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In this paper, we investigate local properties in the system of completely integral mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity, finite-representability and WEP in the system of completely integral mapping spaces. First we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping spaces. Furthermore we prove that ℂ is the unique nuclear operator space and the unique exact operator space in this system. We also show that ℂ is the unique operator space which is finitely representable in {Tn}n∈ℕ in this system. As corollaries, Kirchberg's conjecture and QWEP conjecture in the system of completely integral mapping spaces are false. [ABSTRACT FROM AUTHOR]

In this paper, we investigate properties concerning some recently introduced finite coarse shape invariants—the k-th finite coarse shape group of a pointed topological space and the k-th relative finite coarse shape group of a pointed topological pair. We define the notion of finite coarse shape group sequence of a pointed topological pair X , X 0 , x 0 as an analogue of homotopy and (coarse) shape group sequences and show that for any pointed topological pair, the corresponding finite coarse shape group sequence is a chain. On the other hand, we construct an example of a pointed pair of metric continua whose finite coarse shape group sequence fails to be exact. Finally, using the aforementioned pair of metric continua together with a pointed dyadic solenoid, we show that finite coarse-shape groups, in general, differ from both shape and coarse-shape groups. [ABSTRACT FROM AUTHOR]

The requirement of RMS (voltage and current) measurements under a fraction of the AC period has become increasingly attractive in power systems. Some of these power applications are responsible for voltage stabilization in distribution lines when the voltage correction should be made in a short time, no more than one or two periods of the AC signal. Previously developed RMS correction applications must be validated in real-world situations characterized by an abrupt change (discontinuity) in voltage magnitude occurring even during a single AC period. Such circumstances can substantially influence the RMS estimation and, therefore, should be considered. This article suggests a mathematically based approach, validated in the laboratory, that improves the accuracy of a voltage RMS estimation for the appropriate measurement devices. It produces better results in cases where the RMS assessment should be done in a fraction of the AC period. [ABSTRACT FROM AUTHOR]

We consider extensions of non-singular maps which are exact, respectively K-mixing, or at least have a decomposition into positive-measure exact, respectively K-mixing, components. The fibers of the extension spaces have countable (finite or infinite) cardinality and the action on them is assumed surjective or bijective. We call these systems, respectively, fiber-surjective and fiber-bijective extensions. Technically, they are skew products, though the point of view we take here is not the one generally associated with skew products. Our main results are an Exact and a K-mixing Decomposition Theorem. The latter can be used to show that a large number of periodic Lorentz gases (the term denoting here general group extensions of Sinai billiards, including Lorentz tubes and slabs, in any dimension) are K-mixing. [ABSTRACT FROM AUTHOR]

This paper investigates the role of quadrature exactness in the approximation scheme of hyperinterpolation. Constructing a hyperinterpolant of degree n requires a positive-weight quadrature rule with exactness degree 2n. We examine the behavior of such approximation when the required exactness degree 2n is relaxed to n + k with 0 < k ≤ n . Aided by the Marcinkiewicz–Zygmund inequality, we affirm that the L 2 norm of the exactness-relaxing hyperinterpolation operator is bounded by a constant independent of n, and this approximation scheme is convergent as n → ∞ if k is positively correlated to n. Thus, the family of candidate quadrature rules for constructing hyperinterpolants can be significantly enriched, and the number of quadrature points can be considerably reduced. As a potential cost, this relaxation may slow the convergence rate of hyperinterpolation in terms of the reduced degrees of quadrature exactness. Our theoretical results are asserted by numerical experiments on three of the best-known quadrature rules: the Gauss quadrature, the Clenshaw–Curtis quadrature, and the spherical t-designs. [ABSTRACT FROM AUTHOR]

Minimal free resolutions of a finitely generated module over a polynomial ring S = k [ x ] , with variables x = { x 1 , ... , x n } and a field k have been extensively studied. Almost all the results in the literature about minimal free resolutions give their Betti numbers, that is, the ranks of the free modules in the resolution at each degree. Several techniques have been developed to compute Betti numbers, making this a manageable problem in many cases. However, a description of the differentials in the resolution is rarely given, as this turns out to be a more difficult problem. The main purpose of this article is to give a criterion to check when a graded free complex of an S-module is exact. Unlike previous similar criteria, this one allows us to give a description of the differentials using the combinatorics of the S-module. The criterion is given in terms of the Betti numbers of the resolutions in each degree and the set of columns of the matrix representation of the differentials. In the last section, and with the aim of illustrating how to use the criterion, we apply it to one of the first better-understood cases, the edge ideal of the complete graph. However, this criterion can be used to give an explicit description of the differentials of a resolution of several monomial ideals such as the duplication of an ideal, the edge ideal of a cograph, etc. [ABSTRACT FROM AUTHOR]

