Argument Of Function Research Articles

SOFTWARE ANALYSIS OF STRUCTURE BLOCK-CYCLIC BASIC MATRIX OF DCT

Context. The matrix notation is used to formalize the subject area within the framework of the algebraic approach. Effective computation of the discrete cosine transforms uses the reduction of a harmoniс basis to a block-cyclic matrix structure with the subsequent calculation of the transform using fast cyclic convolutions. An analysis of the structure of the basic block matrix of transforms provides a synthesis of algorithms of effective discrete cosine transforms of arbitrary sizes. The software implementation of the analysis of block-cyclic structures generates a description of the structure, which allows to reduce the computational complexity of the algorithm of effective discrete cosine transform and to perform parallelization of computation the cyclic convolutions.Objective. The work is to determine the algorithmic features of the analysis of the structure of a block-cyclic matrix containing integer arguments of basic harmonic functions, which will reduce the computational complexity of the synthesized discrete cosine transform algorithm based on cyclic convolutions.Method. Search and analysis by enumerating elements of the matrix with a variable step, taking into account the blockiness and cyclicity of the formed basis matrix of the discrete cosine transform, allows you to quickly analyze the structure of the block matrix of transform in comparison with full scanning.Results. Algorithmic and software for analyzing the structure of a block-cyclic basis matrix have been developed, with the help of which an array of data parameters for a formal description of the basis matrix structure of a discrete cosine transform is determined. The analysis of the structure of the base matrix allows us to determine the presence of identical cyclic submatrices placed horizontally or vertically relative to each other and, thereby, reduce the number of cycles of convolutions.Conclusions. An effective analysis of the block-cyclic structure of the basis matrix based on the developed software is an important part of the fast algorithm synthesis process, which provides a reduction in computational complexity and the ability to parallelize the implementation of the discrete cosine transform. The developed algorithmic and software for performing the analysis of the structure of a block-cyclic matrix can also be used to analyze the structure and search for the corresponding submatrices in any matrices with integer, real, and zero elements.

ON THE DIRICHLET PROBLEM FOR AN ELLIP-TIC FUNCTIONAL-DIFFERENTIAL EQUATION WITH AFFINE TRANSFORMATION OF THE ARGUMENT

The paper considers the Dirichlet problem for an elliptic functionaldifferential equation containing a combination of shifts and contractions of the argument of an unknown function under the Laplace operator. Sufficient conditions for unique solvability are established. It is also shown that the problem can have an infinite-dimensional variety of solutions. This work is done in the framework of the State Contract in accordance with the Additional Agreement No. 075-03-2020-239/2 from 07.07.2020, registry No. 248, Budgetary Classification Code 01104730290059611, for the project titled ‘Non-linear singular integro-differential equations and boundary value problems’. The authors also acknoowledge support by the Russian Foundation for Basic Research (project no. 18-41-200001p-a).

Computational aspects of speed-dependent Voigt and Rautian profiles

For accurate line-by-line modeling of molecular cross sections several physical processes “beyond Voigt” have to be considered. For the speed-dependent Voigt and Rautian profiles (SDV, SDR) and the Hartmann-Tran profile the difference w(iz−)−w(iz+) of two complex error functions (essentially Voigt functions) has to be evaluated where the function arguments z ± are given by the sum and difference of two square roots. These two terms describing z ± can be huge and the default implementation of the difference can lead to large cancellation errors. First we demonstrate that these problems can be avoided by a simple reformulation of z−. Furthermore we show that a single rational approximation of the complex error function valid in the whole complex plane (e.g. by Humlíček, 1979 or Weideman, 1994) enables computation of the SDV and SDR with four significant digits or better. Our benchmarks indicate that the SDV and SDR functions are about a factor 2.2 slower compared to the Voigt function, but for evaluation of molecular cross sections this time lag does not significantly prolong the overall program execution because speed-dependent parameters are available only for a fraction of strong lines.

On Asymptotic Behavior of Zeta Singularities for Compact Locally Symmetric Spaces

We obtain precise estimates for the number of singularities of Selberg’s and Ruelle’s zeta functions for compact, higher-dimensional, locally symmetric Riemannian manifolds of strictly negative sectional curvature. The methods applied in this research represent a generalization of the methods described in the case of a compact Riemann surface. In particular, this includes an application of the Phragmen-Lindelof theorem, the variation of the argument of certain zeta functions, as well as the use of some classical analytic number theory techniques.

