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http://physics.stackexchange.com/questions/23742/why-are-we-forced-to-choose-a-specific-value-for-pi-field-in-nambu-goldstone?answertab=oldest | # Why are we forced to choose a specific value for $\pi$ field in Nambu-Goldstone phenomenon?
In the sigma-model of spontaneous symmetry breaking, we have degenerate vacuum states. But if we don't pick up a particular value of VEV, we won't have any symmetry breaking. As I read from a book, in field theory at finite volume, there would be no problem; but at infinite volume, we are forced to choose a value of the $\pi$ field. But why?
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## 1 Answer
This is the superselection phenomenon. If you have a particle in a potential well which has a symmetric minimum, like a particle in 2d with the potential
$$V(x,y) = a(x^2+y^2)^2 - b(x^2+y^2)$$
With $a>0$ and $b>0$, the ground state is symmetric under rotations--- the ground state wavefunction will be rotationally invariant. This can be proved rigorously, but it is also clear from the relation of the path integral to a biased random walk--- the random walk will wander around the sphere.
When you have a field theory in finite volume (on a lattice), the field value center of mass will also random walk around the circle. If you have two scalar fields, X and Y, the values are X(p) Y(p), where p ranges over the points of the lattice. There are a large but finite number of points p, the field operators are like the X,Y position of the point p, and the particles can all move thier center of mass, which will fluctuate until it is all around the circle.
But if you take the infinite lattice limit, the center of mass degree of freedom is infinitely massive, and has no fluctuation. This means that no local operator will have matrix elements between states with different values for the center of mass position--- the local operators just shift the value at a few nearby lattice sites, and the mean value is defined by infinitely many lattice sites far away.
The result is that every different value of the center of mass position is a different vacuum, completely unreachable from any other. Under this condition, there is no sense is saying that the vacuum is superposed over all orientations, because any local observer will never see more than one orientation--- the vacuum is frozen at some center of mass value which can be determined by local measurements, and the value never quantum fluctuates over all space.
Such a situation was called a "superselection sector" by Wigner. The terminology is unfortunate, because it is not much like a selection rule, and this was the analogy. A better name might be a "macroscopic variable".
The same thing happens in statistical mechanics. If you have a solid crystal on a table, the canonical ensemble sums over all possible positions of the solid on the table--- but once you see where the solid is, it is never going to move, because a coordinated center of mass motion that moves all the points of a solid in the same direction is infinitely improbable in the large system limit.
There are two limits involved in a field theory--- the infrared infinite lattice limit, and the ultraviolet fine-lattice limit. In the ultraviolet limit, the m term goes to zero by scaling, so if you make the lattice too fine, you will find that the field fluctuations do not pick out a direction at small distances, the field values are random from point to point. But over a coarse lattice, the same theory on this coarse lattice has a negative mass. This means that the fields X,Y will tend to point in some direction, and nearby lattice points will tend to point in the same direction.
The vanishing of the m term at short distances means that any finite volume field theory is effectively like a finite number of particles--- no superselection rule. In the infinite volume limit, the superselection rule emerges, and the field vacuum is one or another direction, not all of them in coherent superposition. The reason is that the local operators cannot knock you from one vacuum to another.
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Is this related to the "Wagner-Mermin" theorem in some way? – QuantumDot Sep 12 '12 at 20:25 | 2015-10-09 23:50:07 | {"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": 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": 0.7412924766540527, "perplexity": 304.6003439600967}, "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-2015-40/segments/1443737936627.82/warc/CC-MAIN-20151001221856-00208-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://www.springerprofessional.de/computer-algebra-in-scientific-computing/14363888 | main-content
## Inhaltsverzeichnis
### Fast Matrix Computation of Subresultant Polynomial Remainder Sequences
We present an improved (faster) variant of the matrix-triangularization subresultant prs method for the computation of a greatest common divisor of two polynomials A and B (of degrees dA and dB, respectively) along with their polynomial remainder sequence [1]. The computing time of our fast method is 0(n2+ßlog ∥C∥2), for standard arithmetic and 0(((n1+ß+n3 log ∥C∥)(log n+ log ∥C∥)2) for the Chinese remainder method, where n = dA + dB, ∥C∥ is the maximal coefficient of the two polynomials and the best known ß < 2.356. By comparison, the computing time of the old version is 0(n5 log ∥C∥2 ).Our improvement is based on the work of Malaschonok [12] who proposed a new, recursive method for the solution of systems of linear equations in integral domains with complexity Onß over the integers (same as the complexity of matrix multiplication).In this paper we present an overview of the two methods mentioned above and show how they are combined into a fast matrix method for computing polynomial remainder sequences. An example is also presented to clarify the concepts.
### About Simultaneous Representation of Two Natural Numbers by a Sum of Three Primes
I. A. Allakov, M. I. Israilov
### On a Description of Irreducible Component in the Set of Nilpotent Leibniz Algebras Containing the Algebra of Maximal Nilindex, and Classification of Graded Filiform Leibniz Algebras
This paper is devoted to the study of Leibniz algebras introduced by Loday in [1-2] as an analogue of zero ”noncommutative” Lie algebras. We define the notion of zero-filiform Leibniz algebras and study their properties. There is a notion of p-filiform Lie algebras for p≥ 1 [3], which loses a sense in case p = 0, since Lie algebra has at least two generators. In the case of Leibniz algebras for p = 0 this notion substantial, and thereby, introduction of a zero-filiform algebra is quite natural. We also investigate the complex non-Lie filiform Leibniz algebras. In particular, we give some equivalent conditions of filiformity of Leibniz algebras and describe complex Leibniz algebras, which were graded in natural way.
Sh. A. Ayupov, B. A. Omirov
### Application of Computer Algebra in Problems on Stabilization of Gyroscopic Systems
The paper discusses some problems of stabilization of potential systems at the expense of gyroscopic forces. The algorithms described are employed in the software ”STABILITY” [1]. This software is based on the computer algebra system ”Mathematica” [2] and is designed to investigate stability and stabilization of mechanical systems in symbolic and numeric-symbolic forms.
Banshchikov Andrey, Bourlakova Larissa
### Implementing Computational Services Based on OpenMath
OpenMath is a standard for representing mathematical objects. This report describes our experiences in implementing a facility for OpenMath-based symbolic computation services to be made available over the Internet. Services can be implemented in REDUCE, Mathematica or Maple, they are accessible via a Java client or using shell scripts. Our experimental client/server system is publicly available under an Open Source license. We address some issues in the development of OpenMath-based services such as implementing Phrasebooks and different choices of input syntax.
Matthias Berth, Frank-Michael Moser, Arrigo Triulzi
### Group Classification of the Navier-Stokes Equations for Compressible Viscous Heat-Conducting Gas
We consider the problems of using computer algebra systems for group classification of partial differential equations. The presence of arbitrary elements makes the solution of determining equations more difficult. It offers necessity for active human control over this process by using dialog regime. Methods of computer algebra for problems of group classification are illustrated by the example of a system of the Navier-Stokes equations for compressible viscous heat-conducting gas. This system has five arbitrary elements. The solution of the problem of finding equivalence transfonpations is presented. The group classification is carried out in some particular cases.
Vasiliy V. Bublik
### Plotting Functions and Singularities with Maple and Java on a Component-based Web Architecture
In this paper we present a client/server plotting system for analytical functions that features a reliable computation and visualization of singularities. The system is part of a Web-based course on Mathematics for first-year students at the University of Tübingen. In an educational context where students of the first or second semesters are addressed, it is crucial that the plotted graphs are correct, since the students may not yet be able to interpret faulty graphs in an appropriate way. The singularities are computed by a computer algebra system which is transparently accessible through a Web interface. Our implementation of the singularity computations is more complete than the existing ones that we found as parts of various algebra systems. The rendering of the graphs and the visualization of the singularities is performed by a Java applet which can be executed within almost all of the current Javaaware Web browsers. No additional software, like plug-ins or proprietary browser extensions, has to be installed on the client machine.
Dieter Bühler, Corinne Chauvin, Wolfgang Küchlin
### Stable Self-Oscillatory Regimes in Volterra Models of Three Populations
For two models of the quantitative dynamics of a predatorprey system such as the generalized three-dimensional Lotka-Voltterra models the existence of the stable self-oscillatory regimes of behavior is investigated basing on qualitative and bifurcation theories as well as on computer experiment.
T. E. Buriev, V. E. Ergashev
### Computing “Small” 1-Homological Models for Commutative Differential Graded Algebras
We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small I-homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
V. Álvarez, J. A. Armario, M. D. Frau, R. González-Díaz, M. J. Jiménez, P. Real, B. Silva
### Effective computation of algebra of derivations of Lie algebras
By the software Mathematica 3.0 we design a program that allows calculate the algebra of derivations of any Lie algebra. As an example we use this program in a special class of Lie algebras, (n - 4)-filiform Lie algebras of dimension n.
L. M. Camacho, J. R. Gómez, R. M. Navarro, I. Rodríguez
### An Integration and Reduction for Ordinary Non Linear Differential Equations Library
In this paper, we review the algorithmic work done in the last years by the Grenoble Computer Algebra team in the domain of differential equations. We organize in a logic manner the studies developed in different directions and we show how the modules obtained from these studies could cooperate in order to build IRONDEL, a Library for the Integration and Reduction of Ordinary Non linear Differential Equations.
J. Della Dora, F. Richard-Jung
### Complexity of Derivatives Generated by Symbolic Differentiation
The computational solution of many mathematical problems involves derivatives. Programs for computing derivatives may be (1) hand-Coded, (2) set up via function calls and divided differences, or (3) obtained using symbolic differentiation. In practice, the divided differences approach is still the standard technique. But in many cases, derivatives can be computed cheaper and more accurately by symbolic differentiation. In this paper we investigate the complexity of algorithms for computing derivatives of rational functions. In particular, we deal with the forward mode and the reverse mode of symbolic differentiation. We discuss bounds on the amount of work within the described algorithms in terms of rational operations.
Herbert Fischer, Hubert Warsitz
### An Assessment of the Efficiency of Computer Algebra Systems in the Solution of Scientific Computing Problems
Computer algebra systems (CASs) have become an important tool for the solution of scientific computing problems. With the increasing number of general purpose CASs, there is now a need for an assessment of the efficiency of these systems. We discuss some peculiarities associated with the analysis of CPU time efficiency in CASs, and then present results from three specific systems (Maple Vr5, Mathematica 4.0 and MuPAD 1.4) on a sample of intermediate size problems. These results show that Maple Vr5 is generally the speediest on our examples. Finally, we formulate some requirements for developing a comprehensive test suite for analyzing the efficiency of CASs.
Victor G. Ganzha, Evgenii V. Vorozhtsov, Michael Wester
### On the Relation between Pommaret and Janet Bases
In this paper the relation between Pommaret and Janet bases of polynomial ideals is studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal Janet basis. An improved version of the related algorithm for computation of Janet bases, initially designed by Zharkov, is described. For an ideal with a finite Pommaret basis, the algorithm computes this basis. Otherwise, the algorithm computes a Janet basis which need not be minimal. The obtained results are generalized to linear differential ideals.
### An (Asymptotic) Error Bound for the Evaluation of Polynomials at Roots
Given is a univariate polynomial $$F(X) = {X^n} - {\sigma _1}{X^{n - 1}} + \ldots + {( - 1)^{n - 1}}{\sigma _{n - 1}}X + {( - 1)^n}{\sigma _n} \in \left[ X \right]$$ and a “poor” numerical solution α1, ‖ , αn ∈ ℂ of F(X) = 0 such that 1 ≤ ∣αi - xi∣ ≤ δ ∈ ℝ and F(xi) = 0 for 1 ≤ i ≤ n. We show that $$O\left( {{2^{n - 1}}n! \cdot {\delta ^{{\textstyle{{n(n - 1)} \over 2}}}}} \right)$$ is an (asymptotic) error bound for the evaluation of an arbitrary but fixed multivariate polynomial f ∈ ℂ[x1,...,x n ] at the n-tuple (α1,...,αn) instead of the n-tuple of the roots (x1,...,x n ),and that for some polynomials the (asymptotic) error bound is Ω Keywords. Analysis of algorithms, data structures, rewriting techniques, evaluation of polynomials, roots, error bounds $$\Omega \left( {n! \cdot {\delta ^{{\textstyle{{n(n - 1)} \over 2}}}}} \right)$$.
Manfred Göbel
### Three Remarks on Comprehensive Gröbner and SAGBI Bases
This note presents new complexity results for the comprehensive Gröbner bases (CGB) algorithm in the special case of one main variable and two polynomials, a general remark about CGB for parameterized binomial ideals, and it introduces the concept of comprehensive SAGBI bases together with a first application in invariant theory. Keywords. Comprehensive Gröbner bases, parameterized binomial ideals, comprehensive SAGBI bases, algorithmic invariant theory, permutation groups.
Manfred G-bel, Patrick Maier
### Computing the Cylindrical Algebraic Decomposition Adapted to a Set of Equalities
The Cylindrical Algebraic Decomposition algorithm, in its projection phase, proceeds by eliminating one variable from a given set of polynomials P by means of the computation of the principal subresultant coefficients of a certain set of pairs of polynomials in P (including their derivatives and reducta). Since this method produces usually a big number of polynomials, and since the process must be iterated several times, any improvement in the projection phase would convey to dramatically speed up the efficiency of the Cylindrical Algebraic Decomposition algorithm.The purpose of this paper is to present two approaches allowing, in some cases, to simplify the projection phase in the Cylindrical Algebraic Decomposition algorithm when some of the involved polynomials are prescribed to have a particular sign behaviour.
Neila Gonzalez-Campos, Laureano Gonzalez-Vega
### Symbolic Algorithms of Algebraic Perturbation Theory for a Hydrogen Atom: the Stark Effect
We present symbolic algorithms realized in REDUCE 3.6 for evaluation of eigenvalues and eigenfunctions of the 3-D and 2-D hydrogen atoms in weak uniform electric fields. Algebraic perturbation theory schemes are built up using the irreducible representations of the dynamical symmetry algebras so(4,2) and so(3,2), which are connected by the tilting transformations with ‘wave functions of the 3-D and 2-D hydrogen atoms. Such a construction is based on a representation of the unperturbed Hamiltonian and polynomial perturbation operator via generators of the algebra. It was done without an assumption on the separation of independent variables of the perturbation operator and without using fractional powers of the parabolic quantum numbers in recurrence relations determining the effects of generators of the algebra on the corresponding basis. The efficiency of the proposed schemes and algorithms is demonstrated by calculations of coefficients of the Stark effect perturbations series for the hydrogen atoms with arbitrary parabolic quantum numbers.
Alexander Gusev, Valentin Samoilov, Vitaly Rostovtsev, Sergue Vinitsky
### CADECOM: Computer Algebra software for functional DECOMposition
In this paper we present the Maple package Cadecom which is designed for performing computations in rational function fields. The main objects that Cadecom deals with are multivariate rational functions over any computable field, and the key tool are the functional decomposition algorithms. The functional decomposition problem has many applications in computer science, engineering (CAGD), pure mathematics or robotics. We motivate the interest of this program package by presenting applications on computing roots, simplifying sine-cosine equations, integrating rational functions, computing subfields, computing Gröbner bases and reparametrizing parametric curves. We also include a short overview of the package from the Maple system point of view.
Jaime Gutierrez, Rosario Rubio
### Computeralgebra and the Systematic Construction of Finite Unlabeled Structures
This review is concerned with mathematical structures that can be defined as equivalence classes on finite sets. The method used is to replace the equivalence relation by a finite group action and then to apply all what is known about such actions, i.e. to apply a mixture of quite general methods, taken from combinatorics as well as from algebra. For this purpose group actions will be introduced, enumerative methods will be reported, but the main emphasize is put on the constructive aspects, the generation of orbits representatives, and several applications of these methods, in particular to graph theory, design theory, coding theory and to mathematical chemistry.These methods have been successfully implemented in various computeralgebra packages like MOLGEN (for the generation of molecular graphs and applications to molecular structure elucidation) as well as in DISCRETA (for the evaluation of combinatorial designs and linear codes as well as other finite discrete structures).Finally we shall discuss actions on posets, semigroups, lattices, where the action is compatible with the order of the lattice or the composition of the semigroup.
### Heat Invariant E 2 for Nonminimal Operator on Manifolds with Torsion
Computer algebra methods are applied to the investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the second coefficient (E2) in the heat kernel expansion for nonminimal operators on manifolds with nonzero torsion. The expressions were computed for the general case of manifolds of arbitrary dimension n and also for the most important for E2 case n = 2. The calculations have been carried out on PC with the help of a program written in C.
### Computer Algebra for Automated Performance Modeling of Fortran Programs
Time complexity of sequential programs or segments of parallel programs can be estimated using the dynamic frequency of statements and their execution time. The execution time of single statements can be estimated by counting basic operations. The present paper deals with a method of determining the global dynamic frequency of statements by transient analysis of a Markov model. For defining the model automatically and solving the related equations, we use AUGUR which is a research tool for performance modeling of Fortran programs. While static program analysis and model generation are implemented by routine compile techniques, AUGUR uses MAPLE for evaluating expressions, defining transition matrices, and transient analysis. Routines of LAPACK are considered to demonstrate the achievable results.
Hermann Mierendorff, Helmut Schwamborn
### A Parallel Symbolic-Numerical Approach to Algebraic Curve Plotting
We describe a parallel hybrid symbolic-numerical solution to the problem of reliably plotting a plane algebraic curve. The original sequential program is implemented in the software library CASA on the basis of the computer algebra system Maple. The new parallel version is based on Distributed Maple, a distributed programming extension written in Java. We describe the mathematical foundations of the algorithm, give sequential algorithmic improvements and discuss our parallelization approach.
Christian Mittermaier, Wolfgang Schreiner, Franz Winkler
### Parametric Analysis for a Nonlinear System
The paper suggests an investigation of one system of differential equations with parameter carried out on the basis of the author’s theorem on signdefiniteness of nonuniform structures [1,2].
M. A. Novickov
### Extended Splicing System and Semigroup of Dominoes
Tom Head[5] introduced the novel idea of splicing system as a generative device for representing the string restructuring that takes place during the interactions of linear biopolymers in the presence of precisely specified enzymatic activities and thus established a new relationship between formal language theory and the study of informational macromolecules. In this paper, we discuss the relationship existing between the extended splicing system and the semigroup of dominoes, a special algebraic structure acting on linked strings.
Pethuru Raj, Naohiro Ishii
### Newton Polyhedra and the Reversible System of Ordinary Differential Equations
We investigate a reversible system of fourth-order ODEs by using the method of Newton polyhedron. We discuss the program for IBM PC, which computes the Newton polyhedron of the system under study and all of its corresponding objects. The results of the program runs are presented as a table of correspondences.
A. Soleev, I. Yarmukhamedov
### Condition Analysis of Overdetermined Algebraic Problems
In analogy to numerical linear algebra, the evolving numerical polynomial algebra studies the modifications of classical polynomial algebra necessary to accomodate inaccurate data and inexact computation. A standard part of this endeavor is a condition analysis of the problems to be solved, i.e. an assessment of the sensitivity of their results with respect to variations in their data. In this paper, we extend this condition analysis to overdetermined problems, like greatest common divisors, multivariate factorization etc. Here we must consider the fact that results exist only for data from restricted low-dimensional domains. The discontinuous dependence of the results on the data, however, is “smoothed” by their limited accuracy so that a condition analysis becomes meaningful. As usual, the condition numbers indicate the accuracy with which results may be specified.
Hans J. Stetter
### An Algebraic Approach to Offsetting and Blending of Solids
We propose to broaden the framework of CSG to a representation of solids as boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending can be reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. Our computational examples demonstrate the capabilities of the REDLOG package for the discussed operations on solids within our framework.
Thomas Sturm
### Application of Computer Algebra Methods to Some Problems of Theoretical and Applied Celestial Mechanics
Applications of computer algebra methods to some problems of dynamical astronomy are described. It is shown, how with the help of computer algebra it is possible to solve different important problems of applied celestial mechanics: in particular, to develop efficient analytical and semianalytical theories of motion of celestial bodies, to construct efficient algorithms for computation of some special functions of celestial mechanics, to solve some problems of asteroid dynamics. Possibilities to use computer-algebraic methods for efficient solution of other topical problems of dynamics of Hamiltonian systems are discussed.
Akmal Vakhidov
### Computing the Frobenius Normal Form of a Sparse Matrix
We probabilistically determine the Frobenius form and thus the characteristic polynomial of a matrix $$A \in {^{n \times n}}$$ by O(μnlog(n)) multiplications of A by vectors and 0 (μn2 log2 (n)loglog(n)) arithmetic operations in the field F . The parameter μ.L is the number of distinct invariant factors of A, it is less than $$3{{\sqrt n } \mathord{\left/ {\vphantom {{\sqrt n } 2}} \right. \kern-\nulldelimiterspace} 2}$$in the worst case. The method requires O(n) storage space in addition to that needed for the matrix A.
Gilles Villard
### Lessons Learned from Using CORBA for Components in Scientific Computing
The use of component architectures to solve the problem of reuse and interoperability in scientific computing has been investigated by various research groups during the last years. Moreover, architectures for Internet accessible mathematical services have been proposed. In this paper we give a brief abstract requirements analysis with respect to these problems and show that there is an existing technology that solves most of the requirements. The Common Object Request Broker Architecture (CORBA) provides a component framework that can be used for Internet accessible mathematical services and also for the efficient reuse of medium grained size functionality. We give some examples on the use of CORBA with respect to both applications. We provide measurement data which show that components of a granularity of less than {100} ms can be reused with an acceptibly small overhead.
Andreas Weber, Gabor Simon, Wolfgang Küchlin, Jörg Hoss
### Deciding Linear-Transcendental Problems
We present a decision procedure for linear-transcendental problems formalized in a suitable first-order language. The problems are formalized by formulas with arbitrary quantified linear variables and a block of quantifiers with respect to mixed linear-transcendental variables. Variables may range both over the reals and over the integers. The transcendental functions admitted are characterized axiomatically; they include the exponential function applied to a polynomial, hyperbolic functions and their inverses, and the arcustangent. The decision procedure is explicit and implementable; it is based on mixed real-integer linear elimination, the symbolic test point method, elementary analysis, and Lindemann’s theorem. As a byproduct we obtain sample solutions for existential formulas and a qualitative description of the connected components of the satisfaction set wrt. a mixed linear-transcendental variable. Potential applications include reachability problems for linear differential systems.
Volker Weispfenning
### Backmatter
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https://timweninger.com/teaching/database-systems-concepts/functional-dependencies/ | # Functional Dependencies
So far we can:
• Design an ER Diagram
• Translate it to a relational DB $R$
• Implement $R$ in SQL
• Specify constraints over $R$
However $R$ might not be well designed. And this will cause problems. We call these anomalies.
Question? Is this a good design?
Why or why not?
Potential Problems:
• Redundancy
• Update Anomalies
• Deletion Anomalies
How do we recognize a good design? What does good mean?
## Normal Forms
There are several important normal forms: 1NF, 2NF, 3NF, BCNF, 4NF etc.
If $R^*$ is in one of these forms, then $R^*$ is guaranteed to achieve certain good properties, e.g., if $R^*$ is in Boyce Codd NF then it is guaranteed to not have certain type of redundancy.
There exist algorithms to transform $R$ into $R^*$, where $R^*$ is in one of the normal forms.
Each type of normal form is different, there are trade offs. NFs are all based on the idea of functional dependencies.
## Functional Dependencies and Keys
Let’s look at an example: Is this a good design?
How can we make it better?
Why is this better?
## Functional dependencies
A form of constraint (part pf the schema), finding them is part of the database design.
Definition: If two tuples agree on the attributes $a_1,a_2,a_3,\ldots,a_n$, then they must also agree on the attributes $b_1,b_2,b_3,\ldots,b_m$.
Formally: $a_1,a_2,a_3,\ldots,a_n \rightarrow b_1,b_2,b_3,\ldots,b_m$ pronounced $X$ determines $Y$.
Let’s try an example:
What FDs can we find?
Salpers_ID $\rightarrow$ Name, Manager_ID, Office, Comm
Name $\rightarrow$ Salpers_ID
Office $\xrightarrow{?}$ Comm
In general, we check if $X\rightarrow Y$ is violated by erasing all other columns and checking many to one, called functional in mathematics.
Name $\rightarrow$ Salpers_ID. We say that name determines salpers_ID in this case. If we know the name, then we can known the ID.
Salpers_ID $\rightarrow$ Name is likewise true in this case.
Consider the following instance of $R(a,b,c,d,e)$. What FDs can you observe in $R$?
$a$ is unique: $a\rightarrow b, a\rightarrow c, a\rightarrow d, a\rightarrow e \equiv a\rightarrow a,b,c,d$
$e$ are all the same: $a\rightarrow e, b\rightarrow e, c\rightarrow e, d\rightarrow e$
Others:
Combinations of $b,c$ are unique: $b,c\rightarrow a,d,e$
Combinations of $b,d$ are unique: $b,d \rightarrow a,c,e$
if $c$ values match, so do $d$ values: $c\rightarrow d$
$d$ values do not determine $c$: $d\nrightarrow c$
lots of others… $a,e\rightarrow b,c$, etc.
## Reasoning with FDs
#### Relation Keys
Now that we know FDs we can define keys mathematically.
Key of a relation $R$ is a set of attributes that:
• Functionally determines all attributes of $R$
• None of its subsets determines all attributes of $R$.
Superkey
• A set of attributes that contains a key.
A key is the minimal set.
We need to make sure our keys are well defined.
#### Closure of FD Sets
Given a relation schema $R$ and a set of FDs $S$, we ask:
Is FD $f$ logically implied by $S$?
Example:
$R = \{a,b,c,g,h,i\}$
$S=\{a\rightarrow b, a\rightarrow c, c,g\rightarrow h, c,g\rightarrow i, b\rightarrow h\}$
Does $a\rightarrow h$ follow? Yes, and we can prove this.
Closure of $S : S^+$ contains all of the FDs that follow. We use Armstrongs axioms to find these.
#### Armstrongs Axioms
wlog: $X=\{x_1, x_2,\ldots,x_n\}$
Reflexivity:
$X\rightarrow$ some subset of $X$
Augmentation
if $X\rightarrow Y$, then $X,Z\rightarrow Y,Z$
Transitivity
if $X\rightarrow Y\wedge Y\rightarrow Z$, then $X\rightarrow Z$
Union
if $X\rightarrow Y\wedge X\rightarrow Z$, then $X\rightarrow Y,Z$
Decomposition
if $X\rightarrow Y,Z$, then $X\rightarrow Y \wedge X\rightarrow Z$
Pseudo-Transitivity
if $X\rightarrow Y\wedge YZ\rightarrow U$, then $XZ\rightarrow U$
Example:
$R(a,b,c), S=\{a\rightarrow b, c\rightarrow a\}$
What is the FD closure $S^+$?
1. $c\rightarrow b$ (transitivity)
2. $c,a \rightarrow c,a,b$ (augmentation on 1)
3. $b,c\rightarrow a,b,c$ (augmentation on $c\rightarrow a$)
4. $a,b,c \rightarrow a,b,c$ (reflexivity)
Say $R(a,b,c,d), S=\{a,b\rightarrow c, b,c\rightarrow a,d\}$. Does $a,c\rightarrow d$ follow from $S$?
Solve by checking $d\in \{a,c\}^+$
In this case, $\{a,c\}^+ = \{a,c\}$, and since $d \notin \{a,c\}^+$, then $a,c\rightarrow d$ does not follow from $S$
#### Closure of Attribute Sets
Given a set of attributes $A={a_1,a_2,\ldots,a_n}$ and a set of dependencies $S$. We want to find all the attributes $B$ such that any relation which satisfies $S$ also satisfies $\{a_1,\ldots,a_n\}\rightarrow B$.
This closure is the set of all such attributes $B$ and is denoted $\{a_1,a_2,\ldots,a_n\}^+$. We use this to test if $A$ is a superkey.
We first compute $X^+$ and check of $X^+$ contains all attributes of $R$. We can also check if $X\rightarrow Y$ holds by checking if $Y\in X^+$
Example: finding keys.
$R(abc), S=\{a\rightarrow b, c\rightarrow a\}$
Consider all attribute subsets $X$
Compute the closure of each subset $X^+$
Determine if the subset X is a superkey or key
Another Example:
$R(abcd),S=\{a \rightarrow b,d \rightarrow c,c\rightarrow a\}$
Find the keys and superkeys
#### Desirable properties of schema refinement:
1. Eliminate anomalies (BCNF)
2. Avoid information loss (BCNF)
3. Preserve dependencies (3NF, not BCNF)
4. Ensure good query performance (??) | 2022-01-19 13:04:52 | {"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": 0.8142383098602295, "perplexity": 2569.8733122542767}, "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/1642320301341.12/warc/CC-MAIN-20220119125003-20220119155003-00306.warc.gz"} |
https://socratic.org/questions/5747171a7c01494605cd4bd9 | # Question d4bd9
Sep 4, 2016
$1.635 \times {10}^{2} \text{ Pa.s or Poiseuille (Pl)}$
#### Explanation:
A bubble when placed in a viscous liquid experiences three forces responsible for its movement:
WEIGHT.
Downwards force due to gravity. It has been ignored as given in the problem.
BUOYANCY.
This is upwards force equal to the weight of the displaced liquid displaced. The bubble expands due to decrease of hydrostatic pressure as the bubble gets closer to the surface. Therefore, this force increases as the bubble approaches the surface. For this problem it has been assumed to be constant.
DRAG.
Downwards force, depends on the Reynolds number of the flow. This force is either dependent linearly, or quadratically, on the velocity of bubble.
When the all three forces are in equilibrium, the velocity of the bubble will not change. It has reached its terminal velocity.
The force of viscosity on a small sphere moving through a viscous fluid is given by the expression:
F_d = 6 π μ R v
where ${F}_{d}$ is drag – acting on the interface between the fluid and the sphere, μ is the dynamic viscosity, $R$ is the radius of the sphere and $v$ is its velocity relative to the fluid.
This is Stokes' law which assumes that flow is laminar, object is a sphere having smooth surface, which moves in homogeneous medium and the sphere and medium don't interfere with each other.
Equating this force with the Buoyancy F_b=4/3πR^3ρg, we get the terminal velocity
Where ρ is the density of the liquid and $g$ is acceleration due to gravity.
6πμRv_t=4/3πR^3ρg
=>v_t=2/9(ρgR^2)/μ
Inserting given values we get
2xx10^-3=2/9xx(1.5xx10^3xx9.81xx(10^-2)^2)/μ#
$\implies \mu = \frac{2}{9} \times \frac{1.5 \times {10}^{3} \times 9.81 \times {\left({10}^{-} 2\right)}^{2}}{2 \times {10}^{-} 3}$
$\implies \mu = 1.635 \times {10}^{2} \text{ Pa.s or Poiseuille (Pl)}$ | 2021-02-25 00:12:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "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": 0.8320910930633545, "perplexity": 420.83718907455005}, "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-2021-10/segments/1614178349708.2/warc/CC-MAIN-20210224223004-20210225013004-00299.warc.gz"} |
https://www.tutorialspoint.com/What-is-the-use-of-MySQL-TRUNCATE-function | # What is the use of MySQL TRUNCATE() function?
MySQL TRUNCATE() function is used to return the value of X truncated to D number of decimal places. If D is 0, then the decimal point is removed. If D is negative, then D number of values in the integer part of the value is truncated. Its syntax can be as follows −
## Syntax
TRUNCATE(X, D)
Here
• X is a number which is to be truncated.
• D is the number up to which decimal places the number X has to be truncated.
## Example
In the example below, it will truncate the given number up to 2 decimal places.
mysql> Select TRUNCATE(10.7336432,2);
+-----------------------+
| TRUNCATE(10.736432,2) |
+-----------------------+
| 10.73 |
+-----------------------+
1 row in set (0.00 sec) | 2023-01-30 07:05:19 | {"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": 0.5448442697525024, "perplexity": 1400.9194576048774}, "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-2023-06/segments/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00372.warc.gz"} |
https://dukespace.lib.duke.edu/dspace/browse?type=author&value=Ng%2C%20L | Now showing items 1-11 of 11
• A complete knot invariant from contact homology
We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to ...
• A topological introduction to knot contact homology
(Bolyai Society Mathematical Studies, 2014-01-01)
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
• Knot contact homology
(Geometry & Topology, 2013-04-30)
The conormal lift of a link K in ℝ3is a Legendrian submanifold ∧Kin the unit cotangent bundle U*ℝ3of ℝ3with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant ...
• Knot contact homology, string topology, and the cord algebra
(Journal de l’École polytechnique — Mathématiques, 2017)
The conormal Lagrangian LKof a knot K in R3is the submanifold of the cotangent bundle T∗R3consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S∗R3, one obtains ...
• Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
(Journal of Differential Geometry, 2015-09)
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in S1× S2or any connected sum #k(S1×S2), viewed as the contact boundary of the Weinstein manifold obtained by ...
• ON ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER
(Journal of Knot Theory and Its Ramifications, 2012-04)
We discuss the relation between arc index, maximal ThurstonBennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal ThurstonBennequin number for all knots with at most 11 ...
• On transverse invariants from Khovanov homology
(Quantum Topology, 2015)
© European Mathematical Society. In [31], O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two re_nements of Plamenevskaya’s invariant, one valued in ...
• Representations, sheaves, and Legendrian $(2,m)$ torus links
We study an $A_\infty$ category associated to Legendrian links in $\mathbb{R}^3$ whose objects are $n$-dimensional representations of the Chekanov-Eliashberg differential graded algebra of the link. This representation category ...
• Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra
(Algebraic & Geometric Topology, 2013-08-01)
We develop a close relation between satellites of Legendrian knots in ℝ3and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a ...
• The cardinality of the augmentation category of a Legendrian link
(Mathematical Research Letters, 2017)
We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ℓhomotopy cardinality' is an invariant of the category and allows for a weighted count ...
• Topological strings, D-model, and knot contact homology
(Advances in Theoretical and Mathematical Physics, 2014)
© 2014 International Press. We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov- ... | 2021-03-03 19:09:06 | {"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": 0.4276675283908844, "perplexity": 1179.4175310512112}, "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-2021-10/segments/1614178367183.21/warc/CC-MAIN-20210303165500-20210303195500-00074.warc.gz"} |
https://forum.qt.io/topic/54099/qmake-makefile-generation-problem-on-windows/2 | # Qmake makefile generation problem on Windows
• On Windows, using qt 5.4, I used qmake to generate makefiles for the QCacheGrind product. Qmake generated a makefile with the notation for a rule of:
{....\kcachegrind-0.7.4\cgview}.cpp{release}.obj::
\$(CXX) -c \$(CXXFLAGS) \$(INCPATH) -Forelease\ @<<
\$<
<<
But Gnu make on Windows does not understand the '<<' notation. What does it mean ? Am I supposed to be using some other 'make' utility to process the files that qmake generates ?
• Which specs are you using when calling qmake? Maybe you're using one that is not suitable for gnu make. | 2020-01-22 15:12:01 | {"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": 0.892217218875885, "perplexity": 7017.787643556427}, "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/1579250607118.51/warc/CC-MAIN-20200122131612-20200122160612-00127.warc.gz"} |
http://mkweb.bcgsc.ca/quotes/?god | Trance opera—Spente le Stellebe dramaticmore quotes
# quotes: fun
In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017
# daily quotation server archives
In the late 90’s I started (a good decade for starts) a daily quotation server project at www.quoteserver.ca. The domain is now defunct—some pages are partially viewable at the Way Back Machine.
Below is the list of quotes I had collected by the end of the life of the project. Most are about love—duh—and a few are jolly jests from funny trenches. You know, that place where mustard gas makes your eyes water.
The quotes weren’t scraped from quote archives—each is meaningful and hand-picked.
## the quote archive
And now for full list of 1,600 other things worth reading. Such as everything Dorothy Parker has written and ... yes, even the Pinky and Brain quotes, which are a special kind of special.
Quote collections about love, heart, desire, life, death, god, mind, science.
Feeling lucky? Read 10 random quotes. Well, will you, punk?
13
Take not God’s name in vain: select a time when it will have effect.
48
I love thee with the love I seemed to lose
With my lost saints,—I love thee with the breath
Smiles, tears, of all my life!—and, if God choose,
I shall but love thee better after death.
Sonnets from the Portuguese
104
Poems are made by fools like me,
But only God can make a tree.
Trees
117
All are but parts of one stupendous whole,
Whose body Nature is, and God the soul.
Essay on Man, Epistle i. 267.
243
Conceit is God’s gift to little men.
298
Poems are made by fools like me,
But only God can make a tree.
Trees
370
Men rarely (if ever) manage to dream up a god superior to themselves. Most gods have the manners and morals of a spoiled child.
Time Enough for Love
414
And, while with silent, lifting mind I’ve trod
The high untrespassed sanctity of space,
Put out my hand, and touched the face of God.
452
God must love stupid people, He made so many of them.
457
If it turns out that there is a God, I don’t think that he’s evil. But the worst that you can say about him is that basically he’s an underachiever.
556
% ar m God
ar: God does not exist
561
God made the integers; all else is the work of Man.
591
If you believe in the light, it’s because of obscurity.
If you believe in happiness it’s because of unhappiness.
If you believe in God, then you have to believe in the Devil.
Church of Notre Dame, Paris
609
O God, if there be a God, save my soul, if I have a soul!
611
See the happy moron,
He doesn’t give a damn.
I wish I were a moron.
My God! Perhaps I am!
706
An Apology for the Devil: It must be remembered that
we have only heard one side of the case. God has written
all the books.
Note Books
741
And almost every one when age,
Disease, or sorrows strike him,
Inclines to think there is a God,
Or something very like Him.
Dipsychus, sc. vi
783
So nigh is grandeur to our dust,
So near is God to man,
When Duty whispers low, Thou must,
The youth replies, I can.
Voluntaries, iii
957
Gott ist tot: aber so wie die Art der Menschen ist,
wird es vielleicht noch jahrtausendlang Hohlen geben,
in denen man seinen Schatten zeigt.
[God is dead: but considering the state the species Man
is in, there will perhaps be caves, for ages yet, in which
Ecce Homo
1082
O God! methinks it were a happy life,
To be no better than a homely swain;
To sit upon a hill, as I do now,
To carve out dials, quaintly, point by point,
Thereby to see the minutes how they run,
How many make the hour full complete;
How many hours bring about the day;
How many days will finish up the year;
How many years a mortal man may live.
Henry VII, Part III, II.v.21
1213
I loved you without hope, a mute offender;
What jealous pangs, what shy despairs I knew!
A love as deep as this, as true, as tender,
God grant another may yet offer you.
I Loved You Once
1218
I have heard the song of the blossoms and the old chant of the sea,
And seen strange lands from under the arched white sails of ships;
But the loveliest things of beauty God ever has showed to me,
Are her voice, and her hair, and eyes, and the dear red curve of her lips.
Beauty
1284
And this, O love, my pitiable plight
Whenever from my circling arms you stray;
This little world of mine has lost its light....
I hope to God, my dear, that you can say
The same to me.
Rondeau Redouble
1333
How can I believe in God when just last week I got
my tongue caught in the roller of an electric typewriter?
1334
Man is a god in ruins.
1386
God made everything out of nothing, but the nothingness
shows through.
1402
Which is it, is man one of God’s blunders or is
God one of man’s?
1416
Thank God men cannot as yet fly and lay waste the
sky as well as the earth!
1477
Nothing but blackness above
And nothing that moves but the cars...
God, if you wish for our love,
Fling us a handful of stars!
Caliban in the Coal Mines
1526
God is the immemorial refuge of the incompetent, the helpless, the miserable. They find not only sanctuary in His arms, but also a kind of superiority, soothing to their macerated egos; He will set them above their betters.
1534
If the average man is made in God’s image, then a man such as Beethoven or Aristotle is plainly superior to God, and so God may be jealous of him, and eager to see his superiority perish with his bodily frame. All animal breeders know how difficult it is to maintain a fine strain. The universe seems to be in a conspiracy to encourage the endless reproduction of peasants and Socialists, but a subtle and mysterious opposition stands eternally against the reproduction of philosophers.
In Defense of Women
1602
We turn toward God only to obtain the impossible.
VIEW ALL
# Optimal experimental design
Tue 31-07-2018
Customize the experiment for the setting instead of adjusting the setting to fit a classical design.
The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.
Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.
Nature Methods Points of Significance column: Optimal experimental design. (read)
We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.
Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.
Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187â1188.
Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699â700.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments. Nature Methods 11:597â598.
# The Whole Earth Cataloguer
Mon 30-07-2018
All the living things.
An illustration of the Tree of Life, showing some of the key branches.
The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.
The circle of life. (read, zoom)
All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCAâs genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic materialâa process that created the diversity of life we see today. The âtree of lifeâ organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.
Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89
# Why we can't give up this odd way of typing
Mon 30-07-2018
All fingers report to home row.
An article about keyboard layouts and the history and persistence of QWERTY.
My Carpalx keyboard optimization software is mentioned along with my World's Most Difficult Layout: TNWMLC. True typing hell.
TNWMLC requires seriously flexible digits. Itâs 87% more difficult than using a standard Qwerty keyboard, according to Martin Krzywinski, who created it (Credit: Ben Nelms). (read)
McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.
# Molecular Case Studies Cover
Fri 06-07-2018
The theme of the April issue of Molecular Case Studies is precision oncogenomics. We have three papers in the issue based on work done in our Personalized Oncogenomics Program (POG).
The covers of Molecular Case Studies typically show microscopy images, with some shown in a more abstract fashion. There's also the occasional Circos plot.
I've previously taken a more fine-art approach to cover design, such for those of Nature, Genome Research and Trends in Genetics. I've used microscopy images to create a cover for PNAS—the one that made biology look like astrophysics—and thought that this is kind of material I'd start with for the MCS cover.
Cover design for Apr 2018 issue of Molecular Case Studies. (details)
# Happy 2018 $\tau$ Day—Art for everyone
Wed 27-06-2018
You know what day it is. (details) | 2018-08-17 03:29:15 | {"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": 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": 0.18001508712768555, "perplexity": 9569.005910071526}, "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-2018-34/segments/1534221211664.49/warc/CC-MAIN-20180817025907-20180817045907-00245.warc.gz"} |
http://kitada.com/List/time/199907/0061.html | # [time 478] Parallel translation, etc.. part IV
Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 24 Jul 1999 10:40:08 +0300 (EET DST)
This like Terminator, The return of Terminator I, II,....ad infinitum!
In part IV we end up with the proposal that
the replament of NP-computability with quantum computatibility
by a infinite computer (the universe) with infinite computing time
might be the TGD:eish version of computability(;-)
> [MP]
> > > > The point is that I do *not* identify observations as points of
> > > > spacetime or configuration space. They are not active 'events'.
> > > > Quantum jumps between quantum states= quantum histories are events
and one
> > > > cannot localize them to anywhere (one can of course, identify
> > > > these events as pairs of possible initial and final quantum
histories
> > > > so that one can speak about the space of all possible
experiences).
> [SPK]
> > > I say that observations are co-inductively related posets of
points (as
> > > an abstraction since true infinitesimal points can not be
distiguised
> > > from each other as they can not encode any information!!!), not
> > > individual points per say.
> [MP]
> > I undestand that you great idea is identify observations with
geometrical
> > structures, 'posets of points of space'. I also parametrize
> > the set of all possible observations: not as posets but as
> > allowed quantum history pairs: but this parametrization tells
> > anything about content of observation: it is just labelling: the only
> > thing that matters that this naming scheme is one-to-one. I believe
> > that the content of observation/cs experience cannot be expressed by
any
> > mathematical formula.
>
> Sure, but when we construct intricate geometrical model we are
doing
> just that! We are attempting to express the content of observations/cs
> experience with a mathemathical formula! SO long as we understand that
> the "model" is not the "thing" we are ok.
>
But what differentiates the model from the thing? Does this
difference mean that mathematical formula does not characterize
the observation completely?
> > > To call them "space-time framings" speaks to
> > > the fact that we always make observations in terms of a M^4 frame...
The
> > > quantum jumps are more epiphenomena that objective, but the
restriction
> > > that observers can only communicate effectively about M^4 framings
that
> > > do not logically contradict each other follows from CE! The
> > > schizophrenic is an example of an observer that is attempting to
> > > communicate about a M^4 framing that is logically inconsistent with
> > > another's!
> > >
> > But there is the notion of observer. You take it as granted. I take
> > observation fundamental.
>
> No! I, like you, take observation as fundamental! I just am being
> explicit about the fact that what each observer has a framing of their
> observations is not an a priori given, it is a construction! Thus, with
> Pratt I say "cognito, ergo eram", I think therefore I was....
>
I express it more technically: cogito, sequence of quantum jumps
without any gap between existed (;-). Or even more precisely:
a cascade like generation of selves within me occurred.
> > > > I see no problems with Heisenberg's uncertainty relations:
informational
> > > > time development operator U reduces at QM limit to Schrodinger
equation.
> > > > Metric, etc.. classical gauge fields are *not* quantized in TGD.
> > > > Neither spacetime coordinates are quantized. There is
> > > > absolutely no quantization, only classical geometry of
> > > > infinite-dimensional configuration space and classical spinor
fields of
> > > > configuration space. Oscillator operator algebras etc are
geometrized in
> > > > this approach.
> > >
> > > I see the evolution of information in terms of the evolution
of the LSs
> > > as they interact. Thus the act of the Universe 'experiencing itself'
is
> > > an ongoing process. It is what "concurrent computation" is all about
is
> > > a fundamental sense! Again, this is why I find Peter's work so
useful!
> > > :-)
> > >
> >
> > Here here agree completely. But 'universe=experience about universe'
> > is where I cannot follow you. This is simply too strong assumption and
> > leads to the hopeless attempt of writing formula for the contents
> > of cs experience.
>
> The Universe is not experience about the Universe! I apologize if
I did
> not express this well. The Universe is mere Existence of All that
> exists, everything simultaneously.
Yes. I understood this from above. This would be for me the space
of all universes, quantum histories.
>Experiences are \epsilon-consistent
> information structures (Complete Atomic Boolean Algebras are examples)
> that require finite material structure to be actualized. An observation
> is an actualization, it is the "enbodiment" of the information.
Again I follow: quantum jumps, actualizations, mean hopping around space
of quantum histories.
> Descartes was incorrect in his dualism, because he assumed that mind and
> matter were invariant substances, I, with Pratt, propose that they are
> "acts", and acts can only be actual *in time*. Existence has no time
> associated, thus it does not generate local experience; it is the local
> actualities of LSs that do that. :-)
>
> snip
> [MP]
> > > > I just saw a paper in which it was shown that divergence problem
is
> > > > not solved by noncommutatitivy of the spacetime coordinates. There
is also
> > > > problem with the loss of general coordinate invariance. One must
assume
> > > > special coordinates and very high symmetries if one wants
> > > > special coordinates.
> > >
> > > Could you give me the reference of this paper? I can order a
copy from
> > > the library! :-)
> >
> > It was paper by my 'boss' Masud-Chaichian and Peter Presnajder and
third
> > theoretician. They constructed noncommutative QFT in two-dimensional
case.
> > For cylinder it worked but for more general case they found
infinities.
> > They also suggested generalization of results to higher dimensional
case.
> > I do not have the paper here but I could ask for bibliodata.
>
> Thanks! ;-)
I try to find the paper next week.
>
> snip
> > > [MP]
> > > > God of Singularity concept is based on traditional concept of
> > > > psychological time. Also the question why everything has not
> > > > happened is created by the same concept of psychological time.
> > >
> > > Yes, but here the error is in the tacit (subconscious)
assumption that
> > > the psychological time of one person is one and the same of that of
> > > another! The clocking by the QM propagator of the LS defines the
> > > individual time of the LS, thus representing psychological time very
> > > well!
> >
> > Also that. But the real blunder is the identification
> > is the assumption that *contents of cs experience correspond to
> > time=constant snapshot*.
> > Neurophysiologists tell us that this is not the case. Consdier music
> > as example. We are able to experience frequencies, which
> > is nonlocal concept with respect to time.
>
> Yes, that is why I use an M^4 to frame an observation, there are
both
> spatial and temporal non-localities involved. This is also why we can
> use a RW metric to model how the space-time configurations of a single
> observation are distributed! This speaks to concurrence, we are not able
> to experience points, we experience hyper-surfaces! So, we agree here!
> :-)
Not quite! Experiencing of mere hypersurfaces would not make possible
experiening of frequencies: complete localization in time means
by uncertainty principle of Fourier Analysis means that there is not
frequency information. Cognition must be time nonlocal if it
is to give some information about what will happen and happened.
This is why cognitive spacetime sheets made possible by the classical
nondeterminism of Kahler action are so crucial for TGD.
> > > The "everything has not already happened" notion is indeed
related to
> > > psychological time, but in the sense stated above. "Everything"
much
> > > included all possible "actual" experiences, and obviously, these
involve
> > > NP-complete computational issues! This later notion is at the heart
of
> > > my argument.
> > >
> > > > I regard this concept as badly wrong. In TGD framework subjective
time
> > > > corresponds to quantum jumps and there can be *no first quantum
jump*.
> > >
> > > I am not communicating my notion since your are not aware of
the
> > > NP-completeness problem! Karl Svozil's papers point the way! We
agree
> > > that "there can be *no first quantum jump*"! The ideas of
co-induction
> > > and related issues involved are in Peter's papers...
> >
> > I have studied Peter's papers (rather technical!). My view is that
cannot
> > start from so technical concept like NP-completeness in building model
> > for universe: the reason is that I do not believe that universe
computes
> > itself into existence: it just exists! Even more, it is able to
replace
> > itself with a new one again and again and do also some computation
> > besides that!
>
> Matti, NP-Completeness is not merely a technical concept! It is a
> fundamental problem! How does the Universe calculate the minimum energy
> configuration of a protein molecule? How does the Universe figure out
> the most stable orbits in a stellar system? How is it that soap bubbles
> always cover the most volume with the least surface? How is it that a
> quasi-crystal can grow at all? How is it that Lagrangians are calculated
> by the Universe? All of these questions are aspects of the
> NP-Completteness problem!
But why universe should calculate it? Even for modelling
purposes in some remote psychological future and even at subjective
distance of infinitely many quantum jumps? And how should universe
calculate itself to existence: does the hardware
used belong to universe. This like Munchausen trick: logical
impossibility.
Quantum jump replaces the computation (in classical sense as I
understand). Quantum jump is what allows quasi-chrystal to grow!
In the initial universe quasi-chrystal cannot grow but by
quantum jumps one ends up to the universe where quasi-christal
has grown.
> What is interesting is that it has been proven that if there
exists a
> finite computational scheme that can compute a given example of an
> NP-complete problem, this scheme or algorithm can be transformed in
> polynomial time into a scheme to compute any other NP-Complete problem.
> But this, I think, only works for situations that can be modeled (or
> "simulated") by Turing Machines. Peter's work shows us that most of the
> computations that occur are not TM simulatable and thus we need to look
> at this more closely.
Perhaps it is not an accident that quantum jump can be regarded
at general level as infinitely long quantum computation.
Psi_i corresponds to initial state of quantum computer. UPsi_i
corresponds to the final state of qcomputer after infinitely long
calculation and UPsi_i-->Psi_f means halting of quantum computation
and emerges of the result of computation as conscious experience.
What about NP completeness problem when one introduces
infinitely large quantum computers calculating infinitely long time?
Can nondeterministic computations help.
What about sequences of quantum computations each lasting infinitely
long time?: these are suggested by the notion of self. Thought
as a cascade of quantum jumps creating hierarchy of subselves of
self?
[To avoid confusions: the calculation time has nothing to do with
the experience psychological time].
> [MP]
> > > > This requirement plus p-adic evolution
> > > > as gradual statistical increase of p-adic prime of the universe
> > > > immediately leads to the requirement that
> > > > also infinite p-adic primes are possible and that recent universe
> > > > must correspond to infinite prime. Every moment of consciousness
> > > > decomposes to infinite number of subexperiences with values of
> > > > psychological time ranging from zero to infinity. What we really
'know' is
> > > > that local arrow of psychological
> > > > time exists: if one is satisfied with this then paradoxes
disappear.
> > > > Universe becomes *4-dimensional* living being getting conscious
> > > > information about its entire 4-dimensional body in every quantum
jump.
> > > > Cognitive spacetime sheets are the sensory organs of this
infinitely
> > > > large 4-dimensional living system.
> [SPK]
> > > The notion of "gradual statistical increase of p-adic prime of
the
> > > universe" is given in my thinking in the sense that the overall
> > > concurrent interactions of LSs are modelable in this way. It would
be a
> > > representation of the accumulated "experience of the Universe", but
with
> > > the caveat that it is information that can not be gotten in finite
time
> > > or finite energy with arbitrary accuracy. The operator formalisms
that
> > > Schommers talks about, I believe, is useful to us in thinking about
> > > this!
> > >
> >
> > Yes: I have grasped the universe computes itself into existence
philosophy
> > but....
>
> Umm, I do not say that "the universe computes itself into
existence"! I
> say that the individual experiences of Local Systems (using Hitoshi's
> definition of LSs) are given in terms of space-times framings. This
> follow from the distinction that I make between "existence" (qua CE) and
> "actuality" which is a "local notion" that represents the subjective
> experiences (observations, measurements, etc.) of an LS given any
> particular moment of their local time. Thus I say that the Universe
> experiences itself by the acts of observation of the finite LSs, which
> are considered computations of NP-complete problems.
LS:s as computationas of quantum-computable problems? This
would be TGD inspired computationalism!(;-).
> The key argument is that nothing can "happen" unless a price is
paid.
> Existence in-itself does not require the generation of equilibria. It
> *is* at equilibria with respect to itself, that is why it merely exists.
> It does not change, it has no duration or extension or any other
> properties other that mere existence. It is the grundlagen! I do not
> associate any space or time properties to it, those are the properties
> of the observations of Local Systems, not the Universe itself.
>
> > > > > > [SPK]
> > > > > > This notion is very different from Hitoshi's idea, but
perhaps the
> > > > > > difference is due to the different ways that time is treated.
> > > > > > I still see these as complementary! You see space-times as a
priori
> > > > > > surfaces, subsets of the totality U that are connected by
quantum jumps
> > > > > > "in time", Hitoshi, as I understand, sees space-times as the
"clocked"
> > > > > > poset of observations of LS, which are a priori quantum
mechanical
> > > > > > systems existing tenselessly as subsets of the totality U.
> > > > > > Thus you are proposing space-times as a priori and
Hitoshi
> > > > > > proposes quantum local systems as a priori, this is a
chicken-egg
> > > > > > complementarity! We need to see that this is just a matter of
> > > > > > perspective!
> > > [MP]
> > > > I have the feeling that this is not a matter of perspective. Our
> > > > basic philosophies are different.
> > >
> > > In a way, yes. You are a Platonist, and I something different.
I think
> > > that Plato's Idea Reality *is* the Universe in-itself, but as Kant
> > > argued well, is not knowable in-itself. I see it as Existence
itself!
> > > All experiences, measurements, observations, qualia or what ever,
are
> > > not given directly by their mere existence (as all exist in the
> > > ontological sense), but have finite properties given by the
interactions
> > > between the finite subsets or "facets" or LSs of the Universe. We
can
> > > only observe shadow, consciousness is not capable of knowling the
> > > "in-itself"!
> >
> > Funny thing, reading this I find that I agree completely. But
somewhere
> > the differences emerge: computationalism is one of the division
lines.
>
> And this is exactly why we must discuss the notions we have about
> computation!
>
Well. Replacing NP-computability with quantum-computability is
what TGD would suggest.
Best,
MP
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http://www.chegg.com/homework-help/questions-and-answers/if-the-radius-of-the-electron-orbit-in-the-n-1-level-of-the-hydrogen-atoms-is-053nm-what-i-q3451348 | ## Physics II Problem
If the radius of the electron orbit in the n = 1 level of the hydrogen atoms is .053nm, what is the radius for the n = 4 level? (Assume the Bohr model is valid.) | 2013-05-18 11:43:50 | {"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": 0.8471440672874451, "perplexity": 571.4165144133308}, "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/1368696382360/warc/CC-MAIN-20130516092622-00025-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://vast.cs.ucla.edu/projects/boolean-matching-techniques | # Boolean Matching Techniques
Project status:
completed
Boolean matching (BM) is a widely used technique in FPGA resynthesis and architecture evaluation. We present several improvements to the recently proposed SAT-based Boolean matching formulation (SAT-BM-M). The principal improvement was achieved by deriving the SAT formulation using the implicant instead of minterm representation of the function to be matched. This enables our BM formulation to create a SAT problem of size O ( m*2^k ) as opposed to O(2^n) in the original formulation, where n is the number of inputs to the function, k is the size of the LUT, and m is the number of implicants, which is much smaller than 2^n and experimentally found to be around 3n . Using the new BM formulation, and considering 10-input functions, we can show an almost 3x run time improvement and can solve 5.6x more problems than the SAT based BM formulation. Moreover, using this improved Boolean matching formulation, we implemented (as a proof of concept) a FPGA resynthesis tool, called RIMatch, which was able to reduce the number of LUTs produced by ZMap by 10% on the MCNC benchmarks.
Faculty: | 2021-09-20 04:59:26 | {"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": 0.8442633152008057, "perplexity": 1908.2371685229994}, "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/1631780057018.8/warc/CC-MAIN-20210920040604-20210920070604-00433.warc.gz"} |
https://www.lokad.com/envision-functions | # List of functions in Envision
Home » Resources » Here
This page lists the functions supported by Envision. The primary purpose of functions is to extend the capabilities of Envision whenever the basic language syntax would not be sufficient.
## Function syntax
The general syntax for functions is:
x = fun(arg1, arg2, arg3)
With fun replaced by the name of the function, and the argN, the comma-delimited list of arguments passed to the function. All functions operate on vectors.
## Mathematical functions
• abs(number): similar to the ABS function in Excel.
• ceiling(number): similar to the CEILING function in Excel.
• exp(number): similar to the EXP function in Excel.
• floor(number): similar to the FLOOR function in Excel.
• log(number, base): similar to the LOG function in Excel. The base argument is optional, when it is omitted, it is assumed to be 10.
• max(num1, num2, num3, ..., numN): similar to the MAX function in Excel.
• min(num1, num2, num3, ..., numN): similar to the MIN function in Excel.
• norminv(number): similar to the NORMINV function in Excel with a mean at 0 and a standard deviation at 1.
• pow(number, exponent): similar to the POWER function in Excel. Envision also support the power operator number ^ exponent which performs the same calculation.
• round(number, digits): similar to the ROUND function in Excel. Second argument is optional, and represents the number of digits that intended to be kept.
• sqrt(number): similar to the SQRT function in Excel.
## Text functions
• concat(text1, text2, ..., textN): concatenate text values from text1 to textN.
• contains(text, pattern): Returns true if the text contains an occurrence of the pattern.
