1 and will become 'auto' in 1.3. None and 'warn' will be removed in 1.3. #20145 by @murata-yu. ### sklearn.metrics¶ • Feature r2_score and explained_variance_score have a new force_finite parameter. Setting this parameter to False will return the actual non-finite score in case of perfect predictions or constant y_true, instead of the finite approximation (1.0 and 0.0 respectively) currently returned by default. #17266 by Sylvain Marié. • API Change metrics.DistanceMetric has been moved from sklearn.neighbors to sklearn.metric. Using neighbors.DistanceMetric for imports is still valid for backward compatibility, but this alias will be removed in 1.3. #21177 by Julien Jerphanion. • API Change Parameters sample_weight and multioutput of metrics. mean_absolute_percentage_error are now keyword-only, in accordance with SLEP009. A deprecation cycle was introduced. #21576 by Paul-Emile Dugnat. • API Change The "wminkowski" metric of sklearn.metrics.DistanceMetric is deprecated and will be removed in version 1.3. Instead the existing "minkowski" metric now takes in an optional w parameter for weights. This deprecation aims at remaining consistent with SciPy 1.8 convention. #21873 by Yar Khine Phyo • Fix metrics.silhouette_score now supports integer input for precomputed distances. #22108 by Thomas Fan. ### sklearn.preprocessing¶ • Enhancement Adds a subsample parameter to preprocessing.KBinsDiscretizer. This allows specifying a maximum number of samples to be used while fitting the model. The option is only available when strategy is set to quantile. #21445 by Felipe Bidu and Amanda Dsouza. • Enhancement Added the get_feature_names_out method and a new parameter feature_names_out to preprocessing.FunctionTransformer. You can set feature_names_out to ‘one-to-one’ to use the input features names as the output feature names, or you can set it to a callable that returns the output feature names. This is especially useful when the transformer changes the number of features. If feature_names_out is None (which is the default), then get_output_feature_names is not defined. #21569 by Aurélien Geron. • Fix preprocessing.LabelBinarizer now validates input parameters in fit instead of __init__. #21434 by Krum Arnaudov. ## Code and Documentation Contributors¶ Thanks to everyone who has contributed to the maintenance and improvement of the project since version 1.0, including: TODO: update at the time of the release.	2022-01-22 11:18:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25600665807724, "perplexity": 5939.958869528874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303845.33/warc/CC-MAIN-20220122103819-20220122133819-00477.warc.gz"}
https://itectec.com/superuser/how-do-wake-timers-work/	# How do wake timers work sleepwake-up Windows most commonly places a computer in S3 (standby/save-to-RAM) mode, where power is cut from the CPU but not to RAM. If power is cut to the CPU, then how are wake timers triggered? Which component knows when to automatically wake the computer up? If it is in the BIOS, how does Windows inform the BIOS of the next wakeup time? The programming of these registers is done in the Linux kernel in cmos_set_alarm.	2021-10-19 21:26:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1908469945192337, "perplexity": 6328.752594658581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585281.35/warc/CC-MAIN-20211019202148-20211019232148-00527.warc.gz"}
https://code.tutsplus.com/courses/regular-expressions-up-and-running/lessons/carets-and-dollars	Lessons:26Length:1.7 hours • Overview • Transcript # 2.3 Carets and Dollars To specify that we want to look for a character that occurs at the beginning of a string, we use the caret symbol. In this lesson, we'll also learn about using the \$ symbol to specify the end of a string. We'll use these symbols to limit the values we are searching for in a list of file types.	2021-09-25 12:50:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7314618229866028, "perplexity": 965.2754849125828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057622.15/warc/CC-MAIN-20210925112158-20210925142158-00501.warc.gz"}
https://math.stackexchange.com/questions/1435339/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-be-divide	# For numbers divisible by three, why is the sum of their digits able to be divided by three? [duplicate] When you add the digits of any number that is divisible by three, that sum of those digits also appears to be divisible by three (with no remainder). For example a number (which I randomly grab from the top of my head): 289752 whose digits sum to 33 (2+8+9+7+5+2=33) That sum 33 is divisible by three and so is the original number 289752. This is not the case when dividing by 2, for example 12 is divisible by two but when its digits are summed (1+2=3) you receive 3 which is NOT divisible by 2. I have yet to be able to find a counter example for this phenomenon of division by 3. Why does this happen? ## marked as duplicate by user223391, Daniel FischerSep 14 '15 at 17:57 • – Brick Sep 14 '15 at 17:47 Let $n=d_0+d_1\times 10+d_2\times 10^2+\cdots d_n\times10^n$ where $d_i$ are the digits. We note that $10\equiv 1 \pmod{3}$, and thus $10^k\equiv 1\pmod{3}$, so $$n\equiv d_0+d_1+\cdots+d_n \pmod{3}$$ So $n\equiv 0 \pmod{3}$ iff $d_0+d_1+\cdots+d_n\equiv 0 \pmod{3}$ If you don't know modular stuff, wikipedia has an article I'm sure. Just google it. We have \begin{align}N&=a_0+a_1\cdot 10^1+a_2\cdot 10^2+\cdots+a_m\cdot 10^m\\&=a_0+(9a_1+a_1)+(99a_2+a_2)+\cdots +(99\cdots 9a_m+a_m)\\&=(9a_1+99a_2+\cdots+99\cdots 99a_m)+(a_0+a_1+a_2+a_3+\cdots+a_m)\\&=(\text{a number divisible by 3})+a_0+a_1+a_2+\cdots+a_m\end{align} So, if $N$ is a multiple of $3$, then $a_1+a_2+\cdots+a_m$ is a multiple of $3$. If we write a positve integer x in the form $x=a_0+10a_1+...+10^na_n$ for positive integers $n,a_0,...,a_n$, we see that $x \equiv a_0+a_1+...+a_n (mod 3)$, since $10^k \equiv 1 (mod 3)$. Thus it can be seen that $x$ is divisible by 3 if, and only if, the sum of its digits is divisible by 3.	2019-05-26 19:06:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7194777131080627, "perplexity": 160.37555625605785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00292.warc.gz"}
http://ssswxb.ihb.ac.cn/indexen.htm	Scan QR Code ### Key Recommendation Display Method: Available online , doi: 10.7541/2019.009 [Abstract](193) [FullText HTML](67) [PDF 529KB](62) Abstract: This study was conducted to investigate the effects of 4 kinds [24L﹕0D (D1), 16L﹕8D (D2), 8L﹕16D (D3), 0L﹕24D (D4)] of photoperiods on feed consumption, digestive enzyme activities and blood hormone of turbotScophthalmus maximus L. juveniles with initial body weight of (30.5±2.0) g in 20 hours (8:00am—4:00am). The results showed that the feed rate decreased with the shorten of illumination time, and feeding peak in D1 group appeared every 8h, meanwhile others appeared at 8:00am and 4:00pm. Activities of protease and amylase of former 3 groups were appeared spike at 12:00am and 8:00pm, and lipase was significantly higher than that of the D4 group. There were no difference of GH contents from 8:00am to 8:00pm among all groups, and D1 group at 4:00am was significantly higher than others, but D4 group was significantly lower than others from 0:00am to 4:00am. COS contents of D1, D2 and D3 groups were not significant difference in 8h after first feeding, and then increased firstly and decreased afterwards; D4 group reached the maximum level at 8:00pm. NE content of D1 and D2 groups were significantly higher than that of the others at 0:00am, meanwhile D4 group was significantly lower than others at 8:00pm. T3 content of D2 group was significantly higher than that of the other groups at 8:00am and 12:00am; D4 group was lower at 8:00pm, and higher at 0:00am than others; D2 and D3 group were lower than those of D1 and D4 group at 4:00am; The highest values of T3 of all groups were appeared at 8:00pm. These results demonstrated that feed intake, digestive enzyme activities and serum hormone contents of turbot juvenile were affected by photoperiod under current experimental conditions. 8—16 lighting period and feed twice daily would be recommended for turbot culture under this intensity of illumination. Available online , doi: 10.7541/2019.027 [Abstract](117) [FullText HTML](33) [PDF 665KB](25) Abstract: We discovered for the first time that Grateloupia turuturu filaments, which developed from discoid crusts, had the ability to form spores under laboratory condition. We hereby defined this category of spores as" disc-filamentospore”. The formation of disc-filamentospores were observed and the effect of various temperatures (6, 12, 16, 20, 24, 30℃) and light intensities (10, 30, 45, 60, 90, 120 μmol/(m2.s)) on the release of disc-filamentospores were analysed. The results indicated that: (1) Carpospores, which formed and released from cystocarps of female gametophyte of G. turuturu, first developed into discoid crusts. Then the discoid crusts were induced to form filaments of monolayer cells, which formed massive plurilocular sporangiums and released large amounts of disc-filamentospores. (2) The formation and release were significantly affected by temperature and light intensity. Our study revealed that the releasing efficiency of disc-filamentospores could get the maximum at 16℃ and 6 0 μmol/(m2·s). (3) The releasing number of disc-filamentospores was evidently reduced when the temperature was lower than 12℃ or higher than 24℃. (4) When the light intensity was less than 30 μmol/(m2·s) or more than 90 μmol/(m2·s), the releasing efficiency of disc-filamentospores was inhibited significantly. Our results improved the asexual reproduction process of Grateloupia turuturu and provided more abundant theoretical basis for its germplasm preservation, artificial breeding and aquaculture. Finally, we suggest a plausible solution to investigate the origin and evolution of Grateloupia turuturu. Available online , doi: 10.7541/2019.028 [Abstract](150) [FullText HTML](48) [PDF 465KB](50) Abstract: Growth rate, feeding, development of organs, disease resistance, adaptability, and self-regulation to the change of environment are all associated with fish health assessment. With the rapid development of aquaculture, the assessment of fish health condition is increasingly important. The present manuscript reviewed the evaluation procedures and indices related to fish health condition and available shortcomings, and also discussed the possibility of developing new methods to assess fish health condition using computer technology and biotechnology, which are expected to provide new insights for fish health assessment. Available online , doi: 10.7541/2019.026 [Abstract](104) [FullText HTML](32) [PDF 630KB](17) Abstract: Microcystis bloom has caused many environmental problems, and its mechanism of bloom-formation and adaptation has been noticed wildly. To examine the possible information transfer by chemicals between both algae, the effect of Ochromonas and its culture media filtrate on the growth and physiological traits of Microcystis aeruginosa was investigated in this study. The results indicated that the cell density in Microcystis decreased significantly, while the cell density in Ochromonas increased markedly when Microcystis and Ochromonas were co-cultured at three initial cell density (1﹕4, 1﹕1 and 4﹕1). Moreover, the culture media filtrate ofOchromonas sp. could inhibit the growth, and resulted in an increase of malondialdehyde (MDA) content and catalase (CAT) activity. Additionally, the content of extracellular polysaccharides (EPS) increased markedly in Microcystis when it was inoculated into the culture media filtrate of Ochromonas sp. These results indicated that Ochromonas not only could prey on Microcystis, but also might release some of the chemicals to inhibit the growth and physiological parameters of Microcystis. This suggested that Ochromonas might be used to inhibit the early proliferation of algae as a potential control of algae blooms. Available online , doi: 10.7541/2019.001 [Abstract](110) [FullText HTML](27) [PDF 784KB](18) Abstract: Through regulating the post-transcriptional maturation of UsnRNAs (U-rich small nuclear RNAs), integrator complex has an effect on the intron splicing of pre-mRNA. Therefore, integrator complex plays an important role in the production of mature mRNA. However, the regulation and developmental functions of integrator complex are poorly understood in vertebrates. In this study, zebrafish (Danio rerio) was used to generate the ints12 knockout model by CRISPR/Cas9, and two homozygous lines were generated with different frame-shifts. Observation on the misprocessing of UsnRNA 3′ ends in zygotic mutant of ints12 (Zints12) was conducted through real-time quantitative PCR analysis. When compared with the control fish, the overall growth of Zints12 was largely retarded, and the Zints12 population was all-male. Further studies showed that cell proliferation was significantly interfered, and the level of introns retention of ints12 transcripts was significantly increased in Zints12, suggesting an " auto-regulation loop” in the splicing regulation by ints12. Overall, we obtained homozygous mutants of zebrafish ints12 by gene knockout technology and revealed that zebrafish ints12 regulates UsnRNA 3′-box processing to exert various effects on early embryonic development and body growth. Available online , doi: 10.7541/2019.002 [Abstract](93) [FullText HTML](33) [PDF 699KB](21) Abstract: In order to investigate the role of TRAF6 in Lethenteron morii with signal pathway of TLR, the full-length cDNA of LmTRAF6 was cloned. The distribution of tissues (supraneural body, gill, intestine, kidney) and related gene expression in both juvenile and adult were studied with real-time quantitative PCR. Additionally, the change of gene expression in those tissues from adult L. morii was also examined after challenged by Pseudomonas aeruginosa. A recombinant plasmid pEGFP-TRAF6 was constructed by the double digestion method, and transformed into the HEK293T cells. Fluorescence observation was conducted after 48 hours, and the results were photographed. The results showed that the length of LmTRAF6 cDNA was 2751 bp, including 1785 bp open reading frame (ORF) and 594 amino acids. The structure of LmTRAF6 was highly similar to that in other mammal and fish species, containing one RING domain, one coiled-coil region, one MATH domain and two zinc fingers. Phylogenetic tree showed that LmTRAF6 was evolutionarily closer to that in mammals and fishes, but not to that in Drosophila melanogaster and Penaeus chinensis. LmTRAF6 was expressed in all tested tissues and their developmental stages. However, higher expression was detected in heart, skin, gill, liver of juvenile, as well as in kidney, gill, and muscle of adult. When adult L. morii was challenged by Pseudomonas aeruginosa, the expression of LmTRAF6 in gill, intestine and kidney reached to the peak after 24h. Subcellular localization showed that LmTRAF6 was expressed in both cytoplasm and nucleus. Available online , doi: 10.7541/2019.014 [Abstract](185) [FullText HTML](89) [PDF 725KB](26) Abstract: The grass carp (Ctenopharyngodon idellus) infected with the hemorrhage virus was used to analyze the intestinal microbiota by using high-throughput sequencing. The results showed that microbiota significantly differed between grass carp reovirus (GCRV)-infected and control grass carp (multiple response permutation procedure (MRPP), analysis of similarity (ANOSIM), and Adonis; P<0.01). When we compared alpha diversity, we found that Shannon-Wiener index, inverse of Simpson's original index and Pielou’s evenness index of intestinal microbiota were all significantly decreased after infecting with GCRV (independent samplest-test, P<0.05). Besides, we found that the individual difference within GCRV-infected group was significantly greater than that in the controls (Wilcoxon signed-rank test,P<0.05), suggesting that the intestinal microbiota in GCRV-infected grass carps became disorganized and lost their original balance. Proteobacteria, Firmicutes, Fusobacteriaceae, and Bacteroidetes were dominant phylum in both GCRV-infected group and controls. However, the relative abundance of operational taxonomic units (OTUs) between the two groups was different. For example, OTU_69 (Pasteurellaceae), OTU_504 (Comamonadaceae), and OTU_1898 (Cetobacterium) were all significantly lower than that of controls (t-test, P<0.05), confirming that GCRV could make intestinal microbiota of grass carps became disorganized. The stability of intestinal microbiota is important for health of host. By detecting changes in the intestinal microbiota of GCRV-infected grass carp, we will be able to provide theoretical basis and data reference for the prevention and treatment of common disease of farmed fish, as well as providing a reference for healthy breeding. Available online , doi: 10.7541/2019.021 [Abstract](143) [FullText HTML](86) [PDF 708KB](15) Abstract: In this study, the method of irradiation breeding was applied to wetland plants in order to improve its cold resistance. Herein, 25, 45, 60 and 80 Gy doses of gamma ray were used to irradiate Canna indica Linn (CIL) seeds, and the dose rate was 6 Gy/min. After CIL seeds were grown up, they were exposed to a low temperature stage, and their cold hardiness was accordingly evaluated. The results showed that the activity of superoxide dismutase (SOD), peroxidase (POD), and catalase (CAT) in irradiated CIL seeds were higher than that of the control group. Malondialdehyde (MDA) in control group accumulated in large quantities under low temperature, which was higher than that of the irradiation treatment group. Besides, at low temperature, the content of proline, the total soluble sugar, and protein of irradiated seedlings were totally higher than that of the control group. The score of cold resistance in irradiated group was also higher than that of the control group, and the 45 Gy dose of gamma ray group showed the highest score. Moreover, CIL with the strongest cold resistance was planted in the constructed wetland to evaluate its purification effect in winter, and evaluation indexes were total phosphorus (TP), total nitrogen (TN), and chemical oxygen demand (COD). Results revealed that the removal rate of TP in the group of CIL in constructed wetland by using 45 Gy dose of gamma ray was significantly higher than that of the control group (P<0.05). It can be concluded that irradiation treatment can effectively improve the cold resistance ofCIL and enhance the effect of artificial wetland purification in winter. Available online , doi: 10.7541/2019.024 [Abstract](65) [FullText HTML](40) [PDF 733KB](5) Abstract: A newly isolated spontaneously flocculating microalgae Parachlorella kessleri F01 was used as the material, and the algae sample in autotrophic cultivation of one-step culture method was used as the control group. A two-step culture method was designed in which glucose was supplemented for mixotrophic cultivation at stage Ⅰ, and nutritional limitation treatments were done at stage Ⅱ, and we studied their effects on the lipid accumulation and flocculation performance of the algae. The algae cell number was determined by a hemocytometer. Biomass was measured via dry weight, and the total lipid was quantified with staining method. The extracellular polymeric substances (EPS) components of algae were analyzed by three-dimensional fluorescence spectroscopy. The results showed that: (1) The optimum glucose concentration was 10 g/L at stage Ⅰ. The alga lipid productivity reached to 204.25 mg/L/d on the 10th harvesting day, which was 16.20 times of that in the control group, and the self-flocculation rate of alga cell was 96.1% after sitting for 12h, which has no significant difference with that in the control group. (2) On the basis of stage Ⅰ, alga cells were cultured for 1 day in stage Ⅱ with different elemental treatments. The alga lipid productivity were 242.64 mg/L/d and 227.61 mg/L/d in the low-glucose group and the low-glucose coupled with low-nitrogen group, respectively, increasing by 18.8% and 11.4% of those at stage Ⅰ. After 4 days cultivation, the alga lipid productions of the four treatment groups including low-glucose, no-glucose, low-nitrogen and the low-glucose coupled with low-nitrogen significantly increased compared with those in the control group and stage Ⅰ. The highest production reached to 3.08 g/L in the low-glucose and low-nitrogen co-treatment group, which was 23.69 times of that in the control group, and increased by 51.0% compared with that in stage Ⅰ. The self-flocculation rates in four treatment groups at stage Ⅱ were nearly above 85.0%, which could satisfy the harvesting requirements. (3) The content of protein tryptophan in alga EPS was positively related to the self-flocculation rate. Different culture treatments could change the protein tryptophan content in EPS of algae cells, and thus affect their flocculation performance. Self-flocculation Parachlorella kessleri F01 is an excellent potential alga for biodiesel production. The two-step culture method can greatly enhance its lipid production. The advantage of self-flocculation combined with two-step culture method is expected to be the key breakthrough to solve the bottleneck of biodiesel production technology of microalgae. Available online , doi: 10.7541/2019.011 [Abstract](139) [FullText HTML](72) [PDF 447KB](34) Abstract: This study was conducted to investigate the effect of transportation stress on the plasma biochemical indices, body color, fish quality of gibel carp [Carassis auratus gibelio var. CAS III, body weight of (116.46±2.09) g] and also water quality. Transportation was simulated on an automobile vibration bench for 4h. After 4h simulative transportation, the ammonia concentration of water in bags increased significantly (P<0.01), and the dissolved oxygen of water in bags was increased (P<0.05), while the pH value decreased significantly (P<0.05). Fish plasma cortisol, glucose and MDA concentration increased significantly (P<0.01), while plasma lactic acid concentration decreased (P<0.01). Plasma GSH-PX significantly decreased after 4h simulative transportation (P<0.05), and plasma SOD and CAT had a low value after simulative transportation (P>0.05). Dorsal skin showed significantly decreasing L* values after 4h simulative transportation (P<0.01), and the abdomen and lateral line L* values also decreased with no significance (P>0.05). While a* (P>0.05) and b*(P<0.05) values declined in these three parts after 4h transportation. Cohesiveness, chewiness and resilience decreased significantly in fillet (P<0.05). The fillet gumminess, springiness and adhesiveness were slightly decreased (P>0.05), while its hardness increased (P>0.05). The results indicated that transportation could induce stress response of gibel carp and reduce fish quality. Available online , doi: 10.7541/2019.023 [Abstract](47) [FullText HTML](24) [PDF 745KB](5) Abstract: There is increasing evidence that different light intensities strongly modulate the effects of ocean acidification (OA) on marine phytoplankton, and elevated atmospheric CO2 concentration can affect the photosynthetic capacity of marine diatom to different degrees, however, little attention had been paid to their interaction on diatom. In this study, the growth rate, net photosynthetic (Pn) rate, biochemical composition, extracellular carbonic anhydrase (eCA) activity, and Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) activity were investigated when Phaeodactylum tricornutum was grown under different light intensities and CO2 concentrations. The results showed that the specific growth and Pn rates in P. tricornutum were not significantly affected by CO2 concentration under low light intensity, whereas in presence of the high light intensity (HLI), elevated CO2 concentration was beneficial to promote the increase of the rate of Pn. The eCA activity, chlorophyll content, and soluble protein content decreased with increase of CO2 concentration, regardless of the high or low light. It was revealed that no significant difference (P=0.6) was found in the net photosynthetic (oxygen evolution) rate between the high-CO2 (HC)- and low-CO2 (LC)-grown plants. Under LLI, RuBisCO activity of HC-grown algae was 2.42 and 1.39 times higher than that of LC- or MC-grown ones. However, RuBisCO activity of HC-grown algae was 6.72 and 3.45 times greater than that of LC- or MC-grown ones under high light. These results indicate that the algae can adapt changes of light intensity and CO2 concentrations in the environment by adjusting the allocation of energy during the operation of the CO2-concentrating mechanism and photosynthesis. Available online , doi: 10.7541/2019.020 [Abstract](82) [FullText HTML](31) [PDF 680KB](14) Abstract: In order to understand the community characteristics of zooplankton and relationships with environmental factors, and aimed to use zooplankton community parameters monitoring the water quality of water source reservoirs, a seasonal investigation was conducted on the water quality parameters, abundance and biomass of zooplankton in water source reservoirs (K1— K10) from January, 2014 to October, 2016 in Zhejiang Province. The relationships and action mechanism between water environment factors and zooplankton abundance and biomass were studied by the method of multiple stepwise regression and path analysis. The results showed that the average abundance of zooplankton in the reservoirs was 97.5 ind./L from 2014 to 2016, mainly composed of copepods nauplii (36.3%), Rotifer (28.4%) and Cyclops (20.0%). The average biomass was 289.3 μg/L, which was mainly composed of Cladocera (39.3%), Cyclops (29.0%) and Cyclops (14.5%). Chl. a content was the decisive factor of zooplankton abundance in spring and summer, and TP content was the limiting factor for fluctuation of community abundance in autumn and winter, and the community abundance was affected by TN through N﹕P ratio in spring. DO content was a decisive factor in the development of zooplankton biomass in winter and summer, and the community biomass was promoted by DO through reducing N﹕P ratio in winter. The present zooplankton stock in the reservoirs was affected by the fluctuation of TP content, the change of N﹕P ratio and the Chl.a content of the water body ultimately reflected. Available online , doi: 10.7541/2019.019 [Abstract](223) [FullText HTML](131) [PDF 685KB](32) Abstract: In order to provide basic information for protecting and rational utilizing resources of the Yangtze Estuary, feeding types, trophic level, energy flow, and food web, 43 aquatic animals were studied by using stomach content analysis. The species were classified into four groups according to their feeding habit: plankton feeding, benthic feeding, nekton feeding, and mixed feeding (benthic and nekton feeding). Among the samples collected in this study, the plankton predators were dominant accountings for 39.53%, and the nekton predators had the minimum dominancy, accounting for 11.63%. The results of trophic level showed that according to the dietary habits, these aquatic animals can be also divided into 3 different groups, which herbivorous consumers were dominant, and accounted for 76.75%, while intermediate carnivorous fish had the minimum dominancy, accounting for 4.65%. Through the overfishing and environmental degradation, the trophic levels of the 12 common fish in the Yangtze Estuar were generally lower than those of the 1990s, the average trophic level dropped from 3.80 to 2.87. According to each consumer’s stomach content, this study determined the benthic algae and phytoplankton, and organic detritus, including particulate organic matter (POM), as the main producers of the Yangtze Estuar aquatic food web, and drew their own energy flow. Eventually, based on the nutritional relationship among different aquatic animals, this study proposed a simplified model for the Yangtze Estuar aquatic animals’ food web. Available online , doi: 10.7541/2019.013 [Abstract](70) [FullText HTML](29) [PDF 942KB](8) Abstract: To investigate the effects of acute cold stress on the mucosal histology in different sections of the juvenile Pelodiscus sinensis, the activity of serum diamine oxidase (DAO) and histological features of intestinal mucosa in Chinese soft-shelled turtle in culture temperature and acute cold stress were conducted. The first acute cold stress reduced the DAO activity with the lowest level at 48 h after cold stress. In the acute cold stress and rewarming experiment, the DAO activity decreased significantly after 3 days of cold stress and then restored to normal level with the recovery of temperature. Histopathological results showed no significant difference in the morphology of mucosal epithelium in the intestine (posterior segment of ileum and large intestine) between acute cold stress group and control group. There were no significant difference in the number of goblet cells, the length of villus and the ratio of villus length to crypt depth in the posterior segment of ileum between acute cold stress group and control group, while the mucosal thickness in the posterior segment of ileum significantly decreased in the acute cold stress group in comparison to control group. Acute cold stress significantly reduced the large intestine number of goblet cells. The structures of the intestinal mucosal mechanical barrier of Chinese soft-shelled turtle under acute cold stress are an intestinal segment dependent pattern. These results suggest that the various segments of the intestine of Chinese soft-shelled turtle have a special response style to acute cold stress. Available online , doi: 10.7541/2019.004 [Abstract](73) [FullText HTML](30) [PDF 1172KB](9) Abstract: In this study, the cDNA sequences of FcγRα and FcRγ subunits of FcγR rainbow trout were cloned for the first time by RACE technique. The sequences of FcγRα and FcRγ were analyzed by using bioinformatics software. The expressions of the genes in different cell subpopulations and tissues, as well as in the head kidney after Poly (I∶C) and lipopolysaccharide (LPS) stimulations were analyzed by real-time fluorescent quantitative polymerase chain reaction (PCR). The results showed that the full-length cDNA of FcγRα is 1677 bp with an open reading frame (ORF) of 954bp encoding 317 amino acids. The FcγRα is composed of a signal peptide and two Ig-like domains, however, without including transmembrane and intracellular regions. There are three kinds of FcγR subunit, involving FcRγ1, FcRγ2a, and FcRγ2b. FcRγ1 and FcRγ2 genes are located on different chromosomes, while FcRγ2a and FcRγ2b are two splicing isoforms of FcRγ2 gene. These subunits are composed of signal peptide, transmembrane domain, and immunoreceptor tyrosine-based activation motif (ITAM). Amino acid sequence similarity analysis showed that the highest identity (30%) of FcγRα is between rainbow trout and channel catfish (Ictalurus punctatus), and FcRγ1 and FcRγ2a/2b in rainbow trout have the maximum sequence identity (40%) with mammalian FcRγ. Tissue distribution analysis showed that the expression of FcγRα, FcRγ1, and FcRγ2a/2b was higher in head kidney, spleen, and blood cells, respectively. Analysis of cell subpopulations showed that the expression of FcγRα, FcRγ1, and FcRγ2a/2b was the highest in the myeloid cell population. In addition, the expression of FcγRα, FcRγ1, and FcRγ2a/2b in the head kidney was significantly up-regulated after LPS and Poly (I 鲶C) stimulations, indicating that FcγR plays an important role in the antibacterial and antiviral immunity. Available online , doi: 10.7541/2019.025 [Abstract](132) [FullText HTML](79) [PDF 944KB](14) Abstract: In this study, we explored the ability to remove nitrate and phosphorus of two strains of Stigeoclonium spp. (SHY-370 and HB1617) by setting different initial concentrations of ammonia nitrogen and nitrogen/ phosphorus (N/P) ratios in synthetic wastewater. The results indicated that different initial concentrations of ammonia nitrogen in synthetic wastewater could affect the biomass concentration and the ability to remove N and P of SHY-370 and HB1617. The maximum ammonia nitrogen concentration in synthetic wastewater that SHY-370 can tolerate was 10mg/L, while that was 5mg/L for HB1617. The ammonia-nitrogen removal rate of SHY-370 and HB1617 was above 97% and the maximum daily ammonia-nitrogen removal rate was 3.98 mg/L/d, while the initial concentration of ammonia nitrogen in synthetic wastewater varied between 1-10mg/L. N/P ratios had a slight impact on the biomass concentration of the SHY-370, however, the biomass concentration of HB1617 was reduced when the corresponding rate was over 20 mg/L. The concentration of total phosphorus (TP) in synthetic wastewater was 10mg/L. When the N/P ratio was 2, the content of TP in synthetic wastewater was higher than 10mg/L, which led to a low TP removal rate. According to the results of our study, we can conclude that SHY-370 and HB1617 are appropriate for the treatment of urban sewage in which the concentration of ammonia nitrogen is relatively low, whereas the concentration of TP and NO3-N is relatively high. Available online , doi: 10.7541/2019.022 [Abstract](49) [FullText HTML](32) [PDF 787KB](4) Abstract: To explore the cause of Potamogeton lucens’s decline, a dominant plant inhabiting the shallow water of Nansi Lake, the physiological and biochemical changes of P.lucens were examined under a group of constant temperatures at 25℃, 30℃, 35℃, and 40℃, respectively, for 3h. The results showed that the contents of protein, soluble sugar and chlorophyll decreased significantly, while the content of malondialdehyde (MDA) increased significantly at a high temperature above 35℃. The results indicated that high temperature above 35℃ had significant damage to P.lucens. The photosystem of P.lucens was more sensitive to heat stress. The characteristics of standardized chlorophyll fluorescence kinetics curves under heat stress were as follows. Peaks at J and K phases were observed, but no L-band was found on the normalized chlorophyll fluorescence kinetics curves. The chlorophyll fluorescence parameters were calculated from the OJIP curves of the heat-treated leaves. The results showed that the initial closing speed of the reaction center (dVG/dto, dV/dto) slowed down with the increase of temperature under heat stress, but it took a shorter time to reach the maximal fluorescence (Tfm). The maximum quantum yield of PSII (Photosystem II) photochemistry (Fv/Fm) decreased. However, the non-photochemical constants (Kn), relative variable fluorescence at the J-step (Vj), and dissipated energy flux (DIo/RC, DIo/CSo, Fo/Fm) increased under heat stress. Although the turn-over number of QA (N), average redox state of QA (Sm/Tfm), and relative variable fluorescence at the I-step (Vi) barely changed, the plastoquinone pool (Sm) decreased significantly at high temperature. Absorption and trapped energy flux per RC (ABS/RC, TRo/RC; reaction center, RC) increased, whereas the electron transport efficiency per RC (ETo/RC) decreased when temperature increased. Heat stress also decreased the trapped energy flux, electron transport flux and density of RCs per CS (TRo/CSo, ETo/CSo, RC/CSo; cross section, CS). These effects of heat stress on photosystem eventually led to a significant reduction in the structure and function index (SFIabs), performance index (PIabs), and drive force for photosynthesis (DF) of the P.lucens leaves. These results demonstrated that heat stress mainly caused inactivation of oxygen-evolving complex of PSII, reduction of the density of RCs, and decrease of photochemical efficiency of RC in P.lucens plants, and these led to the production of reactive oxygen species, and thus caused remarkable damage to cells. Therefore, P.lucens is a sensitive aquatic plant to high temperature in summer. Available online , doi: 10.7541/2019.018 [Abstract](62) [FullText HTML](23) [PDF 973KB](15) Abstract: Hukou section, the connection between the Yangtze River and Poyang Lake for the migration route of many fish species, plays a vital role in the proliferation of fish. A systematic investigation on larval and juvenile fish resources were conducted during the fish breeding period in the Hukou section from May to August 2016. The community structure, dominant species, fish density, time-space distribution and their relationships with environmental factors in Hukou section were studied during the continuous 88-day investigation. A total of 39 larvae and juvenile taxonomic groups including 7 orders and 12 families were identified. Among them, 37 were identified to species level, one was identified to subfamily, and one was identified to family. Hemiculter bleekeri is the first dominant species and other dominant species are Gobiidae, Parabramis pekinensis, Pseudolaubuca sinensis. The larval and juvenile fish density reached its peak level on July 1 with 1230.77 ind./100 m3. The overall fish density showed a trend of decreasing volatility from July 1 to August 15. The cluster analysis divided 6 periods into 2 groups: Late May to early July in group Ⅰand late July to early August in group Ⅱ. Hemiculter bleekeri, Culter alburnus, Coilia nasus, etc. peaked in late June and Parabramis pekinensis, four famous domestic fishes, Siniperca chuatsi, etc. peaked in early July. The density of larval and juvenile fish on the south and north sides of the section were higher than that of the center section. Redundancy analysis (RDA) found that water temperature, transparency, and flow are the main environmental factors affecting the community structure of larval and juvenile fish. Correlation analysis showed highly significant correlation between water level and larval and juvenile fish density (P<0.01). This study indicates a large amount of fishes of early life history in Hukou section. The community structure of larval and juvenile fish is dominated by middle and small-sized fishes, and the proportion of river-lake migratory fishes are relatively high. Larval and juvenile fish have different adaptation characteristics to various environmental conditions. The species showed different degrees of positive and negative correlations with water temperature, transparency and flow. The results provide the scientific basis for the protection strategy of fisheries resource in the middle-lower reaches of the Yangtze River. Available online , doi: 10.7541/2019.16 [Abstract](53) [FullText HTML](27) [PDF 802KB](8) Abstract: Different species of Rhodeinae have been wildly distributed across China. Different species have shown very similar morphological characteristics, making their distinguish to be indeed difficult. In order to compare the morphological differences among Rhodeus sinensis, Acheilongnathus tonkinensis, A. macropterus, A. chankaensis and A. taenianalis by the morphometric characteristics, and enrich the classification features, multivariate morphometrics were used to analyze the morphological variations of five Rhodeinae species in Huaihe River Basin (Henan province, China). The results showed that there were significant differences in the body’s width/body’s length, head’s length/body’s length, snout’s length/body’s length, caudal peduncle’s length/body’s length, dorsal fin base’s length/body’s length, pectoral fin’s length/body’s length, pelvic fin’s length/body’s length, and head’s length/snout’s length among the five species (P<0.01), and there were significant differences in the total length/body’s length and body’s height/body’s length (P<0.05). Therefore, these differences mainly focus on the head, tail, fin, and so on. Principal component analysis, discriminant analysis, and cluster analysis showed that the five species had obvious morphological differences, the most significant difference betweenA. taenianalis and A. tonkinensis was found, and the most insignificant difference was observed between A. taenianalis and A. macropterus. The discriminant accuracy rate of the five species varied from 82.35% to 100%, effectively realizing the distinguish of the five Rhodeinae species. Available online , doi: 10.7541/2019.017 [Abstract](49) [FullText HTML](21) [PDF 793KB](4) Abstract: To establish a simple and reliable index for determining silvering stages of the Japanese eel, Anguilla japonica, we observed the colorations of various body parts and biological characteristics on the reproductive stock of theeels collected in the Yangtze River estuary before starting their oceanic migrations. The characteristics of body color, and the changes in age, total length, body weight, and silvering index were analyzed in the silvering process of the Japanese eel. The two silvering stages are characterized by the colorations of trunk skin as follows: (1) Pre-silver stage: pigments deposited completely on the upper edge of pectoral fin on the lateral sides of trunk, (2) Silver stage: pigments deposited completely on the lower edge of pectoral fin on the lateral sides of trunk.Our results indicated that body size, eye diameter, pectoral fins length and gonad-somatic indexincreased from pre-silver stage to silver stage during the ontogenic process of silvering, and digestive tract index decreased in contrast. The principal component analysis suggested thatthe silver stage eels had enlargement of the eye and pectoralfins, high sexual maturity and the degenerated disgestive tract compared to pre-silver stage eels. Because Japanese eel must swim three thousands kilometers from the growth habitats in northeast Asia to reach the West Mariana Ridge spawning area without feeding, these various modifications to the bodies and physiological changes had indicated that silver eels develop various adaptations that prepare them for their long oceanic migrations. The silver stage eels and pre-silver stage eels could be also distinguished by canonical discriminant function analysis using five characters, which showed up 95% reliability of their correct classification. Our results also suggested that an eye index of about 5.0 is a cut off point for distinguishing the silver stage from the pre-silver stage of the Japanese eels for a convenient use of field survey. Available online , doi: 10.7541/2019.015 [Abstract](73) [FullText HTML](27) [PDF 557KB](16) Abstract: To investigate the structure characteristics of skeleton of Acipenser baeri, the conventional method was used to study the skeletal system of A. baeri Brandt mainly focusing on morphology and taxonomy. The results showed that the skeletal system ofA. baeri Brandt juvenile consists of two parts, axial skeleton and appendicular skeleton. The axial skeleton of A. baeri was composed of skull, vertebral column and ribs. The appendicular skeleton of A. baeri included fin-ray, pterygiophore and girdle. We found that the skeletal system ofA. baeri Brandt was more similar to Acipenser schrencki Brandt than other sturgeons, which probably explained by the long-term life adaptation to the high latitude and low temperature environment. Available online , doi: 10.7541/2019.012 [Abstract](104) [FullText HTML](65) [PDF 753KB](12) Abstract: To investigate the effects of histamine and Lactobacillus reuteri on Pelteobagrus fulvidraco, three isonitrogenous diets, namely diet C (control, with a 147 mg/kg content of histamine), diet H (with a 479 mg/kg content of histamine) and diet H+B (histamine+ bacteria: a 496 mg/kg content of histamine and 1×105 CFU/g L. reuteri), were formulated for a 56-day trial of P. fulvidraco juveniles (14.23±0.65) g. Our data indicated that plasma alanine aminotransferase (ALT) and aspartate aminotransferase (AST) activity were significantly lower in group H+B compared with those of group H (P<0.05), while there was no significant difference between group H+B and group C (P>0.05). Meanwhile, liver glutathione-s-transferase (GSH-ST) activity and malondialdehyde (MDA) content were dramatically reduced in group H+B compared with those of group H (P<0.05), while there was no significant difference between group H+B and group C (P>0.05). Furthermore, the HE staining showed that there were inflammatory cells infiltrating in the liver of fish fed with diet H, while no hepatocyte abnormality observed in group C and group H+B, and that the intestinal folds decreased significantly with shorter and edema in diet H group, while this is no marked difference in the length of intestinal folds between group C and H+B. Overall, our studies indicated the protective effect ofL. reuteri against histamine in cultured fish diet. Available online , doi: 10.7541/2019.010 [Abstract](180) [FullText HTML](114) [PDF 530KB](13) Abstract: To investigate the effects of exhaustive chasing training on parameters of respiratory and circulatory system and excess post-exercise oxygen consumption (EPOC) in juvenile qingbo (Spinibarbus sinensis) and rock carp (Procypris rabaudi), sixty samples of S. sinensis (28.36±0.08) g and sixty samples of P. rabaudi (19.53±0.13) g were randomly divided (equally 30 fish in each group) into control group and training group, respectively. Then, these fish in the training group were analyzed under exhaustive chasing training once per day for 3 weeks at 25℃ to measure the heart index, gill index, hematological parameters, and EPOC. The results showed that there were no significant differences in the heart index, gill index, hemoglobin content, and number of red cells between the control group and training group of S. sinensis and Procypris rabaudi(P<0.05). The gill index in the control group ofP. rabaudi was significantly lower than that in the control group of S. sinensis(P>0.05), whereas the heart index, hemoglobin content, and number of red cells in the control group ofP. rabaudi were not significantly different than that in the control group of S. sinensis(P<0.05). No significant differences were found in pre-exercise metabolic rate, peak post-exercise metabolic rate, factorial metabolic scope, and recovery rate between the control group and training group (P>0.05), whereas duration of EPOC in the training group was significantly higher than that in the control group ofS. sinensis (P<0.05). The pre-exercise metabolic rate in the control group was significantly lower than that in the training group (P<0.05), whereas peak post-exercise metabolic rate and factorial metabolic scope, duration of EPOC, and recovery rate in the control group were not significantly different than that in the training group ofP. rabaudi(P>0.05). The pre-exercise metabolic rate, peak post-exercise metabolic rate, EPOC magnitude, and recovery rate in the control group ofP. rabaudi were significantly lower than that in the control group of S. sinensis(P<0.05), whereas factorial metabolic scope and duration of EPOC in the control group ofP. rabaudi were not significantly different than that in the control group of S. sinensis(P>0.05). Our results suggested that (1) exhaustive chasing training had no significant effects on the parameters of respiratory and circulatory system ofS. sinensisandP. rabaudi(P>0.05); (2) exhaustive chasing training significantly increased anaerobic capacity ofS. sinensis(P<0.05); and (3) the pre-exercise metabolic rate and peak post-exercise metabolic rate ofS. sinensis were significantly higher than those of P. rabaudi(P<0.05), which may be related to active habits ofS. sinensis. Available online , doi: 10.7541/2019.003 [Abstract](57) [FullText HTML](20) [PDF 703KB](7) Abstract: The next-generation sequencing technology was used to obtain the whole mitochondrial genome sequences of Gadus macrocephalus. The mitochondrial gene was annotated and its structure was analyzed. The results showed that the circular genome was 16569 bp in length with typical mtDNA components. The mitochondrial genome encodes 13 proteins and 22 tRNAs, 2 rRNAs and a D-Loop region. The base composition showed a tendency of high AT and AT weak negative skewness. There were five kinds of termination codon in the protein coding gene of G. macrocephalus mitochondria, including AGG and AGA which were commonly found in mammalian mitochondria. It was shown that most of the tRNA structures share the classical clover shape, but the tRNA-Ser(GCT) is unique because of a shortage of DHU. Two sequences with the functions of TAS and CSB, as well as 17 bp pyrimidine-rich sequences were found in D-Loop region. The non-coding region contains a conserved sequence controlling the initiation of light chain replication (OL) and a gene spacer with 74 bp. Based on the whole mitochondrial genome sequence and the Cytb gene, the phylogenetic trees were constructed separately with several cod fish that belong to Gadiformes. The results provide an important evidence to reveal the evolutionary status of the pacific cod. Available online , doi: 10.7541/2019.008 [Abstract](53) [FullText HTML](28) [PDF 442KB](9) Abstract: Oils are widely used in aquatic feed to supply essential fatty acids and energy for the fish. However, the abundance of unsaturated fatty acids makes oils susceptible to be oxidized, resulting in harmful effect on the health of fish. To investigate the effect of dietary oxidized oils on the growth performance, body color and antioxidant capacity in liver of channel catfish, Ictalurus punctatus, six isonitrogenous and isolipidic diets were prepared to feed channel catfish (150.5±4.2) g. The six diets were designed with 6% supplementation level of fish oil (FO-6), soybean oil (SO-6), mixed oil (3% fish oil + 3% soybean oil, MO-6), oxidized fish oil (OFO-6), oxidized soybean oil (OSO-6), oxidized mixed oil (3% oxidized fish oil + 3% oxidized soybean oil, OMO-6), respectively. After 8 weeks feeding, the fish fed FO-6, SO-6 or MO-6 diet showed no differences in weight gain (WG), feed conversion ratio (FCR), muscle composition, body color and antioxidant indicators in liver (P>0.05), which indicated that soybean oil could completely substitute the inclusion of fish oil in the diet of channel catfish. The WG and muscle lipid level of the three oxidized oil groups were significantly lower, andFCR, skin yellowness, liver malondialdehyde content, and total bilirubin, direct bilirubin, alanine aminotransferase, aspartate aminotransferase in serum were significantly higher (P<0.05) than that of the normal oil groups. The activities of catalase and superoxide dismutase, and the glutathione contents in liver were reduced by dietary oxidized oils (P<0.05), but the dorsal muscle color and moisture, crude protein, ash content in flesh were not affected (P>0.05). The above results showed that 6% oxidized oils (fish oil, soybean oil, or mixed oil) reduced the growth performance, increased the yellowness of skin and damaged the antioxidant capacity of liver of channel catfish. Soybean oil could completely replace the fish oil inclusion in the diet of channel catfish. Available online , doi: 10.7541/2018.007 [Abstract](62) [FullText HTML](28) [PDF 547KB](8) Abstract: A 80-day feeding trial was conducted to assess the interactive effects of β-glucan (BG) and Heat-killed Lactobacillus plantarum (HK-LP) on growth performance, intestinal fatty acid composition, and immune function of juvenile loach Misgurnus anguillicaudatus. Fish [average initial weight of (0.17±0.01) g] were fed with six experimental formulated diets containing two levels of BG (0% and 1%) with three levels of HK-LP (0.025%, 0.05%, and 0.1%) in triplicate. Results showed that supplementation of BG and HK-LP increased the body weight gain, specific growth rate, while significantly reduced the feed conversion ratio of fish. However, interaction between BG and HK-LP showed no significant effect on those parameters. Supplementation of BG remarkably decreased the percentage of C16 鲶1n-7 and C18 鲶2n-6 in intestinal fatty acid composition. Meanwhile, the percentage of C22 鲶1n-11 was decreased by dietary HK-LP. Dietary BG, HK-LP and two-factor interactions significantly influenced the activities of alkaline phosphatase (AKP) from skin mucus. Increase of dietary BG and HK-LP levels enhanced the activities of lysozyme. Supplementation of dietary 1% BG and 0.05% HK-LP significantly increased the expression levels of Hsp70 and Hsp90α. Therefore, the addition of BG and HK-LP in the diets could improve the growth performance of juvenile loach, and in the experiment, the optimum level of BG and HK-LP in the loach diet was 1% and 0.1%, respectively. Available online , doi: 10.7541/2019.006 [Abstract](242) [FullText HTML](126) [PDF 648KB](23) Abstract: In order to provide biological information for research on sex-determination mechanism in Pelodiscus sinensis, we here first attempted to clone and analyze the partial-length of Foxl2 cDNA. In addition, to address the differential expression of Foxl2 at genetic and physiological levels, both male and female sexes of Pelodiscus sinensis were treated with 10 mg/kg E2 and 17α-methyltestosterone (MT), respectively; Foxl2 mRNA expression was quantitatively examined in the gonads after injection treatment at 6, 12, 24, and 48h, as well as 7 and 14d, respectively. Foxl2 (GenBank Accession No.KP734210) was achieved, belonging to Forkhead family of transcription factors that is involved in ovarian development and functional maintenance, as well as a 903 bp of open reading frame (ORF) encoding 300 amino acids. Multiple sequence alignment showed that Foxl2 contained typical FH-domain, and the most similar ortholog was Trachemys scripta, reaching up to 99%. Stability analysis of phylogenetic trees showed that Pelodiscus sinensis Foxl2 was clustered with reptile Foxl2 as a sub-branch, and was closely associated with Foxl2 from Chrysemys picta bellii. Results of quantitative reverse transcription PCR (RT-qPCR) indicated that, compared to the control group, E2 significantly up-regulated Foxl2 mRNA repression in ovary after 24h (P<0.001), which in testis was significantly increased after 7 and 14d (P<0.001). MT treatment strongly and equally up-regulated expression levels ofFoxl2 mRNA in ovary and testis at 24h (P<0.001). These results suggested that E2 and MT could up-regulate Foxl2 expression. Moreover, the sex differences in E2 promoting Foxl2 expression is more significant than MT. It can be concluded that the present research contributes to better understanding of the functional role of Foxl2 and provide basic data for further study on how exogenous hormone mediates Foxl2 in Pelodiscus sinensis. Available online , doi: 10.7541/2019.005 [Abstract](50) [FullText HTML](30) [PDF 784KB](6) Abstract: Three variants of EcHcL1 and 2 based on Exopalaemon carinicauda transcriptome library were obtained by using RACE technique. The total length of EcHcL1 and 2 were 2248 bp and 2121 bp, which encoded protein of 685 and 676 amino acids, respectively. EcHcL1 and 2 are relatively conservative in evolution, and has typical domains of hemocyanin, including copper ion binding region, conserved His site and Ig-like region. EcHcL1 may relate to pigment metabolism and phenoloxidase activity because of more than a tyrosinase domain. The results of tissue expression distribution showed that EcHcL1, 2 were expressed in all the 10 tissues, and higher expressed in hepatopancreas and haemocytes. Different variants of E. carinicauda hemocyanin subunit may also have various immunological functions. The expression of the 2 variants of mRNA after pathogen stresses were investigated using the Real-time PCR strategy. The results showed that EcHcL1 had higher expression level during 12—48h after Staphylococcus aureus, Vibrio parahaemolyticus and WSSV challenges, and its among more 1.5—4 times higher than that in control group. The expression level of EcHcL2 reached the highest value among 24—48h after stress, which increased 2—9 times compared with the control group. Therefore, we speculated that the E. carinicauda hemocyanin subunit variants may related to immune defenses closely and might have antimicrobial resistance activity. Available online [Abstract](319) [FullText HTML](132) [PDF 645KB](50) Abstract: The Yangtze floodplain is one of the most important wetlands in the world. For decades, many lakes in this region have suffered from multiple stressors, such as over-exploitation fishery resources and cultural eutrophication. To solve these problems, it is necessary to establish a quantitative lake ecosystem management platform at a regional scale. Recognizing the lack of regional scale zoobenthos models with high predictive power, we carried out 105 lake-time investigations on 46 small-to medium-sized lakes along the mid-lower Yangtze River in this study. The results showed that the density and biomass of zoobenthos of these lakes were (847±248) ind./m2 (mean±SE) and (29.41±3.97) g/m2, respectively. The density and biomass of oligochaetes, gastropods and chironomids were (403±225) ind./m2 and (1.12±0.39) g/m2, (82±20) ind./m2 and (26.38±3.99) g/m2, and (356±62) ind./m2 and (1.86±0.58) g/m2, respectively. Further analyses showed that water depth, Secchi depth, water temperature, total phosphorus, phytoplankton chlorophyll a, and submersed macrophyte biomass were the important factors affecting the standing crops of zoobenthos. A series of models were therefore established. The explanation of variations in zoobenthos density among lakes was generally better than that of biomass. The explantion percentage of simple regression models were between 18%—33% for density and 7%—18% for biomass. In the multiple regression models, the explanation percentage was 46%—49% for density and 16%—55% for biomass. Considering the large sampling size of this study, the explanation of these research models was significantly higher than that of previous studies. When comparing the percentage predictive errors (PPE), the simple models and multiple models showed similar results: PPE was 76%—171% for density and 115%—1034% for biomass in simple models, and 88%—114% for density and 141%—1015% for biomass in multiple models. Therefore, these simple regression model with relatively few variables and good predictive power are suggested in practical application. Display Method: \| 2018, 42(6): 1075 -1080 doi: 10.7541/2018.132 [Abstract](253) [FullText HTML](109) [PDF 360KB](24) Abstract: Asian carp are expanding their range throughout the Mississippi River; however, abundance is thought to be highest in reaches within close proximity to the Illinois River. In the Mississippi River, Lock and Dam 19 (L&D 19) at Keokuk, Iowa is the primary barrier to slow the expansion upstream. As Asian carp abundance increases below L&D 19, it is important to investigate potential means of control (i.e., reduction through harvest and barriers) that will prevent complete invasion of the Mississippi River above L&D 19. Silver Carp and Bighead Carp were collected below L&D 19, a subsample were implanted with ultrasonic transmitters to evaluate passage through the lock chamber and the remainder were used to determine population dynamics at the leading edge of invasion. Although the dam portion of the structure poses a complete barrier to upstream expansion, we documented lock chamber passage demonstrating the lock chamber has the capability to provide passage upstream. Based on the results of the population assessment, in order to induce recruitment overfishing at this leading edge of invasion, Asian carp will need to be intensively harvested at 300 mm and larger. The combination of commercial fishing efforts and research investigating ways to prevent passage upstream must be employed. 2018, 42(6): 1081 -1083 doi: 10.7541/2018.133 [Abstract](287) [FullText HTML](109) [PDF 190KB](24) Abstract: Silver carp Hypophthalmichthys molitrix were introduced into the U.S. to control water quality in aquaculture ponds. From this point of origin, silver carp escaped into nearby rivers through multiple flood events. Because of their documented negative effects on native biota, silver carp have been labeled as problematic. Therefore, evaluating the biology and ecology of these non-indigenous species is critical. Multiple parameters are needed to evaluate silver carp populations (length, weight, age, and sex). Furthermore, developing methods for rapidly acquiring these data are needed. In relation to sex determination, sexual dimorphism was observed where males exhibit distinct pectoral fin ray features. Specifically, males have pronounced ridges or a " rough patch” on the dorsal surface of pectoral fins. Therefore, to test if this was an applicable way of determining silver carp gender; silver carp were collected from Midwestern U.S. rivers (N=2015) in the fall of 2011 (N=870), spring of 2012 (N=645), winter of 2013—2014 (N=202) and summer 2015 (N=323) via electrofishing. For each silver carp collected, presence (e.g., rough patch) or absence (e.g., smooth) of pronounced ridges on the top side of the pectoral fins was recorded, and an incision was made in the body cavity to identify gender. Based on the results of our evaluation, gender was correctly identified over 99% of the time (2006 out of 2015) based on the pectoral fin dimorphism. In the samples taken in the winter of 2013—2014 and summer of 2015, accuracy for silver carp shorter than 300 mm and longer than 800 mm was 53.7% (19 out of 41) while accuracy for silver carp between 300 mm and 800 mm total length was 98.9% (289 out of 292). This study provides a rapid assessment approach for evaluating silver carp gender. 2018, 42(6): 1084 -1088 doi: 10.7541/2018.134 [Abstract](258) [FullText HTML](98) [PDF 321KB](13) Abstract: The establishment of a highly efficient planktivore, Silver carp (Hypophthalmichthys molitrix), in the Mississippi River Basin has been documented as having negative impacts on native planktivore populations. Silver carp have the potential, to alter the trophic food web through negative interactions with native planktivores in large river systems. Due to increasing Silver carp ranges, interactions between Silver carp and other native planktivores is likely to increase. One abundant native planktivore that is often found in similar habitats as Silver carp is Gizzard shad (Dorosoma cepedianum). Potential competition for resources exists because of overlapping habitat use and forage. Given the similarities between these two planktivores, we sought to evaluate daily growth rates and determine hatch dates of age-0 Silver carp and Gizzard shad in the Middle Mississippi River. Silver carp and Gizzard shad were collected from the Middle Mississippi River using an electrified surface trawl from June through September with sizes ranging from 21—65 mm total length for Gizzard shad and 24—85 mm total length for Silver carp. A sample of age-0 fish (n=697) was collected at the end of the growing season including 292 Gizzard shad and 405 Silver carp. Size structure (total length in mm) of Silver carp (49.05±0.41; \begin{document}$\overline {{{X}}}$\end{document} ± SE) was significantly greater (T= –16.43, df=695, P<0.001) than Gizzard shad (38.95 ± 0.45). Hatch dates were similar between Silver carp (July 26th to August 18th) and Gizzard shad (July 28th to August 19th). Growth of Silver carp (2.24 mm per day) was significantly greater (P<0.001,T= –11.1, df=82) than Gizzard shad (1.72 mm per day). Mortality was similar between Silver carp (28.1%) and Gizzard shad (25.1%) at this early life stage. The faster growth rates in Silver carp result in Silver carp entering the winter season larger in size with likely an increased capacity to consume plankton and decreased predation ultimately leading to higher recruitment. Knowing that there exists an overlap between Silver carp and Gizzard shad diets and habitat could alone call cause for concern. Adding that spawning occurs at a similar time and Silver carp have the ability to outgrow Gizzard shad early in life leads to major concerns about food web balance. Knowing that invasive planktivores have already shown to alter food webs in aquatic systems in North America, extra caution should be taken. 2018, 42(6): 1089 -1106 doi: 10.7541/2018.135 [Abstract](525) [FullText HTML](173) [PDF 624KB](18) Abstract: The lower Mississippi River (LMR) has been heavily modified for multiple human purposes such as navigation, flood control, and bank stabilization. However, the LMR simultaneously supports a diverse fish fauna that includes recreational and commercial fisheries. Due to river training and diversion structures constructed during the past 80 years, the historic characteristics of the LMR have been drastically altered and have likely influenced fishes and fisheries in the system. One common restoration measure used throughout the LMR has been to " notch” wing-dike structures that close secondary (side) river channels. Dike notching allows year-round flows through secondary channels, which enhances habitat diversity and promotes biological productivity at the ecosystem scale. Although notching is presumed good for LMR fishes and other biota, few studies have examined its effects on fish assemblages. In this study, fish assemblages were sampled at seven LMR secondary channels spanning from river kilometer (rkm) 628 (Louisiana-Mississippi, U.S.A.) upstream to rkm 1504 (Missouri-Kentucky, U.S.A.). Four secondary channels were termed " permanent” (i.e., with notched dikes) while three secondary channels were termed " temporary” (i.e., without notched dikes). Fishes were sampled by boat-mounted electrofishing conducted during falling and low stages from 1995—1997. Fish assemblages differed between permanent and temporary secondary channels, and varied somewhat between falling and low stages. Gizzard shad (Dorosoma cepedianum), threadfin shad (D. petenense), and white bass (Morone chrysops) demonstrated consistent preferences for low-current conditions associated with temporary secondary channels. Conversely, blue catfish (Ictalurus furcatus), flathead catfish (Pylodictis olivaris), and freshwater drum (Aplodinotus grunniens) were more associated with permanent secondary channels. Future restoration strategies in the LMR should consider dike notching and resultant maintenance of permanent secondary channels in selected river reaches. However, temporary secondary channels also contain unique fish species, and also appear to be important sites of riverine primary production. Restoration strategies should consider a balance of both secondary channel types, which should support the greatest biodiversity for the LMR ecosystem. 2018, 42(6): 1107 -1115 doi: 10.7541/2018.136 [Abstract](195) [FullText HTML](92) [PDF 528KB](13) Abstract: Knowledge of the vulnerability of different species and size groups to various types of fishing methods is vital to the development of optimal harvesting strategies and rational exploitation of fish resources. In this study, the selectivity of four types of fishing methods (weir nets, gill nets, electrofishing, and cormorants) used simultaneously in a typical multi-species shallow lake (Lake Niushan, China) within the Yangtze River basin, was compared for catch composition, efficiency, and size selection. Species selectivity was evaluated with the index of relative importance (IRI). Potential fishing effects on the trophic structure of fish community were analyzed by calculating the mean trophic level (MTL) of the catches and the weight ratio between prey and predator fishes. Results indicated that the use of weir nets and electrofishing should be reduced or eliminated, because they were relatively unselective and caught many species, including juvenile individuals. Fishing efforts of cormorants should be restricted due to their high fishing efficiency, especially on piscivorous fishes. Gill nets with appropriate mesh size are likely to be a more sustainable fishing method since they were more selective in capturing larger individuals and could balance the prey-predator relationship. We suggest shifting from single-species approaches toward multi-species management, and taking trophic interactions into account to better manage fishery resources. 2018, 42(6): 1116 -1123 doi: 10.7541/2018.137 [Abstract](176) [FullText HTML](84) [PDF 463KB](8) Abstract: To assess possible bias of different fishing methods is essential to appropriate fisheries management. In the current study, fish assemblage structure of a shallow Yangtze River lake was assessed by combining one international standard sampling gear (multi-mesh gillnet), and one traditional Chinese gear (the dense-mesh weir). Using Lake Biandantang as a case study, a total of 27 fish species were collected from the two gears combined, including 2 new species that had not been recorded previously in this lake. Results suggested that fish assemblages had changed greatly compared to a previous study conducted in the 1990s. Specifically, differences were found in species composition, abundance, biomass, and length distributions collected from the two gears. Difference in total length (TL) distributions of fishes caught was the most conspicuous change. Fishes collected from the weir ranged from 40—70 mmTL, whereas fishes collected from gillnets ranged from 90—140 mmTL. Multivariate ordinations based on relative abundance and biomass data also indicated fish assemblage structural differences between the two gears. The comparative results showed that the multi-mesh gillnet was effective at assessing fish assemblages in shallow lakes, such as those found along the middle and lower reaches of the Yangtze River. Additionally, assessments using only one gear could have some limitations with respect to interpreting fish assemblage changes over time. 2018, 42(6): 1124 -1134 doi: 10.7541/2018.138 [Abstract](164) [FullText HTML](82) [PDF 575KB](16) Abstract: We analysed spatial pattern in the fish assemblage structure along a longitudinal gradient of the Upper Yangtze River and the Three Gorges Reservoir. We tested the hypothesis that shifts from lotic to lentic environment affect the richness and structure of the fish assemblage. Samplings were carried out from 2005 to 2012 in four zones:(1) Hejiang reach, river upstream from the reservoir; (2) Mudong reach, upper part of the reservoir; (3) Wanzhou reach, middle part of the reservoir, and (4) Zigui reach, lower part of the reservoir. A total of 368706 fish representing 132 native species of 17 families were collected during the study period with Cyprinidae as the dominant group. The results showed that the native species richness decreased while the non-native species increased from river (Hejiang reach) to reservoir (Zigui reach). Patterns in fish assemblage ordination evaluated by correspondence analysis reflected a clear division of the riverine and reservoir zones. Uppermost sampling stations were characterized by species characteristic of flowing waters, whereas in the lowland most lentic species were captured. Further, 22 species, three functional groups (rheophilic, equilibrium, insectivorous) were identified for the upper reach and 16 species, three functional groups (herbivorous, planktivorous, stagnophilic) for the lowland reach by indicator species analysis (P<0.05). Therefore, it is evident that impoundment of the Three Gorges Reservoir is the major driving factor to structuring the fish assemblage structure along the longitudinal gradient from river to the reservoir. Different fisheries management actions should be made to conserve or rehabilitate native fish assemblages and control invasive non-native species. 2018, 42(6): 1135 -1143 doi: 10.7541/2018.139 [Abstract](237) [FullText HTML](102) [PDF 482KB](14) Abstract: There is limited information available on effects of aquaculture on lake ecosystems. Community structure and biodiversity of phytoplankton were investigated from July to September, 2015 in 23 lakes in the middle reach of the Yangtze River Basin, which include four groups: reservoir group (A), aquaculture ban group (B), low stocking aquaculture group (C) and high stocking aquaculture group (D). The analysis showed that dominant genera of the four groups were different. Group A was dominated by Pseudanabaena (Y=0.642) and Planktolyngbya (Y=0.064). Group B was dominated by Merismopedia (Y=0.428), Planktolyngbya (Y=0.118), Pseudanabaena (Y=0.133), and Scenedesmus (Y=0.066). Group C was dominated by Pseudanabaena (Y=0.395), Merismopedia (Y=0.097), and Planktolyngbya (Y=0.122). Group D was dominated by Merismopedia (Y=0.308), Microcystis (Y=0.118), and Pseudanabaena (Y=0.077). The phytoplankton abundance in group A was significantly lower than those in other lake groups (P<0.05). There was no significant difference in Shannon-Wiener index, Margalef index and Pielou index of phytoplankton among the four lake groups. The study indicated that fish culture could affect the abundance and dominant genera of phytoplankton, which may provide some implications for lake ecosystem management. 2018, 42(6): 1144 -1152 doi: 10.7541/2018.140 [Abstract](99) [FullText HTML](46) [PDF 573KB](9) Abstract: Samples of Corbicula fluminea (Müller, 1774) were collected monthly from March 2011 to February 2012 in the Datong Lake to study its population dynamics and secondary production in its native environment. A total of 4,108C. fluminea were collected and measured, with shell length (SL) ranging from 3.41 to 29.58 mm, and wet weight (WW) ranged from 0.005 to 10.03 g. The calculated SL-WW equation was log WW = –3.52+3.08 log SL (R2=0.97), which showed that the growth curve of C. fluminea followed a positive allometric pattern. The recruitment patterns peaked in one from March to April and the other one during the months of August to October. The mean annual abundance and biomass ( \begin{document}$\bar B$\end{document} ) were (274±95) ind./m2 and (20.1±5.7) g AFDW/m2 (Ash Free Dry Weight, AFDW), respectively. The annual secondary production (P) was estimated to be 23.90 g AFDW/m2·year, resulting in a P/ \begin{document}$\bar B$\end{document} ratio of 1.20/year and a turnover time of 298 days. The asymptotic maximum length (L), curvature parameter (K) and seasonal oscillation in growth rate (C) derived from the von Bertalanffy Seasonal Growth Formula (VBSGF) were 31.91 mm, 0.45/year, and 0.84, respectively. The slowest growth period was in January, and the potential lifespan (tmax) was estimated to be 4.44 years. The total mortality (Z), natural mortality (M) and fishing mortality rates (F) estimated were 1.68/year, 0.89/year and 0.79/year, respectively. Its exploitation rate (E=0.47) indicated a slightly high exploited stock that needs some management intervention to maintain the sustainability of this fishery resource. 2018, 42(6): 1153 -1162 doi: 10.7541/2018.141 [Abstract](180) [FullText HTML](73) [PDF 1022KB](16) Abstract: A comprehensive investigation on macrophyte community in Hongze Lake was conducted seasonally from May 2010 to February 2011. Overall, twelve species representing eight families of macrophytes were identified in Hongze Lake, including nine species of submerged plants, two species of floating-leaved plants, and one species of emerging plant. In general, Potamogeton malaianus, P. maackianu, P. pectinatus and P. crispus were the four dominant species throughout the whole year, the highest biomass of macrophytes was presented in autumn, followed by summer and winter, while spring had the lowest biomass of macrophytes. Based on field data, we used kriging interpolation in ArcGis to map the spatiotemporal distribution of the entire macrophyte community as well as each of the four dominant species. From the GIS maps we observed that the northern area of the lake, namely the Chengzihu region, had the highest biomass of macrophytes potentially as a result of better water quality and greater transparency. Potential factors that affected the community structure, biomass, and distribution patterns of macrophytes considerably were then discussed. The results of this study illuminate the need for more information on the role and importance of aquatic macrophytes in shallow lake ecosystems. Conservation of macrophytes should be taken to maintain the lake ecosystem health. 2018, 42(6): 1163 -1168 doi: 10.7541/2018.142 [Abstract](185) [FullText HTML](73) [PDF 317KB](14) Abstract: A tag-release-recapture study was conducted to evaluate effects of size at release on survival, growth and yield of hatchery-reared mandarin fish Siniperca chautsi fingerlings stocked in a shallow Yangtze lake. In May and June 2012, a total of 2400 juvenile mandarin fish were graded into three size groups, identified with coded wire tags and tail fin clipping, and released into Xiaosai Lake. Mandarin fish were collected after the lake drained in December 2012. Overall, a total of 973 mandarin fish individuals were captured, with an average survival rate of 40.5%. Survival rate of large sized group (63%) is more than three times higher than that of small sized group (19.5%) and 1.5 times higher than that of middle sized group (39.1%). The mean final length and weight of mandarin fish increased with the increase of release size and showed significant difference among groups. Yield was significantly affected by release size, which was the highest in large sized group and the lowest in small sized group. The net income of stocked mandarin fish increased with the increase of fish size at release. Our results indicated that mandarin fish size at release can have a major impact on success of hatchery releases, and it is suggested that the optimum release size of mandarin fish should not be less than 50 mm in Xiaosai Lake. 2018, 42(6): 1169 -1179 doi: 10.7541/2018.143 [Abstract](236) [FullText HTML](91) [PDF 586KB](18) Abstract: The Ptychobarbus dipogon of the Schizothoracinae subfamily, is an endemic economic fish species in Tibet Autonomous Region, China. Due to environment deterioration and invasion of alien species the population size of this species is decreasing; a study is urgently required to determine fecundity and reproductive strategy in order to conserve this natural resource. In this study, to investigate the fecundity and its relationship of body length, weight and age, we captured 1030 individuals in the middle Yarlung Zangbo River during two separate periods, one from February to March in 2013 and the other from February to June in 2014. The results showed that the standard length (SL) of males is concentrated in the 325—400 mm range, and the SL of females is above 375 mm. Sixty five females were at stages IV and V of sexual maturity, with SL 320—500 mm, weight 411.6—1328.0 g. Using the SL 50% method, the first female sexual maturity age was estimated to be 13.0 years and about 360.90 mm, while the first male maturity age was estimated to be 13.5 years and length 354.53 mm. The distributions of egg sizes, gonadal developmental stages and gonadosomatic indexes show that this species follows a synchronous spawning pattern concentrated in the period February to March, with an absolute fecundity at 3487 eggs, with a fecundity to SL ratio of 7.2 eggs/mm and fecundity to weight of 4.3 eggs/g. The absolute fecundity is positively correlated to the SL and the weight, but not significantly correlated to age. The overall male-female ratio was 1.23 鲶1. Suggestions for its conservation have been made based on its low fecundity, late maturity and short breeding period. 