Many philosophers, computer scientists, and cyberneticists still consider it possible that a computer, described as a Turing machine, can effectively have intelligence. They are not talking about the present but the future of a possible computer to have the same properties as human intelligence. In this brief paper, I will provide some basic arguments that prove the impossibility of such a thinking machine. These arguments will be presented in four parts: the mental experiment of the Chinese Room, the argument from exactness, the argument from phenomenology, and the argument from abstraction. The first argument proves that mechanical manipulation of symbols is not understanding. The second argument proves that logic and mathematics are exact, which is a quality of understanding missing in the material world. The third argument proves that logical laws are unconditional, while physical laws are relative to material conditions. Finally, the last argument proves that abstraction is an operation of the intellect that is required for creative decision making. Neither animals nor any material system manifests abstraction.

The requirement of RMS (voltage and current) measurements under a fraction of the AC period has become increasingly attractive in power systems. Some of these power applications are responsible for voltage stabilization in distribution lines when the voltage correction should be made in a short time, no more than one or two periods of the AC signal. Previously developed RMS correction applications must be validated in real-world situations characterized by an abrupt change (discontinuity) in voltage magnitude occurring even during a single AC period. Such circumstances can substantially influence the RMS estimation and, therefore, should be considered. This article suggests a mathematically based approach, validated in the laboratory, that improves the accuracy of a voltage RMS estimation for the appropriate measurement devices. It produces better results in cases where the RMS assessment should be done in a fraction of the AC period.

We consider the random β -transformation K β , defined on { 0 , 1 } N × [ 0 , ⌊ β ⌋ ] β - 1 ] ], that generates all possible expansions of the form x = ∑ i = 0 ∞ a i β i , where a i ∈ { 0 , 1 , ... , ⌊ β ⌋ } }. This transformation was introduced in [3–5], where two natural invariant ergodic measures were found. The first is the unique measure of maximal entropy, and the second is a measure of the form m p × μ β , with m p the Bernoulli (p , 1 - p) product measure and μ β is a measure equivalent to the Lebesgue measure. In this paper, we give an uncountable family of K β -invariant exact g -measures for a certain collection of algebraic β 's. The construction of these g -measures is explicit and the corresponding potentials are not locally constant. [ABSTRACT FROM AUTHOR]

We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the randomness in environments, and reduce them into two different groups. Secondly, we give the definition of exactness for Markov operator cocycles and show that Lin’s criterion for exactness can be naturally extended to the case of Markov operator cocycles. Finally, in the class of asymptotically periodic Markov operator cocycles, we show the Lasotaâ€"Mackey type equivalence between mixing, exactness and asymptotic stability. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Social Sciences & Humanities Researches is the property of Mugla Sitki Kocman University, Institute of Social Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied. Almost all the results in the literature about minimal free resolutions give their Betti numbers, that is, the ranks of the free modules in the resolution at each degree. Several techniques have been developed to compute Betti numbers, making this a manageable problem in many cases. However, a description of the differentials in the resolution is rarely given, as this turns out to be a more difficult problem. The main purpose of this article is to give a criterion to check when a graded free complex of an S-module is exact. Unlike previous similar criteria, this one allows us to give a description of the differentials using the combinatorics of the S-module. The criterion is given in terms of the Betti numbers of the resolutions in each degree and the set of columns of the matrix representation of the differentials. In the last section, and with the aim of illustrating how to use the criterion, we apply it to one of the first better-understood cases, the edge ideal of the complete graph. However, this criterion can be used to give an explicit description of the differentials of a resolution of several monomial ideals such as the duplication of an ideal, the edge ideal of a cograph, etc.

This paper focuses on the approximation of continuous functions on the unit sphere by spherical polynomials of degree n via hyperinterpolation. Hyperinterpolation of degree n is a discrete approximation of the L 2 -orthogonal projection of the same degree with its Fourier coefficients evaluated by a positive-weight quadrature rule that exactly integrates all spherical polynomials of degree at most 2 n. This paper aims to bypass this quadrature exactness assumption by replacing it with the Marcinkiewicz–Zygmund property proposed in a previous paper. Consequently, hyperinterpolation can be constructed by a positive-weight quadrature rule (not necessarily with quadrature exactness). This scheme is referred to as unfettered hyperinterpolation. This paper provides a reasonable error estimate for unfettered hyperinterpolation. The error estimate generally consists of two terms: a term representing the error estimate of the original hyperinterpolation of full quadrature exactness and another introduced as compensation for the loss of exactness degrees. A guide to controlling the newly introduced term in practice is provided. In particular, if the quadrature points form a quasi-Monte Carlo (QMC) design, then there is a refined error estimate. Numerical experiments verify the error estimates and the practical guide. [ABSTRACT FROM AUTHOR]