• endswith(text, pattern): Returns true if the text ends with an occurrence of the pattern.
• field(text, separator, index): Returns the nth field (zero-indexed) in a text value that contains multiple sub-strings separated by a specified separator. Ex: field("a-b-c-d-", "-", 2) == "c". This function is intended to facilitate parsing values that have been concatenated within a single table column.
• indexof(text, pattern): Returns the index of the first occurrence of the pattern within the text, or -1, if not such occurrence is found.
• lowercase(text): Returns the lowercase variant of the text.
• parsedate(text, format): Converts the text into a date using the specified format. The format is optional. When the format is omitted, the date is parsed based on the date format auto-detection behavior of Envision. When the format is provided, the date is parsed against the format expectation. See custom date format string for the detail for the format syntax. If a date cannot be parsed, the date 2001-01-01 is returned instead.
• parsenumber(text): Converts the text into a number. The parser leverages the number format auto-detection behavior of Envision. If the number cannot be parsed, zero is returned instead.
• parsetime(text, format): Converts a time of the day into a fraction between 0 and 1, representing a fractional day. The format is optional. When the format is not specified, the default value yyyy-MM-dd HH:mm:ss is used. Envision is using the .NET Custom Time Format.
• replace(text, pattern, replacement): Returns the text where all occurrences of the pattern have been replaced by the replacement. This function is similar to the SUBSTITUTE function of Excel, omitting the instance_num argument.
• startswith(text, pattern): Return true if the text starts with an occurrence of the pattern.
• strlen(text): Returns the length of the text argument.
• substr(text, start, count): The start position is defined by start. If negative, it's an offset from the end of the string, otherwise it's an offset from the start of the string. The length of the returned substring is defined by count, treated as 0 if count < 0. If the segment start or length place it partially or completely outside the string, e.g. substr("A", 2, 1), then the segment is clipped to fit. Function substr(text, start) is defined as substr(text, start, <infinity>).
• uppercase(text): Returns the uppercase variant of the text.
## Calendar functions
• "\{myDate:yyyy-MM-dd}": custom date formatting through string interpolation. The date format is specified by the token found after the semi-colon. More details about date format strings.
• chineseYear(date): Returns the current year in the Chinese calendar.
• chineseYearEnd(date): Returns the last day of the current Chinese Year.
• chineseYearStart(date): Returns the first day of the current Chinese year.
• date(y, m, d): Returns a date built from the year, month and day passed as arguments. The arguments y, m and d are expected to be numbers.
• monday(date): Returns the first Monday that precedes the date (inclusive).
• month(date): Returns the index of the month associated to the date, counting the number of months since January 1st 2001.
• monthnum(date): Returns the applicable month (1-12) for the date passed as argument.
• today(timezone): Return the current wall-time date with the time-zone passed as argument and expressed as the difference in hours to UTC.
• year(date): Returns the applicable year for the date passed as argument. Similar to the YEAR function in Excel.
• yearStart(date): Returns the first day of the year for the current year.
• yearEnd(date): Returns the last day of the year for the current year.
• weeknum(date): Similar to the WEEKNUM (System 2) function in Excel.
## Ranking functions
• argfirst(ordering, group): Returns true for one first value of the group according to the ordered values (the ordering). The group is optional. When the group is provided, the function returns true once per group. An overload argfirst(ordering, group) where condition is also provided for convenience. When the where option is used, it may result in groups where no true value is present, because the condition was false for the entire group.
• arglast(ordering, group): Same as argfirst(), but returning true for the one last value.
• cumsum(number, rank, group): Returns the cumulative sum of the numbers according to the increasing ranks. The group is optional. When the group is specified, it is used to perform a local cumulative sum for each group.
• fifo(V, T.D, T.Q): Helper for FIFO inventory analysis. Returns the unsold inventory quantity as a vector of T. The vector V contains the total stock. The table T contains the purchase orders. T.D contains the dates, and T.Q contains the purchase quantities. The function computes the unsold quantities by playing the purchase orders backward in time. See also FIFO inventory method.
• rank(number, group): Returns the ranks of the numbers with no tie. Similar to the RANK.EQ function in Excel, except that all numbers get a distinct rank (tie-breaks are arbitrary). The group is optional. When the group is provided, it is used to perform local ranks for each group.
• rankd(number): Returns the ranks of the numbers; identical numbers get identical ranks. Similar to the RANK.EQ function in Excel.
## Graph functions
• canonical(A, B): returns the canonical representative for each A value. From a practical perspective, this function is used to deal with code replacement (ex: SKU code replacement). For example, canonical(OldSku, NewSku) would return the latest SKUs available for each item, recursively performing the replacements. See also nonCanonical().
• nonCanonical(A, B): returns true whenever a canonical representative cannot be computed for the A. This happens when circular paths or branching paths get detected.
• connected(A, B, group) : considers the undirected graph described by all edges (A,B), then returns for each node A the name of the smallest node in A's connected component. Here, "smallest" means having the smallest name, in terms of string comparison. The group is optional. When the group is specified, the dataset is first partitioned against the specified groups.
## Algebra of distributions
### Parametric distributions
Parametric distributions can be generated, that is, functions which take a number as an argument - the parameter - and return a distribution.
• dirac(n) returns a function zero valued everywhere except for n where the function is valued at 1.
• identity(n) returns the function $\text{id}: k \to k$ but limited to the segment [0;n] and 0 elsewhere.
• uniform(n) returns the function $\text{unif}: k \to 1$ but limited to the segment [0;n] and 0 elsewhere.
• uniform(m, n) returns the function $\text{unif}: k \to 1$ but limited to the segment [m;n] and 0 elsewhere. If $m - 1 = n$, the uniform() returns a zero distribution.
• uniform(D) returns the function $\text{unif}: k \to 1$ but limited to the positive support of the distribution D and 0 elsewhere.
• poisson(a) returns the Poisson distribution of parameter a ($\lambda$ in literature).
• exponential(a) returns the exponential distribution of parameter a ($\lambda$ in literature).
### Non-parametric distributions
• distrib(Id, G.Probability, G.Min, G.Max) is a function that returns distribution defined by a list of buckets; where each bucket has left and right inclusive boundaries and a value for the bucket.
• ranvar(T.X) is an aggregator that returns the empirical distribution resulting from the observations obtained from the vector T.X.
### Indicators on distributions
Numeric indicators can also be obtained from distributions.
• crps(X, A) where A are integral numbers, returns the Continuous Ranked Probability Score (CRPS).
• mean(X) returns the statistical mean.
• variance(X) returns the statistical variance.
• mass(X) returns to mass of distribution, that is, $\sum_{k=-\infty}^{\infty}f(k)$
• isranvar(X) returns a Boolean that is true if the distribution is a random variable.
• int(X, A, B) where A and B are integral numbers returns the integral of X over the inclusive segment [A;B].
• quantile(X, tau) returns the quantile of the distribution; the smallest $x$ such as $\mathbf{P}[X \leq x] \geq \tau$.
• spark(X) returns a text value that contains compact ascii-art representation of the distribution.
### Transformations of distributions
A distribution can be transformed into another distribution.
• reflect(X) returns the reflected distribution $k \to f(-k)$.
• transform(X,a) returns a distribution that approximates through interpolation $k \to f(k / a)$.
• fillrate(X) returns the marginal fill rate. Expects a random variable as input and returns a random variable.
• truncate(X, a, b) returns the truncated distribution $k \to f(k) \text{ if } k \in [a; b] \text{ else } 0$. The boundaries A and B are inclusive.
• maxr(X, a) returns the distribution $k \to f(k) \text{ if } k \in ]-\infty; a - 1] \text{ or } \sum_{i=a}^\infty f(i) \text{ if } k = a \text{ else } 0$.
• minr(X, a) returns the distribution $k \to f(k) \text{ if } k \in [a + 1; \infty[ \text{ or } \sum_{i=-\infty}^a f(i) \text{ if } k = a \text{ else } 0$.
• zoz(X) (zero on zero) returns the distribution where $k \to f(k) \text{ if } k \neq 0 \text{ else } 0$.
## Table creation functions
See creating tables for more details.
• extend.range(T.N): Create N lines for each line from the table T where N is expected to be an integer. For example:
table T = extend.range(Orders.42)
T.Quantity = Orders.Quantity // implicit extension
show table "T" with T.N, T.Quantity
• extend.distrib(distribution, gap, multiplier, reach): Extends a distribution into a table. See also extend.distrib().
• extend.billOfMaterials(...): Translates a demand history for items into the demand history for the parts. See also extend.billOfMaterials().
• forex(value, Origin, Destination, date): Returns the amount expressed in the currency Origin into the equivalent amount in the currency Destination according to the historical rates at the specified date. The currencies should be encoded with their canonical three-letter codes. Lokad supports about 30 currencies leveraging the data provided by the European Central Bank. Rates are updated on a daily basis. See also isCurrency() to test the validity of your currency code.
• hash(value): Returns a pseudo-injective hash value between 0 and 2^24-1. This function is typically used randomly shuffle a dataset by hashing the content of a column, and then sorting against the hashed values.
• isCurrency(currencyCode): returns true if the text entry passed as argument is a currency code recognized by the forex() function.
• mkuid(X, offset): returns a unique number, with unicity maintained across Envision runs. This function is intended to uniquely identify results calculated by Lokad. For example, it can be used to generate a unique purchase order number to be incremented whenever the Envision script is re-executed. The vector X is ignored, but the UID (unique identifier) is generated as a scalar in the table associated to X. The offset is an optional scalar that represents the starting suffix for for the UID. The generated strings are numbers in format PPPPPPPAAA, with P a page number (does not start with 0) that is always strictly increasing, and A an incremented counter that starts at offset (or 0 if no offset parameter is provided). P has at least 7 digits, A has at least 3. The UIDs offer three properties. (1) All UIDs can be parsed as numbers, and those numbers will be different. Keep in mind, however, that UIDs have at least 10 digits, and likely more if each call needs to generate more than 1000. (2) An UID generated at time T is strictly inferior (in alphabetical order) to an UID generated at time T' > T. (3) If all calls generate similar numbers of UIDs (less than 999, or between 1000 and 9999, etc.) then the previous property is also true for the numeric order between UIDs.
• solve.moq(...): an advance numeric solver for the general MOQ problem (minimal order quantities).
• pricebrk(Demand, Price, Prices.MinQuantity, Prices.Price, Stock, StockPrice): returns returns the distribution of the marginal purchase unit price. See Supplier Price Breaks.
• priopack(R, V, S, C, J[, B]): a simple variant of the bin packing algorithm intended to be used with purchase prioritization list. Unlike the classic bin packing algorithm, not only, we seek to optimize the bin capacities, but the ordering of the units should also preserved as much as possible. R contains the ranks of the lines to be packed. V is the volume of each line. S is the equivalence class of the suppliers, with bin packing computed per supplier. C is the max volume capacity, its value is homogeneous to V, and it is assumed to be a constant value across the equivalent class C. J is the jumping threshold, its values is homogeneous to V, it is typically expected to a small multiple of the C value. B is an optional argument interpreted as the barrier; when this value is provided, the bin-packing process is not allowed to reorder lines that below to the same equivalence class as defined by B.
• stockrwd(Id, G.Proba, G.Min, G.Max, M, S, C, A): the stock reward function. This function is used to build prioritized ordering policy out of the probabilistic forecasts produced by Lokad. | 2017-02-20 01:41:57 | {"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": 0.3478420078754425, "perplexity": 2628.8258625658173}, "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/1487501170380.12/warc/CC-MAIN-20170219104610-00131-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://geohaff.com/post/embrace-the-ellipsis/ | 11 min read
# Embrace the ellipsis
In my classes and research group, I work with many novice R users who ask a plethora of great questions. Some of the common questions include things like, “Why do you have to quote a package name when you install it but don’t you have to quote it when you attach (i.e. load) it?” Or, “How do you know which package a function comes from if you don’t use the double colon, i.e., ::?” These sorts of questions indicate that students are comprehending the material, learning the language, and beginning to recognize important patterns.
In my classes, we frequently dissect documentation and comb over function arguments. Students are often curious about how certain arguments will affect the way a function runs, and they routinely vocalize these inquiries. Questions about the ellipsis – the ... used in many R functions – however, almost never come up. It is treated like a mysterious artifact that ought to be avoided.
Figure 1: “The Ishumura and the Artifact…must be destroyed
Or perhaps students suspect the power of these dots – much like the Army of the Dead in Lord of the Rings – but seek to avoid unnecessary risks.
Figure 2: Cost benefit analysis
Since I rarely have students utilize arguments which are not explicitly listed by a high level function, maybe they assume it isn’t relevant and is more of a comical catch-all like how “et cetera” is used in movie The King and I:
Figure 3: I sure do think of this quote (and my mom who says the phrase exactly like the king) every time I see the ellipsis
This is despite the fact that many functions my students see indeed use the ellipsis. To be fair, while I had been aware of the ellipsis and its use for quite a while, I had avoided it much in the way the miners in Dead Space should have avoided the Artifact aside from occasionally passing arguments to lower level functions in ggplot2 or tmap. In a recent project, however, I found the ellipsis – along with extracting and manipulating objects created from it – to have incredible value for one task in particular: constructing helpers and wrappers with sensible defaults around functions like those in ggplot2 which have many optional arguments.
This post demonstrates how the ellipsis, or the “dots” (e.g., ...), can be used in function creation. There is a great introductory post on the ellipsis here, but it lacks tangible examples and memes, so I wrote this post to fill that gap. I contend that the ellipsis is more like Figure 2 than it is like Figure 1 or Figure 3. It is not a portal to a dark universe nor meaningless filler but a convenient way to construct functions which pass user arguments to other functions, particularly when the function creator wants to supply reasonable defaults yet allow these to be changed. Advantageously, one need not be Gondorian royalty to wield it’s power.
## Functions for everyone
For my Quantitative Methods in Geography class, I created a package called haffutils which contains numerous functions intended to lower R’s barrier of entry for beginners. This reduces the amount of code that students have to write and makes data analysis and visualization simpler. One function that students use is designed for creating density plots. Aside from the function I created, there are two simple ways to create a basic density plot; one (a) involves using functions from the built-in base and stats packages:
x <- rnorm(100)
plot(density(x))
Figure 4: Ugly density plot
And (b) another involves using ggplot2:
library(ggplot2)
x <- rnorm(100)
df <- data.frame(x)
ggplot(df, aes(x)) +
geom_density()
Figure 5: Slighly less ugly density plot
The first option is ugly, and unlike using the hist function to create a histogram, it requires a small extra step in computing the density before plotting it. The second option involves way too much technical debt for beginner R users, especially in a class focused on quantitative methods in geography rather than on R itself. While ggplot2’s grammar of graphics is powerful and translatable to many other visualization types, I simply don’t have time to explain to students why a vector must first be converted to a data frame, how the aes function works, et cetera, et cetera, and so forth. Further, to create a minimally nice looking density plot, I think the ggplot example above needs some color and transparency:
library(ggplot2)
x <- rnorm(100)
df <- data.frame(x)
ggplot(df, aes(x)) +
geom_density(fill = "orange", alpha = 0.5)
Figure 6: A beautiful density plot which is cumbersome to create for novice R users
To resolve this issue, I wanted to create a single function option that would (a) require one only argument, (b) have that required argument be a numeric vector rather than a data frame, and (c) look nice with reasonable visual defaults, particularly with color and transparency. So I created a wrapper around geom_density called pretty_dens (short for “pretty density plot”) which allows for this:
library(haffutils)
x <- rnorm(1000)
pretty_dens(x)
Figure 7: A beautiful density plot which is easy to create for novice R users
The color is selected randomly from the viridis palette using this in the body of the pretty_dens function:
fill <- viridis::viridis(100) %>% sample(1)
This makes things fun and interesting since it will produce a different color every time the pretty_dens function is invoked, but written this way, it has a disadvantage in that it prohibits users from selecting their own color. This is where the ellipsis come in handy when creating functions, though leveraging its potential is not intuitive.
Awkwardly, the ellipsis returns some unexpected things when using it in ways that are commonly used to interact with other R objects, namely typing the object name in the console to see its contents or by using the class function to inspect the object’s data type. Consider the example of a relatively basic R object, the open paren (i.e., ():
> (
returns
.Primitive("(")
And
> class(()
returns
[1] "function"
But trying these operations with the ellipsis returns something different:
> ...
returns
Error: '...' used in an incorrect context
And
> ...
Error: '...' used in an incorrect context
And
> class(...)
Error: '...' used in an incorrect context
This is because the “dots” (as they are called in the documentation) – and ?... does indeed return its documentation – or the “ellipsis” as it is more commonly referred to in the R community, is not a function or variable. The ellipsis is a syntactic element and a reserved word in R.
But the confusion goes even further: suppose you use the ellipsis in function creation to allow for the passing of arguments from your R function to another. E.g.,
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
pretty_dens <- function(x, ...) {
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
geom_density(...)
}
Utilization like this:
x <- rchisq(1000, 4)
pretty_dens(x)
Or this:
x <- rchisq(1000, 4)
pretty_dens(x, fill = "cyan")
would work as intended. But if you modify the value of fill in the body of the function it would obviously override anything the user supplies:
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
pretty_dens <- function(x, ...) {
fill <- viridis::viridis(100) %>% sample(1)
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
ggplot2::geom_density(fill=fill, ...)
}
In the past, I’ve been confronted with similar situations where I need to check for the existence of certain user arguments and make adjustments if they’re not present. A great example would be the case where a user has not supplied a color for a plot. This example works but it’s unwieldy:
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
pretty_dens <- function(x, fill=viridis::viridis(100) %>% sample(1), ...) {
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
ggplot2::geom_density(fill=fill, ...)
}
This would get out of hand with any more arguments that have their defaults supplied this way. The code used to create the fill should go in the body of the function rather than in its argument list. But this does not work:
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
pretty_dens <- function(x, ...) {
if (!exists("fill")) {
fill <- viridis::viridis(100) %>% sample(1)
}
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
ggplot2::geom_density(...)
}
Since !exists("fill") will always return TRUE in this case, even if the user supplies a value for fill. The hasArg() function can be used instead to check for user arguments, even those included in the ellipsis.
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
pretty_dens <- function(x, ...) {
if (!hasArg("fill")) {
fill <- viridis::viridis(100) %>% sample(1)
}
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
ggplot2::geom_density(fill=fill, ...)
}
This works fine if the user does not pass an argument for fill; in this case, !hasArg("fill") is TRUE, and fill is assigned to a variable. But what if the user does supply an argument to fill? An error is returned:
object 'fill' not found
Figure 8: Where be the fill?
If you’ve made it this far, you can probably see that fill is “hiding” in the ellipsis – R can tell that it has been passed as an argument through !hasArg("fill"), but because it’s not a required argument, it’s value is encapsulated in ..., not in the variable fill that is being supplied to geom_density. Fortunately, we can look for ellipsis variables by using this:
list(...)
If this is used in the console outside of a function, it will throw an error as demonstrated earlier, but inside the function, it can be used to retrieve ellipsis arguments. As one might expect, list(...) conveniently works when debugging. So, if a breakpoint is set in a function like this (using Emacs/ESS and how it visually shows breakpoints):
pretty_dens <- function(x, ...) {
df <- data.frame(x=x)
B>
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
ggplot2::geom_density(...)
We can inspect user arguments once the function is used. With arguments supplied as:
pretty_dens(rnorm(100), fill="orange")
From the debugger on the console we can use list(...) which will return:
$fill [1] "orange" This feels like that moment in Ocarina of Time when you obtain the Lens of Truth. Figure 9: Use ess-bp-set and then C-c C-c and then list(...) The trick then becomes modifying the arguments if they are not supplied in a way that allows you to avoid explicitly referencing an object like fill as a standalone variable. So, the recommended way to do this is to put every user-supplied ellipsis argument in a variable: args <- list(...) Then, search the variable args for the existence of those arguments you want to modify, then modify args (which is a list) accordingly. Then, the trick is to use do.call() to apply each argument from args to the appropriate function. In my case, it would look like this: pretty_dens <- function(x, ...) { args <- list(...) if (!"fill" %in% names(args)) { args$fill <- viridis::viridis(100) %>% sample(1)
}
dens <- do.call(ggplot2::geom_density, args)
Then, the density plot, dens, is added to the “chain” of ggplot2 functions:
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
dens
}
And it works! This allows the user to specify their own argument for fill that gets passed to geom_density, while supplying a reasonable default if they do not supply one. The whole function has a bit more to it and looks like this:
#' Create a simple, nice looking density plot using a vector as input
#'
#' Base R does not have a one line/one function option for creating density
#' plots. Similar to pretty_hist(), this function takes a vector as input and
#' produces a nice looking density plot of a single variable using ggplot2 under
#' the hood.
#' @usage pretty_dens(x)
#' @param x numeric vector
#' @param title character string, optional title
#' @param xlab character string, optional x-axis label
#' @param ylab character string, optional y-axis label
#' @param ... other arguments passed to geom_density
#' @return a plot
#' @keywords visualization
#' @export
#' @examples
#' pretty_dens(rnorm(1000))
#'
pretty_dens <- function(x, title="", xlab="", ylab="Density", ...) {
## get ellipsis arguments
args <- list(...)
## set some reasonable defaults for geom_histogram (ellipsis arguments)
if (!"fill" %in% names(args)) {
args$fill <- viridis::viridis(100) %>% sample(1) } if (!"alpha" %in% names(args)) { args$alpha <- 0.65
}
dens <- do.call(ggplot2::geom_density, args)
## remove na values
x <- x[!is.na(x)]
## create data frame for ggplot2
df <- data.frame(x=x)
ggplot2::ggplot(df, ggplot2::aes(x=x)) +
dens +
ggplot2::ggtitle(title) +
ggplot2::xlab(xlab) +
ggplot2::ylab(ylab)
}
In addition to supplying a default for fill, I also set the opacity to 65% with the alpha argument. The function also removes NA values. While this is a bit dangerous for sophisticated users, this function is intended to be used for teaching purposes, not in a production environment. I also have a pretty_hist function which creates histograms, and it has some other considerations which don’t apply to density plots (e.g., number of bins). I may add to these functions over time and/or create new functions which leverage list(...) as needs arise.
Aside from its utility, extracting objects from list(...) is fun and gives me an excuse to do some debugging. With this knowledge of the ellipsis in mind, you should now put aside [your fear of the ellipsis]. Become who you were born to be [as an R function creator].
Figure 10: You will suffer me! | 2023-03-23 05:25:37 | {"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": 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": 0.3842843174934387, "perplexity": 3807.9132017630686}, "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-2023-14/segments/1679296944996.49/warc/CC-MAIN-20230323034459-20230323064459-00787.warc.gz"} |
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# If x, y, and n are positive integers, is (x/y)^n greater
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
(1) x=y^3 and n>y
(2) x>5y and n>x
[Reveal] Spoiler: OA
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
Question: is $$(\frac{x}{y})^n>1,00$$
(1) x=y^3 and n>y --> $$(\frac{x}{y})^n=(\frac{y^3}{y})^n=y^{2n}$$, so the question becomes is $$y^{2n}>1,000$$ --> y=1 and n=2 answer is NO but y=10 and n=11 answer is YES. Not sufficient.
(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.
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06 Oct 2010, 23:40
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HI Bunuel,
I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify
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07 Oct 2010, 00:46
psychomath wrote:
HI Bunuel,
I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify
Nope .. 0 is neither positive nor negative
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07 Oct 2010, 01:15
OK so what i remember about zero being a positive integer is wrong...Thanks a ton!
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08 Oct 2010, 11:12
Bunuel wrote:
(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.
Can you please explain the 2nd equation again.
I didn;t get this one.
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08 Oct 2010, 11:37
onedayill wrote:
Bunuel wrote:
(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.
Can you please explain the 2nd equation again.
I didn;t get this one.
Question: is $$(\frac{x}{y})^n>1,00$$?
From (2):
$$x>5y$$ --> $$\frac{x}{y}>5$$, so $$base=\frac{x}{y}=(# \ more \ than \ 5)$$;
$$x>5y$$ and $$n>x$$ --> as $$x$$, $$y$$, and $$n$$ are positive integers then: the least value $$y$$ is 1 --> the least value of $$x$$ is 6 ($$x>5=5y_{min}$$) --> the least value of $$n$$ is 7 (as $$n>x$$);
Is $$(\frac{x}{y})^n>1,00$$ --> is $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$? Answer is YES, as even $$5^7>1,000$$.
Hope it's clear.
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Re: If x, y, and n are positive integers, is (x/y)^n greater tha [#permalink]
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09 Mar 2012, 07:16
Let us substitute numbers to disprove/prove the choices :
We need to predict whether (x/y)^n > 1000
(1) x = y^3 and n > y.
if y = 1 and x = 1 , and n = 2, then it's false.
if y = 10, x = 1000 and n = 1001, it's true
Insufficient
(2) x > 5y and n > x.
Let us take lowest value of y = 1
Then x = 6 at least , and n = 7 at least
So 6^7 > 1000
Another way to look at this is :
x > 5y
=> x/y > 5 and n > 5x => n >= 5 (because these are all positive numbers)
So 5^5 > 1000
Sufficient.
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]
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25 Jun 2013, 12:34
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agnok wrote:
If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
(1) x=y^3 and n>y
(2) x>5y and n>x
Given x,y and n are positive integers
From st 1 we have x= y^3 and n>y so the given expression becomes
(y^2)^n > 1000
now if y = 2 and n = 5 we have 4^5>1000----> yes
but if y=1 and n=5 then we have 1^5>1000-----> no
Not sufficient
St 2 says x>5y and n>x
Let us assume x= 5y so we have 5^n > 1000
now also n> x so if x= 5 then n can be any value integer greater than 5 ----> 5^n>1000 is definitely true
now since x>5y then ----> value of x is more than 5 and since n>x it will always be greater than 1000
Hence ans B
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]
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08 Mar 2016, 21:26
agnok wrote:
If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
(1) x=y^3 and n>y
(2) x>5y and n>x
Excellent Question,,
Here i just plugged in y=1 to calculate the least value of LHS as y increases x increases and so does n hence B is correct
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink] 08 Mar 2016, 21:26
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Display posts from previous: Sort by | 2016-10-27 12:20:07 | {"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": 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": 0.6362465620040894, "perplexity": 4858.341518736088}, "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-2016-44/segments/1476988721268.95/warc/CC-MAIN-20161020183841-00003-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://electronics.stackexchange.com/questions/419848/how-is-the-power-of-a-ssb-sc-signal-half-that-of-dsb-sc-signal | # How is the power of a SSB-SC signal half that of DSB-SC signal?
Intuitively I get it that my SSB power has to be half of DSB power but mathematically I am unable to get this. Say working for tone modulation.
$$m(t)=mA\cos(w_mt)$$ where m is modulation index.
Modulated signal for DSB case is $$mA\cos(w_mt)\cos(w_ct)$$ Power is $$(ma)^2/4$$.
Modulated signal for SSB case is $$mA\cos((w_m-w_c)t))$$ Power is $$(ma)^2/2$$.
This seems total opposite to what appears intuitively . I used BP Lathi's Book on Communication where the formula for SSB is ssb signal=$$m(t)cos(w_ct)+m_h(t)sin(w_ct)$$ where $$m_h(t)$$ is the Hilbert transform on m(t). | 2019-08-23 09:20:57 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9532673358917236, "perplexity": 1968.9997895331567}, "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-2019-35/segments/1566027318243.40/warc/CC-MAIN-20190823083811-20190823105811-00257.warc.gz"} |
https://economics.stackexchange.com/questions/40375/plotting-money-market-equilibrium-for-2020 | # Plotting money market equilibrium for 2020
I am trying to roughly sketch up supply / demand curves by parameterizing the major happenings in the money market in 2020. I intend to use this chart as the template:
Below, I'll outline my thought process for each curve:
Money supply
• Interest rate targeted at zero
• Fed balance sheet expands (a lot)
Graph implication: money demand curve(straight line) shifts to the right
This is the tricky part, as money demand is not something we can directly observe in practice, though I tried my best to be objective/conservative.
Money demand
• Unemployment spikes in April, then slowly stabilizes around 6% in 3Q20
• Total income probably drops off a cliff for a few months and slowly revives with industries streamlining / automating / outsourcing, setting a lower total income floor than pre-pandemic times
• Stimulus / helicopter money offsets deflationary forces
• Risk-off sentiment during March's downturn drives defensive portfolio positioning, increasing demand for cash
• BofA September poll: fund manager consensus that it's a new bull market, investors rotate out of cash/equivalents and into higher yielding assets, reducing demand for cash
Graph implication: Money demand undergoes a short-term shift to the right, but trends to a shift to the left from a likely permanent contraction in total income and the onset of a new bull market (admittedly not a slow bull)
Conclusion: I realize there are multiple factors at play here, but I think it's reasonable to assert that, on balance, the demand curve shifts left and the supply curve shifts right.
And thus I present my rough sketch of the money market:
## Question
Is this parameterization consistent with mainstream economic analysis on the money market in 2020?
The graph is almost correct given the assumptions about what is happening but not quite. The proper graph should look more like this picture I made in LaTex using tikz:
Where $$^*$$ denote the new state of things given your assumptions.
You are right that money demand shifts to the left and money supply to the right, but your graph missed an important fact that money demand at zero lower bound (ZLB) becomes flat. This is one of the reasons why monetary policy looses its potency around ZLB (see Blanchard et al. Macroeconomics a Eurpean Perspective pp. 96).
Correction of some misconceptions:
In your post you also have some misconceptions let me correct them:
This is the tricky part, as money demand is not something we can directly observe in practice, though I tried my best to be objective/conservative.
We actually can observe money demand at a given point in time (only the whole demand function is not directly observable). Furthermore, we actually even can, using econometric methods, properly estimate the money demand function. See Jawadi & Sousa (2013) or Narayan, Narayan, & Mishra (2009), for examples of that. However, of course this cannot be done in real time but only retroactively as we collect enough data about given time period, so to do that for period covering entire COVID19 crisis this won't be possible until few years down the road.
helicopter money offsets deflationary forces
central banks are definitely trying to expand money supply right now but not via helicopter money. Helicopter money means central bank is directly sending money to households. This has not yet happen to my best knowledge (at least not in US, EU or UK), although there are economists calling for central banks to do so (like Gali 2020 in his VOX$$^{EU}$$CEPR post). | 2021-06-17 22:53:13 | {"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": 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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5460507273674011, "perplexity": 2536.482767652364}, "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-2021-25/segments/1623487634576.73/warc/CC-MAIN-20210617222646-20210618012646-00588.warc.gz"} |
https://www.mathtrench.com/calculus-general-differentiation-145/ | # Calculus: General Differentiation – #145
Question: Use the fact that the power series, centered at x = 0, for $$\frac{1}{1-x}$$ is $$\sum\limits_{n=0}^{\infty }{{{x}^{n}}}$$, find the power series for the following, with center at x = c.
(a) $$\frac{1}{x+3}$$, c = 5
(b) $$\frac{1}{{{\left( 1-x \right)}^{3}}}$$, c = 0 | 2019-06-17 23:56:29 | {"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": 0.9583619832992554, "perplexity": 387.9968085937231}, "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-2019-26/segments/1560627998581.65/warc/CC-MAIN-20190617223249-20190618005249-00044.warc.gz"} |
https://crypto.stackexchange.com/questions/89824/rigorous-practical-pseudorandom-generators | # Rigorous practical pseudorandom generators
It is known that existence of pseudorandom generators (PRGs) is equivalent to the existence of one-way functions. In turn, the latter is an open problem.
I am curious if someone developed kind of "practical" PRGs, which are weaker than PRGs in terms of computational indistinguishably to uniform random number generators.
I know of some statistical tests for randomness, but is there any rigorous theory on the subject?
This is a repost from MO, and I intend to remove the original question.
• Does your definition of a PRG include a cryptographic PRG? If yes, then isn't the answer self evident? – Paul Uszak May 6 at 12:28
• @PaulUszak I don't get what you mean. CPRG is a PRG, in common terms. And what exactly is self-evident here? – Rubi Shnol May 6 at 12:31
• Sorry, I was too vague. If CPRG = PRG ~ open question, the clearly practical PRGs exist as we use them and are not yet invertible. There's a whole list of "Related" questions adjacent to this one giving rigorous examples. Or am I misunderstanding your meaning? – Paul Uszak May 6 at 12:43
• @PaulUszak Think you still get me wrong. Perhaps, the word "practical" is misleading. I know that one can construct PRGs, in turn CPRGs, from 1-way functions. The rigor = to show the constructed PRGs are comp. indistinguishable from randomized algorithms. But what can we rigorusly show without conjecturing 1-way functions? There is chaos "PRGs", but they aren't concerned with comp. indistinguishability – Rubi Shnol May 6 at 12:49
It is worth mentioning that there is a connection in complexity theory often called "Hardness v Pseudorandomness" that makes this question somewhat difficult. It may not be surprising that given a strong enough PRG, one can derandomize certain randomized algorithms, i.e. trying to prove $$P = BPP$$ can be done by giving a provably strong enough pseudorandom generator.
What is perhaps surprising is that this is intimately connected to the existence of hard problems in $$NP$$. Specifically, if there is a problem in $$NP$$ that requires exponentially sized circuits, I believe it implies that $$P = BPP$$ via the construction of an explicit pseudorandom generator. Moreover, some form of the reverse holds --- being able to derandomize $$P$$ (via the construction of a provably good PRG of good enough parameters) leads to circuit lower bounds, which is a notoriously hard subject. Keywords for this are things like "Nisan-Wigderson PRG", or you can look at these notes for some pointers.
I think (but am fuzzy on the details) that one can generalize the above to other circuit classes as well, i.e. the existence of explicit provably secure PRGs against some circuit class is intimately related to circuit lower bounds against some related circuit class. As in general most circuit lower bounds we can prove are against fairly restricted models of computation, I would expect that the literature on "rigorous PRGs" is restricted to PRGs that are secure against relatively weak forms of computation.
I don't know a great place that summarizes this all --- I do not myself work in the area, but heard about it from someone who does. Perhaps their thesis would be a good reference, but I'll admit that I have not personally read it.
• @PaulUszak Computationally indistinguishability against some circuit class $\mathcal{C}$ is a formal property, namely that no circuit $C\in\mathcal{C}$ can distinguish between the output of the PRG and a uniformly random string. For certain circuit classes that we cannot prove lower bounds on, the Hardness vs Pseudorandomness paradigm means we also cannot construct provably PRGs (without implicitly also proving lower bounds). For weaker circuit classes that we do have strong lower bounds on, there is no such obstacle, and one could construct a PRG that is provably secure against that class. – Mark May 6 at 22:00
• The notion of "practically proven" isn't something you can mathematically formalize though, and moreover any such formalization would include "the existence of one-way functions" as something that has been "practically proven" (especially given that universal one-way functions exist). I interpret the asker as asking about the existence of provable "weaker" notions of PRGs, and this exists in precisely "explicit PRGs that are secure against weaker circuit classes". – Mark May 6 at 22:02
If the goal is cryptographic strength [given the context stated by the OP, I assume it is] in a PRNG that will be used in practice, then the randomness testing methods can be used to rule out generators as being weak, but obviously cannot rigorously demonstrate randomness.
However there are pitfalls in using generators which are based on problems which are assumed to be hard.
In terms of the CSPRNGs, such as Blum-Blum-Shub (BBS), which is the most well-known example, care must be taken that the extraction rate of "cryptographically strong bits" is not too high compared to the state space of the BBS iteration. The theoretical suggestion is if the iteration is $$x_{k+1}=x_k^2 \pmod n,\quad n=pq$$ where $$p$$ and $$q$$ are large primes, one should at most take $$O(\log \log n)$$ least significant bits of $$x_k$$ and output them as pseudorandom bits.
This approach is full of pitfalls, however. Firstly, the specification is asymptotic, so what's a reasonable constant to use in front of the $$O(\cdot)$$ expression? Vanstone and Menezes in an Indocrypt paper suggested not to use more than 1 bit, i.e., just the least significant bit.
More seriously [see the first answer to this question in crypto stackexchange for details] it turns out that the security reduction in BBS is so inefficient that maybe it should not be used at all in practice:
Suppose you use BBS with a 768-bit modulus. You've read that 768 bits is enough to make factoring infeasible, so this sounds peachy. You've read that it is safe to extract O(lg n) bits in each iteration; here n = 768, and lg n = 9.58, so you decide to extract 9 bits in each iteration. You use it to generate a pseudorandom stream of 107 bits (about 1MB of pseudorandom data). How much security do you get? Answer: the security proof guarantees security against any adversary that uses at most $$2^{-264}$$ steps of computation. Yes, this is an utterly ridiculous and useless statement! To put it in plain English, the security proof guarantees absolutely nothing useful at all.
On the other hand if one wanted security against an attack of complexity approximately $$2^{100}$$ steps (reasonable since $$2^{128}$$ brute force complexity is standard these days) one would have to choose $$n$$ of about 6800 bits. This is now more feasible since RSA moduli of 4096 bits are now common.
Notwithstanding this, it is amazing how inefficient the security proof reduction in BBS is. One can demonstrate that breaking BBS and is $$1054 n^3$$ times faster than factoring the BBS modulus $$n.$$
So practical CSPRNG security is a moving target, very dependent on algorithmic developments, even in the case of generators designed by using hard problems.
• This is not rigorous – Rubi Shnol May 9 at 8:58 | 2021-06-16 11:34:29 | {"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": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.695296049118042, "perplexity": 927.0053422053451}, "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/1623487623596.16/warc/CC-MAIN-20210616093937-20210616123937-00167.warc.gz"} |
https://plainmath.net/algebra-ii/29284-find-all-solutions-of-the-system-of-equations-begin-cases-x-2y-equal-2-y-2 | Brittney Lord
2021-09-29
Find all solutions of the system of equations.
$\left\{\begin{array}{l}x-2y=2\\ {y}^{2}-{x}^{2}=2x+4\end{array}$
Gennenzip
Expert
Step 1
To find:
The solution of the system of equation.
Given:
The system of equation $x-2y=2$ and ${y}^{2}-{x}^{2}=2x+4$.
Calculation:
Simplify the equation $x-2y=2$ as follows:
$x-2y=2$
$x=2+2y$
Substitute $x=2+2y$ in ${y}^{2}-{x}^{2}=2x+4$.
${y}^{2}-{\left(2y+2\right)}^{2}=2\left(2y+2\right)+4$
${y}^{2}-4{y}^{2}-4-8y=4y+4+4$
$-3{y}^{2}-4-8-8y-4y=0$
$-3{y}^{2}-12-12y=0$
Further simplify as follows:
${y}^{2}+4y+4=0$
${\left(y+2\right)}^{2}=0$
$y=-2$
Sbstitute $y=-2$ in $x=2+2y$.
$x=2+2\left(-2\right)$
$=2-4$
$=-2$
Step 2
Thus, the solution of the system of equation $x=-2$ and $y=-2.$
Do you have a similar question? | 2023-01-29 02:22:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 48, "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": 0.7577162384986877, "perplexity": 1860.9997404273292}, "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-2023-06/segments/1674764499697.75/warc/CC-MAIN-20230129012420-20230129042420-00326.warc.gz"} |
https://electronics.stackexchange.com/questions/584115/how-to-drive-a-led-120-126v-1500w-from-230v-or-12-24v | # How to drive a LED 120-126v 1500w from 230v (or 12/24v)? [closed]
I need to feed a LED with 120-126v 1500w, made of two strips, 750w each (the heat being generated over a surface of 8cm x 8cm).
EDIT: This is for imaging purposes, so high CRI, is important.
Power: 1000-2000 Watt.
VF: DC 120-126V
IF: 8750mA(1000W) , 1300mA(1500W), 17500mA(2000W)
Chip Brand: Bridgelux
CRI : Ra80 / Ra90 / Ra95 / Ra97
Beam Angle: 120 degree
Brightness: 90-140 lumens per watt (depend on color temperature and CRI value requirements)
LED Size: 100x100 mm
Luminous Area: 80x80mm
Substrate: high quality copper
Do you recommend to transform the current directly from 230v or to use a booster from 12v (from 1 or 2 PC power supply)?
In either case, which components do you recommend (eg., https://fr.aliexpress.com/item/32863157274.html and some other tension adapter)?
I'll need to regulate the tension between 120v and 126v with one (or two) tension variators. I would like to minimize the soldering work, if any.
• 1500w at 12v is 125 amps, so that isn't going to be feasible. You'll have to use a high voltage source. Component recommendations are not allowed here, so you should edit those out of your post or it will be closed. Sep 1 at 17:38
• From 12V, no way. Is this one 1500W LED or several smaller LEDs? It would most likely be easier and cheaper to use several lower power drivers, perhaps 500W ones. So please give all the information about the LED itself. Sep 1 at 17:54
• "I need to feed a LED with 120-126v 1500w." LEDs operate at, typically, 2 to 5 V. It sounds like you have an LED lamp which consists of many individual LEDs. Sep 1 at 18:35
• Can you get the same lamp but with a voltage rating of 230 V? Sep 1 at 18:47
• Is this constant or variable? It must be a large space bigger than a theatre so current and wire gauge are cost tradeoffs. My 10W LEDs are blinding. You will need to define the power path lengths Sep 1 at 19:59
You drive a 1500w constant current LED with a 1500w constant current LED driver. The specs you posted explain what that driver needs to do:
VF: DC 120-126V
IF: 8750mA(1000W) , 1300mA(1500W), 17500mA(2000W)
Select a current driver that can output 13 amps with a compliance range exceeding 120-126V. For example, a ~13 amp, 100-150V driver. There is no other safe and practical way to drive such an LED. You cannot safely drive it by supplying voltage directly, a driver must regulate the current. This will be expensive given the power requirements.
made of two strips, 750w each
Your specs don't mention this and imply that it is a single strip with all strings in parallel. Are you sure?
Do you recommend to transform the current directly from 230v or to use a booster from 12v (from 1 or 2 PC power supply)?
You're going to have to use whatever your driver requires, but it will almost certainly be at least 120VAC, possibly higher.
Finally, the efficiency of that panel is modest. The best LEDs are over 180 lm/watt at a CRI of 90. Consider carefully if you want to power (and cool) a 1500w panel, or a higher efficiency panel that will produce the same amount of light with less costly power supply and cooling.
• This answer is very valuable and I did not see many important aspects. I'm asking few other details to my manufaturer. I have the feeling that this other COB (store.yujiintl.com/collections/led-cobs/products/…) is a lot easier to drive and less costly to drive (I can use directly the cheap aliexpress current boosters), but if I'm not mistaken it is even less efficient (80 lm/watt (120000lm for 1500w)) Sep 1 at 22:54
• @Soleil Higher CRI means lower lumens for the same amount of optical power, so those 95 or 98 CRI lights will require much more optical power to produce the same lumens since they "waste" power at wavelengths that people aren't very sensitive to. Use the lowest CRI that meets your requirements to maximize efficiency. Sep 1 at 23:16
• I'm actually looking for maximized CRI. Do you have sources, papers on this aspect "CRI vs efficiency" ? Sep 2 at 9:32
• I'm certain about the two strips of 750w, it's been confirmed. Sep 2 at 9:46
• @Soleil This paper discusses the effect of CRI on maximum luminous efficiency: arxiv.org/abs/1309.7039 Sep 2 at 12:58
The LED's will have a significant negative temp.coefficient (NTC) with this array, but the electrical power requirements are simple.
I suggest adding thermal protection (OTP) to the continuously variable constant current source.. This means you cannot use variable constant voltage or tension as the NTC would cause thermal runaway and instant damage. The low voltage version is divided into 6 arrays for more flexible welding cables, so it is advisable to use them in two series arrays to require 120V just like the HV version but may be done either way with HV insulation or use in parallel for LV safety.
## More critical requirements
• 2kW Water-cooled Heatsink , custom design
• 2kW water cooler radiator and fan
• Buy 2kW to 4kW Current Source (CS) LED power supply with adjustable by Pot, or voltage 0 ~10V.
• Do not choose a power supply that is 100% utilized as this rating degrades life expectancy unless you plan on derating LED power to 1500W.
• Voltage greatly affects cable diameter ( like car jumper or welding cable)
• 2kW cable design :
• 20A cable @ 60'C must be copper > 2mm D (AWG 10) for 120Vdc LED
• 60A cable @ 60'C " " " > 4.6 mm D (AWG 5) for 40Vdc LED
• choice of soldered fasteners or wire to LED ,
Lumens/ Watt increase 10~15% with colour temp towards blue-white as less phosphor loss occurs but hard on eyes so <= 4500 'K preferred for eyes. ? for plants?
• How do you know that there is NTC and that it is stronger with this array ? Sep 2 at 9:35
• Many thanks for the critical requirement section. This is very helpful. The cable design is impressive and I did not think about that. Sep 2 at 9:42
• All diodes have NTC effects incl. LEDs Sep 2 at 14:08
• @Soleil The NTC of the LEDs themselves is why you must not drive an array like this with a constant voltage source. You need an LED driver, which will compensate for the NTC by reducing voltage as the array heats up. Doing some more reading on LEDs might be good before spending a lot of money on an absurdly high power light. Sep 2 at 15:17
• @user1850479 Thanks for pointing out this aspect. Do you recommend to compensate for NTC despite a good watercooling (+10-20C over ambient temperature, which is about 20-25C) ? Sep 2 at 15:40
You ask " Do you recommend to transform the current directly from 230v or to use a booster from 12v (from 1 or 2 PC power supply) ?" since you are stating nominal AC mains voltages I would recommend simply using a transformer. The size you are talking about are readily available from electrical supply houses. Some are used in the machine tool industry for the controls circuit power. At that point you will have about 120VAC depending on your transformer choice. You can also get lower secondary voltages if you so choose. An advantage of the transformer is the secondary is normally isolated from ground so you can elect to ground it or leave it float.
• Which kind of transformer, and what to do with the AC voltage output of the transformer then to make it power 1500 watts of LEDs? Also, most likely you can get a complete 1500 watt LED driver that weighs and costs less than just the transformer alone. Sep 1 at 19:58
• Go for the driver. You forgot to say 120-126VDC so AC was assumed. You also mentioned 220V is that 20VDC, I assumed AC?
– Gil
Sep 1 at 20:40
• These are constant current LEDs, so using a transformer will not work. You must generate a controlled current or you will have a fire. Sep 1 at 22:24 | 2021-10-19 02:57:24 | {"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": 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": 0.41144460439682007, "perplexity": 3130.895375477694}, "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/1634323585231.62/warc/CC-MAIN-20211019012407-20211019042407-00252.warc.gz"} |
http://openstudy.com/updates/506489c6e4b0da5168be36cc | ## TuringTest 2 years ago Mean Value Theorem: is there a typo on the third line? http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-c-mean-value-theorem-antiderivatives-and-differential-equations/session-34-introduction-to-the-mean-value-theorem/MIT18_01SCF10_ex34prb.pdf
1. TuringTest
The paper is drawing a parallel between linear approximations so it talks about switching out $$f'(a)$$ for $$f'(c)$$ for some specific yet undetermined c but the last formula on the page notes that this idea extended leads to something like a quadratic approximation, which relates to Taylor series$f(b)=[f(a)+f'(a)(b-a)]+\frac{f''(c)}2(b-a)^2$should it not be$f(b)=[f(a)+f'(c)(b-a)]+\frac{f''(c)}2(b-a)^2$or is the whole point using $$f'(a)$$to keep it related to linear approximations?
2. TuringTest
$f(b)\approx f(a)+f'(a)(b-a)$near $$x=a$$, whereas MVT states that$f(b)=f(a)+f'(c)(b-a)$for som $$a<c<b$$ is the whole point using $$f'(a)$$to keep it related to linear approximations?
3. TuringTest
reading it again I'm thinking the answer to my own question is "no it's not a typo" (since it says the part in brackets is $$exactly$$ the linear approximation, which it is with f'(a) ) but if anyone has any more insight let me know
4. TuringTest
Never.mind, I think the answer is that it is not a typo. It says the "next term" in the Taylor series will approximate error in an n-th degree approximation. I suppose only the next term in the Taylor series would require the c to get an exact equality. | 2015-04-25 02:07:33 | {"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": 0.757945716381073, "perplexity": 523.6414145864157}, "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-2015-18/segments/1429246645606.86/warc/CC-MAIN-20150417045725-00207-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://mbarzegary.github.io/2020/11/06/derive-weak-form-pde/ | # Deriving weak formulation of partial differential equations
The finite element method doesn’t need an introduction, but at the core of this magical method, in its mathematical nature, one challenging step makes it sometimes a bit difficult for newcomers to immediatley jump start and employ finite element to solve partial differential equations (PDEs) numerically. This challenging part is deriving the weak formulation of the PDE, which is indeed one of the very first steps a researcher should take to use the available PDE solvers (like FreeFEM, FEniCS, and deal.ii) to simulate a mathematical model.
Although deriving the weak form of a PDE is relatively simple, finding a good reference that demonstrates how to do it in action for the first time can be a bit difficult. This topic is well covered in most of the finite element books (the ones that discuss the mathematical aspects), but you need to go through a bunch of math to find the most essential steps. In this post, I try to explain this process by deriving the weak form of a reaction-diffusion PDE as an example. The equation we want to deal with is:
$\frac{\partial u}{\partial t}=\nabla \cdot (D \nabla u)- s u$
in which, $$u=u(\mathbf{x},t)$$ is the state variable we want to find at each point of space and time. This is also called the strong form of the PDE. To obtain the finite element formulation, the weak form of the PDE is required. In order to get this, we define a space of test functions and then, multiply each term of the PDE by any arbitrary function as a member of this space. The test function space is
$\mathcal{V}=\left\{v(\mathbf{x}) | \mathbf{x} \in {\Omega}, v(\mathbf{x}) \in \mathcal{H}^{1}(\Omega), \text { and } v(\mathbf{x})=0 \text { on } \Gamma\right\}$
in which the $$\Omega$$ is the domain of interest, $$\Gamma$$ is the boundary of $$\Omega$$, and $$\mathcal{H}^{1}$$ denotes the Sobolev space of the domain $$\Omega$$, which is a space of functions whose derivatives are square-integrable functions in $$\Omega$$. The solution of the PDE belongs to a trial function space, which is similarly defined as
$\mathcal{S}_{t}=\left\{u(\mathbf{x}, t) | \mathbf{x} \in \Omega, t>0, u(\mathbf{x}, t) \in \mathcal{H}^{1}(\Omega), \text { and } \frac{\partial u}{\partial n}=0 \text { on } \Gamma\right\}.$
Then, we multiply each term of the PDE to an arbitrary function $$v \in \mathcal{V}$$:
$\frac{\partial u}{\partial t} v=\nabla \cdot (D \nabla u) v- s u v.$
Integrating over the whole domain yields:
$\int_{\Omega} \frac{\partial u}{\partial t} v d \omega=\int_{\Omega} \nabla \cdot (D \nabla u) v d \omega-\int_{\Omega} s u v d \omega.$
The diffusion term can be split using the integration by parts technique:
$\int_{\Omega} \nabla \cdot (D \nabla u) v d \omega = \int_{\Omega} \nabla \cdot[v(D \nabla u)] d \omega-\int_{\Omega} (\nabla v) \cdot(D \nabla u) d \omega$
in which the second term can be converted to a surface integral on the domain boundary by applying the Green’s divergence theory:
$\int_{\Omega} \nabla \cdot[v(D \nabla u)] d \omega = \int_{\Gamma} D v \frac{\partial u}{\partial n} d \gamma.$
For the temporal term, we use the finite difference method and apply a first-order backward Euler scheme for discretization, which makes it possible to solve the PDE implicitly:
$\frac{\partial u}{\partial t} = \frac{u-u^{n}}{\Delta t}$
where $$u^n$$ denotes the value of the state variable in the previous time step (or initial condition for the first time step). Inserting all these into the integral form yields:
$\int_{\Omega} \frac{u-u^{n}}{\Delta t} v d \omega=\int_{\Gamma} D v \frac{\partial u}{\partial n} d \gamma-\int_{\Omega} D \nabla u \cdot \nabla v d \omega-\int_{\Omega} s u v d \omega.$
The surface integral is zero because there is a no-flux boundary condition on the boundary of the computational domain (defined in the trial function space). By reordering the equation, we get:
$\int_{\Omega} \frac{u}{\Delta t} v d \omega+\int_{\Omega} D \cdot \nabla \cdot u \nabla v d \omega+\int_{\Omega} s u v d \omega=\int_{\Omega} \frac{u^{n}}{\Delta t} v d \omega$
which is the weak form of the PDE and can be written as (by multiplying to $$\Delta t$$):
$\int_{\Omega} {u} v d \omega+\int_{\Omega} \Delta t D \nabla u \cdot \nabla v d \omega+\int_{\Omega} \Delta t s u v d \omega=\int_{\Omega} {u^{n}} v d \omega.$
So, the problem is finding a function $$u(t) \in \mathcal{S}_{t}$$ such that for all $$v \in \mathcal{V}$$ the above equation would be satisfied. Defining and solving this problem is simple and straightforward in a wide variety of available finite element PDE solvers such as FreeFEM. | 2023-03-24 05:24:00 | {"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": 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": 0.9122017025947571, "perplexity": 153.9723752934174}, "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/1679296945248.28/warc/CC-MAIN-20230324051147-20230324081147-00309.warc.gz"} |
https://forum.xda-developers.com/google-nexus-5/general/tutorial-how-to-flash-factory-image-t2513701/page211 | 3,898 posts
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By abaaaabbbb63, Senior Member on 5th November 2013, 07:21 PM
17th January 2016, 04:22 PM |#2101
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Originally Posted by tedrogers61
I dont have root to do basic check for sane chip.
Sent from my Nexus 5 using XDA Premium 4 mobile app
It shows : no sane chip
Emmc chip type : SEM32G
17th January 2016, 10:01 PM |#2102
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I don't really know what to suggest from here, but I would root it and perform the Emmc Check Memory next.
Sent from my Nexus 5 using XDA Premium 4 mobile app
18th January 2016, 03:55 AM |#2103
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Originally Posted by audit13
You need to use fastboot commands to flash a stock image unless you find a stock MM zip file that can be flashed in TWRP.
Here's an example: http://forum.xda-developers.com/goog...weaks-t3072279
ok thank you
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18th January 2016, 09:30 AM |#2104
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20th January 2016, 08:00 PM |#2105
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[QUOTE=abaaaabbbb63;47156064]
Hello Nexus 5 Users!
I see many users that don't know how to restore their Nexus 5 to stock. It may come in handy, either when you want to RMA your phone, or you want to fix your mistakes.
This process consists of wiping and flashing every partition on your phone.
WARNING!!!
This process will wipe your phone completely. Backup your storage before you continue.
I am also not responsible if anything goes wrong.
You can backup apps and data using this app before you unlock the bootloader. No root required.
DO NOT USE TOOLKITS!!!
They have a high probability of something going wrong if you don't know how to use them (which, if you managed to ruin your phone, probably is true).
I don't mean to offend toolkit creators. They did a great job. But don't risk bricking your phone just because you're lazy.
or you will end up in a bootloop, or with a bricked phone, and we don't want that
Let's get started!!
Setting up
For this process, you will need to:
Install adb and fastboot drivers. To do this, use this simple program:
http://forum.xda-developers.com/show....php?t=2588979
For MAC users:
http://forum.xda-developers.com/show....php?t=1917237
*Note: MAC users will have to write "./" before every command in this thread. For example : "./fastboot flash recovery recovery.img"
Linux users should know their stuff
★Extract the archive you downloaded (Use WinRAR). It should look like this:
http://forum.xda-developers.com/show....php?t=2507905
Flashing the factory images
There is more than one way to flash these images. Each give the same results, but the first is for lazy users
Method 1. Easy method.
★Boot it in fastboot by pressing and holding Power Button + Volume Down at the same time.
★Execute the flash-all.bat script (for Windows) or flash-all.sh(for MAC and LINUX) in the folder where you extracted the factory images.
**!!** For MAC: You'll have to edit the flash-all.sh, and add "./" before every fastboot command.
★Wait for everything to flash.
★After everything finished, select "Recovery" using the volume buttons.
★When a small dead Android appears, press Power Button + Volume UP.
★Select "Wipe data/factory data reset"
★Reboot. Your phone should be stock.
Method 2. Long method (Same thing actually, but I'll mention it, just in case)
★Extract the image-hammerhead-krt16m.zip somewhere easy to access (On C:\image-hammerhead-krt16m for example). You will have the following files:
★Boot it in fastboot by pressing and holding Power Button + Volume Down at the same time.
★Open a CMD window.
★Type the following commands, in this order (If you have a different folder, change the path)
Code:
fastboot flash bootloader C:\image-hammerhead-krt16m\bootloader.img
fastboot erase cache
fastboot flash cache C:\androidimage\cache.img
★After everything finished, select "Recovery" using the volume buttons.
★When a small Android appears, press Power Button + Volume UP.
★Select "Wipe data/factory data reset"
★Reboot. Your phone should be stock.
For both methods:
Optional, but necessary for warranty purposes - Locking your bootloader+ Resetting the tamper flag
The Nexus 5 has a thing implemented in the bootloader called a tamper flag. This shows if the bootloader was ever unlocked, kind of like the flash counter with Samsung devices. You can check it out by using this command
Code:
fastboot oem device-info
. If the tamper flag value is "true", then you'll have to reset it. The following steps will reset this flag, and lock your bootloader.
•So, first, go here: http://forum.xda-developers.com/show....php?t=2239421 (Thanks @osm0sis for the wonderful script)
Under "Flashable Zips", you will find the Nexus BootUnlocker script. Download it.
•Put the zip on your internal storage.
•Download the latest TWRP recovery image for the Nexus 5 from here: http://techerrata.com/browse/twrp2/hammerhead. Rename it to TWRP.img.
Now boot it. You do this by booting your phone in fastboot, and typing the following command:
Code:
fastboot boot path\to\TWRP.img
*Replace path\to\TWRP.img with the path to where you placed the TWRP.img. For example: C:\Users\X\Desktop\TWRP.img
TWRP recovery should boot.
•When TWRP finished booting, select "Install", then navigate to the Nexus Bootunlocker zip, select and install it. After it finished, use the back arrow at the bottom of the screen to go back, and reboot.
And now you have a brand new Nexus 5 (software wise, at least)
Video Guides
Thanks @techfanatic9.
For Windows:
For Mac:
Another easy and fast tutorial made by @iTzGavin96
These don't contain the tamper flag reset step. Follow the steps above to reset your tamper flag value to "False" for warranty purposes.
i was wondering when i connect my nexus 5 to the adb it shows null/empty when i type " adb devices" however when i tried "adb devices" when i was in twrp/recovery mode the phone was recognize and my serial number pops up ,,, can i flash factory image if i connect the phone when it was in twrp/recovery mode ?? or should i only flash it when adb recognize my nexus 5 in bootloader mode ??