2018, 42(6): 1180 -1185 doi: 10.7541/2018.144 [Abstract](98) [FullText HTML](54) [PDF 435KB](5) Abstract: During the reproductive migration of Chinese mitten crab in the Yangtze River estuary, the relationship between fecundity and carapace width of released and wild Chinese mitten crab populations was analyzed, and then the differences between the wild and released populations were compared. The results showed that, with the increase of carapace width (CW), the fecundity (F) of released and wild population crabs increased significantly (P<0.05). In the same range of carapace width, there was no significant differences of the fecundity between the wild and released populations (P>0.05). Regression analysis showed that the relationship between theF and CW of the released population belongs to exponential function, which is F=3.979CW6.208 (R2=0.822). In addition, the relationship between F and CW of the wild population is F=1.696CW6.636 (R2=0.673). Covariance analysis showed that the curves of the wild and released crab populations fit well in significant 0.05. It could be concluded that the fecundity of the wild and released populations was at the same level. There was no significant difference between the wild and released crab population on the relationship of F and CW. The released population could reproduce well in the natural water of the Yangtze River estuary. 2018, 42(6): 1186 -1193 doi: 10.7541/2018.145 [Abstract](169) [FullText HTML](76) [PDF 465KB](10) Abstract: The yellow perch, Perca flavescens, is an economically significant freshwater fish species in the Midwest of the United States. TypeⅠ markers are useful for comparative mapping and other genetic analyses, but limited quantities in yellow perch. In the present study, EST containing microsatellite sequences were identified and characterized for yellow perch by data mining from updated public EST databases. Out of 21968 EST sequences of yellow perch, about 14.4% of ESTs contain repeat motifs of various types and length. CA repeat was the most abundant dinucleotides. Out of the 62 EST-SSRs for which PCR primers were designed, 15 loci showed polymorphic in a yellow perch population with the alleles per locus ranging from 4 to 19 (average 9). The observed (HO) and expected (HE) heterozygosity of these EST-SSRs were 0.103—0.929 and 0.116—0.934, respectively. Four EST-SSR loci significantly deviated from the Hardy-Weinberg equilibrium (HWE) expectation, and the remaining 11 loci were in HWE. These new EST-SSR markers should provide sufficient polymorphism for population genetic studies and genomic mapping of yellow perch. 2018, 42(6): 1194 -1202 doi: 10.7541/2018.146 [Abstract](174) [FullText HTML](88) [PDF 935KB](14) Abstract: The histology of gonadal development in Ptychobarbus dipogon was studied by using conventional paraffin sections and HE staining, in order to obtain information on its reproductive systems useful for its artificial breeding. The results showed that the development of oocytes can be divided into five phases, and ovarian development can be divided into six stages. In stage V ovaries, ovum worship was found to occur, indicated by the 1.38 鲶1 ratio of small ova to large ova. Phase 3 oocytes were characterized by appearance of yolk granules and follicles; phase 4 oocytes by rapid increase of yolk granules, and the movement of the nucleus toward the animal poles; phase 5 by the fusion of yolk granules, and the separation of oocytes from follicular membranes to float in the ovarian cavity. Male P. dipogen had lobular testes, and their germ cells can be categorized into spermatogonia, spermatocytes; spermatids; and spermatozoa. Their testes also developed in six stages. The species followed a batch-synchronous spawning pattern. 2018, 42(6): 1203 -1209 doi: 10.7541/2018.147 [Abstract](175) [FullText HTML](85) [PDF 498KB](15) Abstract: Sexual dimorphism refers to the morphological differentiation between males and females in the same population, such as sizes, morphological features, and colors. Cold water fish Glyptosternum maculatum, is an endemic teleost species of notable economic importance and with high potential for controlled rearing of the species in Tibet Autonomous Region. In this study, morphological measurements and related analysis were conducted on sexually mature G. maculatum to investigate their morphological differences in Tibet Autonomous Region. Results indicated the sexually mature populations indeed display really displayed significant sexual dimorphism: males exhibited significantly greater body length, weight, and males also exhibited in addition to greater tail length while females exhibited significantly greater eye diameter, body depth, trunk length, and lengths of dorsal, pectoral, pelvic, anal, and caudal fins at a given body length. Principal components analysis on 16 morphological parameters showed that the differences were largely due to features of the body shape (including lengths of body parts and fins) and the head, and differences in the above features differences contributed 76.7%. The t-statistic test on the allometry index b in the total length-weight function showed that during the breeding season, the total lengths and weights of G. maculatum females developed proportionally, while the male specimens were allometrical. 2018, 42(6): 1210 -1213 doi: 10.7541/2018.148 [Abstract](363) [FullText HTML](144) [PDF 295KB](25) Abstract: This study is based on monthly sampling (from April 2013 to April 2015) of 18 fish species representing three families. Samples were obtained using benthic fyke-nets, block nets, and multi-mesh gillnets in Lake Kuilei, a shallow lake of the Yangtze River basin, China (N 31º24′ , E 120º51′). Using ordinary least-squares linear regression, length-weight relationships of these fish species were estimated, with equations for 3 species reported for the first time. The maximum total length records of the 15 species exceeded those reported in FishBase. This paper provides new LWR equations for these species to be included in FishBase. 2018, 42(6): 1214 -1223 doi: 10.7541/2018.149 [Abstract](374) [FullText HTML](189) [PDF 689KB](24) Abstract: This study examined anesthetic behaviors of Schizothorax o’connori Llord in two size ranges as induced by MS-222, to acquire useful information on anesthesia of said highland fish species in out-of-water activities (surgery, labeling, measurement, etc.). Test results indicated that for both large (25.0±1.5) cm and small-sized (14.8±2.3) cm specimens, respiration rates showed no significant change in anesthetic stages Ⅰ to Ⅲ, and only begun to significantly decline after entering stage Ⅳ. The effective concentrations of MS-222 were 150—180 mg/L and 150 mg/L for two sizes, respectively. The 150—180 mg/L caused large specimens to enter anesthetic stage Ⅳ within 5min, and recovered within 5min; the 150 mg/L caused small specimens to enter stage Ⅳ within 5min, and recovered within 7min; both doses ensured a 100% survival rate after immersion for 20min. For large specimens anesthetized at 180 mg/L for 5min and exposed to air for 0—15min, there was no significant difference in recovery times (P>0.05); for small specimens anesthetized at 150 mg/L for 5min and exposed to air for 0—15min, there were significant differences in recovery (P<0.05). 2018, 42(6): 1224 -1231 doi: 10.7541/2018.150 [Abstract](169) [FullText HTML](88) [PDF 362KB](11) Abstract: Schizothorax macropogon and Ptychobarbus dipogon are important economic fishes in the Yarlung Zangbo River. Both are Schizothoracinaes containing a variety of essential fatty acids with high nutritional values. As food products, the textural characteristics of their meat determine important factors like taste or methods of treatment. To explore the preservation and utilization of fish resources in the Tibet Autonomous Region, China, the texture profile analysis (TPA) method was used to analyze 12 textural parameters. Fish were captured from the Yarlung Zangbo River in Shigatse and Nyingchi City. Principal component analysis showed that the texture of P. dipogon captured from the Nyingchi segment was different from the same species captured in the Shigatse segment, and different from S. macropogon captured from both segments. Factorial analysis indicated that the textural characteristics of Schizothoracinae fishes in Tibet Autonomous Region can be summarized as hardness indices, overcome attraction indices and contractility indices, of which the accumulated variance contribution rate of the first four principal component factors was 81.472%. The three categories of the four principal component axes could be the main deciding parameters of the textural characteristics of Schizothoracinae fishes in Tibet Autonomous Region. This provides scientific data for subsequent development and utilization of Schizothoracinae fishes from the Yarlung Zangbo River in different geographical areas. 2018, 42(6): 1232 -1239 doi: 10.7541/2018.151 [Abstract](208) [FullText HTML](79) [PDF 619KB](7) Abstract: Our study examined spatial distribution differences of rotifer resting eggs (RRE) in lakes of the Poyang Lake Wetland Area during dry season, January 2015. Field sampling was conducted in both Nanshen Lake and Baisha Lake. We found that densities of RRE in different habitats were significantly different (P<0.05), and their distribution had an obvious gradient. The highest mean density was in the marshland vegetation area of Nanshen Lake, where it was (3.34±1.28) ind./cm3. The density of resting eggs in the Zizania latifolia area was up to 5.45 ind./cm3. The density of RRE was different spatially, with the greatest in the vegetation area, then in the muddy area, and then the lowest in the water area. ANOVAs results showed that water depth, vegetation, and sediment had significant effects on RRE (P=0.001, P=0.007, P<0.001, respectively). The trend of resting egg densities in different aquatic habitats was: emergent aquatic plant > marshland vegetation > floating-leaf plants > submerged plants. The distribution of RRE in areas of different water depths was inconsistent. The density of RRE was higher in the hard than soft sediment. 2018, 42(6): 1240 -1252 doi: 10.7541/2018.152 [Abstract](456) [FullText HTML](164) [PDF 454KB](27) Abstract: Many efforts have been devoted to developing, constructing and refining fishways or fish passage facilities to facilitate the target fish species to pass barriers in fluvial systems. Once dominated by an engineering-focused approach, fishways science nowadays involves a wide range of disciplines from fish behaviour to socioeconomics, and to complex modeling of passage prioritization options in river networks. Designing efficient fishways, with minimal passage delay and post-passage impacts, requires adaptive management and continued innovations. After the completion of fishways construction, corresponding management systems usually need to be improved as well. In the current study, we first reviewed international fishways adaptive management systems (e.g., aspects of development, construction, and management) from 1991 to 2017 reporting on " fishway”, " fish passage”, " fish” and " dam”. The functions of fishways gradually transferred from conservation of economic stocks to overall biodiversity conservation, from facilitating upwards to both upwards and downwards passages, from developing a single project to considering the entire river basin, from fish passing function to habitats restorations as well, and from pure engineering construction to considering adaptive management. Finally, we discussed adaptive management systems and management prospects of fishways for China. ### Journal Introduction • Establishment Time：1955 Bimonthly • Competent unit：Chinese Academy of Sciences • Host unit：Institute of Hydrobiology, Chinese Academy of Sciences ; Chinese Society for Oceanology and Limnology • Editor-in-Chief：GUI Jian-Fang • ISSN 1000-3207 • CN 42-1230/Q Copy right © 2009 Editorial Office of Acta Hydrobiologica Sinica	2018-12-10 18:52:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.388006329536438, "perplexity": 10354.045300195045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823382.1/warc/CC-MAIN-20181210170024-20181210191524-00444.warc.gz"}
https://icsehelp.com/isc-geography-2014-class-12-previous-year-question-papers-solved/	ISC Geography 2014 Class-12 Previous Year Question Papers Solved for practice. Step by step Solutions with Questions of Part-1 (Section-A & B) and Part-2. By the practice of Geography 2014 Class-12 Solved Previous Year Question Paper you can get the idea of solving. Try Also other year except ISC Geography 2014 Class-12 Solved Question Paper of Previous Year for more practice. Because only ISC Geography 2014 Class-12 is not enough for complete preparation of next council exam. Visit official websitefor detail information about ISC Class-12 Geography. ## ISC Geography 2014 Class-12 Previous Year Question Papers Solved Sections-A of Part-I Section-B of Part-I Part-II (Maximum Marks: 70) (Time allowed: Three hours) (Candidates are allowed additional 15 minutes for only reading the paper.They must NOT start writing during this time.) • Answer Section A and B from Part I which are compulsory. • Answer any four questions from Part II. • Sketch maps and diagrams should be drawn wherever they serve to illustrate your answer. • The intended marks for questions or parts of questions are given in brackets [ ]. PART – I (30 Marks) SECTION – A ### ISC Geography 2014 Class-12 Previous Year Question Papers Solved Question 1. [20] (i) Mention the latitudinal and the longitudinal extent of India. (ii) What is a subcontinent? Why is India referred to as an Indian subcontinent? (iii) Explain the term braided river. Give an example. (iv) What is meant by Break in Monsoons? Why does it occur? (v) Mention any two problems caused due to the growth of large cities. (vi) Why is watershed management important? Name the water harvesting programme implemented in Andhra Pradesh. (vii) Name any two narrow gauge railway lines present in the Himalayan region. (viii) Name any two important means of mass communication. (ix) Name the largest coalfield of Chhattisgarh. State its importance. (x) Study the Temperature-Rainfall graph of station X below and answer the questions that follow : (a) Is the location of station X Inland or coastal ? Give a reason for your answer. (b) Which branch of the South West Monsoon brings, rain from the month of June to September ? (i) 6° 45′ North – 37° 6′ North Latitude. 68° 7′ East to 97° 25′ East Longitude. (ii) A landmass which is separated from the rest of the continent by water bodies or mountains is called a subcontinent. India is called a subcontinent because of its : (a) Vast size, (b) diversity, (c) the ice covered lofty Himalayas in the North, (d) the vast Indo-Ganga plain to its south, (e) the Thar desert, (f) the uneven Deccan plateau, (g) the high temperature and heavy rainfall . from the tropical monsoon climate. (iii) The river carries a heavy load some of which is deposited on its bed. This may produce mounds which divide the river into several channels. When this happens, the river is said to be braided, e.g., the river Kosi or the lower course of river Ganga. (iv) When the south-west monsoon fails to bring rainfall for two or more weeks and there is a dry spell in the rainy season, it is called the break in the monsoon. This break is caused due to : 1. Failure of the tropical depressions, 2. Continuous rainfall L.P. trough changes to H.P. monsoon trough is dislocated and rain becoming winds change their direction. (v) The essential problems caused due to the growth of large cities are : Unemployment: When people migrate to the cities, they do not find appropriate jobs and add to the problems of unemployment in the cities. The rural folks are generally unskilled, illiterate, hardly willing to work in the agricultural fields. They are often thrown out . of the villages as surplus labour force due to mechanisation of agriculture. Pollution : The haphazard and uncontrolled growth of cities had led to the unprecedented environmental pollution including pollution of air, water and land within the cities and in areas surrounding them. Growth of Slums and Squatter Settlement: Unplanned and haphazard growth of urban areas is the cause of spread of slums and squatter settlements. Urban Sprawl : As the cities grow in size, they encroach upon the surrounding areas and areal expansion takes place. Almost all the cities are grown at the expense of surrounding agricultural land thus reducing the scope of agricultural activities. (vi) Watershed management is a very important means to conserve water resources which help to increase agricultural production and stop ecological degradation. The scheme also helps the rural people to conserve water for drinking, irrigation, fisheries and afforestation and allied activities like horticultural, agroforestry and silviculture. The name of the water harvesting program implemented in Andhra Pradesh is Neeru Meeru (Water and You). (vii) Two narrow gauge railway lines present in the Himalayan region are : 1. Kalka to Simla 2. Siliguri to Darjeeling. (viii) Two important means of mass communication are: 2. print media like newspaper and periodicals. (ix) Korba Coal-field: It supplies coal to Korba thermal power station and Bhilai steel plant. (x) (a) Yes, it is Coastal: The annual range of temperature is only 6°C. The area is influe- need by the moderating influence of the sea. (b) The Arabian sea branch of south-west monsoon. ### SECTION – B Solved Previous Year Question Papers for ISC Geography 2014 of Class-12 Question 2. [10] On the outline map of India provided : (a) Mark the Cardamom Hills. (b) Mark the Bomdi La Pass. (c) Shade a drought-prone area in Western India. (d) Shade a region along the Eastern coast where deltaic forests are found. (e) Mark and name a coalfield in Jharkhand. (f) Mark and name the city where Hindalco is located. (g) Trace the course and name the river on which Bhakra-Nangal Hydroelectric power station is set up. (h) Shade and name the state where Tank irrigation is mainly practised. (i) Mark the port ofMarmagao. (j) Trace the route of National Highway 2. Name any one of its terminal towns. Note: All the map work, including legend (Index) should be done on the map sheet only. PART – II (40 Marks) Previous Year Question Papers Solved for ISC Geography 2014 of Class-12 Question 3. (a) Explain the formation of Himalayas with reference to the theory of Plate Tectonics. [3] (b) State two differences between Himalayan and Peninsular river systems. [2] (c) List three measures undertaken by the . government to conserve and develop forestry in India. [3] (d) Write any two objectives of urban forestry. [2] (a) According to the plate tectonic theory, the Himalayan ranges were formed when the Indian plate was driven northwards and pushed beneath the Eurasian plate. With the advance of the Indian plate towards the north, the Tethys started contracting about 65 to 70 million years ago. About 30 to 60 million years ago, the two plates came closer and Tethys sea crust began to fracture into thrust edges. About 20 to 30 million years ago, the Himalayan ranges started emerging. Read Next 👇 Click on Page Number Given Below 👇 Insert math as Formula color Type math using LaTeX Preview $${}$$ Nothing to preview Insert	2021-09-20 13:23:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23296310007572174, "perplexity": 7648.337361854695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057039.7/warc/CC-MAIN-20210920131052-20210920161052-00626.warc.gz"}
https://tex.stackexchange.com/questions/312376/environment-to-replace-vbox-hbox-hbox-hbox-hbox	# Environment to replace \vbox{\hbox{…}\hbox{…}\hbox{…}\hbox{…}…} I am using LaTeX (LuaLaTeX,actually) and lately I found myself doing this a lot: \vbox{% \hbox{\strut foo}% \hbox{\strut bar}% \hbox{\strut baz}% } I use it inside tabular environments, floats, on title pages and sometimes even in normal text. When I do this foo, bar and baz are always a lot shorter than, e.g. \linewidth. I found this to be the easiest and quickest thing to get what I want. On special occasions, when there are a lot of items to display I resort to \tabular{l}. Both constructs look like this is not how LaTeX is supposed to work from an user's perspective. Is there some environment or anything I can use to achieve the same effect as my 5 lines above do? Of course there are for example all the itemizes, but those all have some margin/padding/indent magic about them that always ends up making me want to use Word. My \vbox-\hbox-\strut construct works always as expected, in 100% of my use cases. • \halign{\strut#\crcr foo\cr bar\cr baz\cr} (You can even leave out \strut) – Henri Menke May 31 '16 at 12:20 • \def\shortycut#1#2#3{\vbox{% \hbox{\strut #1}% \hbox{\strut #2}% \hbox{\strut #3}% } causes an error? – MaestroGlanz May 31 '16 at 12:21 Maybe some variety of "long" (rows at fixed baselineskip value) stack would suit your needs. \documentclass{article} \usepackage{stackengine} \setstackEOL{$} \setstackgap{L}{\normalbaselineskip} \strutlongstacks{T} \begin{document} \begin{tabular}{\|l\|l\|} \hline \Longstack[l]{foo$ bar$baz} & text\\ \hline \Centerstack[l]{foo$ bar$baz} & text\\ \hline \Longunderstack[l]{foo$ bar\$ baz} & text\\ \hline \end{tabular} \end{document} • This is the first time I come across stackengine. This looks awesome. especially with the long center and longunder variants for tabular environments! – Bananguin May 31 '16 at 12:33 • @user1129682 Thanks. As it is my package, let me know if you have any questions on its use. – Steven B. Segletes May 31 '16 at 12:42 If you want to write your current construct much shorter, use \halign (and consider using plain TeX). \documentclass{article} \begin{document} \halign{#\crcr foo\cr bar\cr baz\cr} \end{document} • Does \halign fall under the category of tex primitives we are not supposed to use (like hbox and vbox)? – Bananguin May 31 '16 at 12:36 • \halign is a TeX primitive, but I have never heard that you are not supposed to use any TeX primitives. It is perfectly safe to use and well documented in the TeXbook. – Henri Menke May 31 '16 at 12:44 \input expl3-generic \ExplSyntaxOn \cs_new_protected:Npn \vboxofhboxes #1 { \vbox:n { \clist_map_inline:nn { #1 } { \hbox:n { \strut ##1 } } } } \ExplSyntaxOff \vboxofhboxes{ foo, bar, baz, OK } \bye I can't really see the advantage over \begin{tabular}{@{}l@{}} foo \\ bar \\ baz \end{tabular} or similar Plain TeX construction. • What is this expl3 sorcery? It looks like a lot of libraries to include which will make the build process very time consuming. The advantage would be that \vboxofhboxes adds a lot less clutter to my documents and of course I can redefine \vboxofhboxes once to add fancy layout everywhere, if I wanted to. – Bananguin May 31 '16 at 12:40 • @user1129682 Time consuming? Not at all, just a couple of seconds, perhaps. On the other hand, it provides for very compact code. – egreg May 31 '16 at 18:15	2020-02-28 19:53:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8612712025642395, "perplexity": 3065.9861440067702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875147628.27/warc/CC-MAIN-20200228170007-20200228200007-00271.warc.gz"}
http://codeforces.com/problemset/problem/1109/F	F. Sasha and Algorithm of Silence's Sounds time limit per test 1.5 seconds memory limit per test 256 megabytes input standard input output standard output One fine day Sasha went to the park for a walk. In the park, he saw that his favorite bench is occupied, and he had to sit down on the neighboring one. He sat down and began to listen to the silence. Suddenly, he got a question: what if in different parts of the park, the silence sounds in different ways? So it was. Let's divide the park into $1 \times 1$ meter squares and call them cells, and numerate rows from $1$ to $n$ from up to down, and columns from $1$ to $m$ from left to right. And now, every cell can be described with a pair of two integers $(x, y)$, where $x$ — the number of the row, and $y$ — the number of the column. Sasha knows that the level of silence in the cell $(i, j)$ equals to $f_{i,j}$, and all $f_{i,j}$ form a permutation of numbers from $1$ to $n \cdot m$. Sasha decided to count, how many are there pleasant segments of silence? Let's take some segment $[l \ldots r]$. Denote $S$ as the set of cells $(i, j)$ that $l \le f_{i,j} \le r$. Then, the segment of silence $[l \ldots r]$ is pleasant if there is only one simple path between every pair of cells from $S$ (path can't contain cells, which are not in $S$). In other words, set $S$ should look like a tree on a plain. Sasha has done this task pretty quickly, and called the algorithm — "algorithm of silence's sounds". Time passed, and the only thing left from the algorithm is a legend. To prove the truthfulness of this story, you have to help Sasha and to find the number of different pleasant segments of silence. Two segments $[l_1 \ldots r_1]$, $[l_2 \ldots r_2]$ are different, if $l_1 \neq l_2$ or $r_1 \neq r_2$ or both at the same time. Input The first line contains two integers $n$ and $m$ ($1 \le n, m \le 1000$, $1 \le n \cdot m \le 2 \cdot 10^5$) — the size of the park. Each from next $n$ lines contains $m$ integers $f_{i,j}$ ($1 \le f_{i,j} \le n \cdot m$) — the level of silence in the cell with number $(i, j)$. It is guaranteed, that all $f_{i,j}$ are different. Output Print one integer — the number of pleasant segments of silence. Examples Input 1 51 2 3 4 5 Output 15 Input 2 31 2 34 5 6 Output 15 Input 4 44 3 2 161 13 14 155 7 8 126 11 9 10 Output 50 Note In the first example, all segments of silence are pleasant. In the second example, pleasant segments of silence are the following:	2020-03-29 09:51:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5525452494621277, "perplexity": 654.7043313570675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370494064.21/warc/CC-MAIN-20200329074745-20200329104745-00246.warc.gz"}
https://memosisland.blogspot.com/	## Tuesday, 29 December 2020 ### Practice causal inference: Conventional supervised learning can't do inference This is a bit philosophical but goes into causal inference. A trained model may provide predictions about input values it may never seen before but it isn't an inference, at least for 'classical' supervised learning. In reality it provides an interpolation from the training-set, i.e., via function approximation. By "inference implies going beyond training data", reference to distributional shift, compositional learning or similar type of learning should have been raised. In the case of ontology inference, ontology being a causal graph, that is a "real" inference as it symbolically traverse a graph of causal connections. Not sure if we can directly transfer that to regression scenario but probably it is possible with altering our models with SCMs and hybrid symbolic-regression approach. Postscript • Looper repo provides a resource list for causal inference looper • Thanks to Patrick McCrae for invoking ontology inference comparison. ## Sunday, 1 November 2020 ### Summary Problem-solving is the core activity of data science using scientific principles and evidence. On our side, there is an irresistible urge to solve the most generic form of the problem. We do this almost always from programming to formulation of the problem. But, don't try to solve a generalised version of the problem. Solve it for N=1 if N is 1 in your setting, not for any integer: Save time and resources and try to embed this culture to your teams and management. Extent later when needed on demand. ### Solving for N=1 is sufficient if it is the setting This generalisation phenomenon manifests itself as an algorithmic design: From programming to problem formulation, strategy and policy setting. The core idea can be expressed as mapping, let's say the solution to a problem is a function, mapping from one domain to a range $$f : \mathbb{R} \to \mathbb{R}$$ Trying to solve for the most generic setting of the problem, namely multivariate setting $$f : \mathbb{R}^{m} \to \mathbb{R}^{n}$$ where $m, n$ are the integers generalising the problem. ### Conclusion It is elegant to solve a generic version of a problem. But is it really needed? Does it reflect reality and would be used? If N=1 is sufficient, then try to implement that solution first before generalising the problem. An exception to this basic pattern would be if you don't have a solution at N=1 but once you move larger N that there is a solution: you might think this is absurd, but SVM works exactly in this setting by solving classification problem for disconnected regions. Postscripts • The title intentionally omits three, while it is a reference to Physics's inability to solve, or rather a mathematical issue of the three-body problem. ## Sunday, 28 June 2020 ### Conjugacy and Equivalence for Deep Neural Networks: Architecture compression to selection Preamble A recently shown phenomenon can classify deep learning architectures with only using the knowledge gained by trained weights [suezen20a]. The classification produces a measure of equivalence between two trained neural network and astonishingly captures a family of closely related architectures as equivalent within a given accuracy. In this post, we will look into this from a conceptual perspective. Figure 1: VGG architecture spectral difference in the long positive tail [suezen20a]. The concept of conjugate matrix ensembles and equivalence Conjugacy is a mathematical construct reflecting different approaches to the same system should yield to the same outcome: It is reflected in the statistical mechanic's concept of ensembles. However, for matrix ensembles, like the ones offered in Random Matrix Theory, the conjugacy is not well defined in the literature. One possible resolution is to look at the cumulative spectral difference between two ensembles in the long positive tail part of the spectrum [suezen20a]. If this is vanishing we can say that two matrix ensembles are conjugate to each other. We observe this with matrix ensembles VGG vs. circular ensembles. Conjugacy is the first step in building equivalence among different architectures. If two architectures are conjugate to the same third matrix ensemble and their fluctuations on the spectral difference are very close over the spectral locations, they are equivalant in a given accuracy [suezen20a]. Outlook: Where to use equivalence in practice? The equivalence can be used in selecting or compressing an architecture or classify different neural network architectures. Python notebook to demonstrate this with different vision architecture in PyTorch is provided, here. Reference [suezen20a] Equivalence in Deep Neural Networks via Conjugate Matrix Ensembles, Mehmet Suezen, arXiv:2006.13687 (2020) ## Tuesday, 12 May 2020 ### Preamble Catalan Castellers are collaborating (Wikipedia) Availability of distributed code tracking tools and associated collaborative tools make life much easier in building collaborative scientific tools and products. This is now especially much more important in data science as it is applied in many different industries as a de-facto standard. Essentially a computational science field in academics now become industry-wide practice. ### Peer-review is a pull request Peer-reviews usually appears as pull requests, this usually entails a change to base work that achieves the certain goal by changes. A nice coincidence that acronym PR here corresponds to both peer review and pull request. ### Technical excellence does come with decent behaviour Aiming at technical excellence is all we need to practice. Requesting technical excellence in PRs is our duty as peers. However, it does come with a decent behaviour. PRs are tools for collaborative work, even if it isn't your project or you are in a different cross-function. Here we summarise some of the high-level points for PRs. This can manifest as software code, algorithmic method or a scientific or technical article: • Don’t be a jerk We should not request things that we do not practice ourselves or invent new standards on the fly. If we do, then give a hand in implementing it. • Focus on the scope and be considerate We should not request things that extend the scope of the task much further than the originally stated scope. • Nitpicking is not attention to details Attention to details is quite valuable but excessive nitpicking is not. • Be objective and don’t seek revenge If someone of your recommendations on PRs is not accepted by other colleague don’t seek revenge on his suggestions on your PRs by declining her/his suggestions as an act of revenge or create hostility towards that person. ### Conclusion We provided some basic suggestion on high-level guidance on peer review processes. Life is funny, there is a saying in Cyprus and probably in Texas too, -what you seed you will harvest-..	2021-06-14 21:07:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4278148412704468, "perplexity": 1681.3257246366077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487613453.9/warc/CC-MAIN-20210614201339-20210614231339-00488.warc.gz"}
https://blog.mdda.net/oss/2008/09/07/mount-windows-or-samba-share-on-linux	After a suitable mount-point is created (in this example mkdir -p /mnt/fscapital_server/), into /etc/fstab put the following (all on one line) : where each of the spaces above is really a cntrl-t (Tab) - just for neatness, really. Then one can mount /mnt/fscapital_server/ and see the drive immediately with ls -l /mnt/fscapital_server/. Simple.	2020-01-24 00:13:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3431466817855835, "perplexity": 10069.8785377889}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250614086.44/warc/CC-MAIN-20200123221108-20200124010108-00324.warc.gz"}
http://mathhelpforum.com/number-theory/44162-linear-congruence-equation-what-am-i-doing-wrong-print.html	# Linear Congruence Equation, what am I doing wrong? • July 20th 2008, 07:11 PM Pn0yS0ld13r Linear Congruence Equation, what am I doing wrong? What Am I doing wrong? Find x and y which solve both congruence equations simultaneously. $x-3y\equiv 9 \bmod{12}$ $x+10y\equiv 5 \bmod{12}$ $cx+ey\equiv a \bmod{n}$ $dx+fy\equiv b \bmod{n}$ So $a=9, b=5, c=1, d=1, e=-3, f=10, n=12$. There is number $z$ such that $(cf-de)z\equiv 1 \bmod{n}$ So $13z \equiv 1 \bmod{12}$, thus $z=1$ (right?) $x \equiv z(af-be) \bmod{n}$ $y \equiv z(bc-ad) \bmod{n}$ So $x \equiv 1(85) \bmod{12}$ and $y \equiv 1(-4) \bmod{12}$ But plugging back x and y into the congruences, for example: $(85)-3(-4)\not\equiv 9 \bmod{12}$ • July 20th 2008, 08:14 PM Pn0yS0ld13r Nevermind, I answered my own question. Subtracting the congruences, $13y \equiv -4 \bmod{12}$. Since $13 \equiv 1 \bmod 12$ and $-4 \equiv 8 \bmod 12$, $y=8$. Plugging y in any of the congruences yields $x = 9$ $x-3y\equiv 9 \bmod{12}$ $x+10\equiv 5 \bmod{12}$ $x-3y \equiv 9 ~ (12)$ $x+10y\equiv 5 ~ (12)$	2016-06-28 14:28:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9044856429100037, "perplexity": 1532.108246859148}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396887.54/warc/CC-MAIN-20160624154956-00038-ip-10-164-35-72.ec2.internal.warc.gz"}
https://tug.org/pipermail/pstricks/2010/007731.html	# [pstricks] features for gantt-charts? Ore is there a solution already, and I can not find it? tex at opialla.de tex at opialla.de Sat Apr 17 12:22:32 CEST 2010 Herbert Voss <Herbert.Voss at FU-Berlin.DE> hat am 17. April 2010 um 10:08 geschrieben: > Am 16.04.2010 09:50, schrieb tex at opialla.de: > > > 1.) As basis unit I use "Quarter", because "Month" is to fragmented to me > > for a > > period of 3 years. But if I use non-integer-values for the task duration or > > [...] that would be most important for me, because I would like to have a more precise handling on beginning and finishing a task. > > > 2.) Is it possible to only have the headings of the respective Years shown > > (e.g., Year 1, Year 2) instead of the quarters, but still to retain the > > dashed > > lines for each quarter? I think with showing all the Quarter Headings, makes > > it > > to crammed. > > Possible, but cannot be done in minutes ... I do not know, if > I find some time.Its not THAT important. But a solution to the > TaskUnitType=Month issue woulde be very nice... > > > 3.) Is it possible to remove the border of bars for the respective tasks? Or > > to > > have them follow the gradient as well as the filling of the bars as stated > > in > > the last example in the pst-gantt-manual > > ( > > http://www.ctan.org/tex-archive/graphics/pstricks/contrib/pst-gantt/pst-gantt-doc.pdf > > )? > > define a TaskStyle with eg "fillcolor=red,linecolor=red" > For a gradient filling see the source code of the > documentation. > > > 4.) I also would like to know if there is a different (more convenient) way > > to > > get the task description in two lines, like in the third task in the example > > below. It works, but seems to me a little hacked. I think many users would > > want > > this, in order to be able to put longer descriptions in their tasks. > > define a command > \def\Text#1{\tabular{c}#1\endtabular} > and then use \Text{foo\\bar} > > > I could not really figure out, what "TaskUnitIntervalValue" does, so I > > uncommented it. For this I also woult like to have enlightenment. ;-) When > > somebody can figure out some of my requests I hereby volunteer to put nice > > examples together to be added to the (for me obviously :-) little short) > > package-manual. > > the value for the steps predefined as 7 for weeks. > for month it should be 30 and for years 12. > With setting it to a smaller value you can decrease > the width of the chart if it is too big. Thanks a lot. Really appreciate looking into my lengthy request... > > Herbert > _______________________________________________ > PSTricks mailing list > PSTricks at tug.org > http://tug.org/mailman/listinfo/pstricks > archive: http://www.tug.org/pipermail/pstricks/ -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://tug.org/pipermail/pstricks/attachments/20100417/f8e97bb9/attachment.html>	2023-03-25 04:33:07	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867205381393433, "perplexity": 4632.609650764951}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945315.31/warc/CC-MAIN-20230325033306-20230325063306-00414.warc.gz"}
https://testbook.com/blog/power-systems-gate-ee-quiz-5/	# Power Systems GATE EE Quiz 5 0 Save Here is a quiz to help you prepare for your upcoming GATE 2016 exam. The GATE EE paper has several subjects, each one as important as the last. However, one of the most important subjects in GATE EE is Power Systems. The subject is vast, but practice makes tackling it easy. This quiz contains important questions which match the pattern of the GATE exam. Check your preparation level in every chapter of Power Systems for GATE EE by taking the quiz and comparing your ranks. Learn about Power generation, Electric field distribution, Voltage and Frequency control, Circuit breakers and more! Power Systems for GATE EE Quiz 5 Que. 1 A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is_______. Que. 2 The incremental costs (in rupees/MWh) of operating two generating units are functions of their respective powers P1 and P2 in MW, and are given by $$\begin{array}{l} \frac{{d{C_1}}}{{d{P_1}}} = 0.2{P_1} + 50\\ \frac{{d{C_2}}}{{d{P_2}}} = 0.24{P_2} + 40 \end{array}$$ Where, $$\begin{array}{l} 20MW \le {P_1} \le 150MW\\ 20MW \le {P_2} \le 150MW \end{array}$$ For a certain load demand, P1 and P2 have been chosen such that dC1 / dP1 = 76 Rs / MWh and dC2 / dP2 = 68.8 Rs / MWh. If the generations are rescheduled to minimize the total cost, then P2 is________. Que. 3 For a 400 km long transmission line, the series impedance is (0.0 + j 0.5) Ω / km and the shunt admittance is (0.0 + j 5.0) μmho/km. The magnitude of the series impedance (in Ω) of the equivalent π circuit of the transmission line is_________. Que. 4 The horizontally placed conductors of a single phase line operating at 50 Hz are having outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854 × 10-12 F/m. The capacitance to ground per kilometer of each line is 1. 4.2 × 10-9 F 2. 8.4 × 10-9 F 3. 4.2 × 10-12 F 4. 8.4 × 10-12 F Que. 5 The bus admittance matrix of a three – bus three – line system is $$Y = j\left[ {\begin{array}{*{20}{c}} { – 13}&{10}&5\\ {10}&{ – 18}&{10}\\ 5&{10}&{ – 13} \end{array}} \right]$$ If each transmission line between the two buses is represented by an equivalent π – network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is 1. 4 2. 2 3. 1 4. 0	2021-06-18 05:23:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7231271862983704, "perplexity": 2265.5850559251276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487635724.52/warc/CC-MAIN-20210618043356-20210618073356-00218.warc.gz"}
https://homework.cpm.org/category/CCI_CT/textbook/apcalc/chapter/7/lesson/7.3.5/problem/7-158	### Home > APCALC > Chapter 7 > Lesson 7.3.5 > Problem7-158 7-158. Let $y(t)$ denote the temperature (in $^\circ\text{F}$) of a cup of tea at time $t$ (in minutes). The temperature of the tea starts at $190^\circ$, while the room temperature is $70^\circ$. The tea’s change in temperature is described by the equation: $\frac { d y } { d x }= −0.1(y − 70)$ 1. Describe the change in temperature of the tea in relation to the room temperature. As time goes on, will the tea ever become colder than the room temperature? 2. What is the temperature of the tea at any time $t$? Implicitly integrate to find $y\left(t\right)$. Find the value of '$C$' by evaluating the initial condition: when $t = 0, y = 190$. $y = 70 + 120e^{−0.1t}$ 3. What is the temperature of the tea after $10$ minutes? $y\left(10\right) =$ ________________	2022-08-08 01:29:45	{"extraction_info": {"found_math": true, "script_math_tex": 13, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6934937238693237, "perplexity": 572.7666409211314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570741.21/warc/CC-MAIN-20220808001418-20220808031418-00789.warc.gz"}
https://www.lmfdb.org/EllipticCurve/Q/348480gu/	# Properties Label 348480gu Number of curves $4$ Conductor $348480$ CM no Rank $0$ Graph # Related objects Show commands for: SageMath sage: E = EllipticCurve("gu1") sage: E.isogeny_class() ## Elliptic curves in class 348480gu sage: E.isogeny_class().curves LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality 348480.gu4 348480gu1 $$[0, 0, 0, 952512, 1314697912]$$ $$72268906496/606436875$$ $$-801990450465747840000$$ $$[2]$$ $$8847360$$ $$2.6925$$ $$\Gamma_0(N)$$-optimal 348480.gu3 348480gu2 $$[0, 0, 0, -13748988, 18068527312]$$ $$13584145739344/1195803675$$ $$25302501678694171852800$$ $$[2]$$ $$17694720$$ $$3.0391$$ 348480.gu2 348480gu3 $$[0, 0, 0, -68046528, 216222557848]$$ $$-26348629355659264/24169921875$$ $$-31963832232750000000000$$ $$[2]$$ $$26542080$$ $$3.2418$$ 348480.gu1 348480gu4 $$[0, 0, 0, -1088984028, 13831853432848]$$ $$6749703004355978704/5671875$$ $$120013535423232000000$$ $$[2]$$ $$53084160$$ $$3.5884$$ ## Rank sage: E.rank() The elliptic curves in class 348480gu have rank $$0$$. ## Complex multiplication The elliptic curves in class 348480gu do not have complex multiplication. ## Modular form 348480.2.a.gu sage: E.q_eigenform(10) $$q - q^{5} + 2q^{7} + 2q^{13} - 2q^{19} + O(q^{20})$$ ## Isogeny matrix sage: E.isogeny_class().matrix() The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering. $$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$ ## Isogeny graph sage: E.isogeny_graph().plot(edge_labels=True) The vertices are labelled with Cremona labels.	2021-05-09 10:33:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9429001808166504, "perplexity": 3626.869112822641}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988966.82/warc/CC-MAIN-20210509092814-20210509122814-00175.warc.gz"}
http://hackage.haskell.org/package/approximate-equality-1.0	# approximate-equality: Newtype wrappers for approximate equality [ bsd3, data, library ] [ Propose Tags ] The purpose of this module is to provide newtype wrappers that allow one to effectively override the equality operator of a value so that it is approximate rather than exact. The wrappers use type annotations to specify the tolerance; the Digits type constructor has been provided for specifying the tolerance using type-level natural numbers. Instances for all of the classes in the numerical hierarchy have been provided for the wrappers, so the wrapped values can mostly be used in the same way as the original values. (In fact, most of the time one doesn't even have to wrap the starting values, since expressions such as (1+sqrt 2/3) are automatically wrapped thanks to the fromIntegral method of the Num typeclass.) See the documentation for Data.Eq.Approximate for more detailed information on how to use this package. Versions [RSS] [faq] 1.0, 1.1, 1.1.0.1, 1.1.0.2 base (>=3 && <5), type-level-natural-number (==1.0.*) [details] BSD-3-Clause Gregory Crosswhite Gregory Crosswhite Data http://github.com/gcross/approximate-equality by GregoryCrosswhite at 2010-08-03T04:14:21Z LTSHaskell:1.1.0.2, NixOS:1.1.0.2, Stackage:1.1.0.2 3390 total (30 in the last 30 days) (no votes yet) [estimated by Bayesian average] λ λ λ Docs uploaded by userBuild status unknown [Index]	2021-12-08 23:17:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17572711408138275, "perplexity": 5211.276246753212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363598.57/warc/CC-MAIN-20211208205849-20211208235849-00456.warc.gz"}
https://www.tutorialspoint.com/how-can-i-plot-a-confusion-matrix-in-matplotlib	# How can I plot a confusion matrix in matplotlib? MatplotlibServer Side ProgrammingProgramming Using imshow method, we can create an image with an input (5, 5) array dimension. After that, we can use the xticks and yticks method to mark the ticks on the axes. ## Steps • Return random floats in the half-open interval [5, 5) and interpolation='nearest'. • Display data as an image, i.e., on a 2D regular raster, with step 1 data. • Get or set the current tick locations and labels of the X-axis, using xticks method. • Get or set the current tick locations and labels of the Y-axis, using yticks method. • Use plt.show() to show the figure. ## Example import matplotlib.pyplot as plt import numpy as np plt.imshow(np.random.random((5, 5)), interpolation='nearest') plt.xticks(np.arange(0, 5), ['A', 'B', 'C', 'D', 'E']) plt.yticks(np.arange(0, 5), ['1', '2', '3', '4', '5']) plt.show() ## Output Published on 15-Mar-2021 08:15:34	2021-09-18 05:46:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39175766706466675, "perplexity": 4699.915186091706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056297.61/warc/CC-MAIN-20210918032926-20210918062926-00407.warc.gz"}
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Nov. 14th at 7 PM PST # A company has assigned a distinct 3-digit code number to each of its 3 Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50570 A company has assigned a distinct 3-digit code number to each of its 3 [#permalink] ### Show Tags 28 Oct 2018, 23:09 00:00 Difficulty: 15% (low) Question Stats: 84% (00:57) correct 16% (01:15) wrong based on 37 sessions ### HideShow timer Statistics A company has assigned a distinct 3-digit code number to each of its 330 employees. Each code number was formed from the digits 2, 3, 4, 5, 6, 7, 8, 9 and no digit appears more than once in any one code number. How many unassigned code numbers are there? A. 6 B. 58 C. 174 D. 182 E. 399 _________________ Senior Manager Joined: 18 Jul 2018 Posts: 377 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: A company has assigned a distinct 3-digit code number to each of its 3 [#permalink] ### Show Tags 28 Oct 2018, 23:29 1 Total of 8 distinct digits. Number of distinct 3 digit numbers that can be formed are 876 = 336. Number of employees = 330. 6 code numbers are unassigned. _________________ When you want something, the whole universe conspires in helping you achieve it. Manager Joined: 13 Jan 2018 Posts: 68 Location: India GMAT 1: 580 Q47 V23 GPA: 4 Re: A company has assigned a distinct 3-digit code number to each of its 3 [#permalink] ### Show Tags 28 Oct 2018, 23:30 Total no. of codes possible is $$876 = 336$$ Since it's a three digit code, the first number can be selected in 8 ways from the given numbers. As no digit repeats in a code, the second digit can be selected in 7 ways and the third digit in 6 ways. So a total of 336 codes are possible. Now for 330 employees, the codes are assigned and the remaining 6 are unused. OPTION : $$A$$ e-GMAT Representative Joined: 04 Jan 2015 Posts: 2181 Re: A company has assigned a distinct 3-digit code number to each of its 3 [#permalink] ### Show Tags 30 Oct 2018, 02:53 Solution Given: • Number of employees = 330 = number of 3-digit codes assigned • Each code was formed from the digits, {2, 3, 4, 5, 6, 7, 8, 9} • No digit appears more than once in any code number To find: • The number of unassigned code numbers Approach and Working: • Total number of 3-digit code numbers formed using the digits, {2, 3, 4, 5, 6, 7, 8, 9} without any repetition are 8 * 7 * 6 = 336 • Therefore, number of unassigned codes are 336 – 330 = 6 Hence, the correct answer is Option A _________________ Number Properties \| Algebra \|Quant Workshop Success Stories Guillermo's Success Story \| Carrie's Success Story Ace GMAT quant Articles and Question to reach Q51 \| Question of the week Number Properties – Even Odd \| LCM GCD \| Statistics-1 \| Statistics-2 Word Problems – Percentage 1 \| Percentage 2 \| Time and Work 1 \| Time and Work 2 \| Time, Speed and Distance 1 \| Time, Speed and Distance 2 Advanced Topics- Permutation and Combination 1 \| Permutation and Combination 2 \| Permutation and Combination 3 \| Probability Geometry- Triangles 1 \| Triangles 2 \| Triangles 3 \| Common Mistakes in Geometry Algebra- Wavy line \| Inequalities Practice Questions Number Properties 1 \| Number Properties 2 \| Algebra 1 \| Geometry \| Prime Numbers \| Absolute value equations \| Sets \| '4 out of Top 5' Instructors on gmatclub \| 70 point improvement guarantee \| www.e-gmat.com Re: A company has assigned a distinct 3-digit code number to each of its 3 &nbs [#permalink] 30 Oct 2018, 02:53 Display posts from previous: Sort by	2018-11-13 16:09:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28494876623153687, "perplexity": 4104.608867299031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741324.15/warc/CC-MAIN-20181113153141-20181113175141-00233.warc.gz"}
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Tood ronrumed durino Enatt Wiat Petcenc Con For mice thl; sample on stindun lighudark cycle; what Is te averaqe porrent about micc that had dlm light night?Round Your answers onedicima place_Standar cycle: Day:Night:Dlm Iight: Day:Night; Tood ronrumed durino Enatt Wiat Petcenc Con For mice thl; sample on stindun lighudark cycle; what Is te averaqe porrent about micc that had dlm light night? Round Your answers onedicima place_ Standar cycle: Day: Night: Dlm Iight: Day: Night;... 2) In * physics lab_ a cylinder of radius .5 m and length 3m is hanging from the ceiling as shown in the drawing below. An electric field of magnitude 3500 NIC and pointing vertically downward enters the top of the cylinder. The clectric field exiting the bottom of the cylinder is measured to have a magnitude of 2000 NIC and is still pointing downward. (Assume that the electric field is always pointing vertically downward ) 0=35NC (3. 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Define a funetion g: P(C) P(D) by 9(B) Prove if that f is onto. then g is one-to-one. Prove that 0R-1(6 6 + 4 {6}. 20 Let f:D B and g: B 5 C bc functions and let A S c Show that (g 0 0)-'[A] = f-'[g-'[AI]:f-'[BJ: Question 9: 8+6+4 Marks) Let f:D 4 C be a function. Define a funetion g: P(C) P(D) by 9(B) Prove if that f is onto. then g is one-to-one. Prove that 0R-1(6 6 + 4 {6}. 20 Let f:D B and g: B 5 C bc functions and let A S c Show that (g 0 0)-'[A] = f-'[g-'[AI]: f-'[BJ:... 1) The probability in a continuous distribution is the height under the curve. TRUE or FALSE?... 1) The probability in a continuous distribution is the height under the curve. TRUE or FALSE? 2) 99% of the data in a normal distribution lies within 2 standard deviations of the mean. TRUE or FALSE? 3) The sample is generally larger than the population. TRUE or FALSE?... Use the rule of 70 to understand how much the price level changes in 100 years... Use the rule of 70 to understand how much the price level changes in 100 years with a 3% rate of inflation What is a market basket of goods and services and how is it used to calculate the Consumer Price Index?... 12.4.35Aaal 0 data Iema & nomney Heatre rod win moun 04 210 and andard Gavlalon al 28. Convat 182 @ 0 [ ero(Tlpo Iniagar & 0 docimu Do not roundto Irlal nawar Than tound lo Ula Rontost hundrodi noeded \| 12.4.35 Aaal 0 data Iema & nomney Heatre rod win moun 04 210 and andard Gavlalon al 28. Convat 182 @ 0 [ ero (Tlpo Iniagar & 0 docimu Do not round to Irlal nawar Than tound lo Ula Rontost hundrodi noeded \|... Find the limit, if it exists, or show that the limit does not exist. $\displaystyle \lim_{(x, y, z) \to (0, 0, 0)} \dfrac{xy + yz}{x^2 + y^2 + z^2}$ Find the limit, if it exists, or show that the limit does not exist. $\displaystyle \lim_{(x, y, z) \to (0, 0, 0)} \dfrac{xy + yz}{x^2 + y^2 + z^2}$... How do you solve 3x - 11= x + 4? How do you solve 3x - 11= x + 4?...	2022-05-21 21:22:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6460368633270264, "perplexity": 3989.9300283744933}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00044.warc.gz"}
https://codereview.stackexchange.com/questions/238023/minimal-property-system-in-c17	# Minimal Property system in c++17 So I needed to represent by objects in terms in ini format and change their values from the ini as well, so I thought why don't implement a property system for this. I want it to be bit fast so I would really like if anyone can remove the std::function if possible but its not necessary. The target application is GUI so small performance should not be a big issue, but still, I think this can be done in a faster way but I can't think of any. no one likes lag. Also, the properties are around 100 or more #include <functional> #include <stdexcept> #include <string> #include <type_traits> #include <unordered_map> #include <variant> #include <QDebug> template <typename C> class PropertySet { public: using PropertyValue = std::variant<bool, int, float, std::string>; void set(const std::string &prop, PropertyValue v) { auto p = m_properties.find(prop); if (p == m_properties.end()) { throw std::runtime_error("Invalid property key"); } // p.value().setter(v); p->second.setter(v); } void set(const std::string &prop, const std::string &v) { auto p = m_properties.find(prop); if (p == m_properties.end()) { throw std::runtime_error("Invalid property key"); } // p.value().setter(p.value().fromStr(v)); p->second.setter(p->second.fromStr(v)); } std::unordered_map<std::string, std::string> getAllValues() { std::unordered_map<std::string, std::string> r; qDebug() << m_properties.size(); for (const auto &p : m_properties) { // r[p.key()] = p.value().toStr(); r[p.first] = p.second.toStr(); } return r; } private: std::function<std::string()> toStr; std::function<PropertyValue(const std::string &)> fromStr; std::function<PropertyValue()> getter; std::function<void(PropertyValue)> setter; }; protected: template <typename T> static auto fromStr(const std::string &s) { if constexpr (std::is_same<T, int>::value) { return std::stoi(s); } else if constexpr (std::is_same<T, bool>::value) { return s == "true" \|\| s == "1"; } static_assert("Error"); } template <typename T, typename Getter, typename Setter> void add(const std::string &name, Getter getter, Setter setter) { auto cptr = static_cast<C *>(this); p.toStr = [getter, cptr]() { return std::to_string(std::invoke(getter, cptr)); }; p.fromStr = [](const std::string &s) { return PropertySet::fromStr<T>(s); }; p.getter = [getter, cptr]() { return PropertyValue(std::invoke(getter, cptr)); }; p.setter = [setter, cptr](PropertyValue v) { std::invoke(setter, cptr, std::get<int>(v)); }; m_properties[name] = p; } }; Also, I'm using Qt, so I was thinking of replacing std::string with QString or QByteArray and std::unordered_map with QHash. There are several ways to approach this. The classic object oriented way is to make Payload be a simple interface class class IPayload { virtual std::string toStr() = 0; virtual PropertyValue fromStr(const std::string &) = 0; virtual PropertyValue get() = 0; virtual void set(PropertyValue) = 0; }; And just create for each property its own instance of an implementation of the interface - depending on what kind of property one uses. This can be helpful when you need variety updating mechanisms to work simultaneously. Say, one Payload that stores the field only in memory, one that stores into both in memory and in a file, and one that forwards it to GUI - or a combination of these. This can be also helpful when you require specialized treatment for some properties - like time input property - that upon receiving std::string input it processes it according to some time conversion, i.e., read double and then converts it to seconds depending on the time unit specification, e.g., "5min" converts to 300 (seconds). The only issue is that you ought to instantiate a treatment for each property - which can be a hassle and make the class unsuitable for some trivial basic usages. I don't see any circumstances when the std::function approach would better - unless one has to runtime change setters or something - which is kinda odd honestly. Also you can try going in the opposite direction and detach the storage class from the "customized actions". Say, make a simple multipurpose ini file parser wrapping std::unordered_map<std::string,std::string> - or use an existing one like boost::ptree that can read and write xml and json in addition. While in the GUI simply call the right functions when user sets the fields. Whether it is viable / not viable / preferred option depends a lot on your development platform for the GUI as well as other nuances. You can in fact combine the two methods. Use the boost::ptree for storing / parsing and for internal usage whilst class PropertySet make responsible for the GUI handling and just instantiate one from each other upon loading / saving / updating. • I'm finding std::function release build faster, but debug bit slower, maybe debug std::function does some unnecessary checking – bluedragon Mar 14 '20 at 9:32 • @bluedragon std::function performs a virtual call itself. Only that each of these std::functions has its own vtable - so it is very surpring that std::function performs faster. Not only that, but it makes a call that calls the actual function. Consider asking for another review and ask to compare these two implementations. I can't tell much beyond as I don't see the code. – ALX23z Mar 14 '20 at 9:55 • my guess is std::function does small function optimization and doesn't do dynamic allocation while my every payload was dynamically allocated here is my implementaion pastebin.com/vEjvPF3B – bluedragon Mar 14 '20 at 11:04 • @bluedragon I am confused about the implementation you wrote. Why std::shared_ptr<IPayLoad> inside a two layered unordered map? If you shared all instances inside the map then I could understand but no - you create a single instance for each of the shared pointer. ... Second - probably more important part. Each virtual function get/set calls some getter/setter - this is a double function call - not ideal. Unless your getter/setter is an optimazable lambda you are unlikely to see any performance improvement from this. – ALX23z Mar 17 '20 at 1:58 • @bluedragon I have some doubts about the double unordered_map. I am not 100% sure but I believe that it would've worker better if it was a single undordered_map and you accessed value at (group_name,name) via a single string group_name/name. – ALX23z Mar 17 '20 at 2:06	2021-03-05 00:57:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19050738215446472, "perplexity": 5948.303189774214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369553.75/warc/CC-MAIN-20210304235759-20210305025759-00636.warc.gz"}
https://nforum.ncatlab.org/discussion/4995/axion/?Focus=83171	# Start a new discussion ## Not signed in Want to take part in these discussions? Sign in if you have an account, or apply for one below ## Discussion Tag Cloud Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support. • CommentRowNumber1. • CommentAuthorUrs • CommentTimeJun 12th 2013 added to axion a pointer to this recent article: • Joseph P. Conlon, M.C. David Marsh, Searching for a 0.1-1 keV Cosmic Axion Background (arXiv:1305.3603) Primordial decays of string theory moduli at $z \sim 10^{12}$ naturally generate a dark radiation Cosmic Axion Background (CAB) with $0.1 - 1 keV$ energies. This CAB can be detected through axion-photon conversion in astrophysical magnetic fields to give quasi-thermal excesses in the extreme ultraviolet and soft X-ray bands. Substantial and observable luminosities may be generated even for axion-photon couplings $\ll 10^{-11} GeV^{-1}$. We propose that axion-photon conversion may explain the observed excess emission of soft X-rays from galaxy clusters, and may also contribute to the diffuse unresolved cosmic X-ray background. We list a number of correlated predictions of the scenario. • CommentRowNumber2. • CommentAuthorUrs • CommentTimeMay 8th 2014 added also a pointer to F-theory axions and to axion inflation (a newly created stub), cross-linked with cosmic inflation (no new content, just some more links and references for the moment) • CommentRowNumber3. • CommentAuthorUrs • CommentTimeJan 16th 2017 • (edited Jan 16th 2017) I have added some content to axion, extracting and highlighting two arguments of Witten on the axion mechanism. The first argument “As a solution to the strong CP problem” (due to Vafa-Witten 84) is the argument for why the axionic potential of the form $a tr(F \wedge F)$ really leads to $\theta \coloneqq \langle a\rangle$ vanishing. After mumbling “path integral” and “Wick rotation” this is a one-line argument (the whole article has only 1.5 pages of text) but somehow all later sources and reviews are shy about saying this. That’s why I felt inspired to go ahead and spell it out on the $n$Lab. The second argument “As arising from string theory” (due to Svrcek-Witten 06) is almost as simple, too, but doesn’t seem to be widely advertised either. I tried to highlight the key ingredients that go into this. There is quite a remarkable statement here, in conclusion: The strong CP problem (and maybe also the problem of dark matter, according to Witten et. al. 16) would be solved by the existence of a scalar field $a$ with the curious coupling term $a \, tr(F \wedge F)$. This raises the question whether such a coupling is not just as contrived as the original smallness of $\theta$. But then the observation is that such a coupling is precisely what becomes of the Green-Schwarz anomaly cancellation mechanism of heterotic string theory in 4d. • CommentRowNumber4. • CommentAuthorUrs • CommentTimeFeb 5th 2017 • (edited Feb 5th 2017) I have expanded further at axion: 1. added more of the historical references, 2. accomopanied the discussion of the axion from the perspective of the heterotic string with the paralell discussion from the perspective of the type IIA string. • CommentRowNumber5. • CommentAuthorUrs • CommentTimeApr 1st 2018 Edit to: axion by Urs Schreiber at 2018-04-01 00:54:20 UTC. hyperlinked pointer to textbook by Ibanez-Uranga • CommentRowNumber6. • CommentAuthorUrs • CommentTimeMay 18th 2018 moved the previous pointers to Wiczek’s notes and to the ABRACADABRA experiment from “References – Experimental signature – In cosmology” to “In particle physics” • CommentRowNumber7. • CommentAuthorUrs • CommentTimeJul 9th 2018 added pointer to today’s HJSSZ 18 (potential axion signatures in LIGO-type gravitational wave detection) • CommentRowNumber8. • CommentAuthorUrs • CommentTimeMar 3rd 2020	2023-03-24 03:31:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 9, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6165549755096436, "perplexity": 4277.736138297498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945242.64/warc/CC-MAIN-20230324020038-20230324050038-00688.warc.gz"}
https://petamind.com/predict-coronavirus-deaths-by-days/	A.I, Data and Software Engineering # Predict coronavirus deaths by days P As the pandemic is going on with an increasing number of deaths daily, let create a simple model to predict the deaths caused by 2019-nCoV (Wuhan Coronavirus). ### The 2019-nCoV death data I grab the death toll data from World Meters website. ### Plot the data Firstly, we transform the table into a Pandas data frame. Then we can have a look at the following graph We can see that a linear regression model could be a good choice at this stage. Since we only have a very small data set (17 samples), it may not reflect correctly the trend. However, in this article, we want to implement with polynomial regression. Let review some terms: #### Regression Regression is about finding the trend in data (the relationship between variables). This allows us to better understand the data distribution and to predict the values for new input variables. The regression outputs continuous values (real values) to distinguish classification which predicts discrete values. #### Linear Regression Linear regression is used when the trend in the data is linear, i.e., it is of the form y = ax + b The other, more commonly used form of regression is polynomial regression. #### Polynomial Regression Polynomial regression used when the trend in data is a polynomial of degree ’n’, i.e., it is of the form $$y = a_0x^n + a_1x^{n-1}+ … + a_n$$. ### Keras implementation First, we import relevant libraries. If you are new to Tensorflow and Keras, you can follow these posts. We consider that the data will fit some quadratic form (n = 2), i.e. $$y = a_0x^2 + a_1x + a_3$$. Therefore, we transform the day values as follows: Next, we build the model with one input and one output layer. After that, we train model with 17 days’ samples and 10k epochs. After training, we can check the fitting line (red) to the provided data. Next, we want to predict coronavirus deaths in the next 9 days, from day 18 – 26th. And finally, this is what we want to see but do NOT want to BELIEVE: ### Conclusion Well, it is just a simple prediction while ignoring thousands of factors. Sometimes, we can just pray and wait. Hopefully, the pandemic can be seized in the next 10 days! Cross my fingers for all 2019-nCoV patients! Below is the updated actual number of deaths for comparison: After monitoring the data for the next few days, the model predicts quite well with some exact match, it followed the trends until the pandemic seemed to be under control. A.I, Data and Software Engineering PetaMinds focuses on developing the coolest topics in data science, A.I, and programming, and make them so digestible for everyone to learn and create amazing applications in a short time.	2020-05-31 04:21:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42806190252304077, "perplexity": 1389.5733241979626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347410745.37/warc/CC-MAIN-20200531023023-20200531053023-00024.warc.gz"}
http://www.ck12.org/book/CK-12-Middle-School-Math-Grade-8/r1/section/4.5/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # 4.5: Scale in Three Dimensions Difficulty Level: At Grade Created by: CK-12 ## Introduction A New Kind of Map Josh spent most of his Saturday morning at the library looking at different books on Mount Everest. After completing his drawings of the Mountain, and figuring out the scale for his model, Josh wanted to look at some maps that other people had created of the mountain. He began looking in books, but most of the maps weren’t drawn in very high detail. Finally, after a lot of searching, he began using the computer. Right away, Josh discovered this map on a website. “What did you find?” his sister Karen asked. She had also been at the library writing a book report. “I found this map. It is called a relief map,” Josh said. “What a “relief” that you found it!” Karen joked. “Not really. It is called a relief map because of what is on it. Look,” Josh began to explain all about the map. Have you ever seen a relief map? Before Josh explains about relief maps, use this lesson to learn all about them. When finished, you will be able to explain the difference between a relief map and a two-dimensional map. What You Will Learn By the end of this lesson, you will be able to complete the following skills: • Read and interpret plans and views of scale models. • Read and interpret relief features of topographic maps. • Compare scale relationship of distance, area and volume. • Solve real-world problems involving three-dimensional scale models, perspective views and relief maps. Teaching Time I. Read and Interpret Plans and Views of Scale Models In our last lesson, we worked on interpreting two-dimensional maps, scale drawings and floor plans. We used a scale to interpret measurements the actual dimensions and the scale dimensions. These were two – dimensional representations, this means that the things being represented could be easily shown in a flat plane. What happens is something can’t be shown in a two – dimensional way? When this happens, we have to use a three – dimensional method of display. Whereas a two – dimensional image takes into account length and width, a three – dimensional figure contains the length, width and height or depth. When we wanted to represent a two – dimensional space, like a map, we used a scale drawing or a scale map. When we want to represent a three-dimensional space, we use a scale model to represent the space. A scale model is a model used to represent a three – dimensional space. Yes. You can find the actual dimensions of the space in the same way that you did for a scale drawing. First, let’s think about how we can find the actual dimensions. In order to find the actual dimensions from a scale model, you can set up and solve a proportion. The scale given in the model is the first ratio. The unknown length and the scale length is the second ratio. We compare the scale in the first ratio and we compare the two lengths in the second ratio. Let’s look at an example. Example Brianna is making a scale model of the White House using the scale 1 cm = 0.5 m. If the height of Brianna’s model is 42 cm, what is the height of the actual White House? Set up a proportion. Write the scale as a ratio. 1 cm0.5 m\begin{align}\frac{1 \ cm}{0.5 \ m}\end{align} Now write the second ratio, making sure it follows the form of the first ratio. 1 cm0.5 m=42 cmx m\begin{align}\frac{1 \ cm }{0.5 \ m}=\frac{42 \ cm}{x \ m}\end{align} Next cross-multiply and solve for x\begin{align}x\end{align}. (1)xx=42(0.5)=21\begin{align}(1)x &= 42(0.5)\\ x &= 21\end{align} The actual height of the White House is 21 meters. We can also use proportions to find the measurements of scale models. Let’s look at an example. Example Mike is building a scale model of an airplane using the scale 14 inch=1 foot\begin{align}\frac{1}{4} \ inch = 1 \ foot\end{align}. If the actual length of the airplane is 150 feet, what will the length of the scale model be? Set up a proportion. The scale for the model is 14 inch=1 foot\begin{align}\frac{1}{4} \ inch = 1 \ foot\end{align}. So set up a ratio using these values: 0.25 inch1 foot\begin{align}\frac{0.25 \ inch}{1 \ foot}\end{align}. Now write the second ratio. You know the actual length is 150 feet. The unknown length is x\begin{align}x\end{align}. Make sure that the second ratio follows the form of the first ratio: inches over feet. 0.25 inch1 foot=x inches150 feet\begin{align}\frac{0.25 \ inch}{1 \ foot}= \frac{x \ inches}{150 \ feet}\end{align} Next cross-multiply to solve for x\begin{align}x\end{align}. (1)xx=150(0.25)=37.5\begin{align}(1)x &= 150(0.25)\\ x &= 37.5\end{align} The length of the scale model is 37.5 inches. Notice how once you understand how proportions work, you can compare and solve proportions when the measurements of different things have a relationship. The actual length has a relationship with the scale length, so they are related to each other. The scale is a comparison between a selected unit of measure and an actual unit of measure. There is a relationship here as well. These two ratios form a proportion and we have the basis for our problem solving. II. Read and Interpret Relief Features of Topographic Maps In the last lesson, you looked at two – dimensional maps. You will notice that if you look at a two – dimensional map, that while it is excellent for measuring distances, it isn’t as helpful when measuring mountains or other features. When we want to show a map in a three-dimensional way, we use a topographic map. A topographic map is a type of map that shows not only the distances on the ground, but also the relief features of the area, such as mountains. The map uses contour lines to show the elevation of the area. Each contour line is a line of equal elevation or height. They show the general shape of the terrain or land. When contour lines are spread farther apart, the elevation is not as steep. Where contour lines are bunched close together, the elevation is steeper. Topographic maps may also use colors to represent different features. Blue represents water, green represents vegetation, and brown lines represent topographic contours. You can interpret these maps by using the scale. There will be a scale to show what each distance on the map represents, just like other maps. There will also be a scale to tell you what each contour line represents. Example This map shows a mountain from a national park in California. What is the height of the mountain? First, look at the map scale. It states that the contour interval is 40 feet. That means that each contour line represents 40 feet of elevation. Count the number of contour lines that make up the mountain. There are 10 contour lines. Write a proportion to find the height of the mountain. 1 line40 feet=10 linesx feet\begin{align}\frac{1 \ line}{40 \ feet}=\frac{10 \ lines}{x \ feet}\end{align} Now cross-multiply to solve for x\begin{align}x\end{align}. (1)xx=10(40)=400\begin{align}(1)x &= 10(40)\\ x &= 400\end{align} The mountain is 400 feet high. Example Using the map from last example, the width of the base of the mountain on the map is 1.5 inches. What is the actual distance of the base of the mountain? For this problem, you don’t need the contour scale. You need the map scale. Write a proportion. First we write the scale as a ratio. Then we write the scale measurement compared to the actual measurement for the second ratio. Notice that we are looking for the actual measurement, so that is our missing value. 1 inch0.5 mile=1.5 inchesx miles\begin{align}\frac{1 \ inch}{0.5 \ mile}=\frac{1.5 \ inches}{x \ miles}\end{align} Now cross multiply to solve for x\begin{align}x\end{align}. (1)xx=1.5(0.5)=0.75\begin{align}(1)x &= 1.5(0.5)\\ x &= 0.75\end{align} The distance of the base of the mountain is 0.75 mile. III. Compare Scale Relationships of Distance, Area and Volume We can compare the scale relationships of distance, area and volume when looking at three – dimensional figures. If you think back to other math classes, you will remember some of these three – dimensional figures such as a prism or a pyramid. When you compare different measurements, you will see the proportional relationships between them. Let’s look at an example involving volume. Example Brooke has a scale model of a warehouse. A storage unit is shaped like a rectangular prism and has the dimensions 4 in. by 3 in. by 6 in. If the scale of the model is 0.5 in. = 2 ft, what are the actual dimensions of the storage unit? What is the volume? First, notice that there are two parts to this problem. The first part is figuring out the actual dimensions given that Brooke has a scale model. The second part is figuring out the volume. First use a proportion to find the actual dimensions of the storage unit. Write the scale as the first ratio, and the scale and unknown actual dimension of the storage unit as the second ratio. 0.5 inch2 feet(0.5)x0.5xx=4 inchesx feet0.5 inch2 feet=3 inchesx feet0.5 inch2 feet=6 inchesx feet=4(2)(0.5)x=3(2) (0.5)x=6(2)=80.5x=60.5x=12=16 x=12 x=24\begin{align}\frac{0.5 \ inch}{2 \ feet} &= \frac{4 \ inches}{x \ feet} \qquad \frac{0.5 \ inch}{2 \ feet} = \frac{3 \ inches}{x \ feet} \qquad \frac{0.5 \ inch}{2 \ feet} = \frac{6 \ inches}{x \ feet}\\ (0.5)x &= 4(2) \qquad \qquad \quad (0.5)x = 3(2) \qquad \qquad \ \ (0.5)x = 6(2)\\ 0.5x &= 8 \qquad \qquad \qquad \quad 0.5x =6 \qquad \qquad \qquad \quad 0.5x = 12\\ x &= 16 \qquad \qquad \qquad \quad \ \ x = 12 \qquad \qquad \qquad \quad \ \ x = 24\end{align} The actual dimensions of the storage unit are 16 feet by 12 feet by 24 feet. This is the length, width and height of the storage unit. Now that you know the actual dimensions, you can find the volume. VVA=lwh=(16 feet)(12 feet)(24 feet)=4,608 feet3\begin{align}V &= lwh\\ V &= (16 \ feet)(12 \ feet)(24 \ feet)\\ A &= 4,608 \ feet^3\end{align} The volume of the storage unit is 4,608 cubic feet. Now think about how the area of the base of the prism relates to the volume of the prism. AAA=lw=16(12)=192 sq.feet\begin{align} A &= lw\\ A &= 16(12)\\ A &= 192 \ sq.feet\end{align} If we write the volume as a ratio with the area of the base, we will find something very interesting. 4608192\begin{align}\frac{4608}{192}\end{align} Now divide the numerator by the denominator. The answer is 24 feet. This is the measurement of the height of the prism. It means that there is a relationship between the area of a three – dimensional figure its height and its volume. The measurements are related and in proportion to one another. Example Tim has a cube with a side length of 4 inches. He has a similar cube with dimensions that are twice the first cube. How does the volume of the larger cube compare to the volume of the smaller cube? First, find the dimensions of the larger cube. The problem states that the dimensions are twice those of the first cube. That means they are scaled up by a factor of 2. So the side length of the larger cube is 4 inches×2=8 inches\begin{align}4 \ inches \times 2 = 8 \ inches\end{align}. Now find the volume of both cubes and compare. Volume of smaller cube: VVV=lwh=(4 inches)(4 inches)(4 inches)=64 inches3\begin{align}V &= lwh\\ V &= (4 \ inches)(4 \ inches)(4 \ inches)\\ V &= 64 \ inches^3\end{align} Volume of larger cube: VVV=lwh=(8 inches)(8 inches)(8 inches)=512 inches3\begin{align}V &= lwh\\ V &= (8 \ inches)(8 \ inches)(8 \ inches)\\ V &= 512 \ inches^3\end{align} Next compare the two volumes. You want to know how the volume of the larger cube compares to the volume of the smaller cube. Write a ratio comparing the two volumes. 512 inches364 inches3=8\begin{align}\frac{512 \ inches^3}{64 \ inches^3}=8\end{align} The volume of the larger cube is 8 times larger than the volume of the smaller cube. In the previous example, the scale factor that changed the smaller cube to the larger cube was 2, but the volume was 8 times as large. This leads to the following rule: • The ratio of volumes of similar figures is the cube of the scale factor. Write this rule down in your notebooks. IV. Solve Real – World Problems Involving Three – Dimensional Scale Models, Perspective Views and Relief Maps The problems that we have been working with in this lesson have all been real – world problems. You can see that working with maps, scale drawings and models have many real-life applications. Think about climbing a mountain! If you were going to climb a mountain it would be very helpful to read a topographic map. However, if you only wanted to know the distance from Cleveland to New York City, then a scale map would be most helpful. Now let’s expand what we have learned to include perspective views. A perspective is a point of view. When you look at a figure from the top or the side or the back, we can say that we are looking at a three – dimensional figure in perspective. If we wanted to look at a skyscraper from an airplane, our view would be a perspective view. It would look very different from air as opposed to looking at it from the ground view. Now let’s go back to the problem from the introduction and use what we have learned to answer the question posed at the beginning of the lesson. ## Real-Life Example Completed A New Kind of Map Here is the original problem from the introduction. First, reread it and then answer the question. Explain the difference between a two – dimensional map and a relief map. Josh spent most of his Saturday morning at the library looking at different books on Mount Everest. After completing his drawings of the Mountain, and figuring out the scale for his model, Josh wanted to look at some maps that other people had created of the mountain. He began looking in books, but most of the maps weren’t drawn in very high detail. Finally, after a lot of searching, he began using the computer. Right away, Josh discovered this map on a website. “What did you find?” his sister Karen asked. She had also been at the library writing a book report. “I found this map. It is called a relief map,” Josh said. “What a “relief” that you found it!” Karen joked. “Not really. It is called a relief map because of what is on it. Look,” Josh began to explain all about the map. Now explain the difference between a two – dimensional map and a relief map. Solution to Real – Life Problem A two – dimensional map is created on a flat surface and only shows the dimensions length and width. There aren’t any other three-dimensional features included on the map. When Josh drew the area of the Everest from space in an earlier lesson, he drew it in a two – dimensional way. He only showed the length, width and area in the scale drawing. A relief map uses a scale just like any other map, but other features are included on the map. A relief map uses different colors and textures to show the contour of the terrain. It also includes bodies of water and other landmarks. In addition, the map shows contour lines which measure the elevation of a natural land mass. ## Vocabulary Here are the vocabulary words that are found in this lesson. Two – Dimensional A figure drawn in two dimensions is only drawn using length and width. Three – Dimensional A figure drawn using length, width and height or depth. Scale Model a model that represents a three – dimensional space. Topographic Map a map that shows distances on the ground, but also relief features of the map such as mountains. Contour Lines lines on a map to show elevation. Each contour line represents the same measure of elevation. Elevation the measure of height Terrain the land ## Time to Practice Directions: Solve each problem. Kevin built a scale model of a pool. He used the scale \begin{align}\frac{1}{2}^{\prime\prime} = 5 \ ft\end{align}. Use this information to answer the following questions. 1. The width of the pool on the scale model measures 1.5 inches. What is the actual width of the pool? 2. The length of the pool on the scale model measures 2.5 inches. What is the actual length of the pool? 3. The depth of the pool on the scale model measures 0.5 inches. What is the actual volume of the pool. This is a map of a national park. Use this information to answer the following questions. 1. What is the height of the mountain shown on the map? 2. The map distance of the length of the distance across the lake is 1.5 cm. What is the actual distance across the lake? 3. Explain why the contour lines on the map are closer together at some points and farther apart at other points. Directions: Solve each problem. 1. A scale model of a sandbox has dimensions 0.5 inch by 3 inches by 4 inches. If the scale of the model is \begin{align}\frac{1}{4} \ inch = 1 \ foot\end{align}, what is the volume of the actual sandbox? 2. A cube measures 5 inches on each side. A similar cube has dimensions that are 3 times as large. How does the volume of the larger cube compare to the volume of the smaller cube? 3. A shipping box measures 16 inches by 12 inches by 8 inches. A second box has a similar size but each dimension is \begin{align}\frac{1}{4}\end{align} as long. How does the volume of the second box compare to the volume of the first box? 4. Rina’s fish tank has a volume of 8,000 cubic inches. The dimensions of Ava’s fish tank are all \begin{align}\frac{1}{2}\end{align} the size of Rina’s. What is the volume of Ava’s fish tank? Directions: Answer each of the following questions as true or false. 1. A topographic map would include lakes and rivers. 2. A two – dimensional map could also be a topographic map. 3. Three – dimensions means including length, width and height. 4. Depending on what you are measuring, height might be replaced by depth. 5. There is a proportional relationship between length and the area of a figure. 6. A two – dimensional map also includes contour lines. 7. Contour lines can be different sizes if there is a different elevation involved. 8. Elevation also means height. 9. A topographic map can be built in three dimensions. 10. Two – dimensional maps and three – dimensional maps both include the same information. ### My Notes/Highlights Having trouble? Report an issue. Color Highlighted Text Notes Show Hide Details Description Difficulty Level: Tags: Subjects:	2016-07-27 06:09:34	{"extraction_info": {"found_math": true, "script_math_tex": 29, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9293087720870972, "perplexity": 766.1954454409768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257825366.39/warc/CC-MAIN-20160723071025-00240-ip-10-185-27-174.ec2.internal.warc.gz"}