We study the exact multiplicity of positive solutions to the one-dimensional Dirichlet problem $$\displaylines{ -(|u'|^{p-2}u')' = \lambda u^{s-1} - \mu u^{r-1} \quad \text{in } ]0,1[\cr u(0) = u(1) = 0, }$$ where $r\in]0,1[$, $p\in]1,+\infty[$, $r

Copyright of Beytulhikme: An International Journal of Philosophy is the property of Beytulhikme: An International Journal of Philosophy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We give necessary and sufficient conditions for nuclearity of Cuntz–Nica–Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping-stone to tackle product systems over quasi-lattices that are controlled by the free abelian lattice and satisfy a minimality property. Our setting accommodates examples like the Baumslag–Solitar lattice for $n=m>0$ and the right-angled Artin groups. More generally, the class of quasi-lattices for which our results apply is closed under taking semi-direct and graph products. In the process we accomplish more. Our arguments tackle Nica–Pimsner algebras that admit a faithful conditional expectation on a small fixed point algebra and a faithful copy of the coefficient algebra. This is the case for CNP-relative quotients in-between the Toeplitz–Nica–Pimsner algebra and the Cuntz–Nica–Pimsner algebra. We complete this study with the relevant results on exactness. [ABSTRACT FROM AUTHOR]

In the incoming communication system, especially for the battery constrained Internet of Things devices, consumption of power resources will be a critical performance metric. This point shows importance when throughput minimal requirement and interference limit have been carried out. This paper investigates such a power allocation problem in a multiple-parallel-channel wireless system to minimize the sum power consumed by the entire system, while meeting the sum power constrains for each group of channels and the whole system as well as meeting the throughput constraints for each of the groups and the system. Sum power minimization itself is also a key issue for margin-adaptive loading. Resorting to geometric concepts, an algorithm named as the group virtual bottom power water-filling (GVB-PWF) is proposed to solve the problem, including the large-scale problems, which computes the exact solution with a low degree of the polynomial computational complexity. Optimality of the proposed algorithm is also proved strictly. To the best of our knowledge, no prior algorithm in the open literature offered such an optimal solution to the proposed problem, with the merit of exactness and efficiency. Simulation results demonstrate that the proposed power allocation algorithm uses less power about 25%, compared with the popular primal-dual interior-point method with the same amount of computations. [ABSTRACT FROM AUTHOR]

This study aims to introduce the notions of injectivity, local reflexivity, exactness, and nuclearity in the system ( (Γ 2 c (⋅ , ⋅) , γ 2 c (⋅)) ). We find that every dual operator space is injective in the system ( (Γ 2 c (⋅ , ⋅) , γ 2 c (⋅)) ) and nuclearity is equivalent to exactness in this system. As a corollary, we prove that Kirchberg's conjecture on the equivalence of exactness and local reflexivity for C* -algebras is false in this system, i.e., there exists a C*-algebra A that is locally reflexive in this system but is not exact in this system. [ABSTRACT FROM AUTHOR]

We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a semi-direct product akin to the restricted wreath product but constructed from the second nilpotent product. We then show that if two discrete groups have the Haagerup property, the restricted second nilpotent wreath product of them also has the Haagerup property. We finally show that if a discrete group is abelian, then the restricted second nilpotent wreath product constructed from it is unitarizable if and only if the acting group is amenable. [ABSTRACT FROM AUTHOR]

In this paper we describe when a partial isometry generates an amenable C ∗ -algebra or an amenable Banach algebra. [ABSTRACT FROM AUTHOR]