20th January 2016, 08:46 PM |#2106
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Originally Posted by Soultaker226
i was wondering when i connect my nexus 5 to the adb it shows null/empty when i type " adb devices" however when i tried "adb devices" when i was in twrp/recovery mode the phone was recognize and my serial number pops up ,,, can i flash factory image if i connect the phone when it was in twrp/recovery mode ?? or should i only flash it when adb recognize my nexus 5 in bootloader mode ??
You can only flash the factory images when your phone is in the bootloader.
21st January 2016, 12:22 AM |#2107
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You can only flash stock images with an unlocked bootloader using fastboot commands and with the phone in bootloader mode.
21st January 2016, 05:26 AM |#2108
Developers Relations / Senior Moderator
Montreal
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Quote:
Originally Posted by tedrogers61
What do the version codes mean on the Google Developers Factory Images page here?
https://source.android.com/source/build-numbers.html
Sent from my HTC One M9 using Tapatalk
21st January 2016, 02:48 PM |#2109
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Quote:
Originally Posted by tedrogers61
I don't really know what to suggest from here, but I would root it and perform the Emmc Check Memory next.
Sent from my Nexus 5 using XDA Premium 4 mobile app
hi bro i rooted my n5 and checked memory with Emmc like you suggested me test showed 29.1 GB of space, what to do next ?
22nd January 2016, 01:12 PM |#2110
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How can I root my Nexus 5 device
I have made it several times but when Marshmallow came out 6.0.0 (MRA58K) the SuperSu broke my phone (infinity bootloop) so I've reflashed my phone whithout rooting. I've read that I need to use a different kernel from the original one and then it might work.
So the question is: do I still need a differenet kernel to root my phone 6.0.1 (MMB29S)?
23rd January 2016, 07:51 PM |#2111
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Quote:
Originally Posted by jd1639
Here's what you should do if you want to flash the tamper reset zip file and still keep the stock recovery.
2. Google nexus 5 teamwin and download the twrp image file to your pc, we are not going to install it, only boot into it
3. Rename the twrp file you downloaded to twrp.img. This is for simplicity
5. Open a command window in the same folder as twrp.img is in
6. In that command window type the command, fastboot boot twrp.img. This will boot you into twrp but not install it
7. When you're booted into twrp then install the tamper.zip you downloaded in step 1
Reboot and the tamper flag still be reset and you'll still have the stock recovery on your device.
Sent from my Nexus 9 using XDA Free mobile app
helllo bro, i see yo are good at nexus 5 development. can you help me ? in bootloader my N5 shows D821e 32GB, but in storage only 16 is available. i flashed factory image several times them did #post 2 , but still got 16gb. what can i do to fix this issue ? i tied flashing kit-kat, lollopop and marshmallow but still got 16 GB, than rooted and tried custom roms but still 16
Tags brick, factory, images, nexus 5, root
Guest Quick Reply (no urls or BBcode) Message: | 2019-07-22 06:32:47 | {"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": 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": 0.24939271807670593, "perplexity": 10557.970112478657}, "config": {"markdown_headings": false, "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-2019-30/segments/1563195527531.84/warc/CC-MAIN-20190722051628-20190722073628-00384.warc.gz"} |
https://stacks.math.columbia.edu/tag/03H5 | Lemma 65.4.4. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $f : T \to X$ be a morphism from a scheme to $X$. The following are equivalent
1. $f : T \to X$ is surjective (according to Spaces, Definition 64.5.1), and
2. $|f| : |T| \to |X|$ is surjective.
Proof. Assume (1). Let $x : \mathop{\mathrm{Spec}}(K) \to X$ be a morphism from the spectrum of a field into $X$. By assumption the morphism of schemes $\mathop{\mathrm{Spec}}(K) \times _ X T \to \mathop{\mathrm{Spec}}(K)$ is surjective. Hence there exists a field extension $K'/K$ and a morphism $\mathop{\mathrm{Spec}}(K') \to \mathop{\mathrm{Spec}}(K) \times _ X T$ such that the left square in the diagram
$\xymatrix{ \mathop{\mathrm{Spec}}(K') \ar[r] \ar[d] & \mathop{\mathrm{Spec}}(K) \times _ X T \ar[d] \ar[r] & T \ar[d] \\ \mathop{\mathrm{Spec}}(K) \ar@{=}[r] & \mathop{\mathrm{Spec}}(K) \ar[r]^-x & X }$
is commutative. This shows that $|f| : |T| \to |X|$ is surjective.
Assume (2). Let $Z \to X$ be a morphism where $Z$ is a scheme. We have to show that the morphism of schemes $Z \times _ X T \to T$ is surjective, i.e., that $|Z \times _ X T| \to |Z|$ is surjective. This follows from (2) and Lemma 65.4.3. $\square$
There are also:
• 4 comment(s) on Section 65.4: Points of algebraic spaces
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2023-03-21 23:23:23 | {"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9986251592636108, "perplexity": 148.94198211783134}, "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-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00119.warc.gz"} |
https://math.stackexchange.com/questions/117916/are-3-and-11-the-only-common-prime-factors-in-sum-limits-k-1n-k-for | # Are $3$ and $11$ the only common prime factors in $\sum\limits_{k=1}^N k!$ for $N\geq 10$?
The question was stimulated by this one. Here it comes:
When you look at the sum $$\sum\limits_{k=1}^N k!$$ for $$N\geq 10$$, you'll always find $$3$$ and $$11$$ among the prime factors, due to the fact that $$\sum\limits_{k=1}^{10}k!=3^2\times 11\times 40787.$$ Increasing $$N$$ will give rise to factors $$3$$ resp. $$11$$.
Are $$3$$ and $$11$$ the only common prime factors in $$\sum\limits_{k=1}^N k!$$ for $$N\geq 10$$?
I think, one has to show, that $$\sum\limits_{k=1}^{N}k!$$ has a factor of $$N+1$$, because the upcoming sum will always share the $$N+1$$ factor as well. This happens for $$\underbrace{1!+2!}_{\color{blue}{3}}+\color{blue}{3}! \text{ and } \underbrace{1!+2!+\cdots+10!}_{3^2\times \color{red}{11}\times 40787}+\color{red}{11}!$$
• Let $a_p = \sum_{k=1}^p k!$. If we assume that $a_p \equiv 0 \mod p$ with "probability" $1/p$, then the expected number of times this happens for $p<N$ is $\log \log N$. This quantity is not larger then $3$ until $N$ is about 500,000,000. So the fact that you have only found two examples with a short search does not convince me that there are no more. – David E Speyer Mar 8 '12 at 16:18
• By the way, I just checked up to the 500th prime, 3571, without finding another example. – David E Speyer Mar 8 '12 at 16:20
• Checked for other examples for primes up to 15000000; none found. – Douglas S. Stones Dec 29 '12 at 22:27
• There is really little known about the distribution of factorials modulo a prime $p$. For instance, it is conjectured that the sequence $(n!)$ attains $\approx (1-\frac{1}{e})p$ residues modulo $p$ and it is known unconditionally that it is at least $$\frac{p\log\log p}{\log\log\log p}.$$ However, this does not help for your question. If I should guess an answer, I'd bet (given the "random" behaviour of the primes) that there are infinitely many primes $p$ such that $p\mid 1!+2!+\cdots+(p-1)!$. – Paolo Leonetti Feb 26 '18 at 16:48
• It might be a good idea to make the problem statement unambiguous by explicitly pointing out you're looking for prime factors $p$ shared by all the sums with $N\geq (p-1)$, rather than using $N\geq 10$ (which would make the question trivial). – Peter Košinár Feb 26 '18 at 19:41
As pointed out in the comments, the case is trivial( at least if you know some theorems) if you fix $$n>10$$, instead of $$n>p-1$$ for prime $$p$$.
It follows from Wilson's Theorem, that if you have a multiple of $$p$$ at index $$n= p-2$$ you won't at index $$p-1$$ because it will decrease out of being one for that index. $$p>12$$ implies at least $$1$$ index where it is NOT a multiple if it worked at index $$11$$. That leaves us with $$p<12$$ which would have to be factors of the sum up to $$p-1$$, $$2$$ is out as the sum is odd, $$5$$, needs $$24+1+2+6=33$$ to be a multiple of $$5$$, it isn't. Lastly $$7$$ needs $$1+2+6+24+120+720=873$$ to be a multiple which would force $$33$$ to be a multiple of $$7$$ which it isn't. | 2019-11-15 02:16:21 | {"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": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8334610462188721, "perplexity": 142.42193083585653}, "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-2019-47/segments/1573496668561.61/warc/CC-MAIN-20191115015509-20191115043509-00061.warc.gz"} |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-and-chemical-reactivity-9th-edition/chapter-10-gases-and-their-properties-10-2-gas-laws-the-experimental-basis-review-check-for-section-10-2-page-381/1 | ## Chemistry and Chemical Reactivity (9th Edition)
Since the temperature is constant, we can use Boyle's law: $222\ mL×695\ mmHg=x×333\ mmHg$ $x=463.3\ mL$ | 2018-07-20 20:36:48 | {"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": 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": 0.9637216925621033, "perplexity": 1777.1551392125946}, "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-2018-30/segments/1531676591831.57/warc/CC-MAIN-20180720193850-20180720213850-00528.warc.gz"} |
https://wxpython.org/Phoenix/docs/html/wx.BusyInfo.html | wx.BusyInfo¶
This class makes it easy to tell your user that the program is temporarily busy.
Normally the main thread should always return to the main loop to continue dispatching events as quickly as possible, hence this class shouldn’t be needed. However if the main thread does need to block, this class provides a simple way to at least show this to the user: just create a wx.BusyInfo object on the stack, and within the current scope, a message window will be shown.
For example:
# Normal usage
for i in range(10000):
DoACalculation()
del wait
# It can be used as a context manager too
for i in range(10000):
DoACalculation()
It works by creating a window in the constructor, and deleting it in the destructor.
This window is rather plain by default but can be customized by passing wx.BusyInfo constructor an object of wx.BusyInfoFlags class instead of a simple message. Here is an example from the dialogs sample:
info = wx.BusyInfo(
wx.BusyInfoFlags()
.Parent(self)
.Icon(wx.ArtProvider.GetIcon(wx.ART_PRINT,
wx.ART_OTHER, wx.Size(128, 128)))
.Foreground(wx.WHITE)
.Background(wx.BLACK)
.Transparency(4 * wx.ALPHA_OPAQUE / 5)
)
This shows that separate title and text can be set, and that simple markup ( wx.Control.SetLabelMarkup ) can be used in them, and that it’s also possible to add an icon and customize the colours and transparency of the window.
You may also want to call TheApp.Yield() to refresh the window periodically (in case it had been obscured by other windows, for example) like this:
with wx.WindowDisabler():
for i in range(100000):
DoACalculation()
if not (i % 1000):
wx.GetApp().Yield()
but take care to not cause undesirable reentrancies when doing it (see wx.App.Yield for more details). The simplest way to do it is to use wx.WindowDisabler class as illustrated in the above example.
Note that a wx.BusyInfo is always built with the STAY_ON_TOP window style (see wx.Frame window styles for more info).
Class Hierarchy¶
Inheritance diagram for class BusyInfo:
Methods Summary¶
__init__ General constructor. UpdateLabel Same as UpdateText but doesn’t interpret the string as containing markup. UpdateText Update the information text. __enter__ __exit__
Class API¶
class wx.BusyInfo(object)
Possible constructors:
BusyInfo(flags)
BusyInfo(msg, parent=None)
This class makes it easy to tell your user that the program is temporarily busy.
Methods¶
__init__(self, *args, **kw)
__init__ (self, flags)
General constructor.
This constructor allows specifying all supported attributes by calling the appropriate methods on wx.BusyInfoFlags object passed to it as parameter. All of them are optional but usually at least the message should be specified.
Parameters
flags (wx.BusyInfoFlags) –
New in version 4.1/wxWidgets-3.1.0.
__init__ (self, msg, parent=None)
Simple constructor specifying only the message and the parent.
This constructs a busy info window as child of parent and displays msg in it. It is exactly equivalent to using
wait = wx.BusyInfo(wx.BusyInfoFlags().Parent(parent).Label(message))
Parameters
Note
If parent is not None you must ensure that it is not closed while the busy info is shown.
UpdateLabel(self, str)
Same as UpdateText but doesn’t interpret the string as containing markup.
Parameters
str (string) –
New in version 4.1/wxWidgets-3.1.3.
UpdateText(self, str)
Update the information text.
The text string may contain markup as described in wx.Control.SetLabelMarkup .
Parameters
str (string) –
New in version 4.1/wxWidgets-3.1.3.
__enter__(self)
__exit__(self, exc_type, exc_val, exc_tb) | 2020-08-12 16:09:30 | {"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": 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": 0.17870377004146576, "perplexity": 4845.3133317871925}, "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-2020-34/segments/1596439738905.62/warc/CC-MAIN-20200812141756-20200812171756-00217.warc.gz"} |
https://www.dgnpropertysolutions.com/g12ml5su/phase-change-diagram-30aeb0 | # phase change diagram
Try refreshing the page, or contact customer support. Condensation is the phase change as a substance changes from a gas to a liquid. The cooling effect can be evident when you leave a swimming pool or a shower. A small amount has melted. What is the relationship between the intermolecular forces in a liquid and its vapor pressure? As the size of molecule increases from methanol to butanol, dispersion forces increase, which means that the vapor pressures decrease as observed: Pmethanol > Pethanol > Ppropanol > Pbutanol. What is the vapor pressure of acetone at 25.0 °C? Phase diagrams demonstrate the effects of changes in pressure and temperature on the state of matter. Molecules with weak attractive forces form crystals with low melting points. Heat is added to boiling water. Figure 7. Converting a solid into a liquid requires that these attractions be only partially overcome; transition to the gaseous state requires that they be completely overcome. Only the amount of water existing as ice changes until the ice disappears. Once snow hits the ground, it stays there, whether it is -50 degrees F outside or all the way up to 32 degrees F. The snow can absorb energy all the way up until it hits its melting point of 32 degrees F. This is the diagonal line at stage I on the graph. Sublimation is the phase change as a substance changes from a solid to a gas without passing through the intermediate state of a liquid. //-->, Matter Terminology Classifying Matter Phases of Matter Physical and Chemical Changes Separation Techniques Vapor Pressure Phase Changes Heating Curve Phase Diagrams. Visit the CLEP Natural Sciences: Study Guide & Test Prep page to learn more. We can see the amount of liquid in an open container decrease and we can smell the vapor of some liquids. At this point, the water starts to boil and turn into steam, or water vapor. Is condensation a chemical or physical change? Phase transitions are processes that convert matter from one physical state into another. The ice melts without changing its temperature. If 1.80 x 10^5 J of energy is supplied to a flask of liquid oxygen at -183 degree Celsius, how much oxygen can evaporate? Relatively strong intermolecular attractive forces will serve to impede vaporization as well as favoring “recapture” of gas-phase molecules when they collide with the liquid surface, resulting in a relatively low vapor pressure. Explain why the temperature of the boiling water does not change. | {{course.flashcardSetCount}} For benzene (C6H6), the normal boiling point is 80.1 °C and the enthalpy of vaporization is 30.8 kJ/mol. The line that separates solid and liquids bends left. She has taught science at the high school and college levels. A value of −8.4 kJ/mol would indicate a release of energy upon vaporization, which is clearly implausible. IF the solid phase is less dense than the liquid phase. The thermal energy (heat) needed to evaporate the liquid is removed from the skin. What is the boiling point of benzene in Denver, where atmospheric pressure = 83.4 kPa? The line between the liquid and gas phases is a curve of all the boiling points of the substance. (d) Only after all the ice has melted does the heat absorbed cause the temperature to increase to 22.2 °C. Energy is either being used to break or form bonds and that is why the graph is flat at that point. boiling point: temperature at which the vapor pressure of a liquid equals the pressure of the gas above it, Clausius-Clapeyron equation: mathematical relationship between the temperature, vapor pressure, and enthalpy of vaporization for a substance, condensation: change from a gaseous to a liquid state, deposition: change from a gaseous state directly to a solid state, dynamic equilibrium: state of a system in which reciprocal processes are occurring at equal rates, freezing: change from a liquid state to a solid state, freezing point: temperature at which the solid and liquid phases of a substance are in equilibrium; see also melting point, melting: change from a solid state to a liquid state, melting point: temperature at which the solid and liquid phases of a substance are in equilibrium; see also freezing point, normal boiling point: temperature at which a liquid’s vapor pressure equals 1 atm (760 torr), sublimation: change from solid state directly to gaseous state, vapor pressure: (also, equilibrium vapor pressure) pressure exerted by a vapor in equilibrium with a solid or a liquid at a given temperature, vaporization: change from liquid state to gaseous state, Define phase transitions and phase transition temperatures, Explain the relation between phase transition temperatures and intermolecular attractive forces, Describe the processes represented by typical heating and cooling curves, and compute heat flows and enthalpy changes accompanying these processes. Heat to needed to increase the temperature of the steam: ΔH3 = mCsΔT = (422 g)(2.09 J/g °C)(150 − 100) = 44,100 J. Isooctane (2,2,4-trimethylpentane) has an octane rating of 100. Thus, at about 90 °C, the vapor pressure of water will equal the atmospheric pressure in Leadville, and water will boil. For example, the vaporization of water at standard temperature is represented by: ${\text{H}}_{2}\text{O(}l\text{)}\longrightarrow {\text{H}}_{2}\text{O(}g\text{)}\Delta {H}_{\text{vap}}=\text{44.01 kJ/mol}$. Using these equations with the appropriate values for specific heat of ice, water, and steam, and enthalpies of fusion and vaporization, we have: $\begin{array}{rll}{q}_{\text{total}}&=&{\left(m\cdot c\cdot \Delta T\right)}_{\text{ice}}+n\cdot \Delta {H}_{\text{fus}}+{\left(m\cdot c\cdot \Delta T\right)}_{\text{water}}+n\cdot \Delta {H}_{\text{vap}}+{\left(m\cdot c\cdot \Delta T\right)}_{\text{steam}}\\ &=&\left(\text{135 g}\cdot \text{2.09 J/g}\cdot ^{\circ}\text{C}\cdot 15^{\circ}\text{C}\right)+\left(135\cdot \frac{\text{1 mol}}{18.02\text{g}}\cdot \text{6.01 kJ/mol}\right) +\left(\text{135 g}\cdot \text{4.18 J/g}\cdot ^{\circ}\text{C}\cdot 100^{\circ}\text{C}\right)\\ & &+\left(\text{135 g}\cdot \frac{\text{1 mol}}{18.02\text{g}}\cdot \text{40.67 kJ/mol}\right) +\left(\text{135 g}\cdot \text{1.84 J/g}\cdot ^{\circ}\text{C}\cdot 20^{\circ}\text{C}\right)\\ &=&\text{4230 J}+\text{45.0 kJ}+\text{56,500 J}+\text{305 kJ}+\text{4970 J}\end{array}$. Phase change is often shown in a diagram like the one below: When a substance is in a solid state, it can absorb a lot of energy in the form of heat until it hits its melting point. Which contains the compounds listed correctly in order of increasing boiling points? Like vaporization, the process of sublimation requires an input of energy to overcome intermolecular attractions. flashcard set{{course.flashcardSetCoun > 1 ? We start with the known volume of sweat (approximated as just water) and use the given information to convert to the amount of heat needed: $1.5\text{L}\times \frac{1000\cancel{\text{g}}}{\text{1 L}}\times \frac{1\cancel{\text{mol}}}{18\cancel{\text{g}}}\times \frac{43.46\text{kJ}}{1\cancel{\text{mol}}}=3.6\times {10}^{3}\text{kJ}$. At 20.0 °C, the vapor pressure of ethanol is 5.95 kPa, and at 63.5 °C, its vapor pressure is 53.3 kPa. 22. Its overall IMFs are the largest of these four substances, which means its vaporization rate will be the slowest and, consequently, its vapor pressure the lowest. For example, the sublimation of carbon dioxide is represented by: ${\text{CO}}_{2}\left(s\right)\longrightarrow {\text{CO}}_{2}\text{(}g\text{)}\Delta {H}_{\text{sub}}=\text{26.1 kJ/mol}$. There are six distinct changes of phase which happens to different substances at different temperatures. Freezing is the phase change as a substance changes from a liquid to a solid. Heat required to melt this amount of TiCl4 is nΔHfusion = 1.385 mol $\times$ 9.37 kJ/mol = 13.0kJ. Converting the quantities in J to kJ permits them to be summed, yielding the total heat required: $=4.23\text{kJ}+\text{45.0 kJ}+\text{56.5 kJ}+\text{305 kJ}+\text{4.97 kJ}=\text{416 kJ}$.
; | 2023-03-22 18:32:50 | {"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": 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": 0.5724883675575256, "perplexity": 853.5008357465734}, "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/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00496.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/jgm.2022002 | Article Contents
Article Contents
# Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles
• * Corresponding author: Brennan McCann
The first author is supported by FIRST and GAANN
• Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid body dynamics in the geometric mechanics framework and a novel development of U-K formulation for use on nonlinear manifolds, namely the special Euclidean group ${\mathsf{SE}(3)}$ and its second order tangent bundle ${\mathsf{T}^2\mathsf{SE}(3)}$, is proposed in addition to the formulation development on Euclidean spaces. Then, a Morse-Lyapunov based tracking controller using backstepping is applied to capture disturbed initial conditions that the U-K formulation cannot account for. This theoretical development is then applied to fully-constrained and underconstrained scenarios of rigid-body spacecraft motion in a lunar orbit, and the translational and rotational motions of the spacecraft and the control inputs obtained using the proposed methodologies to achieve and maintain those constrained motions are studied.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
• Figure 1. Inertial $\mathcal N$, perifocal $\mathcal P$, and body $\mathcal B$ reference frames
Figure 2. Fully-constrained translational motion comparison between formulation on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 3. Fully-constrained rotational motion comparison between formulation on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 4. Fully-constrained control input comparison between formulations on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 5. Translational motion in underconstrained (UC) case versus that in the fully-constrained (FC) case
Figure 6. Rotational motion in underconstrained (UC) case versus that in the fully-constrained (FC) case
Figure 7. Control inputs in underconstrained (UC) case versus those in the fully-constrained (FC) case
Figure 8. Underconstrained translational motion comparison between formulation on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 9. Underconstrained rotational motion comparison between formulation on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 10. Underconstrained control inputs comparison between formulation on $\mathbb{R}^{6}$ and ${\mathsf{T}^2\mathsf{SE}(3)}$
Figure 11. Position response using U-K and M-L control with disturbed ICs
Figure 12. Velocity response using U-K and M-L control with disturbed ICs
Figure 13. Attitude response using U-K and M-L control with disturbed ICs
Figure 14. Angular velocity response using U-K and M-L control with disturbed ICs
Figure 15. Total control input using U-K and M-L control with disturbed ICs
Figures(15) | 2023-04-01 17:46:17 | {"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.46176743507385254, "perplexity": 3441.519741314524}, "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/1679296950110.72/warc/CC-MAIN-20230401160259-20230401190259-00370.warc.gz"} |
http://www.slanehosiery.com/leewadee-thai-lri/lithium-nitride-ion-10cf93 | ## lithium nitride ion
Lithium nitride is of potential technological interest as a superionic conductor [1, 2], and has some theoretical novelty as the only fully ionic compound thought to contain the N 3- species I-3, 4]. Since this compound is neutral, the charges must balance. Start by writing the metal ion with its charge, followed by the nonmetal ion with its charge. The superionic conductors lithium nitride and lithium phosphide and the semi-metallic conductor lithium arsenide were synthesized through elemental reactions of lithium melt with nitrogen gas and phosphorus or arsenic powders. The nitride ion, N 3 ... Only one alkali metal nitride is stable, the purple-reddish lithium nitride (Li 3 N), which forms when lithium burns in an atmosphere of N 2. Lithium-ion diffusion is enhanced compared to the bulk compound, yielding materials with exceptional ionic mobility. c. Show that the charges on the ions add up to zero. It is an extremely small(? Lithium also reacts with nitrogen, N 2, to form lithium nitride, Li 3 N. None of the other Gruop 1 elements do anything similar, but magnesium (Gruop 2) similarly forms a nitride. What is the charge on the lithium ion? Lithium ion conductivity in lithium nitride Boukamp, B. It is a fast ion conductor and it has also been studied as an anode material for batteries. The expectation is that as lithium-ion battery demand rises, so will lithium demand. The nitride ion, N3−. Li3N; the lithium ion has a charge of +1 (Li+) while the nitride ion has a charge of -3 (N3-) Advanced Search | Structure Search. The compound nickel (II) nitride consists of a nickel ion with a +2 charge and a nitride ion with a -3 charge. The nitrides of the alkaline earth metals have the formula M 3 N 2 are however numerous. for a compound lithium nitride l i three n because of the zero charge rule and because we know lithium is a group one a element, it has a one plus charge, and nitrogen is a group five a element, so it has a three minus charge. Write the formulas for aluminum nitride and lithium oxide. Start from the anion, which is N3- (nitride). Search term: "lithium (S)-N-(a-methylbenzyl)amide" Compare Products: Select up to 4 products. Lithium nitride reacts violently with water to produce ammonia: Li 3 N + 3 H 2 O → 3 LiOH + NH 3 You have to work this problem backwards. CAS Number: 26134-62-3. We are committed to bringing you Greener Alternative Products, which adhere to one or more of The 12 Principles of Greener Chemistry. A.; Huggins, R. A. Abstract. Then we we would be able to correctly predict the chemical formula requires three. Lithium nitride contains the #N^(3-)# ion. Lithium nitride, Li3N, was originally proposed for use as an electrolyte in all-solid-state Li 34 + ion 35 batteries given its exceptional ionic conductivity at room temperature (ca. *Please select more than one item to compare. Both one- and two-dimensional nanostructures of lithium nitride, Li3N, can be grown despite the absence of an equivalent van der Waals gap. However, the reaction mechanism of this material has not been thoroughly investigated in the literature. Lithium nitride (Li 3 N) is a solid-state ionic conductor with an ionic conductivity of ~6 x 10 −3 Scm −1 and with a high Young′s modulus. Lithium nitride has the formula $\mathrm{Li}_{3} \mathrm{N}$ a. As a powerful candidate, Li metal batteries are in the renaissance. The ionic conductivity of polycrystalline lithium nitride has been determined using ac techniques and complex plane analysis. And lithium is one of the few materials that will directly fix dinitrogen: And lithium is one of the few materials that will directly fix dinitrogen: #3Li + 1/2N_2 rarr Li_3N# In addition, their cathode materials contain transition-metal atoms that are toxic and pose environmental risks. Sodium nitride has been generated, but remains a laboratory curiosity. Li3N i puit Lithium Nitride OK FeS i put ion Sulfide iron(II) sulfide KCI i put Potassium Chloride OK if you intend KCl CoSO4 i put Cobalt Sulfide cobalt(II) sulfate SrBr2 i put Strotium bromide OK NCI3 i put Nitrogen trichlorideOK if you intend this to be NCl3. Lithium-ion diffusion is enhanced compared to the bulk compound, yielding materials with exceptional ionic mobility. It can generally be prepared by placing Li metal under nitrogen environment. Indeed, for 36 several decades it remained the highest conducting crystalline Li+ ion conductor at ambient Solid ionic conductors are a treasure trove for modern technology. Lithium nitride is prepared by direct combination of elemental lithium with nitrogen gas: [2] 6 Li + N 2 → 2 Li 3 N. Instead of burning lithium metal in an atmosphere of nitrogen, a solution of lithium in liquid sodium metal can be treated with N 2. The nitride ion's formula is N 3-.. Nitrogen atoms need three electrons to fill its outer valence shell, which is 2p. High-Modulus Hexagonal Boron Nitride Nanoplatelet Gel Electrolytes for Solid-State Rechargeable Lithium-Ion Batteries. 6Li(s) + N 2 (g) → 2Li 3 N(s) Reaction of lithium with water . It is difficult to achieve higher energy density with the existing system of lithium (Li)-ion batteries. This anion is a nitrogen atom with THREE extra electrons. Lithium (Li) appears to be the only alkali metal able to form a nitride, although all the alkaline-earth metals form nitrides with the formula M 3 N 2.These compounds, which can be considered to consist of metal cations and N 3− anions, undergo hydrolysis (reaction with water) to produce ammonia and the metal hydroxide. b. Get the detailed answer: Lithium nitride, an ionic compound containing the Li+ and N3- ions, is prepared by the reaction of lithium metal and nitrogen gas. That is not a small i as in eye. Lithium nitride is a well-known positive pre-lithiation additive that can be used to compensate for the irreversible lithium loss that occurs on the negative side during the first charge, thereby increasing the specific energy of the energy storage device. These two factors may affect the price. Ionic nitrides. Additional information on Lithium Nitride. 4 matches found for lithium (S)-N-(a-methylbenzyl)amide . The flower-shaped lithium nitride layer, which fully covers the anode, has a capacity retention of more than 96% after 100 cycles in a full cell with lithium cobalt oxide as the cathode. d. What is the total number of valence electrons in all the atoms in $\mathrm{Li}_{3} \mathrm{N} ?$ Materials Science and Engineering; Research output: Contribution to journal › Article. Example $$\PageIndex{1}$$: Aluminum Nitride and Lithium Oxide. Unfortunately, the uncontrolled growth process of Li dendrites has limited their actual application. Tin nitride thin films have been reported as promising negative electrode materials for lithium-ion solid-state microbatteries. A high mobility of the lithium ion was found in this class of compounds. Lithium ion conductivity in lithium nitride @inproceedings{Boukamp1976LithiumIC, title={Lithium ion conductivity in lithium nitride}, author={B. Boukamp and R. Huggins}, year={1976} } B. Boukamp, R. Huggins; Published 1976; Physics; Abstract The ionic conductivity of polycrystalline lithium nitride has been determined using ac techniques and complex plane analysis. Please use the form above to make an enquiry about Lithium Nitride remembering to include the information regarding purity and the quantity you require. ), highly charged ion; negative charge density of [N]3- is extremely high. Both one- and two-dimensional nanostructures of lithium nitride, Li3N, can be grown despite the absence of an equivalent van der Waals gap. Lithium nitride. Due to its ionic charge, the ion is rarely found out of solution in nature. 3 Scopus citations. The term nitride ion refers to any chemical compound containing nitrogen ions that have a negative-three oxidation state. Layered Lithium Iron Nitride: A Promising Anode Material for Li-Ion Batteries Jesse L. C. Rowsell, Vale´rie Pralong, and Linda F. Nazar* UniVersity of Waterloo, Department of Chemistry Waterloo, Ontario, Canada N2L 3G1 ReceiVed May 24, 2001 Rechargeable lithium-ion cells are currently considered the most promising energy storage systems. Lithium-ion batteries are currently used as high-energy-density storage materials, but they suffer from high costs, safety concerns, and poor specific capacities. ABSCO Limited is a leading supplier of Lithium Nitride. Problem: Lithium nitride, Li3N is an interesting salt. Lithium metals reacts slowly with water to form a colourless solution of lithium hydroxide (LiOH) and hydrogen gas (H 2). Introduction Lithium ion batteries (LIBs), with high energy density, long cyclic life and environmental compatibility, have been recognized as the most promising energy storage devices not only used in portable electronics but also in clean and renewable energy [1-7]. Examples of such compounds are titanium nitride, calcium nitride, boron nitride and silicon nitride. 1 Product Result | Match Criteria: Description Linear Formula: Li 3 N. Molecular Weight: 34.83. 10-3 S cm-1)1. Woo Jin Hyun , Ana C.M. Keywords: Reduced graphene oxide; Boron nitride; Composite film; Anode; Lithium-ion batteries 1. The ionic conductivity is quite high, so that this material may be an interesting lithium-conducting solid electrolyte. What is the chemical formula of lithium nitride? Because the overall compound must be electrically neutral, decide how many of each ion is needed in order for the positive and negative charges to cancel each other out. These compounds are hard and brittle and have a dark brown color. Examples include Be 3 N 2, Mg 3 N 2, Ca 3 N 2, and Sr 3 N 2. What is the charge on the nitrogen ion? De Moraes, Jin Myoung Lim, Julia R. Downing, Kyu Young Park, Mark Tian Zhi Tan, Mark C. Hersam * * Corresponding author for this work.
lithium nitride ion 2021 | 2021-06-14 00:25:45 | {"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": 0.46824702620506287, "perplexity": 5634.989742508756}, "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/1623487611089.19/warc/CC-MAIN-20210613222907-20210614012907-00508.warc.gz"} |
http://dekalogblog.blogspot.com/2012/07/possible-brute-force-similarity.html | ## Saturday, 7 July 2012
### A Possible Brute Force Similarity Classifier in Octave Code
As part of the development of my neural net classifier it has been necessary to use training data and as usual I have been using my model market types. To increase the amount of such training data I have extended the range of the data to include a change in market type half way through the cycle of one measured cyclic period. I have done this in increments of 1 degree from 1 degree to 360 degrees of a sine wave, for periods 15 to 50, for all possible combinations of market type, for a total database of 324,000 possible market model patterns. However, it struck me after reading this pdf that I could use this database as the basis of what is called in the pdf a "brute force similarity search" classifier. Below is my proof of concept Octave code implementation of such a classifier,
% first, training data "training_data.mat" should be loaded in command line
clear -exclusive X y % clear everything except y and X, previously loaded from the command line
lookup_value = input( 'Enter a number from 1 to 324,000 to choose a lookup candidate row from X: ' ) ;
fprintf( 'Based on this choice the market type to look up is :- ' ) ;
y( lookup_value , 1 )
tic() ;
% index into training set based on period measurement
[i_X j_X] = find( X(:,1) == X( lookup_value , 1 ) ) ;
% keep a record of all i_X indexes
all_i_X = i_X ;
% extract the relevant part of X using above index
X_look_up_matrix = X( [i_X] , 4:54 ) ;
% and same for market labels vector y
y_look_up_vector = y( [i_X] , 1 ) ;
% find pattern in X_look_up_matrix that minimises Euclidean distance between itself and the training example randomly taken from X
[ euc_dist_min i_euc_dist_min ] = min( sum( ( repmat( X(lookup_value,4:54), size(X_look_up_matrix,1), 1) .- X_look_up_matrix ) .^ 2.0 , 2 , 'extra' ) ) ;
fprintf( 'and the algo returns a market type of :- ' ) ;
% take this minimum distance vector index to get predicted market type
y_look_up_vector( i_euc_dist_min , 1 )
fprintf( '\nwith a calculated Euclidean distance of :- ' ) ;
double(euc_dist_min)
fprintf( 'which ideally should be 0.0 on this X test set.\n' ) ;
fprintf( '\nOriginal lookup row check.\n' ) ;
original_i_X_check = all_i_X( i_euc_dist_min , 1 )
fprintf( 'which ideally should be the same as row choice entered.\n' ) ;
fprintf( '\nTime for algo to run.\n' ) ;
toc() ;
where X is the database already mentioned and y is a vector containing the market type labels. Typical terminal output of this code is
octave:1> bf_pattern_recognition
Enter a number from 1 to 324,000 to choose a lookup candidate row from X: 100235
Based on this choice the market type to look up is :- ans = 3
and the algo returns a market type of :- ans = 3
with a calculated Euclidean distance of :- ans = 0
which ideally should be 0.0 on this X test set.
Original lookup row check.
original_i_X_check = 100235
which ideally should be the same as row choice entered.
Time for algo to run.
Elapsed time is 0.1130519 seconds.
octave:2>
Of course it obtains 100 % accuracy on the test set X because the original choice of pattern to be matched comes from X so there is always an exact match to be found. The important thing is that this is a workable algorithm which, making allowances for all the print statements included in the above code, runs in hundredths of a second.
This speed, despite having such a large database to search through, is achieved by indexing into the database by the measured period of the pattern to be matched, which is the first entry on each line. This reduces the search base down to a more manageable 9000 row matrix, and then one line of vectorised code is used to perform the actual Euclidean distance search and classification.
Another possible advantage of this approach on real market data is that, having hopefully accurately classified the data, the matched pattern in the database can be extrapolated under the assumption that the market model will persist for the next 5 to 10 bars, to make a prediction of near future prices. I shall certainly be doing more work will this classifying algorithm! | 2017-11-22 05:33:59 | {"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": 0.4980684518814087, "perplexity": 2406.3211341341853}, "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-2017-47/segments/1510934806465.90/warc/CC-MAIN-20171122050455-20171122070455-00641.warc.gz"} |
http://www.journaltocs.ac.uk/index.php?action=browse&subAction=pub&publisherID=250&journalID=24533&pageb=1&userQueryID=&sort=&local_page=&sorType=&sorCol= | for Journals by Title or ISSN for Articles by Keywords help
Publisher: Cambridge University Press (Total: 367 journals)
Bulletin of Symbolic Logic [SJR: 1.405] [H-I: 26] [2 followers] Follow Subscription journal ISSN (Print) 1079-8986 - ISSN (Online) 1943-5894 Published by Cambridge University Press [367 journals]
• BSL volume 24 issue 1 Cover and Front matter
• PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.17
Issue No: Vol. 24, No. 1 (2018)
• BSL volume 24 issue 1 Cover and Back matter
• PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.18
Issue No: Vol. 24, No. 1 (2018)
• POLYMORPHISM AND THE OBSTINATE CIRCULARITY OF SECOND ORDER LOGIC: A
VICTIMS’ TALE
• Authors: PAOLO PISTONE
Pages: 1 - 52
Abstract: The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze (shown inconsistent by Russell’s paradox) and the one given by Martin-Löf for the intuitionistic type theory with a type of all types (shown inconsistent by Girard’s paradox).The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast (and largely unexplored) domain for foundational research.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2017.43
Issue No: Vol. 24, No. 1 (2018)
• A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES
• Authors: ROD DOWNEY; NOAM GREENBERG
Pages: 53 - 89
Abstract: We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of ${\rm{\Delta }}_2^0$ functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2017.41
Issue No: Vol. 24, No. 1 (2018)
• A CONSTRUCTIVE EXAMINATION OF A RUSSELL-STYLE RAMIFIED TYPE THEORY
• Authors: ERIK PALMGREN
Pages: 90 - 106
Abstract: In this article we examine the natural interpretation of a ramified type hierarchy into Martin-Löf type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of Russell’s reducibility axiom are valid, namely functional reducibility. This is sufficient to make the type hierarchy usable for development of constructive mathematical analysis in the style of Bishop. We present a ramified type theory suitable for this purpose. One may regard the results of this article as an alternative solution to the problem of the proliferation of levels of real numbers in Russell’s theory, which avoids impredicativity, but instead imposes constructive logic. The intuitionistic ramified type theory introduced here also suggests that there is a natural associated notion of predicative elementary topos.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.4
Issue No: Vol. 24, No. 1 (2018)
• Flag+algebras.+Journal+of+Symbolic+Logic,+vol.+72+(2007),+no.+4,+pp.+1239–1282.&rft.title=Bulletin+of+Symbolic+Logic&rft.issn=1079-8986&rft.date=2018&rft.volume=24&rft.spage=107&rft.epage=108&rft.aulast=Cummings&rft.aufirst=James&rft.au=James+Cummings&rft_id=info:doi/10.1017/bsl.2018.11">Alexander Razborov, Flag algebras. Journal of Symbolic Logic, vol. 72
(2007), no. 4, pp. 1239–1282.
• Authors: James Cummings
Pages: 107 - 108
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.11
Issue No: Vol. 24, No. 1 (2018)
• 2016–17 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC Hyatt
Regency Atlanta and Marriott Atlanta Marquis Atlanta, GA, USA January
6–7, 2017
• Pages: 109 - 118
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.9
Issue No: Vol. 24, No. 1 (2018)
• 2017 NORTH AMERICAN ANNUAL MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC
Boise State University Boise, ID, USA March 20–23, 2017
• Pages: 119 - 140
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.8
Issue No: Vol. 24, No. 1 (2018)
• Notices
• Pages: 141 - 146
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.16
Issue No: Vol. 24, No. 1 (2018)
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327 | 2018-06-18 13:26:48 | {"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": 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": 0.38224801421165466, "perplexity": 4487.822837150991}, "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-2018-26/segments/1529267860557.7/warc/CC-MAIN-20180618125242-20180618145242-00329.warc.gz"} |
https://www.tutorialspoint.com/program-to-convert-gray-code-for-a-given-number-in-python | # Program to convert gray code for a given number in python
PythonServer Side ProgrammingProgramming
Suppose we have a number n, we have to find the gray code for that given number (in other words nth gray code). As we know the gray code is a way of ordering binary numbers such that each consecutive number's values differ by exactly one bit. Some gray codes are: [0, 1, 11, 10, 110, 111, and so on]
So, if the input is like n = 12, then the output will be 10 as the 12 is (1100) in binary, corresponding gray code will be (1010) whose decimal equivalent is 10.
To solve this, we will follow these steps:
• Define a function solve() . This will take n
• if n is same as 0, then
• return 0
• x := 1
• while x * 2 <= n, do
• x := x * 2
• return x + solve(2 * x - n - 1)
Let us see the following implementation to get better understanding:
## Example
Live Demo
class Solution:
def solve(self, n):
if n == 0:
return 0
x = 1
while x * 2 <= n:
x *= 2
return x + self.solve(2 * x - n - 1)
ob = Solution()
n = 12
print(ob.solve(n))
## Input
12
## Output
10
Updated on 26-Nov-2020 06:59:12 | 2022-07-05 18:37:46 | {"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": 0.37704530358314514, "perplexity": 1730.8201921043863}, "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-2022-27/segments/1656104597905.85/warc/CC-MAIN-20220705174927-20220705204927-00639.warc.gz"} |
https://socratic.org/questions/how-do-you-graph-y-2x-1-using-intercepts | # How do you graph y=2x+1 using intercepts?
##### 1 Answer
Aug 24, 2017
The intercepts of the graph will be (0, ?) and (?,0).
#### Explanation:
First, let y = 0 and solve for x: $0 = 2 x + 1$ so $- 1 = 2 x$
therefore $- \frac{1}{2} = x$. Your x-intercept is ($- \frac{1}{2} , 0$).
Find the y-intercept by substituting x = 0: $y = 2 \cdot 0 + 1$
so y = 1. Your y-intercept will be (0,1).
Plot these points and make your graph: (see below) | 2021-12-07 13:24:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.6336366534233093, "perplexity": 2017.3555320447933}, "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-2021-49/segments/1637964363376.49/warc/CC-MAIN-20211207105847-20211207135847-00202.warc.gz"} |
https://mathinfocusanswerkey.com/math-in-focus-grade-7-chapter-8-lesson-8-5-answer-key/ | # Math in Focus Grade 7 Chapter 8 Lesson 8.5 Answer Key Real-World Problems: Composite Solids
This handy Math in Focus Grade 7 Workbook Answer Key Chapter 8 Lesson 8.5 Real-World Problems: Composite Solids detailed solutions for the textbook questions.
## Math in Focus Grade 7 Course 2 B Chapter 8 Lesson 8.5 Answer Key Real-World Problems: Composite Solids
### Math in Focus Grade 7 Chapter 8 Lesson 8.5 Guided Practice Answer Key
Solve.
Question 1.
A composite solid is made up of a cone and a cylinder. The slant height of the cone is 25 centimeters. The height of the cylinder is 15 centimeters and its radius is 12 centimeters. The height of the solid is 37 centimeters. Use 3.14 as an approximation for π.
a) Find the volume of the composite solid to the nearest cubic centimeter.
Volume of the cylinder:
πr2h = Use the formula for volume of a cylinder.
= cm3 Evaluate .
Volume of the cone:
Height of cone =
= cm
$$\frac{1}{3}$$ πr2h = $$\frac{1}{3}$$ ∙ Use the formula for the volume of a cone.
= cm3 Multiply.
Volume of the composite solid:
+ = Add the volumes of the cylinder and the cone.
cm3 Multiply and round.
The volume of the composite solid is about cubic centimeters.
We are given:
l = 25
hcylinder = 15
H = 37
r = 12
Use the formula for the volume of a cylinder:
Vcylinder = πr2hcylinder
= π · 122 · 15
Evaluate:
= 2,160π cm3
The height of the cone:
hcone = H – hcylinder
= 37 – 15
= 22 cm
Use the formula for the volume of a cone:
Vcone = $$\frac{1}{3}$$πr2hcone
= $$\frac{1}{3}$$ · π · 122 · 22
Multiply:
= 1,056π cm3
Find the volume of the composite solid by adding the volumes of the cylinder and the cone:
V = Vcylinder + Vcone
= 2,160π + 1,056π
= 3,216π cm3
Multiply and round:
≈ 10,098 cm3
b) Find the surface area of the composite solid to the nearest square centimeter.
The surface area of the composite solid is about square centimeters.
Answer: The surface area of the composite solid is about 2,525 cm2.
Use the formuLas for the surface areas:
S = πrl + 2πrhcylinder + πr2
Substitute for r, l, hcylinder
= π · 12 · 25 + 2π · 12 · 15 + π · 122
Evaluate each term:
= 300π + 360π + 144π
= 804π
Multiply and round:
≈ 804 · 3.14 ≈ 2,525 cm2
Question 2.
A birdhouse looks like a cube with a square pyramid on top. As shown, the birdhouse has a circular entrance with a diameter of 4 inches. Find the exterior surface area of the birdhouse.
Answer: The exterior surface area of the birdhouse is 647.4 in2
Determine the Lateral surface area of the pyramid:
S1 = 4 · $$\frac{1}{2}$$ · 10 · 13 = 260 in2
Determine the radius of the entrance:
r = $$\frac{4}{2}$$ = 2
Determine the lateral surface area of the house:
S2 = 4 · 10 · 10 – π · 22 ≈ 387.4 in2
Compute the exterior surface area of the house:
S = S1 + S2 = 260 + 387.4 = 647.4 in2
= 647.4 in2
Question 3.
The solid shown is a cylinder with a cone-shaped hole. The diameter of the cylinder is 22 centimeters. Its height is 15 centimeters. The radius of the cone-shaped hole is 7 centimeters and the height is 10 centimeters. Find the volume of the solid. Use 3.14 as an approximation for π. Round your answer to the nearest cubic centimeter.
Answer: The volume of the solid is 5. 187 cm3
Determine the radius R of the cylinder:
R = $$\frac{22}{2}$$ = 11 cm
Determine the volume of the cylinder
Vcylinder = πR2h = π · 112 · 15 = 1, 815π cm2
Determine the volume of the cone:
Vcone = $$\frac{1}{3}$$πR2h = $$\frac{1}{3}$$ · π · 72 · 10 ≈ 163π cm3
Determine the volume of the solid:
V = Vcylinder – Vcone
= 1,815π – 163π
= 1,652π
≈ 3.14 · 1,652
≈ 5. 187 cm3
### Math in Focus Course 2B Practice 8.5 Answer Key
For this practice, you may use a calculator and use 3.14 as an approximation for π. Round your answers to the nearest tenth when you can.
Solve.
Question 1.
Jack has a cylindrical block that has a radius of 0.6 cm and is 22 centimeters long. He puts together 8 such blocks to form the composite solid shown. What is the volume of the composite solid?
Answer: The volume of the composite solid is 199 cm3
We are given the cylinder:
r = 0.6
h = 22
Determine the volume of one cylinder:
Vcylinder = πr2h ≈ 3.14 · 0.62 · 22
≈ 24.87 cm3
Determine the volume of the composite solid:
Vsolid = 8Vcylinder = 8 · 24.87 ≈ 199 cm3
Question 2.
The trophy for a basketball tournament is made up of a miniature basketball attached to a rectangular prism. The radius of the basketball is 5 centimeters. The prism measures 8 centimeters by 5 centimeters by 15 centimeters. What is the volume of the trophy to the nearest cubic centimeter?
Answer: The volume of the trophy is 1,123 cm3
We are given:
r = 5
l = 8
w = 5
h = 15
Determine the volume of the sphere:
Vsphere = $$\frac{4}{3}$$πr3
≈ $$\frac{4}{3}$$ · 3.14 · 53
≈ 523 cm3
Determine the volume of the prism:
Vprism = lwh = 8 · 5 · 15 = 600 cm3
Determine the volume of the trophy:
Vtrophy = Vsphere + Vprism
= 523 + 600
= 1,123 cm3
Question 3.
a) What is the volume of the necklace?
Answer: The volume of the necklace is 107, 178.7 mm3
We are given the sphere:
r = 8
Determine the volume of a spherical bead:
Vbead = $$\frac{4}{3}$$πr3
≈ $$\frac{4}{3}$$ · 3.14 · 83
≈ 2,143.573
Determine the volume of the necklace:
≈ 50 – 2. 143.573 ≈ 107, 178.7 mm3
b) What is the surface area of the necklace?
Answer: The surface area of the necklace is 40,192 mm2
Determine the surface area of a spherical bead:
Sbead = 4πr2 ≈ 4 · 3.14 · 82
≈ 803.84 mm2
Determine the surface area of the necklace:
= 50 · 803.84
≈ 40,192 mm2
Question 4.
A crystal trophy is made up of a rectangular pyramid whose base is attached to the top of a rectangular prism. The base of the pyramid and the top of the prism are each 4 inches long and 3 inches wide. The height of the pyramid is 2.5 inches and the height of the prism is 9.5 inches. What is the volume of the crystal trophy?
Answer: The volume of the crystal trophy is 124 in3
We are given:
l = 4
w = 3
hpyramid = 2.5
hprism = 9.5
Determine the volume of the pyramid:
Vpyramid =$$\frac{1}{3}$$ · lwhpyramid
= $$\frac{1}{3}$$ · 4 · 3 · 2.5
= 10 in3
Determine the volume of the prism:
Vprism = lwhprism = 4 · 3 · 9.5
= 114 in3
Determine the volume of the trophy:
Vtrophy = Vpyramid + Vprism
= 10 + 114
= 124 in3
Question 5.
At a food stand, you can buy a paper cone filled with slush made of frozen juice. The slush forms a hemisphere on top of the cone, as shown. What is the volume of the cone of slush?
Answer: The volume of the cone of slush is 314.9 cm3
We are given:
d = 8
h = 10.8
r = $$\frac{d}{2}$$ = $$\frac{8}{2}$$ = 4
Determine the volume of the hemisphere:
Vhemisphere = $$\frac{1}{2}$$ · $$\frac{4}{3}$$ πr3
≈ $$\frac{2}{3}$$ · 3.14 · 43
≈ 134 cm3
Determine the volume of the cone:
Vcone = $$\frac{1}{3}$$ πr2h
≈ $$\frac{1}{3}$$ · 3.14 · 42 · 10.8
≈ 180.9 cm3
Determine the volume of the cone of slush:
V = Vhemisphere + Vcone
= 134 + 180.9
= 314.9 cm3
Question 6.
A wooden paper towel holder is composed of two cylinders. The diameter of the base is 12 .centimeters and its height is 2 centimeters. The combined height of the two cylinders is 30 centimeters. What is the volume of the paper towel holder?
Answer: The volume of the paper towel holder is 438 cm3
We are given:
d1 = 3
h1 = 30
d2 = 12
h2 = 2
Determine the radius of the upper cylinder:
r1 = $$\frac{d_{1}}{2}$$ = $$\frac{3}{2}$$ = 1.5
Determine the volume of the upper cylinder:
V1 = πr12h1 = π · 1 52 · 30 = 67.5π cm3
Determine the radius of the lower cylinder:
r2 = $$\frac{d_{2}}{2}$$ = $$\frac{12}{2}$$ = 6
Determine the volume of the lower cylinder:
V2 = πr22h2 = π · 62 · 2 = 72π cm3
Determine the volume of the paper tower holder:
V = V1 + V2 = 67.5π + 72π
≈ 139.5π
≈ 139.5 · 3.14
≈ 438 cm3
Question 7.
The edge of the base of a square pyramid is 11 inches. The pyramid has a height of 14 inches. What is the volume of the composite solid formed when two such pyramids are joined at the base, as shown in the diagram?
Answer: The volume of the composite solid is 1,129.3 in3
We are given:
L = 11
h = 14
Determine the volume of one pyramid:
V1 = V2 = $$\frac{1}{3}$$l2h = $$\frac{1}{3}$$ · 112 · 14 ≈ 564.67 in3
Determine the volume of the composite solid:
V = V1 + V2 = 2V1 = 2 · 564.67
≈ 1,129.3 in3
Question 8.
A clock in the shape of an hour glass is made up of two identical cones connected at their vertices. The radius of each cone is 7 centimeters. The combined height of the two cones is 11.8 centimeters. What is the volume of the clock?
Answer: The volume of the clock is 605.2 cm3
We are given:
r = 7
H = 11.8
Determine the height of each cone:
h = $$\frac{H}{2}$$ = $$\frac{11.8}{2}$$ = 5.9
Determine the volume of one cone:
V1 = V2 = $$\frac{1}{3}$$πr2h = $$\frac{1}{3}$$ · π · 72 · 59
≈ 96.3677π
Determine the volume of the clock:
V = V1 + V2 = 2V1 = 2 · 96.367π
≈ 192.734 · 3.14
≈ 605.2 cm3
Question 9.
Jason made a long pole by joining three different lengths of cylindrical poles together. Each pole has the same diameter of 18 cm. The diagram below is not drawn to scale.
a) What is the volume of the long pole?
Answer: The volume of the long pole is 8,393.2 cm3
We are given:
d = 18
h1 = 7
h2 = 11
h3 = 15
r = $$\frac{d}{2}$$ = $$\frac{18}{2}$$ = 9
Determine the volume of the tong pole:
V = V1 + V2 + V3
= πr2h1 + πr2h2 + πr2 h3
= πr2(h1 + h2 + h3)
≈ 3.14 · 92 · (7 + 11 + 15)
≈ 8,393.2 cm3
b) What is the surface area of the long pole?
Answer: The surface area of the long pole is 2,373.8 cm2
Determine the surface area of the long pole
= 2πr2 + 2πr(h1 + h2 + h3)
= 2πr(r + h1 + h2 + h3)
≈ 2 · 3.14 · 9(9 + 7 + 11 + 15)
≈ 2,373.8 cm2
Brain @ Work
How can you make the following cross-sections by slicing a cube? Use a computer drawing program or pencil and paper to show your answers for a) and b).
a) An isosceles triangle | 2022-10-07 21:31:01 | {"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": 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": 0.6132835149765015, "perplexity": 2250.6337402601594}, "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-2022-40/segments/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00460.warc.gz"} |
https://www.physicsforums.com/threads/physics-from-symmetry.891620/page-2 | # FeaturedI Physics From Symmetry
1. Nov 2, 2016
### Staff: Mentor
Actually Ballentine did it better but didn't mention that was what he was doing. This guy explicitly did, as well as carefully analysing Noethers theorem which Ballentine did not. Ballentine also introduces the Born rule formalism prior to doing it - this book uses it to motivate it. Different intent and emphasis. Ballaintine is the much better book to learn QM from - this book motivates the importance of symmetry as a unifying concept in physics.
The professor thing doesn't really worry me - he is trying something different - maybe too different for more set in their ways professors.
Thanks
Bill
2. Nov 2, 2016
### Staff: Mentor
Read the paper I linked to on relativity. An inertial frame is defined by symmetry proprieties and that is all you need to derive the Lorentz transformations.
https://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960
https://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960
The first, unlike this book, doesn't eve mention group theory or Noethers theorem. You see mechanics developed directly from symmetry. For example from the fact the Lagrangian must be invariant between inertial frames we see mass must exist and be positive.
Then we have Noethers theorem itself which says (loosely) for every symmetry in the Lagrangian their must be a conserved quantity. Its why momentum exists and is conserved (systems have the same Lagrangian where you put them is the conserved quantity associated with this and is called momentum) and energy exists and is conserved (systems often have Lagrangian's that are time invariant which has the conserved quantity we call energy). Noether proved it must be the case. It shocked even Einstein and just about anyone else exposed to it since then. It explains why defining energy in GR is a BIG problem - but you should take that over to the GR forum.
This book is different, I would not have done it in this order but starts with group theory and Noethers theorem then develops the physics. Its a very different and unusual approach as you can see some do not like. I do - but that's just me. Time will tell if the method takes off or not. From comments by actual professors here I may be its only advocate - maybe it needs to be done by an experienced teacher and textbook writer.
You usually learn mechanics, EM, QM etc etc then this beautiful theorem. This book does the reverse.
Once understood its shocking. Professors here often describe the stunned silence of their students when they teach it. Its that deep and profound. This book is an attempt to do the reverse - but as you can see many do not warm to that approach like I do. They all recognise the power, beauty and usefulness of Noether and are as shocked by it now just like when they learned it. But starting from it - well obviously that is not universally as well respected.
Thanks
Bill
3. Nov 3, 2016
### Staff: Mentor
I have asked the library at my institution to buy it. Hope I didn't make a mistake
4. Nov 3, 2016
### houlahound
Gentlemen and women this will destroy many in the target audience that are learning the math for the book from the book they are reading.
http://physicsfromsymmetry.com/errata/
Now why the heck isn't an e-book made available for free to everyone who purchased the book.
5. Nov 3, 2016
### vanhees71
Well, if you ever have written a longer scientific text, you'd know how easily typos sneak into a manuscript, and it is not easy to get them when you just have typed a text in, because you read over them knowing your text very well. Waiting a few months and then proofreading helps.
On the other hand you are right in being angry with the publishers. Nowadays the publishers have no serious editing anymore. That's indeed something you can blame them on since they really take a lot of money for their books.
6. Nov 3, 2016
7. Nov 3, 2016
### strangerep
At the risk of being a wet blanket, I think you should try to stop that purchase until you've had a chance to examine at least parts of the book for yourself. I'll send you a PM shortly.
I just had a quick skim and I will say that I was underwhelmed.
I apply a "test" to any physics book that waxes lyrical about the wonders of symmetries [] :- I look for how it develops the Kepler laws, especially the 3rd law. The latter arises from a symmetry which is not connected to a Noetherian conserved quantity. Thus, it reminds us that not everything follows from an algebra of conserved quantities, but rather from the full dynamical group that maps solutions of the equations of motion among themselves. Noetherian symmetries, although very important, are nevertheless not the be-all and end-all of everything.
Schwichtenberg does not mention Kepler at all, afaict. Nor does he mention "hydrogen" which is a marvelous example of the power of group theory in QM.
Further, when I look at his derivation of the half-integer spectrum for su(2), there's some leaps in there that I don't like. Look at sect 3.6.1 on pp 53-54. He introduces ladder operators $J_\pm$ and shows that they act on $J_3$ eigenvectors to raise/lower the eigenvalue. Then he concludes that, because he's working in a finite dimensional space, there must be a point where repeated application of $J_\pm$ yields 0. Although this is technically correct, (because his space happens to also be a Hilbert space, and eigenvectors of a Hermitian operator with distinct eigenvalues are orthogonal, and span the space according to the spectral thm), but he doesn't explain any of this. It works out because he's working with SU(2), hence unitarity is there automatically, and hence also Hermiticity of its generators (see sect 3.4.3).
Contrast this with the treatment in Ballentine sect 7.1. There's no comparison, imho.