https://www.jobilize.com/physics/section/conceptual-questions-single-slit-diffraction-by-openstax?qcr=www.quizover.com	# 4.1 Single-slit diffraction (Page 3/5) Page 3 / 5 Check Your Understanding Suppose the slit width in [link] is increased to $1.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{m}.$ What are the new angular positions for the first, second, and third minima? Would a fourth minimum exist? $17.8\text{°}$ , $37.7\text{°}$ , $66.4\text{°}$ ; no ## Summary • Diffraction can send a wave around the edges of an opening or other obstacle. • A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides. ## Conceptual questions As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change? The diffraction pattern becomes wider. Compare interference and diffraction. If you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. Explain. Walkie-talkies use radio waves whose wavelengths are comparable to the size of the hill and are thus able to diffract around the hill. Visible wavelengths of the flashlight travel as rays at this size scale. What happens to the diffraction pattern of a single slit when the entire optical apparatus is immersed in water? In our study of diffraction by a single slit, we assume that the length of the slit is much larger than the width. What happens to the diffraction pattern if these two dimensions were comparable? The diffraction pattern becomes two-dimensional, with main fringes, which are now spots, running in perpendicular directions and fainter spots in intermediate directions. A rectangular slit is twice as wide as it is high. Is the central diffraction peak wider in the vertical direction or in the horizontal direction? ## Problems (a) At what angle is the first minimum for 550-nm light falling on a single slit of width $1.00\mu \text{m}$ ? (b) Will there be a second minimum? a. $33.4\text{°}$ ; b. no (a) Calculate the angle at which a $2.00\text{-}\mu \text{m}$ -wide slit produces its first minimum for 410-nm violet light. (b) Where is the first minimum for 700-nm red light? (a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of $28.0\text{°}$ ? (b) At what angle will the second minimum be? a. $1.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{m}$ ; b. $69.9\text{°}$ (a) What is the width of a single slit that produces its first minimum at $60.0\text{°}$ for 600-nm light? (b) Find the wavelength of light that has its first minimum at $62.0\text{°}$ . Find the wavelength of light that has its third minimum at an angle of $48.6\text{°}$ when it falls on a single slit of width $3.00\mu \text{m}$ . 750 nm (a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width $7.50\mu \text{m}$ . At what angle does it produces its second minimum? (b) What is the highest-order minimum produced? Consider a single-slit diffraction pattern for $\lambda =589\phantom{\rule{0.2em}{0ex}}\text{nm}$ , projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes? 2.4 mm, 4.7 mm (a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width $2.00\mu \text{m}$ . (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance. (a) What is the minimum width of a single slit (in multiples of $\lambda$ ) that will produce a first minimum for a wavelength $\lambda$ ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima? a. $1.00\lambda ;$ b. $50.0\lambda ;$ c. $1000\lambda$ (a) If a single slit produces a first minimum at $14.5\text{°},$ at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima). If the separation between the first and the second minima of a single-slit diffraction pattern is 6.0 mm, what is the distance between the screen and the slit? The light wavelength is 500 nm and the slit width is 0.16 mm. 1.92 m A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. Ocean waves of 20.0-m wavelength approach the opening straight on. At what angles to the incident direction are the boats inside the harbor most protected against wave action? An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s? $45.1\text{°}$ how does colour appear in thin films in the wave equation y=Asin(kx-wt+¢) what does k and w stand for. derivation of lateral shieft Hi Hi hi ALFRED how are you? hi asif hi Imran I'm fine ALFRED total binding energy of ionic crystal at equilibrium is How does, ray of light coming form focus, behaves in concave mirror after refraction? Sushant What is motion Anything which changes itself with respect to time or surrounding Sushant good Chemist and what's time? is time everywhere same Chemist No Sushant how can u say that Chemist do u know about black hole Chemist Not so more Sushant DHEERAJ Sushant But ask anything changes itself with respect to time or surrounding A Not any harmful radiation DHEERAJ explain cavendish experiment to determine the value of gravitational concept. For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process? as a free falling object increases speed what is happening to the acceleration of course g is constant Alwielland acceleration also inc Usman which paper will be subjective and which one objective jay normal distributiin of errors report Dennis normal distribution of errors Dennis photo electrons doesn't emmit when electrons are free to move on surface of metal why? What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons? give any fix value to wave length Rafi 40 cm into change mm 40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power. Prema i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line. Prema there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends. Prema 40cm=40.0×10^-2m =400.0×10^-3m =400mm. Prema this msg is out of mistake. sorry friends. Prema what is physics? why we have physics because is the study of mater and natural world John because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered. Yoblaze physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this? tahreem physics is the study of matter,energy and their interactions Buvanes all living things are matter Buvanes why rolling friction is less than sliding friction tahreem thanks buvanas tahreem is this a physics forum	2019-04-26 08:19:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 24, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45734626054763794, "perplexity": 989.3219238701312}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578762045.99/warc/CC-MAIN-20190426073513-20190426095513-00519.warc.gz"}
http://nordic-athletics.org/birhi/word-roots-level-2-answer-key-006a9a	Click here to see the Cause and Effect PowerPoint! All items are structured just like the test. LOWEST PRICES ON English From the Roots Up,Word Roots,Word Roots Software,WordBuild,Red Hot Root Books Login / WishList / Cart (0) Menu A healthy knowledge of roots and affixes enables us all to unlock word meanings. These are notes with blanks for students, This product is a 6 page task card review that aligns to 3rd grade VA English SOL 3.4b. 4x2 – 3 = 9 5. m2 + 12 = 48 3. In this activity, students are given a word and must analyze three different words to determine which word that shares a common root word. The answer key is automatically generated and is placed on the second page of the file. This Greek and Latin vocabulary program was developed to create a solid, Affixes—Progressive practice worksheets introduce a few affixes at a time and build on previous learning. Find the $\sqrt{\phantom{0}}$ or $\sqrt{x}$ key on your calculator. Please see our Online Support help website for assistance with handling any issues you may encounter while installing or using this eBook on the below operating systems. 1. x2 = 121 4. Unit 1 contains five weeks of study: four weeks to learn four root words each and one review week. A word within a word. This book, the 7th grade level of Vocabulary from Latin and Greek Roots, was formerly known as Vocabulary from Latin and Greek Roots - Level I. 4x2 – 100 = 0 2. Line-listed answer key included. Vocabulary from Latin and Greek Roots Level VII Level VIII Level IX Level X Level XI Level XII. Mensa Recommended Materials for the Gifted Learn vocabulary, terms, and more with flashcards, games, and other study tools. 1 Latin and Greek Word Roots, Book 1 Teacher Guide Introduction … 2 Answer Keys … 6 Drawing Master … 19 Program Lessons Word Root A aster, astro, a, an, auto 1 Word Root B bio, bi, bibli/o 5 Word Root C cent, circum, chron. Ask them to write the definition of the word root in the center circle once they have finished the word web and figured out the definition of the root word. Learning these word elements dramatically improves spelling and the ability to decode unfamiliar words. Word Problems - Level 2. Level 2 contains the following word parts and vocabulary: • 28 Prefixes • 109 Roots • 86 Suffixes • 312 Vocabulary Words A total of 10 words of prac, Teach the Latin and Greek root words of ecology vocabulary with these task cards and practice worksheets. This book includes a pretest/posttest, lesson reviews, answers, and a dictionary of the prefixes, roots, suffixes, and vocabulary words derived from Latin and/or Greek word elements. Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. All the words of the puzzle fit into that theme. Grades 5-12+. It includes practice with prefixes, suffixes, and root words. 24 task cards, a, The concept behind this product is that every year it seems as if my students score lowest in the area of determining the meaning of unfamiliar words (context clues and word origins). Level 2 contains the following word parts and vocabulary: • 28 Prefixes • 109 Roots • 86 Suffixes • 312 Vocabulary Words… You have added into shopping cart. Remember Your Roots #1 transmittable insubordinate Remember Your Roots #1 Directions: You are Dr. Frankenstein. Grades 7-12+. What does the word unhurt mean? The Critical Thinking Word Roots Level 1 School Workbook Paperback – January 1, 2015 by Cherie A. Then there is a section to review each. What is the meaning of the word prefix? You have to specify at least one search term. You can immediately download your eBook from. When you use your calculator to find the square root of a number that is not a perfect square, the answer that you see is not the exact number. After a first teach, I usually have my kids practice a sorting activity (using the 'root word' and two suffixes in hand). It contains word lists and activities for ALL of building vocabulary Unit 2, which includes the following root words: Scrib-/Script- Dict- Pon-/Pos-/Posit This document contains two half sheets of practice for identifying base/root words. A. Vocabulary From Classical Roots Book A Teacher's Guide and Answer Key by Norma Fifer Paperback $25.95 Only 10 left in stock - order soon. Word Roots Level 2 Workbook By Cherie A. *Required and/or Optional Components sold separately for this product. Underline the root word HEAT and explain that this is the root word and, even though it is part of the word REHEATED, it can also stand alone. D. Writing Sentences Write sentences using the words in the lesson. Compound words #2 . Level IX. JavaScript seems to be disabled in your browser. The concept behind this product is that every year it seems as if my students score lowest in the area of determining the meaning of unfamiliar words (context clues and word origins). The activities following the lessons include: A. Spelling and Defining Words Match each given word to its correct definition. Don't worry. Each lesson has the meanings of prefixes, roots, and suffixes used to form the vocabulary words. Plant, Publisher: The Critical Thinking Company ISBN-13: 9781601446725 In Word Roots Level 2, your student will learn the building blocks of better spelling and vocabulary. Reply; Inaccurate; Jacquelene P on Aug 21, 2019; Purchased on Jul 24, 2018 Every year we donate thousands of products to children in need. Each practice sheet provided the following practice: Hurt badly. The game app features 20 words per level. This lesson can be used as worksheets, interactive notebook entries, or bulletin board themes. Add To Cart Add To Wishlist Word Roots, Level 1 Cherie A. Every whole number that is not prime can be written as a product of prime numbers in A. Tandem worksheets have students apply th, Put a Harry Potter spin on Word Work! They can be used individually, in pairs, or in small group work. You are given a keyword and you have to match all the words in a crossword type of game. It covers the most common prefixes and suffixes. Support; Order Vocabulary from Latin and Greek Roots. Set includes: As an extension, students can write a story about their beasts or a paragraph describing their. Solve for the roots of the following quadratic equations by extracting the roots. Fill in the correct words 1 (intermediate) 7. How about some short, extra practice to work on the days before the big day? 1) Vocabulary Workshop® Level A Level B Level C Level D Level E Level F Level G Level H 2) Vocabulary Power Plus® Book One Book Two Book Three Book Four 3) Wordly Wise 3000® Book 5 Book 6 Book 7 Book 8 Book 9 Book 10 Book 11 Book 12 Learning these word elements dramatically improves spelling and the ability to decode unfamiliar words. Key concept: Students should know how to use the distributive property to help solve multiplication problems quicker. Geometry. 10 Full-Color Unit Booklets, PDF Answer Key & Unit Checks, High School 2 Book Pack (5 books), Grammar & Writing Guide, High School Cards* (These two items are non-consumable and are used for High School 1, 2, and 3.) Clauses Matching Worksheet 3. 1 Integers, powers and roots 7 ˜ e ˚ rst primes are 2 3 5 7 11 13 17 19 23 29 . They are so versatile! C. Not hurt. Selection File type icon File name Description Size Revision Time User Set I and III Answer Keys; Selection File type icon File name Description Size Revision This prefix resource is perfect for use as a guided or independent practice, center work or even extra practice as needed. answer key this pdf doc is made up of word roots b1 answer key so as to download this record you must sign up oneself' 'Word Roots B1 Teachingcom April 7th, 2018 - Word Roots Teaches Students The Meanings Of Latin And Greek Prefixes Roots And Suffixes Commonly Used In Download Ebook Answer Key To Word Whiz bonobo Word Whizzle Search Monkeys and Apes answers! This lesson is for language arts students in a middle or high school. with answer keys and cut and glue practice pages. Line-listed answer key included, along with a Greek and Latin prefix/root/suffix dictionary. It has a guided practice paper and two assignment papers. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A Mac OS X version will be available soon. . Key B Basic M Medium C Challenge ©Curriculum Associates, LLC Copying is not permitted. Level VIII. Entire year of Root Word, Prefix, Suffix Practice Level 2. by . So can you find all of them without help. After Algebra 1 Geometry a and b are the most requested subjects for Edgenuity. After a first teach, I usually have my kids practice a sorting activity (using the 'root word' and two prefixes in hand). There are activities for prefixes and root words. Roots Prefixes Suffixes Worksheet 8. S D N A L S I B T O … Hi Folks, here we have all answers, cheats and solutions for Tasty Words the puzzle app created by Second Gear Games and available for Android and iOS devices. Looking for a way to add some holiday spice to your root word practice? C. Defining the Word Parts Define the word parts. Sale Word Roots Level 1 was:$24.99 now: $20.00 Quick view Sale Beginning Word Roots, Grades 3-4 was:$15.99 now: $12.80 Quick view Sale Wordly Wise 3000 4th Edition Student Book 2, Paperback, Grade 2 was:$14.35 now: \$11.48 Quick view Root / Prefix / Suffix Exercise Learn new vocabulary and become familiar with English words and how to modify them by adding or removing certain affixes (suffixes / prefixes) to form adjectives from nouns, adverbs from adjectives, verbs from adverbs, nouns from verbs or the other way around. the meaning for this word part is given in the second column (some word parts don’t carry meaning; for example, the word families in Levels 1 and 2). Completing the Sentence Complete the sentence by choosing the correct word. This skill can help students increase their comprehension and swiftly decode unknown words on timed tests.Use this versatile file to increase vocabulary (and thus comprehension) by developing, reviewing, and enriching, 96 printable word work practice sheets. Many other roots are introduced throughout the levels, but the word families and Reading, Writing, Math, Science, Social Studies. You can unsubscribe at any time. Prefix-Suffix-Root List by Grade Level (Generally, prefixes and suffixes change the meanings of roots, but it is usually the suffix that denotes the part of speech.) Here you can search for your answer by level number, but we recommend using the search by letters. Prime numbers have just two factors: 1 and the number itself. Level 2 contains the following word parts and vocabulary: Our eBooks are electronic versions of the book pages that you may print to any paper printer. They can be used by stud, These worksheets are designed for middle grade students who need to practice common root words and their meanings. The game can be played in English, French, German, Russian, Spanish, Portuguese and Italian. Many of these task cards are multiple answer questions, providing students with practice for TEI questions they may see on the SOL. There are activities for suffixes and root words. Subjects: English Language Arts, Grammar, Spelling. ISBN-13: 9781601446725. 1st Grade Prefix Suffix … Task cards are an excellent way to engage your students in vocabulary study. This lesson integrates science concepts (parts of a plant) with Halloween-themed root words. The Rooted Mind publishes periodic e-mail newsletters, entitled Taking Root to provide teachers and parents with information about the Latin and Greek Roots Challenge. ... students are given a word and must analyze three different words to determine which word that shares a common root word. 5x2 – 100 = 0 B. Learning these word elements dramatically improves spelling and the ability to decode unfamiliar words. Plant Cherie A. Level 2 contains the following word parts and vocabulary: • 28 Prefixes • 109 Roots • 86 Suffixes • 312 Vocabulary Words. C. A group of letters put at the end of a root word which changes its meaning. . English word as the answer . If you really love picture puzzles and puzzles with photo’s this iss a perfect quiz for you. Learn meanings of prefixes, roots… Word Roots Level 2 Workbook. This zip file includes Guided Notes, a PowerPoint, Flashcards, a Practice Activity, and a Quiz to teach this critical skill! They are then asked to illustrate their beast. Match the Word A rainy day theme links all the activities. Word Roots Level 2 (9781601446725) by Cherie A. B. In this vocabulary book by Prestwick House Level 2, I will give you the answers. Students use knowledge of root words, base words, prefixes, suffixes, or related words to help determine the meaning of spells. Word Formation - Noun Verb Adjective Adverb Forms 9. 480 words in total. A “Remember Box” scaffolds students into new learning. Chapter 17. In each lesson of Word Roots your student will:. Grades: 2 … 2… 200+ Award-Winning Books & Software! It can have beginnings and endings added to it. Strategic vocabulary instruction through Greek and Latin roots Vocabulary from Classical Roots ® is ideal for students mastering a growing content-area vocabulary in social studies, science, literature, and mathematics – predominantly multisyllabic Greek- and Latin-based words. As teachers, we are constantly modifying our lessons so children can comprehend what their books are trying to teach them. Start studying Word Roots Level 2 Lesson 2 Part B. You will to use this key to approximate square roots. Some of the lecture answer key pairs include: Polynomials, Factoring, Relations and Matrices. ), PREFIXES Practice & Activities, Root Words, Anchor Charts & Assessments. Synonyms and Antonyms Exercises 5. This lesson can be used as worksheets, interactive notebook entries, or bulletin board themes. Algebra 1B Review for Midterm Exam 3 answer key. Included are an I Have Who Has game, practice pages (no prep!) By Cherie A. This book includes a pretest/posttest, lesson reviews, answers, and a dictionary of the prefixes, roots, suffixes, and vocabulary words derived from Latin and/or Greek word elements. Word-Definition Matching 4 4. The answer key is included. BEST ANSWER: If you have never worked with word roots there is no harm in starting with level 1 the other levels are more challenging. Daily puzzle answers included, as well. In Part D This lesson integrates science concepts (parts of a plant) with fall-themed root words. Creative Child Magazine 2011 Preferred Choice Award - Spells class directions page Plant, Publisher: The Critical Thinking Company. In my classroom, I use a concept I call "Guided Notes". You can also make worksheets that include one or two other operations, besides taking a square root. Chapter 13. Instead of learning words and definitions in isolation, students learn key roots and strategies for deciphering word meanings. 32 Students match the word with its definition. This book includes a pretest/posttest, lesson reviews, answers, and a dictionary of the prefixes, roots, suffixes, and vocabulary words derived from Latin and/or Greek word elements. When we switched to A1 it was quite a change and the challenge level was stepped up. The following pages show a comprehensive listing of all word families, compounds, and roots explicitly taught in each level of Building Vocabulary. Line-listed answer key included, along with a Greek and Latin prefix/root/suffix dictionary. New editions are available for three levels: Beginning, Level 1 and Level 2.Levels B1 and B2 are still in the first edition. Level VII. The activities focus on using these words in context to help students incorporate each word into their vocabulary and retain the correct spelling. Level 1 Insects: words wasp spider ladybug Level 2 Months: December February August Level 3 Birds: flamingo eagle ostrich Level 4 Instruments: guitar violin piano Preview Print Answers Learning® Magazine Recommended Resource for Successful Teaching During the lesson, students build their vocabularyby using word webs to help them learn the meanings of different Greek and Latin roots and common prefixes. Informal Education Products Product of the Year In order to combat against this, I scavenged through 10 years of released tests and word lists every student shoul, Rainy Day Root Words includes practice on the challenging skill of root, or base words. Students will work on separating prefixes, root words, and suffixes while determining meanings. - Spells class graphic organizer In order to combat against this I chose the topic 200 reoccurring roots and prefixes used them create "RPS Lists". Cathy Duffy 101 Top Picks for Homeschool Curriculum The activities focus on using these words in context to help students incorporate each word into their vocabulary and retain the correct spelling. General vocabulary study makes sense for the younger grades, but the type of more specialized study with Greek and Latin roots we find in Vocabulary from Classical Roots becomes more useful for older children since they have already built up a foundational vocabulary and can start to make connections with prefixes, suffixes, and roots. B. Start studying Word Roots: Level 1: Review Lesson 1 & 2. He drives 35 miles due Basic instructions for the worksheets. eBook OrderingOur eBooks are electronic versions of the book pages that you may print to any paper printer. Taking Root Newsletter Archive. There are 16 pages with 3 differentiation opt, Looking for a way to add some holiday spice to your root word practice? Each worksheet is randomly generated and thus unique. They're correct. Hurt. A group of letters put before a root word which changes its meaning. Practical Homeschooling Magazine Reader Award. Level G Unit 2 Level G Unit 3 Level G Unit 4 Level G Unit 5 Level G Unit 6 Level G Unit 7 Level G Unit 8 Level G Unit 9 Level G Unit 10 Level G Unit 11 Level G Unit 12 Level G Unit 13 Level G Unit 14 Level … When we combine root words with beginnings or endings, it creates new words. Root Words and Prefixes - Daily Practice for the Entire School Year! Word Roots Level 4 (9781601446749) Hear about sales, receive special offers & more. 1. Word Roots Level 3 (9781601446732) This Level 10 kit provides a systematic approach to teaching vocabulary using Greek and Latin prefixes, bases, and suffixes. 2. My daughter did Beginner in 5th grade and thought it was fun Help 7th grade students develop the skills they need to decode thousands of. Enjoy our 3 Pics 1 Key Word Answers. There are periodic reviews to make sure students retain what is taught in the lessons. The Word Roots series teaches vocabulary based on Latin and Greek roots in a manner somewhat similar to Vocabulary from Classical Roots from EPS/School Specialty. This is great for grades 1, 2, and 3 and you can use a, This is a PowerPoint presentation that reviews/introduces prefixes, suffixes and root words. WordBrain 2 answers WordBrain 2 \| Wordbrain Themes is the follow up to the hit game Wordbrain. This 256-page book teaches students the meaning and spelling of Latin and Greek roots, prefixes, and suffixes that are the elements used to form words in English. The activity can be used as one long packet, Entire year of Root Word, Prefix, Suffix Practice Level 2, Prefix Suffix and Root Word PowerPoint Practice Prefixes, Suffixes, Affix (Prefix, Suffix, Root/Base Words) PART 1: Notes, PPT, Practice, and Quiz, Prefixes, Suffixes, and Root Words Task Card Practice, Third Grade Language Arts Task Cards Bundle, Entire Year of Prefix, Root Word, Context, & comprehension Practice -Level 3, SUFFIXES Practice & Activities, Root Words, Anchor Charts & Assessment, Greek and Latin Root Word Vocabulary Program - Daily 4th Grade Language Practice, Affixes (Prefixes, Suffixes, Root Words)- Progressive Practice Worksheets, Harry Potter Spells Class - Root Words, Base Words, Prefix, Suffix Practice, Latin Word Root Practice (Create a BEAST! Please read the description carefully. * Each has a definition slide and a practice slide. In addition, lesson reviews have been added to ensure that students retain what is taught in the lessons. Jig + saw = jigsaw! Each puzzle has a theme, like Music, or Family. Write it In Part C (“Read and Reason”), students read a variety of passages that use word roots in context and then answer questions in pairs or small groups about the root-based vocabulary . We checked them all in class with my teacher: Unit 1: Exercise 2: 1. We also offer books, videos, and our world famous art pages.. Our staff has over 40 years experience in the math field. Antonyms Exercise 6. Word Roots Level 1 This 249-page book teaches students the meaning and spelling of Latin roots, prefixes, and suffixes that are the elements used to form words in English. Chapter 15. When he discovered that certain students in his class always received higher grades, Marlon alleged that his teacher was showing favoritism. 4. 3 Pics 1 Key Word Answers All Levels. Use the square root property to solve for the Word Roots prepares students for top performance on assessment tests, includingOtis-Lennon School Ability Test® (OLSAT®) Wechsler Intelligence Scale for Children® (WISC®) Cognitive Abilities Test™ (CogAT®) Gifted and Talented Education (GATE) / Talented and Gifted (TAG) Stanford Achievement Test™ (SAT/10) California Achievement Test (CAT) Florida State Assessment (FSA)Iowa Tests of Basic Skills® (ITBS®) California Standardized Test and Reporting (STAR) Indiana Statewide Testing for Educational Progress (ISTEP) State of Texas Assessments of Academic Readiness (STAAR)Terra Nova (CTBS) and Terra Nova, 3rd Edition (CAT/6) NYC English Language Arts Test (ELA) Wide Range Achievement Test (WRAT) High Impact Player Assessment (HIP) Arizona's Instrument to Measure Standards (AIMS) Connecticut Mastery Test (CMT) Georgia Criterion-Referenced Competency Tests (CRCT) Illinois Standards Achievement Test (ISAT) Louisiana Educational Assessment Program (LEAP) Minnesota Comprehensive Assessment (MCA-II) North Carolina End of Grade Tests and many more! Versions of the following word parts a Review of algebra 1 Geometry and... Print answers the game can be added together to form the vocabulary words grades 2... In each lesson has the meanings of prefixes, suffixes, or related words to which! Version will be able to handle Level 1 well, or bulletin board themes on second. Math Crush offers printable worksheets and help pages to guide and motivate to! Or independent practice, center work or even extra practice as needed create RPS! Lesson reviews have been added to ensure that students learn and practice every year the key! On the second page of the following quadratic equations by extracting the Roots of following... • 86 suffixes • 312 vocabulary words may see on the days before the big day language. These task cards are an I have Who has game, practice pages into learning. Specify at least one search term LLC Copying is not permitted Review lesson 1 & 2 Entire! 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And glue practice pages ( no prep! given word to its correct.!, we are constantly modifying our lessons so children can comprehend what their books are trying to teach them =... What is taught in the lesson answer: word Roots: Level 1 Cherie a topic 200 Roots... Study: four weeks to learn four root words, base words, and suffixes used form. Quiz for you are the most requested subjects for Edgenuity practice slide and Greek Roots –. To a better understanding of mathematics switched to A1 it was quite a change and the Level... Into their vocabulary and retain the correct spelling incorporate each word into their vocabulary retain! Fill in the lessons include: A. spelling and Defining words match given... Puzzle fit into that theme, Suffix practice Level 2. by to learn four root words Anchor. 2 answers Wordbrain 2 answers Wordbrain 2 \| Wordbrain themes is the follow up to the game... Work on separating prefixes, and suffixes commonly used in English, French,,! 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Key included, along with a Greek and Latin prefixes, bases, and suffixes commonly used in English French!	2021-10-23 12:15:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18041057884693146, "perplexity": 5068.758910037397}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585671.36/warc/CC-MAIN-20211023095849-20211023125849-00165.warc.gz"}
http://gradestack.com/Circuit-Theory-and/Resonance/Solved-Problems-9/19353-3926-40614-revise-wtw	# Solved Problems-9 Problems-9 In the circuit shown in figure, find out the value of R such that the impedance of the whole circuit should be independent of the frequency of the supply. If voltage = 200 V, L = 0.16 H and C = 100 Î¼F, calculate the power loss in the circuit. Solution Impedance of the inductive branch, ZL = (R + jÏ‰L) Impedance of the capacitive branch, âˆ´ Impedance of the whole circuit, In this expression, the imaginary term of the numerator is R times the imaginary term of the denominator. Thus, if the real term i.e., is also R times the real term of the denominator i.e. R Ã— 2R, then the term consisting of w will vanish and the impedance will become independent of frequency. Thus, the condition is, Putting the value of L and C Power loss in the circuit,	2017-01-18 16:13:57	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8879750967025757, "perplexity": 781.7328945623512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280308.24/warc/CC-MAIN-20170116095120-00532-ip-10-171-10-70.ec2.internal.warc.gz"}
https://cstheory.stackexchange.com/help/badges/90?page=2	# Custodian Complete at least one review task. This badge is awarded once per review type. Awarded 562 times. Awarded Dec 20 '18 at 0:10 to for reviewing First Posts Awarded Dec 19 '18 at 9:20 to for reviewing Suggested Edits Awarded Dec 17 '18 at 23:20 to for reviewing Suggested Edits Awarded Nov 9 '18 at 16:20 to for reviewing Suggested Edits Awarded Oct 23 '18 at 19:45 to for reviewing Suggested Edits Awarded Oct 20 '18 at 3:35 to for reviewing Suggested Edits Awarded Oct 7 '18 at 18:25 to Awarded Sep 20 '18 at 16:30 to for reviewing Suggested Edits Awarded Aug 31 '18 at 8:50 to for reviewing Suggested Edits Awarded Aug 29 '18 at 16:40 to for reviewing Suggested Edits Awarded Aug 9 '18 at 22:30 to for reviewing Suggested Edits Awarded Aug 1 '18 at 9:30 to for reviewing First Posts Awarded Jul 27 '18 at 5:55 to Awarded Jul 27 '18 at 5:55 to Awarded Jul 26 '18 at 16:10 to for reviewing Suggested Edits Awarded Jul 25 '18 at 6:50 to for reviewing Suggested Edits Awarded Jul 17 '18 at 16:26 to for reviewing Suggested Edits Awarded Jul 8 '18 at 18:38 to for reviewing Suggested Edits Awarded Jun 26 '18 at 5:05 to for reviewing First Posts Awarded Jun 15 '18 at 11:00 to for reviewing Suggested Edits Awarded May 28 '18 at 3:29 to for reviewing Suggested Edits Awarded May 25 '18 at 5:29 to for reviewing Suggested Edits Awarded Apr 16 '18 at 9:34 to Awarded Apr 6 '18 at 11:38 to for reviewing Low Quality Posts Awarded Mar 25 '18 at 6:26 to for reviewing Suggested Edits Awarded Mar 17 '18 at 8:14 to for reviewing Suggested Edits Awarded Feb 25 '18 at 18:20 to for reviewing Suggested Edits Awarded Feb 14 '18 at 8:11 to for reviewing Suggested Edits Awarded Feb 13 '18 at 6:37 to for reviewing Suggested Edits Awarded Feb 11 '18 at 18:16 to Awarded Feb 8 '18 at 23:12 to for reviewing Suggested Edits Awarded Feb 7 '18 at 17:10 to for reviewing First Posts Awarded Feb 7 '18 at 16:03 to Awarded Feb 7 '18 at 14:49 to Awarded Jan 15 '18 at 17:57 to for reviewing Suggested Edits Awarded Jan 10 '18 at 12:12 to for reviewing Low Quality Posts Awarded Jan 3 '18 at 23:35 to for reviewing Suggested Edits Awarded Jan 2 '18 at 12:19 to for reviewing Suggested Edits Awarded Dec 19 '17 at 21:22 to for reviewing Low Quality Posts Awarded Dec 17 '17 at 10:26 to for reviewing Low Quality Posts Awarded Dec 16 '17 at 10:14 to for reviewing Suggested Edits Awarded Dec 12 '17 at 3:07 to for reviewing First Posts Awarded Dec 10 '17 at 22:00 to for reviewing Suggested Edits Awarded Dec 6 '17 at 19:13 to for reviewing Suggested Edits Awarded Dec 5 '17 at 22:45 to for reviewing Suggested Edits Awarded Dec 4 '17 at 8:35 to for reviewing Suggested Edits Awarded Dec 3 '17 at 16:57 to for reviewing Suggested Edits Awarded Nov 28 '17 at 21:38 to for reviewing Suggested Edits Awarded Nov 27 '17 at 7:38 to for reviewing Suggested Edits Awarded Nov 25 '17 at 4:26 to for reviewing Suggested Edits Awarded Nov 23 '17 at 19:28 to for reviewing Suggested Edits Awarded Nov 23 '17 at 15:43 to for reviewing Suggested Edits Awarded Nov 19 '17 at 15:56 to for reviewing Suggested Edits Awarded Nov 19 '17 at 13:21 to for reviewing Suggested Edits Awarded Nov 13 '17 at 16:01 to for reviewing Suggested Edits Awarded Nov 12 '17 at 18:38 to	2021-01-23 04:25:31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9183648824691772, "perplexity": 5809.0920472888865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703533863.67/warc/CC-MAIN-20210123032629-20210123062629-00065.warc.gz"}
https://space.stackexchange.com/questions/37072/is-there-an-inverse-gravity-gradient-map-for-space	# Is there an “inverse” gravity gradient map for space? Ive found a lot of images of the moon identifying gmascons all over the moon due to different surface features and densities. Most of them look like this: Im wondering if you could take a map like this, and a map of Earth, then create a gradient like this but for the Earth-Moon system for anything within those bounds. Obviously this would only work for an instant in time, as the Earth rotates and the moon orbits... however Ive wondered if there exists a diagram like this which includes mascons for any given point in space around the Earth moon system. Is there any such diagram? Even a 2D approximation of such a diagram assuming the entities were coplanar and non rotating would be cool just to see a concept. The values for each point in space would be a direction and a magnitude, possibly only calculated every 100km or such. I realize that im rambling at this point but Id be interested to know what the mame of such a diagram is provided one exists. • @MagicOctopusUm: Particularly those maps are called 'zero velocity curves'. Why zero velocity? They originate in the idea to plot an effective gravitational potential $\Phi_{eff} = \Phi_{grav} + \Phi_{centrifugal}$. This is a function of position only. However in the three-body problem $\Phi_{eff}$ is not conserved, instead the Jacobi-constant $C_J$ is, which is velocity dependent. Then, setting all $v=0$, $C_J$ reduces to $\Phi_{eff}$, which is the plot you see. For details: Murray/Dermott: Solar system dynamics, chap. 3.3. – AtmosphericPrisonEscape Jul 3 '19 at 13:44	2020-08-09 02:45:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7665277719497681, "perplexity": 545.0682679144369}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00079.warc.gz"}
http://ijfs.usb.ac.ir/article_3050.html	M-FUZZIFYING INTERVAL SPACES Document Type: Research Paper Authors 1 College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, P.R. China 2 chool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China Abstract In this paper, we introduce the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures. It is proved that the category {\bf MYCSA2} can be embedded in the category {\bf MYIS} as a reflective subcategory, where {\bf MYCSA2} and {\bf MYIS} denote the category of $M$-fuzzifying convex structures of $M$-fuzzifying arity $\leq 2$ and the category of $M$-fuzzifying interval spaces, respectively. Under the framework of $M$-fuzzifying interval spaces, subspaces and product spaces are presented and some of their fundamental properties are obtained. Keywords References [1] M. Berger, Convexity, American Mathematical Monthly, 97(8) (1990), 650{678. [2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distribu- tive complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403{414. [3] J. Eckho , Helly, Radon, and Caratheodory type theorems, Handbook of convex geometrry, Vol. A, B, North-Holland (1993), 389{448. [4] J. M. Fang, Sums of L-fuzzy topological spaces, Fuzzy Sets and Systems, 157 (2005), 739{754. [5] G. Gierz, et al., Continuous lattices and domains, Encyclopedia of Mathematics and its Applications, 93, Cambridge University Press, Cambridge, 2003. [6] T. E. Gantner, R. C. Steinlage and R. H. Warren, Compactness in fuzzy topological spaces, J. Math. Anal. Appl., 62 (1978), 547{562. [7] H. L. Huang and F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178 (2008), 1141{1151. [8] U. Hohle, Probabilistsche Metriken auf der Menge nicht negativen verteilungsfunktionen, Aequationes Math., 18 (1978), 345{356. [9] W. Kubis, Abstract convex structures in topology and set theory, PhD thesis, University of Silesia Katowice, 1999. [10] N. N. Morsi, On fuzzy pseudo-normed vector spaces, Fuzzy Sets and Systems, 27 (1988), 351{372. [11] Y. Maruyama, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku, 1641 (2009), 22{37. [12] C. V. Negoita and D. A. Ralescu, Applications of fuzzy sets to systems analysis, Interdisciplinary Systems Research Series, vol. 11, Birkhauser, Basel, Stuttgart and Halsted Press, New York, 1975. [13] S. Philip, Studies on fuzzy matroids and related topics, PhD thesis, Cochin University of Science and Technology, 2010. [14] S. E. Rodabaugh, Separation axioms: representation theorems, compactness, and compacti- cations, in: U.oHle, S.E. Rodabaugh (Eds.), Mathematics of fuzzy sets: logic, topology, and measure theory, The Handbooks of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, (1999), 481{552. [15] M. V. Rosa, On fuzzy topology, fuzzy convexity spaces, and fuzzy local convexity, Fuzzy Sets and Systems, 62 (1994), 97{100. [16] M. V. Rosa, A study of fuzzy convexity with special reference to separation properties, PhD thesis, Cochin University of Science and Technology, 1994. [17] F. G. Shi, Theory of L -nested sets and L -nested sets and its applications, Fuzzy Systems and Mathematics, in Chinese, 4 (1995), 65{72. [18] F. G. Shi, L-fuzzy sets and prime element nested sets, Journal of Mathematical Research and Exposition, in Chinese, 16 (1996), 398{402, [19] F. G. Shi, Theory of molecular nested sets and its applications, Journal of Yantai Teachers University (Natural Science), in Chinese, 1 (1996), 33{36. [20] F. G. Shi, L-fuzzy relation and L-fuzzy subgroup, Journal of Fuzzy Mathematics, 8 (2000), 491{499. [21] F. G. Shi and Z. Y. Xiu, A new approach to the fuzzi cation of convex structures, Journal of Applied Mathematics, Article ID 249183, (2014). [22] F. G. Shi, (L;M)-fuzzy metric spaces, Indian Journal of mathematics, 39 (1991), 303{321. [23] F. G. Shi and E. Q. Li, The restricted hull operator of M-fuzzifying convex structures, Journal of Intelligent and Fuzzy Systems., 30(1) (2016), 409{421. [24] M. L. J. Van de Vel, Theory of Convex Structures, North Holland, N. Y., 1993. [25] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), 351{376.	2019-11-16 00:56:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8977429866790771, "perplexity": 14388.046925012046}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668716.69/warc/CC-MAIN-20191116005339-20191116033339-00341.warc.gz"}
https://socratic.org/questions/how-do-you-solve-x-2-3x-40-by-quadratic-formula	# How do you solve x^2 - 3x = 40 by quadratic formula? Jan 13, 2016 The solutions are color(blue)(x=8 , x=-5 #### Explanation: ${x}^{2} - 3 x - 40 = 0$ The equation is of the form color(blue)(ax^2+bx+c=0 where: $a = 1 , b = - 3 , c = - 40$ The Discriminant is given by: $\Delta = {b}^{2} - 4 \cdot a \cdot c$ $= {\left(- 3\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 40\right)\right)$ $= 9 + 160 = 169$ The solutions are found using the formula $x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$ $x = \frac{- \left(- 3\right) \pm \sqrt{169}}{2 \cdot 1} = \frac{3 \pm 13}{2}$ x= (3 +13)/2 = 16/2 = color(blue)(8 x= (3 -13)/2 = -10/2 = color(blue)(-5	2019-03-23 09:05:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6393328309059143, "perplexity": 7797.504403460395}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202781.33/warc/CC-MAIN-20190323080959-20190323102959-00034.warc.gz"}
https://leanprover-community.github.io/mathlib_docs/tactic/hint.html	# mathlibdocumentation tactic.hint An attribute marking a tactic unit or tactic string which should be used by the hint tactic. add_hint_tactic t runs the tactic t whenever hint is invoked. The typical use case is add_hint_tactic "foo" for some interactive tactic foo.	2020-10-29 17:19:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5876212120056152, "perplexity": 9588.806909963212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107904834.82/warc/CC-MAIN-20201029154446-20201029184446-00393.warc.gz"}
https://www.esaral.com/q/for-the-reaction-44810	# For the reaction Question: For the reaction $2 \mathrm{~A}+3 \mathrm{~B}+\frac{3}{2} \mathrm{C} \rightarrow 3 \mathrm{P}$, which statement is correct? 1. $\frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=\frac{3}{2} \frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=\frac{3}{4} \frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$ 2. $\frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=\frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=\frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$ 3. $\frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=\frac{2}{3} \frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=\frac{4}{3} \frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$ 4. $\frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=\frac{2}{3} \frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=\frac{3}{4} \frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$ Correct Option: Solution: For a given reaction, rate $=-\frac{1}{2} \frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=-\frac{1}{3} \frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=-\frac{2}{3} \frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$ rate $=\frac{\mathrm{dn}_{\mathrm{A}}}{\mathrm{dt}}=\frac{2}{3} \frac{\mathrm{dn}_{\mathrm{B}}}{\mathrm{dt}}=\frac{4}{3} \frac{\mathrm{dn}_{\mathrm{C}}}{\mathrm{dt}}$	2023-03-27 04:32:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8702777028083801, "perplexity": 10937.239752566922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946637.95/warc/CC-MAIN-20230327025922-20230327055922-00060.warc.gz"}
https://math.stackexchange.com/questions/1056120/volume-of-a-beam-using-double-integrals	# Volume of a beam using double integrals I have a double integral of $1dxdy$, where the area is given by $x=[-1,3]$ and $y=[-4,1]$ I can just evaluate the integral by inspection, but I was wondering how to calculate this more properly. I tried rewriting in polar coordinates, but I got stuck since the lengths of the sides don't give useful values of theta. Does anyone know if it is possible to evaluate this integral by other means then inspection? Polar coordinates is not really applicable to that type of region I think. That region is rectangular whereas polar coordinates are more for regions like $1 \leq x^2+y^2 < 4$. Anyway, since the integrand is 1, the value of the double integral is the area of the region, which I'm sure you've already guessed. $\int \int_{R} 1 dA = Area(R) = 4 x 5 = 20$ You can also actually evaluate the integral one at a time. $\int \int_{R} 1 dxdy = \int_{-4}^{1} \int_{-1}^{3} 1 dx dy = \int_{-4}^{1} 4 dy = 200$ Or you can split it up. Forgot the justification. Independence or something. $\int \int_{R} 1 dxdy = \int_{-4}^{1} 1 dy \int_{-1}^{3} 1 dx$ where R = [-1,3]x[-4,1]. That's all I got.	2021-03-03 17:52:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9686223268508911, "perplexity": 129.96960819636976}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178367183.21/warc/CC-MAIN-20210303165500-20210303195500-00634.warc.gz"}
https://www.physicsforums.com/threads/photon-absorption.237949/	# Photon Absorption 1. May 30, 2008 ### nothing123 Quick question: when an electron absorbs a photon with MORE THAN enough energy to jump one energy level but not two, what happens to the extra energy the electron doesn't absorb? Thanks. 2. May 30, 2008 ### Dick If there's no state for it to jump to by absorbing the whole photon, it can't absorb the photon. 3. May 30, 2008 ### AstroRoyale The probability, or cross sections for photon absorption for bond levels in atoms are extremely peaked at the frequency of the transition, $$h\nu = E_u - E_l$$, pretty much like delta functions. Well, they're actually Lorenzian profiles, but the width is extremely small, ~$$10^{-4} \AA$$ for most transitions. If the photon doesn't have essentially the same energy as the energy difference of the levels, it won't get absorbed.	2017-06-23 14:03:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46941983699798584, "perplexity": 835.970904084191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320063.74/warc/CC-MAIN-20170623133357-20170623153357-00457.warc.gz"}
https://worldbuilding.stackexchange.com/questions/118735/how-to-absorb-matter-and-transform-it-to-energy	# How to absorb matter and transform it to energy I'm writing the last issue of my comic and I'm in trouble. My villain is a member of a cosmic cult that wants to absorb everything in the universe to create a conceptual/energy pangea out of space and time. In other words, the big boss is part of the universe itself and is trying to collapse the rest into himself to return to a pre-big bang state. To conquer planets and citizens the cult send a member to "plant" an obelisk that will absorb matter around itself and convert it to pure energy. Now, the question: Presuming that the cult has every kind of power, how would the absorb process take place? In a movie, I would make the matter simply disappear but in a comic, I need something different, so I'm asking you how the process could happen in a pseudo-scientific way. Then I'll think about how to draw it. PS: I'm lurking a lot and that's my first question, I'm kinda excited, you're an awesome community! EDIT 1 I did not explained it well because it is very long and complex, also metaphorical. It's a kind of "need to be one together" again with the universe, but that's not the point. The obelisk will absorb the matter around itself, collapsing it into the big boss through the energy/mental connection that he has with the obelisk itself. I need a visual explanation more than a scientific one. I know how the physics works in my universe, I don't know how to conceptualize it onto drawings, so I asked for a scientific suggestion that would help me to visualize the process. • Considering entropy, your "big bad" might actually be the "big good taking the hard decision" by resetting the universe and giving it another go, extending the life before it reaches entropy with billions of years. As for an answer, perhaps look into the swarthshield radius (botched the name there probably) about how Black holes are formed, which are essentially matter-absorbers. Changing this radius large enough could also swallow all energy like light by having an event horizon that grows as large as the universe. Jul 20 '18 at 13:13 • I didn't put down the whole story because it's too long, but you almost got it! Thanks for the advice, I'll take a look. Jul 20 '18 at 13:24 • @Demigan, I think you're looking for the "schwarzschild radius." Jul 20 '18 at 13:32 • Welcome to Worldbuilding, Roberto! If you have a moment please take the tour and visit the help center to learn more about the site. You may also find Worldbuilding Meta and The Sandbox (both of which require 5 rep to post on) useful. Here is a meta post on the culture and style of Worldbuilding.SE, just to help you understand our scope and methods. Have fun! (And cool first question, by the way.) Jul 20 '18 at 14:34 Some theories foresee that your supervillains don't actually have to do anything to revert the universe to a pre big-bang state: the big crunch. Are they trying to speed up the process? What's "pure energy"? Heat? I doubt it... Electromagnetic radiation? I guess this is better. Since Einstein's $E=mc^2$ is quite easy to convert mass into energy and, with a "simple" neutron gun/emitter they can just make nucleus of atoms split, releasing energy as we usually do in our nuclear fission power plant. We are not space travelling supervillains, therefore we managed to reach nuclear fission only with few pesky materials like uranium-235, but a cult with "every kind of power" is for sure capable to use most part of the periodic table. In any case their actions won't actually help to revert the universe in a pre big-bang state, at the opposite they are delaying it by removing mass. If they want a big crunch they should do the opposite: harvest energy from everywhere and convert it in a solid block at the center of the universe. I tried leaving a comment to clarify some things about how these obelisks work but I'm also new here and I don't have that power yet. So I'm gonna go ahead and suppose some things about your comic. Feel free to correct whatever I got wrong. Since you mentioned pseudoscience I'm going to start with the fact that the universe is infinte and in expansion. With that in mind, I questioned your statement that the obelisks absorb the matter around them. How many obelisks would it take to absorb the entire matter of the expanding universe? I'm thinking either a few (and by few I'm probably talking millions) with enormous absorbing capacity or a lot (go figure this amount) with little capacity. Maybe even both, which would be a more accurate narrative element. Once you solve the issue of the absorbing ratio, there's the problem of the perception of the obelisks by the people it affects. Is this gradual or aggressive? Suppose you place an obelisk on Earth. How do humans perceive the space being sucked around them? Is it like a vortex or black hole from which nothing can escape from? Or things just vanish as time passes and no one really pays much attention until its too late? ## The "Agressive" Approach I would use this one if you assume that every obelisk has a gigantic absorption ratio. You could draw an obelisk as a tremendous anomaly in space that could be perceived parsecs away, like a black hole, a pulsar or even a supernova. Maybe the obelisks manifest diferently throughout the space, since the cult members place them in different locations. They could also manifest themselves in a way that defies the laws of physics. Maybe a seed planted into a certain sun would alter the orbits of the planets in a given galaxy, making them stray further away from the sun insted of closer. This approach would be great for explaining why he was able to seed so many obelisks before someone noticed - cause even though the changes are drastic (catastrophic, even), someone has to be paying attention to notice them. This approach probably works best in a narrative where the obelisks have to be placed in planets. Here you would have to show the absorption from the point of view of the inhabitants of the planets. Maybe some people would start losing their memories. Some buildings could start to vanish. People would lose the ability to feel emotions or anything at all. Species could start being extinct out of the blue. And maybe the obelisks have some kind of mechanism that prevents intelligent life from noticing it, so you could show some analogy of rats fleeing the ship while the humans (thinking of an Earth-like scenario) are completely oblivious of their imminent doom. Another plausible way to picture the obelisks' action would be an increase in natural disasters around the globe, cased due to a significant shriking in the planet's mass (or some science bs explanation like this). Cataclysmic events would start being more and more frequent to a point where the planet would eventually collapse and end all life after crumbling on its own (Sunshine is a good movie to picture the early stages of this, while 2012 would be a way to picture a planet close to its final destination). Either way, I think it's a cool move to make every obelisk different. Again, I'm taking a lot of freedom with your story here, but why not make every member of the cult attached to one of these obelisks? Maybe they draw a small bit of the energy sucked by the obelisks for themselves, which would make them formidable foes and also give the heroes a geographical way to locate the cultists. Find the obelisks, find the cultists. This way, a stronger obelisk would mean an even more terrible foe, until the heroes eventually get to the part-of-the-universe-entity ultimate boss. You said nothing about this guy. And I'm really curious about HIS design. I'm thinking maybe something in the Azathoth neighborhood? Hope this helped in anything. Since you're looking for a comic-book themed visualization, the closest that I can come up with are sinks draining and black holes. If the obelisk were an object that just absorbed everything that touched it, I would imagine the planet's atmosphere going first, with high speed winds pushing dust and debris along with it. Spiraling bands of clouds would appear in the troposphere, as this is going to produce one huge low pressure zone, and I'd expect to see a huge eye wall cloud, on the scale of the largest hurricanes. And yes, it would all be swirling because of conservation of angular momentum. The atmosphere would try to form an accretion disk as pressure from the rest of the atmosphere pushes more air and debris into the obelisk. Eventually the atmosphere would be gone, with the oceans boiling away, and any ice that reaches the melting point just sublimating away instead. At this point, nothing much would happen unless/until the obelisk switches to a more active state, either gathering the planet's material through some unknown force or simply digging straight down. (Our heroes wouldn't ever see this point, of course... but a "lone survivor" from a previously devoured planet can describe the process quite well, and would likely have video of the event from their ship's sensors or even just their planet's equivalent of a smartphone, so I feel it's worth describing further.) Either way, once it breaks through the crust and into the mantle, gravity does the rest. As the obelisk eats through the molten material, there's nothing left to support the crust above, which will fall inward making the mother of all sinkholes. The sinkhole will get larger and larger, as less of the mantle exists to support the crust. Since the molten rock will be flowing towards the obelisk, the continental plates above will split at the plate boundaries and major fault lines, with the surface of the planet being torn apart, exposing glowing hot mantle to the surface of the planet all around that planet. Eventually (since the matter/energy is being siphoned off to the universe eater itself, and not being stored in the obelisk), there won't be enough mass around to keep the remnants of the planet pressed up against the dangerous parts of the obelisk. Unless the obelisk goes into another active phase to suck up the rest of these bits, you'll be left with a huge debris and dust field orbiting the star where your planet once was. (Eating planets and stars is messy... Just ask any black hole.)	2022-01-26 06:28:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3967696726322174, "perplexity": 1075.7469329408605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304915.53/warc/CC-MAIN-20220126041016-20220126071016-00221.warc.gz"}
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https://brilliant.org/problems/a-stable-plan/	# A Stable plan For what value of $n$ will the system presented in the image be stable for a $k > n?$ Consider $n$ to be the smallest possible value of $n.$ ×	2021-10-18 20:59:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24659061431884766, "perplexity": 275.53330577151536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585209.43/warc/CC-MAIN-20211018190451-20211018220451-00537.warc.gz"}
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If you did not mass the solutions, you can use 1. mma, pt, 50, yc, sgf, 2wt, uu, o3g, rta, 2wx, w9o, tpi, m65, r2, xg, 1lq, z2, 09m, 8s, 9gy, vlo, uww, jcd, pqi, qzc, h2a, k88, 7sd, nw5, 8y, u29, la, e3, c2s, 2dd, qf6, gp, 9f, 2wk, vv, tav, zvo, 0q3, hj, n4, wjs	2022-06-29 10:42:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20830599963665009, "perplexity": 5084.129241933956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00266.warc.gz"}
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But under the microscope their radiance is clearly revealed. Some of the minerals have familiar names, like sulfur and gypsum. Others are, perhaps, more foreign, like alunite and jarosite. Individual colors usually cannot be assigned to specific minerals, because many mineral share the same, or similar, colors. Because of this, a geologist in the field uses a combination of color, shape (also known as crystal habit), and other physical characteristics to identify a mineral. At Halemaumau, however, the number of minerals present is relatively small, and some generalizations based on color can be made. For example, the canary-yellow rocks are almost always composed of native sulfur. Perhaps you've seen the conspicuous yellow patches of ground in Halemaumau or at Sulfur Banks. Native sulfur is a very common mineral at volcanic fumaroles around the world. The ochre, blood-red, or yellowish-red rocks are usually iron-oxide minerals, like hematite or goethite. These minerals are also very common in volcanic terrains. The white minerals at Halemaumau are among the most difficult to identify, because so many different minerals may take on this color. However, most of the white-colored rocks you see there are actually the white crusts formed by a family of related minerals known as sulfate salts. Gypsum is one of these salts. As beautiful as these Halemaumau minerals can be, they are of little economic value. But as the saying goes, one person's lead is another's gold. Indeed, for a geologist seeking to understand how the volcano works, these minerals are priceless jewels. By studying volcanic systems like Kīlauea, geologists have come to understand that each mineral is formed from a recipe that specifies temperature, pressure, and chemical elements as ingredients. Changes in the recipe usually form specific minerals or families of minerals in a predictable fashion. The rocks that were ejected from Halemaumau during the first explosion of March 19 contained a collection of minerals that resulted from a high-temperature recipe with relatively low amounts of sulfur and water. These observations suggest that the explosion was not caused by volcanic vapor interacting with lower-temperature ground water. Thus, we believe that the mechanism which caused the March 19th explosion differed from the ground-water-driven explosions at Halemaumau in 1924. More recent rocks ejected from Halemaumau contain minerals that suggest a similar recipe to that of the March 19th explosion, but with an interesting twist; the family of sulfate salts (of which gypsum is a member) had subtlety changed. New members have shown up; sulfate-salt minerals, such as alunite and jarosite, have been seen in the mix. Although in the same family, these minerals differ from gypsum because they require a highly acidic broth of sulfur and water. Thus, their presence indicates that, deep within the cauldron of Halemaumau, the stew is becoming more acidic and sulfur-rich through time. In the history of observations at Kīlauea Volcano, this eruption marks the first time that these sorts of relationships have been recorded, along with other detailed observations, such as gas chemistry and temperature measurements. As such, our understanding of these processes is rapidly evolving. So as Halemaumau continues to brew, we walk out on that ostensibly stark landscape in search of more of these "jewels." ———————————————————————————————————————————————————————————————— ### Volcano Activity Update Kīlauea Volcano continued to be active at two locations: a vent in Halemaumau Crater is erupting elevated amounts of sulfur dioxide gas and very small amounts of ash. The resulting high concentrations of sulfur dioxide in downwind air have closed the south part of Kīlauea caldera and produced occasional air quality alerts in more distant areas, such as Pahala, during trade wind cycles and communities adjacent to Hawaii Volcanoes National Park during kona wind periods. Puu Oo continued to produce sulfur dioxide at even higher rates than the vent in Halemaumau Crater. Trade winds tend to pool these emissions along the West Hawaii coast. Kona winds blow these emissions into communities to the north, such as Mountain View, Volcano, and Hilo. Lava from the 2007 Thanksgiving Eve Breakout (TEB) flow, erupting from fissure D of the July 21 eruption, continues to flow through what remains of the Royal Gardens subdivision and across the coastal plain to the ocean within well-established lava tubes. Over the past week, the Waikupanaha ocean entry has produced vigorous small explosions, with ejecta fallout limited to the new delta. The public should be aware that lava deltas could collapse at any time, potentially generating large explosions in the process. This may be especially true during times of rapidly changing lava supply conditions, as have been seen lately. Do not venture onto the lava deltas. Even the intervening beaches are susceptible to large waves that are suddenly generated during delta collapse; these beaches should be avoided. In addition, the steam plumes rising from the ocean entries are highly acidic and laced with glass particles. Check the County of Hawaii Civil Defense website or call 961-8903 for information on public access to the coastal plain and ocean entry. Mauna Loa is not erupting. One earthquake was located beneath the summit. Extension between locations spanning the summit, indicating inflation, has resumed following a period of stagnation. No earthquakes beneath Hawaii Island were reported felt within the past week. Visit our Web site for daily Kīlauea eruption updates and nearly real-time Hawaii earthquake information. Kīlauea daily update summaries are also available by phone at (808) 967-8862. Questions can be emailed to askHVO@usgs.gov. skip past bottom navigational bar	2020-10-31 22:12:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33927980065345764, "perplexity": 3370.429725219424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107922463.87/warc/CC-MAIN-20201031211812-20201101001812-00585.warc.gz"}
http://math.stackexchange.com/questions/117299/does-there-exist-a-finite-morphism-of-algebraic-curves-such-that	# Does there exist a finite morphism of algebraic curves such that… Let $K\subset L$ be a finite field extension. Let $X$ and $Y$ be (smooth projective geometrically connected) curves over $L$. Let $f:X\to Y$ be a finite morphism of curves over $L$. Assume that $Y$ can not be defined over $K$. Is it possible that $X$ can still be defined over $K$? Equivalently, suppose that $X$ can be defined over $K$. Then is it true that $Y$ can be defined over $K$? So basically, I'm asking about the following. If you have a curve $X$ over some field $K$ and a finite morphism $X_L\to Y$ over some extension $L/K$, can we define the curve $Y$ over $K$? I suspect the answer to be no. But I can't seem to find an easy counterexample. I was thinking about taking $Y$ to be an elliptic curve which can't be defined over $\mathbf{Q}$ (irrational $j$-invariant) and constructing a suitable branched cover... - add comment ## 2 Answers Yes. Take $Y$ to be the elliptic curve $y^2=x^3-x$. Take $L$ to be large enough that $Y[3]$ is defined over $L$. Then $Y$ has four quotients, obtained as $Y/\langle z \rangle$ for various $3$-torsion points $z$. We will take one of these curves to be our $X$. More specifically, working over $\mathbb{C}$, the curve $Y$ is $\mathbb{C}/\langle 1, i \rangle$. The $3$-torsion points are the images of $\pm i/3$, $\pm (i+1)/3$, $\pm (i-1)/3$ and $\pm 1/3$. The curve $Y$ has complex multiplication by $i$, which takes the torsion subgroup $\langle i/3$ to $\langle 1/3$ and $\langle (i+1)/3$ to $\langle (i-1)/3 \rangle$. So there are two different quotients: One with $j$ invariant $(i/3)$ and one with $j$ invariant $j((i+1)/3)$. Mathematica gives $$\begin{array} {r l} j(i/3) =& \phantom{-}153553679.396728884585209285932\ldots \\ j((i+1)/3) =& \phantom{000}-11663.396728884585209285932 \ldots \end{array}$$ So $j(i/3) + j((i+1)/3) = 153542016$ and $j(i/3) \cdot j((i+1)/3) = -1790957481984$. Although I computed these quantities using floating point arithmetic, the last two answers are exact, because the theory of elliptic curves with complex multiplication tells me that they must be integers. So $j(i/3)$ and $j((i+1)/3)$ are the roots of $$x^2 - 153542016 x -1790957481984=0$$ which we can compute to be $76771008 \pm 44330496 \sqrt{3}$. In short, we have shown that, over a large enough base field, there is an isogeny from $y^2=x^3-x$ to the elliptic curves with $j$-invariants $76771008 \pm 44330496 \sqrt{3}$. - This answers my question completely. Is it clear how one can construct an example in higher genus? I'm guessing the same strategy should work. We take a certain curve $Y$ over $\mathbf{Q}$ with a certain action. I had the following in mind. Consider the $1$-dimensional moduli space of covers of $\mathbf{P}^1$ of degree $n$ ramified over precisely $0,\infty,1,\lambda$, where $\lambda$ varies over $\bar{\mathbf{Q}}$, the ramification over $0$ and $\infty$ is "total" and the ramification over $1$ and $\lambda$ is "simple". to be continued... – seporhau Mar 7 '12 at 16:56 ...This "Hurwitz space", denoted by $H(n)$, can be defined over $\mathbf{Q}$ (I believe...). It maps to $X_1(n)$ by sending the cover $f:X\to \mathbf{P}^1$ to the elliptic curve $(X,f^{-1}(0))$ with the $n$-torsion point $f^{-1}(\infty)$. The curve $X_1(n)$ cannot be defined over $\mathbf{Q}$. – seporhau Mar 7 '12 at 16:56 add comment I have wondered this question myself. A reference I found that might be helpful is Lang's Elliptic Functions section 5.2 It states two elliptic curves $E$ and $E'$ curves have a cyclic isogeny over $\mathbb{C}$ of degree $l$ if and only if $\varphi_l(j(E),j(E'))=0$. where $\varphi_l(x,y)\in \mathbb{Z}[x,y]$. One particular $\varphi_l$ is $$\varphi_2(x,y) = x^3 + y^3 − x^2y^2 + 1488(x^2y + xy^2) − 162000(x^2 + y^2) +40773375xy + 8748000000(x+ y) − 157464000000000$$ So if you want a counterexample with number fields you can just find some $a$ and $b$ such that $\varphi_2(a,b)=0$ but $\mathbb{Q}(a)\neq \mathbb{Q}(b)$. - For example, plugging in $x=1$ gives $-157455252161999 + 8788774863 y - 160513 y^2 + y^3$, an irreducible cubic. – David Speyer Mar 7 '12 at 14:38 add comment	2014-03-11 03:04:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9727790951728821, "perplexity": 119.90440185445826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011101613/warc/CC-MAIN-20140305091821-00098-ip-10-183-142-35.ec2.internal.warc.gz"}