• Mismatch analysis of suggested parameters from manufacturers. • Evaluation of temporal properties such as rTMS frequency and ppTMS ISI, not only induced electric field intensity. • On-site quality assessment of TMS devices protocols. Small variations in TMS parameters, such as pulse frequency and amplitude may elicit distinct neurophysiological responses. Assessing the mismatch between nominal and experimental parameters of TMS stimulators is essential for safe application and comparisons of results across studies. A search coil was used to assess exactness and precision errors of amplitude and timing parameters such as interstimulus interval, the period of pulse repetition, and intertrain interval of TMS devices. The method was validated using simulated pulses and applied to six commercial stimulators in single-pulse (spTMS), paired-pulse (ppTMS), and repetitive (rTMS) protocols, working at several combinations of intensities and frequencies. In a simulated signal, the maximum exactness error was 1.7% for spTMS and the maximum precision error 1.9% for ppTMS. Three out of six TMS commercial devices showed exactness and precision errors in spTMS amplitude higher than 5%. Moreover, two devices showed amplitude exactness errors higher than 5% in rTMS with parameters suggested by the manufactures. Currently available tools allow characterization of induced electric field intensity and focality, and pulse waveforms of a single TMS pulse. Our method assesses the mismatch between nominal and experimental values in spTMS, ppTMS and rTMS protocols through the exactness and precision errors of amplitude and timing parameters. This study highlights the importance of evaluating the physical characteristics of TMS devices and protocols, and provides a method for on-site quality assessment of multiple stimulation protocols in clinical and research environments. [ABSTRACT FROM AUTHOR]

We study the exact multiplicity of positive solutions to the one-dimensional Dirichlet problem ..., where r ∈ ]0, 1[, p ∈ ]1, + ∞[, r < s < p and λ, μ ∈ ]0, + ∞[. We shed light, in particular, on the case r ∈ ]0, min {s, p/(p + 1)}[, completely determining the bifurcation diagram and solving some related open problems. Our approach relies upon quadrature methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of International Social Research is the property of Journal of International Social Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Purpose: to study the formation of motor action sportswomen different ages depending on the level of sportsmanship. Material and Methods: girls which are specialized in a boat-racing in age groups 13–14 years inspected, 15–16 years, 17–18 years, in every group was for 20–25 persons, in all 72 sportswomen. Motive actions were probed on the method of measuring of training effect developed by us an action, and also the functional state was determined by methods: measuring of sensorimotor reaction is on sound and light irritants, speed of current of air, exactness of implementation of the set muscular effort. Results: testing showed the dynamics of forming motive, namely technique of mastering of receptions and actions, reliability, presence of errors, efficiency of active voice of consciousness in correct implementation of motion in a biomechanics relation. Conclusions: application of this method in the process of sporting preparation will allow to define quality of mastering of technique of the proper motive actions, forming of abilities, subsequent learning and becoming of more difficult motive skills

In this paper, we investigate the power allocation in a multi-user wireless system to maximize the energy efficiency, while meeting the power constrains of each individual user and the whole system. Specifically, a geometric ceiled-water-filling algorithm is proposed to solve this non-linear fractional optimization problem, which can compute exact solutions with a low degree of polynomial computational complexity. Optimality of the proposed algorithm is strictly proved with mathematical analysis. In addition, the proposed algorithm is further extended to the general case with the minimum system-level throughput constraint, considering the quality of service requirement. To the best of our knowledge, no prior algorithm in the open literature offered such optimal solutions to the target problems, with the merit of exactness and the efficiency. Simulation results demonstrate that the proposed power allocation algorithms can improve the energy efficiency by nearly 50%, compared with the conventional Dinkelbach’s method with the same amount of computations. [ABSTRACT FROM AUTHOR]

In the second part of our study, we introduce the concept of global extended exactness of penalty and augmented Lagrangian functions, and derive the localization principle in the extended form. The main idea behind the extended exactness consists in an extension of the original constrained optimization problem by adding some extra variables, and then construction of a penalty/augmented Lagrangian function for the extended problem. This approach allows one to design extended penalty/augmented Lagrangian functions having some useful properties (such as smoothness), which their counterparts for the original problem might not possess. In turn, the global exactness of such extended merit functions can be easily proved with the use of the localization principle presented in this paper, which reduces the study of global exactness to a local analysis of a merit function based on sufficient optimality conditions and constraint qualifications. We utilize the localization principle in order to obtain simple necessary and sufficient conditions for the global exactness of the extended penalty function introduced by Huyer and Neumaier, and in order to construct a globally exact continuously differentiable augmented Lagrangian function for nonlinear semidefinite programming problems. [ABSTRACT FROM AUTHOR]