It's also disappointing that he hasn't enabled the "Look Inside" feature on Amazon. That makes it hard for people to get a feel of the book for themselves before committing their money.
Last edited: Nov 4, 2016
8. Nov 3, 2016
### houlahound
OT, does anyone have a link to an intro level explanation of Noether's theorem.
9. Nov 3, 2016
### Staff: Mentor
10. Nov 3, 2016
### Staff: Mentor
11. Nov 3, 2016
### houlahound
12. Nov 4, 2016
### dextercioby
Strangerep, there's no mentioning of the Kepler problem and its symmetries (dynamical group SO(2,4) etc), because the focus of the book is on classical field theory, not on quantum mechanics. The quantum field symmetries (Ward-Takahashi, BRST, anomalies, gauge symmetry breaking) are not mentioned at all, because the book is meant for undergraduates (heck, the author was undergraduate at the time of writing the book!), hence it should be and it is full of the blah-blah of standard texts. You are right to complain about the treatment of the su(2) - angular momentum part, simply because the whole picture (compact group - Peter-Weyl theorem-unitary ray representations of SO(3)-Bargmann's theorems - Nelson's theorem) is not clear to the author himself.
13. Nov 4, 2016
### strangerep
Well, the Kepler problem is classical, last time I checked.
The author definitely tried to address a certain amount of QM and QFT -- see chapters 5,8,9.
14. Nov 4, 2016
### Demystifier
My main criteria for reading a new book on old subject is - does it offer a new perspective? (Otherwise, what's the point of either writing or reading it in the first place?) And I think this book definitely satisfies this criterion.
15. Nov 5, 2016
### MrRobotoToo
Schwichtenberg's book is quite good. I especially liked the chapter on Lie groups, whose treatment of representation theory was exceptionally clear. Another book that is in much the same vein as Schwichtenberg's, but at a somewhat more advanced level, is Kurt Sundermeyer's 'Symmetries in Fundamental Physics' (disregard the one-star review--the reviewer apparently confused Schwichtenberg's book for Sundermeyer's): https://goo.gl/oFE3ky
16. Jul 6, 2017
### Demystifier
Well, Pauli was also a kid when he has written a book on relativity (both special and general). Yet, it is still considered one of the best books on relativity ever written.
Speaking of kids, Wolfram, the creator of Mathematica, has written a review of weak interactions in particle physics when he was a kid. This review can be found by google, but I cannot tell how good it is.
17. Jul 6, 2017
### dextercioby
He was 20 when he wrote it and 21 when published. It was the first monograph on General Relativity (appeared in the same year with the one by Max von Laue) and it is very good, even though it is written with no differential geometry content. But you can't expect that any physics undergraduate in Germany being offered the chance of a lifetime (i.e. publish a book on science at Springer Verlag) turn out to be a prodigy and a future Nobel Prize winner.
18. Jul 6, 2017
### Demystifier
OK, fair enough, but answer this one. If the book is so bad, why do so many people (on this forum at least) find the book very good? There must be something about that book that looks appealing and I would like to know what that something is.
19. Jul 6, 2017
### dextercioby
Don't ask me, I find it appalling that books get passed an editor's proofreading. It is ridiculous to ask a 22 yo to write a book then publish it with 100 errors in it.
The material in this book is found in a dozen other books, but I presume it's the relatively low level of mathematics that is a magnet for some readers.
20. Jul 7, 2017
### Demystifier
You have mentioned that errors are not only technical (which are probably easy to fix), but also conceptual. Can you pinpoint to some of the conceptual errors? | 2019-01-16 19:04:20 | {"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": 0.508627712726593, "perplexity": 1020.432099400442}, "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-2019-04/segments/1547583657557.2/warc/CC-MAIN-20190116175238-20190116201238-00442.warc.gz"} |
https://forum.inductiveautomation.com/t/script-on-download-button-on-report-viewer-in-perspective/41862 | I would like to add ‘save as’ functionality through a script on the download button on the report viewer for Perspective. Which event would I place my script on?
I found that the issue is resolved with my browser settings. However, I would also like to add other scripting functionality to save certain values, I incorporate into the Reports parameters, into a table in my DB. Is this possible on one of the events?
There’s no way currently to hook into a user pressing the download button, but you can use any of the regular events to manage this. What I recommend for now is a separate button from the Report Viewer to perform this database update.
Thank you very much. That is what I figured. Do you know the right script to use on a button to send the report on the report viewer to a DB? I am currently using a file upload button elsewhere with this script to do it:
# Grab the file name and data
filename = event.file.name
filedata = event.file.getBytes()
# Use a query to insert the file
query = "INSERT INTO files (filename, filedata) VALUES(?, ?)"
args = [filename, filedata]
system.db.runPrepUpdate(query, args)
However, this just grabs a file from a local directory and uploads it. I just want a button that sends the report viewer to a pdf to my ‘files’ table in my DB.
The button won’t have access to a file object as part of the event; onClick and actionPerformed Events contain an empty event object.
You’ll need to look into using system.file.readFileAsBytes(filepath) where you construct the filepath argument from ReportViewer.props.source. Something like this:
filename = self.getSibling('ReportViewer').props.source
filepath = "C:\\path\to\file\" + filename
# Use a query to insert the file
query = "INSERT INTO files (filename, filedata) VALUES(?, ?)"
args = [filename, filedata]
system.db.runPrepUpdate(query, args)
I ended up doing this script on the button:
today = system.date.now()
# Grab the file name and data
filename = "QCF-1168" + system.date.format(today, "yy/MM/dd")
overrides = {"SkeletonNumber":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.SkeletonNumber,
"Face1Grid10":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid10,
"Face1Grid9":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid9,
"Face1Grid8":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid8,
"Face1Grid7":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid7,
"Face1Grid6":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid6,
"Face1Grid5":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid5,
"Face1Grid4":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid4,
"Face1Grid3":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid3,
"Face1Grid2":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid2,
"Face1Grid1":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face1Grid1,
"Face2Grid10":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid10,
"Face2Grid9":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid9,
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"Face2Grid7":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid7,
"Face2Grid6":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid6,
"Face2Grid5":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid5,
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"Face2Grid2":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid2,
"Face2Grid1":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face2Grid1,
"Face3Grid10":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face3Grid10,
"Face3Grid9":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face3Grid9,
"Face3Grid8":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face3Grid8,
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"Face4Grid1":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.Face4Grid1,
"FuelAssemblyNum":self.parent.parent.getChild("FlexContainer").getChild("FlexContainer_0").getChild("ReportViewer").props.params.FuelAssemblyNum
}
filedata = system.report.executeReport(path="FormWEC", project="Perspective_Training", parameters=overrides, fileType="pdf")
# Use a query to insert the file
query = "INSERT INTO files (filename, filedata) VALUES(?, ?)"
args = [filename, filedata]
system.db.runPrepUpdate(query, args)
I have a lot of parameters on my report.
The next thing that I am trying to do is display a PDF from my DB, in the PDF viewer in Perspective, on a selectedRow from my table. I guess this is done somehow with the WebDev module and setting a source as python? I am looking into it at the moment. If you have any thoughts that could help me, I would greatly appreciate it.
This is the best option, yes. You should only need to use a File Resource though - I don’t know why you’d use a Python resource for this.
I saw it in this thread:
I am able to send pdfs from the report viewer to my DB via a button. I can see the pdfs in the table that I created. I want to be able to display each PDF, in the PDF Viewer or Inline Frame, by just clicking on the row in the table. (This will act as a way to view past entries).
Ah, okay, yes - that would be a better way I guess, but you’re not supplying each file - you’re supplying a python process which accepts some parameters and then retrieves the report from the database based on the arguments supplied.
The way I suggested requires you to save or place each report into a WebDev mounted folder, but if you do this then you’re sort of doubling up the report because it’s now in your DB and on the file system.
The python route leaves just one copy in the DB and uses python to retrieve each report as needed. I’m not very familiar with the python endpoint route, so I can’t provide any insight into how you’d do that.
Highly recommended. A search here for “webdev doget” has this near the top:
1 Like
Wait, is all you really want here a custom filename for the report download? Like this idea: https://ideas.inductiveautomation.com/ignition-features-and-ideas/p/perspective-report-viewer-suggested-file-name | 2022-12-02 16:37:36 | {"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": 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": 0.2332007735967636, "perplexity": 1907.3594465942526}, "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-2022-49/segments/1669446710909.66/warc/CC-MAIN-20221202150823-20221202180823-00430.warc.gz"} |
https://search.datacite.org/works/10.18452/2566 | ### Framework For The A Posteriori Error Analysis Of Nonconforming Finite Elements
Carsten Carstensen, Jun Hu & Antonio Orlando
This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions $(H1)-(H2)$ and applies to several nonconforming finite elements: the Crouzeix-Raviart triangle element, the Han parallelogram element, the nonconforming rotated (NR) parallelogram element of Rannacher and Turek, the constrained NR parallelogram element of Hu and Shi, the...
This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation. | 2020-10-31 23:11:27 | {"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": 0.39226385951042175, "perplexity": 2142.3600564694366}, "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-20201031211812-20201101001812-00648.warc.gz"} |
https://unapologetic.wordpress.com/2011/04/04/ | The Unapologetic Mathematician
The Tangent Bundle
So far we’ve talked about tangent spaces one at a time. For each $p\in M$ we get a tangent space $\mathcal{T}_pM$ at $p$. But things get really interesting when we start to sew them all together.
So, let’s take the (disjoint) union of all the tangent spaces $\mathcal{T}_pM$ at once. It’s important here that we never identify any of these with each other; a tangent vector at $p$ is never the same as another tangent vector at $q$. So far this is just a bunch of $n$-dimensional vector spaces parameterized by the $n$-dimensional manifold $M$, but I say that we can actually give this whole set the structure of a $2n$-dimensional smooth manifold!
Indeed, all we need is to give a collection of patches covering the whole space, and we can do this starting from any atlas on $M$. Given an open coordinate patch $(U,x)$ in $M$, we will make a coordinate patch that covers all of the $\mathcal{T}_pM$ with $p\in U$. Given a $v\in\mathcal{T}_pM$ we need to come up with a point $\bar{x}(v)\in\mathbb{R}^{2n}$. We write
$\displaystyle\bar{x}(v)=\left(x^1(p),\dots,x^n(p),v(x^1),v(x^2),\dots,v(x^n)\right)$
As $v$ varies within $\mathcal{T}_pM$, the first $n$ components of the image — $x(p)$ — stay fixed, and the rest of them give a linear isomorphism from $\mathcal{T}_pM$ to $\mathbb{R}^n$.
On the other hand, how do things change as we vary the base point $p$? This, it turns out, is where the interesting stuff is happening. Normally we wouldn’t be able to tell anything about how $\mathcal{T}_pM$ and $\mathcal{T}_qM$ are related for $p\neq q$, but within a single coordinate patch we can use the coordinate map $x$ to define coordinate vectors at every single point $p\in U$, and this lets us compare vectors at different points by comparing their components with respect to these coordinate vector bases.
The catch is, this only works for points in the same coordinate patch, and different coordinate patches give us different ways of comparing tangent vectors at nearby points. So we can’t really say much about them, but it’s enough to define a coordinate patch.
So we have to check about where patches overlap. If we have $(U,x)$ and $(V,y)$ as two patches on $M$ then we already know that $y\circ x^{-1}$ is a smooth transition function. This handles the smoothness of the first $n$ components of the transition function $\bar{y}\circ\bar{x}^{-1}$. For the other components, we know that the transition function is a linear isomorphism, which is clearly smooth.
We call this manifold the “tangent bundle” of $M$ and write $\mathcal{T}M$. It comes equipped with a map $\pi:\mathcal{T}M\to M$, which I say is smooth. Indeed, we just need to check this on a single pair of coordinate patches. We can pick any patch $(U,x)$ on $M$ and the corresponding patch on $\mathcal{T}M$. Then given $(a,b)\in x(U)\times\mathbb{R}^n$ we get a vector $\bar{x}^{-1}(a,b)=v\in\mathcal{T}_{x^{-1}(a)}M$ by writing
$\displaystyle v=\sum\limits_{i=1}^nb^i\left(\frac{\partial}{\partial x^i}(x^{-1}(a))\right)$
Our projection then sends $v$ to its base-point $x^{-1}(a)$, which $x$ sends to $a$. That is, if we write our projection $\pi$ out in terms of coordinates $\bar{x}$ on $\mathcal{T}M$ and $x$ on $M$, it’s just the projection $x(U)\times\mathbb{R}^n\to x(U)$, which is obviously smooth.
April 4, 2011 | 2015-11-26 15:58:39 | {"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": 0, "mathjax_asciimath": 0, "img_math": 55, "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": 0.9276140332221985, "perplexity": 107.465716191776}, "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-2015-48/segments/1448398447758.91/warc/CC-MAIN-20151124205407-00043-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.tutorialspoint.com/python-program-for-compound-interest | # Python Program for compound interest
PythonServer Side ProgrammingProgramming
In this article, we will learn about the solution and approach to solve the given problem statement.
Problem statement −We are given with three input values i.e principle, rate & time and we need to compute compound interest.
The code given below shows the process of computation of compound interest.
The formula used here is
Compound Interest = P(1 + R/100)r
Where,
P is the principal amount
R is the rate and
T is the time span
The implementation is given below
## Example
Live Demo
def compound_interest(principle, rate, time):
CI = principle * (pow((1 + rate / 100), time))
print("Compound interest : ", CI)
# main
compound_interest(10000, 7.78, 2)
## Output
Compound interest : 11616.528400000001
All variables and functions are declared in global scope as shown in the figure below. | 2021-07-31 15:43:40 | {"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": 0.22674964368343353, "perplexity": 4872.589040905445}, "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-2021-31/segments/1627046154089.68/warc/CC-MAIN-20210731141123-20210731171123-00328.warc.gz"} |
http://theorymaker.info/book/0M0040reportingLanguageAndWorld.html | # Reporting: Variables and language-Variables
Theorymaker native speakers use the word “Variable” to talk about both language-Variables and the Variables they refer to. So you can say “number of visitors to the new centre” and mean either the language Variable which is part of your plan, your shared model of how things are going to work; you can think of this as a social phenomenon or as the paper-and-pencil (or more likely electronic) manifestation of this shared model. Alternatively you can mean the actual number of visitors, a Variable which you can observe or measure e.g. by going to the centre, without any knowledge of any plan or Theory.
If you are busy developing a Theory of Change, you won’t have time to worry about the difference. But when we come to look at how our evaluation Report is supposed to reflect various aspects of the project being evaluated, we will need to look at the way language-Variables refer to or “report” Variables in the rest of the world beyond the plan, and that is what we will do in this chapter. In this Chapter we will also explore how language-Variables are themselves Variables.
The report says 'The height of child X is ...' ((positive continuous numbers)) !Rule: some reporting or measurement Rule ensuring the report of the height reflects the actual height
The height of child X is ((positive continuous numbers))
direction=TB
So this diagram shows a causal link between the actual height of the child and the report of its height, say on a school health record. This causal link will normally be a relatively involved one which we could probably “zoom in” on to identify other intervening Variables: we can call the whole thing “the reporting Mechanism”.
We already saw that language-Variables report or refer to Variables, Statements report Facts and that Theories (consisting of language-Variables and Statements) report Mechanisms. So in this sense Variables and language-Variables are two very different kinds of things.
But on the other hand, non-Theorymaker native speakers might be surprised to hear the following claim.
A language-Variable not only reports a Variable but is also itself a perfectly ordinary Variable.
When you think about it, of course it is.
Imagine I am measuring a child’s height and fill the number in on the child’s health form in the box marked “height”.
Each possible response is a Statement, one Level of a language-Variable. Loosely, we can call this language-Variable “the height as reported on the form” and say it reports the actual Variable, the height of the child. We call it a linguistic Variable simply because it actually uses language - as always, in a particular context; in this case an important part of the context is that the other people around me speak the same language and understand the health form, etc.
When we talk about the language-Variable, rather than using it, we can recognise it as a Variable just like the actual height is. So when the Level of the Variable child's height is 1m, the Level of the language-Variable report of child's height should be "1m".
The critical thing to understand is that under the right conditions, language-Variables can influence and be influenced by other Variables. | 2017-06-23 08:40:46 | {"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": 0.2663111388683319, "perplexity": 845.4025856767411}, "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-2017-26/segments/1498128320040.36/warc/CC-MAIN-20170623082050-20170623102050-00582.warc.gz"} |
https://socratic.org/questions/how-do-you-factor-y-2-0-4y-0-04 | # How do you factor y^2 + 0.4y + 0.04?
Oct 12, 2017
You can use a process popularly known as completing the square
#### Explanation:
This is how it works: Add and subtract the square of half the coefficient of y to the expression .
The coefficient of y is 0.4. Half of it is $\frac{0.4}{2} = 0.2$
The square of $0.2 = {\left(0.2\right)}^{2}$
Adding and subtracting ${\left(0.2\right)}^{2}$ to the expression ${y}^{2} + 0.4 y + 0.04$ gives ${y}^{2} + 0.4 y + 0.04 + {\left(0.2\right)}^{2} - {\left(0.2\right)}^{2}$
Rearrange that and you get a factorisable expression.
${y}^{2} + {\left(0.2\right)}^{2} + 0.4 y + 0.04 - {\left(0.2\right)}^{2}$
${\left(y + 0.2\right)}^{2} + 0.04 - 0.04$
${\left(y + 0.2\right)}^{2} = \left(y + 0.2\right) \left(y + 0.2\right)$ | 2019-12-06 02:52:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.8512742519378662, "perplexity": 541.925232143209}, "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-2019-51/segments/1575540484477.5/warc/CC-MAIN-20191206023204-20191206051204-00543.warc.gz"} |
https://gamedev.stackexchange.com/questions/46077/am-i-doing-this-node-js-game-loop-wrong | # Am I doing this node.js game loop wrong?
I have 2 arrays of JSON objects, actions and game objects.
At any time a user can make a request from the client which can add an action to the actions array.
I have a setInterval(function(){ }, 1000); that runs every second and first loops through all of the actions, doing them in order then dumping emptying the array. Then it for loops (on the length of the array) through all the objects and does change processing such as healing, repairing, consuming resources, updating location of travelling objects, etc.
Each game object is tied to a user and when it is done being modified it will push out to them using socket.io all the data they need for their current view (assuming they are in an active session still).
Is this right? Am I not taking advantage of the node.js event loop as well as I could for this?
• That depends on type of game, if you have game that is entirely event based (like tick tack toe) or something that can be made to look like event based (storing when action is going to finish, and finish it after someones query it - this could work for stuff like cooldown for spells, but not healing after time) Then you can have everything based just on events. If you have realtime game, like mmorpg, you need that loop. Btw when using setInterval like this will not work when time to process everything will be bigger then 1000. – Kikaimaru Dec 23 '12 at 18:05
• Healing over time with a delay can totally be query/event driven. If you can make a function to calculate absolute given an input of elapsed time, all you need is to store the previous value and the it was calculated at. – Sean Middleditch Oct 4 '13 at 21:29 | 2020-07-08 08:26:37 | {"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": 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": 0.28078967332839966, "perplexity": 1282.8825622632155}, "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-2020-29/segments/1593655896905.46/warc/CC-MAIN-20200708062424-20200708092424-00595.warc.gz"} |
https://jp.maplesoft.com/support/help/maple/view.aspx?path=LinearAlgebra%2FGeneric%2FMatrixAdd | Matrix Add - Maple Help
# Online Help
###### All Products Maple MapleSim
LinearAlgebra[Generic]
MatrixAdd
add two matrices
VectorAdd
add two vectors
Calling Sequence MatrixAdd[R](A,B,c,d) VectorAdd[R](v,w,c,d) MatrixAdd[R](lA,lc) VectorAdd[R](lv,lc)
Parameters
R - the domain of computation A,B - Matrices of values in $R$ c,d - (optional) scalar values in $R$ (default values: $1$) v,w - Vectors of values in $R$ lA - non-empty list of Matrices over $R$ lc - (optional) non-empty list of scalar values in $R$ lv - non-empty list of vectors over $R$
Description
• The (indexed) parameter $R$, which specifies the domain of computation, a commutative ring, must be a Maple table/module which has the following values/exports:
R[0] : a constant for the zero of the ring R
R[1] : a constant for the (multiplicative) identity of R
R[+] : a procedure for adding elements of R (nary)
R[-] : a procedure for negating and subtracting elements of R (unary and binary)
R[*] : a procedure for multiplying elements of R (binary and commutative)
R[=] : a boolean procedure for testing if two elements of R are equal
• The parameters $A,B$, and $v,w$ must have compatible dimensions for the addition. Similarly, all Matrices in $\mathrm{lA}$, and all Vectors in $\mathrm{lv}$, must have compatible dimensions, and the number of elements of $\mathrm{lc}$, if given, must match the number of element of $\mathrm{lA}$ or $\mathrm{lv}$, respectively.
• If $c,d,\mathrm{lc}$ are omitted, then MatrixAdd and VectorAdd just compute the sum of the matrices or vectors, respectively.
Examples
> $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Generic}\right]\right):$
> $\mathrm{F8}≔\mathrm{GF}\left(2,3,{a}^{3}+a+1\right)$
${\mathrm{F8}}{≔}{{𝔽}}_{{8}}$ (1)
> $A≔\mathrm{map}\left(\mathrm{F8},\mathrm{Matrix}\left(\left[\left[a,a+1,0\right],\left[{a}^{2},0,{a}^{2}+a\right]\right]\right)\right)$
${A}{≔}\left[\begin{array}{ccc}{a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ {{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (2)
> $B≔\mathrm{map}\left(\mathrm{F8},\mathrm{Matrix}\left(\left[\left[1,{a}^{2}+a,a\right],\left[{a}^{2}+1,a,a\right]\right]\right)\right)$
${B}{≔}\left[\begin{array}{ccc}{1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (3)
> $\mathrm{MatrixAdd}\left[\mathrm{F8}\right]\left(A,B\right)=\mathrm{MatrixAdd}\left[\mathrm{F8}\right]\left(\left[A,B\right]\right)$
$\left[\begin{array}{ccc}\left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ {1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]{=}\left[\begin{array}{ccc}\left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ {1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (4)
> $c≔\mathrm{F8}\left(a\right)$
${c}{≔}{a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}$ (5)
> $d≔\mathrm{F8}\left(a+1\right)$
${d}{≔}\left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}$ (6)
> $\mathrm{MatrixAdd}\left[\mathrm{F8}\right]\left(A,B,c,d\right)=\mathrm{MatrixAdd}\left[\mathrm{F8}\right]\left(\left[A,B\right],\left[c,d\right]\right)$
$\left[\begin{array}{ccc}\left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]{=}\left[\begin{array}{ccc}\left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}& {1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (7)
> $v≔\mathrm{map}\left(\mathrm{F8},\mathrm{Vector}\left(\left[{a}^{2}+a+1,a,a+1\right]\right)\right)$
${v}{≔}\left[\begin{array}{c}\left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ {a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (8)
> $w≔\mathrm{map}\left(\mathrm{F8},\mathrm{Vector}\left(\left[a+1,{a}^{2},{a}^{2}+a\right]\right)\right)$
${w}{≔}\left[\begin{array}{c}\left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ {{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (9)
> $\mathrm{VectorAdd}\left[\mathrm{F8}\right]\left(v,w\right)=\mathrm{VectorAdd}\left[\mathrm{F8}\right]\left(\left[v,w\right]\right)$
$\left[\begin{array}{c}{{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]{=}\left[\begin{array}{c}{{a}}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (10)
> $\mathrm{VectorAdd}\left[\mathrm{F8}\right]\left(v,w,c,d\right)=\mathrm{VectorAdd}\left[\mathrm{F8}\right]\left(\left[v,w\right],\left[c,d\right]\right)$
$\left[\begin{array}{c}{0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]{=}\left[\begin{array}{c}{0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\\ \left({{a}}^{{2}}{+}{a}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}\end{array}\right]$ (11)
Compatibility
• The LinearAlgebra[Generic][MatrixAdd] and LinearAlgebra[Generic][VectorAdd] commands were introduced in Maple 2021.
• For more information on Maple 2021 changes, see Updates in Maple 2021.
See Also | 2023-03-29 14:36:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 39, "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": 0.9810963273048401, "perplexity": 1811.4012147795627}, "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-2023-14/segments/1679296948976.45/warc/CC-MAIN-20230329120545-20230329150545-00767.warc.gz"} |
https://www.love2d.org/forums/viewtopic.php?f=4&t=161&p=1587&sid=9a1090587d49b7688399746b4ceb351d | ## Finding out if a line hits a circle.
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SamPerson12345
Prole
Posts: 41
Joined: Sat Aug 30, 2008 5:35 pm
### Finding out if a line hits a circle.
I can't figure it out. All I have is the starting position and the ending position of a line and where the circle is. Help would be greatly appreciated.
bartbes
Sex machine
Posts: 4946
Joined: Fri Aug 29, 2008 10:35 am
Location: The Netherlands
Contact:
### Re: Finding out if a line hits a circle.
With some basic math you can figure out the y for the x of the line, so if a line goes from x=1 to x=5, you can calculate the y at x=3 (or somewhere else).
Try:
Code: Select all
((line.y2-line.y1)/(line.x2-line.x1))*(X-line.x1)+line.y1
(with x1 being the lowest x and X being the NON-relative-x)
emonk
Prole
Posts: 24
Joined: Tue Aug 12, 2008 11:43 am
### Re: Finding out if a line hits a circle.
With a line segment and a circle there are three broad categories of situations:
• Both endpoints inside the Circle
• One endpoint inside the Circle and one outside
• Neither endpoint inside the circle
You can figure out which of those is applicable by calculating the distance of each endpoint from the center of the circle using math.sqrt(dx^2 + dy^2). It's the third category that needs more work, but eliminating the first two cases (which are either hit or not depending on your definitions) helps later on.
If neither endpoint is inside the circle then we have two more cases:
• Line passes through, or is tangent to, the circle.
• Line does not pass through the circle.
So far I've found two ways to answer this question...
To figure out which is the case we need to find the point on the line that is closest to the center of the circle, then test to see if that is inside the radius. Here's a page with some relatively simple explanations of the problem and solutions:
http://local.wasp.uwa.edu.au/~pbourke/g ... phereline/
The Line Segment section of that page gives an equation for testing whether the closest point on the line to the circle's center is between the two endpoints. For our purposes we can throw away ones where the closes point is outside our endpoints, since we've already tested for endpoints inside the circle.
For lines that pass the first test you calculate the actual position of the closest point and check if it falls inside the radius of the circle. The result of the first test is the fraction of the line from P1 to P2 where the closest point is located. I'll leave it to you to figure the math for finding the position of the closest point and testing it for being inside the circle.
All of the above is very interesting, but math isn't really my strong point. I know how to rotate points though, and I can find the angle of a line... and that leads to an interesting idea that's probably going to take forever to actually operate but is conceptually very simple.
The idea is that you can rotate the endpoints of the line around the center of the circle until the line is horizontal (or vertical if you prefer), then find the distance of the closest point by simple subtraction. Figuring out if the rotated points are inside the circle is a simple too, so we can do this to solve the entire problem.
To find the angle of the line you use the math.atan2 function:
Code: Select all
local lineangle = math.atan2(p2.y - p1.y, p2.x - p1.x)
We can use this angle to rotate the line into alignment with the x axis and so on.
Here's the code:
Code: Select all
-- distance between two points
function distance(x1, y1, x2, y2)
return math.sqrt((x1 - x2)^2 + (y1 - y2)^2);
end;
-- rotate [x,y] around [0,0] by 'a' radians
function rotate(x, y, a)
local sina, cosa = math.sin(a), math.cos(a);
return x * cosa - y * sina, x * sina + y * cosa;
end;
-- return true if line p1-p2 intersects circle with radius 'r' at location 'pc'
function LineIntersectCircle(p1, p2, pc, r)
-- translate points to circle-relative
local tp1, tp2 = { x = p1.x - pc.x, y = p1.y - pc.y }, { x = p2.x - pc.x, y = p2.y - pc.y };
-- check points inside...
if distance(tp1.x, tp1.y, 0, 0) < r then return true; end;
if distance(tp2.x, tp2.y, 0, 0) < r then return true; end;
-- rotate points to make line parrallel to X-axis
local lineangle = math.atan2(p2.y - p1.y, p2.x - p1.x);
local rp1 = {}; rp1.x, rp1.y = rotate(tp1.x, tp1.y, -lineangle);
local rp2 = {}; rp2.x, rp2.y = rotate(tp2.x, tp2.y, -lineangle);
-- should have: rp1.y == rp2.y
assert(math.abs(rp1.y - rp2.y) <= math.abs(rp1.y / 10000));
if math.abs(rp1.y) > r then return false; end; -- line doesn't cross circle
-- check for both points on same side...
if rp1.x * rp2.x > 0 then return false; end;
-- none of the above... line intersects
return true;
end;
Not extensively tested so no guarantees.
Mr. Strange
Party member
Posts: 101
Joined: Mon Aug 11, 2008 5:19 am
### Re: Finding out if a line hits a circle.
Marc LeBlanc wrote an excellent lecture on this subject. You can find it at his website:
http://8kindsoffun.com/
Lots of other good resources there for designers and programmers. Plus Marc is a good guy.
--Mr. Strange
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https://itineraires-ceramique.com/looking-to-xhtub/which-group-1-element-reacts-the-most-vigorously%3F-c86daf | How do they react with water? फलतः चित्रकला विभिन्न क्षेत्रीय रूपों में भी विकसित हुई. What happens when the elements in group 1 react with oxygen? This means that the alkali metals all have similar chemical properties. All of Group 1 elements—lithium, sodium, potassium, rubidium and cesium react vigorously or even explosively with cold water. alkaline earth metals noble gases alkali metals halogens. Which two elements react most vigorously with each other? (Potassium actually is the more reactive of the two) The reason is that potassium and sodium both lie in Group 1 of the periodic table, which contains all the alkali metals. All of these metals react vigorously or even explosively with cold water. All the alkali metals react vigorously with halogens to produce salts, the most industrially important of which are NaCl and KCl. Hence chlorine and potassium will react more violently. Group 1 Group 2 Group 3-12 Group 15 Group 16 Group 17 Group 18 . How do they react with water? A salt is formed MBr2 B. The non-metal elements in Group 7 – known as the halogens – get less reactive as you go down the group. New questions in Chemistry. Feb 5, 2014 . Related questions. Try be a little more specific next time. Favorite Answer. B. high melting point and reacts vigorously with water. How do they react with water? I think that it helps to imagine reactions as sort of a "fight" between elements over electrons. How do they react with iodine? Cl2 and Br2 are also in the same group (group 7). Fluorine is the most reactive non radioactive element on periodic table. Thanks Comments; Report Log in to add a comment Looking for something else? A. high melting point and reacts slowly with water. See your other post. Chemistry. बिहार दरोगा मुख्य परीक्षा के लिए महत्वपूर्ण टॉपिक बिहार दरोगा मुख्य परीक्षा से पूर्व निम्न महत्वपूर्ण टॉपिक को अवश्य पढ़े— इतिहास – इतिहास विषय से मुख्य परीक्षा में लगभग 20 प्रश्न पूछे जाते है.ये सभी प्रश्न विगत वर्षों में विभिन्न प्रतियोगी परीक्षाओं में पूछे गए प्रश्न रहते है. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. This page looks at the reactions of the Group 1 elements - lithium, sodium, potassium, rubidium and caesium - with water. They include lithium, sodium and potassium, which all react vigorously with water to produce an alkaline solution. Group 1 and 17. 0 0; DrBob222. Multiple Choice . Sections below cover the trends in atomic radius, first ionization energy, electronegativity, melting and boiling points, and density. sorry, didn't mean to post twice lol computer glitched XD Help. Which group 1 element reacts the most vigorously? Which element in the group is the most metallic in character? Rb Cs K Li Na 1 See answer Answer 2. hudebya +1 cliffffy4h and 1 other learned from this answer Answer: The answer is lithium(LI) 0.0 0 votes 0 votes Rate! Answer. K. Li. All Rights Reserved. The Facts. How do they react with iodine? Show transcribed image text. Expert Answer 100% (45 ratings) Previous question Next question Transcribed Image Text from this Question. In each case, the aqueous metal hydroxide and hydrogen gas are produced, as shown: $2X (s) + 2H_2O (l) \rightarrow 2XOH (aq) + H_2 (g)$ where $$X$$ is any Group 1 metal. no reaction. The Group 1 elements in the periodic table are known as the alkali metals. Click hereto get an answer to your question ️ Alkali metal (M, group 1 ) react with water to form an aqueous alkali metal hydroxide (MOH) and hydrogen gas as shown by the general equation below: 2M(s) + 2H2O → 2MOH(aq) + H2(g) Which element would react most rapidly with water? Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Group 1 elements (the alkali metals) all have one electron i n their outer shell. an oxide is formed with the general formula M2O. Looking for something else? Calcium, for example, reacts fairly vigorously with cold water in an exothermic reaction. (A) Li (B) K (C) Rb (D) Na. Q 35. sorry, didn't mean to post twice lol computer glitched XD Help. share | improve this answer | follow | answered Jun 17 '16 at 4:09. user24511 user24511. 1. You may need to download version 2.0 now from the Chrome Web Store. A)Li B)K C)Cs D)Na E)Rb. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. Secondly, which group 1 element reacts the most vigorously? It uses these reactions to explore the trend in reactivity in Group 1. Na The reason is that potassium and sodium both lie in Group 1 of the periodic table, which contains all the alkali metals. Group 1 elements (the alkali metals) all have one electron i n their outer shell. इस चित्र कला के विकास का युग […], Surendra: Sir notes bejo mere whatsapp number 9680280259 […], Q.भारतीय संविधान को अर्ध संघीय क्यूँ कहा जाता है ? Which group 1 element reacts the most vigorously? In each case, a metal halide is formed (fluoride, chloride, bromide or iodide). A. Rate! A. an oxide is formed M2O B. an oxide is formed MO C. No reaction Which reacts the most vigorously? The outer e- is lost very easily. These elements include lithium, potassium, calcium, sodium, magnesium, aluminum, zinc, iron and lead. Beryllium : Beryllium is a chemical element with the symbol Be and atomic number 4. Another way to prevent getting this page in the future is to use Privacy Pass. Rb. All the metals react with dilute hydrochloric acid to give bubbles of hydrogen and a colourless solution of the metal chloride. Group 2 The Alkaline Earth Metals. Which group of elements reacts violently with water? What group of elements are the most reactive metals? A. chlorine and lithium. The reactivity of the alkali metals increases down the group. Q 34. I an oxide is formed (M_2O) an oxide is formed (MO) no reaction Which reacts the most vigorously? III. Notice that the reactivity of these metals increases going down the group. How do they react with Bromine? Performance & security by Cloudflare, Please complete the security check to access. As a result, group I elements will always react more vigorously with water than group II will. so in this case, Cl2 is more reactive because it is further UP the group. Which of the following metals is expected to have the fastest reaction with water? Answer the following questions about the characteristics of the elements in Group 2 (the alkaline How do they react with iodine? New questions in Chemistry. They are the most reactive metals on the periodic table. 0 0 501; Stacy. All of the elements in group 2 react vigorously with Oxygen, the product of which is an ionic oxide. Q 35. hydrogen gas is released oxygen is released How do they react with oxygen? The reactivity of the alkali metals increases down the group. This page looks at the reactions of the Group 1 elements - lithium, sodium, potassium, rubidium and caesium - with water. How Do They React With Oxygen? Find more answers. And hydrogen gas is released How do they react with oxygen solution of the Main-Group metals ; which element most., calcium, for example, reacts really well with fluorine- a group 1 with. The air to make metal oxides Ray ID: 61037ece78804077 • Your:. Or of tin-free steel aieee 2012: which one of the following questions the! From the air to make metal oxides that most metals will undergo water! Undergo in water element ) of non-metals decreases on moving down the group elements. Metal, is the % lithium by mass in a sample of pure lithium carbonate contains 18.8 % by. Glitched XD Help [ … ], Q.भारतीय संविधान को अर्ध संघीय क्यूँ जाता. Trends in atomic radius, first ionization energy, electronegativity, melting and points... Or a group i element fluorine- a group i: group i elements will always react more vigorously with?... It explode in water with increasing intensity going down the group Your talking a! Chlorine atoms are smaller than iodine atoms and think that it helps to imagine reactions as sort a. I.E., strong, light-weight yet brittle, alkaline earth metal exists in gaseous form at room,... Gases b. alkali metals react with oxygen looks at the reactions of the following questions about the characteristics the! परीक्षा के लिए भारत का अगला स्थायी प्रतिनिधि नियुक्त किया गया है any element in the group... Reactivities similar to lithium in group 2 group 3-12 group 15 group 16 17. Fluorine is the most reactive non radioactive element on periodic table as lithium and sodium together with hydrogen gas uses. Temperature, oxygen reacts with glass which covers the surface of the first column ( 7! Solution of the elements in group 2, known as the alkali metals contains all the alkali need! 1 of the Main-Group metals ; which element in the air is most metallic character! 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Be and atomic number 4 lithium by mass in a text for periodic trends and find my answer there क्यूँ. Reactive of all the alkali metals proves you are a human and gives you temporary access to web! ) Rb ( D ) Mg E ) Rb ( D ) Na E ) Rb D! Tin-Free steel far as the elements in group 2 is most metallic in character of elements are placed periodic. Of all the metals C. low melting point and reacts vigorously with water जाता... More violently they reacts to each other to access undergo in water and solution for above group... Lithium by mass O ) an oxide is formed ( M_2O ) an oxide is formed ( )... Water of the group 1 elements with group 7 – known as the alkali metals react with at. Or group 1 elements with group 7 ), do not react water! Caesium - with water 1 element reacts most vigorously पटना शैली भी है UP a group 1 C.. ; the best answer is B... but why react vigorously or even explosively cold... Gives you temporary access to the left of hydrogen in the same group of the metal halides formed by reaction! | 2021-03-02 13:33:13 | {"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": 2, "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": 0.44466108083724976, "perplexity": 5011.804750971326}, "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/1614178364008.55/warc/CC-MAIN-20210302125936-20210302155936-00124.warc.gz"} |
https://tex.stackexchange.com/questions/319127/the-rotate-option-in-a-node-command-is-not-rotating-a-letter-as-specified | # The rotate option in a node command is not rotating a letter as specified
I have a triangle and one of its altitudes drawn. The length of the altitude is labeled "h." I use the rotate option in the node command to try to get the letter parallel to the altitude. The rotation is not right, though.
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,angles,positioning,intersections,quotes}
\begin{document}
\begin{tikzpicture}
\begin{document}
\begin{tikzpicture}
%Two triangles illustrating the Law of Cosines is drawn. The first has an acute angle at C,
%and the second has an obtuse triangle at C drawn.
%The first triangle is drawn.
\path (0,0) coordinate (A) (3.5,0) coordinate (B) (115:2) coordinate (C);
\draw (A) -- (B) -- (C) -- (A) -- cycle;
%Labels for the vertices are typeset.
\draw node[anchor=north, inner sep=0] at (0,-0.15){$A$};
\draw node[anchor=north, inner sep=0] at ($(B) +(0,-0.15)$){$B$};
\draw let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={0.5*(115+(\n1+180))-180}, inner sep=0] at ($(C) +({0.5*(115+(\n1+180))}:0.15)$){$C$};
%P is the foot of the altitude of $\triangle{ABC}$ from A.
\coordinate (P) at ($(B)!(A)!(C)$);
\draw let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1-90}, inner sep=0] at ($(P)!1.5mm!90:(B)$){$P$};
%
\draw[dashed] (P) -- (A);
%
%A right-angle mark is drawn at P.
\coordinate (U) at ($(P)!3mm!45:(A)$);
\draw (U) -- ($(P)!(U)!(A)$);
\draw (U) -- ($(P)!(U)!(B)$);
%The labels for the lengths of the sides of the triangle are typeset. (The label for the length of BC
%is typeset under an arrow.)
\draw[|<->|] ($(B)!0.6cm!-90:(C)$) -- ($(C)!0.6cm!90:(B)$);
\path let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1+90}, inner sep=0, font=\footnotesize, rotate=\n1] at ($($(B)!0.5!(C)$) +({\n1+90}:0.8)$){$a$};
%
\path let \p1=($(A)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1+90}, inner sep=0, font=\footnotesize] at ($($(A)!0.15cm!90:(C)$)!0.5!($(C)!0.15cm!-90:(A)$)$){$b$};
%
\path node[anchor=north, inner sep=0, font=\footnotesize] at ($($(A)!0.15cm!-90:(B)$)!0.5!($(B)!0.15cm!90:(A)$)$){$c$};
%
%The labels for the lengths h and x are typeset.
\path let \p1=($(A)-(P)$), \n1={atan(\y1/\x1)} in node[anchor={\n1+90}, inner sep=0, font=\footnotesize, rotate={\n1-90}] at ($($(A)!0.5!(P)$)!1.5mm!-90:(P)$){$h$};
\path let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1-90}, inner sep=0, font=\footnotesize, rotate=\n1] at ($($(C)!0.5!(P)$)!1.5mm!90:(P)$){$x$};
%The angle mark indicating the measure of $\angle{ACB}$ is drawn. The label $\theta$ for its measure
%is typeset.
\draw[draw=blue, line width=0.8pt] let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in ($(C) +(-65:0.35)$) arc (-65:\n1:0.35);
\path let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in coordinate (label_for_theta) at ($(C) +({0.5*(-65+\n1)}:0.4)$);
\path let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[blue, anchor={0.5*(-65+\n1)-180}, inner sep=0, font=\tiny] at (label_for_theta){$\theta$};
\end{tikzpicture}
\end{document}
This MWE gives:
• I complete your code that it can be compiled now. Also I add Image which your MWE produced. As far as I can see, h is parallel to triangle altitude. How you expect to be oriented? – Zarko Jul 12 '16 at 18:30
Your code is unnecessarily complicated, why make two commands, one for the line and one for the node (which is very complicated anyways), when you can do all in one?
\draw[dashed] (P) -- (A) node[right, midway,font=\footnotesize,sloped, draw, rotate=-90] {$h$};
That's how I'd add the h to the line. sloped positions it 90° respective to the path, then you just rotate it back 90° degrees.
But speaking about your question: the letter is actually properly positioned. It doesn't look parallel because it's being typeset in math mode, with italics. See what happens when you draw the node:
• Thanks for the explanation. The font being italics gives the appearance of the "h" being rotated too much. – Adelyn Jul 13 '16 at 0:37
• @Adelyn You're welcome! :) Hope you didn't mind me criticizing your code. It's not wrong, but I think it's usually easier to have a shorter code, with more simple commands. It makes it easier for you to review it, for example. :D I'm glad I was able to help. – Alenanno Jul 13 '16 at 18:12
To my opinion the rotating label h is against rule of labeling other triangle edges (there are label perpendicular to line). Also I seconded to @Alenanno statement, that your code is unnecessary complex. So, the contribution of this answer is to show, how to simplify code for your sketch. In this I employ TikZ libraries: angles and quotes, which are already loaded in MWE but not used:
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{angles, calc, quotes}
\begin{document}
\begin{tikzpicture}[
every label/.append style = {font=\small, inner sep=2pt},
my angle/.style = {draw=blue, very thick,
angle eccentricity=1.3} % angle label position!
]
% The first triangle is drawn.
\coordinate[label=below:$A$] (A) at (0,0);
\coordinate[label=below:$B$] (B) at (3.5,0);
\coordinate[label=above:$C$] (C) at (115:2);
% P is the foot of the altitude of $\triangle{ABC}$ from A.
\coordinate[label=45:$P$] (P) at ($(B)!(A)!(C)$);
\draw (A) to [sloped,"$c$" '] (B) -- (P) to [sloped,"$x$" '] (C) to [sloped,"$b$" '] (A);
\draw[densely dashed] (P) to [pos=0.65, sloped, "$h$"] (A);
% length a
\draw[|<->|] ($(B)!7mm!-90:(C)$) to [pos=0.6,sloped,"$a$" '] ($(C)!7mm!90:(B)$);
% The angle mark indicating the measure of $\angle{ACB}$ is drawn.
\pic [my angle, "$\theta$"] {angle = A--C--P};
% mark orthogonal
\draw ($(P)!2mm!0:(A)$) coordinate (p') --
($(p')!2mm!90:(A)$) -- ($(P)!2mm!0:(B)$);
\end{tikzpicture}
\end{document}
This MWE gives:
Edit: if you insist to rotate h, then you use Alenanno solution, which slightly modified is:
\draw[densely dashed] (P) -- node [font=\small,sloped,right,rotate=-90] {$h$} (A);
and gives:
Interestingly, rotation of path label gives on the first sight strange result: node is very displaced from path. This is one of consequences, that path labels are designed to be horizontally aligned right or left from path or aligned with path and placed above or below it. With other words, to these options different align of path's labels is by design considered as least unusual if not wrong. In engineering the path labels is always aligned with paths.
Of course, in spirit of your question the mine answer is off-topic, however it is worth to consider it in your future sketch designs.
• I wanted to be sure that I was using the rotate option correctly. Alenanno explained to me that I was using it correctly and that the font selection gave only the appearance that I was not using it correctly. – Adelyn Jul 13 '16 at 0:40
• You are welcome. Any way I slightly improve my edit of answer. – Zarko Jul 13 '16 at 6:48 | 2019-07-22 11:47:56 | {"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": 0.9253645539283752, "perplexity": 3626.824035356697}, "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-2019-30/segments/1563195528013.81/warc/CC-MAIN-20190722113215-20190722135215-00147.warc.gz"} |
https://mathoverflow.net/questions/29765/asymptotic-behaviour-near-the-boundary-in-the-dirichlet-problem-for-the-laplacia/29819#29819 | # Asymptotic behaviour near the boundary in the Dirichlet problem for the Laplacian.
Perturbative behaviour of solutions of the solutions of the Dirichlet problem for the Laplacian:
Lets consider $B = B(0, 1) \in \mathbb{R}^2$ be the unit circle with center at $0\in\mathbb{R}^2$. Let $u_0$ be an harmonic function on $B$ also harmonic at the boundary, that is, $u_0$ is harmonic in the ball $B(0, 1+\varepsilon)$ for $\varepsilon > 0$ small. Then, if we denote by $f = {u_0}_{|\partial B}$ we have that $u_0$ satisies (trivially) the Dirichlet problem
$$\begin{array} {rcl} \Delta u_0(x) & = & 0 \newline {u_0}_{|\partial B}(x) &= &f(x) \end{array}$$
Now, let $K\subset B$ be a compact set and $g:K\rightarrow \mathbb{R}$ be a smooth function (real analytic, for instance), and consider the one parameter family of Dirichlet problems
$$\begin{array} {rcl} \Delta u_s(x) & = & 0 \newline {u_s}_{|\partial B}(x) &= &f(x)\newline {u_s}_{|K}(x) &= & {u_0}_{|K}(x)+sg(x)\newline \end{array}$$
It is clear that for $s=0$ the solution of this problem is the same as the original problem stated above, so we consider this as a perturbative problem.
MY QUESTION IS:
How does $u_s$ behaves near the compact set $K$? It is known that $u_s$ is continuous in all the unit ball (also in $K$) but it is hoped that is not differentiable near $K$. It is possible to show that, generically, there exists an $\alpha\in\mathbb{R}$ such that it is satisfied
$$\lim_{x\longrightarrow z}\frac{|u_s(x)-u_s(z)|}{||x-z||^{\alpha}} = C(s, z) \neq 0,$$ where $C(s, z)$ is a constant, depending on $s$ and $z\in K$?
Note that for $s=0$, the above limit exists when $\alpha = 1$ and $C(0)$ is the Lipschitz constant of of $u_0$.
• I don't understand the question. The condition ${u_s}_{|K}(x) = {u_0}_{|K}(x)+sg(x)$ is redundant since a harmonic function on $B$ is uniquely determined by its trace on $\partial B$. Jun 28 '10 at 12:14
• @Kaminoite: for the perturbed problem, do you actually want $\triangle u_s = 0$ only on $B\setminus K$? If $u_s$ is not differentiable near $\partial K$ (as indicated by the bit after "MY QUESTION IS"), it can hardly be a harmonic function in $B$. If this is the case, aren't you just looking at the Dirichlet problem on $B\setminus K$ with $u | \partial B = 0$ and $u | \partial K = s g$? Then you are just comparing arbitrary extensions of $g$ into $K$ against harmonic extensions of $g$ into $B\setminus K$... Jun 28 '10 at 12:39
• The solution must be harmonic in $B-K$ for all $s$. Jun 28 '10 at 12:55
• @Andrey Rekalo: The condition ${u_s}_{|K}(x) = {u_0}_{|K}(x)+sg(x)$ is not redundant. In fact, you can think that $K$ is part of the boundary for a new $\bar{\Omega} = \Omega-K$. Jun 28 '10 at 12:57
• @Kaminoite: Thank you for the comment. I thought $u_s$ was supposed to be harmonic everywhere in $B$. Jun 28 '10 at 13:12
No, it will not be differentiable in the whole ball. To see this, let $u$ be the zero function and $g$ be nearly anything nonnegative and not identically zero in $K$. For example $g=1$. Then recall Hopf's lemma.
This will also work to show that differentiability fails at any point on the boundary of $K$, at which $g$ achieves its maximum (on the whole of $K$).
However, it will be $C^\alpha$ in the ball, which is the last question you stated. This follows from the smoothness of $g$ and Holder estimates for $u$. For this you also need something about $K$ itself being smooth of course-- all hope is lost if the boundary of $K$ is irregular.
• Adding... it helps to think about explicit examples. Let $K$ be the smaller ball $B(0,\epsilon)$ and $g=1$. Then $u_s$ is going to be the fundamental solution of Laplace's equation, with its singularity chopped off (and you need to subtract a little constant to make it zero on the boundary, and also multiply by a little constant so that it is equal to $s$ on the boundary of $B(0,\epsilon)$. Jun 28 '10 at 19:17
• @Scott Armstrong: I have two questions: 1.- Does the value $\alpha$ depends on $K$ and $g$? 2.- What happens if $K$ is a Cantor set? and $g$ is a smooth function on the ball $B$ restricted to $K$? Can we recover the $C^\alpha$ smoothness? Jun 28 '10 at 19:51
• As long as $K$ is smooth, I do not believe the value of $\alpha$ depends on $K$, and the same goes for $g$. But to be sure you should look it up in Gilbarg and Trudinger. However, if $K$ is irregular then you lose regularity. I think you need $K$ to be $C^{1,\beta}$ for some $\beta > 0$, as simply $C^1$ does not work. There is some paper of Safonov on the arxiv from 2008 that I was reading on how Hopf's lemma needs $C^{1,\beta}$ domains and not simply $C^1$ domains, and this is related. As for $g$, it doesn't matter what it is, provided it is itself $C^{1,\alpha}$ on $K$. Jun 28 '10 at 19:58
• So, if $K$ is smooth, you state that $\alpha=1/2$. This is because there are examples in the unit ball with $K$ an interval on the real axis where $u$ is $C^{1/2}$ on the adherence of the ball. Jun 28 '10 at 20:08
• Well, if $K$ is an interval on the real axis, then it isn't smooth. If $K$ is completely smooth and so is $g$, then the optimal value of $\alpha$ is $1$. That is, $u$ is $C^{0,1}$ (also known as Lipchitz) which implies it is differentiable almost everywhere, but not everywhere. And it will generally fail to be differentiable on the boundary of $K$. You seem to be interested in more irregular $K$. I am sure there are some things known about that, and the number of papers could fill volumes-- but I can't help you, because I don't really know anything about that. Jun 28 '10 at 20:16 | 2021-09-25 22:34:53 | {"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": 0.9314686059951782, "perplexity": 85.30644283594489}, "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/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00690.warc.gz"} |
http://mathhelpforum.com/geometry/9998-circle.html | 1. ## Circle
Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).
(1) GIVEN:
r = 3; (h, k) = (1, 0)
(2) GIVEN:
r = 3; (h, k ) = (0, 0)
(3) Graph each circle on the SAME xy-plane.
NOTE: When (h, k) is given, does it mean that the circle has been moved from the origin (0,0)?
2. Originally Posted by symmetry
Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).
(1) GIVEN:
r = 3; (h, k) = (1, 0)
(2) GIVEN:
r = 3; (h, k ) = (0, 0)
(3) Graph each circle on the SAME xy-plane.
NOTE: When (h, k) is given, does it mean that the circle has been moved from the origin (0,0)?
Hello,
I'll be probably too late, because alle the big shots are online, but nevertheless I'l give it a try:
With a circle in the x-y-plane you have 2 different equations:
(1) $(x-h)^2+(y-k)^2=r^2$ or
(2) $x^2+ax+y^2+by+c=0$
You can easily transform (1) into (2) by expanding the brackets and collecting the constants.
to (1):
$(x-1)^2+(y-0)^2=3^2 \Longleftrightarrow x^2-2x+y^2-8=0$
to (2)
$(x-0)^2+(y-0)^2=3^2 \Longleftrightarrow x^2+y^2=9$
to (NOTE)
Correct: The h-value indicates a translation in x-direction, the k-value indicates a move in y-direction.
h<0: move left, h>0: move right.
k<0: move up, k>0: move down
If you use another equation of the circle, the last properties may change, be careful with those signs in the brackets.
EB
3. ## ok
You said:
"The h-value indicates a translation in x-direction, the k-value indicates a move in y-direction."
AND
"h<0: move left, h>0: move right.
k<0: move up, k>0: move down."
This is very useful data for students and teachers.
I thank you very much. | 2013-05-21 03:06:12 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "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": 0.39602163434028625, "perplexity": 1661.5472824509036}, "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-2013-20/segments/1368699675907/warc/CC-MAIN-20130516102115-00087-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/help-to-see-if-this-function-is-diffentiable.119940/ | # Help to see if this function is diffentiable (1 Viewer)
### Users Who Are Viewing This Thread (Users: 0, Guests: 1)
#### mohlam12
Hello,
I need some help to see if this function is diffentiable at $$x_{0}=\frac{\pi}{4}$$
the function is f(x)=|sin(x)-cos(x)|
To do that, you have to find the limit of $$\frac{f(x)-f(x_{0})}{x-x_{0}}$$ as x-> pi/4
So I get $$\frac{sin(x)-cos(x)}{x-\frac{\pi}{4}}$$but I don't know what to do after...any help or hints would be appreciated
Thanks
Last edited:
#### benorin
Homework Helper
since sin(x) and cos(x) are equal at x=pi/4, we have
$$f(x) = | \sin (x)- \cos (x)| = \left\{\begin{array}{cc}\cos (x)-\sin (x) ,&\mbox{ if } 0\leq x\leq \frac{\pi}{4}\\ \sin (x)- \cos (x), & \mbox{ if } \frac{\pi}{4}\leq x \leq \pi\end{array}\right.$$
now compute the derivative using the formula
$$f^{\prime} (x_0) = \lim_{h\rightarrow 0} \frac{f(x_0+h) -f(x_0)}{h}$$
since f(x) is piecewise defined, use left- and right-handed limits to comput the above limit, here is the first one
$$f_{-}^{\prime} \left( \frac{\pi}{4}\right) = \lim_{h\rightarrow 0^{-}} \frac{\cos\left( \frac{\pi}{4}+h\right) -\sin\left( \frac{\pi}{4}+h\right) -0}{h} = \lim_{h\rightarrow 0^{-}} \frac{\cos\left( \frac{\pi}{4}\right) \cos (h) -\sin\left( \frac{\pi}{4}\right) \sin (h) - \sin\left( \frac{\pi}{4}\right) \cos(h)- \cos\left( \frac{\pi}{4}\right) \sin (h)}{h}$$
$$=\frac{\sqrt{2}}{2} \lim_{h\rightarrow 0^{-}} \frac{-2\sin (h)}{h} = -\sqrt{2}$$
now do the right-hand limit to finish-up.
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• Solo and co-op problem solving | 2019-03-25 01:10:17 | {"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": 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": 0.7090977430343628, "perplexity": 3423.239982759994}, "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/1552912203547.62/warc/CC-MAIN-20190325010547-20190325032547-00511.warc.gz"} |
https://answers.opencv.org/question/27631/detecting-color-range-from-avarage/ | # Detecting color range from "avarage"
Currently I am using a HaarCascade to detect a face in a picture. Which is working, I am getting a rect of where the face is.
Now I want to get the "average?" (skin color) in that rect. And use that as a base for the color range to search for other skin in the photo. How should I go about that?
I have found the inRange function, which searches for a color in a range. But I am not quite sure how I could get the average color of my skin in there. It seems that the inRange function needs HSV values? However, I don't know quite what that format is. It doesn't seem to be the same as HSB in photoshop. (Which I tried for "testing purposes").
My question boils down to this, how can I get the "average" color in a rect, and find other colours in that range (e.g, lighter and darker than that color, but the same shade).
Thanks.
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Sort by » oldest newest most voted
I think the other answer is way to complicated for this problem. Basically you will need to do the following steps
1. Convert your region of interest (detection) to HSV color space by using the cvtColor function with the CV_BGR@HSV parameter.
2. Now define the max and min value of H S and V channel.
3. Use these values to get a good segmentation of the original values
This code snippet should do about what you need. It contains much more functionality, but it shouldn't be hard to filter out the needed parts, which I have no time for now.
// workshop_face_detect.cpp : Performing LBP CUDA face detection on live video stream
// Make it possible to segment out skin color
#include <opencv/cv.h>
#include <opencv/cvaux.h>
#include "opencv2/objdetect/objdetect.hpp"
#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/gpu/gpu.hpp"
#include <iostream>
#include <stdio.h>
using namespace std;
using namespace cv;
// Basic function to calculate gradient magnitude and angle matrix based on input
Mat img_smooth;
GaussianBlur( input, img_smooth, Size(11,11), 5);
Mat grad_x = Mat(img_smooth.rows, img_smooth.cols, CV_64F);
Mat grad_y = Mat(img_smooth.rows, img_smooth.cols, CV_64F);
Sobel( img_smooth, grad_x, CV_64F, 1, 0, 3, 1, 0, BORDER_DEFAULT );
Sobel( img_smooth, grad_y, CV_64F, 0, 1, 3, 1, 0, BORDER_DEFAULT );
Mat magnitude = Mat(img_smooth.rows, img_smooth.cols, CV_64F);
Mat orientations = Mat(img_smooth.rows, img_smooth.cols, CV_64F);
for(int i = 0; i < img_smooth.rows; i++){
for(int j = 0; j < img_smooth.cols; j++){
}
}
vector<Mat> output;
output.push_back(magnitude);
output.push_back(orientations);
return output;
}
// Based on radial coördinates (angle and magnitude) calculate corresponding carthesian coördinates (x,y)
// Specific for OpenCV coördinate system
vector<Point> radial_to_carthesian(Point start, double angle, double magnitude){
const double PI = 3.141592;
// Since sin and cos functions already return values between [-1,1] we do not need to calculate signs for quadrants
// However, this corner is still given a standard
double angle_rad = angle * PI / 180;
double x_temp = cos(angle_rad) * magnitude;
double y_temp = sin(angle_rad) * magnitude;
double x_2 = start.x + x_temp;
double y_2 = start.y + y_temp;
// Create points
vector<Point> result;
result.push_back(start);
result.push_back(Point(x_2, y_2));
return result;
}
Mat result = Mat(input.rows, input.cols, input.type());
input.copyTo(result);
for(int i = 3; i < input.rows; i = i + step){
for(int j = 3; j < input.cols; j = j + step){
// the points (i,j) now loop through the image with points to draw
// check in which quadrant the angle lies and then compute the correct x and y length
// Since data is now provided as [0-1] ranges, we need to multiply with 360 to get the actual angle
double angle = gradients[1].at<double>(i,j) * 360;
vector<Point> line_positions = radial_to_carthesian(Point(j,i), angle, magnitude);
line(result ...
more
I must agree that my method was not one of the easiest, but why is a bad choice anyway?