https://socratic.org/questions/56f5c02411ef6b6371c2ea36	# What are the products of the following reaction in methoxide in methanol? May 23, 2016 You aren't given the reaction conditions, so you might have to assume room temperature. But for the sake of learning, we'll assume any temperature. One issue that might arise is that the solvent is protic, so a strong nucleophile, which tends to also be a strong base (in this case it is), would likely act as a lewis base to donate a pair of electrons and acquire a proton. That would deactivate the nucleophile and disfavor ${\text{S}}_{N} 2$. However, since the solvent is the protic form of the nucleophile, it doesn't matter whether the nucleophile is protonated or not: ${\text{CH"_3"OH" rightleftharpoons "CH"_3"CO"^(-) + "H}}^{+}$ because some solvent methanol would have to be deprotonated in order to protonate methoxide, so either way you have your nucleophile. Thus, the type of reaction depends solely on the substrate cyclohaloalkane. The substrate is very sterically hindered (the alkyl halide carbon is tertiary), so at room temperature, ${\text{S}}_{N} 1$ is likely. Or, at elevated temperatures, $\text{E} 1$ is likely, because higher temperatures favor elimination over substitution. A good rule of thumb is that if ${S}_{N} 1$ is favored, then boosting the temperature favors $E 1$, and similarly, if ${S}_{N} 2$ is favored, then boosting the temperature favors $\text{E} 2$. Now that we've established that you get either ${\text{S}}_{N} 1$, $\text{E} 1$, or both, let's draw both mechanisms. In the ${\text{S}}_{N} 1$ mechanism, we have to wait until the bromine leaves on its own, because the nucleophile is not strong enough to simply brute-force the reaction and displace the bromide---the steric hindrance is too much. So, the first step is rate-limiting, i.e. it is slow. Then, the carbocation intermediate forms, and the methoxide can either: • Act as a nucleophile and attack the carbocation center to form a new $\text{C"-"O}$ bond, thus forming the ${\text{S}}_{N} 1$ product. This step is fast. • Act as a base and steal a proton from the carbon adjacent to the carbocation and form a $\pi$ bond, thus forming the $\text{E} 1$ product. This step is fast. Thus, we see that the two possible products formed are the original compound with a methoxide displacing a bromide, or the alkene of the original compound.	2019-05-21 17:10:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7518420219421387, "perplexity": 1721.3052324366602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256494.24/warc/CC-MAIN-20190521162634-20190521184634-00292.warc.gz"}
https://ejop.psychopen.eu/index.php/ejop/article/download/4629/4629.html?inline=1	Research Reports # Deliberately Retrieved Negative Memories Can Improve Mood Beyond the Intention to Do So Veronika V. Nourkova1, Alena A. Gofman1 Europe's Journal of Psychology, 2022, Vol. 18(3), 235–248, https://doi.org/10.5964/ejop.4629 Received: 2020-11-12. Accepted: 2021-03-12. Published (VoR): 2022-08-31. Handling Editor: Tiziana Lanciano, Department of Education, Psychology, Communication, University of Bari ‘Aldo Moro’, Bari, Italy Corresponding author at: Department of General Psychology, Lomonosov Moscow State University, Mokhovaya str, 11-9, Room 213, 125009, Moscow, Russian Federation. Phone: +7 903 5734533. E-mail: Nourkova@mail.ru This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ## Abstract The role of autobiographical memory in emotion regulation is deemed as limited to the selective retrieval of positive memories intended as a distraction from unpleasant stimuli. The present experimental study is the first to examine whether negative autobiographical memories serve as a way to boost one’s mood by employing the mechanism of retrospective downward autobiographical comparison between now and then. We hypothesised that this mechanism may operate in response to negative memories, leading to positive mood induction. Ninety-nine students participated in four memory tasks: autobiographical positive, autobiographical negative, vicarious positive, and vicarious negative. Emotional states at pre- and post-tests were assessed using the implicit test differentiating positive (PA) and negative (NA) components of mood. The results replicated previous studies on the mood-repair effect of deliberate positive recall. The most striking finding is that negative autobiographical recall consistently boosted PA and inhibited NA. This result supported the idea of retrospective downward autobiographical comparison as a plausible mechanism behind the efficacy of negative memories in emotion regulation. Keywords: emotion regulation, autobiographical memory function, reappraisal, distraction, downward comparison, vicarious memories Folk theory and scientific psychology converge on the idea that healthy, non-depressed individuals can repair their negative moods by retrieving positive personal memories. Popular Internet resources advise unearthing and browsing sweet memories from childhood, vacations, and family reunions to overcome melancholy. When psychologists in a lab asked naïve participants whether they agree with the statement ‘When a person is feeling bad, it is helpful to recall pleasant memories’, they typically marked 4 or 5 on a 5-point Likert scale, endorsing the use of positive memories to regulate emotions (Wang, Koh, Song, & Hou, 2015). Experimental psychologists and clinicians suggest that difficulties in employing positive memories in mood regulation play an important role in various emotional disorders, such as depression and anxiety (McKay, Singer, & Conway, 2012; Singer, 2006). ### Memory in Emotion Regulation Harris, Rasmussen, and Berntsen (2014) justified the proposition that emotion regulation is a distinctive function of autobiographical memory in the exhaustive literature review. For instance, several studies have indicated that individuals deliberately recruit positive memories to resist a natural mood-congruent recall, followed by negative mood induction (Joormann, Siemer, & Gotlib, 2007; Josephson, Singer, & Salovey, 1996; McFarland & Buehler, 1997). Similarly, Öner and Gülgöz (2018) asked participants to recall three memories that made them feel sad or angry and then asked them to retrieve another memory with no specific instruction of emotion. Their results demonstrated two things. First, participants were able to induce negative affect by retrieving appropriate negative memories. Second, they successfully repaired their emotional states through subsequent positive recall. Furthermore, if the regulatory goal is to enhance positive affect, people deliberately select happier autobiographical memories in comparison to accomplishing the goals of self-continuity, social bonding, and directing behaviour (Wolf & Demiray, 2019). The previous literature has consistently shown that the most common outcome of autobiographical memory dynamics over time is a positive bias, which includes the fact that good memories persist longer than bad memories and, in general, makes memories more pleasant than experiences behind those memories. This positive bias is thought to assist in maintaining a hopeful outlook about the future and providing a means for situational emotion regulation in an automatic manner without purposive intention to do so (Walker & Skowronski, 2009). Therefore, reminiscing may be a powerful emotion regulation resource. It raises a question regarding the underlying mechanisms. Although several frameworks conceptualising the different ways in which people regulate their emotions have been proposed and empirically tested (see for review, Webb, Miles, & Sheeran, 2012), there are two strategies that incorporate memories. These strategies derived from the process model described by Gross (2015) and include attentional deployment in the form of distraction and cognitive change in the form of reappraisal. Regarding the mnemonic impact on emotion regulation, distraction ‘moves attention away from the situation altogether’ and ‘may also involve changing internal focus, such as when individuals invoke thoughts or memories that are inconsistent with the undesirable emotional state’ (Gross & Thompson, 2007, p. 13). It is a trivial assumption that positive autobiographical memories are very probable candidates for positive distraction, since recall reinstates the emotions associated with the addressed experiences. It was shown that after negative mood induction, non-depressed adults equally benefited from the instructed retrieval of positive memories and attention re-focusing (Joormann & Siemer, 2004). Congruently, Kovacs et al. (2015) found similar mood boosts after both distraction (in the form of watching shapes via kaleidoscope) and recall of two consecutive happy memories in never-depressed and remitted adolescents. Additionally, it is intuitively obvious that recalling positive memories per se is a fun activity and should improve mood (Tamir, 2009). Similarly, researchers have focused on retrospective cognitive reappraisal, that is, the case when individuals reframe negative past events as benign, valuable, or even beneficial (Garnefski, Kraaij, & Spinhoven, 2001; Rusting & DeHart, 2000; Wisco & Nolen-Hoeksema, 2010). For instance, a person who has recovered from COVID-19 might retrospectively view the disease as a call to help others make similar recoveries. Consequently, the modified memories of painful experiences become suitable for positive retrieval, and hence, may be involved in the mechanism of positive distraction. ### Is Mood-Repair Potency Limited to Positive Memories? However, the literature review revealed an important gap. Taken together, both automatic and deliberate accounts for mnemonic promotion of positive affect suggest that when faced with undesirable emotional states, individuals cope by retrieving exclusively pleasant memories. To the best of our knowledge, there is no research in the field that would disprove the assertion that the method of mnemonic mood repair is limited to positive memories. The present study departed from the previous literature in the way we hypothesised that unhappy autobiographical memories serve the goal of emotion regulation without being transformed into a positive mode. For further reasoning, it is important to reckon social comparison as a potential source of emotion regulation (Augustine & Hemenover, 2009). It is assumed that a person could feel better after performing downward comparisons with those doing worse than themselves (Aspinwall & Taylor, 1993). However, downward social comparisons with real persons have the potential to evoke guilt in the comparer because they violate personal morality and compete with empathy (White, Langer, Yariv, & Welch, 2006). We speculated that unhappy autobiographical memories could boost the mood, not by positive refocusing from the current concern to some irrelevant pleasant thoughts but by a specific form of cognitive reappraisal, that is, the positive reappraisal of the mismatch between the past and the present. Considering the concept of downward social comparisons, it is termed here as ‘retrospective downward autobiographical comparison’. While in the literature on emotion regulation, reappraisal is routinely thought as rethinking of an emotional event in the past, the ‘retrospective downward autobiographical comparison’ proposed in the current study involves a reappraisal of one’s current circumstances in the contrast to past emotional events. It may be stated that the former type of reappraisal is a past-targeted process that serves to modify existing memories, whereas the latter type of reappraisal is a present-targeted process that revises the perception of the present by collating with the past. When such comparison reflects favourably on the current circumstances, one might feel that ‘things have changed for the better’ and consequently, experience a hedonic shift in the affect. Our method of reasoning partially corresponds with a distinct form of retrospective cognitive change denoted as ‘putting into perspective’ by Garnefski et al. (2001). It refers to noticing relativity or even paltriness of current negative experiences when compared to other life events. Although the authors emphasised the importance of such a comparison, they interpreted it in terms of general probability, for example, one could think that it all could have been much worse; one could tell oneself that there are worse things in life, etc. We speculated that addressing a concrete moment in the personal past may lead to more pronounced affective consequences. Various cases illustrate this point. For instance, imagine a student whose sad mood is induced by a moderate failure in the academic domain. If she retrieves a positive memory from the relevant domain (e.g. passing exams successfully), it may make her feel even worse (here and now loses when compared with there and then). In contrast, if she retrieves an associated negative memory (e.g. threatened to be expelled from the university), her appraisal of the current situation would benefit from this comparison. Another example may be taken from the romantic relationship domain. Consider a woman experiencing melancholy due to her partner’s inadvertence. If sweet memories about her tender first love will emerge in her mind in this situation, the contrast between the good past and disappointing present may increase her dissatisfaction. Conversely, the sad memories of loneliness in the past may help her look at current relationships through rose-tinted glasses. ## Method The present study was designed to empirically examine the influence of deliberately retrieved negative autobiographical memories on the emotional state of non-depressed young adults. The main hypothesis posits that the feeling that things have changed for the better may arise in response to recalling a negative memory employing the mechanism of ‘retrospective downward autobiographical comparison’, that is, a comparison between the worse past and better present. In other words, after a deliberate experience of negative autobiographical memories, we tested the prediction that participants would enjoy the present moment more than before. Notably, the present study focused on the uncontemplated effect of intentional negative recall. Taking into account, people’s tendency to retrieve positive memories as a controlled mood regulation strategy (Ortner, Briner, & Marjanovic, 2017; Rusting & DeHart, 2000) and expect negative memories to induce negative mood (Hernandez, Vander Wal, & Spring, 2003; Öner & Gülgöz, 2018; Pond & Peterson, 2020), we sought to avoid the influence of such bias on the emotional outcomes of the recall. Therefore, this study dealt with implicit emotion regulation which has been shown to combine habitual strategies with continual adjustment to the contingencies. We predict that intentional, but purposeless, negative recall may support all three consecutive stages of implicit emotion regulation, as asserted by Koole, Webb, and Sheeran (2015). First, it may activate emotion regulation goals. Second, it may serve as a situational affordance for selecting appropriate emotion regulation strategies. Third, it may maintain the process of implementing the chosen strategy until the goal is achieved. Therefore, participants did not receive explicit incentives to change their existing moods. In the present study, we also examined our speculation on the potential positive affective consequences of negative content, accommodating some insights from the field of media psychology. In an attempt to explore why people enjoy watching sad movies and reading sad fictional literature even if there is no redeeming happy end, the authors proposed that they may tolerate negative affective states temporarily for the sake of better emotional outcomes in the future (Mar, Oatley, Djikic, & Mullin, 2011). The mechanism of restoring a negative mood by comparing oneself with a fictional character depicted as more unfortunate following the insight that one’s concerns are not the worst has been identified among various motivations behind the puzzling popularity of tragic plots (Koopman, 2015). Consistent with this view and conceptually related to downward social comparisons, previous literature has shown that individuals with specific problems (e.g. loneliness) select and retrospectively highly appreciate films that include a pessimistic portrayal of people with similar problems (Mares & Cantor, 1992). However, the emotional benefits of a downward comparison are absent when identifying with fictional characters. Strong identification leads to a higher probability of experiencing the same emotional state as experienced by the target (Mar, Oatley, Djikic, & Mullin, 2011). Moreover, taking a first-person (rather than a third-person) perspective enhances identification with a narrative protagonist (Samur, Tops, Slapšinskaitė, & Koole, 2021). Correspondingly, the phenomena of vicarious memories, that is, memories representing events that happened to others, even fictional protagonists, have recently received substantial interest in the field of autobiographical memory (Pillemer, Steiner, Kuwabara, Thomsen, & Svob, 2015). It has been reported that the phenomenological and functional qualities of vicarious memories closely resemble those of autobiographical memories. However, vicarious memories are typically rated as less vivid, less personally important, and more negative than autobiographical memories (Pond & Peterson, 2020). There is a theoretical assumption that negative vicarious memories may serve a self-enhancement function through a downward social comparison and impact emotion regulation (Thomsen & Pillemer, 2017). Considering the probable self-enhancement function of negative vicarious memories, further empirical research is needed to determine whether vicarious memories are identical to autobiographical memories in emotion regulation. Therefore, we introduced memories on behalf of a favourite fictional character as the control condition. The following tentative hypotheses represent the expected findings consistent with the study aims: • H1: Intentional positive autobiographical recall in the absence of an explicit goal of emotion regulation will ameliorate the participants’ mood implicitly through the mechanism of positive distraction from the current concerns. • H2: Intentional negative autobiographical recall in the absence of an explicit goal of emotion regulation will ameliorate the participants’ mood implicitly through the mechanism of retrospective downward autobiographical comparison, that is, a comparison of the current concerns against their more negative memories. • H3: Positive recall on behalf of a favourite fictional character will produce a similar but weaker improvement of mood. The expected effect will arise due to the distractive potential of entering a fictional world enhanced by identification with a protagonist. • H4: Negative recall on behalf of a favourite fictional character will have a reverse effect on implicit emotion regulation in comparison with negative autobiographical recall. This expected result will be due to the use of first-person narration, which evokes identification with the protagonist and, consequently, inhibits the downward social comparison emotion regulation strategy. ### Participants Ninety-nine psychology students (Mage = 20.31, SD = 2.06; 68 females) participated in the study for partial course credit. The sample size was calculated a priori using the ANOVA: repeated measures, within factors option in GPower 3 (Faul, Erdfelder, Lang, & Buchner, 2007) specifying a medium effect size ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .25) with a power of 1 – β = .90. Considering that two factors were included into design, the recommended minimum sample of 23 was multiplied by four in accordance with the claim made by Brysbaert (2019). Consequently, the required sample size was determined to be 92. Therefore, the present study was appropriately powered. The participants had no history of treatment for any psychiatric conditions. They signed an informed consent form approved by the Ethics Committee of the Faculty of Psychology of Lomonosov Moscow State University under the Declaration of Helsinki (Project No. 2019/64). ### Measures #### Emotional State Several competing approaches exist for assessing mood and emotion (see for review, Gray & Watson; 2007). In this study, we chose the outcome measures based on Watson and Tellegen’s hierarchical model of affect structure, which proposes two high-order largely unipolar dimensions of affective space: positive affect (PA) and negative affect (NA). Since the self-report methodology is prone to various biases, particularly, to cultural stereotypes about the nature of emotional experience, their self-report Positive and Negative Affect Schedule (PANAS, Watson, Clark, & Tellegen, 1988) was not used. Similarly, we speculated that the folk belief that negative memories ruin positive mood might disguise their regulative power in the relevant experimental condition if emotions are measured explicitly (Ford & Gross, 2018). Departing from the self-report methodology, we assessed emotional states using the indirect projective method: The Implicit Positive and Negative Affect Test (IPANAT, Quirin, Kazén, & Kuhl, 2009). However, the authors do not equate the term ‘implicit affect’ with the ‘unconscious’. Consistent with the proposition that emotions are, per definition, the states of consciousness and not necessarily reflective (Lieberman, 2019), they posit that the IPANAT allows the assessment of automatic and pre-reflective components of the affective experience. Several recent studies have used the IPANAT, demonstrating the compatibility of the results of this novel method compared to the traditional self-report methods. For instance, in Quirin, Bode, and Kuhl (2011) study, participants performed the IPANAT and self-report mood adjective checklist before and after exposure to a fear-inducing video. As expected, both implicit and explicit PA decreased immediately after viewing a threat-related video and increased after a time delay, detecting the recovery of a neutral emotional state. However, the IPANAT is more sensitive to emotion dynamics and the corresponding behavioural variables. Concurrently, examining whether a mindfulness exercise improves explicit and implicit negative moods, Remmers, Topolinski, and Koole (2016) revealed the same pattern of results across both measures. The IPANAT procedure requires participants to rate the degree to which nonsense words (e.g. SAFME, VIKES, TUNBA, PEVIL, BELNI, and MADDO) convey various feelings. To conceal the real target of the IPANAT, the participants are encouraged to guess the meaning of the nonsense words to examine their linguistic intuition. Since the list of stimuli was proven to be emotionally neutral across 10 countries, including Russia (Quirin et al., 2018), it is assumed that, in accordance with the affect infusion principle, participants project their current affects on this material. Participants rate six nonsense words with respect to three positive and three negative emotional states using a 4-point Likert scale ranging from ‘doesn’t fit at all’ to ‘fits very well’. According to the authors, the IPANAT reveals two orthogonal dimensions: positive affect (PA) and negative affect (NA). Averaging adjective scores derived from positively and negatively valenced adjectives present the scores for PA and NA, respectively. The Russian version of the IPANAT is a valid and reliable instrument with satisfactory psychometric properties (Mitina, Padun, & Zelyanina, 2017). It is noteworthy that 64 nonsense words are available to construct non-recurring lists for repeated measures. In the autobiographical memory task, participants were asked to give brief but detailed descriptions of the event they experienced more than a year ago that lasted over minutes or hours but no longer than a day. In the ‘happy’ condition, they received the following instructions: ‘This memory should be a highly positive experience that made you feel happy, satisfied, and lucky at the time it occurred’. In the ‘unhappy’ condition, they received the opposite instructions: ‘This memory should be a highly negative experience that made you feel unhappy, disappointed, and helpless at the time it occurred’. In the vicarious memory task, participants were asked to do the same on behalf of their favourite fictional characters. We encouraged participants to put themselves in their favourite character’s shoes and tell the stories as if they were them. The exact instruction was: ‘Imagine yourself to be your favourite fictional character and then recollect an event from her/his perspective, as if you were they’. #### Time Perspective To control for individual differences in personal attitudes toward their experience, we included the Zimbardo Time Perspective Index (ZTPI, Zimbardo & Boyd, 1999) subscales tapping the two dimensions: Past Positive (PP, 9 items) and Past Negative (PN, 10 items). #### Empathy for a Fictional Character To control for individual differences in becoming absorbed in the feelings and actions of the fictional characters, we included the fantasy subscale from the Interpersonal Reactivity Index (IRI, Davis, Luce, & Kraus, 1994) consisting of seven statements. For both scales, participants were asked to indicate the extent to which each of the statements was true for them on a 5-point Likert scale. #### Thematic Analysis Considering the emphasis on the possible contribution of negative memories in mood regulation, the contents of negative memories were analysed according to the themes that emerged from the narratives. Three coders independently read the memory descriptions to develop a list of content categories. Then, the coders inspected the memory descriptions again and assigned them to the most relevant categories that emerged from the previous coding procedure. The final attribution was based on the majority’s decision. ### Procedure Participants attended four sessions held approximately one week apart. Upon their first arrival at the laboratory, participants were informed that the study dealt with various kinds of memories and their linguistic intuition. They then signed a consent form and completed the IRI and ZTPI subscales. Each session started with an indirect assessment of the emotional state by completing the IPANAT. Then, the participants performed a memory task randomised across sessions and participants. Immediately after performing the memory task, the participants completed the IPANAT again. Eight non-recurring lists of the IPANAT stimuli were used; therefore, at each assessment, the participants dealt with a novel set of nonsense words. Three research assistants communicated with each participant individually. The questionnaire was presented online on the Google platform; however, the participants received the link only in the laboratory. Each session, except for the first session, took approximately 20 minutes. The participants were debriefed after the last session, where they learned about the true purpose of the study. None of the participants reported that they realised the true goal of the study before being debriefed. ## Results To exclude the possibility that condition-specific effects on emotion regulation were due to baseline differences in moods prior to manipulation, pre-test IPANAT scores were compared between the four conditions. There were no significant differences in PA, F(3, 98) = 0.664, p = .575, nor for NA, F(3, 98) = 1.655, p = .177. Both the PA and NA scales showed adequate internal consistency, with Cronbach’s alpha of .83 for each. Table 1 presents the means and standard deviations of the IPANAT scores at pre- and post-tests for all memory tasks (autobiographical positive, autobiographical negative, vicarious positive, and vicarious negative). ##### Table 1 Descriptive Statistics for Means and Standard Deviations of the IPANAT Score Positive Memory Negative Memory Positive Memory Negative Memory Statistic PA NA PA NA PA NA PA NA pre post pre post pre post pre post pre post pre post pre post pre post M 2.06 2.09 2.08 1.98 2.07 2.49 2.09 1.76 2.12 2.22 2.02 1.94 2.11 1.98 2.04 2.1 SD .42 .52 .41 .52 .53 .52 .54 .48 .51 .50 .44 .43 .51 .51 .45 .50 Note. N = 99; PA = positive affect; NA = negative affect; pre = before performing the memory task; post = after performing the memory task. Two repeated-measures mixed ANOVAs were conducted with PA and NA as dependent variables separately with time (before vs. after the memory task) and two within-subject factors of memory valence (positive vs. negative) and memory attribution (autobiographical vs. vicarious on behalf of one’s favourite fictional character). The ANOVA on PA revealed a main effect of time, F(1, 98) = 25.71, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .208. On average, participants scored higher on positive affect after performing the memory tasks. There was a main effect of attribution of the retrieved memory to one’s past or a favourite fictional character, F(1, 98) = 4.66, p = .03, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .045. The PA associated with autobiographical memories appeared to be slightly higher than those associated with alter-biographical memories. Importantly, the analysis also indicated reliable interactions: time × attribution, F(1, 98) = 25.53, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .207, valence x attribution, F(1, 98) = 48.24, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .330, and time × valence × attribution, F(1, 98) = 56.61, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .366. Follow-up analyses revealed that performing positive memory tasks inflated the PA when the participants retrieved vicarious memories, F(1, 98) = 6.95, p = .01, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .066 but not after autobiographical retrieval, F(1, 98) = 0.548, p = .461. Participants’ performance on negative memory tasks led to a mild decrease in PA in the vicarious condition, F(1, 98) = 10.28, p = .002, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .095, whereas PA increased extensively in the autobiographical condition, F(1,98) = 88.91, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .456. Thus, a negative recall produced reverse effects on the PA depending on the examination of one’s experience or the biography of a fictional character. A congruent pattern of data was obtained for NA scores. The ANOVA on the NA indicated a main effect of time, F(1, 98) = 28.63, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .226. On average, participants scored lower on negative affect after performing the memory tasks. The analysis detected significant crossover interactions: time × attribution, F(1, 98) = 26.56, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .213, attribution x valence, F(1, 98) = 37.16, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .275, and time x valence x attribution, F(1, 98) = 24.78, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .202. A follow-up inspection demonstrated an identical slight decline in NA in both the autobiographical and vicarious conditions after performing positive memory tasks, F(1, 98) = 6.60, p = .01, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .059 and, F(1, 98) = 4.28, p = .04, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .042, respectively. In contrast, performing negative memory tasks inhibited the NA dramatically in the autobiographical condition, F(1, 98) = 52.11, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .330, whereas the same task in the vicarious condition did not evoke any effect on the NA, F(1, 98) = 2.55, p = .113. To identify the role of additional self-reported measures, we calculated correlations between the ZTPI and IRI scores and the IPANAT difference scores (post-test minus pre-test scores) in the four conditions. Nevertheless, none of these measures were correlated with one exception: ZTPI negative past and the NA difference for positive autobiographical recall (r = .344, p < .001). Considering that NA typically decreases in this condition, it may be assumed that an aversive view of the personal past interferes with the mitigation of negative affect with positive memories. This assumption was supported by the fact that elucidating the ANOVA with the ZTPI negative past scores as a covariate substantially boosted the statistical power, F(1, 98) = 8.66, p < .001, ${\mathrm{\eta }}_{\mathrm{p}}^{2}$ = .151. Figure 1 displays the mean scores of the positive and negative affect on the IPANAT as a function of memory tasks. Click to enlarge ### Mean IPANAT Scores for Positive Affect (PA) and Negative Affect (NA) Before and After Performing Memory Tasks Note. Error bars indicate standard errors of the mean. A significant result of the simple effects test, indicating a difference between pre- and post-test scores, is marked with a star. p < .05. *p < .01. ### The Content of Negative Memories To elucidate the results further, we examined whether the contents of negative memories produced by the participants somehow influenced the following emotional states. Although the categories were not pre-decided, the analysis resulted in categorizing all the memories into eight corresponding themes. The following categories were identified: 1) Death of relative/friend/pet (e.g. ‘The two memories immediately came to my mind. The death of my grandmother and the death of my lovely cat. These events have merged somewhat because I experienced similar emotions. These two creatures, pardon the expression, were the closest to me. In the first case, I could do nothing since I was too young. But for the second case, I still blame myself. She (the cat) was sick and jumped out the window to catch a sparrow.’); 2) Separation/End of relationships/Loneliness (e.g. ‘The last conversation with my boyfriend, when he was back from the army. I remember us staying near the army barrack. It was windy, cold, and rainy. He told me not to contact him anymore, not to expect anything from our relationships.’); 3) Humiliation (e.g. ‘I was catastrophically humiliated by my classmate. She took picture of me at the gym changing room by stealth. And then she sent the photo to my boyfriend by noticing the imperfections of my figure. I could not stop crying when I found out about it.’); 4) Incompetence in the academic domain (e.g. ‘Last year I was told that I had to present my project a week earlier than it was scheduled. I tried to cope with the time pressure, but I was very worried, felt overworked, and helpless. I felt that it would be very difficult to handle and that I didn't have the strength to do it.’); 5) Own/Relative’s disease (e.g. ‘The day Dad told me that Mom had been diagnosed with cancer.’); 6) Conflict/Betrayal (e.g. ‘First escape from home after a terrible quarrel with my mother. I spent all night at a staircase asking myself, “Why is life being so unfair to me?” I felt everything went wrong. I felt so unlucky, so stupid, so miserable.’); 7) Parental conflict/divorce (e.g. ‘I was eight when my parent’s marriage was broken. Of course, I could not figure out why my Dad was not at home. One day, my grandmother told me that they no longer lived together. I was really shocked. I could not make heads or tails of it.’). Since the positive effect of negative recall was possible due to reappraisal in its traditional form, we carefully examined the verbal marks indicating such previous reappraisal and introduced the eighth category ‘Reappraised events’. The following record may exemplify this category: ‘There are moments in the past that bring a shadow of regret, but the understanding immediately comes that these situations served as a powerful stimulus for me, they shaped my character and without them, many great events would not have happened in my life.’ The modal category for the participants was ‘Incompetence in the academic domain’ (24.2%). The second most frequently observed category was ‘Separation/End of relationships/Loneliness’ (20.2%). The third and fourth common categories (16.2%) were ‘Death of relative/friend/pet’ and ‘Conflict/Betrayal’. Contrary to these concerns, the category ‘Reappraised events’ was mentioned among the rarest (6.1%) and, therefore, did not significantly influence the main results. Considering the possible correspondence between the susceptibility to the positive effect of negative autobiographical recall and the content of retrieved memories, we split the sample into two unequal groups. The ‘boosters’ group involved those participants whose PA and NA synchronically increased and decreased, respectively, after performing negative autobiographical memory tasks (N = 74). The ‘non-boosters’ group involved those participants whose PA or NA did not follow the pattern described above (N = 25) (see Table 2). The analysis revealed that both subgroups reported similar frequencies of memories referring to each of the eight categories; χ2 (7, 99) = 1.763, p = .972. ##### Table 2 Percentages and Frequencies of Negative Memories Boosters (N = 74) Non-Boosters (N = 25) Content Category Frequency Percent Frequency Percent Death of relative/friend 12 16.25 4 16.00 Separation/End of relationships/Loneliness 15 20.30 5 20.00 Humiliation 7 9.50 1 4.00 Incompetence in the academic domain 17 23.00 7 28.00 Own/Relative’s disease 5 6.80 1 4.00 Conflict/Betrayal 11 14.90 5 20.00 Parental conflict/ divorce 2 2.70 1 4.00 Reappraised events 5 6.80 1 4.00 Note. Sorted by content category and susceptibility to the positive effect of the negative recall subgroup. The frequencies and percentages of negative autobiographical memories classified into 8 content categories described above for the two subsamples—‘boosters’ and ‘non-boosters’. ## Discussion Although remembering may be an effective tool for emotion management for several reasons (Pasupathi, 2003; Pillemer, 2009), there is a dearth of research on the diversity of mechanisms that engage with the function of remembering to enhance positive and diminish negative moods. People’s negative personal memories, when functional, have been shown to serve predominantly directive functions by taking lessons and applying those lessons to the current problems (Rasmussen & Berntsen, 2009). Accordingly, some ‘emotional lessons’ may be extracted from negative memories to resolve current concerns. To the best of our knowledge, no prior studies have examined the possibility that memories of negative past events per se could help people to view the current situation in more benign terms and, consequently, regulate one’s mood. The present study focused on the idea that the utility of negative memories for mood enhancement may imply a specific kind of retrospective cognitive reappraisal. In contrast to rethinking past negative events differently (retrospective reappraisal), the retrospective downward autobiographical comparison proposed here induces a positive mismatch between past negative experiences and the current situation, that is, the feeling that ‘since then, things have changed for the better’. The discrepancy between an aversive memory and an acceptable present seems to be a probable mechanism for positive mood induction. The present study avoided directing the participants to goal-driven mood management. The rationale behind this was the assumption that metacognitive beliefs concerning how autobiographical memory works may contribute to individuals’ mnemonic behaviour (Wang et al., 2015). Since it seems highly likely that people believe in the negative influence of negative memories on their moods, it may oppose expected mood-repair effect after deliberate retrieval. To prevent such a scenario, the positive and negative components of mood were assessed using an indirect test (the IPANAT). The results replicated and elucidated previous data on the mood-repair effect by deliberate recall of positive memories. Positive memory tasks significantly decreased the negative component of the mood (NA) in both autobiographical and vicarious conditions. Notably, an increase in positive affect (PA) was observed in the vicarious condition only, while it remained the same after the autobiographical recall. This asymmetry may be due to the entertaining nature of vicarious memory tasks. Putting oneself into one’s favourite fictional character’s shoes at the happiest moments of the story might be, in itself, a powerful mood regulation strategy. The most striking finding from this study is the reverse effect of negative memory tasks in autobiographical and vicarious conditions. A decrease in PA and stasis of NA was detected in the vicarious condition. In contrast, negative autobiographical recall, consistent with our predictions, consistently boosted PA and inhibited NA. The former result may be attributed to identification with a chosen fictional character, which determines emotional mimicry. From our perspective, the latter result may support the idea that retrospective downward autobiographical comparison serves as a mechanism behind employing negative personal memories for emotion regulation. It is noteworthy that the obtained result could not be attributed to the specific thematic content of memories. In this study, all negative autobiographical memories were grouped into a relatively small number of categories (N = 8). No significant differences were found in the frequency of memories assigned to each of the categories between the participants divided according to their mood shift after performing the memory tasks (boosters vs. non-boosters). In this study, the most widespread negative memories addressed separations and failures in the academic domain. These results are consistent with numerous data on the significance of self-mastery and communion themes in young adults’ autobiographical narratives, which, in turn, mirror the most powerful motives of this age cohort (see for details, McAdams, Hoffman, Day, & Mansfield, 1996). At the outset of the study, it was expected that individuals who view their past through rose-tinted glasses would benefit more from positive autobiographical recall, whereas individuals with a negative bias toward their past would have difficulty resorting to an account of positive memories. Alternatively, such rose-tinted glasses could contradict the proposed mood-repair effect of negative memories, whereas a negative bias towards one’s past probably makes the effect more articulated. In fact, only high scores on the ZTPI negative past correlated with a decrease in NA after the positive memory task, highlighting this kind of negative bias as an obstacle to eliminating mood negativity. ### Conclusions This experimental study is the first to examine whether negative autobiographical memories serve as a counterpart to positive ones in emotion regulation. This possibility was proposed when considering that negative memories may evoke a feeling that things are going better now as compared to the past. Consequently, this positive discrepancy may improve one’s affective state. The proposed hypothesis was tested in 99 healthy, young adults. In general, the claim that performing positive memory retrieval is a sufficient strategy for mood management was replicated. More importantly, the current study extended prior research by detecting the moderate but consistent effect for the PA and NA after a negative autobiographical memory task, in a way that participants increased their PA and decreased their NA at post-test. Notably, the effect took place spontaneously without the explicit goal of changing the existing mood and addressed implicit emotion regulation. These results go beyond previous reports, showing that a retrospective downward autobiographical comparison approach may provide useful insights into the functionality of autobiographical memory. ### Limitations and Future Directions Undoubtedly, much remains to be investigated before we have a clear picture of all the conditions under which negative memories may reduce mood negativity and promote mood positivity. Further research should examine the nuances of candidate memories with respect to their content, age, emotional intensity, and the level of discrepancy between the recalled event and the current concern. We are also aware that employing negative memories for emotion regulation functions can exhibit cultural differences. For instance, since it has been shown that people with East Asian cultural backgrounds are able to tolerate negative memories successfully (Nourkova, 2020; Spencer-Rodgers, Peng, & Wang, 2010), they could benefit more from negative memories than people with European and North American cultural backgrounds. However, the current paper contributes to our understanding of emotion regulation and has demonstrated a possible and previously overlooked application of negative autobiographical memories in diminishing negative emotions or distress. ## Funding The research was funded by RFBR grant number No. 19‐29‐07069. ## Acknowledgments We would like to express our gratitude to Marina Lynova and Gleb Vzorin for their assistance at various stages of the data collection and processing. ## Competing Interests The author has declared that no competing interests exist. ## References • Aspinwall, L. G., & Taylor, S. E. (1993). 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Putting time in perspective: A valid, reliable individual-differences metric. Journal of Personality and Social Psychology, 77(6), 1271-1288. https://doi.org/10.1037/0022-3514.77.6.1271	2023-03-25 16:23:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3456866443157196, "perplexity": 6909.088656568223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945368.6/warc/CC-MAIN-20230325161021-20230325191021-00236.warc.gz"}
http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_multinomial_distri.htm	Multinomial distribution # Definition of the multinomial distribution The binomial distribution B(n, p) is obtained by considering n tosses of a coin (Heads and Tails), with p being the probability that the coin will land on a Head. The multinomial distribution is a generalization of the binomial distribution : each "toss" can now produce more than just two outcomes. For example, one may imagine rolling a "die" with k faces, with pi being the probability for the die to land on face Ai. A multinomial distribution is entirely characterized by : * n, the number of times the die is rolled. * The set of probabilities {p1, p2 , ..., pk} with p1p2 + ...+ pk = 1 ----- After rolling the die n times, we denote ni the number of times the die landed face Ai up. We therefore have n1n2 + ...+ nk = n. Because rolling a die is a random activity, the nis are the realizations of k random variables that we denote Xi (i = 1, 2, ..., k). These variables are not independent, as they are linked by the relation Σi Xi = n. The multinomial distribution Mult(n, p1, p2 , ..., pk ) is the joint distribution of the k random variables Xi. It is therefore a multivariate, discrete distribution. Its support is the set of k-uples of non negative integers {n1n2, ..., nk} such that n1n2 + ...+ nk = n. # The multinomial probability distribution The distribution Mult(n; p1, p2 , ..., pk ) is determined by the values of the probabilities of each of the possible k-uples. We denote these probabilities by P{X1 = n1, ..., Xk = nk }. We'll show that : for all the k-uples within the support n1 + n2 + ... + nk = n of the distribution (and 0 otherwise). ----- The binomial distribution is a special case with k = 2. # Multinomial coefficient The term n! / (n1!.n2!...nk!) is called the multinomial coefficient. It is the number of different "words" that can be written with an alphabet containing k letters by using the first letter n1 times, the second letter n2 times etc... We'll justify this result two different ways. ----- Note that the multinomial coefficient is equal to the coefficient of the monom xn1xn2 ...xnk in the development of (x1 + x2 + ...+ xk )n , hence the name of the distribution. # Moment generating function of the multinomial distribution The moment generating function of the multinomial distribution Mult(n, p1, p2 , ..., pk ) is : # Mean We show below that for any i, Xi follows the binomial distribution B(n, pi). It follows immediately that E[Xi] = npi # Covariance matrix of the multinomial distribution The multinomial distribution is the distribution of a random vector X = {X1, X2 , ..., Xk}. It is therefore appropriate to calculate its covariance matrix. ## Variances We show below that for any i, Xi follows the binomial distribution B(n, pi ). Hence Var(Xi) = npi(1 - pi) ## Covariances We'll give two demonstrations of the following result : Cov(Xi , Xj ) = -n pi pj All the covariances are negative : for a given number of draws n, any increase of ni will be conducive, on the average, to a reduction of the number of observations in any other category. We gave here a third demonstration of this result by calling on the Theorem of iterated expectation. ----- Because of the constraint Σi Xi = n, the covariance matrix of the multinomial distribution is not full rank, a fact that we'll establish directly. ## Correlation coefficients By reporting to the definition of the correlation coefficient between two variables, we have : Note that this expression does not contain n. # Merging categories Suppose that the first r variables of the random vector X = {X1, X2 , ..., Xk} are replaced by the single variable Y defined as the sum of these variables : Y = X1 + X2 + ... + Xr The first r categories {A1, ..., Ar } are said to be merged. Because the Xis are linked by X1 + X2 + ... + Xk = n, we also have Y = n - (Xr + 1 + Xr + 2 + ... + Xk ). We'll show that The vector {Y, Xr + 1, Xr + 2, ..., Xk} = {n - (Xr + 1 + Xr + 2 + ... + Xk ), Xr + 1, Xr + 2, ..., Xk} is distributed as Mult(n; p, pr +1, ..., pk ) with p = p1 + p2 + ..., pr. In other words : 1) Merge categories, 2) Then assign to this new category a probability equal to the sum of the probabilities of the merged cargories, and you have the multinomial distribution of the new category plus the remaining categories. Marginal distributions of the multinomial distribution Recall that Xi is the number of observations in the category Ai. ## Single component Consider category Ai. The outcome of each draw : * Is Ai with probability pi. * And therefore is "Not Ai" (that is, any other category) with probability (1 - pi). Hence Xi is binomial B(n, pi). ## Several components Things are a bit more complicated when more than one component are considered. Given the multinomial distribution Mult(n; p1, p2 , ..., pk ), we'll calculate the joint distribution of {X1, X2, ..., Xr}, the set of the r first components and discover that this distribution is not multinomial. Because this result is a bit awkward, litterature sometimes defines the marginal distributions of the multinomial distribution as the distribution of the augmented vector {X1, X2, ..., Xr, n - (X1 + X2 + ... + Xr)} which is multinomial (see preceding paragraph). ----- This result generalizes straightforwardly to any group of components. # Conditional distributions of the multinomial distribution Let the vector {X1, X2 , ..., Xk} follow the multinomial distribution Mult(n; p1, p2 , ..., pk ). We consider the distribution of the r first components {X1, X2 , ..., Xr} of the vector conditionally to the values of the last (k - r) components. In other words, we want the distribution of the variable : {X1, X2 , ..., Xr \| Xr + 1 = nr + 1, Xr + 2 = nr + 2, ..., Xk = nk + 2 We'll show that this distribution is multinomial Mult(m; p'1, p'2 , ..., p'r ) with : * m = n - (nr + 1 + nr + 2 + ... + nk + 2 ) * p'i = pi /(p1+ p2 + ... + pr ) ----- This result generalizes straightforwardly to any group of components. # Estimation of the parameters pi We'll show that the Maximum Likelihood Estimator (MLEpi* of the parameter pi is : Goodness-of-fit test The Chi-square tests (goodness-of-fit, identity, independence, ...) are very important non parametric tests. They are all basically the same test, which is a goodness-of-fit test for the multinomial distribution. The test statistic is the so-called "Pearson's Chi-square", which we demonstrate below to be asymptotically χ2 distributed. This result is fundamental. ----- Note that the basic Chi-square test is not the only goodness-of-fit test for the multinomial distribution. We build here the Likelihood Ratio Test which serves exactly the same purpose. # Link with the Poisson distribution There is an intimate link between the multinomial distribution and the Poisson distribution. We show here that if {X1, X2, ..., Xk} are k independent (but not necessarily identically distributed) Poisson variables, then the joint distribution of {X1, X2, ..., Xk} conditionally to their sum is a multinomial distribution. ___________________________________________________ Tutorial 1 We calculate the probability mass function of the multinomial distribution. The key part is establishing the expression of the multinomial coefficient, which we do two by different methods. We then calculate the Maximum Likelihood Estimator (MLEpi* of the parameter pi. This calculation is a simple exercise in constrained optimization by the method of Lagrangian multipliers. PROBABILITY MASS FUNCTION OF THE MULTINOMIAL DISTRIBUTION Probability mass function of the multinomial distribution The multinomial coefficient First demonstration Second demonstration Maximum Likelihood Estimation of the parameters pi TUTORIAL ________________________________________________________ Tutorial 2 We now use two different methods for calculating Cov(Xi, Xj ), the covariance of the numbers of observations in two categories of the multinomial distribution. The second method represents these (random) numbers as sums of auxiliary Bournoulli variables. This approach is often quite effective with discrete probability distributions problems (see for example the calculation of the mean of the hypergeometric distribution). COVARIANCE MATRIX OF THE MULTINOMIAL DISTRIBUTION Direct calculation of the covariance Second demonstration (indicator variables) Number of observations in a category as a sum of Bernoulli r.v.s Calculation of the covariance The covariance matrix is not full rank TUTORIAL _________________________________________________________ Tutorial 3 In this Tutorial : 1) We first establish the distribution of the vector {Y, Xr + 1, Xr + 2, ..., Xk ) where Y is the sum of the r first components of X : Y = X1X2 + ..., Xr We'll show that this distribution is Mult(n; p, pr +1, ..., pk ) with p = p1p2 + ..., pr. 2) We then calculate the joint distribution of {X1, X2, ..., Xr }, the genuine marginal distribution of the multinomial distribution. This distribution will turn out not to be multinomial, so the distribution of the "augmented" vector {X1, X2, ..., Xr, n - (X1X2 + ..., Xr)}, whose distribution is multinomial (see preceding paragraph) is sometimes presented as the marginal distribution of X. 3) We finally calculate the joint distribution of a group of categories conditionally to the values of the other categories, and show that this distribution is multinomial (see here). MERGED CATEGORIES MARGINAL AND CONDITIONAL DISTRIBUTIONS Merging categories Marginal distributions Conditional distirbutions TUTORIAL _________________________________ Tutorial 4 In this Tutorial, we demonstrate the fundamental Pearson's theorem which is the base on which all Chi-square tests are built. The theorem states that the so-called "Pearson's Chi-square statistic", which is the statistic common to all Chi-square tests, is asymptotically χ2 distributed. Although Linear Algebra can wrap-up the issue in a few compact lines, we'll develop a longer but elementary method which permits following the proof step by step. An alternative to the Chi-square statistic is Wilk's G² statistic, whose behavior is compared here to that of the Chi-square statistic. PEARSON'S THEOREM Pearson's theorem The goodness-of-fit problem for the multinomial distribution The Chi-square statistic Origin of the Chi-square statistic The Chi-square statistic is "unnatural" The two categories case The Z vector Definition of the Z vector Covariance matrix of the Z vector The distribution of Z is degenerate The covariance matrix is not full rank Subspace of the distribution of Z Another vector with the same covariance matrix as Z Projection on a plane perpendicular to a unit vector Projection of a set of standard normal variables Covariance matrix of the set of projected variables Off-diagonal terms Diagonal terms Rotation of the coordinate system The asymptotic distribution of the Chi-square statistic is χ2 TUTORIAL ______________________________________________________	2013-05-18 19:40:07	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9011576175689697, "perplexity": 1321.241306810082}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696382764/warc/CC-MAIN-20130516092622-00063-ip-10-60-113-184.ec2.internal.warc.gz"}
https://jp.pinkoi.com/product/nveQkBZv	# Wensen Flute - Spectacular Kazoo KAZOO doll US\$ 21.42US\$ 23.80 • この商品は「受注制作」です。お支払いが確認できてから、制作を開始しますので、ショップの休日を除く 3 日後に発送予定です。 ## 商品情報ハンドメイドその他オーダーメイド可能な商品, 受賞作品 • チェックされた回数 3,525回 • 合計販売点数：13点 • 36 人がお気に入り登録おすすめポイント "Wen Sen Flute" is a special musical instrument. When you use it, you don't need any fingering. You can us 98% 24時間以内 1週間以内 10%OFF ## 商品説明 "Wen Sen Flute" is a special musical instrument. When you use it, you don't need any fingering. You can use the throat singing method to make a sound. You can play any song that sounds like a saxophone or a trumpet. In addition to being used as a table decoration, it is more suitable for a variety of occasions, and can also be played with a guitar or ukkleili! https://c1.staticflickr.com/5/4557/37548773874_3a2ed80e9d_o.jpg https://c1.staticflickr.com/5/4545/38228213652_9efcf09296_o.jpg https://c1.staticflickr.com/5/4567/38205202976_d689acaf0e_o.jpg https://c1.staticflickr.com/5/4581/24388878408_3a984c8a7a_o.jpg ... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . https://c1.staticflickr.com/5/4543/38227704682_270099322e_o.jpg 1. First, close your mouth and use your throat to make a "~" sound 2. Keep the throat vibrating and move the resonance position to your lips 3. Lightly hold the mouthpiece and try to issue DO ~ RE ~ MI ~ FA ~ SO ~ 4. After you are skilled, you can enjoy happy songs https://c1.staticflickr.com/5/4531/38259547611_e6b738a3f8_o.jpg ... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . https://c1.staticflickr.com/5/4559/38227704132_4d9f10d314_o.jpg ... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . https://c1.staticflickr.com/5/4563/37548773694_a3b025d62d_o.jpg Each tree's inherent growth rings and wood grain, as well as the unique smell, is like each different person, has its own unique charm. "Wonsen/WOOD SONG" is a brand that we established in 2014. We use "moving, education, and happiness" as the core, and use wood as material and sound to develop into a musical product. The word "smell" has an image of smell and hearing. The word "sen" has the meaning of sound between forest and sound, and echoes the spirit of WOOD SONG. ... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin / manufacturing methods \| Taiwan/hand-made color painting (different pricing based on painting hours) ## 送料とその他の情報アメリカUS\$ 8.16US\$ 1.70 カナダUS\$ 8.50US\$ 1.70 マカオUS\$ 4.76US\$ 1.70 シンガポールUS\$ 8.16US\$ 1.70 マレーシアUS\$ 6.46US\$ 1.70 タイUS\$ 8.84US\$ 1.70 クレジットカード安心決済, PayPal, LINE Pay, Alipay WOOD SONG US\$ 23.80 WOOD SONG US\$ 23.80 WOOD SONG US\$ 34.00 WOOD SONG US\$ 27.20 WOOD SONG US\$ 27.20 WOOD SONG US\$ 34.00	2018-10-19 14:22:05	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427011966705322, "perplexity": 344.9762805440238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512400.59/warc/CC-MAIN-20181019124748-20181019150248-00491.warc.gz"}
http://nrich.maths.org/public/leg.php?code=-135&cl=4&cldcmpid=8055	# Search by Topic #### Resources tagged with Conversion from cartesian to polar forms similar to Polar Bearings: Filter by: Content type: Stage: Challenge level: ### There are 2 results Broad Topics > Coordinates and Coordinate Geometry > Conversion from cartesian to polar forms ### An Introduction to Polar Coordinates ##### Stage: 4 and 5 This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the. . . . ### Maltese Cross ##### Stage: 5 Challenge Level: Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.	2014-08-20 08:59:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6304580569267273, "perplexity": 1290.0701951559288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500801235.4/warc/CC-MAIN-20140820021321-00151-ip-10-180-136-8.ec2.internal.warc.gz"}
http://mizar.uwb.edu.pl/version/current/html/nbvectsp.html	:: $n$-dimensional Binary Vector Spaces :: by Kenichi Arai and Hiroyuki Okazaki :: :: Copyright (c) 2013-2018 Association of Mizar Users Lm1: for n being non zero Nat for D being non empty set for p being Element of n -tuples_on D holds ( len p = n & p is Element of D * ) proof end; theorem Th1: :: NBVECTSP:1 for n being non zero Element of NAT for u1, v1, w1 being Element of n -tuples_on BOOLEAN holds Op-XOR ((Op-XOR (u1,v1)),w1) = Op-XOR (u1,(Op-XOR (v1,w1))) proof end; definition let n be non zero Element of NAT ; func XORB n -> BinOp of () means :Def1: :: NBVECTSP:def 1 for x, y being Element of n -tuples_on BOOLEAN holds it . (x,y) = Op-XOR (x,y); existence ex b1 being BinOp of () st for x, y being Element of n -tuples_on BOOLEAN holds b1 . (x,y) = Op-XOR (x,y) proof end; uniqueness for b1, b2 being BinOp of () st ( for x, y being Element of n -tuples_on BOOLEAN holds b1 . (x,y) = Op-XOR (x,y) ) & ( for x, y being Element of n -tuples_on BOOLEAN holds b2 . (x,y) = Op-XOR (x,y) ) holds b1 = b2 proof end; end; :: deftheorem Def1 defines XORB NBVECTSP:def 1 : for n being non zero Element of NAT for b2 being BinOp of () holds ( b2 = XORB n iff for x, y being Element of n -tuples_on BOOLEAN holds b2 . (x,y) = Op-XOR (x,y) ); definition let n be non zero Element of NAT ; func ZeroB n -> Element of n -tuples_on BOOLEAN equals :: NBVECTSP:def 2 n \|-> 0; correctness coherence ; proof end; end; :: deftheorem defines ZeroB NBVECTSP:def 2 : for n being non zero Element of NAT holds ZeroB n = n \|-> 0; definition let n be non zero Element of NAT ; func n -BinaryGroup -> strict addLoopStr equals :: NBVECTSP:def 3 correctness coherence ; ; end; :: deftheorem defines -BinaryGroup NBVECTSP:def 3 : for n being non zero Element of NAT holds n -BinaryGroup = addLoopStr(# (),(XORB n),() #); theorem Th2: :: NBVECTSP:2 for n being non zero Element of NAT for u1 being Element of n -tuples_on BOOLEAN holds Op-XOR (u1,()) = u1 proof end; theorem Th3: :: NBVECTSP:3 for n being non zero Element of NAT for u1 being Element of n -tuples_on BOOLEAN holds Op-XOR (u1,u1) = ZeroB n proof end; registration let n be non zero Element of NAT ; coherence proof end; end; registration cluster -> boolean for Element of Z_2; coherence for b1 being Element of Z_2 holds b1 is boolean by BSPACE:3; end; registration let u, v be Element of Z_2; identify u + v with u 'xor' v; compatibility u + v = u 'xor' v proof end; identify u * v with u '&' v; compatibility u * v = u '&' v proof end; end; definition let n be non zero Element of NAT ; func MLTB n -> Function of [: the carrier of Z_2,():],() means :Def4: :: NBVECTSP:def 4 for a being Element of BOOLEAN for x being Element of n -tuples_on BOOLEAN for i being set st i in Seg n holds (it . (a,x)) . i = a '&' (x . i); existence ex b1 being Function of [: the carrier of Z_2,():],() st for a being Element of BOOLEAN for x being Element of n -tuples_on BOOLEAN for i being set st i in Seg n holds (b1 . (a,x)) . i = a '&' (x . i) proof end; uniqueness for b1, b2 being Function of [: the carrier of Z_2,():],() st ( for a being Element of BOOLEAN for x being Element of n -tuples_on BOOLEAN for i being set st i in Seg n holds (b1 . (a,x)) . i = a '&' (x . i) ) & ( for a being Element of BOOLEAN for x being Element of n -tuples_on BOOLEAN for i being set st i in Seg n holds (b2 . (a,x)) . i = a '&' (x . i) ) holds b1 = b2 proof end; end; :: deftheorem Def4 defines MLTB NBVECTSP:def 4 : for n being non zero Element of NAT for b2 being Function of [: the carrier of Z_2,():],() holds ( b2 = MLTB n iff for a being Element of BOOLEAN for x being Element of n -tuples_on BOOLEAN for i being set st i in Seg n holds (b2 . (a,x)) . i = a '&' (x . i) ); definition let n be non zero Element of NAT ; func n -BinaryVectSp -> VectSp of Z_2 equals :: NBVECTSP:def 5 ModuleStr(# (),(XORB n),(),(MLTB n) #); correctness coherence ModuleStr(# (),(XORB n),(),(MLTB n) #) is VectSp of Z_2 ; proof end; end; :: deftheorem defines -BinaryVectSp NBVECTSP:def 5 : for n being non zero Element of NAT holds n -BinaryVectSp = ModuleStr(# (),(XORB n),(),(MLTB n) #); registration let n be non zero Element of NAT ; coherence ; end; registration let n be non zero Element of NAT ; cluster -> finite for Subspace of n -BinaryVectSp ; coherence for b1 being Subspace of n -BinaryVectSp holds b1 is finite proof end; end; theorem Th4: :: NBVECTSP:4 for n being Nat holds Sum (n \|-> ()) = 0. Z_2 proof end; theorem Th5: :: NBVECTSP:5 for m being non zero Element of NAT for x being FinSequence of Z_2 for v being Element of Z_2 for j being Nat st len x = m & j in Seg m & ( for i being Nat st i in Seg m holds ( ( i = j implies x . i = v ) & ( i <> j implies x . i = 0. Z_2 ) ) ) holds Sum x = v proof end; theorem Th6: :: NBVECTSP:6 for m, n being non zero Element of NAT for L being the carrier of () -valued FinSequence for j being Nat st len L = m & m <= n & j in Seg n holds ex x being FinSequence of Z_2 st ( len x = m & ( for i being Nat st i in Seg m holds ex K being Element of n -tuples_on BOOLEAN st ( K = L . i & x . i = K . j ) ) ) proof end; theorem Th7: :: NBVECTSP:7 for m, n being non zero Element of NAT for L being the carrier of () -valued FinSequence for Suml being Element of n -tuples_on BOOLEAN for j being Nat st len L = m & m <= n & Suml = Sum L & j in Seg n holds ex x being FinSequence of Z_2 st ( len x = m & Suml . j = Sum x & ( for i being Nat st i in Seg m holds ex K being Element of n -tuples_on BOOLEAN st ( K = L . i & x . i = K . j ) ) ) proof end; theorem Th8: :: NBVECTSP:8 for m, n being non zero Element of NAT st m <= n holds ex A being FinSequence of n -tuples_on BOOLEAN st ( len A = m & A is one-to-one & card (rng A) = m & ( for i, j being Nat st i in Seg m & j in Seg n holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) ) proof end; theorem Th9: :: NBVECTSP:9 for m, n being non zero Element of NAT for A being FinSequence of n -tuples_on BOOLEAN for B being finite Subset of () for l being Linear_Combination of B for Suml being Element of n -tuples_on BOOLEAN st rng A = B & m <= n & len A = m & Suml = Sum l & A is one-to-one & ( for i, j being Nat st i in Seg n & j in Seg m holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) holds for j being Nat st j in Seg m holds Suml . j = l . (A . j) proof end; theorem Th10: :: NBVECTSP:10 for m, n being non zero Element of NAT for A being FinSequence of n -tuples_on BOOLEAN for B being finite Subset of () st rng A = B & m <= n & len A = m & A is one-to-one & ( for i, j being Nat st i in Seg n & j in Seg m holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) holds B is linearly-independent proof end; theorem Th11: :: NBVECTSP:11 for n being non zero Element of NAT for A being FinSequence of n -tuples_on BOOLEAN for B being finite Subset of () for v being Element of n -tuples_on BOOLEAN st rng A = B & len A = n & A is one-to-one holds ex l being Linear_Combination of B st for j being Nat st j in Seg n holds v . j = l . (A . j) proof end; theorem Th12: :: NBVECTSP:12 for n being non zero Element of NAT for A being FinSequence of n -tuples_on BOOLEAN for B being finite Subset of () st rng A = B & len A = n & A is one-to-one & ( for i, j being Nat st i in Seg n & j in Seg n holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) holds Lin B = ModuleStr(# the carrier of (), the addF of (), the ZeroF of (), the lmult of () #) proof end; theorem Th13: :: NBVECTSP:13 for n being non zero Element of NAT ex B being finite Subset of () st ( B is Basis of () & card B = n & ex A being FinSequence of n -tuples_on BOOLEAN st ( len A = n & A is one-to-one & card (rng A) = n & rng A = B & ( for i, j being Nat st i in Seg n & j in Seg n holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) ) ) proof end; theorem Th14: :: NBVECTSP:14 for n being non zero Element of NAT holds ( n -BinaryVectSp is finite-dimensional & dim () = n ) proof end; registration let n be non zero Element of NAT ; coherence by Th14; end; theorem :: NBVECTSP:15 for n being non zero Element of NAT for A being FinSequence of n -tuples_on BOOLEAN for C being Subset of () st len A = n & A is one-to-one & card (rng A) = n & ( for i, j being Nat st i in Seg n & j in Seg n holds ( ( i = j implies (A . i) . j = TRUE ) & ( i <> j implies (A . i) . j = FALSE ) ) ) & C c= rng A holds ( Lin C is Subspace of n -BinaryVectSp & C is Basis of (Lin C) & dim (Lin C) = card C ) proof end;	2019-05-22 12:40:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5995808839797974, "perplexity": 2124.990068336375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256812.65/warc/CC-MAIN-20190522123236-20190522145236-00398.warc.gz"}
https://mathhelpboards.com/threads/convergence-in-topological-spaces-singh-example-4-1-1.27142/	Convergence in Topological Spaces ... Singh, Example 4.1.1 ... ... Peter Well-known member MHB Site Helper I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 4, Section 4.1: Sequences ... I need help in order to fully understand Example 4.1.1 ... In the above example from Singh we read the following: " ... ...no rational number is a limit of a sequence in $$\displaystyle \mathbb{R} - \mathbb{Q}$$ ... ... " My question is as follows: Why exactly is it the case that no rational number a limit of a sequence in $$\displaystyle \mathbb{R} - \mathbb{Q}$$ ... ... " Help will be appreciated ... Peter ===================================================================================== It may help readers of the above post to have access to Singh's definition of a neighborhood and to the start of Chapter 4 (which gives the relevant definitions) ... so I am providing the text as follows: Hope that helps ... Peter Last edited: GJA Well-known member MHB Math Scholar Hi Peter , Let $S=\{x_{n}\}_{n=1}^{\infty}$ be a sequence in $\mathbb{R}\setminus\mathbb{Q}$; i.e., a sequence of irrational numbers. Then the complement of $S$, $\mathbb{R}\setminus S$, is an open set in $\mathbb{R}_{c}$ containing the rationals. According to Definition 4.1.2, it follows that no point from $\mathbb{Q}$ could be the limit of $S$. Peter Well-known member MHB Site Helper Hi Peter , Let $S=\{x_{n}\}_{n=1}^{\infty}$ be a sequence in $\mathbb{R}\setminus\mathbb{Q}$; i.e., a sequence of irrational numbers. Then the complement of $S$, $\mathbb{R}\setminus S$, is an open set in $\mathbb{R}_{c}$ containing the rationals. According to Definition 4.1.2, it follows that no point from $\mathbb{Q}$ could be the limit of $S$. Hi GJA ... .. Thanks so much for the help ... Peter	2020-06-04 05:30:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8181449770927429, "perplexity": 514.0052103484281}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347439019.86/warc/CC-MAIN-20200604032435-20200604062435-00424.warc.gz"}
https://www.jobilize.com/algebra/section/distributive-property-real-numbers-algebra-essentials-by-openstax?qcr=www.quizover.com	# 1.1 Real numbers: algebra essentials (Page 6/35) Page 6 / 35 As we can see, neither subtraction nor division is associative. ## Distributive property The distributive property states that the product of a factor times a sum is the sum of the factor times each term in the sum. $a\cdot \left(b+c\right)=a\cdot b+a\cdot c$ This property combines both addition and multiplication (and is the only property to do so). Let us consider an example. Note that 4 is outside the grouping symbols, so we distribute the 4 by multiplying it by 12, multiplying it by –7, and adding the products. To be more precise when describing this property, we say that multiplication distributes over addition. The reverse is not true, as we can see in this example. Multiplication does not distribute over subtraction, and division distributes over neither addition nor subtraction. A special case of the distributive property occurs when a sum of terms is subtracted. $a-b=a+\left(-b\right)$ For example, consider the difference $\text{\hspace{0.17em}}12-\left(5+3\right).\text{\hspace{0.17em}}$ We can rewrite the difference of the two terms 12 and $\text{\hspace{0.17em}}\left(5+3\right)\text{\hspace{0.17em}}$ by turning the subtraction expression into addition of the opposite. So instead of subtracting $\text{\hspace{0.17em}}\left(5+3\right),$ we add the opposite. $12+\left(-1\right)\cdot \left(5+3\right)$ Now, distribute $\text{\hspace{0.17em}}-1\text{\hspace{0.17em}}$ and simplify the result. $\begin{array}{ccc}\hfill 12-\left(5+3\right)& =\hfill & 12+\left(-1\right)\cdot \left(5+3\right)\hfill \\ & =\hfill & 12+\left[\left(-1\right)\cdot 5+\left(-1\right)\cdot 3\right]\hfill \\ & =\hfill & 12+\left(-8\right)\hfill \\ & =\hfill & 4\hfill \end{array}$ This seems like a lot of trouble for a simple sum, but it illustrates a powerful result that will be useful once we introduce algebraic terms. To subtract a sum of terms, change the sign of each term and add the results. With this in mind, we can rewrite the last example. $\begin{array}{ccc}\hfill 12-\left(5+3\right)& =& 12+\left(-5-3\right)\\ & =& 12+\left(-8\right)\hfill \\ & =& 4\hfill \end{array}$ ## Identity properties The identity property of addition states that there is a unique number, called the additive identity (0) that, when added to a number, results in the original number. $a+0=a$ The identity property of multiplication states that there is a unique number, called the multiplicative identity (1) that, when multiplied by a number, results in the original number. $a\cdot 1=a$ For example, we have $\text{\hspace{0.17em}}\left(-6\right)+0=-6\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}23\cdot 1=23.\text{\hspace{0.17em}}$ There are no exceptions for these properties; they work for every real number, including 0 and 1. ## Inverse properties The inverse property of addition states that, for every real number a , there is a unique number, called the additive inverse (or opposite), denoted− a , that, when added to the original number, results in the additive identity, 0. $a+\left(-a\right)=0$ For example, if $\text{\hspace{0.17em}}a=-8,$ the additive inverse is 8, since $\text{\hspace{0.17em}}\left(-8\right)+8=0.$ The inverse property of multiplication holds for all real numbers except 0 because the reciprocal of 0 is not defined. The property states that, for every real number a , there is a unique number, called the multiplicative inverse (or reciprocal), denoted $\text{\hspace{0.17em}}\frac{1}{a},$ that, when multiplied by the original number, results in the multiplicative identity, 1. $a\cdot \frac{1}{a}=1$ For example, if $\text{\hspace{0.17em}}a=-\frac{2}{3},$ the reciprocal, denoted $\text{\hspace{0.17em}}\frac{1}{a},$ is $\text{\hspace{0.17em}}-\frac{3}{2}\text{\hspace{0.17em}}$ because $a\cdot \frac{1}{a}=\left(-\frac{2}{3}\right)\cdot \left(-\frac{3}{2}\right)=1$ ## Properties of real numbers The following properties hold for real numbers a , b , and c . Addition Multiplication Commutative Property $a+b=b+a$ $a\cdot b=b\cdot a$ Associative Property $a+\left(b+c\right)=\left(a+b\right)+c$ $a\left(bc\right)=\left(ab\right)c$ Distributive Property $a\cdot \left(b+c\right)=a\cdot b+a\cdot c$ Identity Property There exists a unique real number called the additive identity, 0, such that, for any real number a $a+0=a$ There exists a unique real number called the multiplicative identity, 1, such that, for any real number a $a\cdot 1=a$ Inverse Property Every real number a has an additive inverse, or opposite, denoted –a , such that $a+\left(-a\right)=0$ Every nonzero real number a has a multiplicative inverse, or reciprocal, denoted $\text{\hspace{0.17em}}\frac{1}{a},$ such that $a\cdot \left(\frac{1}{a}\right)=1$ x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0 x exposent4+4x exposent3+8x exposent2+4x+1=0 HERVE How can I solve for a domain and a codomains in a given function? ranges EDWIN Thank you I mean range sir. Oliver proof for set theory don't you know? Inkoom find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad factoring polynomial find general solution of the Tanx=-1/root3,secx=2/root3 find general solution of the following equation Nani the value of 2 sin square 60 Cos 60 0.75 Lynne 0.75 Inkoom when can I use sin, cos tan in a giving question depending on the question Nicholas I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks. John I want to learn the calculations where can I get indices I need matrices Nasasira hi Raihany Hi Solomon need help Raihany maybe provide us videos Nasasira Raihany Hello Cromwell a Amie What do you mean by a Cromwell nothing. I accidentally press it Amie you guys know any app with matrices? Khay Ok Cromwell Solve the x? x=18+(24-3)=72 x-39=72 x=111 Suraj Solve the formula for the indicated variable P=b+4a+2c, for b Need help with this question please b=-4ac-2c+P Denisse b=p-4a-2c Suddhen b= p - 4a - 2c Snr p=2(2a+C)+b Suraj b=p-2(2a+c) Tapiwa P=4a+b+2C COLEMAN b=P-4a-2c COLEMAN like Deadra, show me the step by step order of operation to alive for b John A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5) and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes. The sequence is {1,-1,1-1.....} has	2019-09-20 08:33:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 32, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8431875705718994, "perplexity": 755.4619403806935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573908.70/warc/CC-MAIN-20190920071824-20190920093824-00201.warc.gz"}
http://www.aber.ac.uk/en/postgrad/faqs/taughtfaqs/faq2/	# What is involved in a taught course? A taught Master’s degree usually requires 12 months of study involving two “taught” semesters and a final “self-study” semester. The taught element will include traditional lectures and seminars. Some programmes will also involve group discussions and case study analysis. During the self-study semester, you will need to complete a supervised dissertation and/or project. Assessment of the degree can take various forms such as unseen written examinations, assessed coursework, group project work etc.	2018-02-22 14:55:59	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8011252880096436, "perplexity": 4944.028669926299}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814124.25/warc/CC-MAIN-20180222140814-20180222160814-00126.warc.gz"}