In this two-part study, we develop a unified approach to the analysis of the global exactness of various penalty and augmented Lagrangian functions for constrained optimization problems in finite-dimensional spaces. This approach allows one to verify in a simple and straightforward manner whether a given penalty/augmented Lagrangian function is exact, i.e., whether the problem of unconstrained minimization of this function is equivalent (in some sense) to the original constrained problem, provided the penalty parameter is sufficiently large. Our approach is based on the so-called localization principle that reduces the study of global exactness to a local analysis of a chosen merit function near globally optimal solutions. In turn, such local analysis can be performed with the use of optimality conditions and constraint qualifications. In the first paper, we introduce the concept of global parametric exactness and derive the localization principle in the parametric form. With the use of this version of the localization principle, we recover existing simple, necessary, and sufficient conditions for the global exactness of linear penalty functions and for the existence of augmented Lagrange multipliers of Rockafellar-Wets’ augmented Lagrangian. We also present completely new necessary and sufficient conditions for the global exactness of general nonlinear penalty functions and for the global exactness of a continuously differentiable penalty function for nonlinear second-order cone programming problems. We briefly discuss how one can construct a continuously differentiable exact penalty function for nonlinear semidefinite programming problems as well. [ABSTRACT FROM AUTHOR]

The purpose of this paper to identify deviations fidelity spatial contours of industrial robots, determine the error pattern detected, and define the ways to solve the problem.The paper presents the research results of fidelity spatial contours done by Fanuc M- 710iC/50 industrial robot when moving along a predetermined path. The proposed method uses a QC20-W ballbar wireless system of Renishaw company, designed to diagnose the state of the measurement and playback linear and angular displacements of the CNC.The solutions to adapt the QC20-W ballbar system to the constructive peculiarities of industrial robots with five or more independently controlled axes are given. The stages of the preparation of diagnostic systems and software robot movements are described.According to study results of errors that arise while playing back the programmed motions of a fixed point of robot capture in three mutually perpendicular planes its practical accuracy has been defined when performing movements in a given region of the working area, thereby allowing us, eventually, to draw a conclusion on the possibility to use a robot in one technological process or another.The study has resulted in emerging the guidelines for the operation of industrial robots with five or more independently controlled axes. Using these guidelines enables us to increase the playback accuracy of the industrial robot to 0.01 mm.

We prove a necessary and sufficient condition for embeddability of an operator system into ${\mathcal{O}}_{2}$. Using Kirchberg’s theorems on a tensor product of ${\mathcal{O}}_{2}$ and ${\mathcal{O}}_{\infty }$, we establish results on their operator system counterparts ${\mathcal{S}}_{2}$ and ${\mathcal{S}}_{\infty }$. Applications of the results, including some examples describing $C^{\ast }$-envelopes of operator systems, are also discussed. [ABSTRACT FROM AUTHOR]

A bounded linear operator T, which acts on some separable complex infinite dimensional Hilbert space, is said to be $$*$$ -amenable if the $$C^*$$ -algebra generated by T is amenable. In the present paper, the stability of $$*$$ -amenability under similarity is studied. It is proved that each operator similar to T is $$*$$ -amenable if and only if T is a polynomially compact operator of order at most two. [ABSTRACT FROM AUTHOR]

An important task in mathematical sciences is to make quantitative predictions, which is often done via the solution of differential equations. In this paper, we investigate why, to perform this task, scientists sometimes choose to use numerical methods instead of analytical solutions. Via several examples, we argue that the choice for numerical methods can be explained by the fact that, while making quantitative predictions seems at first glance to be facilitated by analytical solutions, this is actually often much easier with numerical methods. Thus we challenge the widely presumed superiority of analytical solutions over numerical methods. [ABSTRACT FROM AUTHOR]

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is stable under measure equivalence and W*-equivalence. [ABSTRACT FROM AUTHOR]

Basic properties of varieties of tactical thought of handballers are considered. The level of their display is shown for the sportswomen of different qualification. 78 sportswomen took part in research. For determination of parameters of tactical and playing thought the method of «Balltest» is utillized in an attack and defence. Priority of exactness and speed of thought is set depending on the level of sporting trade of handballers. Different influence of speed of thought is well-proven on the rightness of decision of playing situations of different orientation in the handballers of mass digits and high level of display of the indicated properties of thought for the sportswomen of high qualification. It is discovered that a level of display of basic properties of tactical thought is in defence substantially below of other varieties of thought. It is marked that with the increase of trade of players there were possibilities to growth of quantitative and speed parameters of tactical thought.

It is presented the ground of level of speed-power possibilities of basketball-players for implementation of exact long transmission of ball on distance 20 - 27 meters. The tables of distance of landing of ball at his passing through the conditional «point of reception» depending on distance and corner of flight of ball are expected. It is recommended to individualize the size of training distance of long transmission in accordance with its index in test exercise. For achievement of stable exactness of long transmission, it is necessary to develop ability of players to pass a ball on distance 30 - 39 meters.