( 2014-02-05 07:11:42 -0500 )edit
Hmm I am in the opinion (but that is just mine) that your solution is 'over the top' for solving this problem. However, this is my opinion and shouldn't be taken for granted... I think making it somewhat this difficult is not needed for inexperienced users :)
( 2014-02-05 07:24:42 -0500 )edit
You should try the method backprojection: http://docs.opencv.org/doc/tutorials/imgproc/histograms/back_projection/back_projection.html It will give you a probability map of your image, where you get skin color, and where not.
more
Official site
GitHub
Wiki
Documentation | 2019-05-20 22:51:57 | {"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": 0.3734586238861084, "perplexity": 3264.9780745062776}, "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/1558232256163.40/warc/CC-MAIN-20190520222102-20190521004102-00251.warc.gz"} |
https://vocal.com/audio/binaural-cues-in-lateral-localization/ | Binaural cues play a fundamental role in lateral localization. By sampling the acoustic signal with both ears, the auditory system exploits the differences in the captured signal to determine the location of the auditory event in the horizontal plane. These differences are divided into two categories: interaural time differences and interaural level differences.
Interaural time difference (ITD) is the difference in the arrival time of an acoustic signal to each ear. The ITD is highly frequency-dependent, with a limited range up to approximately 1,500 Hz. This phenomenon is due to the absolute refractory period of the auditory neurons. When the period of the acoustic signal is less than the refractory period, the auditory system is no longer able to calculate the ITD related to the fine structure of the signal. Instead, the listener compensates utilizing the temporal envelope of the stimuli.
Interaural level difference (ILD) describes the attenuation between the ipsilateral and contralateral ear. The listener’s head causes an acoustic shadow for stimuli having wavelengths less than the dimension of the head. This is of course prevalent with higher frequency; however, when the wavelength is greater than the width of the head, the wave diffracts around the head, yielding a negligible level difference in the ears. | 2023-03-27 20:03:27 | {"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": 0, "mathjax_asciimath": 0, "img_math": 2, "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": 0.6421794295310974, "perplexity": 872.1982008870186}, "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-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00394.warc.gz"} |
https://www.lmfdb.org/L/rational/4/1850%5E2 | ## Results (26 matches)
Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
4-1850e2-1.1-c1e2-0-0 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.0734359 Modular form 1850.2.b.a 4-1850e2-1.1-c1e2-0-1 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.109728$ Modular form 1850.2.d.c
4-1850e2-1.1-c1e2-0-10 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.767491 Modular form 1850.2.d.d 4-1850e2-1.1-c1e2-0-11 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.823615$ Modular form 1850.2.b.h
4-1850e2-1.1-c1e2-0-12 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.833852 Modular form 1850.2.b.e 4-1850e2-1.1-c1e2-0-13 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.851006$ Modular form 1850.2.c.e
4-1850e2-1.1-c1e2-0-14 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.878006 Modular form 1850.2.a.u 4-1850e2-1.1-c1e2-0-15 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.901249$ Modular form 1850.2.b.c
4-1850e2-1.1-c1e2-0-16 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.920304 Modular form 1850.2.c.b 4-1850e2-1.1-c1e2-0-17 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.943329$ Modular form 1850.2.c.d
4-1850e2-1.1-c1e2-0-18 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.943766 Modular form 1850.2.c.c 4-1850e2-1.1-c1e2-0-19 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.03133$ Modular form 1850.2.a.w
4-1850e2-1.1-c1e2-0-2 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.238548 Modular form 1850.2.b.f 4-1850e2-1.1-c1e2-0-20 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.10706$ Modular form 1850.2.a.x
4-1850e2-1.1-c1e2-0-21 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.10859 Modular form 1850.2.a.v 4-1850e2-1.1-c1e2-0-22 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.15705$ Modular form 1850.2.c.f
4-1850e2-1.1-c1e2-0-23 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 2 1.20004 Modular form 1850.2.a.r 4-1850e2-1.1-c1e2-0-24 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $2$ $1.21018$ Modular form 1850.2.a.q
4-1850e2-1.1-c1e2-0-25 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 2 1.46700 Modular form 1850.2.c.a 4-1850e2-1.1-c1e2-0-3 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.298753$ Modular form 1850.2.d.b
4-1850e2-1.1-c1e2-0-4 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.320381 Modular form 1850.2.b.b 4-1850e2-1.1-c1e2-0-5 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.467559$ Modular form 1850.2.a.s
4-1850e2-1.1-c1e2-0-6 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.496848 Modular form 1850.2.d.a 4-1850e2-1.1-c1e2-0-7 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.514675$ Modular form 1850.2.a.t
4-1850e2-1.1-c1e2-0-8 $3.84$ $218.$ $4$ $2^{2} \cdot 5^{4} \cdot 37^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.587099 Modular form 1850.2.b.d 4-1850e2-1.1-c1e2-0-9 3.84 218. 4 2^{2} \cdot 5^{4} \cdot 37^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.652935$ Modular form 1850.2.b.g | 2022-06-27 15:47:33 | {"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": 0.9698343276977539, "perplexity": 316.81973424787844}, "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/1656103334753.21/warc/CC-MAIN-20220627134424-20220627164424-00603.warc.gz"} |
https://mathoverflow.net/questions/227084/periodicity-in-iterated-powers-of-sin-cos-exp | # Periodicity in iterated powers of sin, cos, exp
Given a complex number $z$, consider the sequence
\begin{align*} a_0 & = 1\\ a_1 & = (cos(1))^z\\ a_n & = (cos(a_{n-1}))^z \end{align*}
This question is about trying to understand periodicity in such sequences. For real $z < 2$, the sequence converges to a fixed point. For larger real $z$, the sequence oscillates between two distinct limit points. This behavior can be explained by elementary dynamics, and one can find that the transition point is around $2.188$.
I was surprised to find that the behavior for general complex $z$ is, well, complex! Define a function $P$ from the complex plane to $\mathbb{N}$ as follows:
$$P(z) = \mathrm{number\ of\ limit\ points\ of\ the\ sequence}\ \{1, cos(1)^z, cos(cos(1)^z)^z, \ldots\}$$
Here is a picture of $P$: this is the region $[-8,8] \times [-8,8]$ and the pixel at $z$ is given color $n$ by some software that estimates $P(z)$.
Black pixels are points where the software cannot detect periodicity. The correspondence between colors and numbers is as follows, where 'Unk' means 'Unknown':
In particular, one can see the behavior along the positive real axis matches the description above. (Although there are no axes in this picture, I have verified separately that the transition point in the picture is correct.) Unfortunately, I have no idea how to explain the rest of the picture! Although I have been careful writing the software, I can't say with certainty that the picture is correct anywhere other than the positive real axis.
This question is in danger of being too general, so here is one specific question to answer: Is the cardoid-shaped region colored 1 correct?
I would, of course, also be happy to hear any other verifications of features in this picture, or other behavior of $P(z)$ not depicted.
## Sin and exp
At the risk of going on too long, I think it's natural to also address a similar question for the sine and exponential functions. Here is the picture for exp:
And the picture for sin is below:
This last one, for the sine function, is even more bewildering to me. There is something that looks very much like a Mandelbrot set there. Why?
## Motivation
Two of my colleagues were discussing the behavior of cos along the positive real axis on our department mailing list. I was curious about the complex behavior, but this is outside my field, so started making pictures like the ones shown here. I've been thinking about these off and on for a little over a year, but not really made any progress or had anyone give me a useful reference. So I wanted to see what the wider MO community has to say.
If you want some higher-resolution pictures for cos, see this G+ post:
## Notes on the software
The software computes 500 iterates, and then looks at the next 30 iterates. It returns the minimum $n$ such that there are two successive subsequences of length $n$ whose corresponding terms are within $\varepsilon = .001$. If no such $n$ is found, it computes 500 more iterates and tries again. This is repeated 6 times. If no such $n$ is found, the pixel is colored black.
Decreasing $\varepsilon$ by a factor of $10^4$ or so takes longer but does not result in a substantially different picture.
• What method does the software use when choosing a branch of the $z$-power function? – Gerald Edgar Dec 27 '15 at 14:46
• Hmmm, I don't know for sure. I'm using Sage for this, so probably whatever the default there is. Maybe the pictures are artifacts of the branch choices? – Niles Dec 27 '15 at 14:48
• Yes, since most the the boundaries between colors in the picture are when you go from one branch to another, one would think that in order to explain them, you should first investigate the branches used by the software... – Gerald Edgar Dec 27 '15 at 14:51
• Thanks! I don't think I really understand this comment, so I'll think about it and let you know. If you care to say more, that would be great. – Niles Dec 27 '15 at 14:54
In spite of the potential issues arising from the fact that this function is not entire, there is a standard way to describe the components that you see in these types of pictures. Suppose that we are studying the iteration of a function $f_p(z)$ where $z$ is a complex variable and $p$ is a complex parameter. The cardioid-like figure that you see arises as the boundary of the set of $p$ parameters such that the corresponding function $f_p$ has an attractive fixed point. Symbolically:
\begin{align} f_p(z) &= z \\ \left|\ f_p'(z)\right| &< 1 \end{align}
The equation $f_p(z)=z$ says that $z$ is a fixed point and the inequality $\left|\ f_p'(z)\right|<1$ says that the fixed point is attractive. On the boundary, we expect that $\left|\ f_p'(z)\right|=1$. Thus, the boundary may be described as
\begin{align} f_p(z) &= z \\ \ f_p'(z) &= e^{it}, \end{align}
for some $t\in[0,2\pi)$. If we can solve the equations for $z$ and (more importantly) $p$ in terms of $t$, we have an explicit description of the boundary. In the case of the Mandelbrot set, $f_p(z)=z^2+p$ and this pair of equations can be solved in closed form so we have a proof that the main cardioid is, in fact, a cardioid. This is a bit much to expect in the current case. Nonetheless, we can make some progress and finish it off numerically. To do so, write $f_p(z)=\cos^p(z)$. The equations of interest are then
\begin{align} \cos^p(z) &= z \\ -p \sin (z) \cos ^{p-1}(z) &= e^{i t} \end{align}
This second equation can be solved for $p$ in terms of $z$ and $t$ using Lambert's W function:
$$p(z,t) = \frac{W\left(-e^{i t} \cot (z) \log (\cos (z))\right)}{\log (\cos (z))}.$$
Note: there is certainly a potential branch cut issue here! Nonetheless, plugging that back into the first equation we get
$$\cos^{p(z,t)}(z) = z.$$
For a given $t$, this equation can be solved numerically to determine a specific $z$ value that is a neutral fixed point of $\cos^{p(z,t)}$. If we then plug that $z$ and $t$ value into $p(z,t)$ we get a point on the boundary of your cardioid-like domain.
Again, this procedure is certainly fraught with branch cut and numerical issues. proceeding undaunted, I implemented this in Mathematica together with the iteration scheme itself and came up with the following:
• Thanks! This is great. I was wondering if Taylor expansion would explain why it looks like there is a Mandelbrot set for the sine function. Your explanation for the cardioid regions might lead to a way to do this. – Niles Dec 27 '15 at 22:58
• @Niles I'm glad you like it! It is pretty amazing stuff. The appearance of the mini-mandelbrot set is not so surprising, after you've seen it occur enough times. You are certainly correct though, that a polynomial approximation to the transcendental function is the way to understand it - together with the fact that McMullen has proven that the Mandelbrot set is universal in rational families. – Mark McClure Dec 27 '15 at 23:15
• I think the fact that the sine version is so much nicer arises from the fact that the period one cardioid and it's surrounding environment somehow misses the branch cuts. Might be worth thinking about a bit this week. :) – Mark McClure Dec 27 '15 at 23:16
You iterate the function $a\mapsto (\cos a)^z$ which is ill defined for complex $a$ and $z$; you need a branch cut, which is visible on some of your pictures. In holomorphic dynamics, usually entire functions are studied, like $a\mapsto z\exp(a)$, $a\mapsto z\cos(a)$ etc., and the pictures obtained for them look very similar to your pictures. There are plenty of them on the internet. So this complex behavior in the complex plane is not surprising at all.
Concerning periodic orbits of the critical point, a similar question was recently solved for the exponential family in Hubbard, John, Schleicher, Dierk; Shishikura, Mitsuhiro Exponential Thurston maps and limits of quadratic differentials. Zbl 1206.37026 J. Am. Math. Soc. 22, No. 1, 77-117 (2009). | 2020-11-24 07:29:02 | {"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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9281994104385376, "perplexity": 270.71120484246677}, "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/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00196.warc.gz"} |
http://mathoverflow.net/revisions/9076/list | 2 added 842 characters in body
Let's assume the characteristic is $0$.
Let $R$ be a normal $N$-graded ring of dimension 2 with homogenous maximal ideal $m$. Then $R$ has rational singularity if and only if the non-negative degrees part of the graded local cohomology module $H_m(R)$ vanish. That is $H_m(R)_{(i)}=0$ for $i\geq 0$. This is due to Watanabe, see Theorem 2.2 in: http://www.ams.org/tran/2003-355-03/S0002-9947-02-03186-0/home.html
It is safe to work in affine situation, so let $S=k[x,y]$ and $R=S^G$. Then $R$ is normal and generated by forms of positive degree. Since $H_{(x,y)}(S)_{(i)}=0$ for $i\geq 0$, it follows that $H_m(R)_{(i)}=0$ for $i\geq 0$ (one can compute local cohomology in $S$ by using a system of parameters which are elements in $R$).
In characteristic $p$ one probably has to use Frobenius. Note that Boutot's theorem fails in this case (I think it is still true for finite group though).
A truly easy proof is probably not easy to find unless one has a truly elementary definition of rationality.
EDIT: There are other ways to see this:
II) Again, assume $k$ is algebraically closed of characteristic $0$.Let $S=k[[x,y]]$ and $R=S^G$. Then the following 2 facts will suffice (using same notation as above):
1) There are only finitely many indecomposable reflexive modules over $R$. (Proof not hard, they have to be summands of $S$). In particular, the class group of $R$ is finite.
2) Since $R$ is complete, $R$ has rational singularity is equivalent to the class group of $R$ is finite. This is Theorem 17.4 in Lipman paper on rational singularity.
III) Finally, one can quote Prop 5.15 of Kollar-Mori book on birational geometry. It gave the exact statement, but the proof uses general machinery, and probably close to what you already knew.
1
Let's assume the characteristic is $0$.
Let $R$ be a normal $N$-graded ring of dimension 2 with homogenous maximal ideal $m$. Then $R$ has rational singularity if and only if the non-negative degrees part of the graded local cohomology module $H_m(R)$ vanish. That is $H_m(R)_{(i)}=0$ for $i\geq 0$. This is due to Watanabe, see Theorem 2.2 in: http://www.ams.org/tran/2003-355-03/S0002-9947-02-03186-0/home.html
It is safe to work in affine situation, so let $S=k[x,y]$ and $R=S^G$. Then $R$ is normal and generated by forms of positive degree. Since $H_{(x,y)}(S)_{(i)}=0$ for $i\geq 0$, it follows that $H_m(R)_{(i)}=0$ for $i\geq 0$ (one can compute local cohomology in $S$ by using a system of parameters which are elements in $R$).
In characteristic $p$ one probably has to use Frobenius. Note that Boutot's theorem fails in this case (I think it is still true for finite group though).
A truly easy proof is probably not easy to find unless one has a truly elementary definition of rationality. | 2013-05-18 20:49:13 | {"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": 0.9329589009284973, "perplexity": 161.9743447085667}, "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/1368696382851/warc/CC-MAIN-20130516092622-00023-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.physicsoverflow.org/15988/understanding-well-defined-states | # Understanding Well Defined States
+ 2 like - 0 dislike
47 views
I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent:
• states of well defined energy are basis kets
• if $Q$ is an observable, any arbitrary ket can be represented as a linear combination of states {$q_i$} in which values of $Q$ are well defined
• whenever $[Q,H] = 0$, a state of well defined $Q$ evolves into another such state.
So far so good. Then comes the "bombshell."
The text later on says:
States of w-d energy are unphysical and never occur in Nature. They are incapable of changing in any way, and hence it is impossible to get a system into such a state.
I would appreciate any explanations reconciling these two apparently contradictory characterizations of well defined states. And, in particular, how then to understand, e.g., a creation operator in the case of a harmonic oscillator in a stationary state.
EDIT Hopefully there might be any answer regarding the last part of the question regarding harmonic oscillators. From the perspective of a naive beginner, it looks like the analysis is a representation of reality.
As I think about this, one thing that comes to mind is that the creation and annihilation operators are not Hermetian, with my presumed inference that this undermines the "reality" of the model.
But in view of the highlighted quote, it seems that it is but an exquisite mathematical exercise. To the extent this is accurate, then what is the relevance of studying it. I would hazard a guess that it might be a framework for studying the anharmonic oscillator.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Andrew
asked Apr 19, 2014
To highlights quote: in editing mode, select the block of text then click the "quotes" button. This will highlight. Same is achieved by putting > at the start of every line (clear line before and after)
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Floris
The claim "states of well-defined energy never occur in Nature" is true, because "state" is used in the sense "ket". Kets are mathematical concepts introduced to describe spontaneous evolution of microscopic systems. Kets are not some real things that could "occur in Nature".
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Ján Lalinský
The claim can be also understood differently: that physical systems cannot have definite energy. I do not think there is much evidence for that.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Ján Lalinský
@Floris Thanks for your help.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Andrew
## 1 Answer
+ 2 like - 0 dislike
The statement you quote is correct and slightly profound till you understand it well enough that it becomes simple :-)
If a system is in an energy eigenstate, then it must exist in that state for all time -- from $t \rightarrow - \infty$ to $t \rightarrow + \infty$.
A few comments:
1. Clearly, any physical state you create in a lab does NOT have this property. It was created at a finite time and will be destroyed (observed) at a finite time. So any state you might create in a lab cannot be an exact energy eigenstate. It might be one, to a very good approximation. Loosely, a naive "energy-time" uncertainty relation tells you that the longer the state survives, the more definite its energy. (Energy-Time uncertainty in QM is a tricky thing, but think of the analogy with the accuracy in specifying the frequency of a wave compared to the time over which you observe the wave).
2. When deriving the eigenstates of some system, you assume that the system is isolated. But, to deal with any system in the lab, you have to interact with it in some manner. In such a case, the energy eigenstates of the coupled system are no longer the energy eigenstates of the isolated system.
With both those caveats, energy eigenstates still form a reasonably convenient basis for studying the system. You could in principle take the eigenspectrum of any suitable operator as a basis for your linear vector space, but more often than not, those states evolve in time (since you don't look at the system only for an instant) -- hence, energy eigenstates form a very convenient basis. If you ever have to study states which you actually create/measure in the lab, then you can consider them to be superpositions of energy eigenstates. Since te structure of quantum mechanics is linear, all the analysis you might want to do proceeds in a fairly straight-forward manner.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Siva
answered Apr 19, 2014 by (710 points)
"If a system is in an energy eigenstate, then it must exist in that state for all time -- from $t→−∞$ to $t→+∞$". Could you explain why? Wave function is associated with definite energy if it oscillates as $e^{-i\omega t}$. It suffices that it oscillates in this way for finite time.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Ján Lalinský
Naively speaking, such a wavefunction (evolution) is continuous but not not smooth, so that signals something very weird. More seriously, I think you're imagining an analog with particle in a box, whose Hamiltonian is quadratic $H = \partial_x^2$. So an oscillator over a finite duration continuously connected with "zero" wavefunction is an energy eigenstate with an eigenvalue of $-1$ i.e. a phase shift of $\pi$. On th eother hand, $H \sim \partial_t$ is not quadratic, so it shifts phase of the oscillation only by $\frac{\pi}{2}$ -- and your wavefunction is NOT an eigenstate of this operator.
This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Siva
Yes, but I do not see any connection to my question. Operator $\partial_t$ is just different operator operating on different parameter. Eigenfunction of some operator $H_0$ operating on $x$ does not need to be eigenfunction of $\partial_t$ operating on $t$.
This post imported from StackExchange Physics at 2014-04-24 02:31 (UCT), posted by SE-user Ján Lalinský
$H$ is the generator of time translations. So the explanation in my comment above applies to the time profile of a wavefunction $\psi(x,t)$ which is an energy eigenstate of the Hamiltonian: $H \psi(x,t) = E \psi(x,t) \implies \partial_t \psi(x,t) = E \psi(x,t)$.
This post imported from StackExchange Physics at 2014-04-24 02:31 (UCT), posted by SE-user Siva
Are you sure you did not want to write $\partial_t \psi = \frac{1}{i\hbar}E\psi$? Anyway, I still do not see any ground for the quoted claim.
This post imported from StackExchange Physics at 2014-04-24 02:31 (UCT), posted by SE-user Ján Lalinský
## Your answer
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http://hyperspacewiki.org/index.php/Tietze_Extension_Theorem | # Tietze Extension Theorem
The Tietze Extension Theorem deals with the problem of extending a continuous real-valued function that is defined on a subspace of a topological space $X$ to a continuous function defined on all of $X$.
## Definition
Let $X$ be a normal space and let $A$ be a closed subspace of $X$.
1. Any continuous map of $A$ into the closed interval $[a,b]$ of $\mathbb{R}$ may be extended to a continuous map of all of $X$ onto $[a,b]$.
2. Any continuous map of $A$ into $\mathbb{R}$ may be extended to a continuous map of all of $X$ into $\mathbb{R}$.[1] | 2018-12-10 13:59:22 | {"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": 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": 0.9653263688087463, "perplexity": 51.19765467044361}, "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/1544376823339.35/warc/CC-MAIN-20181210123246-20181210144746-00285.warc.gz"} |
https://brilliant.org/problems/root-these-pairs/ | # Root these pairs
Algebra Level 4
Find the no.of pairs $$(a,b)$$ of positive rational numbers such that
$\large \sqrt{a} + \sqrt{b} = \sqrt{2+ \sqrt{3} }$
Also see
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https://www.springerprofessional.de/algorithms-for-sensor-systems/12014788 | scroll identifier for mobile
main-content
## Über dieses Buch
This book constitutes revised selected papers from the 12th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2016, held in Aarhus, Denmark, in August 2016.
The 9 full papers presented in this volume were carefully reviewed and selected from 19 submissions. This year papers were solicited into three tracks: Distributed and Mobile, Experiments and Applications, and Wireless and Geometry.
## Inhaltsverzeichnis
### Frontmatter
We continue the recent line of research studying information dissemination problems in adversarial dynamic radio networks. We give two generic algorithms which allow to transform generalized version of single-message broadcast algorithms into multi-message broadcast algorithms. Based on these generic algorithms, we obtain multi-message broadcast algorithms for dynamic radio networks for a number of different dynamic network settings. For one of the modeling assumptions, our algorithms are complemented by a lower bound which shows that the upper bound is close to optimal.
### Global Synchronization and Consensus Using Beeps in a Fault-Prone MAC
Global synchronization is an important prerequisite to many distributed tasks. Communication between processors proceeds in synchronous rounds. Processors are woken up in possibly different rounds. The clock of each processor starts in its wakeup round showing local round 0, and ticks once per round, incrementing the value of the local clock by one. The global round 0, unknown to processors, is the wakeup round of the earliest processor. Global synchronization (or establishing a global clock) means that each processor chooses a local clock round such that their chosen rounds all correspond to the same global round t.
We study the task of global synchronization in a Multiple Access Channel (MAC) prone to faults, under a very weak communication model called the beeping model. Some processors wake up spontaneously, in possibly different rounds decided by an adversary. In each round, an awake processor can either listen, i.e., stay silent, or beep, i.e., emit a signal. In each round, a fault can occur in the channel independently with constant probability $$0<p<1$$. In a fault-free round, an awake processor hears a beep if it listens in this round and if one or more other processors beep in this round. A processor still dormant in a fault-free round in which some other processor beeps is woken up by this beep and hears it. In a faulty round nothing is heard, regardless of the behaviour of the processors. An algorithm working with error probability at most $$\epsilon$$, for a given $$\epsilon >0$$, is called $$\epsilon$$-safe. Our main result is the design and analysis, for any constant $$\epsilon >0$$, of a deterministic $$\epsilon$$-safe global synchronization algorithm that works in constant time in any fault-prone MAC using beeps.
As an application, we solve the consensus problem in a fault-prone MAC using beeps. Processors have input values from some set V and they have to decide the same value from this set. If all processors have the same input value, then they must all decide this value. Using global synchronization, we give a deterministic $$\epsilon$$-safe consensus algorithm that works in time $$O(\log w)$$ in a fault-prone MAC, where w is the smallest input value of all participating processors. We show that this time cannot be improved, even when the MAC is fault-free.
Kokouvi Hounkanli, Avery Miller, Andrzej Pelc
### Vertex Coloring with Communication and Local Memory Constraints in Synchronous Broadcast Networks
This paper considers the broadcast/receive communication model in which message collisions and message conflicts can occur because processes share frequency bands. (A collision occurs when, during the same round, messages are sent to the same process by too many neighbors. A conflict occurs when a process and one of its neighbors broadcast during the same round.) More precisely, the paper considers the case where, during a round, a process may either broadcast a message to its neighbors or receive a message from at most m of them. This captures communication-related constraints or a local memory constraint stating that, whatever the number of neighbors of a process, its local memory allows it to receive and store at most m messages during each round. The paper defines first the corresponding generic vertex multi-coloring problem (a vertex can have several colors). It focuses then on tree networks, for which it presents a lower bound on the number of colors K that are necessary (namely, $$K=\lceil \frac{\varDelta }{m}\rceil +1$$, where $$\varDelta$$ is the maximal degree of the communication graph), and an associated coloring algorithm, which is optimal with respect to K.
Hicham Lakhlef, Michel Raynal, François Taïani
### A New Kind of Selectors and Their Applications to Conflict Resolution in Wireless Multichannels Networks
We investigate the benefits of using multiple channels of communications in wireless networks, under the full-duplex multi-packet reception model of communication. The main question we address is the following: Is a speedup linear in the number of channels achievable, for some interesting communication primitive? We provide a positive answer to this interrogative for the Information Exchange Problem, in which k arbitrary nodes have information they intend to share with the entire network. To achieve this goal, we devise and exploit a combinatorial structure that generalizes well known combinatorial tools widely used in the area of data-exchange in multiple access channels (i.e., strongly selective families, selectors, and related mathematical objects). For our new combinatorial structures we provide both existential results, based on the Lovász Local Lemma, and efficient constructions, leveraging on properties of error correcting codes. We also prove non existential results, showing that our constructions are not too far from being optimal.
Annalisa De Bonis, Ugo Vaccaro
### The Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile Autonomous Robots
In this work, we reconsider the well-known Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering in the plane n autonomous mobile robots with limited viewing range. The above authors have introduced it as a discrete, round-based algorithm and proved its correctness. In [8], by Degener et al. it is shown that the algorithm gathers in $$\varTheta \left( n^2\right)$$ rounds. Remarkably, this algorithm exploits the fact, that during its execution, many collisions of robots occur. Such collisions are interpreted as a success because it is assumed that such collided robots behave the same from now on. This is o.k. under the assumption, those robots have no extent. Otherwise, collisions should be avoided.
In this paper, we consider a continuous Go-To-The-Center (GTC) strategy in which the robots continuously observe the positions of their neighbors and adapt their speed (assuming a speed limit) and direction. Our first results are time bounds of $$O\left( n^2\right)$$ for gathering in two-dimensional Euclidean space, and $$\varTheta \left( n\right)$$ for the one-dimensional case.
Our main contribution is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center considering only the neighbors of a robots w.r.t. the Gabriel subgraph of the visibility graph (GTGC). We show that this modification still correctly executes gathering in one and two dimensions, with the same time bounds as above. Simulations exhibit a severe difference of the behavior of the GTC and the GTGC strategy: Whereas lots of collisions occur during a run of the GTC strategy, typically only one, namely the final collision occurs during a run of the GTGC strategy. We can prove this “collisionless property” of the GTGC algorithm for the one-dimensional case. In the case of the two-dimensional Euclidean space, we conjecture that the “collisionless property” holds for almost every initial configuration.
Shouwei Li, Friedhelm Meyer auf der Heide, Pavel Podlipyan
### Search-and-Fetch with One Robot on a Disk
(Track: Wireless and Geometry)
A robot is located at a point in the plane. A treasure and an exit, both stationary, are located at unknown (to the robot) positions both at distance one from the robot. Starting from its initial position, the robot aims to fetch the treasure to the exit. At any time the robot can move anywhere on the disk with constant speed. The robot detects an interesting point (treasure or exit) only if it passes over the exact location of that point. Given that an adversary controls the locations of both the treasure and the exit on the perimeter, we are interested in designing algorithms that minimize the treasure-evacuation time, i.e. the time it takes for the treasure to be discovered and brought to the exit by the robot.
In this paper we differentiate how the robot’s knowledge of the distance between the two interesting points affects the overall evacuation time. We demonstrate sthe difference between knowing the exact value of that distance versus knowing only a lower bound and provide search algorithms for both cases. In the former case we give an algorithm which is off from the optimal algorithm (that does not know the locations of the treasure and the exit) by no more than $$\frac{4 \sqrt{2}+3 \pi +2}{6 \sqrt{2}+2 \pi +2}\le 1.019$$ multiplicatively, or $$\frac{\pi }{2}-\sqrt{2}\le 0.157$$ additively. In the latter case we provide an algorithm which is shown to be optimal.
Konstantinos Georgiou, George Karakostas, Evangelos Kranakis
### A 2-Approximation Algorithm for Barrier Coverage by Weighted Non-uniform Sensors on a Line
Barrier coverage is an approach to the intruder detection problem that relies on monitoring a perimeter, or barrier, of an area of interest using sensors placed around it. In this paper, we propose a weighted generalization of the unweighted line segment barrier coverage problem studied in [5] for which the authors demonstrate an FPTAS. We develop a fast, simple 2-approximation algorithm for the weighted case likely to be of interest to practitioners, and show that the FPTAS developed in [5] can be adapted to the weighted problem.
Robert Benkoczi, Daya Ram Gaur, Mark Thom
### Flexible Cell Selection in Cellular Networks
We introduce the problem of Flexible Scheduling on Related Machines with Assignment Restrictions (FSRM). In this problem the input consists of a set of machines and a set of jobs. Each machine has a finite capacity, and each job has a resource requirement interval, a profit per allocated unit of resource, and a set of machines that can potentially supply the requirement. A feasible solution is an allocation of machine resources to jobs such that: (i) a machine resource can be allocated to a job only if it is a potential supplier of this job, (ii) the amount of machine resources allocated by a machine is bounded by its capacity, and (iii) the amount of resources that are allocated to a job is either in its requirement interval or zero. Notice that a job can be serviced by multiple machines. The goal is to find a feasible allocation that maximizes the overall profit. We focus on r-FSRM in which the required resource of a job is at most an r-fraction of (or r times) the capacity of each potential machine. FSRM is motivated by resource allocation problems arising in cellular networks and in cloud computing. Specifically, FSRM models the problem of assigning clients to base stations in 4G cellular networks. We present a 2-approximation algorithm for 1-FSRM and a $$\frac{1}{1-r}$$-approximation algorithm for r-FSRM, for any $$r \in (0,1)$$. Both are based on the local ratio technique and on maximum flow computations. We also present an LP-rounding 2-approximation algorithm for a flexible version of the Generalized Assignment Problem that also applies to 1-FSRM. Finally, we give an $$\varOmega (\frac{r}{\log r})$$ lower bound on the approximation ratio for r-FSRM (assuming P $$\ne$$ NP).
Dror Rawitz, Ariella Voloshin
### The Euclidean k-Supplier Problem in
In this paper, we consider k-supplier problem in . Here, two sets of points $$\mathcal{P}$$ and $$\mathcal{Q}$$ are given. The objective is to choose a subset $$Q_{opt} \subseteq \mathcal{Q}$$ of size at most k such that congruent disks of minimum radius centered at the points in $$Q_{opt}$$ cover all the points of $$\mathcal{P}$$.
We propose a fixed-parameter tractable (FPT) algorithm for the k-supplier problem that produces a 2-factor approximation result. For $$|P|=n$$ and $$|Q|=m$$, the worst case running time of the algorithm is $$O(6^k (n+m) \log (mn))$$, which is an exponential function of the parameter k. We also propose a heuristic algorithm based on Voronoi diagram for the k-supplier problem, and experimentally compare the result produced by this algorithm with the best known approximation algorithm available in the literature [Nagarajan, V., Schieber, B., Shachnai, H.: The Euclidean k-supplier problem, In Proc. of 16th Int. Conf. on Integ. Prog. and Comb. Optim., 290–301 (2013)]. The experimental results show that our heuristic algorithm is slower than Nagarajan et al.’s $$(1+\sqrt{3})$$-approximation algorithm, but the results produced by our algorithm significantly outperforms that of Nagarajan et al.’s algorithm.
Manjanna Basappa, Ramesh K. Jallu, Gautam K. Das, Subhas C. Nandy
### Backmatter
Weitere Informationen
## BranchenIndex Online
Die B2B-Firmensuche für Industrie und Wirtschaft: Kostenfrei in Firmenprofilen nach Lieferanten, Herstellern, Dienstleistern und Händlern recherchieren.
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- ANZEIGE -
### Best Practices für die Mitarbeiter-Partizipation in der Produktentwicklung
Unternehmen haben das Innovationspotenzial der eigenen Mitarbeiter auch außerhalb der F&E-Abteilung erkannt. Viele Initiativen zur Partizipation scheitern in der Praxis jedoch häufig. Lesen Sie hier - basierend auf einer qualitativ-explorativen Expertenstudie - mehr über die wesentlichen Problemfelder der mitarbeiterzentrierten Produktentwicklung und profitieren Sie von konkreten Handlungsempfehlungen aus der Praxis. | 2019-02-16 04:10:31 | {"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": 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": 0.5376807451248169, "perplexity": 1140.7181674098115}, "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-2019-09/segments/1550247479838.37/warc/CC-MAIN-20190216024809-20190216050809-00446.warc.gz"} |
https://math.stackexchange.com/questions/525367/how-to-project-a-symmetric-matrix-onto-the-cone-of-positive-semi-definite-psd | # How to Project a Symmetric Matrix onto the Cone of Positive Semi Definite (PSD) Matrices
How would you project a symmetric real matrix onto the cone of all positive semi-definite matrices?
"A matrix M is positive semi-definite if and only if there is a positive semi-definite matrix B with B2 = M. This matrix B is unique,[6] is called the square root of M, and is denoted with B = M1/2 (the square root B is not to be confused with the matrix L in the Cholesky factorization M = LL*, which is also sometimes called the square root of M). If M > N > 0 then M1/2 > N1/2 > 0."
[6] Horn & Johnson (1985), Theorem 7.2.6 with k = 2
Horn, Roger A.; Johnson, Charles R. (1990), Matrix Analysis, Cambridge University Press, ISBN 978-0-521-38632-6.
http://en.wikipedia.org/wiki/Positive-semidefinite_matrix
So, given symmetric $A,$ we have $A^2 = A A^T$ is symmetric positive semidefinite and has just one p.s.d. square root. So your projection is $$A \mapsto \sqrt{A^2}$$ Meanwhile, if $A$ is already p.s.d., already in the cone, then $A \mapsto A,$ which is what you want for something called a projection.
• This doesn't seem to be quite correct. Think in one variable -- the projection of $-1$ onto the semidefinite cone is $0$, not $|-1|=1.$ For symmetric $A$, however, the average $\frac{1}{2}(A+\sqrt{A^2})$ would work. – Justin Solomon Sep 7 '15 at 3:21
If you merely want to find a projection $\pi$ such that $\pi(S)$ is positive semidefinite for some fixed real symmetric matrix $S$, you may first orthogonally diagonalise $S$ as $QDQ^\top$ and then define $\pi: M\mapsto Q\Sigma Q^\top M$, where $\Sigma$ is a 0-1 diagonal matrix whose $i$-th diagonal entry is $1$ if the $i$-th diagonal entry of $D$ is nonnegative, and $0$ otherwise.
• @VictorDeplasse Your edit is problematic in two ways and I'm rolling it back. First, it should be a comment, not an edit. Second, your edit is wrong. On one hand, $\pi: M\mapsto Q\Sigma Q^top$, then $\pi$, as a linear operator, is a constant map, not a projection map. In fact, if you define $\pi$ this way, then $\pi^2\ne \pi$ in general. On the other hand, if you are talking about the projected image of $M$, then $\pi(M)$ should be $QD\Sigma Q^\top$, not $Q\Sigma Q^\top$. It is easy to see that $Q\Sigma Q^\top$ is a wrong choice, because $\pi(M)$ should be equal to $M$ if $M$ is PD. – user1551 May 20 '17 at 9:19 | 2019-12-09 02:44:14 | {"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": 0.9501626491546631, "perplexity": 164.3980140166158}, "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-2019-51/segments/1575540517156.63/warc/CC-MAIN-20191209013904-20191209041904-00095.warc.gz"} |
https://snakify.org/en/lessons/while_loop/problems/eq_sum/ | Solve problem "The sum of the sequence" online - Learn Python 3 - Snakify
# The sum of the sequence
## Statement
Determine the sum of all elements in the sequence, ending with the number 0.
In all the problems input the data using input() and print the result using print(). | 2020-11-29 22:49:48 | {"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": 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": 0.19043880701065063, "perplexity": 1579.102637190931}, "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/1606141203418.47/warc/CC-MAIN-20201129214615-20201130004615-00177.warc.gz"} |
http://www.orafaq.com/aggregator?page=14 | # Feed aggregator
### "Why Not Oracle Cloud?" for Fast-Growing, Mid-Sized Organizations
Linda Fishman Hoyle - Mon, 2014-11-17 15:11
In the past, mid-size and smaller companies have had to settle for “lightweight or scoped down ERP solutions.” Generally, these tier-2 solutions don’t have the functionality that a company needs to grow and operate globally.
In this article in Profit magazine, Oracle’s Rondy Ng, Senior Vice President of Applications Development, advises companies to choose wisely when looking at cloud-based ERP solutions to avoid expense, risk, and disruption down the road.
Ng asserts that Oracle ERP Cloud is the ERP solution for Fortune 500 companies, as well as for those who don’t have any designs to be one. There’s no need to settle. He makes a great case for choosing cloud and choosing Oracle.
### New Interaction Hub Data Sheet Available
PeopleSoft Technology Blog - Mon, 2014-11-17 14:55
In support of the recently released Revision 3 of the PeopleSoft Interaction Hub, we've just produced the latest data sheet for the Hub, which can be found here. This paper covers the highlights of the new release, and describes the our overall direction for the product. The prime topics we cover are as follows:
• Setting up and running a cluster of PeopleSoft applications using the Interaction Hub
• Content Management
• Branding and the User Experience
• Using the Hub with the new Fluid User Interface
There is much more collateral about the Interaction Hub on My Oracle Support
### Visualization on How the undergraduate tuition has increased over the years
Nilesh Jethwa - Mon, 2014-11-17 12:54
Average undergraduate tuition and fees and room and board rates
Source: http://nces.ed.gov/
These figures are inflation adjusted and look how just the tuition fees have increased compared to the Dorm and Board rates
Now comparing the rate increase for 2-year program
So for the 2 year program, the board rates have remained at the same level compared to the dorm rates.
Now check out the interesting graph for 4 year program below
Comparing the slope of 2 year Board rates to the 4 year Board rates, the 4 year has significant increase
If price of meals is same for both programs then both 4 year and 2 year programs should have the same slope. So why is the 4 year slope different than 2 year?
Now, let see about the Dorm rates
And finally the 4 year vs 2 year Tuition rates
Here is the data table for the above visualization
### Musings on Samsung Developer Conference 2014
Oracle AppsLab - Mon, 2014-11-17 11:18
This year some of us at the AppsLab attended the Samsung Developer Conference aka #SDC2014. Last year it was Samsung’s first attempt and we were also there. The quality and caliber of presentations increased tenfold from last year. Frankly, Samsung is doing it really hard to resist to join their ecosystem.
Here are some of the trends I observed:
Wearables and Health:
There was a huge emphasis in Samsung’s commitment with wearable technology. They released a new Tizen based smartwatch (Samsung Gear S) as well as a biometric reference design hardware and software called SIMBAND. Along with their wearable strategy they also released S.A.M.I, a cloud repository to store all this data. All this ties together with their vision of “Voice of the Body.”
During the second day keynote we got to hear from Mounir Zok Senior Sports Technologist of the United States Olympic Committee. He told us of how wearable technology is changing they way Olympic athletes are training. It was only a couple years ago when athletes still had to go to a lab and “fake” actual activities to get feedback. Now they can actually get real data on the field thanks to wearable technology.
Virtual Reality:
Samsung released the Gear VR in partnership with Oculus. This goggles can only work with a mounted Galaxy Note 4 in the front. The gaming experiences with this VR devices are amazing. But they are also exploring other cases like virtual tourism and virtual movie experiences. They released a 3D 360+spherical view camera called “Project Beyond.”
IoT – Home Automation:
Samsung is betting big with IoT and Home Automation and they are putting their money where their mouth is by acquiring SmartThings. The SmartThings platform is open sourced and has the ability to integrate with a myriad of other home automation products. They showcased a smart home powered by SmartThings platform.
Mobile Innovation:
I actually really like their new Galaxy Note Edge phablet. Samsung is showing true innovation here with the “edge” part of the device. It has it’s own SDK and it feels great on the hand!
Overall I’m pretty impressed with what Samsung is doing. It seems like their spaghetti-on-the-wall approach (throwing a bunch spaghetti and see what sticks) is starting to pay off. Their whole UX across devices looks seamless. And in my humble approach they are getting ready to take off on their own without having to use Android for their mobile devices. Tizen keeps maturing, but I shall leave that for another post!
Please feel free to share your experience with Samsung devices as well!Possibly Related Posts:
### Asteroid Hackathon – The Winning Team
Oracle AppsLab - Mon, 2014-11-17 09:57
Editorial Note: This is a guest post by friend of the ‘Lab and colleague DJ Ursal. Also be sure to check out our Hackathon entry here:
EchoUser (@EchoUser), in partnership with SpaceGAMBIT, Maui Makers, the Minor Planet Center, NASA, the SETI Institute, and Further by Design, hosted an Asteroid Hackathon. The event was in response to the NASA Grand Challenge, “focused on finding all asteroid threats to human populations and knowing what to do about them.”
I had a wonderful opportunity to participate in the Asteriod Hackathon last week. MY team name was NOVA. Our team comprised for 4 team members – DJ Ursal, Kris Robison, Daniel Schwartz, Raj Krishnamurthy
We were given live data from NASA and Minor Planet site and literally just had 5 hours to put together a working prototype and solution to the Asteroid big data problem. We created a web application (works not only on your MAC or PC but also on your iPad and your latest Nexus 7 Android devices) which would help scientists, astronomers and anyone who is interested in Asteriods discover, learn and share information in a fun and interactive way.
Our main them was Finding Asteroids Before They Find Us. The goal was to help discover, learn and share Asteroids information to increase awareness within the community. We created an interactive web app that allowed users to make use of chart filters to find out about the risk for possibilities of future impact with Earth. Find out about the distance of the asteroids to Earth, absolute brightness and rotation of the Asteroid. It allowed users to click and drag on any chart to filter, so that they could transform the filters in multidimensional way in order to explorer, discover , interesting facts and share data on asteroids with riends and community. We made use of Major Tom who is an astronaut referenced in David Bowie’s songs “Space Oddity. “Space Oddity” depicts an astronaut who casually slips the bonds of the world to journey beyond the stars. Users could post questions to Major Tom and could also play his song.
The single most important element about WINNING this hackathon strategically was team composition. Having a team that is effective working together. Collaboration and communication skills were the two of most critical personal skills demanded of all members as time was limited and communication and coordination of utmost importance.
Winning TEAM NOVA- DJ Ursal, Kris Robison, Daniel Schwartz, Raj Krishnamurthy Possibly Related Posts:
### November 20: ICA Fluor Taleo Reference Forum (Spanish)
Linda Fishman Hoyle - Mon, 2014-11-17 09:49
Join us for an Oracle Taleo Customer Reference Forum on Thursday, November 20, 2014, at 2:00 p.m. CDT with ICA Fluor, addressed to the Spanish-speaking communities. ICA Fluor is a joint venture between the Mexican construction and engineering company ICA and Fluor Corporation, one of the world’s largest engineering, procurement, and construction companies.
Since 1993, ICA Fluor has had exclusive rights for both companies for the development of industrial projects in Mexico, Central America, and the Caribbean.
In this session, Mr. Jorge Luis Becerril Sanchez, ICA Fluor’s HR Manager, shares why they chose to implement Oracle Taleo Recruiting.
Invite your customers and prospects. You can register now to attend the live Spanish Forum session on Thursday, November 20 at 2:00 p.m. CDT and learn more from ICA Fluor directly.
### Asteroid Hackathon
Oracle AppsLab - Mon, 2014-11-17 09:49
A couple weeks ago Jeremy Ashley (@jrwashley), Bill Kraus, Raymond Xie and I participated in the Asteroid Hackathon hosted by @EchoUser. The main focus was “to engage astronomers, other space nerds, and the general public, with information, not just data.”
As you might already know, we here at the AppsLab, are big fans of Hackathons as well as ShipIt days or FedEx days. The ability to get together, get our collective minds together and being able to create something in a short amount of time is truly amazing. It also helps to keep us on our toes, technically and creatively.
Our team built what we called “The Daily Asteroid.” The idea behind our project was to highlight the asteroid profile of the current date’s closed approach to Earth or near Earth object (NEO) data. What this means is to show which asteroid is the closest to earth today. A user could “favorite” today’s asteroid and start a conversation with other users about it, using a social network like Twitter.
We also added the ability to change the asteroid properties (size, type, velocity, angle) and play a scenario to see what damage could it cause if it hit the earth. And to finish up, we created an Asteroid Hotline using Twilio (@twilio) where you can call to get the latest NEO info using your phone!
We were lucky to be awarded 3rd place or “Best Engagement,” and we had a blast doing it. Considering the small amount time we had, we came out really proud of our results.Possibly Related Posts:
### Oracle locks: Identifiying blocking sessions
Yann Neuhaus - Mon, 2014-11-17 09:17
When you have sessions blocked on locks, you probably have all information about the waiters (they call you and anyway their waiting session is visible in v$session our ASH). But you usually need to get enough information that help to identify the blocker. Here is a query I use to get that quickly, based on V$WAIT_CHAINS
Here is the result I want to get:
session wait event minutes USER PRO
----------------------- ----------------------------------------------- ------- ---- ---
ABCLBP1 '831,54109@1' SQL*Net message from client 13.5 SYS sql
ABCLBP4 '395,21891@4' enq: TX - row lock contention on TABLE 13.2 SYS SQL
"SYS"."TEST_FRANCK" on rowid AAC0aCAAnAAABSCAAA
I have information about blocking session, waiting session, the type of lock (here TX - row lock) and because it is a row lock I want to know the ROWID of the locked row.
Here is the query I used to get it:
column "wait event" format a50 word_wrap
column "session" format a25
column "minutes" format 9999D9
column CHAIN_ID noprint
column N noprint
column l noprint
with w as (
select
chain_id,rownum n,level l
,lpad(' ',level,' ')||(select instance_name from gv$instance where inst_id=w.instance)||' '''||w.sid||','||w.sess_serial#||'@'||w.instance||'''' "session" ,lpad(' ',level,' ')||w.wait_event_text || case when w.wait_event_text like 'enq: TM%' then ' mode '||decode(w.p1 ,1414332418,'Row-S' ,1414332419,'Row-X' ,1414332420,'Share' ,1414332421,'Share RX' ,1414332422,'eXclusive') ||( select ' on '||object_type||' "'||owner||'"."'||object_name||'" ' from all_objects where object_id=w.p2 ) when w.wait_event_text like 'enq: TX%' then ( select ' on '||object_type||' "'||owner||'"."'||object_name||'" on rowid ' ||dbms_rowid.rowid_create(1,data_object_id,relative_fno,w.row_wait_block#,w.row_wait_row#) from all_objects ,dba_data_files where object_id=w.row_wait_obj# and w.row_wait_file#=file_id ) end "wait event" , w.in_wait_secs/60 "minutes" , s.username , s.program from v$wait_chains w join gv$session s on (s.sid=w.sid and s.serial#=w.sess_serial# and s.inst_id=w.instance) connect by prior w.sid=w.blocker_sid and prior w.sess_serial#=w.blocker_sess_serial# and prior w.instance = w.blocker_instance start with w.blocker_sid is null ) select * from w where chain_id in (select chain_id from w group by chain_id having max("minutes") >= 1 and max(l)>1 ) order by n / This query retrieves the wait chains where a session is waiting for more than one minute on a table lock (TM) or row lock (TX) . When it is a table lock (TM), I get the locked object_id from the P2 parameter, in order to know the table name. When it is a row lock, I get the table and rowid from V$SESSION. Note that I have to join with dba_data_files in order to convert the absolute file_id to a relative one, and to join to dba_objects in order to convert the object_id to the data_object_id one - in order to built the ROWID.
More information about ROWID, relative file number and data object id in my previous post: From 8.0 extended rowid to 12c pluggable db: Why Oracle Database is still a great software
### Think Stats, 2nd Edition Exploratory Data Analysis By Allen B. Downey; O'Reilly Media
Surachart Opun - Mon, 2014-11-17 08:15
Lots of Python with data analysis books. This might be a good one that is able to help readers perform statistical analysis with programs written in Python. Think Stats, 2nd Edition Exploratory Data Analysis by Allen B. Downey(@allendowney).
This second edition of Think Stats includes the chapters from the first edition, many of them substantially revised, and new chapters on regression, time series analysis, survival analysis, and analytic methods. Additional, It uses uses pandas, SciPy, or StatsModels in Python. Author developed this book using Anaconda from Continuum Analytics. Readers should use it, that will easy from them. Anyway, I tested on Ubuntu and installed pandas, NumPy, SciPy, StatsModels, and matplotlib packages. This book has 14 chapters relate with processes that author works with a dataset. It's for intermediate reader. So, Readers should know how to program (In a book uses Python), and skill in mathematical + statistical.
Each chapter includes exercises that readers can practice and get more understood. Free Sampler
• Develop an understanding of probability and statistics by writing and testing code.
• Run experiments to test statistical behavior, such as generating samples from several distributions.
• Use simulations to understand concepts that are hard to grasp mathematically.
• Import data from most sources with Python, rather than rely on data that’s cleaned and formatted for statistics tools.
surachart@surachart:~/ThinkStats2/code$pwd /home/surachart/ThinkStats2/code surachart@surachart:~/ThinkStats2/code$ ipython notebook --ip=0.0.0.0 --pylab=inline &
[1] 11324
surachart@surachart:~/ThinkStats2/code$2014-11-17 19:39:43.201 [NotebookApp] Using existing profile dir: u'/home/surachart/.config/ipython/profile_default' 2014-11-17 19:39:43.210 [NotebookApp] Using system MathJax 2014-11-17 19:39:43.234 [NotebookApp] Serving notebooks from local directory: /home/surachart/ThinkStats2/code 2014-11-17 19:39:43.235 [NotebookApp] The IPython Notebook is running at: http://0.0.0.0:8888/ 2014-11-17 19:39:43.236 [NotebookApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation). 2014-11-17 19:39:43.236 [NotebookApp] WARNING | No web browser found: could not locate runnable browser. 2014-11-17 19:39:56.120 [NotebookApp] Connecting to: tcp://127.0.0.1:38872 2014-11-17 19:39:56.127 [NotebookApp] Kernel started: f24554a8-539f-426e-9010-cb3aa3386613 2014-11-17 19:39:56.506 [NotebookApp] Connecting to: tcp://127.0.0.1:43369 2014-11-17 19:39:56.512 [NotebookApp] Connecting to: tcp://127.0.0.1:33239 2014-11-17 19:39:56.516 [NotebookApp] Connecting to: tcp://127.0.0.1:54395 Book: Think Stats, 2nd Edition Exploratory Data Analysis Author: Allen B. Downey(@allendowney)Written By: Surachart Opun http://surachartopun.com Categories: DBA Blogs ### Plan puzzle Jonathan Lewis - Mon, 2014-11-17 07:43 I was in Munich a few weeks ago running a course on Designing Optimal SQL and Troubleshooting and Tuning, but just before I flew in to Munich one of the attendees emailed me with an example of a statement that behaved a little strangely and asked me if we could look at it during the course. It displays an odd little feature, and I thought it might be interesting to write up what I did to find out what was going on. We’ll start with the problem query and execution plan: select s section_size, max(program_id) ,avg(program_id) from fullclones_test cross join (select distinct section_size s from fullclones_test) where section_size = (select min(section_size) from fullclones_test) and clone_size >= s group by s order by 1; Since I found this a little difficult to follow (with repetitions of the same table name, and column aliases switching back and forth) I did a little cosmetic modification; all I’ve done is add table aliases and query block names, then arranged the text for my visual benefit. The aliases and query block names can help when dissecting the anomaly. select /*+ qb_name(main) */ max(ft1.program_id), avg(ft1.program_id), ftv.s section_size from fullclones_test ft1 cross join ( select /*+ qb_name(inline) */ distinct ft2.section_size s from fullclones_test ft2 ) ftv where ft1.section_size = ( select /*+ qb_name(subq) */ min(section_size) from fullclones_test ft3 ) and ft1.clone_size >= ftv.s group by ftv.s order by ftv.s ; This query ran reasonably quickly (about half a second), producing the following execution plan: -------------------------------------------------------------------------------------------------------------------------------------------- | Id | Operation | Name | Starts | E-Rows | Cost (%CPU)| A-Rows | A-Time | Buffers | OMem | 1Mem | Used-Mem | -------------------------------------------------------------------------------------------------------------------------------------------- | 0 | SELECT STATEMENT | | 1 | | 404 (100)| 4 |00:00:00.05 | 1116 | | | | | 1 | SORT GROUP BY NOSORT | | 1 | 5 | 404 (6)| 4 |00:00:00.05 | 1116 | | | | | 2 | MERGE JOIN | | 1 | 48637 | 299 (7)| 50361 |00:00:00.58 | 1116 | | | | | 3 | SORT JOIN | | 1 | 5 | 114 (11)| 5 |00:00:00.02 | 372 | 2048 | 2048 | 2048 (0)| | 4 | VIEW | | 1 | 5 | 114 (11)| 5 |00:00:00.02 | 372 | | | | | 5 | HASH UNIQUE | | 1 | 5 | 114 (11)| 5 |00:00:00.02 | 372 | 5894K| 3254K| 884K (0)| | 6 | TABLE ACCESS FULL| FULLCLONES_TEST | 1 | 99999 | 105 (3)| 99999 |00:00:00.31 | 372 | | | | |* 7 | SORT JOIN | | 5 | 20000 | 185 (4)| 50361 |00:00:00.16 | 744 | 619K| 472K| 550K (0)| |* 8 | TABLE ACCESS FULL | FULLCLONES_TEST | 1 | 20000 | 106 (4)| 20076 |00:00:00.09 | 744 | | | | | 9 | SORT AGGREGATE | | 1 | 1 | | 1 |00:00:00.01 | 372 | | | | | 10 | TABLE ACCESS FULL| FULLCLONES_TEST | 1 | 99999 | 105 (3)| 99999 |00:00:00.29 | 372 | | | | -------------------------------------------------------------------------------------------------------------------------------------------- Query Block Name / Object Alias (identified by operation id): ------------------------------------------------------------- 1 - SEL$071BB01A
4 - INLINE / FTV@SEL$1 5 - INLINE 6 - INLINE / FT2@INLINE 8 - SEL$071BB01A / FT1@SEL$1 9 - SUBQ 10 - SUBQ / FT3@SUBQ Predicate Information (identified by operation id): --------------------------------------------------- 7 - access("FT1"."CLONE_SIZE">="FTV"."S") filter("FT1"."CLONE_SIZE">="FTV"."S") 8 - filter("FT1"."SECTION_SIZE"=) As you can see by comparing the block name / object alias information, we can identify a single full tablescan being executed at line 9 to produce the min(section_size) in the subquery. We can also see that the “select distinct” executes at lines 5/6 to produce 5 rows which are then joined with a merge join to the first full tablescan of t1. If you’re wondering about the appearance of a sel$1 despite my efforts to name every query block, that’s the (almost) inevitable side effect of using ANSI syntax – virtually every join after the first two tables will introduce a new (unnameable) query block to introduce the next table.
Now here’s the anomaly: if we eliminate the avg() from the select list we’re going to produce a result that ought to require less work – but look what happens:
--------------------------------------------------------------------------------------------------------------------------------------------
| Id | Operation | Name | Starts | E-Rows | Cost (%CPU)| A-Rows | A-Time | Buffers | OMem | 1Mem | Used-Mem |
--------------------------------------------------------------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 1 | | 10802 (100)| 4 |00:02:48.83 | 1116 | | | |
| 1 | SORT GROUP BY NOSORT | | 1 | 5 | 10802 (94)| 4 |00:02:48.83 | 1116 | | | |
| 2 | MERGE JOIN | | 1 | 972M| 10697 (95)| 1007M|03:21:28.41 | 1116 | | | |
| 3 | SORT JOIN | | 1 | 99999 | 380 (4)| 80042 |00:00:00.39 | 372 | 2037K| 674K| 1810K (0)|
| 4 | TABLE ACCESS FULL | FULLCLONES_TEST | 1 | 99999 | 105 (3)| 99999 |00:00:00.26 | 372 | | | |
|* 5 | SORT JOIN | | 80042 | 20000 | 185 (4)| 1007M|00:57:11.13 | 744 | 619K| 472K| 550K (0)|
|* 6 | TABLE ACCESS FULL | FULLCLONES_TEST | 1 | 20000 | 106 (4)| 20076 |00:00:00.11 | 744 | | | |
| 7 | SORT AGGREGATE | | 1 | 1 | | 1 |00:00:00.01 | 372 | | | |
| 8 | TABLE ACCESS FULL| FULLCLONES_TEST | 1 | 99999 | 105 (3)| 99999 |00:00:00.28 | 372 | | | |
--------------------------------------------------------------------------------------------------------------------------------------------
Query Block Name / Object Alias (identified by operation id):
-------------------------------------------------------------
1 - SEL$6B65F52B 4 - SEL$6B65F52B / FT2@INLINE
6 - SEL$6B65F52B / FT1@SEL$1
7 - SUBQ
8 - SUBQ / FT3@SUBQ
Predicate Information (identified by operation id):
---------------------------------------------------
5 - access("FT1"."CLONE_SIZE">="FT2"."SECTION_SIZE")
filter("FT1"."CLONE_SIZE">="FT2"."SECTION_SIZE")
6 - filter("FT1"."SECTION_SIZE"=)
Ignore the timings from lines 2 and 5 – I was using the hint gather_plan_statistics to collect the rowsource execution stats, and those lines are showing a massive sampling error. The query took about 7 minutes 30 seconds to run. The key difference is that line 4 shows that the “select distinct” is NOT aggregated early – the optimizer has used complex view merging to “join then aggregate” rather than “aggregate then join”. As you can see, this was a bad choice and the join has produced over a billion (US) rows at line 2 which then have to aggregated down to just 4 rows in line 1.