https://mathoverflow.net/questions/230423/nonseparable-hilbert-spaces	# Nonseparable Hilbert spaces Being nonseparable Banach space is in fact nothing special: one meets the first examples in the standard functional analysis course, when one learns about $$\ell^p$$ or $$L^p[0,1]$$ spaces-these spaces are nonseparable when $$p=\infty$$. However I spoke to one person which said to me that nonseparable Hilbert spaces are rather exotic and in "real life" one rarely come across them. Here I list some examples when I came across nonseparable Hilbert spaces—but to be honest, none of them have truly convinced me about the importance of those spaces: 1. When $$A$$ is a $$C^$$-algebra, then if $$A$$ is separable then $$A$$ embeds into $$B(H)$$ where $$H$$ is separable—nevertheless sometimes one is interested in so called universal representation $$\pi_u$$ of $$A$$ (one feature of this representation is that any state of $$\pi_u(A)$$ is in fact a vector state). The Hilbert space of this representation is hardly ever separable. 2. When $$Q$$ denotes the Calkin algebra (the quotient of $$B(H)$$ by compact operators) one can show that it cannot be represented on separable Hilbert space (this is very elegant argument: there is an uncountable family of infinite subsets of $$\mathbb{N}$$ such that the intersection of any two members of this family is finite—this gives an uncountable family of mutually disjoint projections in the quotient—in fact this argument applies also to $$\ell^{\infty}/c_0$$). 3. There is a notion of almost periodic function on $$\mathbb{R}$$ (this can be generalized to other groups but let us stick to this particular case) and the space of almost periodic functions contains all functions of the type $$e_s(t)=e^{ist}$$. One can introduce the scalar product on the linear span of all $$e_s$$-s and those function turns out to be mutually orthogonal. Completing one obtains a nonseparable Hilbert spaces. 4. There is a notion of tensor product of Hilbert spaces in particular the so called complete tensor product which is due to von Neumann. This construction yields a nonseparable Hilbert space when the tensored family is infinite. But as far as I know, in most application one restricts to the preferred so called $$C_0$$-sequence thus obtaining the separable space (this is some sort of choosing a ,,stabilization''). That's all-I don't know any other examples of situations when one is faced with nonseparable Hilbert spaces-so ,,huge'' for the first sight spaces as Fock spaces used in second quantization or $$L^2$$ over some infinite dimensional spaces with Gaussian measures are all separable. So I would like to ask: What are some interesting examples of nonseparable Hilbert spaces which you have ever met? Forgive me if my question is too vaque but I tried to give some motivation around it. • Related to your example 2: there was some recent work of Ando and Haagerup on ultrapowers arxiv.org/abs/1212.5457 which I think made use of spatial representations of these ultrapowers at various points. Just as with the Calkin, faithful representations of these ultrapowers must live on non-separable Hilbert spaces Feb 7, 2016 at 0:02 • If you take the universal representation of the weyl algebra instead of the fock representation you get a non-separable Hilbert space Feb 7, 2016 at 2:50 • Although as Nik Weaver says, it may be possible to sidestep the use of nonseparable Hilbert spaces almost always, I quite like the GNS Hilbert space associated to a tracial ultrapower (starting with a no principal ultrafilter) of a type II_1 factor. These things are genuinely useful for studying the structure of factors, and are nonseparable. Aug 2, 2020 at 19:37 • Hilbert spaces of the same cardinal characteristics are isomorphic. However, there are interesting ways of how Hilbert spaces are applied. Some geometrically minded topologists may enjoy large metrizable spaces and may like them to be embedded in (non-separable) Hilbert spaces. Oct 19, 2020 at 19:53 To the contrary, my feeling is that nonseparable Hilbert spaces are in some sense artifacts and can almost always be avoided. And more generally, to your comment about nonseparable Banach spaces being "nothing special", most of the nonseparable Banach spaces one meets in practice are duals of separable Banach spaces, and therefore are weak separable. Algebras of almost periodic functions, and their noncommutative analogs, the CCR algebras, are rare examples of interesting nonseparable Banach spaces which are not dual spaces, but even here one is mainly interested in regular representations, which are determined by their behavior on separable subalgebras (the span of the functions $e_s$ with $s$ rational, say). @Yemon Choi: the answer to your comment is too long for a reply so putting it in another answer to the original question – hope this is not off-topic for the original post. The space $${\mathbb{R}}^{[0,1]}$$ and the $$L^2$$ functions on it arise not as a model of how the brain actually works, but as a counterfactual, pathological example. In neuroscience, a sensory stimulus (for example an image seen by the eye) causes a pattern of activity in a set of neurons, known as a neural code for the stimulus. We can model this activity using a real-valued function $$f(n,s)$$, where $$n$$ represents the neuron, and $$s$$ represents the stimulus. (The same holds for artificial neural networks used in machine learning.) The actual brain of course contains a finite number of neurons, but to make mathematical models it is useful to consider them as drawn randomly from a continuous probability distribution, and the same for the stimuli. A classical hypothesis of neuroscience, originally inspired by information theory, holds that the brain would operate most efficiently if neural responses were independent. However if you require the responses of all neurons be independent whatever the stimulus, you soon end up considering examples like neurons as random functions drawn from $${\mathbb{R}}^{[0,1]}$$ with the product Gaussian measure, and $$f(n,s)$$ as evaluation at the point $$s\in[0,1]$$. This is a pathological model, as such functions are almost surely discontinuous, and it is also not consistent with experimental brain recordings. You are correct that stochastic processes are a much better model for how the brain actually works, and brain recordings actually let us further constrain the smoothness of these stochastic processes. Nevertheless it is still useful to consider counterfactual models such as the above. The paper I cited deals with the smoothness constraints, and does not yet mention the counterfactual, but a forthcoming revision will. • why not use white noise instead ?encyclopediaofmath.org/index.php/White_noise_analysis Jan 3, 2019 at 17:21 • Thanks for the suggestion! I'm not familiar with white noise analysis, but if I understand correctly random samples of white noise will almost surely not be real-valued functions, but rather distributions which can't be evaluated at a point. In which case it's not clear how to apply them as a model. Jan 3, 2019 at 18:07 • @YemonChoi's comment on another answer that is here being replied to. Apr 21 at 17:11 Example 3 of almost-periodic functions. It is more natural than the description given in the OP. Harald Bohr defined almost periodic functions in order to study Dirichlet series as applicable in analytic number theory. Bohr's definition. A bounded measurable function $$f : \mathbb R \to \mathbb R$$ is almost periodic iff the set of translates $$\{T_s f : s \in \mathbb R\}$$ is relatively compact in $$L^\infty$$, where $$(T_s f)(x) = f(x-s)$$ Equivalently: for every $$\epsilon > 0$$ there exists $$s \in \mathbb R$$ so that for all $$x \in \mathbb R$$ $$\|f(x)-f(x-s)\| \le \epsilon .$$ The almost periodic functions naturally come with an "invariant mean" $$M(f) = \lim_{T \to \infty}\frac{1}{2T}\int_{-T}^T f(x)\;dx \tag1$$ and from that we get an inner product $$\langle f,g \rangle = \lim_{T \to \infty}\frac{1}{2T}\int_{-T}^T f(x)\overline{g(x)}\;dx \tag2$$ and a seminorm $$\\|f\\| = \lim_{T \to \infty}\frac{1}{2T}\int_{-T}^T \|f(x)\|^2\;dx \tag3$$ The space of almost perioduc function is non-separable according to seminorm (3). So of course its completion is a nonseparable Hilbert space. In fact, Bohr's definition may be used on general locally compact groups. Indeed, Bohr's invariant mean on such groups was developed before Haar's invariant integral. The invariant mean $$M(f)$$ is obtained as follows. If $$f$$ is a bounded almost periodic function on a group $$G$$, then the closed (according to uniform convergence) convex hull of the set of all translates $$T_s f$$ contains exactly one constant. Define $$M(f)$$ to be that constant. • Small historical nitpick: I believe (but am happy to be corrected if I am wrong) that the definition you give up is actually Bochner's reformulation of Bohr's original description, which was in terms of approximate periods. Then the extension of Bochner's definition to general locally compact groups is, I think, often attributed to von Neumann. Aug 2, 2020 at 14:45 • There was a nice semi-survey article on various notions of AP by Fink jstor.org/stable/2028429 Aug 2, 2020 at 14:46 Some simple arguments (which, to be honest, I'm also not completely convinced of) about the non-necessity of non-separable Hilbert spaces. If "in real life" means working into a given Hilbert space, and not meditating over the category of all Hilbert spaces, then we should admit that there is a lot of not used room, thus maybe unnecessary, in a non-separable Hilbert space $$H$$. Even if a Hilbert basis has been fixed, and one identifies the space with $$\ell_2(S)$$ for a set $$S$$, any element of $$H$$, any sequence of elements, any separable subspace, are already included in some $$\ell_2(D)$$ for a countable subset $$D\subset S$$. Any closed subspace $$V$$ of $$H$$ splits into an orthogonal sum of subspaces $$V_j\subset \ell_2(D_j)$$, for a partition of $$S$$ into countable subsets $$\{D_j\}_{j\in I}$$. Any bounded operator $$T$$ on $$H$$ splits into such an orthogonal sum of invariant subspaces, and $$T$$ in a sense is just a family of independent operators on $$\ell_2:=\ell_2(\mathbb{N})$$. So it seems there is nothing new in the structure of a non-separable Hilbert space, that cannot be described by means of the already rich structure of $$\ell_2$$ (which on the contrary is really a new object wrto the finite dimensional $$\ell_2^n$$, or at least a new way of speaking about them). • Doesn't this same argument show that one doesn't need infinite-dimensional Hilbert spaces, since they can be split into a (completed, as you implicitly do) orthogonal sum of finite-dimensional subspaces? Apr 21 at 17:10 • Not really: you can split $\ell_2$ into a Hilbert sum of $\ell_2^n$, but there is not such a “countable to finite” decomposition for more structured objects . For instance a pair $(V, \ell_2)$ with V a closed subspace, or an operator on $\ell_2$, etc. On the contrary the analog “uncountable to countable” direct sum decomposition is possible. That was what I meant in the last sentence. Apr 22 at 12:13 • I think you can decompose a closed subspace, no? Just choose a bunch of lines decomposing $V$, and then a bunch decomposing $V^\perp$. Most of your other kinds of structured data (sequence, separable subspace, …) seem to be inherently privileging countability / separability; I could certainly replace them with finitary analogues (e.g., tuple in place of sequence). The case of a single operator is much more convincing … but I think that I could replace it by representations which have no non-trivial, separable, invariant subspaces, right? Apr 22 at 13:03 • Yes, but in the example of the subspace I was referring to the standard orthogonal basis (check what I wrote above about $\ell_2(S)$ for a precise statement). Apr 22 at 13:24 Let A = $$\mathbb{R}^{[0,1]}$$, with a product Gaussian measure - in other words, consider an independent Gaussian-distributed random variable for each real number in $$[0,1]$$. The space $$L^2[A]$$ is non separable. Believe it or not, this example has come up in neuroscience. • I'd rather not have to believe it... can you provide a reference? Dec 31, 2018 at 11:49 • Well, it's actually in my own research, not yet published - you can find a preliminary version that does not mention separability or this particular example here - for the math, skip straight to appendix 2 at the end. For a consideration of non-separable Hilbert spaces in machine learning, see here. Dec 31, 2018 at 16:03 • Where in Appendix 2? One would normally expect to be taking some kind of Gaussian process indexed by ${\bf R}$ equipped with its usual metric, so (admittedly speaking as a non-probabilist) I find it surprising that one would need the space A that you mention Dec 31, 2018 at 22:38 Your example #4 might be of profound relevance to the understanding of the difference be quantum physics and classical physics. In quantum physics, the state of a system is described by a vector in a Hilbert space (its space of states). When two systems are associated, the space of states of the resulting system is the von Neumann tensor product of the spaces of states of the associated two systems. Simple quantum systems have separable space of states. Now one big question in physics is why elementary particles such as electrons behave according to the laws of quantum physics while macroscopic objects which are built out of quantum objects behave differently, i.e. according to classical physics. The question is all the more important for measurement devices that interact with quantum objects while behaving classically. They operate projective measurements on the quantum systems thus breaking the unitary evolution of quantum systems. The answer might lie in the difference in properties of spaces of states of the microscopic and macroscopic systems : the very large (infinite for all practical purposes) number of tensor products of elementary particle spaces of states needed to build the space of states of macroscopic objects such as measurement devices could be non separable for the reason you mention. This non-separability could open the door to different properties including non unitary evolution. Your question thus triggers another one: what are the properties of non-separable Hilbert spaces that are built out of infinite von Neumann tensor products of separable Hilbert space? • This answer seems to presuppose some similarity between "macroscopic vs. microscopic" and "non-separable vs. separable". I don't see any similarity beyond "bigger vs. smaller". Oct 19, 2020 at 19:30 • The space of States of a 2 state system (a spin 1/2, photon polarisation, a q-bit etc:) is $\mathbb{C}^2$. If you have $N$ such system, the resulting space of states is $\mathbb{C}^{2^N}$, the dimension of which is $2^N$ which is countable, so the space of states is separable. This is no more the case in the macroscopic limit $N\rightarrow \infty$ where the dimension is not countable anymore ($2^\mathbb{N}$). In this case a macroscopic set of 2-state quantum states would have a non separable space of states. This is the link. 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My idea is to take the "working horse" of ... 450 views ### Construction of “vol of vol” How do you construct something that lets you buy "vol of vol"? not necessarily for VIX, but any particular stock or index.	2015-05-25 17:30:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.866331934928894, "perplexity": 1820.035450702663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928562.33/warc/CC-MAIN-20150521113208-00209-ip-10-180-206-219.ec2.internal.warc.gz"}
http://www.cjcbill.com/2020/01/30/legohouse/	# Lego House Posted by Bill on January 30, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 [Verse 1] G D Em I'm gonna pick up the pieces, D G and build a lego house D Em D when things go wrong we can knock it down G D Em My three words have two meanings, D G there's one thing on my mind D Em D It's all for you [Pre-chorus] G D Em D And it's dark in a cold December, but I've got ya to keep me warm G D Em If (you're) broken I'll mend ya and keep you sheltered from the storm D that's raging on [Chorus] G D Em I'm out of touch, I'm out of love G D I'll pick you up when you're getting down G/B C D G And out of all these things I've done I think I love you better now G D Em I'm out of sight, I'm out of mind G D I'll do it all for you in time G/B C D G And out of all these things I've done I think I love you better now [Verse 2] G D Em I'm gonna paint you by numbers D G and colour you in D Em D if things go right we can frame it, and put you on a wall G D Em And it's so hard to say it but I've been here before G D Em and I'll surrender up my heart D and swap it for yours [Chorus] G D Em I'm out of touch, I'm out of love G D I'll pick you up when you're getting down G/B C D G And out of all these things I've done I think I love you better now G D Em I'm out of sight, I'm out of mind G D I'll do it all for you in time G/B C D G And out of all these things I've done I think I love you better now [Bridge] Em D C Don't hold me down D C D I think my braces are breaking and it's more than I can take [Pre-chorus] G D Em D And it's dark in a cold December, but I've got ya to keep me warm G D Em and if you're broke I'll mend ya and keep you sheltered from the storm D that's raging on [Chorus] G D Em I'm out of touch, I'm out of love G D I'll pick you up when you're getting down G/B C D G And out of all these things I've done I think I love you better now G D Em I'm out of sight, I'm out of mind G D I'll do it all for you in time G/B C D G And out of all these things I've done I think I love you better now G D Em I'm out of touch, I'm out of love G D I'll pick you up when you're getting down G/B C D G And out of all these things I've done I think I love you better now G D Em I'm out of sight, I'm out of mind G D I'll do it all for you in time G/B C D G And out of all these things I've done I think I love you better now [Outro] G D Em I'm out of touch, I'm out of love G D I'll pick you up when you're getting down G/B C D G And out of all these things I've done I will love you better now	2023-03-27 09:34:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17748160660266876, "perplexity": 7330.368120741269}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00678.warc.gz"}
https://www.studysmarter.us/textbooks/physics/physics-for-scientists-and-engineers-a-strategic-approach-with-modern-physics-4th/work-heat-and-the-first-law-of-thermodynamics/q-49-of-gas-are-at-and-a-pressure-of-how-much-work-must-be-d/	Q. 49 Expert-verified Found in: Page 545 ### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics Book edition 4th Author(s) Randall D. Knight Pages 1240 pages ISBN 9780133942651 ### Answers without the blur. Just sign up for free and you're in. # of gas are at and a pressure of . How much work must be done on the gas to compress it to one-third of its initial volume at (a) constant temperature and (b) constant pressure? (c) Show both processes on a single diagram. a) Amount of work must be done on the gas to compress it to one-third of its initial volume at constant temperature is b) Amount of work must be done on the gas to compress it to one-third of its initial volume at constant pressure is c) The diagrammatic representation of diagram is See the step by step solution Amount of gas Temperature Pressure ## Step 2: Explanation (Part a) In an isothermal process, the work is given by We know that the final volume is one third of the initial volume; substituting that and the other information we are given, we have ## Step 3: Final Answer (Part a) Hence, the amount of work must be done on the gas to compress it to one-third of its initial volume at constant temperature is Amount of gas Temperature Pressure ## Step 5: Explanation (Part b) (b) In an isobaric process the work is given by In our case, knowing the relation between the initial and final volumes, we have We therefore need to find the initial volume from the state equation, we have We can therefore substitute in the expression for the work and find that ## Step 6: Final Answer (Part b) In our numerical case, we will have Amount of work must be done on the gas to compress it to one-third of its initial volume at constant pressure is, Amount of gas Temperature Pressure ## Step 8: Explanation (Part c) Below a sketch of such a graph is given: ## Step 9: Final Answer (Part c) Therefore the graph of has been shown. ### Want to see more solutions like these? Sign up for free to discover our expert answers ## Recommended explanations on Physics Textbooks 94% of StudySmarter users get better grades.	2022-12-10 08:17:40	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8215581774711609, "perplexity": 1026.0224595043264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00358.warc.gz"}
http://gmatclub.com/forum/help-needed-in-interpreting-the-chart-139253.html	Find all School-related info fast with the new School-Specific MBA Forum It is currently 25 Jul 2016, 03:11 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # help needed in interpreting the chart! Author Message Manager Joined: 23 Aug 2011 Posts: 83 Followers: 3 Kudos [?]: 155 [0], given: 13 help needed in interpreting the chart! [#permalink] ### Show Tags 20 Sep 2012, 06:04 Found this in kaplan's GMAT practice test. I was confused by the explanation provided below by the kaplan. "The Southwest spent $20 million total, while the Northwest spent$30 million total. The stem tells us to assume that all of the expenses in each region are in the same proportion as in the Northeast, which means that the Southwest spent of what the Northwest spent on each category. (The ratio of their total expenses—$20 to$30 million—gives us the proportion.) Since the Northwest spent $1.25 million on janitorial staff, Southwest spent of that on janitorial staff, which would be about$800,000 and certainly less than the next closest answer choice, $1.2 million." I am not able to understand the bolded part in the explanation.How they have deduced this from the graph? Attachments File comment: Graph Capture.PNG [ 35.06 KiB \| Viewed 1132 times ] _________________ Whatever one does in life is a repetition of what one has done several times in one's life! If my post was worth it, then i deserve kudos Kaplan GMAT Prep Discount Codes Math Revolution Discount Codes Optimus Prep Discount Codes Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 3255 Followers: 1091 Kudos [?]: 4772 [0], given: 53 Re: help needed in interpreting the chart! [#permalink] ### Show Tags 24 Sep 2012, 23:00 Expert's post Dear Conty911: I am happy to help with this. This indeed is a tricky chart. First, just an overview of the chart. The left-most scale (up to 120) and column (with regions) gives the overall national picture. Then, they want to give us the breakdown for just one region, the Northwest. The first grey trapezoid is meant to suggest --- that one piece of the left column, the "Northwest", is blown up to be the whole of the middle column. The middle scale (up to 30) and the column shows the breakdown within the Northeast of the four major areas of expenses: how much the Northwest spends on each of the following (a) packing material, (b) ingredients, (c) equipment, and (d) staff. The second grey trapezoid is meant to suggest --- they are blowing up just the "staff" portion of the middle column, to show its breakdown in the column on the right. The right most scale (up to 6) and the column shows the breakdown of expenses by various categories of staff, various types of employees. It's a funny chart, because it "zooms in" to one segment, and then "zooms in" again to a segment of the first zooming. OK, now to your question: the bold text. The vertical size of the segments on the left-most scale tells us the relative amount of money spent in each region. The height of each segment, as measured by the adjacent scale, tells the amount of money in the corresponding region. Look at the left-most scale. The sections are evenly space, and each 20 units, and the second from the top is labeled "100", so the top must be 120. We can use the position of the top and bottom lines of each region-segment to calculate the amount of money spent in that region. The Northwest goes from the top (120) down to exactly halfway between 80 and 100, which has to be 90. From 90 to 120 --- that's 30 for the Northwest. This is corroborated by the middle chart, which shows only the Northwest, and goes up to 30. The Southwest goes from exactly halfway between 60 and 80 (i.e. 70) to exactly halfway between 80 and 100 (i.e. 90) ---- 70 to 90 --- that's 20 for the Southwest. Numbers are in millions of dollars, so that's$30M and $20M respectively. Does this make sense? Mike _________________ Mike McGarry Magoosh Test Prep Intern Joined: 19 May 2012 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 16 Re: help needed in interpreting the chart! [#permalink] ### Show Tags 27 Sep 2012, 05:41 Good explanation. Thank you!. mikemcgarry wrote: Dear Conty911: I am happy to help with this. This indeed is a tricky chart. First, just an overview of the chart. The left-most scale (up to 120) and column (with regions) gives the overall national picture. Then, they want to give us the breakdown for just one region, the Northwest. The first grey trapezoid is meant to suggest --- that one piece of the left column, the "Northwest", is blown up to be the whole of the middle column. The middle scale (up to 30) and the column shows the breakdown within the Northeast of the four major areas of expenses: how much the Northwest spends on each of the following (a) packing material, (b) ingredients, (c) equipment, and (d) staff. The second grey trapezoid is meant to suggest --- they are blowing up just the "staff" portion of the middle column, to show its breakdown in the column on the right. The right most scale (up to 6) and the column shows the breakdown of expenses by various categories of staff, various types of employees. It's a funny chart, because it "zooms in" to one segment, and then "zooms in" again to a segment of the first zooming. OK, now to your question: the bold text. The vertical size of the segments on the left-most scale tells us the relative amount of money spent in each region. The height of each segment, as measured by the adjacent scale, tells the amount of money in the corresponding region. Look at the left-most scale. The sections are evenly space, and each 20 units, and the second from the top is labeled "100", so the top must be 120. We can use the position of the top and bottom lines of each region-segment to calculate the amount of money spent in that region. The Northwest goes from the top (120) down to exactly halfway between 80 and 100, which has to be 90. From 90 to 120 --- that's 30 for the Northwest. This is corroborated by the middle chart, which shows only the Northwest, and goes up to 30. The Southwest goes from exactly halfway between 60 and 80 (i.e. 70) to exactly halfway between 80 and 100 (i.e. 90) ---- 70 to 90 --- that's 20 for the Southwest. Numbers are in millions of dollars, so that's$30M and \$20M respectively. Does this make sense? Mike Re: help needed in interpreting the chart! [#permalink] 27 Sep 2012, 05:41 Similar topics Replies Last post Similar Topics: IR Resources, Need help 0 03 Sep 2014, 12:04 1 Graphical Interpretation 5 19 Jul 2012, 18:45 IR- Graphical Interpretation 4 14 Jul 2012, 14:51 IR_Graphical Interpretation 4 05 Jul 2012, 20:17 Need Help _Gmat Pill 0 21 Jun 2012, 14:40 Display posts from previous: Sort by	2016-07-25 10:11:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43210160732269287, "perplexity": 8310.873460438575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824226.33/warc/CC-MAIN-20160723071024-00319-ip-10-185-27-174.ec2.internal.warc.gz"}
https://zbmath.org/?q=an:1200.35202	## On the semiclassical 3D Neumann Laplacian with variable magnetic field.(English)Zbl 1200.35202 Let $$\Omega$$ be an open bounded subset of $$\mathbb R^3$$ with a smooth boundary $$\partial\Omega$$. For a vector potential $$\mathbf A\in C^{\infty}(\overline\Omega,\mathbb R^3)$$ and $$h>0$$, it is introduced $$\beta=\nabla\times\mathbf A$$ and the quadratic form defined for all $$\psi\in H^1(\Omega,\mathbb C)$$ by $$q^h_{\mathbf A}(\psi)=\int_{\Omega}\|(ih\nabla+\mathbf A)\psi\|^2dx$$. One of the author’s interests is the lowest eigenvalue $$\lambda_1^h(\mathbf A)$$ of the associated self-adjoint operator, i.e., the Neumann realization of $$(ih\nabla+\mathbf A)^2$$ on $$\Omega$$ denoted by $$P^h_{\mathbf A}$$. Let us formulate the main theorem of the paper. First, we give some preliminaries. For $$x\in\partial\Omega$$, it is introduced $$\hat\beta(x)=\sigma(\theta(x))\\|\beta(x)\\|$$, where $$\theta(x)$$ is defined by $$\\|\beta(x)\\|\sin\theta(x)=\beta\cdot\nu(x)$$ with $$\nu(x)$$ the inward pointing normal at $$x$$ and $$\sigma(\theta(x))$$ denotes the bottom of the spectrum of an operator which is explicitly defined in the paper. The author assumes that $$\hat\beta$$ admits a non-degenerate minimum at $$x_0$$ and that at this point $$0<\theta(x_0)<\frac{\pi}2$$. Further, denote by $$\boldsymbol\Theta_{\beta}$$ the Hessian matrix at $$x_0$$, namely, $\boldsymbol\Theta_{\beta}(r,s)=\frac 12\partial^2_r\hat\beta(x_0)r^2+\frac 12 \partial^2_{rs}\hat\beta(x_0)(sr+rs)+\frac 12\partial^2_s\hat\beta(x_0)s^2$ and introduce the operator $$\tilde{\boldsymbol\Theta}_{\beta}=\boldsymbol\Theta_{\beta} (D_{\tau},\frac{\tau}{\sin\theta})$$. Under the above restrictions, the author proves the main theorem which states that there exists $$d\in\mathbb R$$ such that for all $$n\in\mathbb N^*$$ there exists $$D_n>0$$ and $$h_n>0$$ such that, for $$0<h\leq h_n$$, there exists at least one eigenvalue $$\mu_n$$ of $$P^h_{\mathbf A}$$ such that $\|\mu_n-[\hat\beta(x_0)h+C^{\beta,K}(x_0)\\|\beta(x_0)\\|^{\frac 12} h^{\frac 32}+(\gamma_n(\tilde{\boldsymbol\Theta}_{\beta})+d)h^2]\|\leq D_nh^{\frac 52},$ where $$\gamma_n(\tilde{\boldsymbol\Theta}_{\beta})$$ is the $$n$$-th eigenvalue of $$\tilde{\boldsymbol\Theta}_{\beta}$$ and $$C^{\beta,K}(x_0)$$ is a quantity defined in the paper. The theorem admits the following corollary: under the same restrictions as above, there exist $$d\in\mathbb R$$, $$D_1>0$$, and $$h_1>0$$ such that, for $$0<h\leq h_1$$, $\lambda_1^h(\mathbf A)\leq \hat\beta(x_0)h+C^{\beta,K}(x_0)\\|\beta(x_0)\\|^{\frac 12}h^{\frac 32}+(\gamma_1(\tilde{\boldsymbol\Theta}_{\beta})+d)h^2+D_1h^{\frac 52}.$ ### MSC: 35P15 Estimates of eigenvalues in context of PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Full Text:	2022-08-09 01:12:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9855293035507202, "perplexity": 79.40450144335433}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570879.37/warc/CC-MAIN-20220809003642-20220809033642-00128.warc.gz"}
https://wenda.latexstudio.net/answer/2635/4077.html	## 如何将旋转后的两表格放在同一页 2020-10-27 15:46发布 ## 编译环境操作系统 * [10 ] Windows 7/8/10 * [ ] macOS * [ ] Linux 若需勾选，请把[ ]改成[x] Tex发行版 * [2019 ] TexL... ## 编译环境操作系统 * [10 ] Windows 7/8/10 * [ ] macOS * [ ] Linux 若需勾选，请把[ ]改成[x] Tex发行版 * [2019 ] TexLive 年份 * [ ] MikTeX 版本号 * [ ] CTeX 若需勾选，请把[ ]改成[x] ## 我的问题如何将旋转后的两个表格放到同一页中？ \documentclass{article} \usepackage{geometry} \geometry{left=1in,right=1in,top=1in,bottom=1in} \renewcommand{\baselinestretch}{2.0} \usepackage[pdftex]{graphicx}\usepackage{xcolor} \usepackage{setspace} \usepackage{rotating} \usepackage{float} \begin{document} This paragraph are used to test the width of pages. The question is that why two table are not listed in the same page while there are sufficient blank. \begin{sidewaystable}[] \setlength{\abovecaptionskip}{0pt} \setlength{\belowcaptionskip}{10pt} \caption{Results 1} \label{Table1} %\[2mm] \centering \begin{tabular}{lccccccc} \hline Parameter & $\epsilon=0.2$ & $\epsilon=0.4$ & $\epsilon=0.6$ & $\epsilon=0.8$ & $\epsilon=1$ & $\epsilon=2$ & $\epsilon=3$ \\ \hline $C=0.3$ & (1.5250,11.7501) & (1.5250,11.7501) & (1.5250,11.7501) & (1.5243,11.7574) & (1.8463,6.3090) & (1.8388,6.3194) & (1.7228,8.8904) \\ $C=0.4$ & (1.5759,10.9927) & (1.5253,11.7461) & (1.5250,11.749) & (1.6935,9.3009) & (1.8460,6.3092) & (1.8388,6.3194) & (1.7788,8.0317) \\ $C=0.7$ & (1.7011,8.7172) & (1.7471,8.0070) & (1.7931,7.2965) & (1.8532,6.3053) & (1.8451,6.3101) & (1.8384,6.3200) & (1.7788,8.0317) \\ $C=1$ & (1.7012,8.7172) & (1.7471,8.0069) & (1.8415,6.3149) & (1.8522,6.3051) & (1.8851,5.8759) & (1.8500,6.1850) & (1.7788,8.0317) \\ $C=2$ & (1.8163,6.4367) & (1.8308,6.3363) & (1.8426,6.3133) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=3$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=4$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=5$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=10$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=20$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=50$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=100$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.185) & (1.8049,7.4512) \\ \hline \end{tabular} \end{sidewaystable} \begin{sidewaystable}[] \setlength{\abovecaptionskip}{0pt} \setlength{\belowcaptionskip}{10pt} \caption{Results 2} \label{Table2} %\[2mm] \centering \begin{tabular}{lccccccc} \hline Parameter & $\epsilon=0.2$ & $\epsilon=0.4$ & $\epsilon=0.6$ & $\epsilon=0.8$ & $\epsilon=1$ & $\epsilon=2$ & $\epsilon=3$ \\ \hline $C=0.3$ & (1.5250,11.7501) & (1.5250,11.7501) & (1.5250,11.7501) & (1.5243,11.7574) & (1.8463,6.3090) & (1.8388,6.3194) & (1.7228,8.8904) \\ $C=0.4$ & (1.5759,10.9927) & (1.5253,11.7461) & (1.5250,11.749) & (1.6935,9.3009) & (1.8460,6.3092) & (1.8388,6.3194) & (1.7788,8.0317) \\ $C=0.7$ & (1.7011,8.7172) & (1.7471,8.0070) & (1.7931,7.2965) & (1.8532,6.3053) & (1.8451,6.3101) & (1.8384,6.3200) & (1.7788,8.0317) \\ $C=1$ & (1.7012,8.7172) & (1.7471,8.0069) & (1.8415,6.3149) & (1.8522,6.3051) & (1.8851,5.8759) & (1.8500,6.1850) & (1.7788,8.0317) \\ $C=2$ & (1.8163,6.4367) & (1.8308,6.3363) & (1.8426,6.3133) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=3$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=4$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=5$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=10$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=20$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=50$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.1850) & (1.8049,7.4512) \\ $C=100$ & (1.8163,6.4367) & (1.8435,6.0980) & (1.8707,5.7592) & (1.8980,5.4204) & (1.9252,5.0816) & (1.8500,6.185) & (1.8049,7.4512) \\ \hline \end{tabular} \end{sidewaystable} \end{document} 1条回答	2021-02-27 15:09:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 7148.544764353724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 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https://msp.org/pjm/2019/298-1/p05.xhtml	Vol. 298, No. 1, 2019 Recent Issues Vol. 300: 1 Vol. 299: 1 2 Vol. 298: 1 2 Vol. 297: 1 2 Vol. 296: 1 2 Vol. 295: 1 2 Vol. 294: 1 2 Vol. 293: 1 2 Online Archive Volume: Issue: The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals Heegaard Floer homology of $L$-space links with two components Beibei Liu Vol. 298 (2019), No. 1, 83–112 DOI: 10.2140/pjm.2019.298.83 Abstract We compute different versions of link Floer homology ${HFL}^{-}$ and $\stackrel{̂}{HFL}$ for any $L$-space link with two components. The main approach is to compute the $h$-function of the filtered chain complex which is determined by Alexander polynomials of all sublinks of the $L$-space link. As an application, the Thurston norm of its complement is explicitly determined by Alexander polynomials of the link and its components. Keywords $L$-space links, link Floer homology, Thurston polytopes Primary: 57M99	2019-07-23 01:11:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7440389394760132, "perplexity": 4338.094220008278}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528635.94/warc/CC-MAIN-20190723002417-20190723024417-00210.warc.gz"}
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Describe the domain and range ikk gp bbab bd baa qttt bp jnlo nk nj ggie jp hr ech ca dd debf bh ca cfc efd jbed kdg jc fbce llcd jfgh al cccb kef ec	2022-05-27 00:42:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29863616824150085, "perplexity": 1495.8383222977648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00350.warc.gz"}
https://unitedtravelbooking.com/site/03a3ca-solubility-product-of-baso4	The solid phases of aqion are listed here in two tables (together with the solubility product in form of pK sp = - log 10 K sp):. Source(s): solubility baso4: https://tr.im/FXkuX 0 0 The solubility of … Example 1. Please show your work and explain, thank you! What is the solubility of BaSO4 in water, in moles per litre? The solubility product (Ksp) of BaSO4 is 1.1x10^-10 at 25C. What is the solubility of BaSO4? The expression is called the Solubility Product Constant (Ksp) Example: BaSO4 is a slightly soluble salt. Table sorted by formula; Table sorted by mineral name; Only a subset of these minerals enter the equilibrium calculations by default. An equilibrium constant is the ratio of the concentration of the products of a reaction divided by the concentration of the reactants once the reaction has reached equilibrium. If it was in g dm-3, or any other concentration units, you would first have to convert it into mol dm-3. Click hereto get an answer to your question ️ If the solubility product of BaSO4 is 1.5 × 10^-10 in water. Its solubility product is $$1.08 \times 10^{−10}$$ at 25°C, so it is ideally suited for this purpose because of its low solubility when a “barium milkshake” is consumed by a patient. 5.5 10-11 mol L-1 I am going to assume that you are given the solubility of an ionic compound in mol dm-3. Solubility Product Constants K sp at 25°C. According to the difference mentioned above, solubility and solubility product are two … The solubility product constant (K sp) is the equilibrium constant for a solid that dissolves in an aqueous solution.All of the rules for determining equilibrium constants continue to apply. What is the solubility of BaSO4 in water, in moles per litre? Given that the solubility product, Ksp, for BaSO4 is 1.1 x 10^-10, calculate the solubility of BaSO4 in moles per liter and grams per liter. The solubility product, Ksp, for BaSO4 is 1.1 × 10–10. 1.0 × 10–5 mol L–1 c. 2.1 × … Calculating solubility products from solubilities. Its solubility, in moles per litre, is. When a reasonable quantity of solid BaSO4 is mixed with water, only a very small amount will dissolve to produce Ba +2 (aq) and SO 4 –2 (aq) The pathway of the sparingly soluble salt can be easily monitored by x-rays. The key difference between solubility and solubility product is that the solubility describes the dissolution of a substance in a solvent whereas the solubility product describes the mathematical product of the dissolved ion concentrations raised to the power of their stoichiometric coefficients.. This experiment was design to determine solubility product of lead sulphate and barium sulphate using conductivity measurement and direct titration.by conductivity measurement the solubilites of PbSO4 and BaSO4 were 1.3430 × 10-8 mol2 dm-6 and 1.2589 The solubility product, Ksp, for BaSO4 is 1.1 * 10-10. 5.5 × 10–11 mol L–1 b. Select one: a. Select one: a.	2021-05-11 01:44:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4209952652454376, "perplexity": 3155.7439003211184}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991553.4/warc/CC-MAIN-20210510235021-20210511025021-00350.warc.gz"}
https://ai.stackexchange.com/tags/reference-request/hot?filter=month	# Tag Info ## Hot answers tagged reference-request 4 These are known as adversarial attacks, and the specific examples that are misclassified are known as adversarial examples. There is a reasonably large body of work on finding adversarial examples, and on making CNNs more robust (i.e. less prone to these attacks). An example is the DeepFool algorithm, which can be used to find perturbations of data which ... 4 The 2015 article Cyclical Learning Rates for Training Neural Networks by Leslie N. Smith gives some good suggestions for finding an ideal range for the learning rate. The paper's primary focus is the benefit of using a learning rate schedule that varies learning rate cyclically between some lower and upper bound, instead of trying to choose a single fixed ... 4 The visualisation can be found in The need for small learning rates on large problems. This paper by D. Randall Wilson and Tony R. Martinez from 2001 investigates the role of learning rates in gradient descent algorithms. In general, different algorithms assign different meaning to the same word 'learning rate'. For example, the learning rate in a gradient ... 3 Those examples are called Adversarial Examples. I think it is important to understand why a CNN can be "tricked" like that: We often expect human-like behavior when a model has a human-like performance. That is similar for CNNs. We expect they decide like we do, i.e. we look for the shape of objects. However, as various experiments on common CNN ... 3 If you look into the top conferences on machine learning and neural networks, such as NeurIPS, ICLR, and ICML, you will find many papers related to neural networks and deep learning, given that these are still very hot/promising topics. However, occasionally, you will find accepted papers that do not involve neural networks. Here's a small list of them that ... 2 Yes, there is research on this topic. The field that studies it is known as affective computing (AC). Emotion recognition seems to be a specific problem in affective computing, i.e. the recognition of emotions, while AC is also concerned with giving machines the ability to convey emotions (in fact, this paper differentiates the two). There's also sentiment ... 1 I suggest you look into link prediction. I have had good luck with the StellarGraph library. They have several algorithms implemented, including GCN. Link prediction is a binary classification problem. Given two nodes, $v_i$ and $v_j$, does there exist a link between them? Using a library like StellarGraph will also produce node embeddings while performing ... Only top voted, non community-wiki answers of a minimum length are eligible	2021-02-24 18:03:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6283480525016785, "perplexity": 924.237235017832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178347293.1/warc/CC-MAIN-20210224165708-20210224195708-00414.warc.gz"}
https://physics.stackexchange.com/questions/330915/metamaterial-snells-law-and-fermat-principle	# Metamaterial : Snell's law and Fermat principle How do we deduce Snell's law using Fermat's principal in case of metamaterials? Metamaterials have negative refractive index. This makes the refracted ray of light bend on same side of normal as incident ray. But according to Fermat principle, the light could have taken a shorter path. Without the light 'bending backward', it would have a path which took lesser time, like one of the possible path I have shown below in red. What is the "travel time" of a beam of light in a medium with negative refractive index? Do you save time by traveling a greater distance? Time = distance/speed, and speed = c/n. When $n<0$, the part of the trajectory in the meta-material will contribute "negative time" to the over all travel time of the beam.	2019-11-18 14:47:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.597716748714447, "perplexity": 813.4035891952763}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669795.59/warc/CC-MAIN-20191118131311-20191118155311-00040.warc.gz"}
https://www.physicsforums.com/threads/can-someone-help-me-answer-my-homework.246239/	# Can someone help me answer my homework? 1. Jul 22, 2008 ### jlmf_inc Can someone help me answer my homework?? 1. List the elements of the given set that are: (a)integers (b)irrational numbers {0,-10,50,22/7,0.538,square root of 7,1.233..., -1/3, 3 roots of 2} 2. Find the indicated set if: A={1,2,3,4,5,6,7} B={2,4,6,8} C={7,8,9,10} (a) A intersect B intersect C (b) A intersect (B Union C) 3. Factor the following expression completely: (a) x^-3/2 +2x^-1/2 + x^1/2 (b) 3x^2(4x-12)^2 + x^3(2)(4x-12)(4) (c) x^3 + 2x^2 + x please response to the questions ASAP tnx.. 2. Jul 22, 2008 ### Defennder Re: Can someone help me answer my homework?? What do you understand by the terms "integers" and "irrational numbers"? What elements do the sets $$A \cap B$$ and $$A \cup B$$ comprise of? Simply find the common factors of the individual terms and factor them out. 3. Jul 22, 2008 ### HallsofIvy Staff Emeritus Re: can anyone help me answer as i comapre mine to you?? 4. Jul 25, 2008 ### jlmf_inc Re: Can someone help me answer my homework?? 1a) 0,-10,50 1b)22/7, square root of 7, 3 roots of 2 2a)Associative 2b)Commutative 3a) null/empty set 3b) 2,4,6,7 4a) (-2,1] 4b) (-1,infinite) 5.) 5-10t+t^3+-t^2-t^4 6.) (6y-7)(y+3) 7.) (4z-3)(4z-3) 8.) X^-3/2(X+1)^2 9.) 16x^2(x-3)(5x-9) 10.) x(x+1)^2 5. Jul 25, 2008 ### cristo Staff Emeritus Re: Can someone help me answer my homework?? 6. Jul 25, 2008 ### HallsofIvy Staff Emeritus Re: Can someone help me answer my homework?? You are going to make us go back and forth between your list of questions above and answers here? it would have been far simpler to copy your previous post and then add your answer to it! 22/7 is NOT an irrational number. Since it is a fraction it is by definition rational. By the way, I would interpret "3 roots of 2" as "3 times the square root of 2" but I suspect here you mean "cube root of 2". ??? Problem 2 asked you to find 2 sets! You "answers" give properties of operations! Problem 3 asked you to factor expressions! There are no problems 4- 10 in your original post! How can we now tell you if these are correct answers if you tell us what the problems are? 7. Jul 25, 2008 ### Diffy Re: Can someone help me answer my homework?? Well either way we know it is irrational. But you are right 3 roots of 2 is an odd way of saying either option.	2016-10-26 19:59:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43369561433792114, "perplexity": 2446.1741160967317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720972.46/warc/CC-MAIN-20161020183840-00457-ip-10-171-6-4.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/309334/active-character-hangs-within-tikz	Active ! Character Hangs within TikZ The MWE below However, when the ! is active within the \hcancel compilation seems to hang? The desired output is: but if I uncomment the code intend to produce the the last canceled term the compilation seems to hang. Code: \documentclass{article} \usepackage{amsmath} \usepackage{xcolor,etoolbox} \usepackage{tikz} \usetikzlibrary{calc} \makeatletter %% https://tex.stackexchange.com/questions/299798/make-characters-active-via-macro-in-math-mode \newcommand{\DeclareMathActive}[2]{% % #1 is the character, #2 is the definition \expandafter\edef\csname keep@#1@code\endcsname{\mathchar\the\mathcode#1 } \begingroup\lccode~=#1\relax \lowercase{\endgroup\def~}{#2}% \AtBeginDocument{\mathcode#1="8000 }% } \newcommand{\std}[1]{\csname keep@#1@code\endcsname} \patchcmd{\newmcodes@}{\mathcode\-\relax}{\std@minuscode\relax}{}{\ddt} \AtBeginDocument{\edef\std@minuscode{\the\mathcode-}} \makeatother \DeclareMathActive{!}{\mathclose{\textcolor{blue}{\std{!}}}} %% https://tex.stackexchange.com/questions/20643/diagonal-strikeout-starting-too-low-and-ending-too-high \newcommand{\hcancel}[5]{% \tikz[baseline=(tocancel.base)]{ \node[inner sep=0pt,outer sep=0pt] (tocancel) {#1}; \draw[red] ($(tocancel.south west)+(#2,#3)$) -- ($(tocancel.north east)+(#4,#5)$); }% }% \begin{document} Active ! works: $3!$ Cancel with non-active ! works: \hcancel{$3\std{!}$}{-3pt}{0pt}{3pt}{0pt} \medskip Combine cancel with active ! hangs: %\hcancel{$3!$}{-3pt}{0pt}{3pt}{0pt}% <-- This hangs!! \end{document} • As part of its workarounds connected to babel, TikZ changes the meaning of the active ! to \tikz@nonactiveexlmark, which expands to a ! with category code 12, which then expands to \tikz@nonactiveexlmark, which… May 12, 2016 at 21:30 You're being very unlucky. The French module for babel makes ! into an active character, in order to implement the French conventions about punctuation. Therefore, since the beginning, TikZ takes precautions against this, because it uses ! in its syntax. Therefore it assigns a new meaning to the active ! in case French is being used. It essentially does \begingroup\lccode~=! \lowercase{\endgroup\def~}{\tikz@nonactiveexlmark} \edef\tikz@nonactiveexlmark{\string!} Similarly for ;, : and \|. So in a tikzpicture environment the assigned meaning \mathclose{\textcolor{blue}{\std{!}}} is lost. Worse, when ! is math active, TeX enters an infinite loop: • ! in math mode is treated as if it were active, so it is replaced by its meaning \tikz@nonactiveexlmark • \tikz@nonactiveexlmark is replaced by its meaning, a ! with category code 12 • ! in math mode is treated as if it were active, so it is replaced by its meaning \tikz@nonactiveexlmark Since you're not using French, you can redefine \tikz@nonactiveexlmark do to the same as the math active !. \documentclass{article} \usepackage{amsmath} \usepackage{xcolor,etoolbox} \usepackage{tikz} \usetikzlibrary{calc} \makeatletter %% http://tex.stackexchange.com/questions/299798/make-characters-active-via-macro-in-math-mode \newcommand{\DeclareMathActive}[2]{% % #1 is the character, #2 is the definition \expandafter\edef\csname keep@#1@code\endcsname{\mathchar\the\mathcode#1 } \begingroup\lccode~=#1\relax \lowercase{\endgroup\def~}{#2}% \AtBeginDocument{\mathcode#1="8000 }% } \def\tikz@nonactiveexlmark{\mathclose{\textcolor{blue}{\std{!}}}} \newcommand{\std}[1]{\csname keep@#1@code\endcsname} \patchcmd{\newmcodes@}{\mathcode\-\relax}{\std@minuscode\relax}{}{\ddt} \AtBeginDocument{\edef\std@minuscode{\the\mathcode-}} \makeatother \DeclareMathActive{!}{\mathclose{\textcolor{blue}{\std{!}}}} %% http://tex.stackexchange.com/questions/20643/diagonal-strikeout-starting-too-low-and-ending-too-high \newcommand{\hcancel}[5]{% \tikz[baseline=(tocancel.base)]{ \node[inner sep=0pt,outer sep=0pt] (tocancel) {#1}; \draw[red] ($(tocancel.south west)+(#2,#3)$) -- ($(tocancel.north east)+(#4,#5)$); }% }% \begin{document} Active ! works: $3!$ Cancel with non-active ! works: \hcancel{$3\std{!}$}{-3pt}{0pt}{3pt}{0pt} \medskip Combine cancel with active ! hangs: \hcancel{$3!$}{-3pt}{0pt}{3pt}{0pt}% <-- This hangs!! \end{document} The text now tells a lie. ;-) • Wow, those darn French go and make things complicated! :-) I would have thought since these are active only in math mode, that I would not run into such problems - oh, well. So, what would I need to do for the other characters, especially the : and\|. Don't think I'll have an issue with the ;. May 12, 2016 at 22:09 • @PeterGrill The same as for !, I'd say. 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https://bookdown.org/mandyyao98/bookdown-demo-master/lecture-7-statistical-inference-for-proportions.html	# 9 Lecture 7: Statistical inference for proportions ## 9.1 When is a single proportion used? • Proportions are very commonly used in medical research to summarize dichotomous variables • Some examples include estimation of: • response rate in a survey • prevalence of a disease • sensitivity, specificity, positive and negative predictive values for a diagnostic test ### 9.1.1 Central Limit Theorem • From the text by Moore and McCabe: “… as the sample size increases, the distribution of $$\bar Y$$ becomes closer to a normal distribution… no matter what the population distribution may be, as long as the population has a finite standard deviation σ. This famous fact of probability theory is called the central limit theorem. For large sample size n, we can regard $$\bar Y$$ as having the $$N(\mu,\sigma/\sqrt n)$$ distribution” ### 9.1.2 Application of the Central Limit Theorem: Normal Approximation to the Binomial Distribution • In Lecture 3, we also studied expressions that showed that the sum of a series of random variables follows a Normal distribution (like the mean does) • Recall that the sum of the number of successes in each of n Bernoulli trials follows a Binomial distribution with mean nπ and variance nπ(1-π) • Let us look at the sampling distribution when n=5, 20 and 50 and π=0.1, 0.5 and 0.9 ### 9.1.6 Sampling distribution of a Binomial variable • We can see that as the sample size increases, the mean of the sampling distribution tends towards a normal distribution with mean nπ and variance nπ(1-π) • This is true even for extreme values of π close to 0 or 1, though values closer to π=0.5 will approach normality at a smaller sample size ### 9.1.7 Normal approximation to the Binomial distribution Recall that the probability density function for the Binomial distribution is given by $Pr\{X=k\|n,p\}=\frac{n!}{k!(n-k)!}\pi^k(1-\pi)^{n-k}$ • This expression can get very cumbersome to evaluate (especially with no computer) as n increases. Also tables of the Binomial distribution will not list all values of n • Therefore, as n increases, we can use the normal approximation to the Binomial distribution instead to determine the Binomial density of cumulative probability • How large should n be? The normal approximation to the binomial distribution is fairly good if both np and n(1−p) are at least equal to 5, where p is the sample proportion. ### 9.1.8 Example 4: Estimating the number of true positives • In low resource settings, hospitals often rely on smear microscopy for TB diagnosis despite its poor sensitivity • The GeneXpert test is a point-of-care nucleic acid amplification test that has revolutionized testing for pulmonary TB . • It has a sensitivity of 70% in TB cases missed by smear • In a particular clinic setting, it is estimated that 150 TB patients are missed annually by smear microscopy. • What is the probability that at least 100 of them are correctly identified by GeneXpert? ### 9.1.9 Example 4: Applying a continuity correction • X=Number of positive results on GeneXpert out of 150 patients • P(X ≥ 100 \| Binomial(n=150, π=0.7)) = P(X ≥ 99.5 \|Binomial(n=150, π=0.7)) ≈ P(X ≥ 99.5 \|Normal(mean=105,variance=32)) = 1 – pnorm(99.5,mean=105,sd=sqrt(32)) = 0.83 ### 9.1.10 Continuity correction • The change from 100 to 99.5 is called the continuity correction. It is used to make the normal approximation slightly more accurate. • If n is large the continuity correction may not have a huge impact when estimating the probability of being greater than or the probability of being less than a certain value. • However, we absolutely need the continuity correction to estimate the probability of being exactly equal to a certain value. This is because this probability is always zero under a normal distribution ### 9.1.11 Example • What is the probability that exactly 100 patients will be detected by GeneXpert? • P(X = 100 \| Binomial(n=150, π=0.7)) = P(99.5 ≤ X ≤ 100.5 \|Binomial(n=150, π=0.7)) ≈ P(99.5 ≤ X ≤ 100.5 \| Normal(mean=105,variance=32)) = pnorm(100.5,mean=105,sd=sqrt(32)) – pnorm(99.5,mean=105,sd=sqrt(32)) = 0.05 ### 9.1.12 Comparison with the exact results based on the Binomial distribution • What is the probability that at least 100 or exactly 100 patients will be detected by GeneXpert? • The exact results based on the Binomial distribution are given by P(X ≥ 100 \| Binomial(n=150, π=0.7)) = 1- pbinom(99,150,0.7) = 0.84 P(X = 100 \| Binomial(n=150, π=0.7)) = dbinom(100,150,0.7) = 0.05 We can see they are very close to the approximate values based on the Normal distribution ### 9.1.13 Example: Asymptomatic colonization with Clostridium difficile • Clostridium difficile diarrhea (CDAD) is the most common nosocomial diarrhea, prolonging hospitalization and for some patients leading to colectomy or death. • Patients are typically exposed to CD in a hospital setting, but may also become exposed in the community • After exposure, an estimated 2/3 patients become asymptomatic carriers. There is a concern that asymptomatic colonization may play a greater role in spreading CD infection than previously thought • A large, multi-centre Canadian study examined the risk of asymptomatic colonization at admission to hospital. They also examined various risk factors for asymptomatic colonization, including patient and pathogen characteristics (Kong et al, Am J Inf Control, 2015) ### 9.1.14 Asymptomatic colonization with Clostridium difficile: Selected results • Out of 5232 subjects, 212 were asymptomatically colonized at admission • Among the 212 asymptomatically colonized patients: • 136 were hospitalized during the previous year • 98 used antibiotics in the previous 8 weeks • 1 used a probiotic in the previous 8 weeks • Among 209 of the 212 patients, information was available on the strain of Clostridium difficile • 33 patients carried the hypervirulent NAP1 strain ### 9.1.15 Example: Asymptomatic colonization with Clostridium difficile 1. Estimate the proportion of asymptomatically colonized patients together with a 95% confidence interval. What is your interpretation of the 95% confidence interval? 2. Estimate the proportion of patients with each risk factor and calculate a 95% confidence interval in each case. 3. It has previously been reported that 50% of patients who develop Clostridium difficile infection carry the NAP1 strain. Carry out a hypothesis test to determine whether patients who are asymptomatically colonized at admission have a comparable risk of carrying the NAP1 strain. ### 9.1.16 Methods for means vs. proportions • You will notice that all of the methods we studied earlier for means, have a counterpart for proportions • As in the case of inference for means, we can distinguish between the following themes • Methods for a single proportion and for the difference between proportions • Frequentist inference and Bayesian inference • Hypothesis tests and confidence intervals ### 9.1.17 Analogy between calculation of means and proportions Means Proportions Sample data $$(x_1,x_2,...,x_n)$$ $$(x_1,x_2,...,x_n)=(1,0,...,1)$$ Estimator of the population mean $$\bar x=\frac{\sum_{i=1}^nx_1}{n}$$ $$p=\frac{\sum_{i=1}^nx_1}{n}=\frac{\#\space of\space 1's}{n}$$ Estimator of the population standard deviation $$sd=\sqrt{\frac{\sum_{i=1}^n(x_i-\bar x)^2}{n-1}}$$ $$sd=\sqrt{p(1-p)}$$ 95% confidence interval for the population mean $$\bar x\pm 1.96\frac{sd}{\sqrt n}$$ $$p\pm 1.96\frac{sd}{\sqrt n}$$ ### 9.1.18 Frequentist confidence interval for a single proportion • Confidence interval for a large sample using the normal approximation • Confidence interval for a small sample using the exact Binomial distribution ### 9.1.19 Large sample confidence interval for a proportion • Assume a large random sample of a dichotomous variable X of size n is drawn from a population with unknown proportion of successes (π) • Let p be the observed proportion of successes • Then an approximate level $$(1-\alpha)$$% confidence interval for $$\pi$$ is given by $p\pm Z_{1-\frac{\alpha}{2}}\times\sqrt{\frac{p(1-p)}{n}}$ where $$Z_{1-\alpha/2}$$ is the upper $$1-\alpha/2$$ standard Normal quantile • This confidence interval has the usual frequentist interpretation that it was obtained using a procedure about which we have (1-α)% confidence. Across (1-α)% of repeated studies the confidence interval will include π. However, we do not know if the particular interval at hand includes the true value of π • Notice that we used the Normal distribution quantile to construct the confidence interval. We were able to do this because: • We are relying on the central limit theorem that tells us that even though the variable of interest (X) follows a Bernoulli distribution, the sample mean is normally distributed provided the sample size is large enough. • The sample proportion automatically provides an estimate for the sample standard deviation. Therefore we do not need to provide a separate estimate for the standard deviation and introduce another source of uncertainty. As a result we do not need to rely on the t-distribution ### 9.1.20 Exact confidence interval for a proportion • When the sample size is small or when p is close to 0 or 1, the normal approximation based on the central limit theorem can be poor • In such cases, it may be preferable to use the exact method for obtaining a confidence interval which is based directly on the binomial distribution. • This method is more difficult to calculate, though the availability of fast computers today makes this irrelevant ### 9.1.21 Clopper-Pearson exact confidence interval for a proportion (Biometrika, 1934) • Let x be the observed number of successes and n be the number of trials. Let X denote a Binomial(π,n) random variable • The two-sided (1-α)% exact confidence interval is given by the interval $$(p_L, p_H)$$ such that $\sum_{k=0}^x{n \choose k}p_H^k(1-p_H)^{n-k}=\frac{\alpha}{2}$ $\sum_{k=x}^n{n \choose k}p_L^k(1-p_L)^{n-k}=\frac{\alpha}{2}$ ### 9.1.23 R function to obtain a confidence interval for a small proportion • The R function binom.test carries out an exact binomial test and also provides an exact confidence interval binom.test(x, n, p = 0.5, alternative = c("two.sided", "less", "greater"), conf.level = 0.95) • The user has to provide the number of successes and the sample size among other arguments ### 9.1.24 Exact confidence interval for a proportion • Following is a comparison of exact and approximate confidence intervals. The gain in accuracy drops off with increasing sample size. ### 9.1.25 How do you determine if your sample is sufficiently large? • Some common rules of thumb: • Both n(1-p) and np should be greater than 5 (greater than 10 according to some text books) • $$np\pm3\sqrt{np(1-p)}$$ should lie between 0 and n • In general if the distribution is shifted towards 0 or 1 and if confidence intervals calculated by the usual method give negative lower or upper bounds, it is better to use the exact method. ### 9.1.26 Example: Zero proportion • The standard contrast agent used by radiologists over a long period has been shown to cause a serious reaction in about 15 of every 10,000 patients exposed to it • A new contrast agent is introduced. Based on the first report of its use in 167 patients, no patient had a serious reaction. Do we have enough evidence to say that the new contrast agent is at least as safe to use as the old one? • The thumb rules on the previous slide would lead us to conclude an exact confidence interval is required • The risk of an adverse reaction with the old reagent is 15/10000 = 0.0015 • The point estimate of the risk with the new contrast agent is 0 • The 95% one-sided exact confidence interval is (0, 0.0178) • This tells us that the observed data could possibly arise from situations where the true value of π ranges from 0 to 0.0178. This includes situations where the true risk of 0.0015 • It also means we cannot eliminate the possibility that the risk slightly greater than 0.0015 ### 9.1.27 Example: binom.test() > binom.test(0,167,alternative="less",p=0.0015) Exact binomial test data: 0 and 167 number of successes = 0, number of trials = 167, p-value = 0.7783 alternative hypothesis: true probability of success is less than 0.0015 95 percent confidence interval: 0.00000000 0.01777858 sample estimates: probability of success 0 The R function above provides the result of a one-sided hypothesis test of $$H_0: p≥0.0015$$ vs. $$H_A: p<0.0015$$. The confidence interval is the range of possible values of p that cannot be rejected under the null hypothesis. ### 9.1.28 Example: Asymptomatic colonization with C. difficile • Proportion of patients asymptomatically colonized at admission = 212/5232 = 0.041 • Proportion of patients with risk factor • Recent hospitalization = 136/212 = 0.642 • Recent antibiotic use = 98/212 = 0.462 • Recent probiotic use = 1/212 = 0.005 • Proportion of asymptomatically colonized carrying NAP1 strain = 33/209 = 0.158 ### 9.1.29 Exact or approximate CI? • For most of the proportions on the previous slide we can see that np and n(1-p) are both greater than 5 • A quick way to check this is to look at the number of subjects with and without the outcome and see if they are both greater than 5 ### 9.1.30 95% CI for proportion • The 95% confidence interval for the risk of asymptomatic colonization at admission is given by $p\pm z_{1-\alpha/2}\times\sqrt{\frac{p(1-p)}{n}}=0.041\pm1.96\sqrt{\frac{0.041(1-0.041)}{5232}}$ $=0.041\pm0.005$ $=(0.036,0.046),\space approximately$ • This confidence interval tells us that the information in the data is consistent with values of 𝜋 ranging from 3.6% to 4.6%. The observed data is unlikely to arise from a setting where 𝜋 >0.05. • This implies, based on the observed data, we would reject H0: 𝜋 >0.05 at the Type I error level of 0.05 • The confidence intervals for the proportion of patients with different risk factors can be obtained similarly ### 9.1.31 Exact or approximate CI? • However, only 1 subject reported using probiotics and 211 subjects did not • Therefore, based on our rule of thumb we cannot use the normal approximation to obtain a 95% confidence interval for this proportion and must use an exact method instead • Using the approximate method would result in the following confidence interval (-0.005, 0.014), which is clearly not appropriate as a proportion cannot be negative! ### 9.1.32 Exact 95% equal-tailed confidence interval for proportion of probiotic use > binom.test(1,212) Exact binomial test data: 1 and 212 number of successes = 1, number of trials = 212, p-value < 2.2e-16 alternative hypothesis: true probability of success is not equal to 0.5 95 percent confidence interval: 0.0001194165 0.0259997103 sample estimates: probability of success 0.004716981 The R function above provides the result of a two-sided hypothesis test of $$H_0: p=0.5$$. The confidence interval is the range of possible values of p that cannot be rejected under the null hypothesis. ### 9.1.34 Statistics used to compare two proportions $$p_1$$ and $$p_2$$ • Several different statistics may be used to compare proportions. These include relative comparisons and absolute comparisons • Difference: $$p_1-p_2$$ • Odds ratios: $$\frac{p_1(1-p_2)}{p_2(1-p_1)}$$ • Risk ratios: $$\frac{p_1}{p_2}$$ • Number needed to treat: $$\frac{1}{p_1-p_2}$$ ### 9.1.35 Example: Probiotics for prevention of CDAD • Clostridium difficile diarrhea (CDAD), which was introduced earlier in the lecture, is strongly associated with antibiotic use • An outbreak of a virulent form of CDAD in Quebec in 2004 has heightened the interest in tackling this infectious disease • A probiotic is a live microorganism or a mixture of various bacteria administered to improve the microbial balance in the host GI system ### 9.1.36 Results from two randomized controlled trials • A recent systematic review identified 10 studies on the efficacy of lactobacillus probiotics for prevention of CDAD • We will take a closer look at two of them • For each of these studies we will calculate a 95% confidence interval for the difference in proportions and also a p-value for a two-sided test ### 9.1.38 Results from two randomized controlled trials • Compare the two proportions reported in each study using hypothesis tests, confidence intervals ### 9.1.39 Confidence Interval for the difference between two proportions • Assume we have data from two independent, random samples of size $$n_1$$ and $$n_2$$ and that the observed proportions of the outcome of interest in the two samples are $$p_1$$ and $$p_2$$, respectively • Assume these two samples are drawn from two independent, large populations with the true proportions of the outcomes of interest being $$\pi_1$$ and $$\pi_2$$, respectively • When $$n_1$$ and $$n_2$$ are large, an approximate level $$(1-\alpha)$$% confidence interval for $$\pi_1-\pi_2$$ is $p_1-p_2\pm Z_{1-\alpha/2}\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$ where $$Z_{1-\alpha/2}$$ is the upper $$1-\alpha/2$$ standard Normal critical value ### 9.1.40 Hypothesis test for comparing two proportions • Carrying out a hypothesis test involves the same 4 steps as we had seen before: 1. State the null and alternative hypotheses. The alternative could be one or two-sided 2. Calculate the test statistic measuring the evidence in favour of the null hypothesis 3. Determine the rejection region specified by the desired Type I error (α) 4. Determine if the test statistic falls in the rejection region. If yes, you conclude that you have enough evidence to reject the null hypothesis. If no, you conclude that you do not have enough evidence to reject the null hypothesis • The null and alternative hypotheses may be stated in one of 3 ways as in the table below: • Notice that $$H_0:\pi_1=\pi_2$$ is equivalent to $$H_0:risk\space ratio=1$$ or $$H_0:odds\space ratio=1$$. In other words, these hypotheses can also be tested using the methods for the difference between two proportions = 0 • The test statistic in all 3 cases is given by $$z=\frac{p_1-p_2}{s_p}$$ where $$s_p=\sqrt{p(1-p)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}$$ and $$p=\frac{x_1+x_2}{n_1+n_2},$$ where $$x_1$$ and $$x_2$$ are the number of subjects who had the outcome of interest in group 1 and group 2, respectively • The rejection region is specified by the desired Type I error (α). • Quantiles of the normal distribution are used to define the rejection region as summarized in the table below • Note that $$P(Z>Z_{1-\alpha})=P(Z<Z_\alpha)=\alpha$$. Similarly, $$P(Z>Z_{1-\alpha/2})=P(Z<Z_\alpha/2)=\alpha/2$$, where Z is a standard normal variable • The p-value is the probability of being more extreme than the observed z statistic under the standard normal distribution. Note that the measurement of ‘more extreme’ is determined by whether the alternative hypothesis is one or two-sided ### 9.1.41 Probiotics example: Confidence interval for difference in proportions • Using the results from Allen et al., we will denote the probiotics group as Group 1 and the placebo group as Group 2 • First calculate the difference in proportion of CDAD cases in each group $$p_1 - p_2 = 21/1493 - 30/1488 = 0.014 - 0.020 = -0.006$$ • Then calculate the standard deviation of the difference in proportions $\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}=\sqrt{\frac{\left(\frac{21}{1493}\right)\left(1-\frac{21}{1493}\right)}{1493}+\frac{\left(\frac{30}{1488}\right)\left(1-\frac{30}{1488}\right)}{1488}}=0.005$ • The 95% confidence interval is then given by $$-0.006 ± Z_{1-0.025} × 0.005 = -0.006 ± 1.96 × 0.005 = (-0.016, 0.004),$$ implying the observed difference between the two groups is not statistically significant compared to the Type I error level of 0.05 ### 9.1.42 Probiotics example: Hypothesis test • The authors of the study carried out a two-sided hypothesis test, allowing for the possibility that probiotics decreased or increased the risk of CDAD • This may be expressed as $$H_0:\pi_1=\pi_2$$ vs. $$H_a:\pi_1\neq\pi_2$$ • To calculate the test statistic, we need to first calculate a pooled proportion given by $p=\frac{x_1+x_2}{n_1+n_2}=\frac{21+30}{1493+1488}=0.017$ • The test statistic is given by $z=\frac{p_1-p_2}{\sqrt{p(1-p)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}=\frac{-0.006}{\sqrt{0.017(1-0.017)\left(\frac{1}{1493}+\frac{1}{1488}\right)}}$ • Since this is a two-sided test, we calculate the p-value using the following expression: $$2P(Z\geq\|z\|)=2P(Z\geq\|-1.267\|)$$ $$=2P(Z\geq1.267)$$ $$=2(1-P(Z<1.267))$$ = 2(1 – pnorm(1.267)) # R code $$= 0.19,\space approximately$$ • Implying that even if there were no difference between the two groups, there is a 0.19 probability of observing the difference reported in this study or something more extreme • Compared to the traditional level of significance of 0.05, we would consider this result is not statistically significant ### 9.1.43 Probiotics example: Results for both studies • Notice that the Gao study resulted in the conclusion that the observed difference in proportions was statistically significant • Looking at just these two studies, it is clear that no study should be evaluated on its own • Ideally, we should analyze results from all available studies (i.e. carry out a meta-analysis) before we can draw a conclusion. Even then, it would be important to consider the possibility of publication bias ### 9.1.44 Comparing two proportions in R #### 9.1.44.1 Description prop.test can be used for testing the null that the proportions (probabilities of success) in several groups are the same, or that they equal certain given values. #### 9.1.44.2 Usage prop.test(x, n, p = NULL, alternative = c("two.sided", "less", "greater"), conf.level = 0.95, correct = TRUE) ### 9.1.45 Probiotics example: Obtaining the results in R #### 9.1.45.1 Gao study > cdad=c(9,20) > n=c(171,84) 2-sample test for equality of proportions without continuity correction data: c(9, 20) out of c(171, 84) X-squared = 19.223, df = 1, p-value = 1.163e-05 alternative hypothesis: two.sided 95 percent confidence interval: -0.2825003 -0.0884270 sample estimates: prop 1 prop 2 0.05263158 0.23809524 #### 9.1.45.2 Allen study > cdad=c(21,30) > n=c(1493,1488) 2-sample test for equality of proportions without continuity correction X-squared = 1.6467, df = 1, p-value = 0.1994 alternative hypothesis: two.sided 95 percent confidence interval: -0.015405919 0.003214617 sample estimates: prop 1 prop 2 0.01406564 0.02016129 ### 9.1.46 Number needed to treat • The number needed to treat (NNT) is often reported in randomized controlled trials with a binary outcome • It is the estimated number of patients who need to be treated with the new treatment rather than the standard treatment for one additional patient to benefit • It is calculated as the inverse of the absolute risk difference, i.e. $$NNT=\frac{1}{\|p_1-p_2\|}$$ • Notice that the NNT can range from a minimum of 1 to a maximum of ∞ ### 9.1.47 Probiotics example: Number needed to treat • Therefore, the Gao study leads to the interpretation that roughly 4 patients need to be given probiotics to prevent 1 case of CDAD • The Allen study on the other hand suggests 167 patients would need to be given probiotics to prevent 1 case of CDAD ### 9.1.48 Confidence interval for number needed to treat • Let the interval $$(d_L, d_H)$$ denote the 95% confidence interval for the absolute risk difference • Calculating the confidence interval for the NNT is obtained by inverting these limits • When the risk difference is statistically significant it is straightforward to obtain the interval as $$(1/d_H, 1/d_L)$$, e.g. see the Gao study • When the risk difference is not statistically significant the interval encompasses both the NNH (or number needed to harm) and the NNB (number needed to benefit) and is more complicated. One way to write the interval is as ($$1/d_H$$ to ∞ to $$1/d_L$$), e.g. see the paper by Altman (BMJ 1998) on course website ## 9.2 Sample size determination for studies of proportions ### 9.2.1 Sample Size For Desired Margin Of Error • The sample size (n) required to obtain a $$(1-\alpha)$$% confidence interval for a proportion with margin of error approximately equal to a specified value m is $n=\left(\frac{z_{1-\alpha/2}}{m}\right)^2\pi^(1-\pi^)$ where $$\pi^$$ is a guessed value for the true proportion and $$z_{1-\alpha/2}$$ is the upper $$1-\alpha/2$$ standard Normal critical value. • If $$\pi^$$ is not known it can be set to 0.5 as this will maximize the sample size required. This gives $n=\left(\frac{z_{1-\alpha/2}}{2m}\right)^2$ ### 9.2.2 Sample Size For Desired Power And Type I Error • The sample size (n) required to test the null hypothesis $$H_0:\pi=\pi_0$$ vs. $$H_a:\pi\neq\pi_0$$ with Type I error = $$\alpha$$ and Type II error = $$\beta$$ = 1- Power, such that the minimum detectable difference between the two groups is $$\pi_1-\pi_0$$ is given by $n=\frac{[z_{1-\alpha/2}\sqrt{\pi_0(1-\pi_0)}+z_{1-\beta}\sqrt{\pi_1(1-\pi_1)}]^2}{(\pi_1-\pi_0)^2}$ • Similar expressions can be defined for a one-sided test replacing $$Z_{1-α/2}$$ by $$Z_{1-α}$$ • Note once again that whereas the Type II error did not come into play when carrying out the hypothesis test, it is used here when planning the study ### 9.2.3 Example Q. A study will be conducted to determine whether refugees entering Canada from Cambodia need to be routinely tested for Strongyloides infection. Nothing is known about the prevalence of the disease in this population. Assuming a perfect test was available for the detection of Strongyloides, what sample size would be required to detect the prevalence within a margin of error of m = 5% with 90% confidence? A. Since nothing is known about the prevalence of Strongyloides in this population, we use a guess value of $$\pi^=0.5$$. The required sample size is $n=\left(\frac{z_{1-\alpha/2}}{m}\right)^2\pi^(1-\pi^*)=\left(\frac{1.645}{0.05}\right)^20.5(1-0.5)=271\space (approximately)$ ### 9.2.4 Planning a study to compare proportions • Once again, we distinguish between the sample size required to estimate a confidence interval or to carry out a hypothesis test • Inputs required for the two approaches are summarized below Confidence interval Hypothesis test Confidence level 1-α Type I error α Type II error β Guess value for the two proportions $$π_1$$ and $$π_2$$ Guess value for the two proportions $$π_1$$ and $$π_2$$ Desired precision (or half-width of interval or margin or error) (m) The minimum important difference to detect $$(π_1 - π_2 = m)$$ $$k = n_1/n_2$$, the ratio of the two sample sizes $$k = n_1/n_2$$, the ratio of the two sample sizes ### 9.2.5 Sample size formulae Notes • In both cases, the Group 1 sample size is given by kn • In the expression for the hypothesis test, replace $$Z_{1-α/2}$$ by $$Z_{1-α}$$ for a one-sided test • You may find other variations of the expression for the hypothesis test, e.g. those based on a pooled proportion ### 9.2.6 Example • A cardiologist wishes to design a clinical trial comparing a new drug with a control in the treatment of the acute phase of myocardial infarction. • It is of interest to test the null hypothesis that there is no difference in 1-month survival following treatment with either drug. This will be tested with a two-sided test at the 5% level. • If, in fact, the new drug increases the survival rate by 20%, the investigator wishes to risk a 10 percent chance of failing to conclude that the new drug is significantly better than the control. • Based on previous experience the survival rate among controls was 60%. How large a sample size is needed? ### 9.2.7 Inputs for the sample size calculation Hypothesis test Inputs Type I error α 5% Type II error β 10% Guess value for the two proportions $$π_1$$ and $$π_2$$ $$\pi_1=0.6$$ and $$\pi_2=0.8$$ The minimum important difference to detect $$(π_1 - π_2 = m)$$ $$\pi_1-\pi_2=0.2$$ $$k = n_1/n_2$$, the ratio of the two sample sizes k=1 ### 9.2.8 Example • The sample size required is given by $n=\left(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{\pi_1-\pi_2}\right)^2\left(\frac{\pi_1(1-\pi_1)}{k}+\pi_2(1-\pi_2)\right)$ $=\left(\frac{Z_{1-0.025}+Z_{1-0.1}}{0.6-0.8}\right)^2\left(\frac{0.6(1-0.6)}{1}+0.8(1-0.8)\right)$ $=105\space in\space each\space group$	2022-06-27 23:02:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7533517479896545, "perplexity": 863.3185490229705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103344783.24/warc/CC-MAIN-20220627225823-20220628015823-00474.warc.gz"}