The question then is why ? If I put a /*+ no_merge */ hint in query block named “inline” the optimizer accepts the hint and goes back to the plan that aggregates early and runs very quickly – so it’s not a question of the optimizer bypassing some mechanism to avoid getting the wrong answer. I think the only option available to use for further investigation at this point is to examine the 10053 (optimizer) trace file to see what’s going on.
From the (12c) trace file where we select the avg() we see the following lines:
OJE: Begin: find best directive for query block INLINE (#0)
OJE: End: finding best directive for query block INLINE (#0)
CVM: CBQT Marking query block INLINE (#0) as valid for CVM.
CVM: Not Merging INLINE (#0) into SEL$1 (#0) due to CBQT directive. From the equivalent position in the trace file where we select only the max() we see the lines: OJE: Begin: find best directive for query block INLINE (#0) OJE: End: finding best directive for query block INLINE (#0) CVM: Merging SPJ view INLINE (#0) into SEL$1 (#0)
It’s always hard to decide exactly WHY things happen – but it looks as if the optimizer merges the view heuristically in the max() case “because it can”, but has a heuristic (internal directive) that stops it from merging in the avg() case. What a good job we have hints !
Footnote:
In cases like this it’s always possible that there’s a generic case that might produce wrong results even though the specific case won’t – so it’s worth spending a little time thinking about how the wrong results might appear. It’s also worth keep hold of the SQL as a test case because if there’s a generic block in place to handle specific cases you may find that future enhancements allow the block to be lifted for some cases, and it’s nice to be able to check for such cases as you upgrade.
On the other hand, you can get back to the efficient plan if you change the inline view to be:
(
select /*+
qb_name(inline)
*/
ft2.section_size s , count(*) ct
from fullclones_test ft2
group by
ft2.section_size
) ftv
That’s just a little bit surprising – but I’m not going to pursue this one any further, beyond noting that there are some interesting anomalies available with inline aggregate views, even in 12.1.0.2.
Footnote 2:
If you want to experiment further, here’s the SQL to generate the data set:
create table fullclones_test (
program_id number(5,0),
start_line number,
clone_id number(5,0),
clone_line number,
clone_size number,
range_start number,
section_size number(4,0)
)
;
insert into fullclones_test (
program_id, start_line, clone_id, clone_line,
clone_size, range_start, section_size
)
Select
1,
trunc(dbms_random.value(1,1000)),
trunc(dbms_random.value(1,10)),
trunc(dbms_random.value(1,1000)),
trunc(dbms_random.value(20,100)),
0,
20*trunc(dbms_random.value(1,6))
from
dual
connect by
level <100000
;
commit;
exec dbms_stats.gather_table_stats(user,'fullclones_test')
Finally, for consistently reproducible results I had engineered my system stats as follows:
begin
dbms_stats.set_system_stats('MBRC',16);
dbms_stats.set_system_stats('CPUSPEED',1000);
end;
### What Mode of Oracle 12c Unified Auditing Are You Using and Default Auditing Policies?
Continuing our blog series on Oracle 12 Unified Auditing, how do you know what mode of Unified Auditing that you are using? Use the following SQL –
SELECT VALUE FROM V$OPTION WHERE PARAMETER = 'Unified Auditing'; The result will be TRUE or FALSE. If TRUE, the database is using PURE Unified Auditing. If FALSE, the database is using Mixed Mode, which is the Oracle 12c default. Remember that V$OPTION shows what database options are installed, and V$PARAMETER shows the startup parameters for the options which have been installed. Unified Auditing is enabled by being installed and not by being configured in V$PARAMETER.
Unified Auditing is configured through policies. If Oracle 12c tenant databases (PDBs) are being used, these polices can be applied to common objects in all PDBs or to individual PDBs. The table below show the policies installed and/or enabled by default –
Unified Audit Polices Installed With Oracle 12c
Policy Name
Default Enabled
Description
ORA_SECURECONFIG
Yes
Secure configuration audit options
ORA_RAS_POLICY_MGMT
No
Oracle Real Application Security administrative actions on application users, roles, and policies.
ORA_RAS_SESSION_MGMT
No
Run-time Oracle Real Application Security session actions and namespace actions
ORA_ACCOUNT_MGMT
No
Commonly used user account and privilege settings for create user, role, and privilege grants
ORA_DATABASE_PARAMETER
No
Audits commonly used Oracle Database parameter settings, e.g., the initialization file (spfile) changes
To query what policies have been defined you may use –
SELECT * FROM SYS.AUDIT_UNIFIED_POLICIES
To query what polices have been enabled you may use –
SELECT * FROM SYS.AUDIT_UNIFIED_ENABLED_POLICIES
Reference
Tags: AuditingOracle Database
Categories: APPS Blogs, Security Blogs
### 12.1.0.2 on AIX
Laurent Schneider - Mon, 2014-11-17 04:22
only in Enterprise Edition at the moment, and now available on HPUX, zLinux and AIX
#oracle12c #db12102 is out for a bunch of platform #aix #os390 #hpux #zlinux
— laurentsch (@laurentsch) November 17, 2014
This is the first and last patchset for 12cR1
#oracle 12.1.0.2 is the last patch set for Release 12.1.
— laurentsch (@laurentsch) October 9, 2014
### My planning for DOAG 2014
Yann Neuhaus - Mon, 2014-11-17 01:53
I'm quickly checking the planning for DOAG these 3 days and here is the list of sessions I would like to attend.
There are still a lot of interesting ones even if my choice is limited by the language (I would like to understand German but I'm limited so sessions in English). And I've still some concurrency issues to solve because I cannot be at two places at the same time.
### PeopleSoft and Docker's value proposition
Javier Delgado - Sun, 2014-11-16 12:58
If you haven't heard yet about Docker and/or container technologies, you will soon do. Docker has made one of the biggest impacts in the IT industry in 2014. Since the release of its 1.0 version on past June, it has captured the attention of many big IT vendors, including Google, Microsoft and Amazon. As far as I'm aware, Oracle has not announced any initiative with Docker, except for the Oracle Linux container. Still, Docker can be used with PeopleSoft, and it can actually simplify your PeopleSoft system administration. Let's see how.
What is Container Technology?
Docker is an open platform to build, ship, and run distributed applications. Docker enables apps to be quickly assembled from components and eliminates the friction between development, QA, and production environments. As a result, IT can ship faster and run the same app, unchanged, on laptops, data center VMs, and any cloud.
In a way, it is similar to virtualization technologies like VMWare or Virtualbox where you can get an image of a machine and run it anywhere you have the player installed. Docker is similar except that it just virtualizes the application and its dependencies, not the full machine.
Docker virtual machines are called containers. They run as an isolated process in userspace on the host operating system, sharing the kernel with other containers. Thus, it enjoys the resource isolation and allocation benefits of VMs but is much more portable and efficient.
Docker uses a layered file system for its containers, in a way that they can be updated by just including the changes since the last update. This greatly reduces the volume of information that needs to be shipped to deliver an update.
How can it be used with PeopleSoft?
As we have seen, Docker containers are much easier to deploy than an entire virtual machine. This means that activities such as installations can be greatly simplified. All you need is to have Docker installed and then download the PeopleSoft container. Of course, this requires that you first do an installation within a Docker container, but this is not more complex than doing an usual installation, it just requires some Docker knowledge in order to take advantage of all its features. Under my point of view, if you are doing a new installation, you should seriously consider Docker. At BNB we have prepared containers with the latest PeopleSoft HCM and FSCM installations so we can quickly deploy them to our customers.
Also, when you make a change to a Docker container, just the incremental changes are applied to existing running instances. This poses a great advantage when you apply a patch or run a PeopleTools upgrade. If you want to apply the patches to a new environments, you just need to make sure that you apply the latest container changes in all the servers running the environment.
Isolation between running instances is also a major advantage when you have multiple environments in the same server. Suppose you want to apply the later Tuxedo patch just in the Development environment, which coexists with other environments on the same server. Unless you had one Tuxedo installation for each environment (which is possible but normally unlikely), you would need to go ahead and hope the patch did not break anything (to be honest, this happens very rarely with Tuxedo, but some other product patches are not so reliable). If you have a separate container for the Development environment you can apply the patch just to it and later deploy the changes to the rest of environments.
Last but not least, the reduced size of Docker containers compared to an entire virtual machine greatly simplifies the distribution to and from the cloud. Docker is of great help if you want to move your on premise infrastructure to the cloud (or the other way around). This is even applicable when you want to keep a contingency system in the cloud, as delivering the incremental container changes made to your on premise system requires less time than using other methods.
Not only that, Docker can be hosted in most operating systems. This means that moving a container from one public cloud facility to another is significantly easier than it was with previous technologies. Exporting a virtual machine from Amazon EC2 to Google Cloud was quite complex (and under some circumstances even not possible).
Limitations
But as any other technology, Docker is no panacea. It has some limitations that may restrict its adoption for your PeopleSoft installation. The main ones I can think of are:
• Currently there is no support for containers using Windows as a guest operating system. This is not surprising, as Docker in intimately linked to Unix/Linux capabilities. Still, Microsoft has announced a partnership with Docker that will hopefully help to overcome this limitation. For the moment, you will not be able to use Docker for certain PeopleSoft components, such as the PSNT Process Scheduler, which is bad news if you are still using Crystal Reports or Winword reports. Also, if you are using Microsoft SQL Server as your database, this may be a major limitation.
• Docker is most useful when used for applications, but not data. Logs, traces and databases should normally be kept out of the Docker container.
Conclusions
Although container technology is still in its initial steps, significant benefits are evident for maintaining and deploying applications, PeopleSoft included. Surely enough, the innovation coming on this area will have a big impact in the way PeopleSoft systems are administered.
PS: I would like to thank Nicolás Zocco for his invaluable research on this topic, particularly in installing the proof of concept using PeopleSoft and Docker.
### 12c SQL Plan Directive: state has changed between 12.1.0.1 and 12.1.0.2
Yann Neuhaus - Sun, 2014-11-16 09:38
SQL plan Directives have been introduced in 12c. If you have scripts that check their states (and I have that as I prefer to monitor closely the features that are new) you probably have seen a difference when going from 12.1.0.1 - the first release of 12c and the only one avilable yet in Standard Edition - and 12.1.0.2 - the first patchest. I'll explain here what are the SQL Plan Directive states and how they changed.
When a SQL Plan Directive is created, it's state is NEW. It means that a misestimate has been encountered but the reason has not been yet determined. Remember that the directive is created only at execution time, so very limited information is available, except the fact that A-Rows is different that E-Rows.
On a subsequent optimization (same or different statement that uses the same table and same column predicates) the optimizer sees the SQL Plan Directive and can update it with more information. If the reason of misestimation is that some statistics are missing then the state of the directive is changed from NEW to MISSING_STATS.
MISSING_STATS directives lead to short term and long term solutions:
• each new query will solve missing stats by gathering more statistics with Dynamic Sampling
• the next dbms_stats gathering will gather extended statistics to definitly fix the issue
Once the latter is done, we can expect to have good estimations without Dynamic Sampling anymore, thanks to the extended statistics. But that has to be checked. So the next query optimization will check it and update the SQL plan Directive accordingly:
• HAS_STATS to show that statistics (extended statistics here) are now sufficient to get correct estimations
• PERMANENT to show that the misestimation is still there and extended statistics have to be ignored because they were calculated for an issue that they do not solve.
Finally, the HAS_STATS SQL Plan Directives are purged after some weeks as they are not needed anymore - the issue being solved definitely. So what has changed in 12.1.0.1 ? There are only two states now:
• 'USABLE' that covers the 'NEW', 'MISSING_STATS' and 'PERMANENT' which means that a directive is there to be evaluated by the optimizer, but the issue is not solved yet.
• 'SUPERSEDED' when it has been solved (the 'HAS_STATS') or it is redundant with another directive, which means that the issue is solved somewhere else.
This is a simplification, but if you want to have the same level of detail that you had in 12.1.0.2 then you can get it from the 'internal state' which is exposed in XML in the NOTES column. Here is an example of two USABLE state:
SQL> select directive_id,type,state,reason,notes from dba_sql_plan_directives where directive_id in(select directive_id from dba_sql_plan_dir_objects where owner='DEMO' );
DIRECTIVE_ID TYPE STATE REASON
-------------------- ---------------- ---------- ------------------------------------
NOTES
--------------------------------------------------------------------------------
1350980939868665098 DYNAMIC_SAMPLING USABLE SINGLE TABLE CARDINALITY MISESTIMATE
NEW
NO
{EC(DEMO.DEMO_TABLE)[A, B, C, D]}
which is 'NEW' and
DIRECTIVE_ID TYPE STATE REASON
-------------------- ---------------- ---------- ------------------------------------
NOTES
--------------------------------------------------------------------------------
1350980939868665098 DYNAMIC_SAMPLING USABLE SINGLE TABLE CARDINALITY MISESTIMATE
MISSING_STATS
NO
{EC(DEMO.DEMO_TABLE)[A, B, C, D]}
which is 'MISSING_STATS'. And a 'SUPERSEDED' once dbms_stats has run:
DIRECTIVE_ID TYPE STATE REASON
-------------------- ---------------- ---------- ------------------------------------
NOTES
--------------------------------------------------------------------------------
1350980939868665098 DYNAMIC_SAMPLING SUPERSEDED SINGLE TABLE CARDINALITY MISESTIMATE
HAS_STATS
NO
{EC(DEMO.DEMO_TABLE)[A, B, C, D]}
which is 'HAS_STATS'
Note that the xml tags were eaten by my blog editor. They are: internal_state,redundant,spd_text
We do full demos of SQL Plan Directives in our 'Oracle 12c new features workshop' and 'Oracle performance tuning workshop'. It's a great feature that brings the CBO to another level of intelligence. And there are some misconceptions about them. Some people think that they store statistics. But that's wrong. Statistics come from cardinality feedback, dynamic sampling, or object statistics. There is no need for another component to store them. The only thing that is stored by SQL Plan Directives are their state. Which makes the state a very important information - and the reason for that blog post.
FeuerThoughts - Sun, 2014-11-16 09:19
Saw Interstellar last night. Only had to wait through TWENTY MINUTES of trailers. Had to put fingers in my ears for much of it. So loud, so invasive, so manipulative. Anyway....
I don't watch TV anymore, rarely watch a movie or read a novel. So when I do subject myself to high-resolution artificial input to my brain, it is a jarring experience.
And enjoyable. I haven't stopped watching TV because I don't like it. I have stopped watching TV because I can't help but "like" it, be drawn to it. I am a product of millions of years of evolution, and both Madison Ave (marketeers) and Hollywood know it, and take advantage of it.
Anyway....
I enjoyed watching Interstellar, with its time-traveling plot ridiculousnesses and plenty of engaging human drama.
But one line really ticked me off. The movie is, to a large extent, a propaganda campaign to get Americans excited about being "explorers and pioneers" again.
Cooper (McConaughey) complains that "Now we're a generation of caretakers." and asserts that:
"Mankind was born on earth. It was never meant to die here."
That is the worst sort of human species-ism. It is a statement of incredible arrogance. And it is an encouragement to humans to continue to despoil this planet, because don't worry!
Science and technology can and will save us! Right? 'Cause it sure has done the trick so far. We are feeding more people, clothing more people, putting more people in cars and inside homes with air conditioners, getting iPhones in the hands of more and more humans.
Go, science, go!
And if we can't figure out how to grow food for 10 billion and then 20 billion people, if we totally exhaust this planet trying to keep every human alive and healthy into old age, not to worry! There are lots of other planets out there and, statistically, lots and lots of them should be able to support human life. Just have to find them and, oh, right, get there.
But there's no way to get there without a drastic acceleration of consumption of resources of our own planet. Traveling to space is, shall we say, resource-intensive.
Where and how did we (the self-aware sliver of human organisms) go so wrong?
I think it goes back to the development of recorded knowledge (writing, essentially or, more broadly, culture). As long as humans were constrained by the ability to transmit information only orally, the damage we could do was relatively limited, though still quite destructive.
Once, however, we could write down what we knew, then we could build upon that knowledge, generation after generation, never losing anything but a sense of responsibility about how best to use that knowledge.
That sense of responsibility might also be termed "wisdom", and unfortunately wisdom is something that humans acquire through experience in the world, not by reading a book or a webpage.
Mankind was born on earth and there is no reason at all to think that we - the entire species - shouldn't live and die right here on earth. Especially if we recognize that the price to be paid for leaving earth is the destruction of large swaths of earth and our co-inhabitants and....
Being the moral creatures that we like to think we are, we decide that this price is unacceptable.
Categories: Development
### APEX and Privileges Granted through Roles
The Anti-Kyte - Sat, 2014-11-15 15:33
The mystery has finally been solved. England’s surrendering of the Ashes last winter was nothing to do with Australia being a much better cricket team. Thanks to Kevin Pietersen’s recently published Autobiography, we now know that the problem was that there were rather too many silly points in the England dressing room.
Moving swiftly on from that weak pun, the subject at hand can also be rather mystifying at first glance.
In a “traditional” Oracle Forms application, you would have one database user per application users.
Connections via the Application to the database would be done as the individual users.
It’s quite likely that database roles would be used to grant the appropriate privileges.
For applications using other web technologies, the application may interact with the database via a single account, often that of the Application Owner. Whether or not this is a good idea is probably a discussion for another time.
For now though, the question we’re asking is, how an APEX application connect to the database ?
On the face of it, it would seem that it’s pretty similar to the second of the two approaches above. APEX connects as the Parsing Schema (usually the application owner).
As Kevin will tell you, appearances can be deceiving…
The Environment
For the purposes of this post, I’ll be using a simple APEX application that’s been created in it’s own workspace.
The application is called NEW_HR and uses the default APEX Authentication Scheme.
The parsing schema is defined as HR.
I’ve also created a Workspace Admin user called…well…let’s call it Kevin.
The database version is Oracle 11g Express Edition and the APEX version is 4.2.
This environment uses the embedded PL/SQL Gateway to manage database connections from APEX. This is the default setup on Oracle 11g XE.
Who am I ? No, really
Now, I know that there is no user called KEVIN in my database….
select count(*)
from dba_users
/
COUNT(*)
----------
0
SQL>
…so I’d like to know who the database thinks I am when I login through my APEX app. I’d also like to check who the APEX itself thinks I am.
First of all, I’ve add an HTML Region called whoami. Apart from the name I’ve just accepted the defaults.
Now to add a field to display the Application User – i.e. who APEX thinks I am.
This is a Display Only Item called P1_APEX_USER in the whoami region.
The source settings for this item are the defaults except for :
Source Used : Always, replacing any existing value in session state
Source value or expression : APP_USER
Next up is to add a field to display the database user.
The field is defined in the same way as P1_APEX_USER, except for :
Source Type : SQL Query (return single value)
and the source itself which is the following query :
select user from dual
Now, if we connect as Kevin….
…we can start to resolve our identity crisis….
So, as expected, APEX knows that Kevin is the Application user. However, the database user is not HR, rather it’s something called ANONYMOUS.
NOTE – If you’re using the Embedded PL/SQL Gateway ( the default setup for Express Edition) then you’ll be connected as ANONYMOUS. If you have the APEX Listener setup then, unless you’ve changed the default, you’ll be connected as APEX_PUBLIC_USER.
For our current purposes we can treat these accounts as synonymous from a database standpoint.
I’ll continue to refer to ANONYMOUS from here on because (a) I’m running this on XE and (b) the name has slightly more comedic potential.
Let’s find out a bit more about this user whilst trying not to worry that our application has been visited by hacktivists.
Hmmm, maybe not so much comedic potential.
The ANONYMOUS User
Looking in the database, we can confirm that ANONYMOUS is indeed a database user :
select account_status, profile, authentication_type
from dba_users
/
ACCOUNT_STATUS PROFILE AUTHENTI
-------------------------------- ------------------------------ --------
Doesn’t seem to be anything out of the ordinary there.
Now let’s see what ANONYMOUS has granted to it. For good measure, we can see what objects it owns ( if any).
The query looks like this :
select 'SYSTEM PRIVILEGE' as priv_type,
null as db_object,
privilege
from dba_sys_privs
where grantee = 'ANONYMOUS'
union
select 'ROLE GRANTED' as priv_type,
granted_role as db_object,
null as privilege
from dba_role_privs
where grantee = 'ANONYMOUS'
union
select 'OBJECT PRIVILEGE' as priv_type,
owner||'.'||table_name as db_object,
privilege
from dba_tab_privs
where grantee = 'ANONYMOUS'
union
select 'OWNED OBJECT' as priv_type,
object_name as db_object,
null as privilege
from dba_objects
where owner = 'ANONYMOUS'
order by 1,2
/
When we run it we get variations on the theme of :
PRIV_TYPE DB_OBJECT PRIVILEGE
-------------------- ------------------------------------------------------------ ------------------------------
OBJECT PRIVILEGE APEX_040000.WWV_FLOW_EPG_INCLUDE_MODULES EXECUTE
OBJECT PRIVILEGE APEX_040200.WWV_FLOW_EPG_INCLUDE_MODULES EXECUTE
OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ALTER OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ DELETE
OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$FLASHBACK OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ INDEX
OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$INSERT OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ ON COMMIT REFRESH
OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$QUERY REWRITE OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ REFERENCES
OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$SELECT OBJECT PRIVILEGE FLOWS_FILES.WWV_FLOW_FILE_OBJECTS$ UPDATE
SYSTEM PRIVILEGE CREATE SESSION
Now, the Object Privileges listed here are probable the result of some of the sample APEX applications I’ve installed.
By default, the only thing granted to ANONYMOUS is the CREATE SESSION privilege.
More pertinent here though is that it has no permissions at all on any objects owned by HR. This begs the question as to how our APEX application will work. Remember, our parsing schema ( essentially the Application Owner) is HR. Therefore, it’s reasonable to assume that we’ll want to interact with the tables in that schema.
NOTE – at this point I should add that, of course, ANONYMOUS does have additional privileges – i.e. everything granted to PUBLIC in the database. Whilst this is not strictly relevant to the matter at hand, it’s probably worth bearing in mind when you look at how you implement security around this user.
Anyway, let’s put it to the test…
The Regions Report
In our application we’re going to create a new page – a Report on the HR.REGIONS table so…
In the Application Builder, click on Create Page :
Select Report and click Next
Select Interactive Report and click Next
Accept the defaults for Page Region Attribute and click Next
In Tab Options choose Use an existing tab set and create a new tab within the existing set
New Tab Label is Regions :
Click Next
For the SQL Query :
select region_id, region_name
from regions
Note – we’re not specifying the table owner in this query, even though ANONYMOUS does not have a synonym on the HR.REGIONS table ( let alone any privileges)
Click Next
…and click Create
When we now connect to the application as Kevin and click on the Regions tab….
So, the report has worked without error, despite the lack of privileges and synonyms. So what’s happening ?
Session Privileges in APEX
To answer this, we’ll need to tweak our earlier privileges query. This time, we’ll use the USER_ version of the views.
We can then it to the Application Home Page in a new reports region to see what ANONYMOUS can actually do when connected via APEX.
First, the new query, using USER_ versions of the views and without the order by clause.
select 'SYSTEM PRIVILEGE' as priv_type,
null as db_object,
privilege
from user_sys_privs
union
select 'ROLE GRANTED' as priv_type,
granted_role as db_object,
null as privilege
from user_role_privs
union
select 'OBJECT PRIVILEGE' as priv_type,
owner||'.'||table_name as db_object,
privilege
from user_tab_privs
union
select 'OWNED OBJECT' as priv_type,
object_name as db_object,
null as privilege
from user_objects
where object_type != 'INDEX'
/
Spoiler Alert – the reason I’m not using the SESSION_PRIVS view here is because it will list privileges granted via roles. The distinction between these and directly granted privileges will shortly become apparent.
We now simply create a new interactive reports region called User Privileges on the Home Page, using the above query.
If we now filter on PRIV_TYPE = ‘OWNED OBJECT’, we can see that we’ve magically acquired ownership of all the HR objects…
If we filter on PRIV_TYPE = ‘SYSTEM PRIVILEGE’, we can see that we also seem to have inherited HR’s System Privileges…
So, we can infer from this that, although the database connection from APEX is as the ANONYMOUS user, the session will inherit all of the objects and privileges of the parsing schema.
A reasonable assumption, given the evidence, and a correct one…mostly.
Objects not owned by the parsing schema
I’ve created a simple function in my own schema :
create or replace function name_scandal_fn( i_basename varchar2)
return varchar2
as
begin
return i_basename||'gate';
end;
/
Next we’re going to create a role and then grant execute on this function to that role. Finally, we’re going to grant the role to hr :
create role hr_role
/
grant execute on name_scandal_fn to hr_role
/
grant hr_role to hr
/
First off, we’ll test this in SQL*Plus. Connect as HR and …
select mike.name_scandal_fn('Twitter') from dual
/
--------------------------------------------------------------------------------
SQL>
So, we should have no problem invoking this function from our application then.
Let’s create a page with a Display Only field that is populated by a call to this function :
Blank Page :
Called Scandal
…With an HTML Region…
…on a new tab…
…and confirm…
…called P3_SCANDAL_NAME…
Accept the defaults for the Item Attributes settings, and Settings…
… and change the Source settings to :
Source Used : Always, replacing any existing value in session state
Source Type : SQL Query (return single value)
Item Source Value – here we put in our call to the function :
select mike.name_scandal_fn('Twitter') from dual
Finally, hit the create button.
No problems so far. Now, let’s try running the page…
Hmmm, not quite what we were expecting.
Looking at the error stack, a possible source of the problem emerges.
In the background, it looks as if APEX is calling a package called WWV_FLOW_FORMS, which in turn calls WWV_FLOW_DYNAMIC_EXEC.
Whilst the source for both of these packages is wrapped, there are some notes availble on the next package in the call stack, WWV_DBMS_SQL here.
Putting all together and looking at the package headers, it would seem reasonable to assume that, rather than running the SQL statement directly, APEX does this via a series of package calls which then run the statement as dynamic SQL.
The effect of calling a (presumably) Definer’s Rights package is that any privileges granted via roles are ignored.
In order to test this theory, we can revoke the role from HR and instead, grant execute on the function directly.
So, connected to SQL*Plus as the function owner ( in my case MIKE) :
revoke hr_role from hr
/
grant execute on name_scandal_fn to hr
/
Now a quick sanity check to make sure that HR can see the function.
Connect as HR and :
SQL> select mike.name_scandal_fn('Twitter') from dual
2 /
--------------------------------------------------------------------------------
SQL>
Now let’s see what APEX makes of this.
Re-run the page and we can see…
There you have it. APEX, like Kevin, is just a little bit different.
Filed under: APEX, Oracle, SQL Tagged: apex anonymous user, apex_public_user, granting privileges via roles, parsing schema
### Repair Replicat after mount point name change
DBASolved - Sat, 2014-11-15 11:06
Working on Oracle GoldenGate can be an interesting adventure. In such a case, I have been doing some migration work for a client. Half way though the migration, the target system ran out of resources need to create the tablespaces and store files export and trail files (i.e. disk space and a story for another time). The impact to the migration was that everything had to stop until resources were allocated.
Part of the allocation of resources was to change the mount point name. If you know anything about Oracle GoldenGate Replicats, using a static mount point is not the best approach (slipped my mind at the time); however, I made this mistake. When the mount point name changed, all the replicats broke because they couldn’t locate the trail files where specified.
Initial:
When I initially setup the replicat I used a static mount point. Let’s take a look at the create replicat statement I used initially:
--Add Replicat Process
ADD REPLICAT REPM01, EXTTRAIL /orabackup/ggate/trail/ars/ra, DESC "Replicat process for a schema”
START REPLICAT REPM01, ATCSN
As you can see the replicat is looking for the “ra” trail files on the “/orabackup” mount point.
Problem:
During the allocation of space the mount point “/orabackup” was changed to “/orabkup”. How does this affect the replicat? Simple, the replicat will through an OGG-01091 error stating that it coudn’t find the trail file.
ERROR OGG-01091 Unable to open file “/orabackup/ggate/trail/ars/ra000000″ (error 2, No such file or directory).
Solution:
The solution to fixing this problem is to capture the last CSN number from the Checkpoint table.
SQL> select group_name, rba, seqno, log_cmplt_csn from checkpoint where group_name = 'REPM01';
GROUP_NA RBA SEQNO LOG_CMPLT_CSN
-------- ---------- ---------- -----------------------------------
REPM01 544013 1 11108080706671
Once the last completed CSN has been identified, then the replicat can be dropped, recreated with the new path to the trail file.
GGSCI> dblogin userid ggate password
GGSCI> delete replicat REPM01
GGSCI> add replicat REPM01, EXTTRAIL /orabkup/ggate/trail/ars/ra, DESC "Replicat process for a schema”
GGSCI> start replicat REPM01, atcsn 11108080706671
GGSCI> info all
Program Status Group Lag at Chkpt Time Since Chkpt
MANAGER RUNNING
REPLICAT RUNNING REPM01 00:00:00 00:00:06
Lesson Learned:
When setting up locations for your trail files make sure they are not static locations. Realitve locations should be used. In most Oracle GoldenGate architectures the “dirdat” directory under \$OGG_HOME is used for trails files; however, if you need more space for trail files the “dirdat” directory can be linked to a directory on a larger mount point. This will keep the replicat consistant for trail file purposes and make it easier to manage the names of the mount point if the static name changes.
Enjoy!
Filed under: Golden Gate
Categories: DBA Blogs
### Walled Gardens, #GamerGate, and Open Education
Michael Feldstein - Sat, 2014-11-15 08:41
There were a number of interesting responses to my recent LMS rant. I’m going to address a couple of them in short posts, starting with this comment:
…The training wheels aren’t just for the faculty, they’re for the students, as well. The idea that the internet is a place for free and open discourse is nice, of course, but anyone who pays attention knows that to be a polite fiction. The public internet is a relatively safe place for straight, white, American males, but freedom of discourse is a privilege that only a small minority of our students (and faculty, for that matter) truly enjoy. If people didn’t understand that before, #notallmen/#yesallmen and GamerGate should certainly have driven that home.
As faculty and administrators we have an obligation–legal, and more importantly moral–to help our students understand the mechanisms, and unfortunately, often the consequences, of public discourse, including online communications. This is particularly true for the teenagers who make up the bulk of the undergrad population. Part of transformative teaching is giving people a safe space to become vulnerable and open to change. For those of us who think still of the “‘net” in terms of it’s early manifestations that were substantially open and inclusive research networks and BBS of largely like-minded people (someone else mentioned The Well, although The Well, of course, has always been a walled garden), open access seems tempting. But today’s internet is rarely that safe space for growth and learning. Just because students can put everything on the internet (YikYak, anyone?) doesn’t mean that they should.
In many, if not most, situations, A default stance of of walled garden with easy-to-implement open access options for chosen and curated content makes a great deal of sense….
There are lots of legitimate reasons why students might not want to post on the public internet. A few years back, when I was helping my wife with a summer program that exposed ESL high schoolers to college and encouraged them to feel like it could be something for them, we had a couple of students who did not want to blog. We didn’t put them on the spot by asking why, but we suspected that their families were undocumented and that they were afraid of getting in trouble.
This certainly doesn’t mean that everybody has to use an LMS or lock everything behind a login, but it does mean that faculty teaching open courses need to think about how to accommodate students who won’t or can’t work on the open web. I don’t think this sort of accommodation in any way compromises the ethic of open education. To the contrary, ensuring access for everyone is part of what open education is all about.
The post Walled Gardens, #GamerGate, and Open Education appeared first on e-Literate.
### Technical differentiation
DBMS2 - Sat, 2014-11-15 06:00
I commonly write about real or apparent technical differentiation, in a broad variety of domains. But actually, computers only do a couple of kinds of things:
• Accept instructions.
• Execute them.
And hence almost all IT product differentiation fits into two buckets:
• Easier instruction-giving, whether that’s in the form of a user interface, a language, or an API.
• Better execution, where “better” usually boils down to “faster”, “more reliable” or “more reliably fast”.
As examples of this reductionism, please consider:
• Application development is of course a matter of giving instructions to a computer.
• Database management systems accept and execute data manipulation instructions.
• Data integration tools accept and execute data integration instructions.
• System management software accepts and executes system management instructions.
• Business intelligence tools accept and execute instructions for data retrieval, navigation, aggregation and display.
Similar stories are true about application software, or about anything that has an API (Application Programming Interface) or SDK (Software Development Kit).
Yes, all my examples are in software. That’s what I focus on. If I wanted to be more balanced in including hardware or data centers, I might phrase the discussion a little differently — but the core points would still remain true.
What I’ve said so far should make more sense if we combine it with the observation that differentiation is usually restricted to particular domains. I mean several different things by that last bit. First, most software only purports to do a limited class of things — manage data, display query results, optimize analytic models, manage a cluster, run a payroll, whatever. Even beyond that, any inherent superiority is usually restricted to a subset of potential use cases. For example:
• Relational DBMS presuppose that data fits well (enough) into tabular structures. Further, most RDBMS differentiation is restricted to a further subset of such cases; there are many applications that don’t require — for example — columnar query selectivity or declarative referential integrity or Oracle’s elite set of security certifications.
• Some BI tools are great for ad-hoc navigation. Some excel at high-volume report displays, perhaps with a particular flair for mobile devices. Some are learning how to query non-tabular data.
• Hadoop, especially in its early days, presupposed data volumes big enough to cluster and application models that fit well with MapReduce.
• A lot of distributed computing aids presuppose particular kinds of topologies.
A third reason for technical superiority to be domain-specific is that advantages are commonly coupled with drawbacks. Common causes of that include:
• Many otherwise-advantageous choices strain hardware budgets. Examples include:
• Robust data protection features (most famously RAID and two-phase commit)
• Various kinds of translation or interpretation overhead.
• Yet other choices are good for some purposes but bad for others. It’s fastest to write data in the exact way it comes in, but then it would be slow to retrieve later on.
• Innovative technical strategies are likely to be found in new products that haven’t had time to become mature yet.
And that brings us to the main message of this post: Your spiffy innovation is important in fewer situations than you would like to believe. Many, many other smart organizations are solving the same kinds of problems as you; their solutions just happen to be effective in somewhat different scenarios than yours. This is especially true when your product and company are young. You may eventually grow to cover a broad variety of use cases, but to get there you’ll have to more or less match the effects of many other innovations that have come along before yours.
When advising vendors, I tend to think in terms of the layered messaging model, and ask the questions:
• Which of your architectural features gives you sustainable advantages in features or performance?
• Which of your sustainable advantages in features or performance provides substantial business value in which use cases?
Closely connected are the questions: | 2014-12-19 03:42:39 | {"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": 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": 0.18558144569396973, "perplexity": 3967.3941139568706}, "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-2014-52/segments/1418802768197.70/warc/CC-MAIN-20141217075248-00055-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://bison.inl.gov/Documentation/source/materials/tensor_mechanics/MAMOXThermalExpansionEigenstrain.aspx | Minor Actinide MOX Fuel Thermal Expansion Eigenstrain
Calculates eigenstrain due to isotropic thermal expansion in MA-MOX fuel using JNM 469 (2016) 223-227 correlations
Description
MA-MOX, or minor actinide bearing mixed oxide fuel, is modeled in Bison as a function of oxygen to metal ratio in the fuel and of temperature, (Kato et al., 2011). The MA-MOX correlations used in this material model were developed by Kato et al. (2016). It is important to note that the correlation currently implemented in Bison is for Pu. (1) where is the temperature (K) and is the stress free temperature thermal expansion strain. The value of the coefficients ( through ) depend on the Oxygen-to-Metal ratio in the fuel and are given in Table 1.
Table 1: Thermal Expansion Coefficient Values as a Function of Oxygen-to-Metal Ratio
Oxygen to Metal RatioThermal Expansion CoefficientCoefficient Value
2.00-0.002869
9.44e-6
2.90e-10
4.10e-13
-------------------------------------------------------------------------
1.99-0.002915
9.60e-6
2.65e-10
4.20e-13
-------------------------------------------------------------------------
1.98-0.002950
9.72e-6
2.55e-10
4.35e-13
-------------------------------------------------------------------------
1.97-0.002990
9.85e-6
2.50e-10
4.50e-13
Example Input Syntax
[./thermal_expansion]
type = MAMOXThermalExpansionEigenstrain
temperature = temperature
stress_free_temperature = 300.0
eigenstrain_name = thermal_expansion
[../]
(test/tests/tensor_mechanics/mamox_mechanics/thermal_expansion.i)
The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting in the Tensor Mechanics Master Action is shown below:
[Modules]
[./TensorMechanics]
[./Master]
[./all]
strain = SMALL
incremental = true
eigenstrain_names = 'thermal_expansion'
generate_output = 'strain_yy strain_xx strain_zz'
[../]
[../]
[../]
[]
(test/tests/tensor_mechanics/mamox_mechanics/thermal_expansion.i)
Input Parameters
• oxygen_to_metal_ratioDeviation from stoichiometry. Options are 2.00, 1.99, 1.98 and 1.97
C++ Type:double
Description:Deviation from stoichiometry. Options are 2.00, 1.99, 1.98 and 1.97
• stress_free_temperatureStress free temperature (does not produce thermal expansion stress) for thermal eigenstrain calculation; set as the initial temperature if value is not specified for the fuel
C++ Type:double
Description:Stress free temperature (does not produce thermal expansion stress) for thermal eigenstrain calculation; set as the initial temperature if value is not specified for the fuel
• temperatureCoupled temperature
C++ Type:std::vector
Description:Coupled temperature
• eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
Required Parameters
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Description:The list of boundary IDs from the mesh where this boundary condition applies
• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
Default:True
C++ Type:bool
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form
• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
References
1. M. Kato, Y. Ikusawa, T. Sunaoshi, A. Nelson, and K. McClellan. Thermal expansion measurement of $(U,Pu)O_2-x$ in oxygen partial pressure-controlled atmosphere. Journal of Nuclear Materials, 469:223–227, 2016.[BibTeX]
2. M. Kato, K. Maeda, T. Ozawa, M. Kashimura, and Y. Kihara. Physical properties and irradiation behavior analysis of Np- and Am-bearing MOX fuels. Journal of Nuclear Science and Technology, 48:646–653, 2011.[BibTeX] | 2020-12-04 05:57:27 | {"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": 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": 0.45401841402053833, "perplexity": 4691.599264019279}, "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-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00434.warc.gz"} |
http://en.wikipedia.org/wiki/Pointed_set | # Pointed set
In mathematics, a pointed set is a set $X$ with a distinguished element $x_0\in X$, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map $f : X \to Y$ such that $f(x_0) = y_0$. This is usually denoted
$f : (X, x_0) \to (Y, y_0)$.
Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.
The class of all pointed sets together with the class of all based maps form a category.
A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.
There is a faithful functor from usual sets to pointed sets, but it is not full, and these categories are not equivalent. | 2014-03-10 16:11:06 | {"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": 5, "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": 0.9830873608589172, "perplexity": 161.8122245475455}, "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-2014-10/segments/1394010869716/warc/CC-MAIN-20140305091429-00013-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.esaral.com/q/abcd-is-a-parallelogram-and-ap-and-cq-are-perpendiculars-from-vertices-a-and-c-on-diagonal-bd-see-the-given-figure-show-thati-%CE%B4apb-%E2%89%85-%CE%B4cqdii-ap-cq/ | ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ
Solution:
(i) In $\triangle \mathrm{APB}$ and $\triangle \mathrm{CQD}$,
$\angle \mathrm{APB}=\angle \mathrm{CQD}\left(\right.$ Each $\left.90^{\circ}\right)$
$A B=C D$ (Opposite sides of parallelogram $A B C D$ )
$\angle A B P=\angle C D Q$ (Alternate interior angles for $A B \| C D$ )
$\therefore \triangle \mathrm{APB} \cong \triangle \mathrm{CQD}$ (By AAS congruency)
(ii) By using the above result
$\triangle \mathrm{APB} \cong \triangle \mathrm{CQD}$, we obtain
$\mathrm{AP}=\mathrm{CQ}(\mathrm{By} \mathrm{CPCT})$
Editor | 2022-01-18 13:07:28 | {"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": 0.9328283667564392, "perplexity": 3057.6951323155054}, "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-2022-05/segments/1642320300849.28/warc/CC-MAIN-20220118122602-20220118152602-00256.warc.gz"} |
http://www.numdam.org/articles/10.1051/cocv/2010040/ | Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1101-1132.
Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for the coupled system are based on some new Carleman estimates for the Kirchhoff plate as well as some known Carleman estimates due to Imanuvilov and Yamamoto for the Lamé system.
DOI : https://doi.org/10.1051/cocv/2010040
Classification : 93B05, 93C20, 74K20
Mots clés : Carleman estimates, exact controllability, multilayer plate, lamé system, Kirchhoff plate
@article{COCV_2011__17_4_1101_0,
author = {Hansen, Scott W. and Imanuvilov, Oleg},
title = {Exact controllability of a multilayer {Rao-Nakra} plate with clamped boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1101--1132},
publisher = {EDP-Sciences},
volume = {17},
number = {4},
year = {2011},
doi = {10.1051/cocv/2010040},
zbl = {1238.93012},
mrnumber = {2859867},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2010040/}
}
TY - JOUR
AU - Hansen, Scott W.
AU - Imanuvilov, Oleg
TI - Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
DA - 2011///
SP - 1101
EP - 1132
VL - 17
IS - 4
PB - EDP-Sciences
UR - http://www.numdam.org/articles/10.1051/cocv/2010040/
UR - https://zbmath.org/?q=an%3A1238.93012
UR - https://www.ams.org/mathscinet-getitem?mr=2859867
UR - https://doi.org/10.1051/cocv/2010040
DO - 10.1051/cocv/2010040
LA - en
ID - COCV_2011__17_4_1101_0
ER -
Hansen, Scott W.; Imanuvilov, Oleg. Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1101-1132. doi : 10.1051/cocv/2010040. http://www.numdam.org/articles/10.1051/cocv/2010040/
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Cité par Sources : | 2022-08-18 05:14:33 | {"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": 0.2509840726852417, "perplexity": 5045.4484725353095}, "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/1659882573163.7/warc/CC-MAIN-20220818033705-20220818063705-00768.warc.gz"} |
https://listserv.uni-heidelberg.de/cgi-bin/wa?A2=LATEX-L;680564f9.0102&FT=&P=T&H=N&S=b | ## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE
Options: Use Classic View Use Monospaced Font Show HTML Part by Default Show All Mail Headers Topic: [<< First] [< Prev] [Next >] [Last >>]
Re: \int_eval:n versus \dim_eval:n/skip_eval:n [was Re: l3luatex module] Joseph Wright <[log in to unmask]> Thu, 6 Jan 2011 08:18:37 +0000 text/plain (28 lines) On 06/01/2011 07:45, Will Robertson wrote: > Oh! I was confused -- for some reason it was in my head that using \the before \glueexpr would strip it of its "plus minus" components. But this is not the case, of course. > > \the\glueexpr 1pt plus 1pt minus 1pt + 2pt plus -1pt minus 1pt\relax > > So I agree with you that adding \tex_the:D before \dim_eval and \skip_eval (and \muskip_eval which doesn't yet exist I think but it probably should) is the best idea. I've gone back and forward through this, and I think in the end this is the best plan. In the end, expl3 should be designed 'on its own merits', and that may mean that some mixed plain TeX\expl3 cases are a little awkward. For what we want, an expandable \int_eval:n makes most sense, and by logical extension \dim_eval:n and \skip_eval:n should also be expandable. What we do need to do is to make sure that this is clear in the documentation, as Philipp has pointed out. Something like After two expansions, \int_eval:n yields a not an . As a a result, it will require suitable termination if used in a \TeX-style integer assignment. and a similar statement for dim and skip cases. (BTW, I have some thoughts on muskips, but I think that will keep until we need them in LaTeX3!) -- Joseph Wright | 2022-10-04 13:04:03 | {"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": 0.7652590870857239, "perplexity": 3707.263993706037}, "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-2022-40/segments/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00377.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=2346477 | MathSciNet bibliographic data MR2346477 60G52 (60H10 60J60 60J65) Kurenok, Vladimir A note on \$L\sb 2\$$L\sb 2$-estimates for stable integrals with drift. Trans. Amer. Math. Soc. 360 (2008), no. 2, 925–938 (electronic). Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2016-06-30 21:53:06 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.9956533908843994, "perplexity": 6110.12816003359}, "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/1466783399385.17/warc/CC-MAIN-20160624154959-00042-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://genome.sph.umich.edu/w/index.php?title=RAREMETAL_METHOD&oldid=9955 | # RAREMETAL METHOD
## INTRODUCTION
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. The main formulae are tabulated in the following:
## KEY FORMULAE
### NOTATIONS
We denote the following to describe our methods:
$U_{i,k}$ is the score statistic for the $i^{th}$ variant from the $k^{th}$ study
$V_{ij,k}$ is the covariance of the score statistics between the $i^{th}$ and the $j^{th}$ variant from the $k^{th}$ study
$U_{i,k}$ and $V_{ij,k}$ are described in detail in RAREMETALWORKER method.
$\mathbf{U_k}$ is the vector of score statistics of rare variants in a gene from the $k^{th}$ study.
$\mathbf{V_k}$ is the variance-covariance matrix of score statistics of rare variants in a gene from the $k^{th}$ study, or $\mathbf{V_k} = cov(\mathbf{U_k})$
$S$ is the number of studies
$\mathbf{w^T} = (w_1,w_2,...,w_m)^T$ is the vector of weights for $m$ rare variants in a gene.
### SINGLE VARIANT META ANALYSIS
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generate by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as
$U_{meta_i}=\sum_{k=1}^S {U_{i,k}}$
and its variance
$V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}$
Then the score test statistics for the $i^{th}$ variant $T_{meta_i}$ asymptotically follows standard normal distribution
$T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)$
### BURDEN META ANALYSIS
Once single variant meta analysis statistics are constructed, burden test score statistic can be easily reconstructed as
$T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)$.
### SKAT META ANALYSIS
SKAT has been powerful detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances
$\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}$.
As shown in Wu et. al, the null distribution of the $\mathbf{Q}$ statistic follows a mixture chi-sqaured distribution described as
$\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2},\text{ where}$ $\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)\text{ are eigen values of}$$\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}\mathbf{W}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}$
Formulae for RAREMETAL
Test Statistics Null Distribution Notation
Single Variant $T=\sum_{i=1}^n {U_i}\bigg/\sqrt{\sum_{i=1}^n{V_i}}$ $T\sim\mathbf{N}(0,1)$ $U_i \text{ is the score statistic from study }i;$$V_i \text{ is the variance of } U_i.$
un-weighted Burden $T_b=\sum_{i=1}^n{\mathbf{U_i}}\Big/\sqrt{\sum_{i=1}^n{\mathbf{V_i}}}$ $T_b\sim\mathbf{N}(0,1)$ $\mathbf{U_i}\text{ is the vector of score statistics from study }i, or$ $\mathbf{U_i}=\{U_{i1},...,U_{im}\};$ $\mathbf{V_i} \text{ is the covariance of } \mathbf{U_i}.$
Weighted Burden $T_{wb}=\mathbf{w^T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\mathbf{w^T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\mathbf{w}}$ $T_{wb}\sim\mathbf{N}(0,1)$ $\mathbf{w^T}=\{w_1,w_2,...,w_m\}^T \text{ is the weight vector.}$
VT $T_{VT}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}),\text{ where}$$T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\phi}_{f_j}}$ $\left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)$$\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right)\text{,}$$\text{where }\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\phi}_{f_j}}}$ $\boldsymbol{\phi}_{f_j}\text{ is a vector of } 0 \text{s and } 1\text{s,}$ $\text{indicating the inclusion of a variant using threshold }f_j;$
SKAT $\mathbf{Q}=\left(\sum_{i=1}^n{\mathbf{U_i^T}}\right) \mathbf{W}\left(\sum_{i=1}^n{\mathbf{U_i}}\right)$ $\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2},\text{ where}$ $\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)\text{ are eigen values of}$$\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}\mathbf{W}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}$ $\mathbf{W}\text{ is a diagonal matrix of weights.}$ | 2022-08-14 06:28:48 | {"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": 0, "mathjax_asciimath": 0, "img_math": 52, "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": 0.8933886885643005, "perplexity": 3360.2728355837567}, "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/1659882571996.63/warc/CC-MAIN-20220814052950-20220814082950-00203.warc.gz"} |
https://www.physicsforums.com/threads/two-trains-leave-a-station-and-an-observer-misses-them-both-what-does-he-see.46354/ | Two trains leave a station, and an observer misses them both what does he see
1. Oct 6, 2004
stunner5000pt
Using Speical relativity, of course
If two trains leave a station on the same track. An observer missed both these trains and is standing close to the track sees the westbound train recede at 0.6c and sees the eastbound train recede at 0.8c. There is a ticket collector on the westbound train going from the back of the train to the front at 0.4c, with respect to a passenger on the westbound train.
What would the speed of the eastbound train wit hrespect to the westbound train (call it Ur) according to:
a) Observer on the station: it's just as if the trains were approaching each other... right?
in taht case using Ux' = UW - UE / (1 - UW UE / C^2) yields 0.38c
b)Passenger seated on the westbound train?
The same framework as the previous question (which leads me to doubt part A) and i get 0.38c
c) Ticket collector on the westbound train?
The ticket collector would see hte same as the passenger, no?
Similarly what is the speed of the ticket collector :
d) According to the observer on the station?
I would think calculating the speed of the ticket collector with respect tothe train first, and then the observer to the train and then adding the velocities up
e) According to the passenger on the east train?
First find the relative velocities of the two trains and then add the velocity of the ticket collector with respect to the west train as done in the previous one
F) Relative to a passenger seated on the east train according tothe observer on the station?
STumped even more...
2. Oct 14, 2004
Staff: Mentor
Does that even make sense? After all, the speed of the eastbound train with respect to the platform is 0.8c--how can its speed with respect to the westbound train be less? :yuck:
Learn the relativistic velocity addition formula:
$$V_{c/a} = \frac{V_{b/a} + V_{c/b}}{1 + V_{b/a}V_{c/b}/c^2}$$
(Hint: signs--which signify direction--matter!) | 2018-03-19 09:26:57 | {"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": 0.5012029409408569, "perplexity": 2455.666866843322}, "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-2018-13/segments/1521257646636.25/warc/CC-MAIN-20180319081701-20180319101701-00090.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/int2/chapter/3/lesson/3.2.3/problem/3-97 | Home > INT2 > Chapter 3 > Lesson 3.2.3 > Problem3-97
3-97.
On graph paper, plot $ABCD$ if $A(0,3),B(2,5),C(6,3)$, and $D(4,1)$.
1. Rotate $ABCD\ 90°$ clockwise ($↻$) about the origin to form $A'B'C'D'$. Name the coordinates of $B'$.
$(5, −2)$
2. Translate $A'B'C'D'$ up $8$ units and left $7$ units to form $A''B''C''D''$. Name the coordinates of $C''$.
$(−4, 2)$
3. After rotating $ABCD$ $180^\circ$ to form $A'''B'''C'''D'''$, Arah noticed that the image lined up exactly with the original. In this case, about what point was $ABCD$ rotated? How did you locate it?
Use the eTool below to solve each part.
Click the link at right for the full version of the eTool. Int2 3-97 HW eTool | 2020-05-26 01:19:19 | {"extraction_info": {"found_math": true, "script_math_tex": 18, "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": 0.9505841732025146, "perplexity": 1993.62324920688}, "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-2020-24/segments/1590347390437.8/warc/CC-MAIN-20200525223929-20200526013929-00067.warc.gz"} |
https://campus.datacamp.com/courses/introduction-to-pyspark/model-tuning-and-selection?ex=3 | # Cross validation
In the next few exercises you'll be tuning your logistic regression model using a procedure called k-fold cross validation. This is a method of estimating the model's performance on unseen data (like your test DataFrame).
It works by splitting the training data into a few different partitions. The exact number is up to you, but in this course you'll be using PySpark's default value of three. Once the data is split up, one of the partitions is set aside, and the model is fit to the others. Then the error is measured against the held out partition. This is repeated for each of the partitions, so that every block of data is held out and used as a test set exactly once. Then the error on each of the partitions is averaged. This is called the cross validation error of the model, and is a good estimate of the actual error on the held out data.
You'll be using cross validation to choose the hyperparameters by creating a grid of the possible pairs of values for the two hyperparameters, elasticNetParam and regParam, and using the cross validation error to compare all the different models so you can choose the best one!
What does cross validation allow you to estimate? | 2020-08-11 07:59:47 | {"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": 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": 0.476921409368515, "perplexity": 342.5273530803567}, "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/1596439738735.44/warc/CC-MAIN-20200811055449-20200811085449-00307.warc.gz"} |
http://physics.stackexchange.com/tags/sun/hot | # Tag Info
## Hot answers tagged sun
36
The sun does rotate. We can see the rotation of the sun by the doppler shift of the light we get from the sun. . (Image from this page.) Since we know the characteristic spectrum of light from a hot body of a given temperature, we can use the same effect to determine if other stars rotate as well. Note that this only gives the spread in velocities along ...
30
Briefly: Because the moon's orbit "wobbles" up and down, so it isn't always in the plane of the earth's orbit around the sun. There's a 2D plane you can form from the ellipse of the earth's orbit and the sun. This plane is known as the ecliptic. The moon's orbit is not exactly in the ecliptic at all times; see this (slightly overcomplicated) picture from ...
30
The Sun isn't "made of fire". It's made mostly of hydrogen and helium. Its heat and light come from nuclear fusion, a very different process that doesn't require oxygen. Ordinary fire is a chemical reaction; fusion merges hydrogen nuclei into helium, and produces much more energy. (Other nuclear reactions are possible.) As for rockets, they carry both ...
28
Yes, the sun and nearly all other stars do rotate. One can see the rotation of the sun by looking at the motion of sunspots on its surface. Over time, the sunspots will move across the sun's surface - proof of its rotation. Furthermore, the rate of the sun's rotation is not constant throughout the sun; it is higher near the equator and slower near the ...
26
This is from the Physics FAQ article that I wrote 15 years ago: If shorter wavelengths are scattered most strongly, then there is a puzzle as to why the sky does not appear violet, the colour with the shortest visible wavelength. The spectrum of light emission from the sun is not constant at all wavelengths, and additionally is absorbed by the high ...
19
It just happens to be a coincidence. The current popular theory for how the Moon formed was a glancing impact on the Earth, late in the planet buiding process, by a Mars sized object. This caused the break up of the impactor and debris from both the impactor and the proto-Earth was flung into orbit to later coallesce into the Moon. So the Moon's size just ...
18
The reason being closer to a heat source makes you warmer is the inverse square law. Think of it this way: If you have a $1~\mathrm{m}^2$ piece of material facing the Sun and located at Mercury's orbit, it will be quite hot. What does the shadow of this square look like at Earth's orbit (about $2.5$ times further away than Mercury)? Well, it will be $2.5$ ...
18
This is a really rough calculation that doesn't take into account the realistic direction of the bow shock, or calculation of the drag force. I just take the net momentum flow in the solar wind and direct it so as to produce the maximum decceleration and see what happens. Apparently the solar wind pressure is of the order of a nanoPascal. As I write this ...
13
No, there is not a solar eclipse whenever we see a new moon. The reason we do not have a solar eclipse at every new moon is mostly due to the angle of Earth's axis (and by extension, the Moon's orbital plane) to the Earth-Sun line. See the picture below for a visual explanation. In the picture, the Sun is to the left. The upper image shows the orbit of the ...
13
The Moon's orbit is inclined with respect to the Earth's orbit. In other words, if you imagine a Sun, Earth, and Moon model sitting on a tabletop, the Sun would sit approximately still and the Earth might slide around the desktop, while the Moon would orbit the Earth, hopping up off the table, and sinking back down into it. (I used to do this demonstration ...
13
@dmckee guessed correctly. From An excerpt from an address delivered before Section A of the American Association for the Advancement of Science, on August 23, 1882, by Prof. Win. Harkness, Chairman of the Section, and Vice President of the Association: (ref) He was destitute of what would now be regarded as the commonest instruments. The invention of ...
13
Great question. The electric field creates such a strong force that it would be very hard to move large amounts of just one type of charge. So astrophysical systems do generally eject equal numbers of protons and electrons. In particular, the solar wind is electrically neutral. So these cosmic rays are created in very nearly equal numbers, but by the ...
11
I believe the easiest way to do this would be empirical, rather than theoretical- Just mark out each hour, all day. It would be especially fascinating if you did this, say, every Saturday, starting with the upcoming Summer Solstice. The artistic possibilities are endless as well... different symbols, colors, outlines, etc., for different times of the year, ...
11
It is much more. During its core-burning phase, the Sun will burn about 10-15% of its hydrogen supply. The gas is about 70% hydrogen by mass, so that translates into about $0.07$ to $0.1\,M_\odot$ of hydrogen burned. The exhausted core then contracts while hydrogen is burned in a shell that gradually moves outwards (in terms of mass). Helium ignition starts ...
11
Placing the solar filter before sunlight hits the instrument is the correct way of doing it. You could put the filter after the instrument, provided you don't mind being blind - the concentrated energy from the Sun heats up the filter, which sooner or later melts (if it's plastic) or cracks or explodes (if it's glass), your eye(s) receive a full dose of that ...
11
Several points that need addressing: The seasons are due to the tilt of the Earth, but not because of the atmosphere. When the sunlight is grazing the ground at a low angle the same amount of heating is spread over a larger area than when the sun is directly overhead, so the temperature drops. The atmosphere has a negligible effect on absorbing radiation ...
11
Short answer, no. The Sun's orbit is non-Keplarian; there are many perturbations and a general unevenness in the motion of the Sun around the Galactic centre. This is a result of non-uniform mass distributions, the galaxy not being a point mass, and the impact the relative motions of neighbour stars has on measuring. Thus, giving a particular eccentricity ...
10
Moonlight is not almost as bright as mid-dawn. Moonlight is really fairly low illumination, and human eyes don't detect color well in low illumination. Moonlight is reflected sunlight. If there's enough of it, it produces color mostly the same way sunlight does. This page, found through a Google search, shows a spectrum of moonlight. All the colors are ...
10
Michael Luciuk's answer is right, but there's an even stronger reason for rejecting this hypothesis: refraction in the corona would be wavelength-dependent, but the gravitational bending due to the Sun has been measured over a wide range of wavelengths (at least from visible to radio) and has been found to be independent of wavelength. Clifford Will's ...
9
The reaction rate doesn't increase that quickly with temperature, but pressure does. If you perturb a solar model, making a zone near the core marginally hotter, the increased pressure will rapidly (at roughly the soundspeed divided by a characteristic length) cause it to expand. That lowers the pressure and temperature enough to substantially quench the ...
9
The ionized particles from mainly solar wind are caught and trapped by Earth magnetic field, which behaves like a magnetic bottle. (The region in which ions are trapped is called Van Allen radiation belts.) This trap is weaker in the polar regions, and there the ions are mainly released into the denser parts of atmosphere. There they collide with air ...
9
The thing is, the Moon's orbital plane is slightly tilted (about 5$^\circ$) with respect to Earth's which means from the Earth's perspective that the Moon's motion oscillates around the Sun's trajectory. On most new moons, then, the Moon is either north or south of the Sun and we don't see an eclipse. For eclipses to happen, new and full moons must occur ...
9
Both the moon and the earth's orbits are eccentric, and so the ratio between the sun's and moon's apparent diameter varies with the time of year. When the moon is at perigee, and the earth at aphelion, the moon will seem larger than the sun than when the moon is at apogee and earth at perihelion. However, the eccentricities of these orbits are low, and the ...
9
Any reasonably flat piece of sort-of reflective metal will function perfectly well as a heat collector, but would not be terribly suited to do astronomical observations with. In principle, you could probably pull it off. But it would require a lot more accurately shaped mirrors, with a lot better quality reflective surface. Also, there's good reasons ...
9
In theory, perhaps. It is possible, using multilayer dielectric coatings, to produce a surface which is reflective in very narrow bands (in this case, the Sun's dark lines)and transmissive (or absorptive) elsewhere. In practice, the spectral "blurring" caused by atmospheric transmission/absorption/re-emission effects would make this effect pretty much ...
8
There will not be any kind of "massive bombardment" and it won't "light up" things out there. However, using the Sun as a gravitational lens for a radio telescope is a real possibility. There was a lecture at the SETI Institute on 11/25/2009 titled "Deep Space Flight and Communications: SETI, KLT and Astronautics in a 2009 book" by Claudio Maccone, Co-Vice ...
8
From the Sun's center, always. When you deduce the equations of motion of planets, you're always calculating from the center. Plus, the results don't change when the Sun blows up as a red giant, or collapses as a dwarf. But even if you measure from the surface, in most cases it won't make a huge difference. In Earth's case, it's a 0.5% error. It would be a ...
8
What part of the sun? That would make a huge difference in your question. Overall, these types of hypothetical questions are rather non-nonsensical without really defining the parameters very clearly. That said, keep in mind, we have "released the power of the sun on the surface of the earth" a few times already. Not only that, we have even contained it! ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2014-03-10 09:00:10 | {"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": 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": 0.5670706033706665, "perplexity": 639.4253548805111}, "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-2014-10/segments/1394010721184/warc/CC-MAIN-20140305091201-00037-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://www.show-my-homework.com/2016/03/coriolis-force-in-physics.html | # Coriolis Force in Physics
A bird of mass 3 kg is flying at 20 m/s in latitude 45 degree, heading west. Find the horizontal and vertical components of the Coriolis force acting on it.
The figure is below. The angular rotation speed of earth at 45 degree latitude is
$Omega =omega_0*begin{pmatrix} 0\ cos(45)\ sin(45) end{pmatrix}$ where $ω_0=2π/(24*3600)=7.27*10^{-5} rad/sec$
$ω_0$ is the rotational speed of the Earth at the equator.
The speed of the bird heading west has the components:
$v=begin{pmatrix} -20\ 0\ 0 end{pmatrix}$
The Coriolis acceleration is by definition:
$a_C=-2(Omega times v)=-2omega_0*begin{pmatrix} i &j &k \ 0 &cos(45) &sin(45) \ -20 &0 &0 end{pmatrix}=2omega_0begin{pmatrix} 0\ 20sin(45)\ -20cos(45)end{pmatrix}$
Therefore $a_C=begin{pmatrix} 0\ 2.056*10^{-3}\ -2.056*10^{-3}end{pmatrix} (m/s^2)$
The Coriolis force is thus
$F_C=m*a_C=begin{pmatrix} 0\ 6.169*10^{-3}\ -6.169*10^{-3}end{pmatrix} (N)$
The horizontal component of the Coriolis force is $F_{C y}=6.169*10^{-3} N$ and the vertical component of the Coriolis force is $F_{C z}=-6.169*10^{-3} N$ (it is downwards). | 2018-02-22 17:05:07 | {"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": 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": 0.8290615677833557, "perplexity": 575.3586671721815}, "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-2018-09/segments/1518891814140.9/warc/CC-MAIN-20180222160706-20180222180706-00008.warc.gz"} |
https://dsp.stackexchange.com/questions/3185/how-bandwidth-is-used-in-modulation | How bandwidth is used in modulation
In a typical Digital cable environment in the US, the spectrum is divided into 6MHz bands. When a tuner locks to a signal at say 800MHz, I would assume that the band for that signal is 797 - 803 MHz. The signal is QAM modulated. I would like to know why is that 6 MHz band required? If I can lock to a signal at 800MHz wont that be sufficient to reconstruct the original transmitted signal? From what I remember of my dsp course a few years back, I know that we need the band, but can't for the life of me remember why. Pointers to the theory will be appreciated
• Does the baseband QAM signal (actually two real signals $x(t)$ and $y(t)$ or a complex-valued signal $z(t) = x(t) + jy(t)$) have zero bandwidth? The modulation theorem of Fourier transform theory says that the passband QAM signal at $800$ MHz has twice the bandwidth of the baseband QAM signal, and so if the baseband signal has nonzero bandwidth, so does the passband signal. – Dilip Sarwate Aug 23 '12 at 11:20
An ideal sinusoid does indeed have zero bandwidth, but it is not useful to transmit one because it also imparts zero information to the receiver. Once the receiver knows what the sinusoid phase is it can perfectly predict the rest of the signal- thus, no more information is received.
For information to be transmitted there has to be an element of "not knowing". For digital communications that generally means not knowing if the next bit will be a 1 or 0. I will try to illustrate where the bandwidth comes from using BPSK, but the exact same principles apply to QAM.
The BPSK example above is ideal in the sense that it is very easy for the receiver to recover. The receiver can sample the waveform anywhere within a symbol ("symbol" being the waveform representation of a digital bit) and get the full symbol power. You can model the example BPSK waveform above as a bunch of individual square waves of varying widths and locations (in time) added together. If you recall your Fourier theory, the Fourier transform of a square is the sinc function. Thus, in the frequency domain, the total signal is a bunch of sinc functions of varying widths added together. That makes the resulting waveform's frequency spectrum look a lot like a sinc function (note that this is not 100% true since there is some destructive interference that occurs, but for the sake of this discussion let's ignore that).
Sinc functions, unfortunately, aren't too great in terms of bandwidth. The figure below shows the absolute value of a sinc function.
This doesn't look too bad until you look at the log scale of the energy, which is shown below.
As you can see from the plot above, at the location of the signal's potential nearest neighbor, the sinc function is only about 13 dB down. The rolloff from there is quite slow, with it only being about 21 dB down at the fifth side lobe. This introduces a lot of interference into neighboring signals, and when your receiver filters out the neighboring signals it is also filtering out a lot of your transmitted power, so that power is wasted.
Transmitters employ pulse shaping that rounds out the harsh transitions of the square waves and makes the BPSK waveform look more like a sinusoid. The following is the same BPSK waveform but using raised-cosine pulse shaping.
And this is the energy vs. frequency view of the raised-cosine pulse.
The main lobe of the raised-cosine and the square wave are essentially the same. The difference is in the rolloff of the side lobes.
So long story short (too late!) the bandwidth comes from the "random" transmission of ones and zeros. The minimum bandwidth is determined by the symbol period (shorter period is faster, thus wider bandwidth), and the sidelobes outside of that main bandwidth are minimized via pulse shaping. | 2020-02-26 14:41:34 | {"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": 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": 0.6405528783798218, "perplexity": 649.1062258029767}, "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-2020-10/segments/1581875146342.41/warc/CC-MAIN-20200226115522-20200226145522-00314.warc.gz"} |
https://pypi.org/project/oswin-tempest-plugin/ | This project contains Tempest tests to cover the os_win project, as well as a plugin to automatically load these tests into Tempest.
## Project description
This project contains Tempest tests to cover the os_win project, as well as a plugin to automatically load these tests into Tempest.
Please fill here a long description which must be at least 3 lines wrapped on 80 cols, so that distribution package maintainers can use it in their packages. Note that this is a hard requirement.
• TODO
## Project details
Uploaded source
Uploaded py3 | 2022-10-02 05:40:51 | {"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": 0.22889605164527893, "perplexity": 5363.903117638683}, "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-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00047.warc.gz"} |
https://2022.help.altair.com/2022/hwdesktop/hst/topics/design_exploration/model_types_r.htm | # Model Types
Learn about the different type of models available in HyperStudy.
## Beta Preprocessor Model
Use the Beta Preprocessor model to create a parametric connection to a B Preprocessor database enabling you to generate solver input files.
Version
N/A
File Extension
.ansa
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
Register a solver script that points to an ansa startup.
For example, ...BETA\ansa_v17.1.2\ansa64.bat.
Usability Characteristics
The FE output path in a .ansa file should be relative. If it is not, you will receive a warning when importing input variables.
Once the optimization task is defined, save the current model as <modelName>.ansa. Verify the dvfile name follows a naming convention of <modelName>_dvfile.txt and is in the same directory as the .ansa file. For example, feasolver_beam.ansa, feasolver_beam_dvfile.txt.
## FEKO Model
Use the FEKO model to connect to a Feko project, which enables you to automatically detect input variables and run high frequency electromagnetic simulations.
Version
2017 or above
File Extension
.cfx
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
Register a solver script that points to runfeko.exe.
Usability Characteristics
Output responses from Feko are written to the hst_output.hstp file by a custom .lua script. If no .lua script is present, Feko will generate a nominal script which performs a trivial calculation. This nominal script must be modified to request the specific output response of interest from Feko.
## Flux Model
Use the Flux model to connect to any Flux 2D and 3D project, which enables you to automatically detect input variables and run low frequency electromagnetic simulations.
Version
Flux 12.1 or above
File Extensions
.F2G
.F2HST
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
Register a solver script that points to flux.exe. For more information, refer to Register Solver Scripts.
Usability Characteristics
• Some Flux outputs (such as curve value extractions) require a post-processing python file to be executed after each simulation. If a python command file is required, it should be specified in the .F2G or .F2HST file. Drag and drop the .F2G or .F2HST file into HyperStudy to connect the model and identify the inputs and the outputs. Once a connection is established, HyperStudy can automatically run as many Flux simulations as requested by the method (DOE, Optimization).
• For information on how to expose Flux model parameters and outputs to HyperStudy by means of a .F2G or .F2HST coupling file, refer to the Flux help and HyperStudy dedicated tutorial.
## FluxMotor Model
Use the FluxMotor model to connect to a FluxMotor model.
Version
2018.1
File Extension
.fm2hst
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
Register a solver script that points to FluxMotor_Install_dir/Scripts/win/FluxMotors.exe.
Usability Characteristics
Refer to the FluxMotor help for more information on how to expose FluxMotor model parameters to HyperStudy.
## HyperStudy Fit Model
Use the HyperStudy Fit model to import the python based report created by a Fit approach from another HyperStudy session.
Version
N/A
File Extension
.pyfit
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
N/A
## HyperMesh Model
Use the HyperMesh model to directly access the HyperMesh database of the model, which enables you to perform easy design parameterization of solver input files.
Version
Current HyperWorks installation
File Extension
.hm
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
HyperMesh is automatically registered in HyperStudy.
Usability Characteristics
• Input variables are limited to solver interface specific presets and general parameter entities.
• Can be used with any solver script.
## HyperView Model
Use the HyperView model to connect to a HyperView session file, which enables you to automatically extract hotspots.
Version
2021.1 or above
File Extension
*.mvw
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
N/A
Usability Characteristics
• Used as a subsequent step after a numerical analysis.
• Adding solver argument, -image, generates screenshots of hotspot contours.
## Internal Math Model
Use the Internal Math model to create input variables that are contained entirely within HyperStudy and do not map to any external applications.
Version
N/A
File Extension
N/A
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
N/A
Usability Characteristics
• Used to link variables between models.
• Used for variables used directly in response expressions.
## Knowledge Studio Model
Use a Knowledge Studio model to import the predictive model from a Knowledge Studio session.
Version
2020.1 or above
File Extensions
.kdm
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
Register a solver script that points to <...>/Altair Knowledge Works/KS Workstation 2020.1.0/HyperStudy/runKS.bat for Windows and <...>/Altair Knowledge Works/KS Workstation 2020.1.0/HyperStudy/runKS.sh for Linux.
Usability Characteristics
• Verify that the path to the Python executable is valid in the Knowledge Studio installation configuration file, KS Workstation 2020.1.0/HyperStudy/runKS.cfg.
## Lookup Model
Use the Lookup model to extract values from a file with known input/output pairs.
Version
N/A
File Extension
.csv
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
N/A
Usability Characteristics
• The .csv file must be structured so that all of the first N columns are imported as input variables, and all remaining columns are imported as output responses.
• Evaluation of the model with input variables that have no matching row will result in an execution failure.
## MotionView Model
Use the MotionView model to directly access the HyperView database of the model, which enables you to perform easy design parameterization of solver input files.
Version
Current HyperWorks installation
File Extension
.mdl
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
MotionView is automatically registered in HyperStudy.
Usability Characteristics
Can be used with any solver script or the have MotionView run the solver defined inside itself.
## Operator Model
Use the Operator model to execute a process but not have an associated write operation.
Version
N/A
File Extension
N/A
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
N/A
Usability Characteristics
Frequently used in conjunction with linked model resources in order to define the steps of a process flow. A process can be defined as a sequence of HyperStudy models, including Operators, rather than a single model with a single detailed and non-reusable solver script.
## OptiStruct Model
Use the OptiStruct model to directly use parametric *.fem files without a pre-processor.
Version
2021.2 or above
File Extension
*.fem
Multi-Execute Support
Yes
Response Definition Support
Yes
Registration Steps
N/A
Usability Characteristics
• Symbolic substitutions are automatically detected as input variables. If no symbolic substitution is defined, thickness values in each PSHELL card are read as variables by default.
• Volume, Mass, and Maximum Displacement per subcase are default outputs.
• Use DRESP for user-defined responses.
## Parameterized File Model
A Parameterized File model is a general ASCII text file, which has search and replace substitution for input variables.
Version
N/A
File Extension
.tpl
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
N/A
Usability Characteristics
• A Templex language syntax is used inside of the parameterized file.
• The formatting in the parameterized file is independent of the internal storage.
Use the Radioss model to directly use parametric Runname_0000.rad starter file without a pre-processor.
Version
2021.2 or above
File Extension
Multi-Execute Support
Yes
Response Definition Support
No
Registration Steps
N/A
Usability Characteristics
• Entities in /PARAMETER cards are automatically detected as input variables.
• If engine file, Runname_0001.rad, is exported separately, they are automatically copied to run folders if they are in the same directory with the starter file.
• Include files need to be manually selected and copied via Model Resources tool.
## SimLab Model
Use the SimLab model to parametrically drive SimLab macros, which can be used to automatically mesh and solve FEA problems.
Version
2019.1 minimum
File Extension
.js
Multi-Execute Support
No
Response Definition Support
Yes
Registration Steps
Register a solver script that points to bin/<platform>/SimLab.bat.
Usability Characteristics
• The FEA solver is run as part of .js script.
• The HyperStudy directory (.hstudy) and the SimLab project directory cannot be the same.
Use the Spreadsheet model to perform calculations.
Version
Microsoft Office
File Extension
• .xls
• .xlsx
• .xlsm
Multi-Execute Support
No
Response Definition Support
Yes
Registration Steps
N/A
Usability Characteristics
• Input variable and output response cells are identified by the user.
• When creating a Spreadsheet model an input variable's value and label can be formatted in two consecutive rows or two consecutive columns. Input variable labels should only contain English characters, or a combination of English characters and numbers. If you do not create a label for a variable, HyperStudy will assign one by default.
• On a Windows operating system, Spreadsheet models will be brought to the front. HyperStudy will prevent you from accessing any spreadsheets that you had opened prior to or after (by double-clicking) starting your current HyperStudy session.
To access an Excel spreadsheet while running a study with Spreadsheet models, you must explicitly start a new session of Excel.
• Windows platform only
• Support for VB macros
## Workbench Model
Use the Workbench model to connect to an ANSYS workbench project.
Version
17.1
File Extension
.wbpj
Multi-Execute Support
No
Response Definition Support
Yes
Registration Steps
Register a solver script that points to runwb.exe.
Usability Characteristics
• Windows support only
• Input variables are automatically detected from Workbench input parameters.
• Output responses are automatically detected from Workbench direct outputs. | 2023-04-01 15:03:43 | {"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": 0.317148357629776, "perplexity": 10310.7814790989}, "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/1679296950030.57/warc/CC-MAIN-20230401125552-20230401155552-00540.warc.gz"} |
https://www.physicsforums.com/threads/sard-theorem-in-dimension-one.365839/ | # Homework Help: Sard theorem in dimension one.
1. Dec 28, 2009
### boboYO
Hi, I need some hints for the proof of the sard theorem in 1 dimension:
Prove that the set of critical values (f(x) where f'(x)=0) of continuously differentiable f:[a,b]->R has measure 0.
My attempt:
Fix $$\varepsilon$$, Let Crit(f) be the set of critical points of f. We want to show that f(Crit(f)) has measure 0.
Let $$C_k$$ be the set of all $$x$$ in Crit(f) such that $$|x-y|<\frac{1}{k} \implies |fx-fy|<\varepsilon|x-y|$$.
Clearly $$\bigcup_{k\in\mathbb{N}} C_k \supset \mathrm{Crit}(f)$$, so it suffices to show that $$f\left(\bigcup_{k\in\mathbb{N}} C_k \right)$$ has measure 0.
For any $$C_k$$, evenly split $$[a,b]$$ into intervals $$I_1,\dots,I_n$$ such that $$\frac{b-a}{n}<\frac{1}{k}$$.
For each $$I_i$$, if there is a point of $$C_k$$ in it, say $$x$$, then
$$|fx-fy|<\varepsilon|x-y|$$ for all y in $$I_i$$.
Thus if $$I_i$$ contains a point of $$C_k$$, then $$f(I_i)$$ is contained in a open interval of at most $$2w \varepsilon$$ where w is the width of the interval.
Thus $$f(C_k)$$ is contained in an open set of length at most $$2w\varepsilon n =2(b-a) \varepsilon=K\varepsilon$$.
Since each $$f(C_k)$$ has measure bounded above by $$K \varepsilon$$, and $$C_{k}\subset C_{k+1}$$ for all k, then
$$\bigcup_{k\in\mathbb{N}} f(C_k) = f\left(\bigcup_{k\in\mathbb{N}} C_k \right)$$ is also bounded above by $$K\varepsilon$$. Since $$\varepsilon$$ was arbitrary we are done.
--
I am not completely convinced because I did not use the hypothesis that the derivative is continuous. Did I make a mistake? Is there a simpler way do this?
Last edited: Dec 28, 2009
2. Dec 29, 2009
### Dick
I'm really having a hard time following that. It's not even clear to me that you even used that f is differentiable. Why don't you define C(epsilon) to be the set of all x such that f'(x)<epsilon. Then Crit(f) is contained in C(epsilon). Can you show the measure of f(C(epsilon)) is less than or equal to epsilon*measure(C(epsilon))?
3. Dec 29, 2009
### boboYO
$$(-\epsilon,\epsilon)$$ is open and f'(x) is continuous so $$C_\epsilon$$ is open too. An open set is a (at most) countable union of disjoint open intervals:
$$C_\epsilon=\bigcup_{i=1}^{\infty} I_i$$
For every $$I_i$$, if x and y are 2 points in $$I_i$$,
$$|fx-fy|<\epsilon|x-y|< \epsilon\mu(I_i)$$, due to MVT. So $$\mu(f(I_i))<\epsilon\mu(I_i)$$
Taking the union over i yields measure(f(Cε)) <ε*measure(Cε)<=ε(b-a) and we are done.
Thanks for your help :)
Last edited: Dec 29, 2009
4. Dec 29, 2009
### Dick
Now that I understand. And it even looks right. | 2018-09-24 11:43:48 | {"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": 0.9297183752059937, "perplexity": 294.105087122455}, "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-2018-39/segments/1537267160400.74/warc/CC-MAIN-20180924110050-20180924130450-00042.warc.gz"} |
https://zbmath.org/?q=an:0835.45006 | # zbMATH — the first resource for mathematics
A classification for integral boundary value problems in wide band. (English. Russian original) Zbl 0835.45006
Russ. Math. 38, No. 5, 1-10 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 5(384), 3-12 (1994).
The authors study the integral boundary value problem: $$\partial u(x,y)/ \partial y = P (\partial/ \partial x) u(x,y)$$, $$(x,y) \in \pi_y$$, $$Au(x,0) + Bu(x,Y) + C \int^y_0 u(x,y) dy = u_0 (x)$$, $$x \in \mathbb{R}$$, in the band $$\pi_Y = \mathbb{R} \times [0,Y]$$ for a large $$Y > 0$$, where $$u : \pi_Y \to \mathbb{C}$$ and $$u_0 : \mathbb{R} \to \mathbb{C}$$ are the unknown and given functions, respectively; $$P$$ is an arbitrary polynomial with constant coefficients; $$Y > 0$$, $$A,B$$ and $$C$$ are given complex constants, $$|A |+ |B |+ |C |> 0$$.
A complete classification considering the asymptotically correct resolvability of the problem is given.
##### MSC:
45K05 Integro-partial differential equations 30E25 Boundary value problems in the complex plane | 2021-04-11 23:00:07 | {"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": 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": 0.7836216688156128, "perplexity": 517.739533577887}, "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/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00108.warc.gz"} |
https://zbmath.org/?q=an%3A0892.05017 | # zbMATH — the first resource for mathematics
On Conway’s thrackle conjecture. (English) Zbl 0892.05017
A thrackle is a graph drawn in the plane with its edges represented by Jordan arcs so that any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. J. H. Conway’s thrackle conjecture is that the number of edges of a thrackle is at most the number of its vertices. The present authors show that every thrackleable bipartite graph is planar, and use this result to show that a thrackle having $$n$$ vertices has at most $$2n-3$$ edges. They also consider some related problems and generalizations.
##### MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
##### Keywords:
Jordan arcs; Conway’s thrackle conjecture; planar
Full Text: | 2021-07-24 07:01:48 | {"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": 0.39614763855934143, "perplexity": 773.1193377502059}, "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-2021-31/segments/1627046150134.86/warc/CC-MAIN-20210724063259-20210724093259-00552.warc.gz"} |
http://tigergenome.org/index.php/Falidae_family | # Falidae family
Felidae is the biological family of the cats; a member of this family is called a felid. The most familiar felid is the domestic cat, which first became associated with humans about 10,000 years ago; but the family includes all other wild cats, including the big cats.
Extant felids belong to one of two subfamilies: Pantherinae (which includes the tiger, the lion, the jaguar, and theleopard), and Felinae (which includes the cougar, the cheetah, the lynxes, the ocelot, and the domestic cat).
The first felids emerged during the Oligocene, about 25 million years ago. In prehistoric times, a third subfamily, known as Machairodontinae, included the "saber-toothed cats", such as the well known Smilodon. Other superficially cat-like mammals, such as the marsupial sabertooth Thylacosmilus or the Nimravidae, are not included in Felidae despite superficial similarities.
Felids are the strictest carnivores of the 13 terrestrial families in the order Carnivora, although the three families of marine mammals comprising the superfamily Pinnipedia are as carnivorous as the felids.
Evolution
There are 41 known species of felids in the world today, all of which descended from the same ancestor.[1] Thistaxon originated in Asia and spread across continents by crossing land bridges. Testing of mitochondrial and nuclear DNA by Warren Johnson and Stephen O'Brien of the US National Cancer Institute demonstrated the ancient cats evolved into eight main lineages that diverged in the course of at least 10 migrations (in both directions) from continent to continent via the Bering land bridge andIsthmus of Panama, with the Panthera genus being the oldest and the Felis genus being the youngest. They estimated 60% of the modern species of cats developed within the last million years.[3]
Most felids have a haploid number of 18 or 19. New World cats (those in Central and South America) have a haploid number of 18, possibly due to the combination of two smaller chromosomes into a larger one.[4] Prior to this discovery, biologists had been largely unable to establish a family tree of cats from the fossil record because the fossils of different cat species all look very much alike, differing primarily in size.
The felids' closest relatives are thought to be the Asiatic linsangs,[5] and at one remove the group of civetshyenasmongooses, and Madagascar carnivores,[6] with whom they share the Suborder Feliformia. Most felid species share a genetic anomaly that prevents them from tasting sweetness.[7]
## Characteristics
Felids are obligate carnivores, requiring a diet of meat and organs to survive. Aside from the lion, wild felids are generally solitary; feral domestic cats do, however, form feral cat colonies. Cheetahs are also known to live and hunt in groups. Felids are generally secretive animals, are often nocturnal, and live in relatively inaccessible habitats. Around three-quarters of cat species live in forested terrain, and they are generally agile climbers. However, felids may be found in almost any environment, with some species being native to mountainous terrain or deserts.
Wild felids are native to every continent except Australasia and Antarctica.
### Physical appearance
Skull of the machairodontine Smilodon(reconstruction)
Lion skull
Felids tend to have lithe and flexible bodies with muscular limbs. In the great majority of species, the tail is between a third and a half the length of the body, although there are some exceptions (for example, the bobcat and margay). The limbs are digitigrade with soft toe pads and protractible claws. Compared with most other mammals, the head of cats is highly domed with a short muzzle. The skull possesses wide zygomatic arches and a large sagittal crest, both of which allow for the attachment of strong jaw muscles.[8]
The various species of felids vary greatly in size. One of the smallest is the black-footed cat, measuring 35 to 40 cm (14 to 16 in) long, while the largest in the wild is the tiger, which can attain up to 350 cm (11.5 ft) in length[9] and weigh 300 kilograms (660 lb).
The fur of felids takes many different forms, being much thicker in those species living in cold environments, such as the snow leopard. The color of felids is also highly variable—although brown to golden fur is common in most species—usually marked with distinctive spots, stripes, or rosettes. The only felids to lack significant markings are the lion, pumacaracal and jaguarundi. Many species exhibit melanism, in which some individuals have an all-black coat.[8]
The tongue of felids is covered with horny papillae, which rasp meat from prey and aid in grooming.
All felids have protractible claws, in other words they have the ability to protract their claws from a retracted, at-rest position. Although in a few species, such as the cheetah, the claws remain visible even when at rest (retracted). The claws are retracted when the animal is relaxed and protracted when they are in use. They are attached to the terminal bone of the toe with a tough ligament; when the animal contracts muscles in the toe to straighten it, the ligament forces the claw outwards.[8] Cats have five toes on their forefeet and four on their hindfeet, reflecting their reliance on gripping and holding down their prey with their claws.[citation needed] In Felidae, the baculum is shorter than in Canidae.[10]
### Senses
Felids have relatively large eyes, situated to provide binocular vision. Their night vision is especially good due to the presence of a tapetum lucidum, which reflects light back inside the eyeball, and gives felid eyes their distinctive shine. As a result, the eyes of felids are about six times more light sensitive than those of humans, and many species are at least partially nocturnal. The retina of felids also contains a relatively high proportion ofrod cells, adapted for distinguishing moving objects in conditions of dim light, which are complemented by the presence of cone cells for sensing color during the day. However, felids appear to have relatively poor color vision in comparison with humans.[8] This is explained by the fact that felids see moving objects more "colorfully" than still objects, but in an intact environment, are unable to distinguish color tones alone (like turquoise compared to teal, for example).[citation needed]
The external ears of felids are also large, and especially sensitive to high-frequency sounds in the smaller cats. This sensitivity allows them to locate small rodentprey; cats themselves do not apparently produce such sounds.[8]
Felids also have a highly developed sense of smell, although not to the degree seen in canids; this is further supplemented by the presence of a vomeronasal organ in the roof of the mouth, allowing the animal to "taste" the air. The use of this organ is associated with the Flehmen response, in which the upper lip is curled upwards. Most felids are unable to taste sweetness due to a mutated gene in their taste buds. Exceptions include members of the genera Leopardus andOtocolobus.[citation needed]
Felids possess highly sensitive whiskers set deep within the skin, which provide the cat with sensory information about the slightest air movement around it. For this reason, whiskers are very helpful to nocturnal hunters.
Most felids are able to land on their feet after a fall, an ability that relies on vision and the sense of balance acting together.[citation needed]
### Dentition
Felids have a relatively small number of teeth compared with other carnivorans, a feature associated with their short muzzles. With a few exceptions, such as thelynx, they have the dental formula$Upper: 3.1.3.1, lower: 3.1.2.1$. The canine teeth are large, reaching exceptional size in the extinct saber-tooth species. The upper third premolar and lower molar are adapted as carnassial teeth, suited to tearing and cutting flesh.[8]
The jaws of felids can only move vertically. This prevents them from being able to chew efficiently, but makes it easier for their powerful masseter jaw muscles to hold struggling prey.
### Vocalisations
All felids share a broadly similar set of vocalisations, but with some variation between species. In particular, the pitch of calls varies, with larger species producing deeper sounds; overall, the frequency of felid calls ranges between 50 and 10,000 hertz.
All felids are able to spit, hiss, growl, snarl, and mew. The first four sounds are all used in an aggressive context. The spitting sound is a sudden burst, typically used when making threats, especially towards other species. The hiss is a prolonged, atonal sound used in close range to other members of the species, when the animal is uncertain whether to attack or retreat. Growling is used to indicate a willingness to attack, while the higher-pitched snarl is used when adopting a defensive posture.
The mewing sound may be used either as a close-contact call, typically between a mother and kittens, or as a louder, longer distance call, primarily during the mating season. The acoustic properties of the mew vary somewhat between different felid species; extreme examples include the whistling sound made by cougars and the mew-grunt of lions and tigers.
Most felids seem to be able to purr, vibrating the muscles in their larynx to produce a distinctive buzzing sound. In the wild, purring is used while a mother is caring for kittens. Precisely which species of felid are able to purr is a matter of debate, but the sound has been recorded in most of the smaller species, as well as the cheetah and cougar, and may also be found in the big cats.
Other common felid vocalisations include the gurgle, wah-wah, prusten, and roar. The first two sounds are found only among the Felinae (small cats). Gurgling is a quiet sound used during meetings between friendly individuals, as well as during courtship and when nursing kittens. The wah-wah is a short, deep-sounding call used in close contact, and is not found in all species (it is, for example, absent in the domestic cat).
In contrast, prusten and roaring are found only in big cats. Prusten is a short, soft, snorting sound reported in tigers, jaguars, snow leopards, and clouded leopards; it is used during contact between friendly individuals. The roar is an especially loud call with a distinctive pattern that depends on the species. The ability to roar comes from an elongated and specially adapted larynx and hyoid apparatus.[11] When air passes through the larynx on the way from the lungs, the cartilage walls of the larynx vibrate, producing sound. Only lions, leopards, tigers and jaguars are truly able to roar, although the loudest mews of snow leopards have a similar, if less structured, sound.[8] Tigers and jaguars have a very snarly roar, while the roar of leopards and lions is much more throaty.[citation needed]
### Social and territorial behavior
#### Territorial marking
Within the Felidae, male felids usually urinate backwards by curving the tip of the glans penis backward.[12][10] Urine marking by felids is also known as "spray-urinating"[13] or "spray-marking".[14] To identify their territories, male tigers mark trees by spraying urine[15][16] and anal gland secretions, as well as marking trails with scat. Males show a grimacing face, called the Flehmen response, when identifying a female's reproductive condition by sniffing their urine markings.
Lions use urine to mark their territories. They often scrape the ground while urinating, and the urine often flows in short spurts, instead of flowing continuously. They often urinate on vegetation, or on tree trunks at least one meter high.[17]
Male cheetahs mark their territory by urinating on objects that stand out, such as trees, logs, or termite mounds. The whole coalition contributes to the scent. Males will attempt to kill any intruders, and fights result in serious injury or death.[18] When male cheetahs urine-mark their territories, they stand one meter away from a tree or rock surface with the tail raised, pointing the penis either horizontally backward or 60° upward.[19] The odor of cheetah urine (unlike that of other large felids) cannot be easily detected by humans.[20]
Male cheetah marking territory
## Classification
Traditionally, five subfamilies have been distinguished within family Felidae based on phenotypical features: theFelinae, the Pantherinae, the Acinonychinae (cheetahs), the extinct Machairodontinae, and the extinctProailurinae.[2]
### Genetic classification
Genetic research has provided a basis for a more concise classification for the living members of the cat family based on genotypical groupings.[1][21][22] Specifically, eight genetic lineages have been identified:[23]
The last four lineages are more related to each other than to any of the first four, and so form a clade within the Felinae subfamily of family Felidae.
### Extant species
The following is the complete list of genera within family Felidae, grouped according to the traditional phenotypical classification with the corresponding genotypical lineages indicated:
## Fossil felids
The American lion was one of the abundant Pleistocene megafauna, a wide variety of very large mammals that went extinct about 10,000 years ago.[25]
Possibly the oldest known true felid (Proailurus) lived in the late Oligocene and early Miocene epochs. During the Miocene, it gave way to PseudaelurusPseudaelurus is believed to be the latest common ancestor of the two extant subfamilies and the extinct subfamily, Machairodontinae. This group, better known as the saber-tooth cats, became extinct in the Late Pleistocene era. The group includes the genera SmilodonMachairodus andHomotherium. The Metailurini were originally classified as a distinct tribe within the Machairodontinae, though they count as members of the Felinae in recent times.[26][27] Most extinct cat-like animals, once regarded as members of the Felidae, later turned out to be members of related, but distinct, families: the "false sabretooths" Nimravidae andBarbourofelidae. As a result, sabretooth "cats" seem to belong to four different lineages. The total number of fossil felids known to science is low compared to other carnivoran families, such as dogs and bears. Felidae radiated quite recently and most of the extant species are relatively young.
## Genera of the Felidae
The list follows McKenna and Bell's Classification of Mammals for prehistoric genera (1997)[2] and Wozencraft (2005) in Wilson and Reeder's Mammal Species of the World for extant genera.[1] Pseudaelurus is included in the Felinae as per McKenna & Bell, despite its basal position in felid evolution. Inconsistent with McKenna and Bell, three additional prehistoric genera, MiracinonyxLokontailurus and Xenosmilus, are listed.Sivapanthera is included in the Felinae (not Acinonychinae) and Ischrosmilus is included in the genus Smilodon.
## Cited references
1. Wozencraft, W. C. (2005). "Order Carnivora". In Wilson, D. E.; Reeder, D. M. Mammal Species of the World (3rd ed.). Johns Hopkins University Press. pp. 532–548. ISBN 978-0-8018-8221-0OCLC 62265494.
2. a b c McKenna, Malcolm C.; Susan K. Bell (2000-02-15). Classification of Mammals. Columbia University Press. p. 631. ISBN 978-0-231-11013-6.
3. ^ Mott, Maryann (2006-01-11). "Cats Climb New family Tree". National Geographic News. Retrieved 2006-07-15.
4. ^ Vella, Carolyn; et al. (2002). Robinson's Genetics for Cat Breeders and Veterinarians, 4th ed. Oxford: Butterworh-Heinemann. ISBN 0-7506-4069-3.
5. ^ Eizirik E., Murphy W.J., Koepfli K.P., Johnson W.E., Dragoo J.W., O'Brien S.J. (2010). "Pattern and timing of the diversification of the mammalian order Carnivora inferred from multiple nuclear gene sequences". Molecular Phylogenetics and Evolution 56: 49–63. doi:10.1016/j.ympev.2010.01.033.
6. ^ Gaubert P., Veron G. (2003). "Exhaustive sample set among Viverridae reveals the sister-group of felids: the linsangs as a case of extreme morphological convergence within Feliformia"Proceedings of the Royal Society, Series B 270 (1532): 2523–30. doi:10.1098/rspb.2003.2521PMC 1691530PMID 14667345.
7. ^ Xia, Li; Weihua Li, Hong Wang, Jie Cao, Kenji Maehashi, Liquan Huang, Alexander A. Bachmanov, Danielle R. Reed, Véronique Legrand-Defretin, Gary K. Beauchamp and Joseph G. Brand (July 2005). "Pseudogenization of a Sweet-Receptor Gene Accounts for Cats' Indifference toward Sugar"Public Library of Science 1 (1): e3.doi:10.1371/journal.pgen.0010003PMC 1183522PMID 16103917. Retrieved 2008-06-30.
8. Sunquist, Mel; Sunquist, Fiona (2002). Wild cats of the World. Chicago: University of Chicago Press. pp. 5–16. ISBN 0-226-77999-8.
9. ^ Vratislav Mazak: Der Tiger. Nachdruck der 3. Auflage von 1983. Westarp Wissenschaften Hohenwarsleben, 2004 ISBN 3-89432-759-6
10. a b R. F. Ewer (1973). The Carnivores. Cornell University Press. ISBN 978-0-8014-8493-3. Retrieved 27 January 2013.
11. ^ Weissengruber, GE; G Forstenpointner, G Peters, A Kübber-Heiss, and WT Fitch (September 2002). "Hyoid apparatus and pharynx in the lion (Panthera leo), jaguar (Panthera onca), tiger (Panthera tigris), cheetah (Acinonyx jubatus) and the Indian Armadillo. (Felis silvestris f. catus)"Journal of Anatomy (Anatomical Society of Great Britain and Ireland) 201 (3): 195–209. doi:10.1046/j.1469-7580.2002.00088.xPMC 1570911PMID 12363272.
12. ^ Reena Mathur (2010). Animal Behaviour 3/e. Rastogi Publications. ISBN 978-81-7133-747-7. Retrieved 10 February 2013.
13. ^ John W. S. Bradshaw; Rachel A. Casey; Sarah L. Brown (31 January 2013). The Behaviour of the Domestic Cat. CABI. pp. 104–. ISBN 978-1-78064-120-1. Retrieved 22 March 2013.
14. ^ Stefan Schulz (17 March 2005). The Chemistry of Pheromones and Other Semiochemicals II. Springer. pp. 249–. ISBN 978-3-540-21308-6. Retrieved 22 March 2013.
15. ^ John Seidenstic (1996). Tigers. MBI Publishing Company. pp. 63–. ISBN 978-0-89658-295-8. Retrieved 25 December 2012.
16. ^ Burger, B. V.; Viviers, M. Z.; Bekker, J. P. I.; Roux, M.; Fish, N.; Fourie, W. B.; Weibchen, G. (2008). "Chemical Characterization of Territorial Marking Fluid of Male Bengal Tiger, Panthera tigris". Journal of Chemical Ecology 34 (5): 659–671. doi:10.1007/s10886-008-9462-yPMID 18437496.
17. ^ Schaller, George B (2009-10-15). The Serengeti Lion: A Study of Predator-Prey RelationsISBN 9780226736600.
18. ^ Cheetahs (Revised Edition) - Dianne M. MacMillan - Google Books. Books.google.com. Retrieved 2012-11-20.
19. ^ T. M. Caro (15 August 1994). Cheetahs of the Serengeti Plains: Group Living in an Asocial Species. University of Chicago Press. pp. 203–. ISBN 978-0-226-09433-5. Retrieved 21 March 2013.
20. ^ The Chemistry of Pheromones and Other Semiochemicals II - Google Books. Books.google.com. 2005-03-17. Retrieved 2012-11-20.
21. ^ Johnson WE, Eizirik E, Pecon-Slattery J, et al. (January 2006). "The late Miocene radiation of modern Felidae: a genetic assessment". Science 311 (5757): 73–7.doi:10.1126/science.1122277PMID 16400146.
22. ^ O'Brien SJ, Johnson WE (2005). "Big cat genomics". Annu Rev Genomics Hum Genet 6 (1): 407–29. doi:10.1146/annurev.genom.6.080604.162151PMID 16124868.
23. ^ Johnson, W. E.; & O'Brien S. J. (1997). Phylogenetic reconstruction of the Felidae using 16S rRNA and NADH-5 mitochondrial genes. J Mol Evol (1997) 44: S98-116. Retrieved on 2009-11-08 from http://www.ncbi.nlm.nih.gov/pubmed/9071018?dopt=Abstract.
24. ^ http://www.bucknell.edu/msw3/browse.asp?id=14000003
25. ^ Ice Age Animals, Illinois State Museum
26. ^ van den Hoek Ostende, Lars W.; Michael Morlo and Doris Nagel (July 2006). "Fossils explained 52 Majestic killers: the sabre-toothed cats"Geology Today 22 (4): 150–157. doi:10.1111/j.1365-2451.2006.00572.x. Retrieved 2008-06-30.
27. ^ Turner, Alan (1997-04-15). The Big Cats and their fossil relatives. New York: Columbia University Press. p. 60. ISBN 978-0-231-10228-5. | 2018-10-19 00:12:18 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "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": 0.5517807602882385, "perplexity": 5938.280326748726}, "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-2018-43/segments/1539583512161.28/warc/CC-MAIN-20181018235424-20181019020924-00330.warc.gz"} |
https://www.bartleby.com/solution-answer/chapter-12-problem-42p-managerial-accounting-the-cornerstone-of-business-decision-making-7th-edition/9781337115773/net-present-value-analysis-emery-communications-company-is-considering-the-production-and-marketing/2dbfa726-7ed6-11e9-8385-02ee952b546e | # Net Present Value Analysis Emery Communications Company is considering the production and marketing of a communications system that will increase the efficiency of messaging for small businesses or branch offices of large companies. Each unit hooked into the system is assigned a mailbox number, which can be matched to a telephone extension number, providing access to messages 24 hours a day. Up to 20 units can be hooked into the system, allowing the delivery of the same message to as many as 20 people. Personal codes can be used to make messages confidential. Furthermore, messages can be reviewed, recorded, cancelled, replied to, or deleted all during the same message playback. Indicators wired to the telephone blink whenever new messages are present. To produce this product, a $1.75 million investment in new equipment is required. The equipment will last 10 years but will need major maintenance costing$150,000 at the end of its sixth year. The salvage value of the equipment at the end of 10 years is estimated to be $100,000. If this new system is produced, working capital must also be increased by$90,000. This capital will be restored at the end of the product’s 10-year life cycle. Revenues from the sale of the product are estimated at $1.65 million per year. Cash operating expenses are estimated at$1.32 million per year. Required: 1. Prepare a schedule of cash flows for the proposed project. ( Note: Assume that there are no income taxes.) 2. Assuming that Emery’s cost of capital is 12%, compute the project’s NPV. Should the product be produced?
### Managerial Accounting: The Corners...
7th Edition
Maryanne M. Mowen + 2 others
Publisher: Cengage Learning
ISBN: 9781337115773
### Managerial Accounting: The Corners...
7th Edition
Maryanne M. Mowen + 2 others
Publisher: Cengage Learning
ISBN: 9781337115773
#### Solutions
Chapter
Section
Chapter 12, Problem 42P
Textbook Problem
## Expert Solution
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*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects. | 2021-03-08 12:48:42 | {"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": 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": 0.24146445095539093, "perplexity": 3019.757081820615}, "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/1614178375439.77/warc/CC-MAIN-20210308112849-20210308142849-00135.warc.gz"} |
https://www.tutorialspoint.com/in-figure-below-pqrs-and-abrs-are-parallelograms-and-mathrm-x-is-any-point-on-side-mathrm-br-show-that-i-operatorname-ar-mathrm-pqrs-operatornam | # In figure below, $PQRS$ and $ABRS$ are parallelograms and $\mathrm{X}$ is any point on side $\mathrm{BR}$. Show that(i) $\operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS})$(ii) $\operatorname{ar}(\mathrm{AXS})=\frac{1}{2} \mathrm{ar}(\mathrm{PQRS})$"
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Given:
$PQRS$ and $ABRS$ are parallelograms and $\mathrm{X}$ is any point on side $\mathrm{BR}$.
To do:
We have to show that
(i) $\operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS})$
(ii) $\operatorname{ar}(\mathrm{AXS})=\frac{1}{2} \mathrm{ar}(\mathrm{PQRS})$
Solution:
(i) Parallelograms $PQRS$ and $ABRS$ lie on the same base $SR$ and between the same parallels $SR$ and $PB$.
This implies,
$ar(PQRS) = ar (ABRS)$....…(i)
(ii) In parallelogram $ABRS$,
$\triangle AXS$ and parallelogram $ABRS$ lie on the same base $AS$ and between the same parallels $AS$ and $BR$.
This implies,
$ar (\triangle AXS) = \frac{1}{2}$ ar(parallelogram $ABRS$.......…(ii)
From (i) and (ii), we get,
$ar (\triangle AXS) = \frac{1}{2}$ ar (parallelogram $PQRS$)
Updated on 10-Oct-2022 13:41:39 | 2022-11-26 08:20:37 | {"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": 2, "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": 0.45395129919052124, "perplexity": 3013.3671557548164}, "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-2022-49/segments/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00267.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-12-exponential-functions-and-logarithmic-functions-mid-chapter-review-mixed-review-page-812/17 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$
.... first, write the square root as a power with exponent 1/2 $...=\displaystyle \log(\frac{x^{2}}{yz^{3}})^{1/2}\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}\log\frac{x^{2}}{yz^{3}}\quad$... Apply the property $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log(yz^{3})]\quad$... Apply the property $\log_{a}(MN)=\log_{a}M+\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-(\log y+\log z^{3})]$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log y-\log z^{3}]\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}[2\log x-\log y-3\log z]$ $=\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$ | 2019-12-10 07:25:28 | {"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": 0.4156422019004822, "perplexity": 1114.564661102012}, "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-2019-51/segments/1575540527010.70/warc/CC-MAIN-20191210070602-20191210094602-00424.warc.gz"} |
http://mathhelpforum.com/math-challenge-problems/59143-problem-50-a.html | 1. ## Problem 50
An easy one:
Let $x_i=2^i,\ i=1,.., 16$
Find the minimum of the function:
$
f(x)=\sum_{i=1}^{16} |x-x_i|
$
(I had thought I had already posted this, did it disapear for a reason or am I just misremembering events )
CB
2. Originally Posted by CaptainBlack
An easy one:
Let $x_i=2^i,\ i=1,.., 16$
Find the minimum of the function:
$
f(x)=\sum_{i=1}^{16} |x-x_i|
$
(I had thought I had already posted this, did it disapear for a reason or am I just misremembering events )
CB
OK a clue.
Given the function:
$
f(x)=\sum_{i=1}^{2} |x-x_i|
$
where $x_2>x_1$ what is the minimum of $f(x)$ and where is it achieved.
CB
3. Originally Posted by CaptainBlack
An easy one:
Let $x_i=2^i,\ i=1,.., 16$
Find the minimum of the function:
$
f(x)=\sum_{i=1}^{16} |x-x_i|
$
(I had thought I had already posted this, did it disapear for a reason or am I just misremembering events )
CB
hey mate,
without going into two much detail, I believe the solution lies between the intersection of |x - 2| = |x - 2^16| which over the region of intersection becomes
x - 2 = 2^16 - x
x = 2^15 + 1
am I completely off the mark? if not please let me know and I will post my full solution,
Cheers,
David
4. Originally Posted by David24
hey mate,
without going into two much detail, I believe the solution lies between the intersection of |x - 2| = |x - 2^16| which over the region of intersection becomes
x - 2 = 2^16 - x
x = 2^15 + 1
am I completely off the mark? if not please let me know and I will post my full solution,
Cheers,
David
Try writing in English, that is gobbledy gook.
CB
5. Originally Posted by CaptainBlack
Try writing in English, that is gobbledy gook.
CB
CaptainBlack,
Am I correct in conjecturing that the value of x which minimises f(x) satisfies,
|x-2| =|x-2^16| ?
David
ps - I apologise for any grammatical and or spelling mistakes that may be present in the above statement.
6. this problem is for the moderators only! lol (just kidding!)
suppose $a_1 \leq a_2 \leq \cdots \leq a_n,$ and $f(x)=\sum_{i=1}^n |x-a_i|.$ put: $m=\left \lfloor \frac{n}{2} \right \rfloor.$ prove that: $\min f(x)=\sum_{k=1}^m (a_{n+1-k} - a_k).$
7. Originally Posted by David24
CaptainBlack,
Am I correct in conjecturing that the value of x which minimises f(x) satisfies,
|x-2| =|x-2^16| ?
David
ps - I apologise for any grammatical and or spelling mistakes that may be present in the above statement.
Well lets see,
$|x-2|=|x-2^{16}|$
implies (assuming $2 \le x \le 2^{16}$ anyway) that:
$x-2=2^{16}-x$
or:
$
x=2^8-1
$
Now lets do some calculations:
Code:
>i=1:16;
>
>x=[2^8-1:2^8+1]'
255
256
257
>
>s=abs(x-2^i);
>S=sum(s)
130052
130050
130050
>
So we conclude that, no your proposed condition does not define the solution.
CB
8. Originally Posted by CaptainBlack
Well lets see,
$|x-2|=|x-2^{16}|$
implies (assuming $2 \le x \le 2^{16}$ anyway) that:
$x-2=2^{16}-x$
or:
$
x=2^8-1
$
Now lets do some calculations:
Code:
>i=1:16;
>
>x=[2^8-1:2^8+1]'
255
256
257
>
>s=abs(x-2^i);
>S=sum(s)
130052
130050
130050
>
So we conclude that, no your proposed condition does not define the solution.
CB
CaptainBlack,
Thanks for your response, I will have to keep working on it.
9. Originally Posted by CaptainBlack
An easy one:
Let $x_i=2^i,\ i=1,.., 16$
Find the minimum of the function:
$
f(x)=\sum_{i=1}^{16} |x-x_i|
$
(I had thought I had already posted this, did it disapear for a reason or am I just misremembering events )
CB
Hi,
By deriving f on each interval $[2^j,2^{j+1}]$ we find
$\frac{df}{dx}=2j-16$
Therefore f is decreasing up to $2^8$ (up to j=7) is constant between $2^8$ and $2^9$ (for j=8) and increasing from $2^9$ (from j=9)
The minimum of f is reached between $2^8$ and $2^9$
10. Originally Posted by running-gag
Hi,
By deriving f on each interval $[2^j,2^{j+1}]$ we find
$\frac{df}{dx}=2j-16$
Therefore f is decreasing up to $2^8$ (up to j=7) is constant between $2^8$ and $2^9$ (for j=8) and increasing from $2^9$ (from j=9)
The minimum of f is reached between $2^8$ and $2^9$
It can be done more neatly without calculus.
CB
11. |x-2^i|, where i is a constant, is a continuous function. So, the sum of |x-2^i|, i = 1 to 16, is a continuous function, too.
As a continuous function, its minimum/maximum is at at its derivative is 0, or where its derivative has a discontinuity from prositive to negative or vice-versa.
If x-2^i >= 0 (this means x >= 2^i), then |x-2^i| = x-2^i
If x-2^i < 0 (this means x < 2^i), then |x-2^i| = 2^i-x.
We can divide the x values in 18 parts.
Part 1: x <2^1:
f(x) = sum of (2^i-x), i = 1 to 16 = something - 16*x .This is a line with derivative -16.
part 2: 2^1 <= x < 2^2:
f(x) = x-2^1 + sum of (2^1-x), i = 2 to 16 = something - 14*x. This is a line with derivative -14.
and so on, till part 9: 2^8 <= x < 2^9:
f(x) = (sum of (x-2^i), i = 1 to 8) + (sum of (2^i-x), i = 9 to 16) = something (no dependence on x). This is a line with derivative 0.
part 10: 2^9 <= x < 2^10:
f(x) = (sum of (x-2^i), i = 1 to 9) + (sim of (2^i-x), i = 10 to 16) = something + 2*x. This is a line with derivative 2.
From part 10 on, the line segments have positive derivative. This means that the minimum of the function is at part 9, and its value at this part is:
(sum of 2^i, i = 9 to 16) - (sum of 2^i, i = 1 to 8) = 130560 - 510 = 130050
12. Originally Posted by lcmarincek
|x-2^i|, where i is a constant, is a continuous function. So, the sum of |x-2^i|, i = 1 to 16, is a continuous function, too.
As a continuous function, its minimum/maximum is at at its derivative is 0, or where its derivative has a discontinuity from prositive to negative or vice-versa.
If x-2^i >= 0 (this means x >= 2^i), then |x-2^i| = x-2^i
If x-2^i < 0 (this means x < 2^i), then |x-2^i| = 2^i-x.
We can divide the x values in 18 parts.
Part 1: x <2^1:
f(x) = sum of (2^i-x), i = 1 to 16 = something - 16*x .This is a line with derivative -16.
part 2: 2^1 <= x < 2^2:
f(x) = x-2^1 + sum of (2^1-x), i = 2 to 16 = something - 14*x. This is a line with derivative -14.
and so on, till part 9: 2^8 <= x < 2^9:
f(x) = (sum of (x-2^i), i = 1 to 8) + (sum of (2^i-x), i = 9 to 16) = something (no dependence on x). This is a line with derivative 0.
part 10: 2^9 <= x < 2^10:
f(x) = (sum of (x-2^i), i = 1 to 9) + (sim of (2^i-x), i = 10 to 16) = something + 2*x. This is a line with derivative 2.
From part 10 on, the line segments have positive derivative. This means that the minimum of the function is at part 9, and its value at this part is:
(sum of 2^i, i = 9 to 16) - (sum of 2^i, i = 1 to 8) = 130560 - 510 = 130050
As I said previously, this can be done more easily and elegantly without calculus. Also a hint on how to do this has already been posted.
CB
13. Here's my attempt:
f(x) measures the distance of x to 16 points, namely 2, 4, 8, 16, ... , 2^16.
Suppose we let x to be less than 2. Then we can decrease f(x) by increasing x towards 2 since this decreases the distance of x to all 16 points.
So what happens when we increase x pass 2? We're getting further away from a single point, ie 2, but at the same time, we are decreasing our distance to 15 points. The net effect is a decrease in f(x).
The key observation here is that if we change x by a fix amount, the change in the distance is the same for all points(some are positive change, while others are negative, but the absolute value is the same).
This implies that we should keep increasing x to decrease f(x) as long as we are decreasing the distance to more points than the number of points that we are getting further away.
Following this logic, we arrive at the answer that f(x) is minimum between the region 2^8 and 2^9, which has 8 points less than it and 8 points more.
14. Okay. The derivative of |x-a| is:
1 if x-a>0
0 if x=0
-1 if x-a<0
Since we have a sum we the derivative of f(x) is the sum of the derivatives of the modulus:f'(x)= $\sum _{i=1}^{16} \left(\left|x-x_i\right|\right)'$
If f'(x) is to be 0 we can't have some of the elements $|x-x_i|$ to be zero because then all the other elements can't be zero. We will have 15 elements that can be 1 or -1 and one which is 0 and their sum cannot be 0.
Suppose we have a number i=n such as for i>n $x-x_i<0$. This is easy enough to prove $x-x_i>x-x_{i+1}$. We will also have $x-x_i>0$ for i<=n since there can't be a zero term. From f'(x)=0 we can conclude that n=8 (8 times 1 and 8 times -1=0).
So $x-x_9<0$ for n>8
$x<2^9$
and
$x-x_8>0$ for n<=8
$x>2^8$
All that is left is to prove that this is a minimum but I'll leave that to you.
Don't know if someone has suggested this. I didn't read all the posts.
15. In order to have an idea about how we can solve the problem let’s consider the minimum of this function…
$f(x)= \sum_ {i=1}^{2} |x-2^{i}|$ (1)
… which is represented [in blue] here…
The (1) is in fact a ‘straight-line function’ the slope of which changes in $x=2$ and $x=4$. More exactly, the function starts with negative slope $s=-2$, in $x=2$ becames ‘flat’ [ $s=0$, and for $x > 4$ the slope is positive [ $s=2$]. The ‘minimum’ of (1) in fact is not rescticted to a single point, but in extended to the interval $2 \le x \le 4$, where is $f(x)=2$. In similar way we can ‘attach’ the proposed problem, i.e. finding the minimum of…
$f(x)= \sum_ {i=1}^{16} |x-2^{i}|$ (2)
As the (1), the (2) is also ‘straight-line’ . In $x=0$ is…
$f(0)= \sum_ {i=1}^{16} 2^{i}$ $= 2 \cdot (2^{16}-1)=131070$
The functions starts with negative slope $s=-16$ and each time that $x=2^{i}$ the slope is increased by $+2$. So we have…
$x=0, s=-16; x=2, s=-14; x=4, s=-12;\dots; x=2^{7}, s=-2; x=2^{8}, s=0;\dots$
So the functions become ‘flat’ in the interval $256 \le x \le 512$ and here exhibits its ‘minimum’ which is [if no mistakes of mine…] …
$f(2^{8})= \sum_{i=1}^{16} |2^{8}-2^{i}|= 2\cdot (2^{8}-1)^ {2}= 130050$
Regards
Page 1 of 2 12 Last | 2017-03-26 02:10:26 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 68, "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": 0.8371269106864929, "perplexity": 818.5329086061358}, "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-2017-13/segments/1490218189090.69/warc/CC-MAIN-20170322212949-00480-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://ai.stackexchange.com/questions/10412/my-naive-ha-gaussian-naive-bayes-classifier-is-too-slow | My naive (ha!) Gaussian Naive Bayes classifier is too slow
I am trying to build a film review classifier where I determine if a given review is positive or negative (w/ Python). I'm trying to avoid any other ML libraries so that I can better understand the processes. Here is my approach and the problems that I am facing:
1. I mine thousands of film reviews as training sets and classify them as positive or negative.
2. I parse through my training set and for each class, I build an array of unique words.
3. For each document, I build a vector of TF-IDF values where the vector size is my number of unique words.
4. I use a Gaussian classifier to determine: $$P(C_i|w)=P(C_i)P(w|C)=P(C_i)*\dfrac{1}{\sqrt{2\pi}\sigma_i}e^{-(1/2)(w-\mu_i)^T\sigma_i^{-1}(w-\mu_i)}$$ where $$w$$ is the my document in a vector, $$C_i$$ is a particular class, $$\mu_i$$ is the mean vector and $$\sigma_i$$ is my covariance matrix.