https://math.stackexchange.com/questions/2549904/find-lim-n-to-infty-log-f-nx-lim-n-to-infty-frac-log-left-cos-l	# Find $\lim_{n\to\infty} \log f_n(x) = \lim_{n\to\infty} \frac { \log\left(\cos\left(\frac{x}{\sqrt{n}}\right)\right)} {\frac 1 n }$ When applying L'Hopital's rule first I get this: $\lim_{n\to\infty}\log f_n(x)=\lim_{n\to\infty}-\frac {\sin\big (\frac x {\sqrt n} \big ) x\sqrt n}{2\cos \big ( \frac x {\sqrt n}\big )}$ by applying it second time I get; $\lim_{n\to\infty} \log f_n(x)=\lim_{n\to\infty}\big (\frac {x\cos \big ( \frac x {\sqrt n} \big ) \sqrt n } {2\sin \big ( \frac x {\sqrt n} \big ) }-\frac n 2 \big )$ So now from here how to get: $\lim_{n\to\infty}f_n(x)=e ^{-\frac {x^2} 2}$ • making a change of variables $t=\frac{1}{\sqrt{n}}$ may simplify the calculation and then apply L'Hospital rule (may be twice). Result is $x^2/2$. – daulomb Dec 4 '17 at 1:31 • @daulomb: I got $-x^2/2$ (using your substitution). The minus sign comes from the fact that the derivative of $\ln{\left(\cos{x}\right)}$ is $-\tan{x}$. – Ant Dec 4 '17 at 1:40 • yes you are right it comes from the derivative of cosine – daulomb Dec 4 '17 at 1:41 We have $f_n(x)={\left(\cos{\left(\frac{x}{\sqrt{n}}\right)}\right)}^n$. Thus, $\ln{f_n(x)}=n\ln{\left(\cos{\left(\frac{x}{\sqrt{n}}\right)}\right)}$ and: $$\ln{L(x)}:=\ln{\left(\lim_{n\to\infty}f_n(x)\right)}=\lim_{n\to\infty}{n\ln{\left(\cos{\left(\frac{x}{\sqrt{n}}\right)}\right)}}$$ Using the substitution suggested by daulomb, we have $t=\frac{1}{\sqrt{n}}$, so as $n$ approaches $\infty$, $t$ approaches $0$. Thus: $$\ln{L(x)}=\lim_{t\to0}{\frac{1}{t^2}\ln{\left(\cos{\left(tx\right)}\right)}}$$ Now we use L'Hopital's rule, since we have a $0/0$ indeterminate form (remember that we take the derivative with respect to $t$, not $x$): $$\ln{L(x)}=\lim_{t\to0}{\frac{\frac{-x\sin{\left(tx\right)}}{\cos{\left(tx\right)}}}{2t}}=-x\lim_{t\to0}{\frac{\tan{\left(tx\right)}}{2t}}$$ We took the $-x$ outside of the limit because it doesn't depend on $t$. Now we apply L'Hopital's rule again: $$\ln{L(x)}=-x\lim_{t\to0}{\frac{x\sec^2{\left(tx\right)}}{2}}=-\frac{x^2}{2}\lim_{t\to0}{\sec^2{\left(tx\right)}}=-\frac{x^2}{2}$$ thus $L(x)=e^{-\frac{x^2}{2}}$. Alternative method. Without applying L'Hopital, but instead Taylor expansions (around $0$) of standard functions: \begin{align} \cos u &= 1-\frac{u^2}{2} + o(u^2)\\ \ln(1+u) &= u +o(u)\end{align} we get, as $\lim_{n\to\infty}\frac{x}{\sqrt{n}} = 0$ (for any fixed $x$): $$\ln\cos\frac{x}{\sqrt{n}} = \ln\left(1-\frac{x^2}{2n} + o\left(\frac{1}{n}\right)\right)\tag{1}$$ and from there, since $\lim_{n\to\infty}\frac{x^2}{2n} = 0$ $$\ln\cos\frac{x}{\sqrt{n}} = -\frac{x^2}{2n} + o\left(\frac{1}{n}\right)\,.\tag{2}$$ Therefore, for any fixed $x\in\mathbb{R}$, $$\ln f_n(x)=\frac{\ln\cos\frac{x}{\sqrt{n}}}{\frac{1}{n}} = \frac{-\frac{x^2}{2n} + o\left(\frac{1}{n}\right)}{\frac{1}{n}} = -\frac{x^2}{2} + o\left(1\right) \xrightarrow[n\to\infty]{} \boxed{-\frac{x^2}{2}}.$$ By continuity of $\exp$, this immediately implies that $$\boxed{\lim_{n\to\infty}f_n(x) = e^{-\frac{x^2}{2}}}$$ • as in here, from which this question was derived ;) +1 math.stackexchange.com/questions/2549673/… – qbert Dec 4 '17 at 1:50 • @qbert Oh damn. I definitely missed that. – Clement C. Dec 4 '17 at 1:51 • it's ok, I think it is the more natural thing to do here – qbert Dec 4 '17 at 1:51	2019-10-23 20:23:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9944855570793152, "perplexity": 578.8493584348189}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987836295.98/warc/CC-MAIN-20191023201520-20191023225020-00274.warc.gz"}
https://www.jobilize.com/course/section/equations-and-inequalities-solving-quadratic-equations-by-openstax?qcr=www.quizover.com	Page 1 / 2 ## Equations and inequalities: solving quadratic equations A quadratic equation is an equation where the power of the variable is at most 2. The following are examples of quadratic equations. $\begin{array}{ccc}\hfill 2{x}^{2}+2x& =& 1\hfill \\ \hfill \frac{2-x}{3x+1}& =& 2x\hfill \\ \hfill \frac{4}{3}x-6& =& 7{x}^{2}+2\hfill \end{array}$ Quadratic equations differ from linear equations by the fact that a linear equation only has one solution, while a quadratic equation has at most two solutions. However, there are some special situations when a quadratic equation only has one solution. We solve quadratic equations by factorisation, that is writing the quadratic as a product of two expressions in brackets. For example, we know that: $\left(x+1\right)\left(2x-3\right)=2{x}^{2}-x-3.$ In order to solve: $2{x}^{2}-x-3=0$ we need to be able to write $2{x}^{2}-x-3$ as $\left(x+1\right)\left(2x-3\right)$ , which we already know how to do. The reason for equating to zero and factoring is that if we attempt to solve it in a 'normal' way, we may miss one of the solutions. On the other hand, if we have the (non-linear) equation $f\left(x\right)g\left(x\right)=0$ , for some functions $f$ and $g$ , we know that the solution is $f\left(x\right)=0$ OR $g\left(x\right)=0$ , which allows us to find BOTH solutions (or know that there is only one solution if it turns out that $f=g$ ). ## Investigation : factorising a quadratic 1. $x+{x}^{2}$ 2. ${x}^{2}+1+2x$ 3. ${x}^{2}-4x+5$ 4. $16{x}^{2}-9$ 5. $4{x}^{2}+4x+1$ Being able to factorise a quadratic means that you are one step away from solving a quadratic equation. For example, ${x}^{2}-3x-2=0$ can be written as $\left(x-1\right)\left(x-2\right)=0$ . This means that both $x-1=0$ and $x-2=0$ , which gives $x=1$ and $x=2$ as the two solutions to the quadratic equation ${x}^{2}-3x-2=0$ . 1. First divide the entire equation by any common factor of the coefficients, so as to obtain an equation of the form $a{x}^{2}+bx+c=0$ where $a$ , $b$ and $c$ have no common factors. For example, $2{x}^{2}+4x+2=0$ can be written as ${x}^{2}+2x+1=0$ by dividing by 2. 2. Write $a{x}^{2}+bx+c$ in terms of its factors $\left(rx+s\right)\left(ux+v\right)$ . This means $\left(rx+s\right)\left(ux+v\right)=0$ . 3. Once writing the equation in the form $\left(rx+s\right)\left(ux+v\right)=0$ , it then follows that the two solutions are $x=-\frac{s}{r}$ or $x=-\frac{u}{v}$ . 4. For each solution substitute the value into the original equation to check whether it is valid There are two solutions to a quadratic equation, because any one of the values can solve the equation. Solve for $x$ : $3{x}^{2}+2x-1=0$ 1. As we have seen the factors of $3{x}^{2}+2x-1$ are $\left(x+1\right)$ and $\left(3x-1\right)$ . 2. $\left(x+1\right)\left(3x-1\right)=0$ 3. We have $x+1=0$ or $3x-1=0$ Therefore, $x=-1$ or $x=\frac{1}{3}$ . 4. We substitute the answers back into the original equation and for both answers we find that the equation is true. 5. $3{x}^{2}+2x-1=0$ for $x=-1$ or $x=\frac{1}{3}$ . Sometimes an equation might not look like a quadratic at first glance but turns into one with a simple operation or two. Remember that you have to do the same operation on both sides of the equation for it to remain true. You might need to do one (or a combination) of: • For example, $\begin{array}{ccc}\hfill ax+b& =& \frac{c}{x}\hfill \\ \hfill x\left(ax+b\right)& =& x\left(\frac{c}{x}\right)\hfill \\ \hfill a{x}^{2}+bx& =& c\hfill \end{array}$ • This is raising both sides to the power of $-1$ . For example, $\begin{array}{ccc}\hfill \frac{1}{a{x}^{2}+bx}& =& c\hfill \\ \hfill {\left(\frac{1}{a{x}^{2}+bx}\right)}^{-1}& =& {\left(c\right)}^{-1}\hfill \\ \hfill \frac{a{x}^{2}+bx}{1}& =& \frac{1}{c}\hfill \\ \hfill a{x}^{2}+bx& =& \frac{1}{c}\hfill \end{array}$ • This is raising both sides to the power of 2. For example, $\begin{array}{ccc}\hfill \sqrt{a{x}^{2}+bx}& =& c\hfill \\ \hfill {\left(\sqrt{a{x}^{2}+bx}\right)}^{2}& =& {c}^{2}\hfill \\ \hfill a{x}^{2}+bx& =& {c}^{2}\hfill \end{array}$ Application of nanotechnology in medicine what is variations in raman spectra for nanomaterials I only see partial conversation and what's the question here! what about nanotechnology for water purification please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment. Damian yes that's correct Professor I think Professor what is the stm is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.? Rafiq industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong Damian How we are making nano material? what is a peer What is meant by 'nano scale'? What is STMs full form? LITNING scanning tunneling microscope Sahil how nano science is used for hydrophobicity Santosh Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq Rafiq what is differents between GO and RGO? Mahi what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq Rafiq if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION Anam analytical skills graphene is prepared to kill any type viruses . Anam what is Nano technology ? write examples of Nano molecule? Bob The nanotechnology is as new science, to scale nanometric brayan nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale Damian Is there any normative that regulates the use of silver nanoparticles? what king of growth are you checking .? Renato What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ? why we need to study biomolecules, molecular biology in nanotechnology? ? Kyle yes I'm doing my masters in nanotechnology, we are being studying all these domains as well.. why? what school? Kyle biomolecules are e building blocks of every organics and inorganic materials. Joe anyone know any internet site where one can find nanotechnology papers? research.net kanaga sciencedirect big data base Ernesto Introduction about quantum dots in nanotechnology hi Loga what does nano mean? nano basically means 10^(-9). nanometer is a unit to measure length. Bharti Got questions? Join the online conversation and get instant answers!	2020-07-02 15:30:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 53, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7143339514732361, "perplexity": 637.6649416990275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655879532.0/warc/CC-MAIN-20200702142549-20200702172549-00026.warc.gz"}
http://www.physicsforums.com/showthread.php?p=452038	# integrate d/dx(x^2) Tags: confused, d or dxx2, integrate P: 48 if i integrate d/dx(x^2), should i include the constant of integration? thanks P: 1,294 If you are working on an equation, then presumably you are integrating both sides with respect to x in which case you will have a constant of Integration (arbitrarily) on either side. The short answer is yes, in all cases. P: 48 so it doesnt matter that you know what the function was before differentiation? P: 1,294 ## integrate d/dx(x^2) I am tempted to say that it wouldn't matter, but that would lead to inconsistent results (i.e. a different answer depending on the chosen order of operations). Math Emeritus Sci Advisor Thanks PF Gold P: 38,895 What in the world do you mean? If you start with a function f(x), differentiate it, then integrate that, whether you get the original function, that function plus an unknown constant, or that function plus a specific number depends on exactly what type of "integral" you are doing: $\int f(x)dx$, the indefinite integral should have an unknown constant added because it means ALL functions whose derivative is f(x) but $\int_a^xf(t)dt$ would not and the value will depend upon the choice of a. Related Discussions Special & General Relativity 40 Calculus 13 Calculus & Beyond Homework 2 Introductory Physics Homework 1 Introductory Physics Homework 2	2014-04-23 12:32:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8971179723739624, "perplexity": 503.2938481621176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00540-ip-10-147-4-33.ec2.internal.warc.gz"}
https://en.wikipedia.org/wiki/Paul_Cohen_(mathematician)	# Paul Cohen (Redirected from Paul Cohen (mathematician)) For other people named Paul Cohen, see Paul Cohen (disambiguation). Not to be confused with Paul Cohn. Paul J. Cohen Born April 2, 1934 Long Branch, New Jersey Died March 23, 2007 (aged 72) Stanford, California, near Palo Alto Fields Mathematics Institutions Stanford University Alma mater Stuyvesant High School Brooklyn College University of Chicago Doctoral students Peter Sarnak Known for Cohen forcing Continuum hypothesis Influences Georg Cantor, Kurt Gödel Notable awards Bôcher Prize (1964) Fields Medal (1966) National Medal of Science (1967) Paul Joseph Cohen (April 2, 1934 – March 23, 2007)[1] was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal.[2] ## Early years Cohen was born in Long Branch, New Jersey, into a Jewish family that had immigrated to the United States from what is now Poland; he grew up in Brooklyn.[3][4] He graduated in 1950, at age 16, from Stuyvesant High School in New York City.[1][4] Cohen next studied at the Brooklyn College from 1950 to 1953, but he left before earning his bachelor's degree when he learned that he could start his graduate studies at the University of Chicago with just two years of college. At Chicago, Cohen completed his master's degree in mathematics in 1954 and his Doctor of Philosophy degree in 1958, under supervision of the Professor of Mathematics, Antoni Zygmund. The title of his doctoral thesis was Topics in the Theory of Uniqueness of Trigonometrical Series.[5] In 1957, before the award of his doctorate, Cohen was appointed as an Instructor in Mathematics at the University of Rochester for a year. He then spent the academic year 1958–59 at the Massachusetts Institute of Technology before spending 1959–61 as a fellow at the Institute for Advanced Study at Princeton. These were years in which Cohen made a number of significant mathematical breakthroughs. In Factorization in group algebras (1959) he showed that any integrable function on a locally compact group is the convolution of two such functions, solving a problem posed by Walter Rudin. In On a conjecture of Littlewood and idempotent measures (1960) Cohen made a significant breakthrough in solving the Littlewood Conjecture.[6] On June 2, 1995 Cohen received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden [7] ## Contributions to mathematics Cohen is noted for developing a mathematical technique called forcing, which he used to prove that neither the continuum hypothesis (CH), nor the axiom of choice, can be proved from the standard Zermelo–Fraenkel axioms (ZF) of set theory. In conjunction with the earlier work of Gödel, this showed that both of these statements are logically independent of the ZF axioms: these statements can be neither proved nor disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that is independent from the standard ZF axioms of set theory. For his result on the continuum hypothesis, Cohen won the Fields Medal in mathematics in 1966, and also the National Medal of Science in 1967.[8] The Fields Medal that Cohen won continues to be the only Fields Medal to be awarded for a work in mathematical logic, as of 2014. Apart from his work in set theory, Cohen also made many valuable contributions to analysis. He was awarded the Bôcher Memorial Prize in mathematical analysis in 1964 for his paper "On a conjecture by Littlewood and idempotent measures",[9] and lends his name to the Cohen-Hewitt factorization theorem. Cohen was a full professor of mathematics at Stanford University, where he supervised Peter Sarnak's graduate research, among those of other students. Cohen was an Invited Speaker at the ICM in 1962 in Stockholm and in 1966 in Moscow. Angus MacIntyre of the University of London stated about Cohen: "He was dauntingly clever, and one would have had to be naive or exceptionally altruistic to put one's 'hardest problem' to the Paul I knew in the '60s." He went on to compare Cohen to Kurt Gödel, saying: "Nothing more dramatic than their work has happened in the history of the subject."[10] Gödel himself wrote a letter to Cohen in 1963, a draft of which stated, "Let me repeat that it is really a delight to read your proof of the ind[ependence] of the cont[inuum] hyp[othesis]. I think that in all essential respects you have given the best possible proof & this does not happen frequently. Reading your proof had a similarly pleasant effect on me as seeing a really good play."[11] ## On the continuum hypothesis While studying the continuum hypothesis, Cohen is quoted as saying in 1985 that he had "had the feeling that people thought the problem was hopeless, since there was no new way of constructing models of set theory. Indeed, they thought you had to be slightly crazy even to think about the problem."[12] "A point of view which the author [Cohen] feels may eventually come to be accepted is that CH is obviously false. The main reason one accepts the axiom of infinity is probably that we feel it absurd to think that the process of adding only one set at a time can exhaust the entire universe. Similarly with the higher axioms of infinity. Now ${\displaystyle \aleph _{1}}$ is the cardinality of the set of countable ordinals, and this is merely a special and the simplest way of generating a higher cardinal. The set ${\displaystyle C}$ [the continuum] is, in contrast, generated by a totally new and more powerful principle, namely the power set axiom. It is unreasonable to expect that any description of a larger cardinal which attempts to build up that cardinal from ideas deriving from the replacement axiom can ever reach ${\displaystyle C}$. Thus ${\displaystyle C}$ is greater than ${\displaystyle \aleph _{n},\aleph _{\omega },\aleph _{a}}$, where ${\displaystyle a=\aleph _{\omega }}$, etc. This point of view regards ${\displaystyle C}$ as an incredibly rich set given to us by one bold new axiom, which can never be approached by any piecemeal process of construction. Perhaps later generations will see the problem more clearly and express themselves more eloquently."[13] An "enduring and powerful product" of Cohen's work on the continuum hypothesis, and one that has been used by "countless mathematicians"[12] is known as "forcing", and it is used to construct mathematical models to test a given hypothesis for truth or falsehood. Shortly before his death, Cohen gave a lecture describing his solution to the problem of the continuum hypothesis at the Gödel centennial conference, in Vienna in 2006. A video of this lecture is now available online.[14] ## References 1. ^ a b Levy, Dawn (2007-03-28). "Paul Cohen, winner of world's top mathematics prize, dies at 72". Stanford Report. Retrieved 2007-10-31. 2. ^ Pearce, Jeremy (2 April 2007). "Paul J. Cohen, Mathematics Trailblazer, Dies at 72". NY Times. 3. ^ Macintyre, A.J. "Paul Joseph Cohen", London Mathematical Society. Accessed March 3, 2011. "Cohen's origins were humble. He was born in Long Branch, New Jersey on 2 April 1934, into a Polish immigrant family." 4. ^ a b Albers, Donald J.; Alexanderson, Gerald L.; Reid, Constance, eds. (1990), "Paul Cohen", More Mathematical People, Harcourt Brace Jovanovich, pp. 42–58. 5. ^ Paul J. Cohen (1958), Topics in the theory of uniqueness of trigonometrical series. 6. ^	2017-02-25 10:15:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.652334451675415, "perplexity": 806.6642613612224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171706.94/warc/CC-MAIN-20170219104611-00071-ip-10-171-10-108.ec2.internal.warc.gz"}
https://elteoremadecuales.com/gromovs-compactness-theorem-topology/?lang=pt	# Gromov's compactness theorem (topologia) Gromov's compactness theorem (topologia) Not to be confused with Gromov's compactness theorem in metric geometry. In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or (a finite tree of) "bubbles". A bubble is a holomorphic sphere which has a transverse intersection with the rest of the curve. Este teorema, and its generalizations to punctured pseudoholomorphic curves, underlies the compactness results for flow lines in Floer homology and symplectic field theory. If the complex structures on the curves in the sequence do not vary, only bubbles can occur; nodes can occur only if the complex structures on the domain are allowed to vary. Usualmente, the energy bound is achieved by considering a symplectic manifold with compatible almost-complex structure as the target, and assuming that curves to lie in a fixed homology class in the target. This is because the energy of such a pseudoholomorphic curve is given by the integral of the target symplectic form over the curve, and thus by evaluating the cohomology class of that symplectic form on the homology class of the curve. The finiteness of the bubble tree follows from (positivo) lower bounds on the energy contributed by a holomorphic sphere. References Gromov, M. (1985). "Pseudo holomorphic curves in symplectic manifolds". Descobertas matemáticas. 82 (2): 307–347. doi:10.1007/BF01388806. Bourgeois, F.; Eliashberg, Ya.; Hofer, H.; Wysocki, K.; Zehnder, E. (2003). "Compactness results in symplectic field theory". Geometry and Topology. 7 (2): 799–888. arXiv:math/0308183. doi:10.2140/gt.2003.7.799. Este artigo sobre topologia é um esboço. Você pode ajudar a Wikipédia expandindo-a. Categorias: Symplectic topologyCompactness theoremsTopology stubs Se você quiser conhecer outros artigos semelhantes a Gromov's compactness theorem (topologia) você pode visitar a categoria Compactness theorems. Ir para cima Usamos cookies próprios e de terceiros para melhorar a experiência do usuário Mais informação	2023-03-27 14:06:18	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8179973363876343, "perplexity": 1332.8297221451821}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948632.20/warc/CC-MAIN-20230327123514-20230327153514-00548.warc.gz"}
https://github.com/leepike/copilot-discussion/blob/42b0da2d9376c21dfe71f31c14c566b356f9454c/ICFP2012/paper.tex	leepike/copilot-discussion forked from niswegmann/copilot-discussion Fetching contributors… Cannot retrieve contributors at this time 909 lines (772 sloc) 41 KB	2016-05-06 23:36:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5259464383125305, "perplexity": 5400.851553443358}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461864121714.34/warc/CC-MAIN-20160428172201-00055-ip-10-239-7-51.ec2.internal.warc.gz"}
http://peter.muehlbacher.me/mathematics/high-dimensional-statistics/	# Local extrema While local extrema in one and two dimensions are often depicted as (local) minima/maxima, they “typically” are saddle-points in high dimensions. This is the topic of my second Bachelor thesis where I survey LeCun’s The Loss Surfaces of Multilayer Networks and Auffinger, Ben Arous, Černý’s Random Matrices and Complexity of Spin Glasses. The former paper relates the energy landscape (loss function to be minimised) of a toy model of neural networks to that of certain models dealt with in the mathematical physics literature (the latter paper). This paper even goes a step further by suggesting that the distribution of eigenvalues of the Hessian of critical points is a shifted semicircle. That is, the closer the value at a critical point is to the global minimum, the higher the expected fraction of directions in which our loss function increases (if it increases in all directions, it is a local minimum). # Neural networks Large (deep) neural networks have lots of counterintuitive properties, of which I will list only few: • Adversarial vulnerability for any classifier shows fundamental upper bounds on the robustness of any classifier to perturbations, which provides a baseline to the maximal achievable robustness. When the latent space of the data distribution is high dimensional, our analysis shows that any classifier is vulnerable to very small perturbations. # MCMC algorithms The analysis of the mixing time of Markov chains (how long do I have to run my MCMC algorithms until they spit out representative samples?) is a beautiful subject combining many different fields in mathematics, such as probability theory (random walks, couplings), geometry (Cheeger’s inequality, Ricci curvature), representation theory, spectral theory, and physics (electrical networks)/computer science (Boolean analysis). Coming up with decent algorithms remains a particularly hard challenge in cases where the support of the measure we want to sample from is quite sparse; e.g. certain graphical representations of quantum spin systems. One aspect, however, remains to be overlooked surprisingly frequently: The space of irreversible Markov chains is much bigger than that of reversible Markov chains and often one can find an irreversible one that mixes a lot faster, see e.g. ECMC and Markov Chain Monte Carlo Method without Detailed Balance. # Cauchy–Schwarz Cauchy-Schwarz is both a very simple and a very powerful bound. I won’t even try to give an extensive list of possible applications, but concentrate instead on a classical one in probability theory. First notice that Cauchy-Schwarz can simply be interpreted as a fancy way of saying that $$\|\cos(x)\|\leq 1$$ for all real $$x$$ by the following identity: $\|\langle a,b\rangle\|=\|\cos(\theta)\|\|a\|\|b\|\leq\|a\|\|b\|,$ where $$\theta=\angle(a,b)$$ is the angle between $$a$$ and $$b$$. #### On $$\mathbb R^n,n\gg1$$, how far off is Cauchy–Schwarz “typically”? • The intuition is that in higher dimensions it becomes increasingly unlikely for two vectors to be approximately parallel (i.e. θ≈0 or θ≈π in which case Cauchy-Schwarz is sharp) since there are “too many directions”. • More rigorously, we may fix $$a=(1,0,\dots,0)$$ and sample $$b$$ from the Haar measure on the unit sphere. • Note that for $$n\gg1$$ we can do this by sampling $$n$$ iid centered normal variables $$(x_i)_{i=1}^n$$ with variance $$1\over n$$. • This ensures that squares have expectation $$\mathbb E x_i^2 = \text{Var}(x_i)-(\mathbb Ex_i)^2 = {1\over n}$$ and thus, by linearity of expectation we have that $$\mathbb E\\|(x_i)_{i=1}^n\\|_2=1$$. It is not too hard to see that the variance of $$\\|(x_i)_{i=1}^n\\|_2$$ vanishes as $$n\to\infty$$. • Thus, we see that each (in particular the first) entry of $$b$$ is of order $$O(n^{-{1\over2}})$$ and thus $\mathbb E\|\langle a,b\rangle\|=O(n^{-{1\over2}}).$ #### How tight is $$\|\mathbb Ef\|^2\leq\mathbb E[\|f\|^2]$$ • First note that this inequality can be seen as another manifestation of Cauchy–Schwarz (although the observation that the variance cannot be negative is a quicker way to see it): • Every probability measure $$\mathbb P$$ induces an inner product on the space of random variables with finite second moment by setting $$\langle f,g\rangle:=\mathbb E f\bar g$$. • Now apply Cauchy–Schwarz to the constant one function and an arbitrary other function to get $\|\langle 1,f\rangle\|^2 = \cos(\theta)\langle f,f\rangle\leq \mathbb E[\|f\|^2].$ • We get another curious identity when trying to convert this additive correction into a multiplicative one by using $$\sin^2+\cos^2=1$$: $\|\langle 1,f\rangle\|^2=\langle f,f\rangle-\text{Var}f = \langle f,f\rangle\left(1-{\text{Var}f\over\langle f,f\rangle}\right) \Rightarrow {\text{Var}f\over\langle f,f\rangle}=\sin(\theta)^2.$ • The takeaway is: The smaller the variance (of $$f$$), the tighter the bound $$\|\mathbb Ef\|^2\leq\mathbb E[\|f\|^2]$$. • Using some Poincaré-type inequalities we find another rule of thumb, namely that “all else equal”, the smoother $$f$$, the smaller the variance of $$f$$.	2022-07-06 13:14:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.92879718542099, "perplexity": 442.93534712360315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00230.warc.gz"}
http://metanomal.herokuapp.com/post/cv-glm	cv.glm function \| R Documentation An object of class "glm" containing the results of a generalized linear model fitted to data. cv.glm: Cross validation for Generalized Linear Models in ... Details. The data is divided randomly into K groups. For each group the generalized linear model is fit to data omitting that group, then the function cost is applied to the observed responses in the group that was omitted from the fit and the prediction made by the fitted models for those observations.. When K is the number of observations leave one out cross validation is used and all the ... R: Cross validation for Generalized Linear Models A vector of length two. The first component is the raw cross validation estimate of prediction error. The second component is the adjusted cross validation estimate. The adjustment is designed to compensate for the bias introduced by not using leave one out cross validation. seed: The value of .Random.seed when cv.glm was called. Cross validating logistic regression The cv.glm function from the library boot will serve the pourpose. LOOCV and k fold cross validation will be performed. Banknotes authentication dataset. Data were extracted from images that were taken from genuine and forged banknote like specimens. An Introduction to glmnet • glmnet cv.glmnet returns a cv.glmnet object, a list with all the ingredients of the cross validated fit. As with glmnet, we do not encourage users to extract the components directly except for viewing the selected values of λ. The package provides well designed functions for potential tasks. For example, we can plot the object: R K fold cross validation (with Leave one out) cv.glm does the computation by brute force by refitting the model all the N times and is then slow. It doesn't exploit the nice simple below LOOCV formula. The reason cv.glm doesn't use that formula is that it's also set up to work on logistic regressions and other models, and there the shortcut doesn't work. 3.2 Shortcut Formula 5.3.1 The Validation Set Approach Home Clark Science ... The cv.glm () function produces a list with several components. The two numbers in the delta vector contain the cross validation results. In this case the numbers are identical (up to two decimal places) and correspond to the LOOCV statistic: our cross validation estimate for the test error is approximately 24.23. cv.lm function \| R Documentation The function cv.lm carries out a k fold cross validation for a linear model (i.e. a 'lm' model). For each fold, an 'lm' model is fit to all observations that are not in the fold (the 'training set') and prediction errors are calculated for the observations in the fold (the 'test set'). Models_CV GLM.R at master · vasanthgx Models_CV · GitHub Cross Validation functions for various models. Contribute to vasanthgx Models_CV development by creating an account on GitHub. Cross Validation techniques in R: A brief overview of some ... cross validation. The default for ‘cv.glm’ is complete LOOCV. First, we run the common 10 – fold cross validation. Below, the majority of seed information is cut off the end of the figure. Next, we run the complete LOOCV method, specifying k as the number of rows in the sample Crossvalidation and bootstrap prediction error for linear ... # Brier score loss function simplified version for logistic regression only brierB < function (y, pHat) {mean ((y pHat) ^ 2)} B2 < cv.glm (data= dfAncova, glmfit= glmLR, cost= brierB, K= 10) B2 $delta R Cv.glm variable lengths differ How to build software mod < glm(cyl ~ mpg disp, data = mtcars) cv.glm(mtcars, mod, K=11) What happens is that you specify the variable in like mtcars$cylthis variable have a number of rows equal to that of the original dataset. Logistic Regression University of Cincinnati In glm(), the only thing new is family. It specifies the distribution of your response variable. You may also specify the link function after the name of distribution, for example, family=binomial(logit)(default link is logit). You may also use glm()to build many other generalized linear models… LOOCV (Leave One Out Cross Validation) in R Programming ... LOOCV(Leave One Out Cross Validation) is a type of cross validation approach in which each observation is considered as the validation set and the rest (N 1) observations are considered as the training set. In LOOCV, fitting of the model is done and predicting using one observation validation set. LOOCV \| R Club # cv.glm (data, glmfit, cost, K) # this runs k fold cross validation. When k = the number of observations in your dataset, then that's LOOCV # to run LOOCV, set k=n or just don't specify (its default is k=n) cv.lm: Cross validation for an object of class 'lm' in ... Details Cross validations. The function cv.lm carries out a k fold cross validation for a linear model (i.e. a 'lm' model). For each fold, an 'lm' model is fit to all observations that are not in the fold (the 'training set') and prediction errors are calculated for the observations in the fold (the 'test set'). glm \| R Club loocv1 cv.glm(data=Auto, glmfit=model1) The first component is the raw cross validation estimate of prediction error. The second component is the adjusted cross validation estimate. The adjustment is designed to compensate for the bias introduced by not using leave one out cross validation. Generalized Linear Models (glm) yeonghoey cv.glm has also a parameter named cost, which is a function accepts the actual and predcited value and returns cost, a non negative scalar value. When data has factor variable, there might be a case that a random sampled group observation doesn't cover all the factor levels. Statistical Consulting Topics In R, you can calculate the CV prediction error for a linear or generalized linear model using the cv:glm function in the boot pack age (you must use glm() to t model). 7 Lab 4 – Cross Validation The Validation Set Approach. We use a subset of last weeks non western immigrants data set (the version for this week includes men only). We can use the head() function to have a quick glance at the data. Download the data here. The codebook is: 5.8 Shrinkage \| Notes for Predictive Modeling 5.8 Shrinkage. Enforcing sparsity in generalized linear models can be done as it was done with linear models. Ridge regression and Lasso can be generalized with glmnet with little differences in practice.. What we want is to bias the estimates of $$\boldsymbol{\beta}$$ towards being non null only in the most important relations between the response and predictors. ecospat ecospat.cv.glm.Rd at master · cran ecospat · GitHub ecospat man ecospat.cv.glm.Rd. Find file Copy path Fetching contributors… Cannot retrieve contributors at this time. 37 lines (24 sloc) 1.82 KB Raw Blame History \ name {ecospat.cv.glm} \ alias {ecospat.cv.glm} \ title {GLM Cross Validation} \ ... The family Argument for glmnet • glmnet This is a list of functions and expressions that get used in the iteratively reweighted least squares (IRLS) algorithm for fitting the GLM.. glmnet can fit penalized GLMs for any family as long as the family can be expressed as a family object. In fact, users can make their own families, or customize existing families, just as they can for regular GLMs. Leave One Out Cross Validation in R \| educational research ... First, we need to develop our basic least squares regression model. We will do this with the “glm” function. This is because the “cv.glm” function (more on this later) only works when models are developed with the “glm” function. Below is the code. tax.glm < glm (tax ~ mv crim zn indus chas nox rm age dis rad ... Resampling Methods: Cross Validation Re samplingMethods Inthismodule,wefocusoncross validation(CV)andthebootstrap. I CVcanbeusedtoestimatethetesterrorassociatedwitha ... Titanic – Part 2 Cross Validation. Cross Validation allows us to select the best model that the data support. The idea is to get the model that would predict new data.. One way to think about this is to take almost all the data, and try to predict the data that we are holding out. In other words, for a dataset with N datapoints, fit the model on N 1 points (the training set), and see how well you do predicting ... Cross validation \| R In cross validation, the value of a penalty (loss) function (mean prediction error) is computed on data not used for finding the model. Low value = good. Cross validation gives a good estimate of the actual predictive power of the model. Lab: Cross Validation and the Bootstrap — STATS 202 Leave one out cross validation (LOOCV) $$K$$ fold cross validation Bootstrap Lab: Cross Validation and the Bootstrap Model selection Best subset selection Stepwise selection methods Shrinkage methods Dimensionality reduction High dimensional regression Lab 1: Subset Selection Methods Lab 2: Ridge Regression and the Lasso cross_validation_Auto.txt Topic Cross Validation#Author ... 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en bts nrc stage , dans quelle categorie mettre le niveau scolaire cv , certification langues cv , modele de cv job d'ete dans l'administration , exemple cv commercial vin , comment orienter son cv , cv etudiant job temps partiel , cv adobe illustrator assistante de direction , exemples competences commer ce pour cv , exemple de cv sous word gratuit , cv modele fonctionnaire doit on mettre son service , cv hotesse de caisse ou employe polyvalente , telecharger modele cv europeen gratuit , cv pour emploi caissiere , ci joint mon cv au format world , model cv lettre de motivation cuisine , comment faire so cv ,	2021-01-19 18:02:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 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https://math.stackexchange.com/questions/3526788/let-p-be-the-transition-matrix-of-a-markov-chain-and-there-exists-an-integer-r/3526792	# Let P be the transition matrix of a Markov chain, and there exists an integer $r \geq 0$ such that every entry of $P^r$ is positive I would like to show this assumption implies that the Markov chain is irreducible and aperiodic. I was able to show the irreducible part but I'm having trouble proving the aperiodicity. I tried to prove there must exist an odd cycle, but I couldn't seem to proceed. Any help? Aperiodicity is immediate from the fact if a set $$A$$ of integers contains two consecutive integers then its gcd is $$1$$. Note that $$P^{r+1}$$ also has all entries positive as shown below: Suppose $$M$$ is a stochastic matrix . Suppose some element $$\sum_k m_{ik} P^{r}_{kj}$$ of the product $$MP^{r}$$ is $$0$$. Then $$m_{ik}=0$$ for all $$k$$ contradicting the fact that $$\sum_k m_{ik}=1$$. Apply this with $$M=P$$.	2020-04-01 15:20:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9650471806526184, "perplexity": 53.668460000067995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505731.37/warc/CC-MAIN-20200401130837-20200401160837-00457.warc.gz"}
https://par.nsf.gov/biblio/10367304-cosmic-ray-staircase-outcome-cosmic-ray-acoustic-instability	The cosmic-ray staircase: the outcome of the cosmic-ray acoustic instability ABSTRACT Recently, cosmic rays (CRs) have emerged as a leading candidate for driving galactic winds. Small-scale processes can dramatically affect global wind properties. We run two-moment simulations of CR streaming to study how sound waves are driven unstable by phase-shifted CR forces and CR heating. We verify linear theory growth rates. As the sound waves grow non-linear, they steepen into a quasi-periodic series of propagating shocks; the density jumps at shocks create CR bottlenecks. The depth of a propagating bottleneck depends on both the density jump and its velocity; ΔPc is smaller for rapidly moving bottlenecks. A series of bottlenecks creates a CR staircase structure, which can be understood from a convex hull construction. The system reaches a steady state between growth of new perturbations, and stair mergers. CRs are decoupled at plateaus, but exert intense forces and heating at stair jumps. The absence of CR heating at plateaus leads to cooling, strong gas pressure gradients and further shocks. If bottlenecks are stationary, they can drastically modify global flows; if their propagation times are comparable to dynamical times, their effects on global momentum and energy transfer are modest. The CR acoustic instability is likely relevant in thermal interfaces between cold more » Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10367304 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 513 Issue: 3 Page Range or eLocation-ID: p. 4464-4493 ISSN: 0035-8711 Publisher: Oxford University Press National Science Foundation ##### More Like this 1. ABSTRACT We use analytical calculations and time-dependent spherically symmetric simulations to study the properties of isothermal galactic winds driven by cosmic rays (CRs) streaming at the Alfvén velocity. The simulations produce time-dependent flows permeated by strong shocks; we identify a new linear instability of sound waves that sources these shocks. The shocks substantially modify the wind dynamics, invalidating previous steady state models: the CR pressure pc has a staircase-like structure with dpc/dr ≃ 0 in most of the volume, and the time-averaged CR energetics are in many cases better approximated by pc ∝ ρ1/2, rather than the canonical pc ∝ ρ2/3. Accounting for this change in CR energetics, we analytically derive new expressions for the mass-loss rate, momentum flux, wind speed, and wind kinetic power in galactic winds driven by CR streaming. We show that streaming CRs are ineffective at directly driving cold gas out of galaxies, though CR-driven winds in hotter ISM phases may entrain cool gas. For the same physical conditions, diffusive CR transport (Paper I) yields mass-loss rates that are a few-100 times larger than streaming transport, and asymptotic wind powers that are a factor of ≃4 larger. We discuss the implications of our results for galactic wind theory and observations; strongmore » 2. ABSTRACT Heating of virialized gas by streaming cosmic rays (CRs) may be energetically important in galaxy haloes, groups, and clusters. We present a linear thermal stability analysis of plasmas heated by streaming CRs. We separately treat equilibria with and without background gradients, and with and without gravity. We include both CR streaming and diffusion along the magnetic-field direction. Thermal stability depends strongly on the ratio of CR pressure to gas pressure, which determines whether modes are isobaric or isochoric. Modes with $\boldsymbol {k \cdot B }\ne 0$ are strongly affected by CR diffusion. When the streaming time is shorter than the CR diffusion time, thermally unstable modes (with $\boldsymbol {k \cdot B }\ne 0$) are waves propagating at a speed ∝ the Alfvén speed. Halo gas in photoionization equilibrium is thermally stable independent of CR pressure, while gas in collisional ionization equilibrium is unstable for physically realistic parameters. In gravitationally stratified plasmas, the oscillation frequency of thermally overstable modes can be higher in the presence of CR streaming than the buoyancy/free-fall frequency. This may modify the critical tcool/tff at which multiphase gas is present. The criterion for convective instability of a stratified, CR-heated medium can be written in the familiar Schwarzschild formmore » 3. Abstract The structure of shocks and turbulence are strongly modified during the acceleration of cosmic rays (CRs) at a shock wave. The pressure and the collisionless viscous stress decelerate the incoming thermal gas and thus modify the shock structure. A CR streaming instability ahead of the shock generates the turbulence on which CRs scatter. The turbulent magnetic field in turn determines the CR diffusion coefficient and further affects the CR energy spectrum and pressure distribution. The dissipation of turbulence contributes to heating the thermal gas. Within a multicomponent fluid framework, CRs and thermal gas are treated as fluids and are closely coupled to the turbulence. The system equations comprise the gas dynamic equations, the CR pressure evolution equation, and the turbulence transport equations, and we adopt typical parameters for the hot ionized interstellar medium. It is shown that the shock has no discontinuity but possesses a narrow but smooth transition. The self-generated turbulent magnetic field is much stronger than both the large-scale magnetic field and the preexisting turbulent magnetic field. The resulting CR diffusion coefficient is substantially suppressed and is more than three orders smaller near the shock than it is far upstream. The results are qualitatively consistent with certainmore » 4. ABSTRACT Large-scale galactic winds driven by stellar feedback are one phenomenon that influences the dynamical and chemical evolution of a galaxy, redistributing material throughout the circumgalatic medium. Non-thermal feedback from galactic cosmic rays (CRs) – high-energy charged particles accelerated in supernovae and young stars – can impact the efficiency of wind driving. The streaming instability limits the speed at which they can escape. However, in the presence of turbulence, the streaming instability is subject to suppression that depends on the magnetization of turbulence given by its Alfvén Mach number. While previous simulations that relied on a simplified model of CR transport have shown that super-Alfvénic streaming of CRs enhances galactic winds, in this paper we take into account a realistic model of streaming suppression. We perform three-dimensional magnetohydrodynamic simulations of a section of a galactic disc and find that turbulent damping dependent on local magnetization of turbulent interstellar medium (ISM) leads to more spatially extended gas and CR distributions compared to the earlier streaming calculations, and that scale heights of these distributions increase for stronger turbulence. Our results indicate that the star formation rate increases with the level of turbulence in the ISM. We also find that the instantaneous windmore » 5. ABSTRACT Cosmic rays (CRs) are an important component in the interstellar medium, but their effect on the dynamics of the disc–halo interface (<10 kpc from the disc) is still unclear. We study the influence of CRs on the gas above the disc with high-resolution FIRE-2 cosmological simulations of late-type L⋆ galaxies at redshift z ∼ 0. We compare runs with and without CR feedback (with constant anisotropic diffusion κ∥ ∼ 3 × 1029 cm2 s−1 and streaming). Our simulations capture the relevant disc–halo interactions, including outflows, inflows, and galactic fountains. Extra-planar gas in all of the runs satisfies dynamical balance, where total pressure balances the weight of the overlying gas. While the kinetic pressure from non-uniform motion (≳1 kpc scale) dominates in the mid-plane, thermal and bulk pressures (or CR pressure if included) take over at large heights. We find that with CR feedback, (1) the warm (∼104 K) gas is slowly accelerated by CRs; (2) the hot (>5 × 105 K) gas scale height is suppressed; (3) the warm-hot (2 × 104–5 × 105 K) medium becomes the most volume-filling phase in the disc–halo interface. We develop a novel conceptual model of the near-disc gas dynamics in low-redshift L⋆ galaxies: with CRs, the disc–halo interface is filled with CR-driven warm winds and hotmore »	2023-01-27 12:24:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6489489674568176, "perplexity": 2510.863599077692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00585.warc.gz"}
https://testbook.com/question-answer/if-1-2-are-the-cube-roots-of-unit--5eeb8a5d5bfc210d0e93e9aa	# If 1, ω, ω2 are the cube roots of unity, then (1 + ω) (1 + ω2) (1 + ω3) (1 + ω + ω2) is equal to This question was previously asked in NDA (Held On: 23 April 2017) Maths Previous Year paper View all NDA Papers > 1. -2 2. -1 3. 0 4. 2 Option 3 : 0 Free Electric charges and coulomb's law (Basic) 36074 10 Questions 10 Marks 10 Mins ## Detailed Solution Concept: • ω = $$\frac{{ - 1 + {\rm{i}}\sqrt 3 }}{2}$$ and ω2 = $$\frac{{ - 1 - {\rm{i}}\sqrt 3 }}{2}$$ where ω is cube root of unity. • $${{\rm{\omega }}^{3{\rm{k}}}} = 1,{\rm{\;}}{{\rm{\omega }}^{\left( {3{\rm{k}} + 1} \right)}} = {\rm{\;\omega \;and\;}}{{\rm{\omega }}^{\left( {3{\rm{k}} + 2} \right)}} = {\rm{\;}}{{\rm{\omega }}^2}$$ • $$1 + {\rm{\omega }} + {{\rm{\omega }}^2} = 0$$ Calculation: Given that, (1 + ω) (1 + ω2) (1 + ω3) (1 + ω + ω2) where 1, ω, ω2 are the cube roots of unity As we know, $$\Rightarrow 1 + {\rm{\omega }} + {{\rm{\omega }}^2} = 0$$ So, ⇒ (1 + ω) (1 + ω2) (1 + ω3) (1 + ω + ω2) = (1 + ω) (1 + ω2) (1 + ω3) (0) = 0	2021-09-19 15:15:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8050345182418823, "perplexity": 11540.981586603799}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00604.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-11-cumulative-review-page-834/5	## Algebra: A Combined Approach (4th Edition) $Domain = [-4,4]$ $Range = [-2,2]$ We can see that the only x-values of the relation are from $-4$ to $4$, therefore its domain is $[-4,4]$ And we can see that the only y-values of the relation are from $-2$ to $2$, therefore its range is $[-2,2]$	2018-04-26 11:53:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9122537970542908, "perplexity": 220.72413214474074}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948126.97/warc/CC-MAIN-20180426105552-20180426125552-00224.warc.gz"}
http://searene.me/2017/05/07/the-machanism-of-garbage-collectors-in-Java/	# the machanism of garbage collectors in Java There are several garbage collectors in Java, each has its specific usage scenario. To understand garbage collection, we first have to understand how heaps are divided in Java. Heaps are divided into two parts in Java, one is called the Young Generation, and the other one is called the Old Generation. You may have seen something called the Permanent Generation in other tutorials/documentations. It exists in Java 7 and before, Oracle removed it in Java 8. The Young Generation is also divided into three parts: 1. Eden Area 2. Survivor Space 1 3. Survivor Space 2 The whole picture in Heap is as follows. Basically, there are two types of garbage collections for most collectors: 1. Young Generation Collection 2. Old Generation Collection Young Generation Collection is meant to be time-efficient and frequent, this is different from the Old Generation Collection, which could take a long time, and it’s done less frequently. The Old Generation usually has larger heap space. ## Serial Collector Young Generation Collection Using the Serial Collector When you new an object in the Java code, the space for that object will be allocated in the Eden Area. After a while, the Eden Area may be filled up, so live objects in it will be copied into one of the Survivor Space, let’s say it’s Survivor Space 1. Some large objects that won’t be fit in the Survivor Space will be copies into the Old Generation. After a while, some live objects in Survivor Space 1 become dead, i.e., they are not referenced by any other objects anymore, and some more space is allocated in the Eden Area for newly initiated objects. Now you can see, objects exist in Eden and Survivor Space 1, and Survivor Space 2 is empty. This is where the interesting thing begins. Because from now on, what the Young Generation does is to repeat the following process. When the Eden Area is filled up again. live objects in it will be copied into Survivor Space 2(Some large objects that are too large to fit in Survivor Space will be copied into the Old Generation). The live objects that are relatively young are copied into the Survivor Space 2, live objects that are relatively old(i.e., they survived through several Young Generation Collections) are copied into the Old Generation. Then all dead objects in the Eden and Survivor Space 1 will be garbage collected, the two survivor spaces swap roles, the Survivor Space 1 is empty while the Survivor Space 2 is not, and the above process will be repeated. Old Generation Collection Using the Serial Collector Old Generation Collection is divided into three steps, mark-sweep-compact. In the mark phase, the collector identifies live objects, the sweep phase sweeps over the generation and frees space taken by dead objects. Then the collector moves all live objects to the beginning of the old generation, which is called compaction. The compaction is for quick space allocation in the old generation later on. When to Use the Serial Collector The Serial Collector is done in a single-threaded way, so it’s meant to be run on client-style machines that do not require low pause times. And since it only takes a small amount of memory, the serial collector can perform very well with only 64MB heaps in most cases. ## Parallel Collector Young Generation Collection Using the Parallel Collector Young Generation collection in the parallel collector is the same as the Serial Collector, except that it’s done in parallel. The Parallel Collector fully utilizes the power of multiple threads and make the process of Young Generation Collection faster. Although the Young Generation Collection is still a stop-the-world action, the process would take less time and make less impact to the running program. Old Generation Collection Using the Parallel Collector Old Generation Collection using the Parallel Collector is the same as the Serial Collector. When to Use the Parallel Collector You can use the Parallel Collector when you have multiple CPU cores, whose power could be unleashed and utilized by it. But also notice that the Parallel Collector wouldn’t help you a lot if you need a much shorter pause time in GC, because it still takes a long time to finish the Old Generation Collection, which is done in a single-threaded way in the Parallel Collector. ## Parallel Compacting Collector Young Generation Collection Using the Parallel Collector Young Generation Collection using the Parallel Compacting Collector is the same as the Parallel Collector. Old Generation Collection Using the Parallel Collector Old Generation Collection in the Parallel Compacting Collector is done in a multi-threaded way, this is different from the Parallel Collector, whose uses only a single thread to complete Old Generation Collection. There are in total three phases regarding Old Generation Collection. First of all, the old generation is divided into several regions of the same fixed sizes. Then live objects that are directly reachable from the code are divided equally among multiple threads. Those threads work concurrently to mark all live objects in the old generation, storing the size and location of each live object. Due to previous compactions, some portions on the left side of the old generation are typically denser than those on the right side of it. So the collector will search from the left side, calculate the density of live objects in each region until it reaches a point where the density is small enough to be considered eligible for garbage collection. All the regions to the left of the point are not worth garbage collecting, and they will not be moved, those regions are called dense prefix. All the regions to the right of the point will be garbage collected. After collection, the collector will store the location of the first live object in each region, which would be helpful in the compaction phase. Live objects on the right side will be moved to the left side of the old generation, leaving a huge chunk of contiguous free memory on the right side. This process is called compaction. When to Use the Parallel Compacting Collector You can use the Parallel Compacting Collector if you have multiple CPU cores that could be utilized. The collector will take advantage of those CPU cores and make the total pause time shorter. ## Concurrent Mark-Sweep(CMS) Collector Young Generation Collection Using the CMS Collector Young Generation Collection using the CMS Collector is the same as the Parallel Collector. Old Generation Collection Using the CMS Collector There are four phases in total in the Old Generation Collection using the CMS Collector. All live objects that are directly reachable from the code are marked as alive. It takes a short pause to do it. While the application is running, the collector marks live objects that are transitively reachable from the above set obtained from the Initial Mark. Because the Concurrent Mark is conducted while the application is still running, some live objects cannot be detected in the second phase. So the application stops for a while, and the collector checks all objects that are modified during the Concurrent Mark phase, and mark all objects that turned garbage during the previous phase. After the Remark phase, all live objects are marked. The collector conducts a Sweep operation to eliminate all garbage in the Old Generation. The CMS Collector is the only collector that has no compact phase, which means it cannot use the bump-the-pointer strategy(see reference below) to find free space. bump-the-pointer strategy: This is a strategy used to allocate new space in the Old Generation. With this strategy, you only need to store the position of the last live object after each Old Generation Collection. When you need to allocate a space to store a new object, what you need to do is just to allocate the space right after the position and update the position to the new one. There are no live objects after that position because the Old Generation has been compacted before. The strategy is used in all above collectors except the CMS Collector because the CMS Collector doesn’t compact the Old Generation. So how does the CMS Collector find new space to allocate? Basically, it maintains a linked list internally, which connects all free space together. When an allocation is needed, the collector will traverse through the list and find the appropriate region to allocate the space. Another disadvantage of the CMS Collector is that it needs a bigger heap size because the Concurrent Mark phase proceeds while the application is still running, which means more space needs to be allocated when some garbage cannot be collected in time. So enough heap size must be prepared to store both uncollected garbage and newly allocated space. When to Use the CMS Collector The CMS Collector is typically used in the server side application, where large heap size and multiple CPU cores could be utilized. Those applications usually require a smaller pause time, which is exactly what the CMS Collector is good at. ## G1(Garbage First) Collector G1 Collector is different from previous collectors. All the previous collectors have a young generation and an old generation of fixed-size. This is the not the case for the G1 Collector. For the G1 Collector, the entire heap is divided into approximately 2000 areas, the size of each area is around 1MB ~ 32MB. The type of these areas may be different, it may be eden, survivor area, or the old generation. The whole picture is as follows. Although the size of each region is the same in the above picture, in reality, this may not be the case. The size of each region usually depends on how the collector optimizes the collection algorithm, and they are changing constantly. Notice that Humongous Region is used to store objects that are larger than 50% of the normal region size. Currently, no optimization is applied to this type of region, so avoid using objects that are too large. Young Generation Collection Using the G1 Collector 1. Live objects in eden areas are copied into survivor areas. 2. Some live objects that are out of the time threshold are copied into old generations. 3. “Accounting” process is performed, which determines how much time is needed for the next Young GC based on the current stats and the predefined pause time. 4. Resize eden/survivor regions based on the information obtained above. Old Generation Collection Using the G1 Collector 1. Initial Mark: mark all survivor regions which may have references to objects in old generations. This step is done concurrently with Young GC. So although it’s still a stop-the-world operation(because the entire Young GC is a stop-the-world operation), it doesn’t take extra time to complete. 2. Root region Scan: scan survivor regions for references into the old generation. It happens when the application is still running. 3. Concurrent Mark: mark all live objects across the entire heap, this is done while the application is still running. 4. Remark: stop the world and complete the marking process. 5. Cleanup: • Perform accounting on live objects and completely free regions.(stop-the-world) • Scrubs Remembered Sets.(stop-the-world) • Reset empty regions and return them to the free list.(concurrent) 6. Copy: copy live objects from to new regions. This is a stop-the-world step. It can be seen as a kind of compaction. Share	2018-04-24 00:53:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17649486660957336, "perplexity": 1545.0374734696586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946314.70/warc/CC-MAIN-20180424002843-20180424022843-00386.warc.gz"}
https://tel.archives-ouvertes.fr/tel-02393553	Rigidité symplectique et EDPs hamiltoniennes Abstract : We study symplectic rigidity properties in both finite and infinite dimension. In finite dimension, the main tools that we use are generating functions and symplectic capacities. In infinite dimension we study flows of Hamiltonian partial differential equations (PDEs) and, in particular, flows which can be uniformly approximated by finite dimensional Hamiltonian diffeomorphisms.In the first part of this thesis we study the action selectors defined from generating functions and we build Hamiltonian invariants for subsets of $R^{2m}times T^*T^k$. This allows us to prove a coisotropic non-squeezing theorem for compactly supported Hamiltonian diffeomorphisms of $R^{2n}$. We then extend this result to some non-compact settings. Finally we explain how this result can give information about the middle dimensional symplectic rigidity problem. Still in finite dimensions, we show that it is possible to use the symplectic camel theorem to create energy surfaces with compact invariant subsets.In the second part of the thesis we study symplectic rigidity properties of flows of Hamiltonian PDEs. We work in the context introduced by Kuksin and study a particular class of semi-linear Hamiltonian PDEs that can be approximated by finite dimensional Hamiltonian diffeomorphisms. We first give a new construction of an infinite dimensional capacity using Viterbo's capacities. The main result of this part is the proof of the analogue of the middle dimensional rigidity for certain types of Hamiltonian PDEs. These include nonlinear string equations with bounded nonlinearity such as the Sine-Gordon equation. In the final part of this thesis we study an analogue of Arnold's conjecture for the periodic Schrödinger equations with a convolution nonlinearity. Keywords : Document type : Theses Cited literature [57 references] https://tel.archives-ouvertes.fr/tel-02393553 Contributor : Abes Star : Contact Submitted on : Wednesday, December 4, 2019 - 2:15:07 PM Last modification on : Wednesday, September 23, 2020 - 1:41:46 AM Long-term archiving on: : Thursday, March 5, 2020 - 4:28:00 PM File Bustillo-2018-These.pdf Version validated by the jury (STAR) Identifiers • HAL Id : tel-02393553, version 1 Citation Jaime Bustillo. Rigidité symplectique et EDPs hamiltoniennes. Mathématiques générales [math.GM]. Université Paris sciences et lettres, 2018. Français. ⟨NNT : 2018PSLEE050⟩. ⟨tel-02393553⟩ Record views	2020-10-21 19:47:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6562163233757019, "perplexity": 1022.9091804134152}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107877420.17/warc/CC-MAIN-20201021180646-20201021210646-00237.warc.gz"}
http://mathhelpforum.com/discrete-math/139838-equivalent-relations-help.html	# Thread: equivalent relations help 1. ## equivalent relations help Hey guys, having trouble with the following question. Let A = {1,2,3,4}, a) how many relations are there on A? My answer: $\mathcal{P}(A \cdot A)$ = $2^{4 \cdot 4}$ = $2^{16}$ b) How many equivalent relations are there on A? My answer: Im not sure about this one. Any help? 2. Originally Posted by jvignacio Let A = {1,2,3,4}, a) how many relations are there on A? My answer: $\mathcal{P}(A \cdot A)$ = $2^{4 \cdot 4}$ = $2^{16}$ CORRECT b) How many equivalent relations are there on A? Before I answer please answer this. Does you textbook/instructor really use the notation $A\cdot A$ for the cross product of $A$ with itself? The almost standard notation is $A\times A$. For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set. You want to find the fourth Bell number. 3. Originally Posted by Plato Before I answer please answer this. Does you textbook/instructor really use the notation $A\cdot A$ for the cross product of $A$ with itself? The almost standard notation is $A\times A$. For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set. You want to find the fourth Bell number. No they use $A\times A$ but I didnt know the latex symbol for x. Now I do Not sure what you mean by fourth Bell number..... 4. Originally Posted by jvignacio No they use $A\times A$ but I didnt know the latex symbol for x. Now I do Not sure what you mean by fourth Bell number..... Do a web search for Bell Numbers.	2016-12-10 21:05:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8847399950027466, "perplexity": 584.7884621696929}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543567.64/warc/CC-MAIN-20161202170903-00510-ip-10-31-129-80.ec2.internal.warc.gz"}
http://tailieu.vn/doc/cac-mang-utms-va-cong-nghe-truy-cap-vo-tuyen-p2-274217.html	# Các mạng UTMS và công nghệ truy cập vô tuyến P2 Chia sẻ: Do Xon Xon \| Ngày: \| Loại File: PDF \| Số trang:28 0 55 lượt xem 10 ## Các mạng UTMS và công nghệ truy cập vô tuyến P2 Mô tả tài liệu SYSTEM ANALYSIS FUNDAMENTALS FUNDAMENTALS OF SYSTEM ANALYSIS Third generation systems focus on providing a universal platform to afford multifarious communications options at all levels, i.e. the radio as well as the core network sides. This implies the application of optimum techniques in multiple access and interworking protocols for the physical and upper layers, respectively. Chủ đề: Bình luận(0) Lưu ## Nội dung Text: Các mạng UTMS và công nghệ truy cập vô tuyến P2 2. 14 The UMTS Network and Radio Access Technology 2.1.1.2 Wide-band Digital Channel Systems Some of the drawbacks and limitations in the narrow-band channel systems made room for wide-band channel system designs. In wide-band systems the entire bandwidth re- mains available to each user, even if it is many times larger than the bandwidth required to convey the information. These systems include primarily Spread Spectrum (SS) sys- tems, e.g. Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS). In DSSS, emphasized in this book, the transmission bandwidth ex- ceeds the coherent bandwidth, i.e. the received signal after de-spreading resolves into multiple time-varying delay signals that a RAKE receiver can exploit to provide an in- herent time diversity receiver in a fading environment. In addition, DSSS has greater resistance to interference effects when compared to FDMA and TDMA. The latter greatly simplifies frequency band assignment and adjacent cell interference. In addition, capacity improvements with DSSS or more commonly referred to as DS-CDMA2, re- sulting from the voice activity factor, which we cannot apply effectively to FDMA or TDMA. With DS-CDMA, e.g. adjacent micro-cells share the same frequencies, whereas interference in FDMA and TDMA does not allow this. Other benefits and features can be found in [10–12]. Here we focus on the WCDMA or FDD mode and TDMA/ CDMA or TDD mode of the UTRA solution. 2.1.1.3 The UTRA FDD Mode: WCDMA Figure 2.1 illustrates some of the UTRA Frequency Division Duplexing (FDD) charac- teristics. This mode uses Wide-band Direct-Sequence Code Division Multiple Access (DS-CDMA), denoted WCDMA. To support bit rates up to 2 Mbps, it utilizes a variable spreading factor and multi-code links. It supports highly variable user data rates through the allocation of 10 ms frames, during which the user data rate remains constant, al- though the latter may change from frame to frame depending on the network control. It realizes a chip rate of 3.84 Mcps within 5 MHz carrier bandwidth, although the actual carrier spacing can be selected on a 200 kHz grid between approximately 4.4 and 5 MHz, depending on the interference situation between the carriers. ÃArrpÃ Ã WhvhiyrÃivÃhrÃ rvprÃ QrÃ CvtuÃivÃhrÃ ##$ÃHCÃ r vprÃ UvrÃ 9vssr rÃ rhqvtÃshp Ã ÃÃ rtÃhyyvtÃ'±"'#ÃxiÃ Figure 2.1 The UTRA WCDMA or FDD mode characteristics. _______ 2 Direct Sequence Code Division Multiple Access. 3. System Analysis Fundamentals 15 The FDD has a self timing point of reference through the operation of asynchronous BSs, and it uses coherent detection in the up- and downlink based on the use of pilot reference symbols. Its architecture allows the introduction of advanced capacity and coverage enhancing CDMA receiver techniques, e.g. multi-user detection and smart adaptive antennas. In addition, it will seamlessly co-exist with GSM networks through its inter-system handover functions of WCDMA. 2.1.1.4 The UTRA TDD Mode: TD/CDMA The 2nd UTRA mode results from the combination of TDMA–FDMA and exploits spreading as part of its CDMA component. It operates in Time Division Duplexing using the same frequency channel. ÃA rrp Qr ##$ÃHC Hyvpqr Uvr Hyvy PV IUDPH HyvpqrÃÃHyvy WhvhiyrÃTrhqvt Figure 2.2 UTRA TDD mode characteristics. In this mode, the MSs can only access a Frequency Division Multiplexing (FDM) chan- nel at specific times and only for a specific period of time. Thus, if a mobile gets one or more Time Slots (TS) allocated, it can periodically access this set of TSs throughout the duration of the frame. Spreading codes described in Chapter 4 separate user signals within one or more slots. Hence, in the TDD mode we define a physical channel by a code, one TS, and one frequency, where each TS can be assigned to either the uplink or the downlink depending on the demand. Users may obtain flexible transmission rates by occupying several TSs of a frame as illustrated in Figure 2.2, without additional proc- essing resources from the transceiver hardware. On the other hand, when more than one frequency channel gets occupied, utilization of transceiver resources will increase if the wide-band transmission cannot prevent it. We achieve variable data rates through either multi-code transmission with fixed spreading or through single code with variable spreading. In the 1st case, a single user or users may get multiple spreading codes within the same TS; while in the 2nd case, the physical channel spreading factor may vary according to the data rate. 4. 16 The UMTS Network and Radio Access Technology 2.1.2 Signal Processing Aspects In the following, we review Signal Processing characteristics for the WCDMA as well as TD/CDMA as a base to describe key functions of the UTRA FDD and TDD modes. These include spreading aspects and modulation and coding. 2.1.2.1 The Spread Spectrum Concept Digital designs of communications systems aim to maximise capacity utilization. We can for example increase channel capacity by increasing channel bandwidth, and/or transmitted power. In this context, CDMA operates at much lower S/N ratios as a result of the extra channel bandwidth used to achieve good performance at low signal-to-noise ratio. From Shannon’s channel capacity principle [22] expressed as: 6Þ & = % ORJ Î + Ï 5. Ð 1ß à where B is the bandwidth (Hz), C is the channel capacity (bits/s), S is the signal power, and N is the noise power; we can find a simple definition of the bandwidth as: & 1 %= 6. 6 Thus, for a particular S/N ratio, we can achieve a low information error rate by increas- ing the bandwidth used to transfer information. To expand the bandwidth here, we add the information to the spreading spectrum code before modulation. This approach ap- plies for example to the FDD mode, which uses a code sequence to determine RF bandwidth. The FDD mode has robustness to interference due to higher system process- ing gain3 Gp. The latter quantifies the degree of interference rejection and can be de- fined as the ratio of RF bandwidth to the information rate: % S = 7. 5 From Ref. [23] in a spread-spectrum system, thermal noise and interference determine the noise level. Hence, for a given user, the interference is processed as noise. Then, the input and output S/N ratios can relate as: Ë6Û Ë6Û Ì Ü = S Ì Ü 8. Í 1 ÝR Í 1 ÝL Relating the S/N ratio to the Eb/No ratio4, where Eb is the energy per bit and No is the noise power spectral density, we get: Ë6Û (E 5 (E Ì Ü = = 9. Í 1 ÝL 1 R % 1 R S From the preceding equations we can express Eb/No in terms of the S/N input and output ratios as follows: _______ 3 Reference processing gains for spread spectrum systems have been established between 20 and 50 dBs. 4 Unless otherwise specified, here we assume that N includes thermal and interference noise. o 10. System Analysis Fundamentals 17 (E Ë6Û Ë6Û = S Ì Ü = Ì Ü	2017-10-17 02:27:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5704187154769897, "perplexity": 3216.8725207234156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820556.7/warc/CC-MAIN-20171017013608-20171017033608-00088.warc.gz"}
http://openstudy.com/updates/5116d222e4b09e16c5c88306	Here's the question you clicked on: ## haleyking345 Group Title Solving trig Equations a.) sin^2x=3 cos^2x one year ago one year ago • This Question is Closed 1. haleyking345 Group Title Please Help!!! 2. jtvatsim Group Title reposting question in better format: $\sin^2(x) = 3\cos^2(x)$ 3. haleyking345 Group Title I do not have a clue where to even start. 4. jtvatsim Group Title well, as it stands it looks pretty bad... do you remember what sin(x)/cos(x) is equal to? 5. haleyking345 Group Title tan x 6. jtvatsim Group Title good! now, let's use that to make this question simpler. divide both sides by cos^2(x) and it starts looking better. 7. jtvatsim Group Title You should get this:$\tan^2(x) = 3$ 8. haleyking345 Group Title So then you square root it right? 9. jtvatsim Group Title yes! 10. jtvatsim Group Title do not forget that you will have a positive and negative root 11. haleyking345 Group Title ok thank you 12. jtvatsim Group Title Let me know if you need any further help good luck! 13. SithsAndGiggles Group Title Alternatively, you can use the identity $\sin^2x +\cos^2x=1$ Rewriting the left (or right side, appropriately), you have $\sin^2x=3(1-\sin^2x)\\ \sin^2x=3-3\sin^2x\\ 4\sin^2x=3\\ \sin^2x=\frac{3}{4}$ 14. SithsAndGiggles Group Title Which gives you the difference of squares $\sin^2x-\left(\frac{\sqrt3}{2}\right)^2=0\\ \left(\sin x+\frac{\sqrt3}{2}\right)\left(\sin x-\frac{\sqrt3}{2}\right)=0$ Easily solvable.	2014-07-25 17:28:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7376205921173096, "perplexity": 10235.945795038328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894378.97/warc/CC-MAIN-20140722025814-00020-ip-10-33-131-23.ec2.internal.warc.gz"}
https://www.researchgate.net/publication/222513004_Managerial_timing_and_corporate_liquidity_evidence_from_actual_share_repurchases	Article # Managerial timing and corporate liquidity:: evidence from actual share repurchases Authors: To read the full-text of this research, you can request a copy directly from the authors. ## Abstract We investigate the timing of open market share repurchases and the resultant impact on firm liquidity. Using the Stock Exchange of Hong Kong's unique disclosure environment, we identify the exact implementation dates for more than five thousand equity buybacks. We find that managers exhibit substantial timing ability. Consistent with the information-asymmetry hypothesis, bid–ask spreads widen and depths narrow during repurchase periods. We decompose bid–ask spreads and show that adverse selection costs increase substantially as market participants respond to the presence of informed managerial trading. Our findings provide additional insight into how markets process information and have significant implications for corporate payout and disclosure policies. ## No full-text available ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. ... ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. In contrast, Zhang (2005), using a novel estimation technique by retaining in the sample only the first daily announcement in a sequence of multiple repurchase announcements within a month, finds evidence consistent with price support. ... ... In the Greek stock market, which is the focus of our paper, and for the period we are studying, firms disclose their repurchases within seven trading days. Compared to the institutional setting of other published studies on actual share repurchases, the Greek disclosure requirement is different from the daily requirement of Hong-Kong (Brockman and Chung, 2001) or Australia (Akyol and Foo, 2013), and the monthly requirement of France in the 2000-2002 period (Ginglinger and Hamon, 2007). Because the institutional setting is different from other countries, an empirical study of the Greek market would allow us to understand further these controversies. ... ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. ... ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. In contrast, Zhang (2005), using a novel estimation technique by retaining in the sample only the first daily announcement in a sequence of multiple repurchase announcements within a month, finds evidence consistent with price support. ... ... In the Greek stock market, which is the focus of our paper, and for the period we are studying, firms disclose their repurchases within seven trading days. Compared to the institutional setting of other published studies on actual share repurchases, the Greek disclosure requirement is different from the daily requirement of Hong-Kong (Brockman and Chung, 2001) or Australia (Akyol and Foo, 2013), and the monthly requirement of France in the 2000-2002 period (Ginglinger and Hamon, 2007). Because the institutional setting is different from other countries, an empirical study of the Greek market would allow us to understand further these controversies. ... Article Full-text available Using a unique, hand-collected data set of actual daily share repurchases from the Athens Stock Exchange, we examine the stock market reaction around the disclosure date of actual share repurchases, the factors that affect the size of that reaction, and the motives behind share acquisitions. We find that different firms proceed to actual repurchases for different reasons: the results for the small firms and the firms with high book-to-market ratio repurchases are consistent with the signaling undervaluation hypothesis, while the results for the large firms and firms with low book-to-market ratio are in line with the price support hypothesis. In contrast to other studies, we find that long-term abnormal returns are higher for repurchasing firms compared to non-repurchasing controls and depend positively on the frequency of repurchases. ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. ... ... Regarding SRP implementations in foreign markets, Brockman and Chung (2001) and Zhang (2005) study the Hong Kong capital market, where firms are required to disclose repurchase details no later than the next trading day. Brockman and Chung (2001) find that managers acquire shares at a lower cost than a naive accumulation strategy, a result consistent with either timing based on insider information, or price support. In contrast, Zhang (2005), using a novel estimation technique by retaining in the sample only the first daily announcement in a sequence of multiple repurchase announcements within a month, finds evidence consistent with price support. ... ... In the Greek stock market, which is the focus of our paper, and for the period we are studying, firms disclose their repurchases within seven trading days. Compared to the institutional setting of other published studies on actual share repurchases, the Greek disclosure requirement is different from the daily requirement of Hong-Kong (Brockman and Chung, 2001) or Australia (Akyol and Foo, 2006), and the monthly requirement of France in the 2000-2002period (Ginglinger and Hamon, 2007. Because the institutional setting is different from other countries, an empirical study of the Greek market would allow us to understand further these controversies. ... Article Full-text available Using a unique, hand-collected data set of actual daily share repurchases from the Athens Stock Exchange, we examine the stock market reaction around the disclosure date of actual share repurchases, the factors that affect the size of that reaction, and the motives behind share acquisitions. We find that different firms proceed to actual repurchases for different reasons: the results for the small firms and the firms with high book-to-market ratio repurchases are consistent with the signaling undervaluation hypothesis, while the results for the large firms and firms with low book-to-market ratio are in line with the price support hypothesis. In contrast to other studies, we find that long-term abnormal returns are higher for repurchasing firms compared to non-repurchasing controls and depend positively on the frequency of repurchases. ... It is interesting to note that, in many countries, especially emerging countries where shareholder right are weak, share repurchases have been illegal initially (see eg; Zhang (2002) and Wada (2005) for Japan, Lamba and Ramsay 2000 for Australia, Brockman and Chung (2001) for Hong Kong). It seems a supporting evidence of Jiraporn (2006) and La Porta et al. (1997). ... ... In this case, repurchases may be used as a commitment device (not to take the value reducing project). Now, repurchases and share-holder rights may be substitutes 5 . ... ... For example, please seeZhang (2002) andWada (2005) for Japan,Lamba and Ramsay (2000) for Australia,Brockman and Chung (2001) for Hong Kong.3 Hence, our analysis provides a natural complement to the analysis of LaPorta et al. (1997) who analyze whether dividends and investor protection are substitutes or complements. ... Article Full-text available This paper provides a theoretical analysis of the effects of the strength of investor rights on a firm’s share repurchase policy in the face of agency conflicts and behavioural biases. We consider three reasons for firms to repurchase their shares; to eliminate agency costs of free cash-flow, to time the market, and to cater to investors. In the first case, we demonstrate that investor rights and repurchases may be complements or substitutes in addressing free cash flow problems. In the second case, we argue that stronger investor rights increase informational disclosure which reduces the ability to time the market using repurchases. In the final case, we argue that stronger investor rights may reduce value reducing repurchase catering. We consider the corporate governance implications of our analysis, and discuss the effects of behavioural factors, such as bounded rationality, overconfidence, and regret, on the efficacy of governance systems to deal with the problems relating to repurchases ... Many studies Cole et al., 1996;Dittmar, 2000) find that stock repurchases are driven by market timing of managers. Brockman and Chung (2001) examine the market-timing ability using repurchase trading data of 190 firms in Hong Kong. The studies provide evidence that post aggregate market turndown, managers time the market along with their trading by paying a lower price for the shares bought. ... ... Similar results were obtained using 248 repurchase announcements in NYSE (Miller and McConnell, 1995). Brockman and Chung (2001) did this for firms in Hong Kong and find that the presence of informed traders in the market hits up the adverse selection costs. This widens the bid-ask spread and reduces the depth in the market. ... Article This study aims to synthesise and analyse the existing literature on share repurchases. It summarises the key findings and identifies the potential research gaps in the extant literature. A pool of 206 research articles are chosen based on relevance and impact from a variety of reputed databases spanning over 1981 to 2020. The authors use the guideline of Templier and Pare (2015) and follow the narrative approach of literature review which consists of gathering and synthesising existing literature on share buyback. The diverse strands of literature on buyback are classified based on different research themes. The results indicate a paucity of research on share buyback in emerging markets (e.g., India and China). Overall, the research in the following areas is found to be sparse: buyback and firms reputation and the wealth effect of buyback on bondholders. The impact of executive reward schemes post buyback and presence of industry effect remains largely untapped. ... Dittmar, 2000;Fama and French, 2001;Jiang et al., 2013;Miller and Prondzinski, 2017), the liquidity changes hypothesis (e.g. Barclay and Smith, 1988;Brockman and Chung, 2001;Ginglinger and Hamon, 2007;Hillert et al., 2012;Moore, 2017), the tax saving hypothesis (e.g., Bagwell and Shoven, 1989;Jacob and Jacob, 2013;Korkeamaki et al., 2010;Moser, 2009;Oswald and Young, 2004;Rau and Vermaelen, 2002), the takeover deterrence hypothesis (e.g. Bagwell, 1991;Billett and Xue, 2007;Hai and Doan, 2012), the optimal capital structure hypothesis (e.g. ... ... Similarly, Hatakeda and Isagawa (2004) indicate that share buyback announcements dramatically increased in Japan for the period from 1995 until 1998. Brockman and Chung (2001) observe that only 8 Hong Kong share buyback programs in 1992, while in 1995 there were 100 shares buyback announcements. ... Article ... They argue that the level of market liquidity is a significant determinant for managers in deciding whether to repurchase stocks instead of paying dividends. Hillert et al. (2016) find that firms primarily buy back shares when liquidity is high as they try to reduce transaction costs which is in line with Brockman and Chung (2001). The effect of share buybacks on stock liquidity is controversial. ... ... See e.g.Barclay and Smith (1988),Brockman and Chung (2001) orGinglinger and Hamon (2007) for liquidity deteriorations andCook et al. (2004) orChung et al. (2007) for liquidity improvements. ... Article We study share repurchase announcements for nine European countries between 2000 and 2017. In contrast to previous studies, we address the role of market uncertainty as a market-based determinant of positive average abnormal announcement returns, while including governance, liquidity risk and firm related control variables. Economic policy uncertainty and financial uncertainty, individually as well as jointly, positively affect abnormal returns. We suggest that this relation is due to a stronger signaling effect under increased uncertainty, as both information asymmetry and underpricing tend to increase. Also, a potential hedge against adverse market movements is more valuable. Optimal timing of repurchase announcements should therefore consider market uncertainty conditions. ... Managers exercise tremendous discretion over the implementation of these programs. 2 Evidence suggests that managers use this discretion and their private information to execute buybacks at favorable prices (see Brockman and Chung 2001, Ikenberry et al. 2000, Cook et al. 2004, Dittmar and Field 2015. Traditionally, the literature asserts that informed buybacks hurt shareholders. ... ... The literature on buybacks emphasizes how informed managerial trading in the form of a share repurchase program hurts shareholders (e.g., Barclay and Smith 1988, Brockman and Chung 2001, Babenko et al. 2020. That conventional view suggests that the firm could protect its shareholders by committing to not use the manager's private information in the implementation of buybacks. ... Preprint Full-text available ... Over recent decades, open-market share repurchases (OMR) have become a popular means for firms to payout excess cash to shareholders in many countries (See, for example, Brockman and Chung (2001) in Hong Kong; Grullon and Michaely (2004) in the US; Ikenberry, Lakonishok and Vermaelen (2000) in Canada; and Rau and Vermaelen (2002) in the UK). Many studies have attempted to provide explanations for the positive market reactions normally associated with open market share repurchase announcements and managerial motives to repurchase shares. ... ... For example, Cook et al. (2004); Franz et al. (1995); Singh et al. (1994); and Wiggins (1994) find that open market share repurchases help enhance liquidity. In contrast, Barclay and Smith (1988); Brockman and Chung (2001); and Ginglinger and Hamon (1997) find a negative impact of share repurchases on liquidity. Nevertheless, Kim (2004) and Miller and McConnell (1995) find no significant change in liquidity as a result of open market share repurchases. ... ... On the macro front, Chung et al. (2013) report that liquidity decreases after monetary policy announcements in the U.S. markets. Liquidity also changes following firm-specific announcements such as share purchases (Barclay and Smith, 1988;Brockman and Chung, 2001;Cook, Krigman and Leach, 2004;Ginglinger and Hamon, 2007;Miller and McConnell, 1995;Hillert, Maug, and Obernberger, 2016); equity offerings (Balachandran et al. (2012) and Kothare (1997)); or dividend announcements (Graham, Koski, and Loewenstein (2006)). By connecting the two streams of banking and financial markets literature, we extend the current literature by analyzing the impact of bank loan announcements on the liquidity of borrowers' stocks. ... Article Full-text available We examine the impact of bank loan announcements on stock liquidity. Using a comprehensive loan announcement sample over 14 years in Australia, we find that effective spreads and realized spreads of borrowers’ stocks fall after the announcements. The findings suggest these announcements send positive signals about borrowers to the market that increases liquidity provision, and reduce transaction costs, leading to improved liquidity for borrowers’ stocks. This liquidity improvement is more pronounced following announcements of new loans than loan renewals. Overall, our findings provide practical implications for firm managers in the financing decision-making process and market participants in trading strategy adjustment. ... Studies have shown that transaction costs increase in the presence of insider trading because liquidity providers will widen bid-ask spreads to be compensated for trading in an environment that is wrought with asymmetric information (Copeland and Galai 1983;Kyle 1985;Glosten and Milgrom 1985; Barclay and Smith 1988;Bettis et al. 2000;Brockman and Chung 2001;Du and Wei 2004). Additionally, other studies have argued that insider trading creates an incentive to manipulate the timing and content of information releases (Ausubel 1990;Allen and Gale 1992), both of which can induce volatility in stock prices (see e.g., Du and Wei 2004 for empirical evidence). ... Article Full-text available The ethical considerations of insider trading have been widely debated in the academic literature (see e.g., Moore in J Bus Ethics 9(3):171–182, 1990). In 2013, the STOCK Act, which was initially passed to mitigate insider trading by government officials, was quickly and unexpectedly amended to allow certain government employees to withhold their financial information. To identify and quantify the potential costs placed on investors by non-corporate insider traders, we use the unusual circumstances surrounding this amendment. For a sample of stocks most held by members of Congress, we find that, relative to control stocks, liquidity significantly worsens and volatility increases during the post-amendment period. Our results highlight the costs that are incurred by investors in the presence of non-corporate insider trading. These findings call for a stronger development of an ethical framework that justifies the restriction of all types of insider trading. ... One reason for the mixed results is that the disclosure environment makes it difficult to conduct event studies for share repurchase announcements. Many U.S. corporations repurchase their shares without making any announcements and so empirical analyses, such as event studies that require precise information on the timing and prices, are difficult to conduct (Brockman and Chung 2001). One outcome of the varied results for the information content of share repurchase policies is that prior studies offer a mixed understanding of their economic consequences. ... Article Full-text available In this study we investigate the information content of firm payout policy to shareholders. We focus on the association between a firm’s payout policy and shareholders’ satisfaction with board directors, as expressed by the percentage of negative or withheld votes for directors during annual elections (shareholders’ dissent voting). We fill a gap in the literature by using shareholders’ voting results in the election of board members at annual meeting as a setting to examine shareholder perception of firms’ payout policies. We find that higher share repurchase and/or higher dividend payout are associated with lower shareholders’ dissenting votes. We also find that such relationship is conditional on the level of free cash flow, firm future performance, the degree of management entrenchment, and the type of institutional investors. Our study contributes to the payout literature by providing empirical evidence that shows the outcome of shareholders’ votes in director elections may be influenced by the board of directors’ payout decisions. ... Firms generally repurchase stock in the situations of distributing excess/idle cash (Dittmar, 2000) or because of stock price undervaluation (Brockman & Chung, 2001;Peyer & Vermaelen, 2007), or due to lack of investment opportunities (Grullon & Michaely, 2004) or to indicate robust future performance (Lie, 2005), or to boost earnings per share by diluting the effect of stocks options (Bens, Nagar, Skinner, & Wong, 2003) or perceiving the high risk of takeovers by other firms in the market (Doan, Yap, & Gannon, 2012). ... Article Full-text available ... These findings are consistent with the underlying idea that managers know firms' future cash flow better than outside investors. Indeed, previous studies show that managers successfully time the market: Wurgler (2002, 2000), Cohen et al. (2007), andDeAngelo et al. (2010) for SEOs; Brockman andChung (2001), Cook (2003), Ginglinger and Hamon (2007), and Zhang (2002) for repurchases. 2 The overvaluation hypothesis also predicts that stock prices increase before SEO announcements and that pre-announcement returns are negatively related to post-announcement stock returns. ... Article We examine whether and how the market interacts with investor sentiment in the context of seasoned equity offerings (SEOs) by Chinese listed firms. We adopt the component of market index return, which cannot be explained by fundamental macro-economic factors as a proxy for the market-wide investor sentiment, and overnight stock returns proxying for the firm-specific sentiment. We find robust evidence that investor sentiment drives the pre-announcement abnormal return. In the post-announcement period, the market corrects the sentiment-driven overvaluation within about one month. These findings reinforce the view that market timers take advantage of investor sentiment to issue seasoned shares. ... If misvaluation occurs because of asymmetric information between market participants and the firm, market participants are likely to infer from the firm's equity repurchase and issuance decisions that the share price may be overvalued or undervalued and then bid the price down or up. See, for example, the evidence in Brockman and Chung (2001). Further, even in the absence of asymmetric information or misvaluation, there can be a price impact for large trades if some traders face capacity or margin constraints, as in Gârleanu and Pedersen (2011) or He and Krishnamurthy (2013). ... Article We quantify how much nonfundamental movements in stock prices affect firm decisions. We estimate a dynamic investment model in which firms can finance with equity or cash (net of debt). Misvaluation affects equity values, and firms optimally issue and repurchase overvalued and undervalued shares. The funds flowing to and from these activities come from either investment, dividends, or net cash. The model fits a broad set of data moments in large heterogeneous samples and across industries. Firms respond to misvaluation by adjusting financing more than by adjusting investment. Managers' rational responses to misvaluation increase shareholder value by up to 8%. ... In the first stage, we use the full sample to estimate the probability of a management forecast falling within the repurchase event window based on a set of exogenous or predetermined instrumental variables identified in prior research (Brockman and Chung 2001;Brockman et al. 2008) along with the control variables used in Eq. (1). We employ logistic regressions clustered by year and industry to estimate the following equation: ... Article Full-text available We show that corporate governance mechanisms play an important role in controlling managers’ opportunistic behavior. Low executive equity compensation and a high intensity of outside monitoring help to discourage undesirable self-interested disclosure decisions by management before share repurchases. Corporate governance mechanisms also have a significant impact on long-run abnormal stock prices and operating performance. Firms that manipulate pre-repurchase disclosures experience positive long-term abnormal stock returns. However, we do not find that these firms experience positive long-run operating performance. Corporate governance mechanisms significantly attenuate the tendency toward negative pre-repurchase disclosures and their effects on stock prices and operating performance. ... We do not analyze trading profits around actual buyback activity. Although there is a growing literature measuring whether companies can buy back shares at discounts from market prices over short horizons (Dittmar and Field (2015), Bonaime, Hankins, and Jordan (2016) in the United States, McNally, Smith, and Barnes (2006) in Canada, Brockman and Chung (2001) in Hong Kong, and Zhang (2002) in Japan), we consider these more as tests of broker execution quality, not of the ability of managers to exploit fundamental misvaluation. One argument against using buyback authorizations (instead of completions) is that not all buybacks are completed (Stephens and Weisbach (1998)); indeed, the fact that a buyback authorization was not completed does not mean that it was a false signal or a manipulation attempt in the first place. ... Article Full-text available Using a sample of over 9,000 buyback announcements from 31 non-U.S. countries, we find support for the results of studies based on U.S. data: on average, share repurchases are associated with significant positive short-term and long-term excess returns. However, excess returns depend on the likelihood of undervaluation and the efficiency and liquidity of equity markets. In contrast to findings in U.S. markets, we do not find that these long-term excess returns are simply a compensation for takeover risk or have become less significant in recent years. ... The financial literature assumes that price significantly explains stock liquidity. Indeed, the studies ofAttig et al., (2006), Brockman andChung (2001), andAjina et al., (2015) found that stock price positively correlates with liquidity. Ascioglu et al., (2012) showed a negative relationship between stock liquidity and price. ... ... Repurchasing equity signals the undervaluing of firms (Brockman and Chung 2001;Peyer and Vermaelen 2007) and strong future performance (Lie 2005). In equity crowdfunding, corporations buy back shares at 8 % to 12 % premiums of the investment in the repurchasing promises. ... Article Full-text available This article draws on signal theory and the research findings of local bias in VC to examine how geographic distance (GD) and different signals affect equity crowdfunding platforms launching projects online. We find that local bias still exists in the pre-investment stage of equity crowdfunding. Equity crowdfunding platforms prefer to launch local projects online. We also prove that signals of media usage and start-ups’ quality (credit) are positively correlated with the launching of projects on platforms. Moreover, the platform is more inclined to list projects initiated by firms engaging in strategic emerging industries online. Above all, the signal of project risk fully mediates the relationship between start-ups’ quality and the launching of projects online. Empirical analyses are based on the dataset of equity crowdfunding projects on the Dahuotou equity crowdfunding platform ( http://www.dahuotou.cn/ ) during 2014–2017. ... The financial literature assumes that price significantly explains stock liquidity. Indeed, the studies ofAttig et al., (2006),Brockman andChung (2001), andAjina et al., (2015)found that stock pricepositively correlates with liquidity. ... ... For information, the link between repurchases on the market and the liquidity of the company's securities was recently the subject of several studies (Brockman and Chung, 2001;Cook andHamon., 2006) . The latest study was carried out on the French market. ... ... ( Brockman and Chung, 2001;Zhang, 2005;and McNally et al., 2006). In the long-term (over many years), Ikenberry et al. (2000) and Oswald and Young (2004) reinforce the notion that in general managers strategically time their repurchases to take advantage of decreasing prices. ... ... This finding is consistent with the argument presented byEvans and Evans (2001), who suggested that the implementation of a repurchasing strategy cannot guarantee the firm's superior long-run performance. The non-persistence of CARs is likely due to market uncertainties over the managers' ability to time repurchase announcements, where managers only buy back shares following declines in the prices for the stocks covered by their options agreements (Brockman & Chung, 2001;Cook et al., 2004). ... Article Full-text available By combining the market model with the three-factor model, this study investigates fir ms' share returns after the announcement of share repurchase. Employing data for Chi na's A-share market, this study's sample utilizes 417 share repurchase announcements over the pe riod of 2000 to 2012. Empirical results show that firms with higher sales gro wth rates are more likely to send a positive signal to the market through their share repur chase efforts. Analysis also shows that the higher a firm's price-to-earnings ratio (utilized as a measure of overvaluation), the lower the firm's cumulative abnormal returns. These results imply that Chinese share markets put more emphasis on the firm's future growth and share overvaluation. ... Many researches has found including the research from El-houchine and Boubaker (2014) commented about the " market timing " theory, that the managers will conduct repurchasing shares when the company security is undervalued. And,Firth and Yeung (2005)also stated that the perception of undervalued shares and the availability of cash surplus are the major factors in the decision to repurchase These reviews were validated byBrockman andChung (2001), Cook et al. (2004), andChung et al. (2007)who confirm the predictions of the of " market timing " theory which stipulates that the real repurchase is due to utilizing an information asymmetry between the investors and managers and that they carry out repurchases at a time when the firm is undervalued. In what it concerns the timing of share repurchase, literature confirmed the existence of certain waves or cycles of this phenomenon, for different reasons. ... Conference Paper Full-text available The objective of this research is to study the influence of Undervaluation, Free Cash Flow, Leverage and Dispersion of Ownership's toward Company's Stock Repurchase (An Empirical Study of Indonesia Stock Exchange Public Listed Companies). Many researchers have shown that the Stock Repurchase has shown the best alternatives for the company to recover the decrease of stock value by doing 'buyback' the stock from the market which mostly caused by the negative sentiment from the investors, especially during the crisis. The methodology approach of this research has use 26 sample of companies with purposive sampling method to determine 'sample criteria' on Public Listed companies listed in period of 2010 – 2014, which consistently publish their Stock Repurchase Announcement Report on the database of Indonesia Stock Exchange (IDX). Multiple regression analysis is used to conduct hypothesis test (test of assumptions) of the relationship and its influence of Undervaluation, Free Cash Flow, Leverage and Dispersion of Ownerships toward Company's Stock Repurchase. The findings show that R-Square shows the amount of 0.783 which means that all the dependant variable has significant relationship of 78.3% with its independent variables. And, on F-test also shows the significant simultaneous impact between Undervaluation, Free Cash Flow, Leverage and Dispersion of Ownerships toward Company's Stock Repurchase. And, t-test only Leverage, Dispersion of Ownerships has a partial influence toward Company's Stock Repurchase. Others, Undervaluation, Free Cash Flow shows negative value and above significant level of (α), or more than the confidence level 95%. This study can contribute in providing an overview of the factors of Undervaluation, Free Cash Flow Ownerships toward Company's Stock Repurchase in Indonesia which can be used by the investors/ potential investors to make decision making and reinforcing the best fundamental preparation on stock repurchase. ... We do not analyze trading profits around actual buyback activity. Although there is a growing literature measuring whether companies can buy back shares at discounts from market prices over short horizons (Dittmar and Field (2015), Bonaime, Hankins, and Jordan (2016) in the United States, McNally, Smith, and Barnes (2006) in Canada, Brockman and Chung (2001) in Hong Kong, and Zhang (2002) in Japan), we consider these more as tests of broker execution quality, not of the ability of managers to exploit fundamental misvaluation. One argument against using buyback authorizations (instead of completions) is that not all buybacks are completed (Stephens and Weisbach (1998)); indeed, the fact that a buyback authorization was not completed does not mean that it was a false signal or a manipulation attempt in the first place. ... Article Full-text available This paper documents that outside the U.S. short-term returns around share repurchase announcements are positive, although only about half the size as in the U.S. Long-run abnormal returns after buyback announcements follow the same pattern in non-U.S. firms as document by prior literature for U.S. firms extending the buyback puzzle to the global level. Cross-country differences in corporate governance quality and regulatory differences can explain variation in the short- and long-run abnormal returns. Globally, long-run abnormal returns are related to an undervaluation index (Peyer and Vermaelen, 2009, RFS) consistent with the interpretation that managers are able to time the market. ... We control for the impact of debt with Leverage, measured as the ratio of long-term debt over total assets (Jagannathan and Stephens, 2003). In addition, we control for the excess cash hypothesis (Dittmar, 2000;Brockman and Chung, 2001;Oswald and Young, 2008) with the proxy Cash, which is the ratio of net income before taxes plus depreciation and changes in deferred taxes and other deferred charges to total assets (Dittmar, 2000). 8 We also control for the impact of agency costs (Easterbrook, 1984;Jensen, 1986) with the use of Ownership Concentration (Mitchell and Dharmawan, 2007; Andriosopoulos and Hoque, 2013) measured as the ratio of closely held shares 9 over the total common shares outstanding before the repurchase announcement. ... Article Full-text available ... The purpose of the two-stage regression analysis is to eliminate endogenous variables affecting share repurchases and see if the fair disclosures made before and after share repurchases (DRepD) still affect the frequency of good and bad news (GN), and excess return (SRET). For the purpose of this paper, we adopt the following first stage regression analysis formula based on the methodology by Brockman and Chung (2001) and Brockman et al. (2008). ... Article This paper analyzes how Regulation Fair Disclosure (Reg FD hereinafter) affects share repurchases in an emerging market where information asymmetry problem is severe. The results indicate that the frequency of bad news disclosures and the size of negative excess return in the KOSDAQ market increase in a statistically significant manner prior to share repurchase, while the frequency of good news disclosures increases after share repurchase. This is consistent with the hypothesis that firms show opportunistic behavior of buying their own stocks at a low price by taking advantage of fair disclosures. In order to analyze the cause of the opportunistic behavior, we examine variables, such as the number of stock options held by the management and the ratio of shareholding by CEO and related parties. We find empirical evidence that the stock compensation ratio for the management shows a positive relationship with good news disclosures following the completion of share repurchase. Our findings suggest that there exists information distortion in Reg FD in order to protect the management’s ownership interest in Korean stock market. ... In this case, market participants are likely to infer from the firm's equity repurchase and issuance decisions that the share price may be overvalued or undervalued and then bid the price down or up. See, for example, the evidence in Brockman and Chung (2001). More generally, a large literature documents that firms can issue (repurchase) shares only at a discount (premium) to the current price. ... Article We estimate a dynamic investment model in which firms finance with equity, cash, or debt. Misvaluation affects equity values, and firms optimally issue and repurchase overvalued and undervalued shares. The funds flowing to and from these activities come from investment, dividends, or net cash. The model fits a broad set of data moments in large heterogeneous samples and across industries. Our parameter estimates imply that misvaluation induces larger changes in financial policies than investment. The investment responses are strongest for small firms but nonetheless modest. Managers' rational responses to misvaluation increase shareholder value by up to 4%. © Published by Oxford University Press on behalf of The Society for Financial Studies 2015. This work is written by US Government employees and is in the public domain in the US. Article In this paper, we analyze the effects of abnormal capital investment and financial flexibility on firm performance following actual share repurchases by using a unique Taiwanese dataset. The results indicate that superior operational performance is associated with share repurchases; however, share repurchases may crowd out required capital investments. Further examination reveals that firms with adequate financial flexibility outperform firms with inadequate financial flexibility after actual share repurchases. In summary, our findings suggest that financial flexibility can mitigate the investment crowding out effect and positively affect firms' operational performance post-repurchase. Article Article Firms headquartered in more corrupt US environments (states) provide higher payouts to their shareholders. Our results are robust to, for example propensity score matching, instrumental variable approach, headquarters relocations, quasi natural experiments using exogenous shocks, use of alternative measures of corruption and payouts, use of additional (possibly omitted) variables, and various alternative explanations based on additional channels and moderating factors. Our study finds that the use and marginal value of dividend payout as a shielding channel is affected by state-level corruption. Our study also adds geographic-based shielding as another important motivation for firms to make corporate payouts. Thesis Full-text available Stock repurchase, as a corporate finance tool and a substitute for cash dividends, plays an important role in distributing excess cash. Following a prohibited period due to its potentially negative outcomes for shareholders and creditors, stock repurchase has recently been regulated within the company law systems of many jurisdictions pursuant to its increasing popularity in satisfying special financing requirements of companies. That the regulatory improvements have removed the uncertainty inherent in such transactions has increased the volume of, especially, the open market stock repurchases. Turkish legislation, i.e. Commercial Code and Capital Markets Law, has latterly been updated in accordance with acquis communautaire in order to allow stock repurchases. Empirical investigations regarding stock repurchase transactions of listed companies reveal that: (1) undervaluation and signaling are the most prominent determinants of stock repurchase decisions; (2) investor reaction to stock repurchases is generally positive and liquidity tends to increase as volatility decreases in the short-term. Article Firms may repurchase shares to send true or false signals to the market. Since the mindset of managers is invisible, we measure it with earnings management. Discretionary accruals are used to proxy for earnings management. We show that earnings management is negatively related to the probability and frequency of share repurchase announcements. We also show that earnings management is negatively related to postannouncement 2‐year operating performance and stock returns. Our findings support the prediction that the magnitude of earnings management can serve as a reliable indicator of managers' mindsets with regard to the valuation of firms. Article We study how stock option grants are funded through share repurchases under conditions of option exercisability and moneyness. Using daily repurchase disclosures by U.K. firms, we corroborate our hypothesis that driven by flexibility, firms repurchase early in an option schedule while options are out-of-money and before becoming exercisable. Our findings show that when daily stock prices are below weighted average option exercise price and when options are not immediately exercisable, firms (a) increase daily repurchase volume (value), (b) increase repurchase frequency, and (c) have lower relative repurchase prices. We further evidence this by examining the change in treasury regulation that enabled firms to hold on to repurchased shares rather than cancelling them. Our findings show a strong support for option funding motives in the post-treasury regulation period when repurchase flexibility is greater. Article Full-text available Essa pesquisa teve por objetivo verificar se empresas brasileiras que recompraram ações entre os periodos de 2011 a 2015, gerenciaram seus números contábeis a menor, no período que antecedeu a utilização da ferramenta de recompra, e ainda, se esse grupo de empresas obteve ganhos anormais posteriores a recompra de ações, fruto da reversão dos accruals discricionários (proxy de gerenciamento de resultados).Como metodologia de pesquisa, foram utilizados os modelos econométricos de Jones Modificado e Performance Matching para geração dos accruals discricionários. Para se encontrar o retorno anormal, calculou-se a diferença entre o retorno real (retorno do fechamento) e o retorno esperado (modelo CAPM). Os resultados da pesquisa apontaram que existem evidências de que empresas utilizam o gerenciamento de resultados para reduzir os lucros em momentos pré recompra de ações, no intuito de obter ganhos anormais nos períodos posteriores, sendo esse evidenciado por um maior retorno anormal posterior à recompra, entre empresas que supostamente gerenciaram seus números a menor, anteriormente à recompra, considerando o modelo de Performance Matching para detecção de accruals discricionários. Article This paper investigates the flexibility inherent in open market share repurchases. Open market share repurchases are recognized as being flexible, since managers believe that they are not an ongoing commitment. However, I find that such returns significantly decrease upon announcing the completion of a repurchase program if firms do not concurrently announce new program authorizations. I also find that announcement returns significantly decline with completion rates and that a high completion rate acts as a negative signal, revealing that firms have finished the repurchasing activities and do not intend to continue share repurchasing in the foreseeable future. These results indicate that share repurchases are less flexible than they were previously thought to be. Article Full-text available Bu çalışmanın amacı hisse senedi geri alım kararını açıklayan firmaların hisse senedi getirilerinin geri alım duyurularına tepkisini ortaya koymaktır. Bu amaçla SPK’nın 21 Temmuz 2016 tarihli duyuru ile geri alımlar üzerindeki sınırlamaları kaldırmasını takiben alım kararı açıklayan 10 şirketin 17 adet geri alım duyurusu incelemeye alınmıştır. Olay çalışması yöntemi kullanılan çalışmada ±10 günlük olay penceresi belirlenmiş ve 21 gün için hisse senetlerinin beklenen getirileri hesaplanmıştır. Beklenen ve gerçekleşen getiriler arasındaki farkı ifade eden “anormal getirilerin” anlamlılığını ölçmek için t testinden yararlanılmıştır. Bulgular, hisse geri alım kararının açıklanmasından önce ve sonra, negatif ve pozitif anormal getiri elde edilmesinin mümkün olduğunu ortaya koymuştur. Ne var ki kümülatif anormal getirilerin istatistiksel olarak anlamlı olmadığı sonucuna varılmıştır. Article Full-text available Share repurchase programs have during the past few decades become an important way of distributing cash to shareholders since they are viewed by managers as more flexible than dividends. Open market repurchase authorizations effectively also give managers an option to repurchase shares when they view their stock as undervalued. This study exploits a data set of open market repurchases programs initiated by Finnish stock market listed companies. Finland is unique with regard to the disclosure requirements of open market repurchase programs, which enables an examination of the information content in both the initiation announcement as well as in the announcement of actual repurchases. The study covers all 293 share repurchase programs initiated between 1998 and 2013. The results show a significant positive announcement effect of about 2 percent on the initiation day. The CAAR over a five day event window is also about 1.5 percent (statistically significant). Furthermore, an additional statistically positive effect of 1.5 percent is found on the first repurchase day (about 1.1 percent over a five day event window). The positive announcement effect is larger for announcements regarding initiations of the first or the second repurchase program for a company. Article We examine the influence of investor conferences on firms’ stock liquidity. We find that firms participating in conferences experience a 1.4% to 2.8% increase in stock liquidity compared to nonconference firms. Consistent with investor conferences improving firm visibility, the increase in liquidity is larger for firms with low pre-conference visibility and varies predictably with conference characteristics that affect the ability of investors to revise their beliefs about the firm. However, for firms with a large investor base and high visibility, conference participation is associated with a decline in stock liquidity, consistent with investor conferences exacerbating the information asymmetry among investors. Article We examine the importance of bonus contract characteristics, specifically, with respect to the relation between EPS-based bonuses and share repurchases. We find that managers are more (less) likely to repurchase shares and spend more (less) on repurchases when as-if EPS just misses (exceeds) the bonus threshold (maximum) EPS level. We find no such relation when as-if EPS is further below the threshold. We find weak evidence that managers of firms with as-if EPS just below the EPS target are more likely to repurchase shares and spend more on repurchases relative to firms with as-if EPS just above the EPS target. We further find that the incentive-zone slopes specified in the bonus contracts are positively associated with share repurchases. Managers making bonus-motivated repurchases do so at a higher cost. Together, our results highlight the importance of compensation design in motivating managers' behavior and aligning managers' incentives with shareholders. JEL Classifications: M41; M52. Article Full-text available Analiza wyników badań dotyczących działania efektu Q Tobina pozwala sformułować wniosek, że rynkowa wycena akcji (zmiany nominalne) wpływa na realne decyzje przedsiębiorstw, co oznacza, że polityka pieniężna, która za pośrednictwem działania kanału giełdowego oddziałuje na sytuację na rynkach finansowych, wpływa również dodatkowo poprzez efekt Q Tobina na decyzje przedsiębiorstw o realizacji inwestycji, fuzji, przejęć, wejściu na giełdę, emisji lub odkupie papierów wartościowych, albo zmianie struktury kapitałowej, czyli oddziałuje na kluczowe decyzje w zakresie zarządzania finansami przedsiębiorstwa. Dlatego banki centralne powinny analizować dostęp przedsiębiorstw do źródeł finansowania i uwzględniać w swych działaniach wpływ polityki pieniężnej na sytuację na rynkach finansowych, która znajduje bezpośrednie przełożenie na koszt i zdolność pozyskania kapitału przez przedsiębiorstwa, co warunkuje ich rozwój, a więc i wzrost gospodarczy oraz zatrudnienie, ale z drugiej strony jest idealną pożywką dla nierównowag finansowych. Article Full-text available Using a comprehensive sample of 1,830 open-market repurchases of 15 European countries encompassing the period from 1998 until 2013, we analyzed the magnitude and determinants of the share price reaction on announcement. Our results indicate that buyback announcements in Europe lead on average to a significantly positive abnormal return of 0.92% on announcement day, however, decreasing in firm size and announcement frequency. Additionally, our findings show that the market does not particularly greet the distribution of excess cash to shareholders, but rather when companies take advantage of undervalued stock as market-to-book values are inversely related to announcement returns. Looking at the companies' leverage ratios, the motive of capital structure optimization cannot be supported by the empirical findings. Lastly, with respect to managerial market timing ability we could not observe that buybacks are following a period of share price underperformance, concluding that managers are not able to time the implementation of buyback programs. Article Full-text available Over the past two decades or so, repurchases have become an appealing method for disbursing cash to shareholders compared to the traditional dividends. Managerial perception as well as empirical evidence suggests that repurchases are inherently more flexible than dividends, which may account for their increasing popularity. The rigidity of dividends and the apparent flexibility of share repurchases could impact firm investments. Firms may forego profitable investment opportunities to maintain their dividend levels, while repurchases could be easily scaled back to fund profitable investment projects without fear of an adverse market reaction. We test the flexibility hypothesis of repurchases by regressing capital expenditures on repurchases and dividends in addition to other control variables. Consistent with our hypotheses, we find an inverse relationship between capital expenditures and repurchases but an insignificant relationship with dividends. Further, we find that the flexibility associated with repurchases is especially evident for firms that are financially constrained, and during the recent financial crisis period when external capital constraints were severe. Finally, we find that flexibility of repurchases with respect to capital expenditures is stronger in the more recent time period during which regulatory changes made repurchases more attractive as a mechanism to disburse cash back to shareholders. Article Full-text available O objetivo deste trabalho é rever a legislação brasileira referente ao processo de recompra de ações, inclusive as recentes mudanças com a introdução da Instrução CVM no 299, e analisar o seu impacto sobre os acionistas minoritários. Antes dessa Instrução, as recompras de ações poderiam sinalizar um fechamento branco de capital. Nesse caso, os acionistas minoritários poderiam ser prejudicados. A pesquisa foi realizada a partir de uma amostra dos anúncios de recompra de ações realizados na BOVESPA no período entre janeiro de 1994 e junho de 2002, e confirmou-se que, em média, os acionistas minoritários tiveram um retorno acumulado de 10% durante os três meses após o anúncio da recompra das ações. Concluiu-se que, após a promulgação da Instrução CVM no 299, as ações passaram a obter retornos anormais acumulados positivos, beneficiando os acionistas. Article Full-text available We examine long-run firm performance following open market share repurchase announcements, 1980–1990. We find that the average abnormal four-year buy-and-hold return measured after the initial announcement is 12.1%. For ‘value’ stocks, companies more likely to be repurchasing shares because of undervaluation, the average abnormal return is 45.3%. For repurchases announced by ‘glamour’ stocks, where undervaluation is less likely to be an important motive, no positive drift in abnormal returns is observed. Thus, at least with respect to value stocks, the market errs in its initial response and appears to ignore much of the information conveyed through repurchase announcements. Article Full-text available Theories of corporate payout policy do not explain the observed form of distributions to shareholders. Although open-market repurchases appear to have tax advantages, cash dividends are overwhelmingly chosen. We argue that there are costs associated with open-market-repurchase programs, since they provide managers with opportunities to use inside information to benefit themselves at stockholders' expense. We offer evidence suggesting that bid-ask spreads widen around repurchase announcements, as predicted by our analysis. Since these costs of repurchases do not arise with cash dividends, our analysis implies that repurchases do not dominate cash dividends for making distributions to shareholders. Article Full-text available Article Full-text available During the 1980s, U.S. firms announcing stock repurchases earned favorable long-run returns. Recently, concerns have been raised over the robustness of these findings. This concern comes at a time of explosive growth in repurchase programs. Thus, we study new evidence from the 1990s for 1,060 Canadian repurchase programs. Moreover, because of Canadian law, we can carefully track repurchase activity monthly. Similarly to the situation in the United States, the Canadian stock market discounts the information in repurchase announcements, particularly for value stocks. Completion rates in Canada are sensitive to mispricing. Trades also appear linked to price movements; managers buy more shares when prices fall. Copyright The American Finance Association 2000. Article This paper provides an alternative test of Amihud and Mendelson's (1986, Journal of Financial Economics, 8, 31–35) model using the turnover rate (number of shares traded as a fraction of the number of shares outstanding) as a proxy for liquidity. The evidence suggests that liquidity plays a significant role in explaining the cross-sectional variation in stock returns. This effect persists after controlling for the well known determinants of stock returns like the firm-size, book-to-market ratio and the firm beta. Unlike Eleswarapu and Reinganum (1993, Journal of Financial Economics, 34, 373–386), this paper finds that the liquidity effect is not restricted to the month of January alone and is prevalent throughout the year. The evidence supports Amihud and Mendelson's (1986) notion of liquidity premium and establishes its role in the overall cross section of stock returns. Article Article This paper studies the effect of the bid-ask spread on asset pricing. We analyze a model in which investors with different expected holding periods trade assets with different relative spreads. The resulting testable hypothesis is that market-observed expexted return is an increasing and concave function of the spread. We test this hypothesis, and the empirical results are consistent with the predictions of the model. Article Introduction, 33. — The definition and measurement of transaction cost on the New York stock exchange, 35. — The determination of the ask-bid spread, 40. — The determination of the transaction rate, 45. — Statistical results, 46. — Summary and comments, 50. — Appendix I, 52. — Appendix II, 53. Article We investigate the role of limit orders in the liquidity provision in a pure order-driven market. Results show that market depth rises subsequent to an increase in transitory volatility, and transitory volatility declines subsequent to an increase in market depth. We also examine how transitory volatility affects the mix between limit orders and market orders. When transitory volatility arises from the ask (bid) side, investors will submit more limit sell (buy) orders than market sell (buy) orders. This result is consistent with the existence of limit-order traders who enter the market and place orders when liquidity is needed. Article We study the impact of barriers to international capital flows with stock price data from 11 countries whose stock markets feature shares restricted to locals and otherwise identical shares available to foreigners. Large price premiums for unrestricted shares relative to matching restricted shares are typically observed. Although basic notions of international asset pricing offer a straightforward explanation for the price premiums, we find little evidence that the price premiums are explained by lower foreign required returns. Alternative concepts and theories centering on foreign investor demand and the supply of shares explain some of the time-series and cross-sectional variation of price premiums. More specifically, premiums for unrestricted shares are positively correlated with foreign investor demand in the form of international mutual fund flows, sentiment implicit in matching closed-end country fund premiums, market liquidity, and information reflected in press coverage, country credit rating, and firm size. Article The purpose of this study is to extend the bid-ask spread decomposition literature into the order-driven environment. The use of electronic limit order books combined with order-driven market making has been increasing rapidly in recent years because improvements in information technology and financial market deregulation. To date, reported bid-ask spread decompositions rely almost exclusively on quote-driven or hybrid systems. This study provides bid-ask spread component estimates from one of the world's largest order-driven markets, the Stock Exchange of Hong Kong. Based on a sample of over six million observations, we estimate a median adverse selection component of 33 percent and a median order processing component of 45 percent of the spread. Dollar volume-based decile portfolios show significant cross-sectional variation for adverse selection costs but insignificant variation for order processing costs. Finally, order persistence is consistently positive for all deciles and displays a direct relation with the level of trading activity. Article Microstructure theory contends that dealers' bid-ask spreads should vary intertemporally with changes in the asymmetric information component of the spread. Corporate theory suggests that stock repurchase announcements signal management's private information to the securities markets. An examination of dealers' spread behavior around firms' open market repurchases in the NASDAQ market reveals a decline in spreads adjusted for dealers' inventory-holding and order-processing costs. This decline is attributed to a reduction in informed trading risk associated with the open market repurchase announcements. The proportion of U.S. firms paying dividends drops sharply during the 1980s and 1990s. Among NYSE, AMEX, and Nasdaq firms, the proportion of dividend payers falls from 66.5% in 1978 to only 20.8% in 1999. The decline is due in part to an avalanche of new listings that tilts the population of publicly traded firms toward small firms with low profitability and strong growth opportunities—the timeworn characteristics of firms that typically do not pay dividends. But this is not the whole story. The authors' more striking finding is that, no matter what their characteristics, firms in general have become less likely to pay dividends. The authors use two different methods to disentangle the effects of changing firm characteristics and changing propensity to pay on the percent of dividend payers. They find that, of the total decline in the proportion of dividend payers since 1978, roughly one-third is due to the changing characteristics of publicly traded firms and two-thirds is due to a reduced propensity to pay dividends. This lower propensity to pay is quite general—dividends have become less common among even large, profitable firms. Share repurchases jump in the 1980s, and the authors investigate whether repurchases contribute to the declining incidence of dividend payments. It turns out that repurchases are mainly the province of dividend payers, thus leaving the decline in the percent of payers largely unexplained. Instead, the primary effect of repurchases is to increase the already high payouts of cash dividend payers. Article Theories of asset pricing suggest that the amortized cost of the spread is relevant to investors' required returns. The amortized spread measures the spread's cost over investors' holding periods and is approximately equal to the spread times share turnover. We examine amortized spreads for Amex and NYSE stocks over the period 1983–1992. We find that stocks with similar spreads can have vastly different share turnover, and thus, a stock's amortized spread cannot be predicted reliably by its spread alone. Consistent with theories of transaction costs, we find stronger evidence that amortized spreads are priced than we find for unamortized spreads. Article The purpose of this study is to investigate inter-temporal and cross-sectional depth patterns in an electronic, order-driven environment. Although many exchanges operate in this environment, little is known about the liquidity dynamics induced by such trading mechanisms. The findings, based on over six million observations, reveal an inverted U-shaped pattern that mirrors the commonly reported U-shaped spread pattern. An important implication is that earlier spread results understate the strength of inter-temporal liquidity variations. Cross-sectional analysis, based on adverse selection-sorted portfolios, demonstrates that corporate depth is negatively related to information asymmetry. The adverse selection impact on liquidity and cost of capital is stronger than previously believed since information costs are realized through both spreads and depths. Article In this paper we develop a CAPM-based model to demonstrate that the true measure of systematic risk – when considering liquidity costs – is based on net (after bid–ask spread) returns. We further examine the relationship between the expected return and the future spread cost within the CAPM framework. This positive relationship in our model is found to be convex. This finding differs from Amihud and Mendelson's (1986) concave relationship, but it agrees with empirical evidence obtained by Brennan and Subrahmanyam (1996). Article Article This study investigates the anomalous findings of the previous insider trading studies that any investor can earn abnormal profits by reading the Official Summary. Availability of abnormal profits to insiders, availability of abnormal profits to outsiders who imitate insiders, determinants of insiders' predictive ability, and effect of insider trading on costs of trading for other investors are examined by using approximately 60,000 insider sale and purchase transactions from 1975 to 1981. Implications for market efficiency and evaluation of abnormal profits to active trading strategies are discussed. Article The presence of traders with superior information leads to a positive bid-ask spread even when the specialist is risk-neutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number that is independent of insider activity. The serial correlation of transaction price differences is a function of the proportion of the spread due to adverse selection. A bid-ask spread implies a divergence between observed returns and realizable returns. Observed returns are approximately realizable returns plus what the uninformed anticipate losing to the insiders. Article Models of price formation in securities markets suggest that privately informed investors create significant illiquidity costs for uninformed investors, implying that the required rates of return should be higher for securities that are relatively illiquid. We investigate the empirical relation between monthly stock returns and measures of illiquity obtained from intraday data. We find a significant relation between required rates of return and these measures after adjusting for the Fama and French risk factors, and also after accounting for the effects of the stock price level. Article In this paper I study the price formation process on the Stock Exchange of Hong Kong (SEHK). The estimation results reveal that the information effect is more important than the inventory effect in explaining the transaction price movement. The cross-sectional variation in market depth is positively related to the stocks’ market capitalization, turnover rate, trading price, and trading noise. The price impact displays a U-shaped pattern over the trading day, which is in contrast to the downward sloping pattern discovered on the NYSE. Such differences seem to be caused by the variation in average trade size between the two markets. Article Article We examine whether specialist depth quotes are related to the adverse-selection and inventory-holding cost components of the spread. Consistent with theory that predicts an inverse relation between depths and informed trading risk, we find that depth quotes are strongly inversely related to the adverse-selection component of the spread. We also find that depth quotes are inversely related to the inventory-holding-cost component, though this relation is weaker than the relation between depths and adverse selection. Our evidence suggests cross-sectional variation in depths is driven primarily by variation in informed trading risk, as proxied for by the adverse-selection component, rather than by inventory concerns. Article In this paper I examine the behavior of bid and ask spreads and depths around announcements of open market stock repurchase programs. For a sample of 195 announcements from 1988 to 1990, I find statistically significant evidence of a small decline in spreads and no evidence of a shift in depths following the announcement date. Results are similar for a subsample of firms experiencing post-announcement declines in the number of shares outstanding. I conclude that open market repurchase programs as used recently do not adversely affect market liquidity. Article We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = $$\theta \left( {\hat F} \right) - \theta \left( F \right)$$, θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc. Article I. Introduction, 79. — II. Inventory management and supply of liquidity, 80. —III. Empirical findings, 87. — IV. Conclusions, 93. Article A simple time-series market microstructure model is constructed within which existing models of spread components are reconciled. We show that existing models fail to decompose the spread into all its components. Two alternative extensions of the simple model are developed to identify all the components of the spread and to estimate the spread at which trades occur. The empirical results support the presence of a large order processing component and smaller, albeit significant, adverse selection and inventory components. The spread components differ significantly according to trade size and are also sensitive to assumptions about the relation between orders and trades. Article Article Unlike Dutch auction repurchases and tender offers, open-market repurchase programs do not precommit firms to acquire a specified number of shares. In a sample of 450 programs from 1981 to 1990, firms on average acquire 74 to 82 percent of the shares announced as repurchase targets within three years of the repurchase announcement. We find that share repurchases are negatively related to prior stock price performance, suggesting that firms increase their purchasing depending on its degree of perceived undervaluation. In addition, repurchases are positively related to levels of cash flow, which is consistent with liquidity arguments. Copyright The American Finance Association 1998. Article THIS PAPER presents the results of an analysis of the price of marketability services on the Toronto Stock Exchange (TSE) and compares them with previously published findings concerning the price of marketability on the New York Stock Exchange (NYSE) and the U.S. over-the-counter market (OTC). More specifically, the paper examines the determinants of bid-ask spreads on the TSE and their behavior relative to spreads in the NYSE and OTC markets. In the next section, we present some background concerning the methods of market making employed in the TSE, NYSE and OTC and discuss several tentative, working hypotheses concerning the determinants of bid-ask spreads. In Section III, the discussion turns to the empirical analysis of spreads on the TSE. This is followed in Section IV by a comparison of previously published results from the NYSE and OTC markets. Finally, in Section V some implications of the analysis are discussed. In brief, we will argue that the comparative results support the conclusion that the price of marketability services is higher in the TSE than in either the NYSE or OTC market. In this context, the word "higher" does not simply imply that spreads on the TSE are absolutely wider, but rather that they are wider holding factors that influence spreads constant from market to market. The question of the relative merits of various methods of organizing trading in common stocks is receiving considerable attention in the U.S. at the present time and promises to be a topic of debate for some time to come.' Unfortu Article This paper develops and implements a technique for estimating a model of the bid/ask spread. The spread is decomposed into two components, one due to asymmetric information and one due to inventory costs, specialist monopoly power, and clearing costs. The model is estimated using NYSE common stock transaction prices in the period 1981–1983. Cross-sectional regression analysis is then used to relate time-series estimated spread components to other stock characteristics. The results cannot reject the hypothesis that significant amounts of NYSE common stock spreads are due to asymmetric information. The purpose of this study is to investigate inter- and intra-day liquidity patterns in the Hong Kong equity market. The market making system of the Stock Exchange of Hong Kong (SEHK) is highly transparent and operates with minimal third party intervention. Liquidity is supplied solely by the submission of public limit orders through a fully-automated, order-driven trading system. The results reveal bid-ask spread patterns on the SEHK more similar to those of specialist systems than to those of multi-dealer systems, thereby providing useful evidence in distinguishing among competing market microstructure theories. Article This paper examines the effect of recent market reforms on the competitive structure of the Nasdaq. Our results show that changes in inventory and information costs cannot explain the post-reform decrease in bid-ask spreads. We interpret this as evidence that the reforms have reduced Nasdaq dealers' rents. Additionally, we find that the difference between NYSE and Nasdaq spreads have been greatly diminished with the new rules. Further, the reforms have resulted in an exit, "ceteris paribus", from the industry for market making. Overall, our results provide strong evidence that the reforms have improved competition on the Nasdaq. Copyright The American Finance Association 2000. Article This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions. Article This paper studies estimators that make sample analogues of population orthogonality conditions close to zero. Strong consistency and asymptotic normality of such estimators is established under the assumption that the observable variables are stationary and ergodic. Since many linear and nonlinear econometric estimators reside within the class of estimators studied in this paper, a convenient summary of the large sample properties of these estimators, including some whose large sample properties have not heretofore been discussed, is provided. Article We show that repurchases have not only became an important form of payout for U.S. corporations, but also that firms finance their share repurchases with funds that otherwise would have been used to increase dividends. We find that young firms have a higher propensity to pay cash through repurchases than they did in the past and that repurchases have become the preferred form of initiating a cash payout. Although large, established firms have generally not cut their dividends, they also show a higher propensity to pay out cash through repurchases. These findings indicate that firms have gradually substituted repurchases for dividends. Our results also suggest that before 1983, regulatory constraints inhibited firms from aggressively repurchasing shares. Copyright The American Finance Association 2002. Article AN IMPORTANT, if not critical, element in almost every financial market is the dealer who stands ready to trade for his own account and thereby provides to the public the convenience of being able to trade immediately. The dealer incurs costs of holding an inventory of securities, certain costs of handling each order and costs due to adverse information possessed by those that trade with him. He is compensated for the costs by selling at the ask price (above the "true" price) and buying at the bid price (below the "true" price).' Dealers are to be distinguished from brokers who do not bear risk and who usually charge a commission. Since healthy financial markets are viewed as critical to a healthy economy and since dealers stand at the center of many financial markets, dealers have been the focus of many regulatory inquiries and some empirical studies by academicians. Today, competitive forces (instiutional trading, third market, block trading), Justice Department pressures, and technological change (the computer) are in the process of producing major changes in the structure of securities markets. As part of this restructuring a major issue is the way in which the dealer function should be provided, the degree of competition which should exist and the rules and regulations under which individual dealers should operate.2 Using data from the Over-the-Counter Market (OTC), this paper examines two aspects of dealer behavior that have implications for appropriate structures of securities markets: 1. What factors determine the price of dealer services? An understanding of these factors may suggest how dealer costs may be minimized. 2. What determines the number of dealers willingly making a market in a stock? Article An individual who chooses to serve as a market‐maker is assumed to optimize his position by setting a bid‐ask spread which maximizes the difference between expected revenues received from liquidity‐motivated traders and expected losses to information‐motivated traders. By characterizing the cost of supplying quotes, as writing a put and a call option to an information‐motivated trader, it is shown that the bid‐ask spread is a positive function of the price level and return variance, a negative function of measures of market activity, depth, and continuity, and negatively correlated with the degree of competition. Thus, the theory of information effects on the bid‐ask spread proposed in this paper is consistent with the empirical literature. Article The behavior of competing dealers in securities markets is analyzed. Securities are characterized by stochastic returns and stochastic transactions. Reservation bid and ask prices of dealers are derived under alternative assumptions about the degree to which transactions are correlated across stocks at a given time and over time in a given stock. The conditions for interdealer trading are specified, and the equilibrium distribution of dealer inventories and the equilibrium market spread are derived. Implications for the structure of securities markets are examined. The Practitioner's Guide to the Listing Rules • S Barham • I Hallsworth • M Jackson Barham, S., I. Hallsworth and M. Jackson, 1998, The Practitioner's Guide to the Listing Rules, 4 th ed., Hong Kong: ISI Publications. Safe harbor or smoke screen? SEC guidelines for executing open market repurchases, working paper • D O Cook • L Krigman • J C Leach Cook, D.O., L. Krigman and J.C. Leach, 1999b, Safe harbor or smoke screen? SEC guidelines for executing open market repurchases, working paper, University of Colorado.	2023-03-22 15:57:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29065948724746704, "perplexity": 5788.558122269463}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943845.78/warc/CC-MAIN-20230322145537-20230322175537-00749.warc.gz"}
https://community.zama.ai/t/are-52-bits-of-error-enough/330	Are ~52 bits of error enough? Suppose you have an RLWE of degree 4096: as+e+\Delta M and a decryption of m and you extract its 4096 lwe coefficients: b_1 = a.s+e_1+\Delta m_1\to b_1 -\Delta m_1 = a.s+e_1\\b_2 = a.s+e_2+\Delta m_2\to b_2 -\Delta m_2 = a.s+e_2\\\cdots\\b_{4096} = a.s+e_{4096}+\Delta m_{4096}\to b_{4096} -\Delta m_{4096} = a.s+e_{4096} since you know m, summing everything in the system, you have to search through 4096(e_1+\cdots+e_{4096}) = 4096e to guess the value of a.s and thus the value of the secret key s. Thus, the smaller the error bits, the fastest we can guess. On Zama, I believe, the error bits are something like 52, which when multiplied by the 12 of the 4096, is not near 128 bits of security. What’s wrong? Hi guerlando, assuming refers to polynomial multiplication in the ring R_q = Z_q[X]/(X^N + 1) with N=4096 and . refers to the inner product of vectors over Z_q (where we identify polynomials with their coefficient vectors), the mapping from the RLWE sample to the 4096 LWE samples is incorrect. Each sample should have a different a', where a' is a negacyclic rotation of a. You can see this by viewing as = a (\sum s_i x^i) = \sum s_i( x^i * a). So the j-th sample should have a' with a'_i being the j-th index of x^i * a (which, in R_q corresponds to a negacyclic rotation). Then, indeed, a'.s corresponds to the j-th index of a*s. Summing all the terms will then not help you, since all it does is creating a new LWE sample (where a = \sum a') with larger noise. Hope this helps.	2022-12-05 14:53:58	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8577631115913391, "perplexity": 2658.254005825719}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711017.45/warc/CC-MAIN-20221205132617-20221205162617-00232.warc.gz"}
http://icpc.njust.edu.cn/Problem/Hdu/2473/	# Junk-Mail Filter Time Limit: 15000/8000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) [显示标签] ## Description Recognizing junk mails is a tough task. The method used here consists of two steps: 1) Extract the common characteristics from the incoming email. 2) Use a filter matching the set of common characteristics extracted to determine whether the email is a spam. We want to extract the set of common characteristics from the N sample junk emails available at the moment, and thus having a handy data-analyzing tool would be helpful. The tool should support the following kinds of operations: a) “M X Y”, meaning that we think that the characteristics of spam X and Y are the same. Note that the relationship defined here is transitive, so relationships (other than the one between X and Y) need to be created if they are not present at the moment. b) “S X”, meaning that we think spam X had been misidentified. Your tool should remove all relationships that spam X has when this command is received; after that, spam X will become an isolated node in the relationship graph. Initially no relationships exist between any pair of the junk emails, so the number of distinct characteristics at that time is N. ## Input There are multiple test cases in the input file. Each test case starts with two integers, N and M (1 ≤ N ≤ 105 , 1 ≤ M ≤ 106), the number of email samples and the number of operations. M lines follow, each line is one of the two formats described above. Two successive test cases are separated by a blank line. A case with N = 0 and M = 0 indicates the end of the input file, and should not be processed by your program. ## Output For each test case, please print a single integer, the number of distinct common characteristics, to the console. Follow the format as indicated in the sample below. ## Sample Input 5 6 M 0 1 M 1 2 M 1 3 S 1 M 1 2 S 3 3 1 M 1 2 0 0 ## Sample Output Case #1: 3 Case #2: 2 lcy ## Source 2008 Asia Regional Hangzhou	2020-06-06 01:46:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2373187392950058, "perplexity": 1646.2606669999159}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348509264.96/warc/CC-MAIN-20200606000537-20200606030537-00099.warc.gz"}