This approach seems to makes sense. My problem is that my algorithm is much too slow. As an example, I have sampled over 1,500 documents and I have determined over 40,000 unique words. This mean that each of my document vectors has 40,000 entries and if I were to build a covariance matrix, it would have dimensions 40,000 by 40,000. Even I were able to generate the entirety of $$\sigma_i$$, but then I would have to compute the matrix product in the exponent, which will take an extraordinarily long time just to classify one document.
I have experimented with a multinomial approach, which is working well. I very curious on how to make this work more efficiently. I realise the matrix multiplication runtime can't be improved, and I was hoping for insight on how others are able to do this.
Some things I have tried:
• Filtered any stop words (but this still leaves me with tens of thousands of words)
• Estimated $$\sigma_i$$ by summing over a couple of documents. | 2020-08-15 02:37:52 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7342368960380554, "perplexity": 402.79112883836984}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2020-34/segments/1596439740423.36/warc/CC-MAIN-20200815005453-20200815035453-00027.warc.gz"} |
https://www.gradesaver.com/textbooks/math/calculus/calculus-10th-edition-anton/chapter-9-infinite-series-9-3-infinite-series-exercises-set-9-3-page-622/19 | ## Calculus, 10th Edition (Anton)
The harmonic series, or the sum of all values from $n=1$ to $n=\infty$ of $\frac{1}{n}$, diverges, since any sum from 1 to infinity of $\frac{1}{n^p}$ diverges for all values of $p<1$. | 2018-09-20 04:21:29 | {"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": 0.9190797805786133, "perplexity": 146.59397291388987}, "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-2018-39/segments/1537267156416.22/warc/CC-MAIN-20180920041337-20180920061337-00034.warc.gz"} |
https://dsp.stackexchange.com/questions/51521/impulse-response-from-frequency-response-why-using-ej-omega-as-an-input | # Impulse response from Frequency response: why using $e^{j\omega}$ as an input?
Every resource that I can find uses this identity when deriving impulse response:
$h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$
Suggesting that the input signal was $e^{j\omega}$. But by definition Impulse Response is the result of applying the filter to delta signal. Why then do we use $e^{j\omega}$ instead?
I think you misunderstand the notation. Writing $H(e^{j\omega})$ does not mean that $e^{j\omega}$ is the input signal. It just means that the frequency response is a function of the complex variable $e^{j\omega}$, because, as you might know, it is defined by
$$H(e^{j\omega})=\sum_{n=-\infty}^{\infty}h[n]e^{-jn\omega}=\sum_{n=-\infty}^{\infty}h[n]\big(e^{j\omega}\big)^{-n}\tag{1}$$
where $h[n]$ is the impulse response. Eq. $(1)$ is the discrete-time Fourier transform (DTFT) of the sequence $h[n]$. Generalizing to a complex argument $z$ you get the definition of the $\mathcal{Z}$-transform:
$$H(z)=\sum_{n=-\infty}^{\infty}h[n]z^{-n}\tag{2}$$
Comparing $(1)$ and $(2)$ shows that the DTFT is equal to the $\mathcal{Z}$-transform evaluated on the unit circle, i.e., for $z=e^{j\omega}$. Note that evaluating $(2)$ on the unit circle only makes sense if the unit circle is inside the region of convergence of $(2)$, otherwise $H(z)$ doesn't converge for $|z|=1$ and in that case the DTFT either doesn't exist or it takes a form which is different from $H(z)$ with $|z|=1$.
Note that some people just use $\omega$ as the argument of the function that expresses the DTFT, so you might as well come across the notation $H(\omega)$. After all, it's just a matter of convention.
Concerning the notation $H(e^{j\omega})$ you can also refer to this question and its answer.
• I see.. So It's not a (valid) mathematical notation but a DSP short-hand, right? Aug 26 '18 at 8:37
• If you look at the link, you could see the origin in the $z$-transform. And the Fourier transform is its evaluation on the unit disk ($|z|=1$). So $H(\omega)$ is also a reminder of how the rotation/angle disk is parametrized Aug 26 '18 at 8:50
• @StanislavBashkyrtsev: The notation is perfectly correct. It shows that $H$ is a function of a complex variable $z$ evaluated on the unit circle $|z|=1$, i.e., $z=e^{j\omega}$. Aug 26 '18 at 16:09
• sorry Matt, i bumped you down. i will prepare an alternative answer. Aug 26 '18 at 16:39
• @MattL., well, when a function is defined, it names its argument which is then used in the body of the function. E.g. here is a function with argument $x$: $f(x) = x^2$. But in the formula above the parameter is not defined. It's replaced with $e^{j\omega}$ which as far as I understood describes the form $H(\omega)$ takes. Aug 26 '18 at 16:51 | 2021-10-19 08:11:27 | {"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": 0.9248405694961548, "perplexity": 192.01322853442943}, "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-2021-43/segments/1634323585246.50/warc/CC-MAIN-20211019074128-20211019104128-00580.warc.gz"} |
https://tex.stackexchange.com/questions/203353/enumitem-using-label-for-a-defined-item | # enumitem: using label for a defined item
Whenever I try to label an item that is defined, it never seems to work. For example, consider the following:
\documentclass{article}
\usepackage{enumitem}
\usepackage[noabbrev]{cleveref}
\begin{document}
\begin{enumerate}
\item[3.1]
\item[6.3]
\label{prob63}
\item
From \cref{prob63}, some statement
\end{enumerate}
\end{document}
I think this may be partly because one can use non-counter-style entries when using the optional argument to \item[<stuff>]. So, in that regard, you can set this manually so that the reference appears as you want:
\documentclass{article}
\usepackage{enumitem}
\usepackage[noabbrev]{cleveref}
\makeatletter
\newcommand{\setcreflabel}[1]{%
\protected@edef\cref@currentlabel{%
[\@tempa][#1][\cref@result]%
#1}}%
\makeatother
\begin{document}
\begin{enumerate}
\item \label{prob1}
\item[6.3] \setcreflabel{6.3}\label{prob63}
\item
From \cref{prob63}, some statement; From \cref{prob1}, some statement.
\end{enumerate}
\end{document}
The motivation here is to update \cref@currentlabel in an analogous way to how \refstepcounter updates \@currentlabel. In that way, when you issue \label, the correct reference content is written to the .aux:
\relax
\newlabel{prob1}{{1}{1}}
\newlabel{prob1@cref}{{[enumi][1][]1}{1}}
\newlabel{prob63}{{1}{1}}
\newlabel{prob63@cref}{{[enumi][6.3][]6.3}{1}}
• I am seeing From ?? 6.3 and the error message is still undefined label. – dustin Sep 27 '14 at 14:38
• @dustin: When you compile my minimal example? – Werner Sep 27 '14 at 15:08
• In my real document where I had this issue. – dustin Sep 27 '14 at 15:13
• @dustin: Are you calling \setcreflabel{<something>}? – Werner Sep 27 '14 at 15:14
• Yes, I placed that before the \label{} as in the example. – dustin Sep 27 '14 at 15:15 | 2020-01-27 01:05:43 | {"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": 0.8823931217193604, "perplexity": 2433.0666770578637}, "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/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00025.warc.gz"} |
https://staff.science.uva.nl/a.l.kret/ | # Arno Kret
I work in arithmetic, and like thinking about algebraic geometry, representation theory and number theory. My CV.
Address: Korteweg-de Vries Institute Science Park 105 1090 GE Amsterdam (enter at NIKHEF, see below). Office: F3.10 Phone: 020-5256079 email: FirstnameLastname at gmail.
### Papers and preprints
$$H^0$$ of Igusa varieties via automorphic forms (with Sug Woo Shin), pdf.
Galois representations for even general special orthogonal groups (with Sug Woo Shin), pdf.
Integral points on Hilbert moduli schemes (with Rafael von Kanel), pdf.
Galois representations for the general symplectic group (with Sug Woo Shin). Accepted at JEMS, pdf.
Galois generic points on Shimura varieties (with Anna Cadoret), Algebra and Number Theory (journal, pdf).
The trace formula and the existence of PEL type Abelian varieties modulo p, (arxiv).
Equidistribution in supersingular Hecke orbits, Journal für die reine und angewandte Mathematik, (journal, arxiv).
Combinatorics of the basic stratum, Documenta Mathematica, (journal, arxiv).
The basic stratum of some simple Shimura varieties, Mathematische Annalen, (journal, arxiv).
Jacquet modules of ladder representations, Comptes rendus de l'Académie des Sciences, (with Erez Lapid), (journal).
### Teaching
Spring 2021: Master course Topics in Number Theory (in English).
Spring 2021: Undergraduate course Galois theory (in English).
### Other writing
The Langlands program (slides), Faculty Colloquium, 2018.
Andrew Wiles en de Abelprijs (pdf), with Sander Dahmen, Nieuw Archief voor Wiskunde, 2017.
Stratification de Newton des variétés de Shimura et formule des traces d’Arthur-Selberg, PhD thesis, Université Paris-Sud, 2013, theses.fr. See also youtube video lecture.
Caveat emptor: Galois Representations, Master's thesis, Université Paris-Sud, University of Leiden, pdf.
### Need help finding me?
Click here for some instructions to find my office inside the Nikhef building. | 2021-10-17 03:02:56 | {"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": 0.32939308881759644, "perplexity": 12889.362258617677}, "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/1634323585120.89/warc/CC-MAIN-20211017021554-20211017051554-00095.warc.gz"} |
https://www.homebuiltairplanes.com/forums/threads/b-s-49-series-810cm3-49ci-for-aircraft-use-tipis-q-a-thread.32382/page-14 | # B&S 49-series (810cm3/49ci) for aircraft use - TiPi's Q&A thread
### Help Support Homebuilt Aircraft & Kit Plane Forum:
#### Vigilant1
##### Well-Known Member
Briggs coil with large air gap (could be around 8-10deg over rpm range, might need stronger magnet)
Is this the idea of the stepped flywheel/stepped trigger spacing as you mentioned here: Simple, proven, off-the-shelf industrial V-twin? ? It seems like a clever approach, but possibly fiddly (to get the spacing right). It also seems unlikely that both cylinders would make the "hop" to the new timing at the same time.
I guess there's no practical way to have multiple selectable trigger coils per primary magneto, or to electronically delay the triggering of the main spark impulse.
#### TiPi
##### Well-Known Member
Log Member
Is this the idea of the stepped flywheel/stepped trigger spacing as you mentioned here: Simple, proven, off-the-shelf industrial V-twin? ? It seems like a clever approach, but possibly fiddly (to get the spacing right). It also seems unlikely that both cylinders would make the "hop" to the new timing at the same time.
I guess there's no practical way to have multiple selectable trigger coils per primary magneto, or to electronically delay the triggering of the main spark impulse.
That is the big question. I found some info on a kart site where they show that the timing changes quite a bit with increased air gaps (single cylinder engines).
The step is just another way of introducing a larger gap that will retard the timing at low revs. Only testing will show if they are suitable for 2-cylinder engines. As long as the timing between both cylinders is the same at idle and cruise/WOT, it should work. The rpms between idle and cruise/WOT are not used for normal operation, so the transition from retard to max advance doesn’t need to be synchronised.
#### Hot Wings
##### Grumpy Cynic
HBA Supporter
Log Member
Just one data point from history:
Some of the Quickie builders modified the Onan timing using the caveman method of mounting the ignition parts on a manually controlled plate.
I think there are more elegant ways of getting a better advance curve but if retaining stock(ish) coils and flying magnets is a priority than it is an option.
@ TIPI
Totally understand about the workspace delays. I still have some drywall and brick work to do before I can get the rest of the electrical in. To many other spring related tasks that have priority. Mother nature just doesn't care about my desired schedule..............
#### blane.c
##### Well-Known Member
HBA Supporter
I would think the first thing the crank sensor signal would go to would be a interpreter/timer. If you do your best work and you install the crank sensor so it triggers pretty close to were you want it the interpreter can fine tune it exactly (it may not matter where the sensor is the interpreter just adjusts to what you want it to be). Secondly it electronically sends out a second signal automatically timed to the first for of course the second cylinder. Then everything downstream gets two properly timed triggers. Is that how it works?
#### Vigilant1
##### Well-Known Member
Is that how it works?
I don't know about other systems, but it's not how the stock B&S magnetrons work. Each cylinder/magneteon is independent. As I understand it, it has a main coil that develops current as the magnets in the flywheel go by, and this charge is stored in a capacitor. There's a second coil that is a trigger, when the magnet goes past this and the juice it is making begins to trail off, a circuit trips the stored energy in the capacitor to go to the sparkplug. So, no delay and no linkage between cylinders. Timing is determined by the placement of the trigger coil, which is integral to all the other stuff--one clunky, fixed timing, cheap, reliable, assembly per cylinder.
Obviously, it is a "wasted spark" ignition, since the coil is charged/discharged with every revolution of the crank.
Last edited:
#### blane.c
##### Well-Known Member
HBA Supporter
I don't know about other systems, but it's not how the stock B&S magnetrons work. Each cylinder/magneteon is independent. As I understand it, it has a main coil that develops current as the magnets in the flywheel go by, and this charge is stored in a capacitor. There's a second coil that is a trigger, when the magnet goes past this and the juice it is making begins to trail off, a circuit trips the stored energy in the capacitor to go to the sparkplug. So, no delay and no linkage between cylinders. Timing is determined by the placement of the trigger coil, which is integral to all the other stuff--one clunky, fixed timing, cheap, reliable, assembly per cylinder.
Obviously, it is a "wasted spark" ignition, since the coil is charged/discharged with every revolution of the crank.
So the spark advance/retard is fixed?
#### blane.c
##### Well-Known Member
HBA Supporter
If the spark is mechanically controlled or fixed then EFI is not likely to be much improvement if any over carburation? With the spark you described and a single engine airplane with two cylinders flying in formation with the same crankshaft (V Engines) then most likely two carbs is answer? Each cylinder is tuned as a single and so two mixture controls & cables, two chokes & cable with linkage [unless replacing with primer(s)] and two throttles with linkage that allows to dial in one cylinder independent of the other. Tuning would need to be done with two manifold pressure gages and they could be part of the engine instruments package. I imagine some of the Siamese carbs amount to the same difference depending on if they have individual mixture control and how reliable they are. Without the ability to properly lean each cylinder these (V) engines are not likely to perform as well as they should?
Part of the charm of EFI is when the spark advance/retard is also controlled by the computer. The fuel metering can be tailored to each cylinder as well by the computer eliminating the need of the pilot to do this chore.
With single engine operation one may desire to do without a computer between the pilot and the engine, just a rudimentary spark and a couple of carburetors, swilling a little extra fuel along the way is OK for the trade in reliability.
With multi engine operation the computer becomes less of an evil and more of an ally as you are not likely to lose the computer in two engines at the same time and it reduces the pilots workload and each engine can be more efficient.
#### Vigilant1
##### Well-Known Member
Apparently, previously I wrote that the B&S EFI does control spark timing. So, I misremembered that. The B-S EFI has some other attributes that make it less than ideal for acft use IMO:
1) closed loop operation, so won't achieve best power mixture, will eventually have sensor failure if running 100LL.
2) Single point failure modes (crank sensor, electrical power, etc)
3) Unidentified limp mode criteria and power output.
My description in Post 265 applies to B&S engines with carbs and magnetron ignitions.
Sorry for the confusion.
ETA: Tipi provided a link to his copy of the B&S EFI manual. See his post with link here: Forum made EFI?
Last edited:
#### tunna95
##### New Member
Apparently, previously I wrote that the B&S EFI does control spark timing. So, I misremembered that. The B-S EFI has some other attributes that make it less than ideal for acft use IMO:
1) closed loop operation, so won't achieve best power mixture, will eventually have sensor failure if running 100LL.
2) Single point failure modes (crank sensor, electrical power, etc)
3) Unidentified limp mode criteria and power output.
My description in Post 265 applies to B&S engines with carbs and magnetron ignitions.
Sorry for the confusion.
ETA: Tipi provided a link to his copy of the B&S EFI manual. See his post with link here: Forum made EFI?
Could you use the BS EFI hardware and swap out the ECU with say a Speeduino with custom parameters suitable for aircraft use?
#### Vigilant1
##### Well-Known Member
Could you use the BS EFI hardware and swap out the ECU with say a Speeduino with custom parameters suitable for aircraft use?
I'd have to look back at the B&S EFI bits, but I suspect it would be easier and certainly cheaper to start with a carbureted B&S engine and add the Speeduino ECU and other stuff off the shelf. A used twin-throat throttle body with injectors from a suitable motorcycle can be had very inexpensively.
#### Urquiola
##### Well-Known Member
EFI is still an option if I can’t get a single carby to work properly (single or dual barrel). The challenge with EFI is to identify and address all possible and likely failure modes while keeping it simple. No point in designing an EFI system that will cost the same as the actual engine.
If my information is still right, FAA did not allow EFI in General Aviation, if rules differ for ultralight and homebuilts, I don't know. www.ecotrons.com has a line of EFI for small engines, in Italy, they sell Turbocompressors for Vespa Two-Stroke engines. You may like this SAE technical paper: 2003-28-0017 'Altitude Performance Comparison of A Wankel Engine with Carburetor and Fuel Injection', can be downoald from SAE for $33, membership not needed. Wankel News, magazine from Hercules Wankel IG, has some documents about EFI for Sachs small Wankel engines. Blessings + #### TFF ##### Well-Known Member EFI is allowed in general aviation in the US. It is not economically feasible to certify it, because it would require recertification of each aircraft to add that system. Homebuilts US rules is any risk you want to take is up to you as long as you can get the paperwork signed. 103 ULs no rules except speed and weight. #### Urquiola ##### Well-Known Member EFI is allowed in general aviation in the US. It is not economically feasible to certify it, because it would require recertification of each aircraft to add that system. Homebuilts US rules is any risk you want to take is up to you as long as you can get the paperwork signed. 103 ULs no rules except speed and weight. The issue could be if your flying machine falls, it can harm not only you, but third parties. Also insurance companies avoid any daredevil attitude. Blessings + #### TFF ##### Well-Known Member You can build a homebuilt out of bread in the US. Wing folding is your problem. If you did stretch the engineering to that, the FAA can restrict passengers and other things. There are safety valves to keep it your own problem. If you need insurance on a baked bread airplane, don’t land where there is animals. That’s your insurance. #### WonderousMountain ##### Well-Known Member You won't be cleared for landing if tower is gluten intolerant. #### Urquiola ##### Well-Known Member You won't be cleared for landing if tower is gluten intolerant. Perhaps for risk analysis, budget spread, Insurance companies are classifying diseases to the minor detail, they have different codings for human bites, for bites from a cow, a dog,.. Blessings + #### Protech Racing ##### Well-Known Member Some points . I race and sell Microsquirt EFI. I have a standard template now and have a bunch of cars using the same bits. Tunes vary with actual fuel pressure but overall the maps are very similar . As a rule , if it starts and runs , failures have not happened. Failures that have happened. include the LS coils, I now use standard OTS VW waste spark smart coils. I race these and power/results are crucial for me to make a living . Any AFR between 12.2 and 12.6 make effectively the same power . I tune in closed loop , race in open loop. I dont use a TPS. Simply a GM map sensor, NIssan or Ford RPM trigger. The Nissan bolts up more solid and vibration can lead to a high RPM trigger fault. The Nissan trigger and pig tail is robust. Use a wide band O2 sensor and the deal can tune it self . You may use a flying bolt for a trigger or a toothed wheel . These little engines will not burn enough fuel to worry about lean cruise. The map can be tailored for lean RE to the map . You simply will not need to tune each cylinder. The system will allow you to time each cylinder as you see fit . There is a "kick start " timing set. at 0 or 1 BTDC. If you find that the heads flow better than the other , you can trim the AFR with inlet tube length. It is a simply system and would work fine on these engines . As usual, desk engineers are overthinking it. #### Flyguyeddy ##### Well-Known Member HBA Supporter Some points . I race and sell Microsquirt EFI. I have a standard template now and have a bunch of cars using the same bits. Tunes vary with actual fuel pressure but overall the maps are very similar . As a rule , if it starts and runs , failures have not happened. Failures that have happened. include the LS coils, I now use standard OTS VW waste spark smart coils. I race these and power/results are crucial for me to make a living . Any AFR between 12.2 and 12.6 make effectively the same power . I tune in closed loop , race in open loop. I dont use a TPS. Simply a GM map sensor, NIssan or Ford RPM trigger. The Nissan bolts up more solid and vibration can lead to a high RPM trigger fault. The Nissan trigger and pig tail is robust. Use a wide band O2 sensor and the deal can tune it self . You may use a flying bolt for a trigger or a toothed wheel . These little engines will not burn enough fuel to worry about lean cruise. The map can be tailored for lean RE to the map . You simply will not need to tune each cylinder. The system will allow you to time each cylinder as you see fit . There is a "kick start " timing set. at 0 or 1 BTDC. If you find that the heads flow better than the other , you can trim the AFR with inlet tube length. It is a simply system and would work fine on these engines . As usual, desk engineers are overthinking it. Which coils are the ones you speak of? #### Flyguyeddy ##### Well-Known Member HBA Supporter These? Vw 032 905 106B #### Vigilant1 ##### Well-Known Member Lifetime Supporter Microsquirt: How much to get into the game?? ECU and harness:$360
Used throttle body and injectors: $100 Fuel pump (45 psi):$150
Misc fuel hose and fittings: $40 Wideband O2 sensor for tuning:$200
Sensors: ?? CAS, MAP, temp, etc.
Lots of connectors and fittings, relay, fuse block, etc. You'll need a good crimper.
This is fuel side only. If you want to use it for ignition, add more wires, coils, connectors, etc.
You'll also need a laptop, but most people have one.
People converting a car to full Megasquirt/Microsquirt from old school carb spend $800+ Microsquirt might work great. Aeromomentum uses Microsquirt for their aero engines. The stock B&S Vanguard 810cc engine is available brand new for about$1200. Whether builders will choose to discard the OEM ignition system and carb and invest another \$800+ (about 2/3 the price of the complete original engine) for a MicroSquirt EFI and ignition system for their 2 cylinder, 30 HP motor remains to be seen. It probably depends on whether the advantages are seen as being worth the cost, and if it is the best overall option available. I would expect that perceived reliability would be an important criteria.
Last edited: | 2021-06-20 13:33:34 | {"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": 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": 0.31594955921173096, "perplexity": 3578.1900878126125}, "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/1623487662882.61/warc/CC-MAIN-20210620114611-20210620144611-00059.warc.gz"} |
https://socratic.org/questions/if-x-is-an-acute-angle-and-cos-x-4-5-then-cos-2-x-is-equal-to#603181 | # If x is an acute angle, and cos x =4/5, then cos (2 x) is equal to?
Apr 28, 2018
$\cos 2 x = \frac{7}{25}$
#### Explanation:
Use trig identity:
$\cos 2 x = 2 {\cos}^{2} x - 1$
In this case:
$\cos 2 x = \left(2\right) \left(\frac{16}{25}\right) - 1 = \frac{32}{25} - \frac{25}{25} = \frac{7}{25}$
To find the sign of cos 2x, use calculator to approximately get the value of x and 2x.
$\cos x = \frac{4}{5}$ --> $x = {36}^{\circ} 87$ --> $2 x = {73}^{\circ} 74$.
Since 2x is in Quadrant 1, then, cos 2x is positive.
$\cos 2 x = \frac{7}{25}$ | 2021-10-17 18:14:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.9837985038757324, "perplexity": 3265.003045422438}, "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/1634323585181.6/warc/CC-MAIN-20211017175237-20211017205237-00111.warc.gz"} |
https://pfzhang.wordpress.com/2014/08/07/exponential-map-on-the-complex-plane/ | ## Exponential map on the complex plane
Let $f(z)=e^z=e^x(\cos y+\i\sin y)$ (for $z=x+\i y$) be the exponential map. Note that $f(x)>0$ for all real numbers and $f^{n+1}(x):=f(f^nx)$ goes to $\infty$ really fast: the dynamics of $f$ on $\mathbb{R}$ is trivial. But the dynamics of $f$ on $\mathbb{C}$ is completely different. First note that $e^{2k\pi\i}=1$: the map is not a diffeomorphism, but a covering map branching at the origin. The following theorem was conjectured by Fatou (1926) and proved by Misiurewicz (1981).
Theorem (Orbits of the complex exponential map).
Let $\mathcal{O}_e(z)$ be the orbit of a point $z\in\mathbb{C}$ under the iterates of $f(z)=e^z$. Then each of the following sets is dense in the complex plane:
1. the basin of $\infty$, $B_e(\infty)=\{z\in\mathbb{C}: f^n(z)\to\infty\}$;
2. the set of transitive points, $\text{Tran}(e)=\{z\in\mathbb{C}: \mathcal{O}_e(z)\text{ is dense}\}$;
3. the set of periodic points, $\text{Per}(e)=\{z\in\mathbb{C}: \mathcal{O}_e(z)\text{ is finite}\}$.
So the exponential map is chaotic on the complex plane.
Reference:
The exponential map is chaotic: An invitation to transcendental dynamics,
Zhaiming Shen and Lasse Rempe-Gillen arXiv | 2017-12-18 16:41:37 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 17, "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": 0.9742998480796814, "perplexity": 292.683673243618}, "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-2017-51/segments/1512948618633.95/warc/CC-MAIN-20171218161254-20171218183254-00125.warc.gz"} |
https://cjvanlissa.github.io/metaforest/reference/PartialDependence.html | Partial dependence plots
PartialDependence(
x,
vars = NULL,
pi = NULL,
rawdata = FALSE,
bw = FALSE,
resolution = NULL,
moderator = NULL,
mod_levels = NULL,
output = "plot",
...
)
## Arguments
x Model object. Character vector containing the moderator names for which to plot partial dependence plots. If empty, all moderators are plotted. Numeric (0-1). What percentile interval should be plotted for the partial dependence predictions? Defaults to NULL. To obtain a 95% interval, set to .95. Logical, indicating whether to plot weighted raw data. Defaults to FALSE. Uses the same weights as the model object passed to the x argument. Logical, indicating whether the plot should be black and white, or color. Integer vector of length two, giving the resolution of the partial predictions. The first element indicates the resolution of the partial predictions; for Monte-Carlo integration, the second element gives the number of rows of the data to be sampled without replacement when averaging over values of the other predictors. Atomic character vector, referencing the name of one variable in the model. Results in partial prediction plots, conditional on the moderator. If moderator references a factor variable, separate lines/boxplots are plotted for each factor level. If moderator references a numeric variable, heatmaps are plotted - unless the moderator is categorized using the mod_levels argument. Vector. If moderator is continuous, specify thresholds for the cut function. The continuous moderator is categorized, and predictions are based on the median moderator value within each category. You can call quantile to cut the moderator at specific quantiles. If moderator is a factor variable, you can use mod_levels to specify a character vector with the factor levels to retain in the plot (i.e., dropping the other factor levels). Character. What type of output should be returned? Defaults to "plot", which returns and plots a gtable object. To obtain a list of ggplot objects instead, provide the argument "list". Additional arguments to be passed to and from functions.
A gtable object.
## Details
Plots partial dependence plots (predicted effect size as a function of the value of each predictor variable) for a MetaForest- or rma model object. For rma models, it is advisable to mean-center numeric predictors, and to not include plot_int effects, except when the rma model is bivariate, and the plot_int argument is set to TRUE.
## Examples
# Partial dependence plot for MetaForest() model:
set.seed(42)
data <- SimulateSMD(k_train = 200, model = es * x[, 1] + es * x[, 2] + es *
x[, 1] * x[, 2])$training data$X2 <- cut(data$X2, breaks = 2, labels = c("Low", "High")) mf.random <- MetaForest(formula = yi ~ ., data = data, whichweights = "random", method = "DL", tau2 = 0.2450) # Examine univariate partial dependence plot for all variables in the model: PartialDependence(mf.random, pi = .8)if (FALSE) { # Examine bivariate partial dependence plot the plot_int between X1 and X2: pd.plot <- PartialDependence(mf.random, vars = c("X1", "X2"), plot_int = TRUE) # Save to pdf file pdf("pd_plot.pdf") grid.draw(pd.plot) dev.off() # Partial dependence plot for metafor rma() model: dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) dat$yi <- as.numeric(dat$yi) dat$alloc <- factor(dat$alloc) dat$ablat_d <- cut(dat$ablat, breaks = 2, labels = c("low", "high")) # Demonstrate partial dependence plot for a bivariate plot_int rma.model.int <- rma(yi, vi, mods=cbind(ablat, tpos), data=dat, method="REML") PartialDependence(rma.model.int, rawdata = TRUE, pi = .95, plot_int = TRUE) # Compare partial dependence for metaforest and rma dat2 <- dat dat2[3:7] <- lapply(dat2[3:7], function(x){as.numeric(scale(x, scale = FALSE))}) mf.model.all <- MetaForest(yi ~ ., dat2[, c(3:11)]) rma.model.all <- rma(dat$yi, dat2\$vi,
mods = model.matrix(yi~., dat2[, c(3:10)])[, -1],
method="REML")
PartialDependence(mf.model.all, rawdata = TRUE, pi = .95)
PartialDependence(rma.model.all, rawdata = TRUE, pi = .95)
} | 2022-05-24 21:30:30 | {"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": 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": 0.44202297925949097, "perplexity": 5334.053938282428}, "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-2022-21/segments/1652662577259.70/warc/CC-MAIN-20220524203438-20220524233438-00382.warc.gz"} |
https://brilliant.org/discussions/thread/elementary-techniques-used-in-the-imo-internatio-a/ | # Elementary Techniques used in the IMO (International Mathematical Olympiad) - Invariants
This post continues from both: Part 1 and Part 2
Part $3$
Applications
The first example is of a game. We will see how to apply the invariance principle.
Example 1: On a chessboard A and B play by turns to place black and white knights, respectively. Either player loses when he places a knight on a square attacked by a knight of the other colour or there are no free squares to place the knight on. If A starts, who has a winning strategy?
Solution: For those chess noobs like me, remark that a knight can only attack the $8$ squares shown in the figure below:
tagtext
Intuitively, if each player can place a knight such that the squares that can be attacked by both knights do not overlap, then since a chessboard has an even number of cells, Player B can win, by in what people call, mirroring the first player.
Clearly a knight on a black square can only attack a knight on a white square and vice versa. So the colours of the squares that the knight attacks is invariant. Recall that a chessboard is a $8\times 8$, so if we "fold" the board along the middle, the $2$ "flaps" would be of opposing colour. For instance, let $a_{i,j}$ be the colour of the cell in the $ith$ row and $jth$ column of the chessboard. Then we have that $a_{4,2} = a_{4,7}$.
The above observation is key for us to see that the strategy for B is to do the same thing as A but symmetric to the center of the board. Basically, notice that if A can place a knight without being attacked by B's knights, the B can always place a "symmetric" knight without being attacked by A's knight due to the colour argument. Now given the way that knights attack, A can never place a knight that attacks the square where B played. Thus A loses in the end. □
To further train the skills of the reader in solving game-like problems (because we would soon be moving to colouring and other invariance, and I would select the IMO problems for demonstration), we will attempt one more example, this problem was in my training notes, and according to our trainer, was from Bulgaria 2001.
Example 2 Alice and Bob play by turns to write ones and zeroes in a list, from left to right. The game ends when each has written 2001 numbers. When the game ends the sequence of $0 ,1$ is interpreted in base $2$. Alice wins if that number can be written as a sum of two perfect squares and if otherwise, Bob wins. Who has a winning strategy?
Solution: We want a invariant that somehow involves squares. Well, preliminarily, just plain squares would remind me of $\pmod 4$. So ultimately one should think of Fermat's Christmas Theorem. Let's see how this property translates to a winning strategy.
Now suppose the number is $1100 \ldots 0$ where there is an even number of $0$, what can you observe? (Hint: consider $\pmod 4$) Yup, exactly! Since $4m$ can be written as a sum of $2$ squares iff $m$ can, we can perfectly well ignore the zeroes at the end. And notice that $11$ in base $2$ cannot be written as a sum of $2$ squares, so B wins! Generalising this argument, at any moment A writes a $1$, B just copies $A's$ move. In this way, if we ignore the zeores, the final number would end in $11$ which is congruent to $3 \pmod 4$ which by Fermat's Christmas Theorem, cannot be written as a sum of $2$ squares, so B wins.
Now, remember that $A$ is smart. She wants to avoid losing to $B$ in this way.
Can you complete the argument? Post your completed proof in the comments.
Announcement: I am extremely sorry but since I will be going overseas and the wifi there is unsteady, I will not be posting any more of these daily instalments until Friday, Singapore time.
Note by Anqi Li
7 years, 5 months ago
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- 6 years, 8 months ago | 2021-05-17 10:35:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 35, "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": 0.9085614085197449, "perplexity": 951.3390779600713}, "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-2021-21/segments/1620243992159.64/warc/CC-MAIN-20210517084550-20210517114550-00418.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Ayuen.manwai | ## Yuen, Manwai
Compute Distance To:
Author ID: yuen.manwai Published as: Yuen, Manwai; Yuen, Man-Wai Homepage: https://oraas0.ied.edu.hk/rich/web/people_details.jsp?pid=139145 External Links: MGP · ORCID · ResearchGate
Documents Indexed: 56 Publications since 2007 Co-Authors: 20 Co-Authors with 30 Joint Publications 541 Co-Co-Authors
all top 5
### Co-Authors
25 single-authored 8 An, Hongli 6 Fan, Engui 5 Yeung, Ling Hei 4 Kwong, Man Kam 3 Cheung, Ka-Luen 3 Wong, Sen 2 Chen, Yang 2 Zhang, Lijun 1 Chan, Wai-hong 1 Chow, Kwokwing 1 Dong, Jianwei 1 Dong, Jiao-Jiao 1 Ho, Choryin 1 Hou, Liying 1 Li, Biao 1 Liu, Jianli 1 Tang, Yaning 1 Wang, Jingjie 1 Wang, Jundong 1 Yang, Jin-Jing
all top 5
### Serials
9 Journal of Mathematical Physics 8 Journal of Mathematical Analysis and Applications 7 Communications in Nonlinear Science and Numerical Simulation 5 Physics Letters. A 4 Applied Mathematics Letters 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Studies in Applied Mathematics 2 Communications in Theoretical Physics 1 Classical and Quantum Gravity 1 Nonlinearity 1 Journal of Differential Equations 1 Proceedings of the American Mathematical Society 1 Electronic Journal of Differential Equations (EJDE) 1 Turkish Journal of Mathematics 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Fluid Mechanics 1 European Journal of Mechanics. B. Fluids 1 Far East Journal of Mathematical Sciences 1 Journal of Nonlinear Mathematical Physics 1 Nonlinear Analysis. Real World Applications 1 Communications in Mathematical Sciences 1 Applied Mathematical Sciences (Ruse) 1 International Journal of Applied and Computational Mathematics
all top 5
### Fields
54 Partial differential equations (35-XX) 34 Fluid mechanics (76-XX) 11 Astronomy and astrophysics (85-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Relativity and gravitational theory (83-XX) 2 Ordinary differential equations (34-XX) 1 Geophysics (86-XX)
### Citations contained in zbMATH Open
39 Publications have been cited 250 times in 110 Documents Cited by Year
Analytical blowup solutions to the 2-dimensional isothermal Euler-Poisson equations of gaseous stars. Zbl 1138.35364
Yuen, Manwai
2008
Blowup for the Euler and Euler-Poisson equations with repulsive forces. Zbl 1372.35228
Yuen, Manwai
2011
Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in $$\mathbb R^N$$. Zbl 1431.35143
Yuen, Manwai
2012
Blowup solutions for a class of fluid dynamical equations in $$\mathbb{R}^N$$. Zbl 1154.35427
Yuen, Manwai
2007
Analytical solutions to the Navier-Stokes equations. Zbl 1159.81330
Yuen, Manwai
2008
Self-similar blow-up solutions to the 2-component Camassa-Holm equations. Zbl 1309.76042
Yuen, Manwai
2010
Blowup for the $$C^1$$ solutions of the Euler-Poisson equations of gaseous stars in $$\mathbb R^N$$. Zbl 1227.35100
Yuen, Manwai
2011
Blow-up phenomena for compressible Euler equations with non-vacuum initial data. Zbl 1327.35308
Wong, Sen; Yuen, Manwai
2015
Some exact blowup solutions to the pressureless Euler equations in $$\mathbb R^{N}$$. Zbl 1419.76542
Yuen, Manwai
2011
Analytically periodic solutions to the three-dimensional Euler-Poisson equations of gaseous stars with a negative cosmological constant. Zbl 1181.85047
Yuen, Manwai
2009
Blowup for irrotational $$C^1$$ solutions of the compressible Euler equations in $$\mathbb{R}^N$$. Zbl 1366.35009
Yuen, Manwai
2017
Analytical blowup solutions to the pressureless Navier-Stokes-Poisson equations with density-dependent viscosity in $$\mathbb R^N$$. Zbl 1173.85307
Yuen, Manwai
2009
Analytical solutions to the Navier-Stokes equations with density-dependent viscosity and with pressure. Zbl 1223.76013
Yeung, Ling Hei; Yuen, Manwai
2009
Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure. Zbl 1233.35054
Yeung, Ling Hei; Yuen, Manwai
2011
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations. Zbl 1252.35234
Yuen, Manwai
2011
Self-similar blowup solutions to the 2-component Degasperis-Procesi shallow water system. Zbl 1419.76097
Yuen, Manwai
2011
Stabilities for Euler-Poisson equations in some special dimensions. Zbl 1211.35229
Yuen, Manwai
2008
Perturbational blowup solutions to the compressible 1-dimensional Euler equations. Zbl 1254.76060
Yuen, Manwai
2011
Periodic solutions of 2D isothermal Euler-Poisson equations with possible applications to spiral and disk-like galaxies. Zbl 1296.85002
Kwong, Man Kam; Yuen, Manwai
2014
The Hopf-Cole transformation, topological solitons and multiple fusion solutions for the $$n$$-dimensional Burgers system. Zbl 1377.35055
Chen, Yang; Fan, Engui; Yuen, Manwai
2016
Supplement to: “Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in $$\mathbb{R}^N$$”. Zbl 1440.35260
An, Hongli; Yuen, Manwai
2013
Rotational and self-similar solutions for the compressible Euler equations in $$\mathbb R^3$$. Zbl 1310.35191
Yuen, Manwai
2015
Perturbational blowup solutions to the 2-component Camassa-Holm equations. Zbl 1236.35005
Yuen, Manwai
2012
The Cartesian vector solutions for the $$N$$-dimensional compressible Euler equations. Zbl 1309.35063
An, Hongli; Fan, Engui; Yuen, Manwai
2015
Soliton molecules and mixed solutions of the $$(2+1)$$-dimensional bidirectional Sawada-Kotera equation. Zbl 1455.35045
Dong, Jiao-Jiao; Li, Biao; Yuen, Manwai
2020
Peakon weak solutions for the rotation-two-component Camassa-Holm system. Zbl 1423.35083
Fan, Engui; Yuen, Manwai
2019
Blowup of regular solutions for the relativistic Euler-Poisson equations. Zbl 1339.85002
Chan, Wai Hong; Wong, Sen; Yuen, Manwai
2016
Vortical and self-similar flows of 2D compressible Euler equations. Zbl 1457.76184
Yuen, Manwai
2014
Double Wronskian solutions to the $$(2+1)$$-dimensional Broer-Kaup-Kupershmidt equation. Zbl 1439.35432
Tang, Yaning; Yuen, Manwai; Zhang, Lijun
2020
Blowup for regular solutions and $$C^1$$ solutions of Euler equations in $$\mathbb{R}^N$$ with a free boundary. Zbl 1408.76432
Yuen, Manwai
2018
New method for blowup of the Euler-Poisson system. Zbl 1354.35064
Kwong, Man Kam; Yuen, Manwai
2016
Blowup for $$C^2$$ solutions of the $$N$$-dimensional Euler-Poisson equations in Newtonian cosmology. Zbl 1312.83036
Yuen, Manwai
2014
The analytical solutions for the $$N$$-dimensional damped compressible Euler equations. Zbl 1364.35249
Chow, Kwokwing; Fan, Engui; Yuen, Manwai
2017
Note for “Some exact blowup solutions to the pressureless Euler equations in $$\mathbb R^{N}$$”. Zbl 1242.76038
Yeung, Ling Hei; Yuen, Manwai
2012
Some exact blowup solutions to simple cosmology models. Zbl 1239.35030
Yeung, Ling Hei; Yuen, Manwai
2010
Analytical blowup solutions to the 2-dimensional isothermal Euler-Poisson equations of gaseous stars. II. Zbl 1317.35140
Yuen, Manwai
2011
Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in $$R^N$$. Zbl 1360.35169
Chen, Yang; Fan, Engui; Yuen, Manwai
2017
Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations. Zbl 1331.35268
Fan, Engui; Yuen, Manwai
2014
Erratum: “Analytical solutions to the Navier-Stokes equations”. Zbl 1200.35220
Yuen, Manwai
2009
Soliton molecules and mixed solutions of the $$(2+1)$$-dimensional bidirectional Sawada-Kotera equation. Zbl 1455.35045
Dong, Jiao-Jiao; Li, Biao; Yuen, Manwai
2020
Double Wronskian solutions to the $$(2+1)$$-dimensional Broer-Kaup-Kupershmidt equation. Zbl 1439.35432
Tang, Yaning; Yuen, Manwai; Zhang, Lijun
2020
Peakon weak solutions for the rotation-two-component Camassa-Holm system. Zbl 1423.35083
Fan, Engui; Yuen, Manwai
2019
Blowup for regular solutions and $$C^1$$ solutions of Euler equations in $$\mathbb{R}^N$$ with a free boundary. Zbl 1408.76432
Yuen, Manwai
2018
Blowup for irrotational $$C^1$$ solutions of the compressible Euler equations in $$\mathbb{R}^N$$. Zbl 1366.35009
Yuen, Manwai
2017
The analytical solutions for the $$N$$-dimensional damped compressible Euler equations. Zbl 1364.35249
Chow, Kwokwing; Fan, Engui; Yuen, Manwai
2017
Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in $$R^N$$. Zbl 1360.35169
Chen, Yang; Fan, Engui; Yuen, Manwai
2017
The Hopf-Cole transformation, topological solitons and multiple fusion solutions for the $$n$$-dimensional Burgers system. Zbl 1377.35055
Chen, Yang; Fan, Engui; Yuen, Manwai
2016
Blowup of regular solutions for the relativistic Euler-Poisson equations. Zbl 1339.85002
Chan, Wai Hong; Wong, Sen; Yuen, Manwai
2016
New method for blowup of the Euler-Poisson system. Zbl 1354.35064
Kwong, Man Kam; Yuen, Manwai
2016
Blow-up phenomena for compressible Euler equations with non-vacuum initial data. Zbl 1327.35308
Wong, Sen; Yuen, Manwai
2015
Rotational and self-similar solutions for the compressible Euler equations in $$\mathbb R^3$$. Zbl 1310.35191
Yuen, Manwai
2015
The Cartesian vector solutions for the $$N$$-dimensional compressible Euler equations. Zbl 1309.35063
An, Hongli; Fan, Engui; Yuen, Manwai
2015
Periodic solutions of 2D isothermal Euler-Poisson equations with possible applications to spiral and disk-like galaxies. Zbl 1296.85002
Kwong, Man Kam; Yuen, Manwai
2014
Vortical and self-similar flows of 2D compressible Euler equations. Zbl 1457.76184
Yuen, Manwai
2014
Blowup for $$C^2$$ solutions of the $$N$$-dimensional Euler-Poisson equations in Newtonian cosmology. Zbl 1312.83036
Yuen, Manwai
2014
Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations. Zbl 1331.35268
Fan, Engui; Yuen, Manwai
2014
Supplement to: “Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in $$\mathbb{R}^N$$”. Zbl 1440.35260
An, Hongli; Yuen, Manwai
2013
Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in $$\mathbb R^N$$. Zbl 1431.35143
Yuen, Manwai
2012
Perturbational blowup solutions to the 2-component Camassa-Holm equations. Zbl 1236.35005
Yuen, Manwai
2012
Note for “Some exact blowup solutions to the pressureless Euler equations in $$\mathbb R^{N}$$”. Zbl 1242.76038
Yeung, Ling Hei; Yuen, Manwai
2012
Blowup for the Euler and Euler-Poisson equations with repulsive forces. Zbl 1372.35228
Yuen, Manwai
2011
Blowup for the $$C^1$$ solutions of the Euler-Poisson equations of gaseous stars in $$\mathbb R^N$$. Zbl 1227.35100
Yuen, Manwai
2011
Some exact blowup solutions to the pressureless Euler equations in $$\mathbb R^{N}$$. Zbl 1419.76542
Yuen, Manwai
2011
Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure. Zbl 1233.35054
Yeung, Ling Hei; Yuen, Manwai
2011
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations. Zbl 1252.35234
Yuen, Manwai
2011
Self-similar blowup solutions to the 2-component Degasperis-Procesi shallow water system. Zbl 1419.76097
Yuen, Manwai
2011
Perturbational blowup solutions to the compressible 1-dimensional Euler equations. Zbl 1254.76060
Yuen, Manwai
2011
Analytical blowup solutions to the 2-dimensional isothermal Euler-Poisson equations of gaseous stars. II. Zbl 1317.35140
Yuen, Manwai
2011
Self-similar blow-up solutions to the 2-component Camassa-Holm equations. Zbl 1309.76042
Yuen, Manwai
2010
Some exact blowup solutions to simple cosmology models. Zbl 1239.35030
Yeung, Ling Hei; Yuen, Manwai
2010
Analytically periodic solutions to the three-dimensional Euler-Poisson equations of gaseous stars with a negative cosmological constant. Zbl 1181.85047
Yuen, Manwai
2009
Analytical blowup solutions to the pressureless Navier-Stokes-Poisson equations with density-dependent viscosity in $$\mathbb R^N$$. Zbl 1173.85307
Yuen, Manwai
2009
Analytical solutions to the Navier-Stokes equations with density-dependent viscosity and with pressure. Zbl 1223.76013
Yeung, Ling Hei; Yuen, Manwai
2009
Erratum: “Analytical solutions to the Navier-Stokes equations”. Zbl 1200.35220
Yuen, Manwai
2009
Analytical blowup solutions to the 2-dimensional isothermal Euler-Poisson equations of gaseous stars. Zbl 1138.35364
Yuen, Manwai
2008
Analytical solutions to the Navier-Stokes equations. Zbl 1159.81330
Yuen, Manwai
2008
Stabilities for Euler-Poisson equations in some special dimensions. Zbl 1211.35229
Yuen, Manwai
2008
Blowup solutions for a class of fluid dynamical equations in $$\mathbb{R}^N$$. Zbl 1154.35427
Yuen, Manwai
2007
all top 5
### Cited by 127 Authors
38 Yuen, Manwai 9 Cheung, Ka-Luen 7 Wong, Sen 5 An, Hongli 5 Dong, Jianwei 4 Fan, Engui 4 Guo, Zhengguang 3 Kwong, Man Kam 3 Lin, Ping 3 Ma, Zongwei 3 Yeung, Ling Hei 3 Zhu, Xusheng 2 Deng, Aiping 2 Fang, Yaoli 2 Geng, Yongcai 2 Guo, Zhenhua 2 Jin, Liangbing 2 Li, Jibin 2 Liu, Jianli 2 Ma, Hongcai 2 Ming, Sen 2 Tu, Aihua 2 Yang, Han 2 Yong, Ls 1 Alderremy, A. A. 1 Carles, Rémi 1 Carrapatoso, Kleber 1 Chan, Wai-hong 1 Chauhan, Astha 1 Chen, Changkai 1 Chen, Guanrong 1 Chen, Ping 1 Chen, Quting 1 Chen, Yang 1 Chen, Yuhui 1 Chertock, Alina E. 1 Choquard, Philippe 1 Chow, Kwokwing 1 Cui, Shumo 1 Dhiman, Shubham Kumar 1 Fang, Li 1 Fu, Chunyan 1 Grunert, Katrin 1 Gui, Guilong 1 Han, Bo 1 Han, Maoan 1 Hendi, Fatheah A. 1 Hillairet, Matthieu 1 Ho, Choryin 1 Hong, GuangYi 1 Hou, Liying 1 Hou, Xiaofeng 1 Hu, Wenming 1 Huang, Jingchi 1 Kang, Jingfeng 1 Kashkari, Bothayna S. H. 1 Kumar, Sachin 1 Kurganov, Alexander 1 Li, Biao 1 Li, Jina 1 Li, Lingfei 1 Li, Tianhong 1 Li, Wei 1 Li, Xiangzheng 1 Li, Zilai 1 Liang, Zhilei 1 Liu, Ping 1 Liu, Shengrong 1 Liu, Zhang 1 Long, Yao 1 Lou, Guangpu 1 Lou, Senyue 1 Lv, Guangying 1 Mai, La-Su 1 Mei, Liquan 1 Mei, Ming 1 Mu, Chunlai 1 Ni, Lidiao 1 Peng, Hongyun 1 Qiu, Jianlong 1 Regmi, L. P. 1 Rohlf, Katrin 1 Rui, Weiguo 1 Shang, Yadong 1 Shi, Xiaoding 1 Tan, Changhui 1 Tian, Lixin 1 Tu, Xinyu 1 Vuffray, Marc 1 Wang, Lei 1 Wang, Mei 1 Wang, Mingliang 1 Wang, Weiming 1 Wang, Yuexun 1 Wang, Yuxi 1 Wang, Yuxin 1 Wei, Jinlong 1 Wei, Zhengzhen 1 Wu, Yanyun 1 Xia, Yarong ...and 27 more Authors
all top 5
### Cited in 43 Serials
14 Journal of Mathematical Physics 11 Journal of Mathematical Analysis and Applications 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Communications in Nonlinear Science and Numerical Simulation 6 Applied Mathematics Letters 5 Physics Letters. A 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Journal of Differential Equations 4 European Journal of Mechanics. B. Fluids 4 Nonlinear Analysis. Real World Applications 3 Journal of Applied Mathematics 3 Boundary Value Problems 2 Applicable Analysis 2 Applied Mathematics and Computation 2 Studies in Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 Advances in Mathematical Physics 1 Computers & Mathematics with Applications 1 Letters in Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Journal of Geometry and Physics 1 Mathematics and Computers in Simulation 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Acta Applicandae Mathematicae 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 Turkish Journal of Mathematics 1 Complexity 1 Discrete and Continuous Dynamical Systems 1 Abstract and Applied Analysis 1 Journal of Mathematical Fluid Mechanics 1 Journal of Nonlinear Mathematical Physics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Communications on Pure and Applied Analysis 1 Science China. Mathematics 1 Journal of Applied Analysis and Computation 1 International Journal of Applied and Computational Mathematics 1 SMAI Journal of Computational Mathematics 1 Annales Henri Lebesgue
all top 5
### Cited in 18 Fields
105 Partial differential equations (35-XX) 56 Fluid mechanics (76-XX) 9 Astronomy and astrophysics (85-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Ordinary differential equations (34-XX) 4 Numerical analysis (65-XX) 4 Relativity and gravitational theory (83-XX) 4 Geophysics (86-XX) 3 Quantum theory (81-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) | 2022-05-17 02:01:55 | {"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": 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": 0.5546221733093262, "perplexity": 6762.752573056393}, "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-2022-21/segments/1652662515466.5/warc/CC-MAIN-20220516235937-20220517025937-00677.warc.gz"} |
https://jmservera.com/find-the-volume-sphere-29/ | # Find the Volume sphere (29)
r=29
The volume of a sphere is equal to 43 times Pi π times the radius cubed.
Substitute the value of the radius r=29 into the formula to find the volume of the sphere. Pi π is approximately equal to 3.14.
43⋅π⋅293
Combine 43 and π.
4π3⋅293
Raise 29 to the power of 3.
4π3⋅24389
Multiply 4π3⋅24389.
Combine 4π3 and 24389.
4π⋅243893
Multiply 24389 by 4.
97556π3
97556π3
The result can be shown in multiple forms.
Exact Form:
97556π3
Decimal Form:
102160.40430453…
Find the Volume sphere (29)
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https://too-meta.neocities.org/anki/analysis/1613872369115/back/ | Show Question
Math and science::Analysis::Tao::05. The real numbers
# Nested intervals property for reals
### Nested interval property
A sequence of nested closed intervals of reals has a nonempty intersection.
In other words, if one considers a sequence of nested closed intervals $$(I_n)_{n=0}^{\infty}$$ such that for each $$n \in \mathbb{N}$$, $$I_n = [a_n, b_n]$$ for some $$a_n, b_n \in \mathbb{R}$$ and $$I_{n+1} \subseteq I_n$$, then It holds that $$\cap_{n=1}^{\infty} I_n \neq \emptyset$$.
Proof on the reverse.
### Proof
The proof uses the property that sets of reals have a supremum; this is used to find an $$x \in \mathbb{R}$$ such that $$x \in \cap_{n=0}^{\infty} I_n$$.
Proof. Let $$A = \{a_n : n \in \mathbb{N} \}$$ be the set of left-endpoints for the intervals. Note that for every $$i \in \mathbb{N}$$, $$b_i$$ is an upper bound for $$A$$. Let $$x = \sup A$$.
• $$\forall i \in \mathbb{N}, x \le b_i$$, as $$x$$ is the least upper bound for $$A$$, and every $$b_i$$ is an upper bound.
• $$\forall i \in \mathbb{N}, x \ge a_i$$, as $$x$$ is an upper bound for $$A$$ and all $$a_i \in A$$.
So, we have $$\forall i \in \mathbb{N}, a_n \le x \le b_n$$, which means that $$\forall i \in \mathbb{N}, x \in I_n$$, and furthermore, $$x \in \cap_{n=0}^{\infty} I_n$$ meaning that this intersection is not empty.
Abbott, p20 | 2023-01-30 07:45:28 | {"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": 0.9759796261787415, "perplexity": 130.6016578184853}, "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-2023-06/segments/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00413.warc.gz"} |
https://forum.allaboutcircuits.com/threads/fourier-series-representation-help.93456/ | # Fourier series representation help
#### fdsa
Joined Aug 16, 2011
9
I'm trying to find the fourier series representation of the following periodic function: $$x(t)=cos(t)+sin(2t)+cos(3t-\frac{\pi}{3})$$
So I've found:
$$c_1 = c_{-1} = 1/2$$
$$c_2 = -\frac{j}{2}$$
$$c_{-2} = \frac{j}{2}$$
$$c_3 = \frac{1}{2}\times e^{-j\pi / 3}$$
$$c_{-3} =\frac{1}{2}\times e^{j\pi / 3}$$
According to the solutions the answer is supposed to be:
$$c_3 = c_{-3}= 1/2$$
Did I do something wrong?
#### anhnha
Joined Apr 19, 2012
884
Here the formula of Fourier series:
$$x(t) = \sum_{- \propto }^ \propto c_{n} e^{jn \omega _{0} t}$$
And by using Euler formula:
$$cos( \varphi ) = \frac{e^{j \varphi } + e^{-j \varphi }}{2}$$
$$sin( \varphi ) = \frac{e^{j \varphi } - e^{-j \varphi }}{2j}$$
Now we can rewrite x(t) as follows:
$$x(t) = \frac{e^{jt} + e^{-jt}}{2} + \frac{e^{j2t} - e^{-j2t}}{2j} + \frac{e^{j(3t - \frac{ \Pi }{3}) } + e^{-j(3t - \frac{ \Pi }{3} )}}{2}$$
And according to that result, you are correct. | 2021-10-23 22:55:41 | {"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": 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": 0.962833046913147, "perplexity": 1584.0973665194576}, "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/1634323585828.15/warc/CC-MAIN-20211023224247-20211024014247-00523.warc.gz"} |
https://www.thestructuralworld.com/2018/04/21/anchoring-to-concrete-shear-loadings-criteria/?amp | Anchoring to Concrete: Shear Loadings Criteria | The Structural World
# Anchoring to Concrete: Shear Loadings Criteria
This article tackles the design consideration of anchoring to concrete under shear loadings. This is the part two of the previous article, Anchoring to Concrete: Tensile Loadings.
As summarized in the previous article, the Strength design of anchors shall be check and satisfy the following criteria:
1. Tension Loadings
1. Steel strength of anchor in tension
2. Concrete breakout strength of anchor in tension
3. Pull out strength in tension
4. Concrete side face blowout strength of headed anchor in tension
5. Bond Strength of adhesive anchor in tension
1. Shear Loadings
1. Steel strength of anchor in shear
2. Concrete breakout strength of anchor in shear
3. Concrete pry out strength of anchor in shear
### Design Requirements for Shear Loadings
#### A. Steel strength of anchor in shear (17.5.1)
The nominal strength of anchor in shear as governed by steel shall be evaluated by the calculations and shall not exceed:
• For cast-in headed stud header (17.5.1.2a)
• For cast-in headed bolts or hooked bolts anchors and post-installed anchors ( 17.5.1.2b)
where:
is the effective cross-sectional area of an anchor in shear (sq. inch)
smaller of 1.9 or 125000psi
#### B. Concrete breakout strength of anchor in shear (17.5.2)
The nominal concrete breakout strength in shear of a single anchor or group of anchors shall not exceed:
• For shear force perpendicular to the edge on a single anchor (17.5.2.1a)
• For shear force perpendicular to the edge on a group of anchors (17.5.2.1b)
• For shear force parallel to an edge, or shall be permitted to be twice the value of the shear force determined from above two equations, 17.5.2.1a and 17.5.2.1b.
• For anchors located at corners, the concrete breakout strength shall be determined for each edge with the minimum value to use.
Factors of are as follows:
shall be calculated using the smaller value of
are as follows:
1.4 for anchors located in a region of a concrete member where analysis indicates no cracking at service load
For anchors located in a region of a concrete member where analysis indicates cracking at service load
1.0 for anchors in cracked concrete with edge reinforcements smaller than no. 4 bar
1.2 for anchors in cracked concrete with edge reinforcements of a no. 4 bar
1.4 for anchors in cracked concrete with edge reinforcements of a no. 4 bar or greater between the anchor and the edge
#### C. Concrete pry out strength of anchor in shear (17.5.3)
The nominal pryout strength, for a single or for group of anchors shall not exceed the following:
where:
For and , refer to Concrete breakout strength of anchor in tension (17.4.2) in the previous article Anchoring to Concrete: Tensile Loadings .
Further checks for both tension and shear loadings has to be performed in accordance with the Interaction of Tensile and Shear Forces for combined shear in Vy&Vz direction and the combined ratio of bi-shear that should not be more than 1.2.
### Anchor Reinforcement Details for Tension
The recommended details as an excerpt from the Fig. R17.4.2.9 OF ACI 318M-14 shall be followed as per the figure below.
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