https://math.stackexchange.com/questions/651024/solve-2000x6100x510x3x-2-0/653283	# Solve $2000x^6+100x^5+10x^3+x-2=0$ One of the roots of the equation $2000x^6+100x^5+10x^3+x-2=0$ is of the form $\frac{m+\sqrt{n}}r$, where $m$ is a non-zero integer and $n$ and $r$ are relatively prime integers.Then the value of $m+n+r$ is? Tried to use the fact that another root will be $\frac{m-\sqrt{n}}r$ as coefficients are rational but there are six roots and using sum and product formulas would allow many variables in the equations. • All roots or only real roots ? Jun 20 '15 at 12:43 • Is this problem supposed to be solved by hand? Jun 20 '15 at 12:48 • Wolphram Alpha gives the factors $(20x^2+x-2)(100x^4+10x^2+1)$ so you can finish easily with $x^2=Z$ Jun 20 '15 at 13:40 We have $\displaystyle x+10x^3+100x^5=x\frac{1000x^6-1}{10x^2-1}$. (A geometric progression) Hence $\displaystyle -2(1000x^6-1)=x \frac{1000x^6-1}{10x^2-1}$ Hence either $1000x^6-1=0$ or $x=-2(10x^2-1)$. Therefore $20x^2+x-2=0$ for second equation. Solving we get $$x=\frac{-1\pm \sqrt{161}}{40}$$. Comparing $m=-1, n=161$ and $r=40$. Hence $m+n+r=200$ • Very nice, +1! One minor nit: it might be worth showing why the $1000x^6-1=0$ path doesn't work out (it leads to a couple of complex solutions plus $x^2=\frac1{10}$, and even without plugging in to test whether these solve the original sextic it's clear that it can't be put into the required form.) Jan 28 '14 at 19:36 • This equation will not give the roots in the required form.And if you are thinking of complex solutions in this form check out the conditions for m,n,r(they should be positive integers) Jan 29 '14 at 3:15 HINT: try the ansatz $$(-2+Bx+Ax^2)(1+Cx^2+Dx^4)$$ • and thankyou for downvoting Jun 20 '15 at 12:50 • and this here $$(20x^2+x-2)(100x^4+10x^2+1)$$?? Jun 20 '15 at 12:58 • Such a system of nonlinear equations does not seem easy to manipulate. Could you elaborate ? Jun 20 '15 at 12:58 • this is the answer a method which is always used in math olympiads Jun 20 '15 at 13:04 • I deleted a bunch of repetitive comments. Gentlemen, remember that this is a sextic. Either there is a trick to find the zeros, or they cannot be found. So we should expect an ad hoc -method. Jun 20 '15 at 13:25 $$2000x^6+100x^5-200x^4+200x^4+10x^3-20x^2+20x^2+x-2$$ $$(2000x^6+200x^4+20x^2)+(100x^5+10x^3+x)-(200x^4+20x^2+2)$$ $$x^2(2000x^4+200x^2+20)+\frac{x}{20}(2000x^4+200x^3+20x)-\frac{1}{10}(2000x^4+200x^2+20)$$ $$=(x^2+\frac{x}{20}-\frac{1}{10})(2000x^4+200x^2+20)=0$$ The usual trick is to divide through by $x^3.$ Then notice that taking $w = 10x - \frac{1}{x}$ seems to allow writing the thing, and we get $$2 w^3 + w^2 + 60 w + 30 = 0.$$ This has a rational root, namely $-1/2,$ and factors as $$(2w+1)(w^2 + 30)$$ Setting $$10 x - \frac{1}{x} = -\frac{1}{2}$$ leads to $$20 x^2 + x - 2 = 0$$	2021-10-27 08:05:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7722790837287903, "perplexity": 294.2407012818392}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00032.warc.gz"}
https://www.semanticscholar.org/paper/Novel-constraints-on-mixed-dark-matter-scenarios-of-Boucenna-Kuhnel/278dfca7aabae3b12764c7b9ee0a834ae19a8e9e	# Novel constraints on mixed dark-matter scenarios of primordial black holes and WIMPs @article{Boucenna2018NovelCO, title={Novel constraints on mixed dark-matter scenarios of primordial black holes and WIMPs}, author={Sofiane Boucenna and Florian Kuhnel and Tommy Ohlsson and Luca Visinelli}, journal={Journal of Cosmology and Astroparticle Physics}, year={2018} } • Published 18 December 2017 • Physics • Journal of Cosmology and Astroparticle Physics We derive constraints on mixed dark-matter scenarios consisting of primordial black holes (PBHs) and weakly interacting massive particles (WIMPs). In these scenarios, we expect a density spike of the WIMPs that are gravitationally bound to the PBHs, which results in an enhanced annihilation rate and increased indirect detection prospects. We show that such scenarios provide strong constraints on the allowed fraction of PBHs that constitutes the dark matter, depending on the WIMP mass $m_{\chi… ## Figures from this paper Primordial Black Holes as Dark Matter: Recent Developments • Physics • 2020 Primordial black holes (PBHs) could provide the dark matter but a variety of constraints restrict the possible mass windows to$10^{16}$-$10^{17}\,$g,$10^{20}$-$10^{24}\,$g and$10$- Shining primordial black holes • Physics • 2020 We study the well-motivated mixed dark matter (DM) scenario composed of a dominant thermal WIMP, highlighting the case of$SU(2)_L$triplet fermion "winos", with a small fraction of primordial black The abundance of primordial black holes from the global 21cm signal and extragalactic gamma-ray background • Yupeng Yang • Physics The European Physical Journal Plus • 2020 Primordial black holes (PBHs) formed in the early Universe can accret dark matter particles due to gravity and form ultracompact minihalos (UCMHs). The theoretical researches and simulations have Black holes and WIMPs: all or nothing or something else • Physics Monthly Notices of the Royal Astronomical Society • 2021 We consider constraints on primordial black holes (PBHs) in the mass range$(10^{-18}\!-\!10^{15})\, \mathrm{M}_{\odot }$if the dark matter (DM) comprises weakly interacting massive particles Constraints on mixed dark matter model of particles and primordial black holes from the Galactic 511 keV line • Physics • 2020 The 511 keV line was first detected in 1970's but its origin is still unknown. It was proposed that positrons from dark matter (DM) particles in the halo of galaxy are possible sources. We consider a Radio bounds on the mixed dark matter scenarios of primordial black holes and WIMPs • Physics • 2022 We study the synchrotron radio emission in the mixed dark matter scenarios consisting of the primordial black holes (PBHs) and the self-annihilating WIMPs (weakly interacting massive particles). The Primordial black holes as dark matter candidates • Physics SciPost Physics Lecture Notes • 2022 We review the formation and evaporation of primordial black holes (PBHs) and their possible contribution to dark matter. Various constraints suggest they could only provide most of it in the mass CMB and 21-cm bounds on early structure formation boosted by primordial black hole entropy fluctuations • Physics Physical Review D • 2021 The dark matter (DM) can consist of the primordial black holes (PBHs) in addition to the conventional weakly interacting massive particles (WIMPs). The Poisson fluctuations of the PBH number density Constraints on stupendously large black holes • Physics • 2020 We consider the observational constraints on stupendously large black holes (SLABs) in the mass range$M \gtrsim 10^{11}\,M_{\odot}$. These have attracted little attention hitherto and we are aware ## References SHOWING 1-10 OF 145 REFERENCES Constraints on primordial black holes as dark matter candidates from star formation • Physics • 2013 By considering adiabatic contraction of the dark matter (DM) during star formation, we estimate the amount of DM trapped in stars at their birth. If the DM consists partly of primordial black holes Limits on primordial black holes from$\mu$distortions in cosmic microwave background • Physics • 2018 If primordial black holes (PBHs) form directly from inhomogeneities in the early universe, then the number in the mass range$10^6 -10^9M_{\odot}$is severely constrained by upper limits to the Gamma-ray constraints on the first stars from annihilation of light WIMPs • Physics • 2012 We calculate the limits on the fraction of viable dark matter minihalos in the early universe to host Population III.1 stars, surviving today as dark matter spikes in our Milky Way halo. Motivated by Cosmological implications of Primordial Black Holes • Physics • 2017 The possibility that a relevant fraction of the dark matter might be comprised of Primordial Black Holes (PBHs) has been seriously reconsidered after LIGO's detection of a$\sim 30 M_{\odot}\$ binary Signatures of non-gaussianity in the isocurvature modes of primordial black hole dark matter • Physics • 2015 Primordial black holes (PBHs) are black holes which may have formed very early on during the radiation dominated era in the early universe. We present here a method by which the large scale Constraints on primordial black holes as dark matter candidates from capture by neutron stars • Physics • 2013 We investigate constraints on primordial black holes (PBHs) as dark matter candidates that arise from their capture by neutron stars (NSs). If a PBH is captured by a NS, the star is accreted onto the Dynamics of primordial black hole formation • Physics • 1999 We present a numerical investigation of the gravitational collapse of horizon-size density fluctuations to primordial black holes (PBHs) during the radiation-dominated phase of the early Universe. Did LIGO Detect Dark Matter? • Physics Physical review letters • 2016 It is considered that the black-hole (BH) binary detected by LIGO may be a signature of dark matter, and reasonable estimates span a range that overlaps the 2-53 Gpc^{-3} yr^{-1} rate estimated from GW150914, thus raising the possibility that LigO has detected PBH dark matter. Primordial Black Holes as Dark Matter: Almost All or Almost Nothing • Physics • 2010 Primordial black holes (PBHs) are expected to accrete particle dark matter around them to form ultracompact minihalos (UCMHs), if the PBHs themselves are not most of the dark matter. We show that if	2022-06-27 23:19:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5611883401870728, "perplexity": 3159.9233503948008}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103344783.24/warc/CC-MAIN-20220627225823-20220628015823-00472.warc.gz"}
http://troncorecords.com/whf9t/ec5766-unsupervised-learning-of-clusters-in-neural-networks	Hebbian Learning has been hypothesize… Neural networks are widely used in unsupervised learning in order to learn better representations of the input data. You can use unsupervised learning to find natural patterns in data that aren’t immediately obvious with just statistical analysis or comparing values. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. This learning process is independent. Latent variable models are widely used for data preprocessing. In this paper, by contrast, we introduce a novel deep neural network architecture to learn (in an unsupervised manner) an explicit non-linear mapping of the data that is well-adapted to subspace clustering. machine-learning neural-network unsupervised-learning. Neural networks based methods, Fuzzy clustering, Co-clustering … –More are still coming every year •Clustering is hard to evaluate, but very useful in practice •Clustering is highly application dependent (and to some extent subjective) •Competitive learning in neuronal networks performs clustering analysis of the input data In simple words, neural networks can be considered mathematical models loosely modeled on the human brain. The ART model allows the number of clusters to vary with problem size and lets the user control the degree of similarity between … Max Net uses identity activation function with $$f(x)\:=\:\begin{cases}x & if\:x > 0\\0 & if\:x \leq 0\end{cases}$$. The task of this net is accomplished by the self-excitation weight of +1 and mutual inhibition magnitude, which is set like [0 < ɛ < $\frac{1}{m}$] where “m” is the total number of the nodes. (Neural networks can also extract features that are fed to other algorithms for clustering and classification; so you can think of deep neural networks as components of larger machine-learning applications involving algorithms for reinforcement learning, classification and regression.) In this way, clustering … There’ve been proposed several types of ANNs with numerous different implementations for clustering tasks. In our framework, successive operations in a clustering algorithm are expressed as steps in a recurrent process, stacked on top of representations output by a Convolutional Neural Network (CNN). When a new input pattern is applied, then the neural network gives an output response indicating the class to which input pattern belongs. Now, we are comfortable with both supervised and unsupervised learning. Join this workshop to build and run state-of-the-art face recognition models offering beyond the human level accuracy with just a few lines of code in Python. In this paper, the learning speed of the supervised neural networks is proposed as novel intelligent similarity measurement for unsupervised clustering problems. So what type of learning is a combination of neural network and genetic algorithm depends on the learning type of neural network. The connections between the output neurons show the competition between them and one of them would be ‘ON’ which means it would be the winner and others would be ‘OFF’. Comparative simulation results of the networks … It mainly deals with finding a structure or pattern in a collection of uncategorized data. Once clustered, you can further study the data set to identify hidden features of that data. To this end, we build our deep subspace clustering networks (DSC-Nets) upon deep auto-encoders, which non-linearly map the data points to a latent space through a series of encoder … Following are some important features of Hamming Networks −. Of these three, the first one can be viewed as “learning with a teacher”, while the remaining two can be viewed as “learning withouta teacher”. Methods: An unsupervised learning method is proposed for a deep neural network architecture consisting of a deep neural network and an MR image generation module. RotNet model trained on the full YFCC100M dataset; 4. DeeperCluster model trained on the full YFCC100M dataset; 2. Some applications of unsupervised machine learning techniques are: 1. Most of these neural networks apply so-called competitive learning rather than error-correction learning as most other types of neural networks do. Haven't you subscribe my YouTubechannel yet? If each cluster has its own learning rate as η i = 1 N i, N i being the number of samples assigned to the i th cluster, the algorithm achieves the minimum output variance (Yair, Zeger, & Gersho, 1992). They are actually traditional neural networks. learning representations for clustering. Clustering is a successful unsupervised learning model that reects the intrinsic heterogeneities of common data gener- ation processes [1], [2], [3], [4]. 3D embeddings of high dimensional data using PowerSFA. Both train error and validation error satisfies me (loss: 0.0881 – val_loss: 0.0867). Get started. In this way, we can show results in a 2-dimensional graph. Unsupervised Learning in Recurrent Neural Networks? You can use any content of this blog just to the extent that you cite or reference. Their design make them special. Surprisingly, they can also contribute unsupervised learning problems. Most of these methods derive from information-theoretic objectives, such as maximizing the amount of preserved information about the input data at the network’s output. Usually they can be employed by any given type of artificial neural network architecture. I said similar because this compression operation is not lossless compression. Herein, it means that compressed representation is meaningful. 8. $$s\:=\:\begin{cases}x, & if\:x \geq 0\\0, & if\:x < 0\end{cases}$$, $$C\:=\:\displaystyle\sum\limits_i s_{i}x_{i}$$. During the training of ANN under unsupervised learning, the input vectors of similar type are combined to form clusters. The proposed learning algorithm called the centroid neural network (CNN) estimates centroids of the related cluster groups in training date. It is a fixed weight network which means the weights would remain the same even during training. K-means is one of the most popular clustering algorithm in which we use the concept of partition procedure. Following are the three important factors for mathematical formulation of this learning rule −, Suppose if a neuron yk wants to be the winner, then there would be the following condition, $$y_{k}\:=\:\begin{cases}1 & if\:v_{k} > v_{j}\:for\:all\:\:j,\:j\:\neq\:k\\0 & otherwise\end{cases}$$. However, if a particular neuron wins, then the corresponding weights are adjusted as follows −, $$\Delta w_{kj}\:=\:\begin{cases}-\alpha(x_{j}\:-\:w_{kj}), & if\:neuron\:k\:wins\\0 & if\:neuron\:k\:losses\end{cases}$$. w0 is the weight adjustable between the input and S-cell. For examle, say I have a 1-dimensional data where samples are drawn randomly from 1 of 2 distributions (similar to Mixture model) as shown in the below histogram . It seems that clustering is based on general shapes of digits instead of their identities. Unsupervised Learning of Image Segmentation Based on Differentiable Feature Clustering. Today, most data we have are pixel based and unlabeled. Autoencoders are trend topics of last years. These kinds of networks are based on the competitive learning rule and will use the strategy where it chooses the neuron with the greatest total inputs as a winner. Facial recognition is not a hard task anymore. asked Mar 20 '13 at 3:12. Lippmann started working on Hamming networks in 1987. A good example of Unsupervised Learning is clustering, where we find clusters within the data set based on the underlying data itself. Magdalena Klapper-Rybicka1, Nicol N. Schraudolph2, and Jurgen¨ Schmidhuber3 1 Institute of Computer Science, University of Mining and Metallurgy, al. Autoencoders are trend topics of last years. I have seen in K-minus clustering that the number of clusters needs to be stated. As an unsupervised classification technique, clustering identifies some inherent structures present in a set of objects based on a similarity measure. 3) Graph Matching Neural Networks. Editors' Picks Features Explore Contribute. Step 1 − Select k points as the initial centroids. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. Revue Française de Photogrammétrie et de Télédé-tection, Société Française de Photogrammétrie et de Télédétection, … Then, the weights from the first layer to the second layer are trained, and so on. To solve the combinatorial optimization problem, the constrained objective 1 Introduction . C-Cell − It is called a complex cell, which combines the output from S-cell and simultaneously lessens the number of units in each array. In this paper, we study unsupervised training Neural networks engage in two distinguished phases. Unsupervised learning can be used for two types of problems: Clustering and Association. To understand this learning rule we will have to understand competitive net which is explained as follows −. It is a hierarchical network, which comprises many layers and there is a pattern of connectivity locally in those layers. Haven't you subscribe my YouTube channel yet , You can subscribe this blog and receive notifications for new posts, Handling Overfitting with Dropout in Neural Networks, Convolutional Autoencoder: Clustering Images with Neural Networks. is implemented using a neural network, and the parameter vector denotes the network weights. Some types of neural networks – like Self Organizing Maps and Adaptive Resonance Theory models – also follow the unsupervised learning paradigm. learning representations for clustering. Compared with the great successes achieved by supervised learning, e.g. Each user is represented by a feature vector that contains the movie ratings that user provided. This means that it is 24 times smaller than the original image. Deep-Clustering. Today, we are going to mention autoencoders which adapt neural networks into unsupervised learning. By considering a cluster, you can find differences in the feature vectors that might be suitable for recommendation (a movie common in the cluster that some m… Then, you should apply a unsupervised learning algorithm to compressed representation. Supervised and unsupervised learning. I want to train a neural network to identify "optimal" threshold value which Separates between 2 clusters/distributions given a data set or a histogram. To understand the rest of the machine learning categories, we must first understand Artificial Neural Networks (ANN), which we will learn in the next chapter. Little work has been done to adapt it to the end-to-end training of visual features on large-scale datasets. On the other hand, including all features would confuse these algorithms. Using unsupervised learning, I was able to create over 10 clusters of the population and determine in which of those clusters the customers are over or under represented. The idea is that you should apply autoencoder, reduce input features and extract meaningful data first. Clustering with unsupervised learning neural networks: a comparative study Wann, Chin-Der D.; Thomopoulos, Stelios C. 1993-09-02 00:00:00 Chin-Der Wann and Stelios C. A. Thomopoulos cdwÂ©ecl.psu.edu ; sctÂ©ecl.psu.edu Decision and Control Systems Laboratory Department of Electrical and Computer Engineering The Pennsylvania State University University Park, PA 16802 ABSTRACT A … What’s more, there are 3 hidden layers size of 128, 32 and 128 respectively. You can think of autoencoders as a generalization of PCA, in which you can learn both higher and lower dimensional, non-linear representations of your data. Abstract: This paper presents an unsupervised method to learn a neural network, namely an explainer, to interpret a pre-trained convolutional neural network (CNN), i.e., explaining knowledge representations hidden in middle conv-layers of the CNN. Example: pattern association Suppose, a neural net shall learn to associate the following pairs of patterns. Learn more Unsupervised Machine Learning. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns fea-ture representations and cluster assignments us-ing deep neural networks. Example: To understand the unsupervised learning, we will use the example given above. F 1 INTRODUCTION. Here ‘a’ is the parameter that depends on the performance of the network. Clustering methods can be based on statistical model identification (McLachlan & Basford, 1988) or competitive learning. Many clustering algorithms have been developed. Among neural network models, the self-organizing map (SOM) and adaptive resonance theory (ART) are commonly used in unsupervised learning algorithms. By clustering the users into groups, you can find people who have similar movie interests or similar dislikes (see Figure 2). This site uses Akismet to reduce spam. Data clustering is a fundamental data analysis tool in the area of data mining [9], [10], pattern recognition [11], [12], [41], image analysis [47], [48], feature extraction [13], [14], vectorquantization[15],[16],imagesegmentation[17],[18], function approximation [19], [20], dimensionality reduction [49], [50] and big data analysis [21], [22]. distance preserving. This network is just like a single layer feed-forward network having feedback connection between the outputs. Creative Commons Attribution 4.0 International License. We’ve already applied several approaches for this problem before. Clustering is a fundamental data analysis method. Clustering, for example, can show how grouped certain continuous values might be, whether related or unrelated. Finally, learning is rarely considered in existing MGM algorithms, not to mention the more challenging MGMC problem, while our method handles both MGM and MGMC with unsupervised learning. Here, si is the output from S-cell and xi is the fixed weight from S-cell to C-cell. This learning process is independent. Deep Neural Network: Predicting beyond the borders. Unsupervised learning algorithms also hold their own in image recognition and genomics as well. Users assign a rating to each movie watched from 1 – 5 (1 being bad, 5 being good). It is useful for finding fraudulent transactions 3. It allows you to adjust the granularity of these groups. The inputs can be either binary {0, 1} of bipolar {-1, 1}. Unsupervised learning is a useful technique for clustering data when your data set lacks labels. In this paper, we give a comprehensive overview of competitive learning based clustering methods. ANNs used for clustering do not utilize the gradient descent algorithm. It is basically an extension of Cognitron network, which was also developed by Fukushima in 1975. Clustering is the most common unsupervised learning algorithm used to explore the data analysis to find hidden patterns or groupings in the data (Fig. In another sense, C-cell displaces the result of S-cell. The results reported here compare neural networks using Kohonen learning with a traditional clustering method (K-means) in an experimental design using simulated data with known cluster solutions. For example, if we consider neuron k then, $$\displaystyle\sum\limits_{k} w_{kj}\:=\:1\:\:\:\:for\:all\:\:k$$, If a neuron does not respond to the input pattern, then no learning takes place in that neuron. Unsupervised detection of input regularities is a major topic of research on feed- forward neural networks (FFNs), e.g., [1–33]. Initialize k prototypes (w1,…,wk), for example we can identifying them with randomly chosen input vectors −, $$W_{j}\:=\:i_{p},\:\:\: where\:j\:\in \lbrace1,....,k\rbrace\:and\:p\:\in \lbrace1,....,n\rbrace$$. Notice that input features are size of 784 whereas compressed representation is size of 32. The S-cell possesses the excitatory signal received from the previous layer and possesses inhibitory signals obtained within the same layer. This kind of network is Hamming network, where for every given input vectors, it would be clustered into different groups. All the nodes are fully interconnected and there exists symmetrical weights in all these weighted interconnections. We do not need to display restorations anymore. A neural net is said to learn supervised, if the desired output is already known. Unsupervised learning does not need any supervision. The scaled input of S-cell can be calculated as follows −, $$x\:=\:\frac{1\:+\:e}{1\:+\:vw_{0}}\:-\:1$$. Noob Saibot Noob Saibot. The weights of the net are calculated by the exemplar vectors. For example, you can use an autoencoder to embed your 80-dimensional features into a lower dimensional space of, say, only 10 features. This tutorial discussed ART and SOM, and then demonstrated clustering by using the k-means algorithm. As we have seen in the above diagram, neocognitron is divided into different connected layers and each layer has two cells. Katherine McAuliffe. Learn how your comment data is processed. Then, you should apply a unsupervised learning algorithm to compressed representation. The idea is that you should apply autoencoder, reduce input features and extract meaningful data first. The networks discussed in this paper are applied and benchmarked against clustering and pattern recognition problems. Clustering automatically split the dataset into groups base on their similarities 2. When a new input pattern is applied, then the neural network gives an output response indicating the class to which input pattern belongs. Autoencoding layer has 2 outputs. Natural clusters structures are observed in a variety of contexts from gene expression [5] … We start with an initial partition and repeatedly move patterns from one cluster to another, until we get a satisfactory result. Clustering can help the company target more effectively or discover segments of potential... Vectors, it is symmetric about the centroid and centroid layer consists 28×28. To a particular pattern or a group of patterns and extract meaningful data first finds patterns from cluster... Network which means the weights would remain the same result as classification does but without predefined! They must have same number of clusters needs to be progressed layer by layer have to understand unsupervised... Left side of this blog just to the second layer are trained, and then demonstrated by. A topographic organization in which the pixel belongs semantic constraints from very few … neural-network! Network which means the competitors never support themselves new unsupervised learning, also known as unsupervised learning of clusters in neural networks. Our experiments show that our method, Prototypical Contrastive learning network having feedback connection between the vectors. There ’ ve already applied several approaches for this problem before t immediately obvious with statistical. Train error and validation error satisfies me ( loss: 0.0881 – val_loss: 0.0867 ) of under. Said similar because this compression operation is not lossless compression lossless compression input pattern is applied then... Features of Hamming networks − unsupervised subspace clustering techniques their similarities 2 inputs be. Underlying data itself process your data and find natural patterns in data unsupervised learning of clusters in neural networks aren ’ immediately... 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https://gmatclub.com/forum/booth-wl-accepted-w-vs-ross-with-91820.html	Booth (WL-->accepted w $$) vs Ross (with$$$) : Business School Reviews Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack It is currently 27 Feb 2017, 15:19 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track Your Progress every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History #### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Booth (WL-->accepted w $$) vs Ross (with$$$) Author Message Intern Joined: 21 Jan 2010 Posts: 10 Schools: Stanford (R1--dinged), Berkeley (R1--dinged), Booth (R2--int), Columbia (R2--dinged), Ross (R2--admit w/$) Followers: 0 Kudos [?]: 6 [1] , given: 1 Booth (WL-->accepted w $$) vs Ross (with$$$) [#permalink] ### Show Tags 24 Mar 2010, 22:38 1 KUDOS Hello gmat clubbers! You've sustained me through the last six months of torture--I would love some of your advice on this last stretch. Here's what it boils down to: I'm admitted to Ross with a full scholarship, and have been waitlisted by Booth. Do I try to pull all the stops in an effort to get off the waitlist? Booth was my top choice, and Ross was my last. I've visited both schools. Ross seems to have an incredibly friendly, warm culture, but three students independently told me that the one critique they would have for Ross is that it's not a very academically focused school. (I'd welcome other viewpoints from Ross students!) I'm trying to do a career switch into quantitative marketing, so academic rigor is key for me. Booth seemed to have a much more staid culture, but I left with no doubt I'd get the training I'm after, and the name carries more prestige than Ross'. Is the training and brand name worth +$100K more than Ross', and not to mention, the stress of waiting and strategizing for several more weeks? Thanks in advance for your thoughts! Last edited by shiny26 on 12 May 2010, 15:38, edited 2 times in total. Manager Joined: 07 Nov 2009 Posts: 160 Location: Milan, Italy Schools: Booth (admitted R1), NYU (interview Mar 4), UT (withdrawn), Rice (admitted R2) plus dings at HBS, Stanford, Wharton and CBS WE 1: Oil and gas Followers: 4 Kudos [?]: 29 [1] , given: 6 Re: Booth (waitlist) vs Ross (with $$) [#permalink] ### Show Tags 25 Mar 2010, 02:31 1 This post received KUDOS Well one thing's for sure - do not give up the Ross offer until you have a cast-iron Booth offer. If it comes down to Ross or gambling on getting in off the WL, take the Ross$$$ - but if you can hold out a little longer before decision time, why not shoot Booth some relevant updates and see? _________________ If I said something intelligent, it was probably by accident. But click "kudos" anyway - it will make me happy. VP Joined: 11 Dec 2006 Posts: 1430 Location: New York, NY Schools: NYU Stern 2009 Followers: 41 Kudos [?]: 221 [1] , given: 6 ### Show Tags 25 Mar 2010, 06:12 2 KUDOS Having been through it before, I don't believe that there's any material difference - neither in academics nor in recruiting opportunities - between any of the top 5. With that, there's no way I would chose Booth over Ross with a scholarship. Of course, this is easy to say in hindsight from the perspective of having gone to a top B-school and I might be signing a completely different tune had it been the other way around, so grain, salt, apply. As to your goals, Booth has a handful of quantitative marketing courses that would be a good fit - but I truly believe it is just a handful (you may know better than I). As to your concern about academics, for all it's world-famous intellectual rigor and all that I found Booth to be pretty easy frankly -- I worked hard to be sure, but I also graduated in the top 5% of my class. If I'd put in half as much effort I'd probably have still graduated with a B average, and if I had done next to nothing, I'd probably have a C. And lets be clear - I'm not some super smart academic powerhouse. I'm average at best. I hear that people end up on academic probation at Booth, but frankly, unless you've been drinking toilet water every morning with some kind of xanax cocktail, I don't understand how this is possible. It would practically take more effort to get a D than it would to get a B. If Booth is supposed to be "hard", I can't imagine what schools known to be "easy" must be like. Manager Joined: 07 Nov 2009 Posts: 160 Location: Milan, Italy Schools: Booth (admitted R1), NYU (interview Mar 4), UT (withdrawn), Rice (admitted R2) plus dings at HBS, Stanford, Wharton and CBS WE 1: Oil and gas Followers: 4 Kudos [?]: 29 [1] , given: 6 Re: Booth (waitlist) vs Ross (with $$) [#permalink] ### Show Tags 25 Mar 2010, 07:49 1 This post received KUDOS Rhyme are you trying to tell me that my preferred morning smoothie is actually detrimental to my health? Toilet water is so refreshing over ice. _________________ If I said something intelligent, it was probably by accident. But click "kudos" anyway - it will make me happy. GMAT Club Legend Affiliations: HHonors Diamond, BGS Honor Society Joined: 05 Apr 2006 Posts: 5926 Schools: Chicago (Booth) - Class of 2009 GMAT 1: 730 Q45 V45 WE: Business Development (Consumer Products) Followers: 315 Kudos [?]: 2053 [1] , given: 7 Re: Booth (waitlist) vs Ross (with$$$) [#permalink] ### Show Tags 25 Mar 2010, 10:03 1 This post received KUDOS britguy wrote: Rhyme are you trying to tell me that my preferred morning smoothie is actually detrimental to my health? Toilet water is so refreshing over ice. No, in your case it's just fine as you are in Britain. Everything there is made of candy and lollipops and everyone wears tophats and belongs to the Ministry Of Silly Walks, so its cool. Intern Joined: 21 Jan 2010 Posts: 10 Schools: Stanford (R1--dinged), Berkeley (R1--dinged), Booth (R2--int), Columbia (R2--dinged), Ross (R2--admit w/$) Followers: 0 Kudos [?]: 6 [1] , given: 1 ### Show Tags 01 Apr 2010, 06:57 2 KUDOS powerka wrote: ### Show Tags 01 Apr 2010, 07:33 2 KUDOS powerka wrote: My opinion is biased due to my background. In Economics circles (and political circles) Chicago has a well known brand. It may have lost value during the last financial crisis, but it still is well known. Better infamous than unknown. Chicago, not Booth. You are right. To be honest, I knew of the Chicago School of thought in economics before, but never associated the University of Chicago b-school with it before I started researching programs. LSE and LBS were much more familiar to me. I agree that in educated circles it is pretty well known, but it is mostly among people interested in Economics on a deeper level than your average college grad. That said, I was actually surprised to see that Michigan is in the top 20 universities internationally in terms of academic reputation. Nevertheless, I have found that in general business circles most people in the EU don't know much about US schools (with the exceptions I mentioned in Finance/Consulting). It would be interesting to see other international opinions, though. I am also a little biased already, after I have done a lot of b-school research. But my advice to the OP would be to proceed from his targeted industries/locations before making a decision. I like Chicago a lot, it is one of the top programs to me, but 100k changes the picture a bit. For example, if you want to do GM, paying additional 100k might not be worth it. I think the best perspectives would come from current students/alumni, as they are not as adulterated by brands as I am as an applicant Manager Joined: 22 Jul 2009 Posts: 191 Followers: 4 Kudos [?]: 264 [0], given: 18 Re: Booth (waitlist) vs Ross (with $$) [#permalink] ### Show Tags 01 Apr 2010, 07:36 Personally, for 100k I would not even doubt it! _________________ Please kudos if my post helps. Intern Joined: 12 Feb 2010 Posts: 25 Schools: Michigan - Ross Class of 2012 WE 1: Oil/Energy/Engineering/Construction Followers: 0 Kudos [?]: 8 [1] , given: 0 Re: Booth (waitlist) vs Ross (with$$$) [#permalink] ### Show Tags 01 Apr 2010, 08:06 1 This post received KUDOS People, let me address a few key points. Academic rigor- you've gotta be kidding me. Shiny26, if you really want academic rigor, you should go for a PhD in physics, chemical engineering or math. All top Mba programs will display similar academic rigor. Both Ross & Booth happen to be great programs. Recruiting - you've already decided that you want to go into quant marketing and not finance. I would acknowledge that for finance, booth kicks ass, but for the rest of fields, both schools are the same. International recognition - beyond h/s/w/Columbia, most business schools go unrecognized past the business circles. On the other hand, since you're in at Ross, you should look up some of the alumni. Ross has a pretty big & influential network in Asia and relatively strong in Europe. Feel- I've visited both schools & I'll second the fact that Ross gives you that warm fuzzy feeling. I've talked to several MBAs from h/s/w/c/k/Ch/etc. and every single one of them emphasizes that warm fuzziness was probably one of the most important factor in their decision for their choice of school. So, go where you feel more welcome than a place by which you're just enamored. Money - this is a no brainer buddy. Getting 100k for going to school- can't get any better than this. People would kill to be in your shoes, I know I would. In the spirit of full disclosure, booth was my top choice too, unfortunately or fortunately, I was turned down. I got into Ross and will be there starting this fall. I too was skeptical about Ross, but that was before I met some of the future classmates. Now, I can easily see having a good time next year while learning a lot too. Add to that, from what I hear about Saturdays at the Big House can't be compared to anything at any other school. Graduating without debt in this economy ( with so much uncertainty with jobs) is the key & what I percieve as an easy choice. Good luck with your decision. (hope to see you at Ann Arbor this fall!) cheers, Cheme Posted from my mobile device Posted from my mobile device Intern Joined: 21 Jan 2010 Posts: 10 Schools: Stanford (R1--dinged), Berkeley (R1--dinged), Booth (R2--int), Columbia (R2--dinged), Ross (R2--admit w/$) Followers: 0 Kudos [?]: 6 [0], given: 1 Re: Booth (waitlist) vs Ross (with $$) [#permalink] ### Show Tags 01 Apr 2010, 11:11 sniperssk: that post is hilarious Thanks for everyone's viewpoint from an international perspective. It's a double-edged consolation that both Booth and Ross don't have that much recognition among non-business circles abroad. I just did a search in Ross' alumni database for people based in England, France, China, India, etc., and am somewhat surprised numbers are lower than I would've expected. I wonder if Chicago's are much higher, or the numbers at schools that clearly have international clout like Harvard. This isn't a huge concern since I plan on working in the US, but it would have been nice to go to a school with a name that carries as China/India gradually take over the world economy. Senior Manager Joined: 12 Apr 2010 Posts: 446 GMAT 1: Q V Followers: 11 Kudos [?]: 100 [0], given: 157 Re: Booth (waitlist) vs Ross (with$$$) [#permalink] ### Show Tags 30 Apr 2010, 00:04 sniperssk lol man rofl, i cant stop laughing. It should have been a commercial This F word sounds a little french to me. Mouth what mouth lol. I didnt know people in MBA were actually capable of making fun. You got a point buddy. Even i was unaware of all the schools except H/S/Lsb/Yale/Berkley. shiny i dont think you need to worry really, most of the schools like Ross, Chicago are well known in MBA circles in INDIA, Booth carries more reputation but i wouldnt say that having a scholarship to go to Ross would put you at any disadvantage. I referred to some pretty lofty MBA alumni and they said that Ross, Dartmouth, Berkley are all pretty well known in Asia MBA circles. So dont sweat too much. Just make some enquiries with any Marketing acquantainces in Asia just to confirm. _________________ If you found the reply to be helpful, give kudos. Intern Joined: 21 Jan 2010 Posts: 10 Schools: Stanford (R1--dinged), Berkeley (R1--dinged), Booth (R2--int), Columbia (R2--dinged), Ross (R2--admit w/$) Followers: 0 Kudos [?]: 6 [1] , given: 1 ### Show Tags 12 May 2010, 17:07 How much more money in the two years does Ross offer you? _________________ Please kudos if my post helps.	2017-02-27 23:19:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33359938859939575, "perplexity": 7993.42931405795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501173866.98/warc/CC-MAIN-20170219104613-00188-ip-10-171-10-108.ec2.internal.warc.gz"}
https://brilliant.org/discussions/thread/triangles-2/	× # triangles. A sequence of triangles is defined as follows- T1 is an isosceles triangle inscribed in a given circle.with one of its equal sides as the base another isosceles triangl(T2) is drawn so that the non intersecting vertices of the triangles T1 and T2 lie on the same arc.this process is continued till infinity.prove that as n approaches infinity Tn is an equilareral triangle. Note by Mayank Shrivastava 3 years, 3 months ago MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$...$$ or $...$ to ensure proper formatting. 2 \times 3 $$2 \times 3$$ 2^{34} $$2^{34}$$ a_{i-1} $$a_{i-1}$$ \frac{2}{3} $$\frac{2}{3}$$ \sqrt{2} $$\sqrt{2}$$ \sum_{i=1}^3 $$\sum_{i=1}^3$$ \sin \theta $$\sin \theta$$ \boxed{123} $$\boxed{123}$$	2018-01-18 12:11:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9993520379066467, "perplexity": 9888.730821665296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887253.36/warc/CC-MAIN-20180118111417-20180118131417-00334.warc.gz"}
http://mathhelpforum.com/algebra/282750-i-don-t-know-how-describe-problem.html	# Thread: I don't know how to describe this problem 1. ## I don't know how to describe this problem 4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform? Answers: 1) 8; 2) 12; 3) 10; 4) 11. I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please. 2. ## Re: I don't know how to describe this problem Originally Posted by Jotaro 4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform? Answers: 1) 8; 2) 12; 3) 10; 4) 11. I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please. #1 - Throw out 8. "A" sang 10. It can't be 8. #2 - What did "C" and "D" sing? "Least" and "Most" imply no ties. Otherwise, superlatives don't work. "C" and "D" must have sung how many songs? Are we getting anywhere? 3. ## Re: I don't know how to describe this problem Originally Posted by Jotaro 4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform? Answers: 1) 8; 2) 12; 3) 10; 4) 11. I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please. Here is my solution: $\dbinom{4}{3}=4$ Four choose three is four. So there are four groups of three. $ABC\quad 3\\ABD\quad 3\\ACD\quad 4\\BCD\quad 2$ Now I leave to you to see that the above meets all requirements. I did that a Venn diagram on four sets. 4. ## Re: I don't know how to describe this problem $\displaystyle 3n=10+8+9+9$	2019-07-15 19:02:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3766045570373535, "perplexity": 1751.5157655898313}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195523840.34/warc/CC-MAIN-20190715175205-20190715201205-00351.warc.gz"}
https://www.doubtnut.com/question-answer/a-line-with-direction-cosines-proportional-to-212-meet-each-of-the-lines-xy-az-nd-x-a2y2z-the-coordi-644637310	Login # A line with direction cosines proportional to 2,1,2 meet each of the lines x=y+a=z nd x+a=2y=2z. The coordinastes of each of the points of intersection are given by Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Updated On: 23-5-2021 Apne doubts clear karein ab Whatsapp par bhi. Try it now. CLICK HERE Loading DoubtNut Solution for you Watch 1000+ concepts & tricky questions explained! 4.5 K+ 200+ Text Solution (3a, 3a, 3a) , (a,a,a)(3a,2a, 3a), (a,a,a)(3a,2a,3a),(a,a,2a)(2a,3a,3a),(2a,a,a) Answer : B Transcript TimeTranscript 00:00 - 00:59even today we are going to discuss and more question the question is that align with direction cosine proportional to 21 to meet each of the line X = 2y + Y equal to Z and X + 1 equal to 2 Y equal to 2 Z the coordinates of each of the point of the intersection are given by estoppel here first line is given as first-line can be written f = 2y + 8 is equal to Z so we can write it as a x b a white + z b a 1 and right by my one and one by one line is given here X + Y is equals to 2 Y is equals to 2 Z so we can write this line as X + if we divide complete equation by to so we can write X + 1 by 2 is equal to y by 1 is equal to Z by one year later state the situation in equals to Arya and thus we creation is equals to clear so why simple 01:00 - 01:59speak and write it as here from the situation we can write it as xyz is equals to there are -108 here and from this equation coordinates can be returned and CO2 l - of Asia and l and health Giza coordinates so let's take this point is P here and this point sq so direction direction ratio aap pic you can be written and here to Lambda 2 into 2 into l - of a class are you take this one and one and one and the sun is l2m to end to the direction cosine of PQ can be written as here I'll oneplus l2l oneplus l2m oneplus and 2 and + sorry - 11 - 11 - l2m 1 -2 can be written as 02:00 - 02:59here and minus minus of h + 101 - m to hear this can be written as l - are here these are the direction cosines as in the question given that direction cosine are proportional to align with direction cosine proportional to 212 here so here are given that direction ratios are 212 Shinchan the question given the right direction wish you are proportional to this one so we can write it easier to L by 2 and minus A minus 6 / 2 is equals to minus A + 1 divided by 1 year in this man is equals to l - A / to hear so by these two coordinates speak and write it as your by these two we can write it has yet to l - 2 + 2 is equal to hear and minus Arya by simplifying the speak and write it is here and this one is minus minus 2 Y + 1 = 2 - of h + 2 03:00 - 03:59= 20 and let's take this one is first here and this one is third year so fast and third we can buy it here to Al minus A minus 1 divided by 2 is equal to l - R2 is cancelled with two years by simplifying the speak and write it is this money Kuchh To l Harish cancel out with our students and is implied and equals to a italika square by substituting Value here we can write it as this one can be written and here when we substitute a liquid is equal to am fine art + 2 is equal to zero the sky is pink line are equal to 3 a year so 3 point P is equal to R R - a&r hear it in value of Rs 3 week and write its 33 - 22 and this money quotes 23838 2A and 3A 48 of P similarly coordinator of you can be written as here to our -2 and -1 is eliya to ella - A L and area so by substituting 04:00 - 04:59value of L equals to a week and write its two a minus b equal to a year and this money quotes free and equal to 1 by comparing from option here we get 38283 and 38283 and a is our correct option which is option vs option B is correct answer explanation thanks for watching	2021-12-01 03:44:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6676414012908936, "perplexity": 751.980907147676}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359082.78/warc/CC-MAIN-20211201022332-20211201052332-00005.warc.gz"}
http://mathhelpforum.com/advanced-algebra/85015-normal-extension-rationals-quick-questions.html	# Math Help - normal extension of the rationals - quick questions 1. ## normal extension of the rationals - quick questions Just trying to get my head around normal extensions. True or False? is a normal extension of is a normal extension of I would say for the first one, true, because it is the splitting field of . For the second one, false, because is irreducible by Eisenstein, and has only one zero > 0 in Could anyone please tell me if these are OK? You can tell the second is not normal because the other two roots are imaginary and $\mathbb{Q}(2^{1/3})\subset \mathbb{R}$. But yeah I think you got it.	2014-07-14 16:01:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6155768036842346, "perplexity": 447.3514276334162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776441023.78/warc/CC-MAIN-20140707234041-00061-ip-10-180-212-248.ec2.internal.warc.gz"}
https://publications.mfo.de/handle/mfo/2818;jsessionid=6AE58BA17D4254CB5C5415559735E729	Now showing items 1-20 of 58 • #### 1751 - Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 [OWR-2017-58] (2017) - (17 Dec - 23 Dec 2017) Since 1950, mathematicians have become increasingly familiar with the digital computer in their professional practice. Previously, however, many other instruments, now mostly forgotten, were commonly used to compute numerical ... • #### 1750 - Network Models: Structure and Function [OWR-2017-57] (2017) - (10 Dec - 16 Dec 2017) The focus of the meeting was on the mathematical analysis of complex networks, both on how networks emerge through microscopic interaction rules as well as on dynamic processes and optimization problems on networks, including ... • #### 1749 - Classical and Quantum Mechanical Models of Many-Particle Systems [OWR-2017-56] (2017) - (03 Dec - 09 Dec 2017) This workshop was dedicated to the presentation of recent results in the field of the mathematical study of kinetic theory and its naturalextensions (statistical physics and fluid mechanics). The main models are the ... • #### 1748 - Reflection Positivity [OWR-2017-55] (2017) - (26 Nov - 02 Dec 2017) The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representation Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, ... • #### 1746 - Variational Methods for Evolution [OWR-2017-54] (2017) - (12 Nov - 18 Nov 2017) Many evolutionary systems, as for example gradient flows or Hamiltonian systems, can be formulated in terms of variational principles or can be approximated using time-incremental minimization. Hence they can be studied ... • #### 1745 - Mathematical Logic: Proof Theory, Constructive Mathematics [OWR-2017-53] (2017) - (05 Nov - 11 Nov 2017) The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of core mathematics and theoretical computer science as well as homotopy type theory and logical aspects ... • #### 1744b - Copositivity and Complete Positivity [OWR-2017-52] (2017) - (29 Oct - 04 Nov 2017) A real matrix $A$ is called copositive if $x^TAx \ge 0$ holds for all $x \in \mathbb R^n_+$. A matrix $A$ is called completely positive if it can be factorized as $A = BB^T$ , where $B$ is an entrywise nonnegative matrix. ... • #### 1744a - Interplay between Number Theory and Analysis for Dirichlet Series [OWR-2017-51] (2017) - (29 Oct - 04 Nov 2017) In recent years a number of challenging research problems have crystallized in the analytic theory of Dirichlet series and its interaction with function theory in polydiscs. Their solutions appear to require unconventional ... • #### 1743b - Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures [OWR-2017-49] (2017) - (22 Oct - 28 Oct 2017) Reflectionless operators in one dimension are particularly amenable to inverse scattering and are intimately related to integrable systems like KdV and Toda. Recent work has indicated a strong (but not equivalent) relationship ... • #### 1743a - Mini-Workshop: PDE Models of Motility and Invasion in Active Biosystems [OWR-2017-48] (2017) - (22 Oct - 28 Oct 2017) Cell migration is crucial for the development and functioning of multicellular organisms; it plays an essential role in, e.g., morphogenesis, immune system dynamics, wound healing, angiogenesis, bacterial motion and biofilm ... • #### 1743c - Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry [OWR-2017-50] (2017) - (22 Oct - 28 Oct 2017) Recent developments exhibit a strong connection between low-dimensional topology and complex algebraic geometry. A common theme is provided by the Alexander polynomial and its many avatars. The mini-Workshop brought together ... • #### 1741 - Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry [OWR-2017-47] (2017) - (08 Oct - 13 Oct 2017) The aim of the workshop was to survey recent developments in fractal geometry, specifically those related to projections and slices of planar self-similar sets, and dimension and absolute continuity of self-similar measures ... • #### 1740 - Spectral Structures and Topological Methods in Mathematical Quasicrystals [OWR-2017-46] (2017) - (01 Oct - 07 Oct 2017) The mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 ... • #### 1739 - Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces [OWR-2017-45] (2017) - (24 Sep - 30 Sep 2017) The workshop covered a number of active areas of research in algebraic geometry with a focus on derived categories, moduli spaces (of varieties and sheaves) and birational geometry (often in positive characteristic) and ... • #### 1738c - Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications [OWR-2017-44] (2017) - (17 Sep - 23 Sep 2017) Lattice polytopes arise naturally in many different branches of pure and applied mathematics such as number theory, commutative algebra, combinatorics, toric geometry, optimization, and mirror symmetry. The miniworkshop ... • #### 1738a - Mini-Workshop: MASAs and Automorphisms of C-Algebras [OWR-2017-42] (2017) - (17 Sep - 23 Sep 2017) The main aim of this workshop was to study maximal abelian -subalgebras of C-algebras from various points of view. A chief motivation is the UCT problem, which asks whether all separable nuclear C-algebras satisfy the ... • #### 1738b - Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton-Okounkov Bodies [OWR-2017-43] (2017) - (17 Sep - 23 Sep 2017) There are several flavors of positivity in Algebraic Geometry. They range from conditions that determine vanishing of cohomology, to intersection theoretic properties, and to convex geometry. They offer excellent invariants ... • #### 1737 - Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications [OWR-2017-41] (2017) - (10 Sep - 16 Sep 2017) Quantum field theory (QFT) may be considered one of the most fundamental frameworks of theoretical physics. Quantum Electrodynamics (QED) is the part of QFT that describes the interaction between matter and light. Although ... • #### 1736 - Automorphic Forms and Arithmetic [OWR-2017-40] (2017) - (03 Sep - 09 Sep 2017) The workshop brought together leading experts and young researchers at the interface of automorphic forms and analytic number theory to disseminate, discuss and develop important recent methods and results. A particular ... • #### 1735 - Komplexe Analysis [OWR-2017-39] (2017) - (27 Aug - 02 Sep 2017) Complex Analysis is a very active branch of mathematics. The aim of this workshop was to discuss recent developments in several complex variables and complex geometry. Topics included singular Kähler–Einstein metrics, ...	2021-04-18 09:17:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41593220829963684, "perplexity": 2000.9961151276962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038469494.59/warc/CC-MAIN-20210418073623-20210418103623-00273.warc.gz"}
https://math.stackexchange.com/questions/3562394/when-is-mathrmhomix-y-to-mathrmhomfx-mathrmlan-ify-an-iso	# When is $\mathrm{Hom}(i(x), y)\to\mathrm{Hom}(f(x),\mathrm{Lan}_i(f)(y))$ an isomorphism? $$\DeclareMathOperator{\Hom}{Hom}\DeclareMathOperator{\Nat}{Nat}$$ Let $$i : A\to B$$ and $$f : A\to C$$ be functors. In the case where $$A=C$$ and $$f$$ is the identity functor, if the left Kan extension of $$f$$ along $$i$$ is pointwise, then it is a right adjoint to $$i$$. In general, we can build a transformation $$\mathrm{Hom}(i(x), y)\to \mathrm{Hom}(f(x),\mathrm{Lan}_i(f)(y))$$ natural in $$x$$ and $$y$$ that specializes to the adjunction in the case of the previous sentence. In general, this transformation only have an initial property (it is a translation of the initial property of $$\mathrm{Lan}_i(f)$$) and is not an isomorphism. An other case where it is an isomorphism arises when we consider the nerve of some functor $$F : A→B$$. It is the left Kan extension of the Yoneda embedding $$A\to [A^{\mathrm{op}},\mathrm{Set}]$$ along $$F$$. The Yoneda lemma says that the morphism above is an isomorphism. Question: Is there something interesting to say about when this morphism is an isomorphism? Some necessary or sufficient condition? (Maybe nothing?) Construction of the morphism. The Yoneda lemma imply that for any functor $$g : B→C$$ (and as above $$i:A\to B$$ and $$f:A\to C$$), the set of natural transformations $$f\to g\circ i$$ is in natural bijection with the natural transformations $$\mathrm{Hom}(i(x), y)\to \mathrm{Hom}(f(x),g(y))\text{.}$$ We can use the end/coend calculus for this: \begin{align} \Nat(f,g\circ i) &\cong \int_x \Hom(f(x), g(i(x)))\\ &\cong \int_x \Hom\left[f(x), ∫_y g(y)^{\Hom(i(x),y)}\right]\\ &\cong ∫_{x,y} \Hom[\Hom(i(x),y), \Hom(f(x),g(y))] \end{align} Thus a Kan extension can equally be defined using the morphism this question is about. There is no implication between "$$f\to g\circ i$$ is an isomorphism" and the property that the corresponding morphism on the other side is an isomorphism (when $$g = \mathrm{Lan}_i(f)$$). Indeed, in the case of the nerve functor, $$f\to g\circ i$$ is not an isomorphism. And in the case of the realization functor, $$f\to g\circ i$$ is an isomorphism but the corresponding transformation is not. I would enjoy an answer involving profunctors to explain how the "bending" works and what corresponds to what (a bit like we can do with the units/counit of an adjunction to make correspond the zig-zag identities with the property that the two natural transformations are inverses). • compositition symbol $\circ$: \circ, right arrow $\to$: \to or \rightarrow, $\cong$: \cong; please see edits so you can improve your formatting. $\int$: \int – amWhy Feb 27 '20 at 17:56 • @amWhy Ok, thank you. I'll do that in the future but I see no difference on my computer between \cong ($\cong$) and ≅ ($≅$). I imagine there is one on yours. By the way I just put back "counit", you replaced it by "count". – Idéophage Feb 27 '20 at 18:07 • What you pasted looked like $\cong$, so I used the corresponding LaTeX symbol. If you meant to use $\equiv$, then use \equiv. Copy and pastes of text symbols deteriorate more easily, and may not be seen consistently by all users. Also, know that I would not "nitpick" if you hadn't already seemed to exhibit some competence in formatting. I thought you might appreciate the pointers. – amWhy Feb 27 '20 at 18:11 • @amWhy Actually I used unicode characters instead of latex commands intentionally, because I have easy access to them on my keyboard and know mathjax supports them (I don't copy/paste! It would be easier to type the latex.). I found some discussions about this issue on the meta: here and there. But anyway it's not important. – Idéophage Feb 27 '20 at 18:31	2021-03-09 11:16:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 25, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9774433970451355, "perplexity": 452.8459589892322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389798.91/warc/CC-MAIN-20210309092230-20210309122230-00624.warc.gz"}
http://dsp.stackexchange.com/questions/7975/how-can-a-filter-have-zero-group-delay	# How can a filter have zero group delay? If you put a wave packet through the passband of a 1st-order low-pass filter, it will be delayed by the group delay of the filter, and remain the same amplitude, right? If you put the same wave packet through a complementary 1st-order highpass filter with the same cutoff frequency, the group delay curve is the same, so the delay of the packet will be the same, but the gain is much lower, so it will be both delayed and attenuated to negligibility. Since the output of the highpass filter is very small, if you sum the outputs of these two filters (as in an audio crossover), I would expect it to be negligibly different from the output of the lowpass filter: Large delayed signal + very small delayed signal = large delayed signal. Yet if you sum the filter responses, the amplitude is 0 dB everywhere, and the phase is 0 everywhere, and therefore the group delay becomes 0, which would mean that the wave packet comes out with no delay and no changes. I don't understand how this can be possible. Don't filters always incur delay? How can a filter (which also has positive group delay) undo the delay caused by the other channel, especially when this is happening in the stopband? Which part am I misunderstanding here? The best-known crossover types with linear phase are first-order non-inverted crossovers, ... The first-order crossover is minimum phase when its outputs are summed normally; it has a flat phase plot at 0°. - The Design of Active Crossovers and Here the result of summing the outputs together produces 0° phase shift, which is to say that the summed amplitude and phase shift of a 1st-order crossover is equivalent to a piece of wire. - Linkwitz-Riley Crossovers: A Primer: 1st-Order Crossover Networks Testing on actual pulses shows how the lowpass (blue) delays the pulse, as expected, and how the highpass (green) can combine with it to produce the original (red) pulse, but how is the highpass pulse occurring before the original if the highpass filter is causal and has positive group delay? Intuition is failing me. It does show that the highpass output is not as negligible as I imagined, and the delay is more negligible than I imagined, and as you move the carrier frequency around, these two properties change in a proportional way (smaller delay requires lower amplitude highpass output to correct it). But I still don't really understand it. - So you're implying that the two filters are matched such that their transfer functions sum to unity (i.e. $H_{lp}(z) + H_{hp}(z) = 1$)? That would also imply that the sum of their impulse responses is just an impulse at $n=0$, which would agree with your observation of zero group delay. I think your assumption that the phase of the two filters sum to zero is probably faulty. – Jason R Feb 25 '13 at 3:24 @JasonR: Yes, 1st-order filters, highpass and lowpass, with the same fc. en.wikipedia.org/wiki/Audio_crossover#First_order – endolith Feb 25 '13 at 5:09 @Jason: endolith is indeed correct. First order hi/lo pass reconstructs perfectly in parallel. There are other cases which do this as well – Hilmar Feb 25 '13 at 13:05 Sorry guys; I was thinking of series cascades only. Disregard. – Jason R Feb 25 '13 at 14:00 There are a couple of interesting aspects of "reconstruction to unity". First, there are two ways of combining two filters: parallel and in series. For a parallel topology it is ALWAYS possible to find a complimentary filter so that the pairs add to unity. It's easy enough, actually. Simply do $\tilde{H}(\omega) = 1-H(\omega)$. In the time domain that means that the impulse response of the complimentary filter is simply the negative of the original impulse response with 1 added to the first sample. So all the "ringy" stuff cancels out. Now the shape of this complimentary filter is not always what one would expect. For a 1st order low pass it actually is a first order high pass but for higher order filters it tends to have over/under swings in the cutoff region. However, it always exists as a stable causal filter. Series (or cascade) "reconstruction to unity" is bit more complicated. Obviously the filters would have to be the inverse of each others, i.e. $\tilde{H}(\omega) = \frac{1}{H(\omega)}$. In general this can be done for any minimum phase filter. The inverse of a minimum phase filter is minimum phase as well and both are causal and stable.	2015-08-02 04:16:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7308179140090942, "perplexity": 854.3764811976446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988962.66/warc/CC-MAIN-20150728002308-00142-ip-10-236-191-2.ec2.internal.warc.gz"}
https://scicomp.stackexchange.com/questions?sort=newest&page=5	# All Questions 7,773 questions 86 views ### What's the minimum step size that can be used in Euler's method before it becomes unreliable? In particular, if Euler's method is implemented on a computer, what's the minimum step size that can be used before rounding errors cause the Euler approximations to become completely unreliable? I ... 105 views ### Why the numerical solution of advection-dominant problem is challenging In many CFD text books, usually there is a dedicated chapter for advection term discretization. Why discretization of such term in advection-dominated problems and near the discontinuities is ... 57 views 106 views ### Clustering with points lying along different 3D planes I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit: There are roughly equal number of points lying along ... 40 views ### Optimize multivariable function with interdependent variables I have a cost function with 2 parameters. The variables are dependent on each other. So, if I just take a partial derivative with respect to one variable the slope is in terms of the other variable ... 112 views ### High-accuracy numerical differentiation I have a $200 \times 200$ matrix representing the values taken by a function over an equally spaced grid. I would like to perform derivatives on it. I am interested in its gradient (i.e. its ... 152 views ### Numerical integration in Python with unknown constant I’d like to solve the below equation for the unknown $T$: $$\int_0^\infty \frac{x^2}{\exp\left(\frac{x}{T}\right)-1}\kappa_x \mathrm{d}x = C,$$ where $C$ is a known constant and $\kappa_x$ is some ... 88 views ### Formulation of the least-squares parameter estimation problem I have a system of 10 ordinary differential equations of the form, $$\frac{dy_1}{dt} = f1(V1,k1,y1,y2)\\ \vdots \\ \frac{dy_{10}}{dt} = f_{10}(V_{10},k_{10},y_{9},y_{10})$$ I want to estimate the ... 150 views I have heard of space-time finite element methods. Although I was able to find some articles that describe the different possible methods from a mathematical point of view (thanks to Space-time finite ... 68 views ### Imposition of Dirichlet BC for Fourier pseudospectral in this paper I was trying to implement the algorithm from the paper "Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh–Benard convection". I am having a hard time to ... 390 views ### What is the state of the art in solving stiff initial value problems? I'm looking for current references on solving stiff ODEs. Most of what I know (say, BDF methods) apparently date back to the 1980's, and I feel like a lot of progress should have been made in that ... 106 views 33 views ### How can I maximise orthonormality between degenerate eigenvectors using ARPACK? I am using ARPACK's zndrv1 to diagonalise a matrix (the context is quantum chemistry). While all vectors have a norm 1, as expected, vectors corresponding to degenerate eigenstates aren't always ...	2019-06-17 12:39:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9015595316886902, "perplexity": 565.4887477461453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998475.92/warc/CC-MAIN-20190617123027-20190617145027-00257.warc.gz"}
https://mathoverflow.net/questions/273938/wishart-type-matrix	# Wishart type matrix Assume a positive semi-definite $M\times M$ matrix $A$, not with full rank, and an $M\times N$ matrix $X$, where $M>N$. The elements of $X$ are independent, zero-mean complex Gaussian with variance $1/M$. My question is simple, what is the distribution of $X^H AX$? From what I have seen, a matrix of form $X^H X$ is Wishart if the rows of $X$ are correlated, but in my case it is the columns. Necessary and sufficient conditions on $A$ for $Q=X^H AX$ to have a Wishart distribution are derived in Wishart and chi-square distributions associated with matrix quadratic forms (1997) and Wishart distributions associated with matrix quadratic forms (2003). In general, the matrix $Q$ can be decomposed as a linear combination of independent Wishart matrices, see On the distribution of matrix quadratic forms (2012). • Understood, and many thanks. It was easily verified that for my case it is not Wishart. I have a follow-up question, perhaps a more difficult one. From the last paper you mentioned, we know that $Q=\sum_{k=1}^K \lambda_k W_k$, where $W_k$ are drawn iid from a certain Wishart distribution. My problem is now that I would like to pass $K\to \infty$. My $\lambda_k$ are then defined from a function $\lambda(x)$, i.e., for a given K, we have $Q=(1/K)\sum_{k=1}^K \lambda (k/K) W_k$. Now, what is the limiting distribution of $Q$? Jul 8 '17 at 21:12 • in the limit $K\rightarrow\infty$ the law of large numbers will ensure that $P(Q)$ tends to a delta function at $Q_{\infty}=\mathbb{1}\,M^{-1}\,{\rm tr}\, A$. Jul 9 '17 at 11:28	2021-12-07 14:20:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.880395770072937, "perplexity": 148.83080123651897}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363400.19/warc/CC-MAIN-20211207140255-20211207170255-00140.warc.gz"}
https://www.sparrho.com/item/averaged-dehn-functions-for-nilpotent-groups/94946a/	# Averaged Dehn Functions for Nilpotent Groups Research paper by Robert Young Indexed on: 20 Sep '07Published on: 20 Sep '07Published in: Mathematics - Group Theory #### Abstract Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality $\delta(l)<Cl^\alpha$ for $\alpha>2$ then it satisfies the averaged isoperimetric inequality $\delta^{\text{avg}}(l)<C'l^{\alpha/2}$. In the case of non-abelian free nilpotent groups, the bounds we give are asymptotically sharp.	2020-11-23 22:15:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8167383670806885, "perplexity": 819.4772841982116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141168074.3/warc/CC-MAIN-20201123211528-20201124001528-00131.warc.gz"}
http://math.stackexchange.com/questions/369215/definition-of-logarithm-in-complex-domain	# Definition of logarithm in complex domain My first question is: What is the proper definition of logarithmic function $f(z)=\ln{z}$. where $z\in \mathbb{C}$. quoting Wikipedia. a complex logarithm function is an "inverse" of the complex exponential function, just as the natural logarithm $\ln{x}$ is the inverse of the real exponential function $e^x$. In a book Calculus Vol 1.By Tom M. Apostol, he tells the function $\ln{x}$ is defined as $\ln{x}=\int_{1}^{x}{\frac1t\;dt}$ $\color{blue}{\star}$ and the function $e^x$ is defined to be it's inverse (rather than the opposite). Some reasons why it is so as per the book and what I have understood is . We can define what is $e^2$ $=$ $e\times e$ . But how can we give such a defintion to $e^{\sqrt{2}}$ or$\large e^{\sqrt{2+\sqrt[3]{3+\sqrt[5]{5}}}}$ or more generally the function $a^x$ when the domain is $\mathbb{R}$. Hence as the funciton $a^x$ is not properly defined for Real domain, how can we think about it's definition of it's inverse(The way Wikipedia and some other books define natural logarithm) So if we are to define $\ln{x}$ as in $\color{blue}{\star}$, it solves all the problem( a proper definition of $\ln{x}$ in real domain , a definition for exponential function in real domain, getting rid of otherwise-circular proofs of some basic theorem in limits involving logarithm and exponential function) Thinking in the same way just like $e^z$ have problems with definition.How can we define it's inverse?. Doing a bit of research through internet I found some bits of information. The first mention of the natural logarithm was by Nicholas Mercator in his work Logarithmotechnia published in 1668,2 although the mathematics teacher John Speidell had already in $\color{red}{1619}$ compiled a table on the natural logarithm.[3] It was formerly also called hyperbolic logarithm,[4] as it corresponds to the area under a hyperbola. It is also sometimes referred to as the Napierian logarithm, although the original meaning of this term is slightly different. Wikipedia entry:Exponential Function The exponential function arises whenever a quantity grows or decays at a rate proportional to its current value. One such situation is continuously compounded interest, and in fact it was this that led Jacob Bernoulli in $\color{red}{1683}$[4] to the number now known as e. Later, in 1697, Johann Bernoulli studied the calculus of the exponential function The dates(as per source) of discoveries suggests such($\color{blue}{\star}$) a definition. So summing up I have two questions. 1.A proper definition of $\ln{z}$ when $z\in \mathbb{C}$ 2.Is't the definition for logarithm in real domain, the one I have mentioned ($\color{blue}{\star}$) is the best/correct (Just because I have only seen a few places it is defined so).? - Using the integral definition isn't a problem; just take any path from $1$ to $z$ that does not go through the branch cut, and you're golden. – Ｊ. Ｍ. Apr 22 at 14:06 @J.M. Nice!. I had thought about some definition like that. But if we follow the definition $\int_{1}^{z}{\frac{1}{t}\;dt}=\ln{z}$ How should I understand the fact that $\ln{z}$ is multivalued function?.(I don't have any idea what is $\int{f}$ where $f$ is a complex function and may be I am speaking foolish, $1/t$ is single valued and taking an integral as a sum how can sum of single valued function be a multivalued function?(I guess it may be because of we can choose any path, Am I right?.)).Thanking you in anticipation. – boywholived Apr 22 at 14:25 If you remember the treatment of complex numbers as points in a plane, consider for instance the line segment joining $1$ and $z$. That can be taken as an integration path. – Ｊ. Ｍ. Apr 22 at 14:29 You can define the complex logarithm as $$Lg(z)=lg(\|z\|)+iArg(z)$$ where $lg$ is the real logarithm and $Arg(z)$ is the principal branch of the argument (that is, $Arg(z)\in(-\pi ,\pi )$ ). The logarithm is defined for all $z$ in $U=\mathbb{C}-\{x\in\mathbb{R} \| x\leq 0\}$. - You can accept the answer if you enjoyed it, sir ;) – Marra Apr 22 at 11:47 Ok nice answer!. (Remember there is a time delay for accepting answers). And don't call me 'sir' I am a only 17 and is at school. – boywholived Apr 22 at 11:53 The exponential function is usually defined as $$\exp:= z\mapsto \sum\limits_{k=0}^{+\infty}\frac{z^k}{k!}$$ Then you find out it's a bijection from $\Bbb R$ to $\Bbb R _+^$ and defined $\ln$ as its inverse function. Then you define for $a>0$, $z\in \Bbb C$, $a^z=e^{z\ln a } = \exp ( z\ln a)$ So $a^x$ is properly defined. Then to defined the logarithm on the complex numbers, it's a bit more complicated. You don't need $\cos$ and $\sin$ to define it but since those functions are introduced earlier, it might help you see what's happening so I'll use them. Define $$\cos:=z \mapsto \Re \exp ( i z)$$ $$\sin := z \mapsto \Im \exp(iz)$$ You can then prove that $$\exp(z) = \exp(\Re z)(\cos \Im z + i \sin \Im z)$$ And as you can see (because you know properties of $\cos$ and $\sin$ that can be proved from the definition above), $\exp(z+2\pi i)=\exp ( z)$. And this is where the trouble starts to define the complex logarithm: You do not have an injection and therefore can't have a bijection either. So you have to restrict the domain to have a bijection which leads to different branches of the logarithm, much like when you search for an angle, you want it modulo $2\pi$. For all $z\in \Bbb C^$, you know you can find a unique $r\in \Bbb R_+^$ and a unique $\theta \in [-\pi,\pi)$ so that $z = r e^{i\theta}$ (again, you "feel" it because of what you were taught but it can be proven). So we define $$Arg:= z = re^{i\theta} \mapsto \theta$$ And then we can define $$Log(z)=\ln \|z\|+i Arg(z)$$ The problem with doing that is that when we cross $\Bbb R_-^$, $Arg(z)$ "jumps" from $-\pi$ to $\pi$, ie it is discontinuous. So we often define $Arg$ in $\Bbb C^* \setminus \Bbb R_-^* = \Bbb C \setminus \Bbb R_-$ to have a continuous function instead. -	2013-12-10 15:48:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9727507829666138, "perplexity": 216.97827990401052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164021936/warc/CC-MAIN-20131204133341-00094-ip-10-33-133-15.ec2.internal.warc.gz"}
http://exoplanets.co/exoplanets-tutorial/extrasolar-planet-corot-7-b.html	Home→ Exoplanets Tutorial → Corot-7 b # Extrasolar Planet Corot-7 b The exoplanet known as Corot-7 b is unusual in many respects. It is one of the smallest planets known, and orbits its parent star very close (less than 2% of the Earth-Sun distance, or $0.0172\pm0.00029$ astronomical units (AU)), and consequently has a very short orbital period of less than 1 Earth day (0.853585 Earth days). This in itself is not unsual, but it is not a gas giant hot Jupiter. Rather, it has a radius of only 1.65 times that of Earth, and it is thought to be a rocky, terrestrial planet. The mass of Corot-7 b has been hotly debated, with different researchers coming up with different answers, in the range of 2 to 9 Earth masses. Its density and composition are therefore also uncertain. Even with this uncertainty in mass, Corot-7 b is consistently an outlier (by a long shot) on a diagram of orbital period versus mass period for confirmed exoplanets. Models that attempt to explain the period versus mass data always have to make an exception for Corot-7 b because they are unable to account for it. Historically speaking, outliers such as Corot-7 b are the objects that will eventually force the development of a correct theory. Any model that cannot account for Corot-7 b must be regarded as incomplete or wrong. The host star for Corot-7 b has a mass similar to our Sun and a radius that is about 87% of that of our Sun. The system is about 489 light years from Earth. You can get instant access to the book Exoplanets and Alien Solar Systems: Reference for the latest mass estimate of Corot-7 b (in August 2012): Hatzes et al. 2012. Just one example of a paper that attempts to interpret the diagram of orbital period versus mass period for confirmed exoplanets: Benitez-Llambay, Masset, and Beauge (2011). File under: Corot-7 b; Rocky, terrestrial planet that is an outlier in the mass-orbital period plane.	2017-06-23 01:34:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5010786056518555, "perplexity": 1588.5956587560036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128319943.55/warc/CC-MAIN-20170623012730-20170623032730-00624.warc.gz"}