Existence results for first derivative dependent \u03d5-Laplacian boundary value problems

Our main concern in this article is to investigate the existence of solution for the boundary-value problem(ϕ(x′(t))′=g1(t,x(t),x′(t)),∀t∈[0,1],ϒ1(x(0),x(1),x′(0))=0,ϒ2(x(0),x(1),x′(1))=0,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& (\\phi \\bigl(x'(t)\\bigr)'=g_{1} \\bigl(t,x(t),x'(t)\\bigr),\\quad \\forall t\\in [0,1], \\\\& \\Upsilon _{1}\\bigl(x(0),x(1),x'(0)\\bigr)=0, \\\\& \\Upsilon _{2}\\bigl(x(0),x(1),x'(1)\\bigr)=0, \\end{aligned}$$ \\end{document} where g_{1}:[0,1]times mathbb{R}^{2}rightarrow mathbb{R} is an L^{1}-Carathéodory function, Upsilon _{i}:mathbb{R}^{3}rightarrow mathbb{R} are continuous functions, i=1,2, and phi :(-a,a)rightarrow mathbb{R} is an increasing homeomorphism such that phi (0)=0, for 0< a< infty . We obtain the solvability results by imposing some new conditions on the boundary functions. The new conditions allow us to ensure the existence of at least one solution in the sector defined by well ordered functions. These ordered functions do not require one to check the definitions of lower and upper solutions. Moreover, the monotonicity assumptions on the arguments of boundary functions are not required in our case. An application is considered to ensure the applicability of our results.

A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

Abstract In this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

Reserved but Principled – and Sometimes Functional: Explaining Decentralisation Preferences Among Regional Bureaucrats

In recent decades, decentralisation measures have been implemented in most advanced democracies. While such reforms may be driven by subnational pressures and demands for empowerment, the central government usually has the deciding power to decentralise. Literature on regional preference has proliferated since the 1990s, though we know little of regional administrative preferences in relation to this process. As policy formulators and implementers, they are directly affected by dispersion of authority downwards, as it directly affects their organisational structures and portfolio of responsibilities. This article analyses decentralisation preferences among regional bureaucrats in Norway in the context of the 2015-2020 Regional Government Reform. Utilising an original survey and testing five explanations, the bureaucrats are generally reserved about taking on additional functions, with support for increasing their portfolio primarily explained by a principled motivation to increase regional autonomy, followed by feelings of regional attachment. Functional arguments also matter, though to a lesser extent. The bureaucrats’ principled, rather than functional, attitude towards regionalisation deviates from theoretical premises of decentralisation literature, while also challenging more underlying notions of bureaucratic thinking, inviting further research into how these dynamics manifest themselves among members of the civil service.

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors’ knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.

PECULIARITIES OF COMPUTATION THE HASHING ARRAYS FOR THE SYNTHESIS OF FAST ALGORITHMS OF DCT I–IV

Actuality. Discrete cosine transforms provide high efficiency of applications in modern information processing facilities. After all, the computation of forward and reverse transforms in the real field is especially important for the effective solution of specific practical problems in the field of information technology. The use of fast transforms with a significant reduction in computational cost requires the development of new efficient methods for synthesizing algorithms and performing them for different types of real discrete transforms.The purpose of the work is to determine the differences and common features of computing hashing arrays for the synthesis of fast algorithms of four basic types of discrete cosine transforms based on cyclic convolutions.Method. The paper analyzes the peculiarities of the computation of hashing arrays based on the cyclic decomposition of a substitution, which is determined from the rows/columns of arguments of the basic functions of the kernel of a discrete cosine transform.Results. The result of the research is to determine and generalize the main differences and common features of the computation of hashing arrays for the formation of block-cyclic structures in the basis matrices of discrete cosine transforms of arbitrary sizes.Conclusions. The research analyzes the peculiarities of computing hashing arrays for four main types of discrete cosine transforms. The basic idea of using a generalized mathematical apparatus to efficiently compute different types of discrete cosine transformations based on cyclic convolutions is to use hashing arrays containing a brief description of the block-cyclic structure of the transformation basis. Hashing arrays are determined by the cyclic decomposition of the substitution and ensure that the basic transformation matrix is reduced to a set of cyclic left submatrices. The analysis of the peculiarities of the choice of the substitution sequences, the execution of the cyclic decomposition of the substitution, the selection of arrays for the formation of hashing arrays provide the possibility of efficient organization of computations for different types and sizes of discrete cosine transforms.

Function argument number identification in stripped binary under PPC and MIPS instruction set

Function argument number identification in stripped binary under PPC and MIPS instruction set

Context-sensitive Rewriting

The appropriate selection of the arguments of functions that can be evaluated in function calls is often useful to improve efficiency, speed, termination behavior, and so on. This is essential, e.g., in the conditional if - then - else operator. We can specify this by associating a set μ(f) of indices of evaluable arguments to each function symbol f . With μ (if - then - else)={1}, only the Boolean argument b in calls if b , then e else e' is evaluated. In the realm of term rewriting, this is called context-sensitive rewriting . It has been proven useful to improve the termination behavior of rewriting computations while it is still able to compute (or approximate) canonical forms like head-normal forms, (infinite) values, and (infinite) normal forms by requiring a few reasonable conditions. This article provides an overview of basic results to use context-sensitive rewriting in practice.

Raising expectations: automating expected cost analysis with types

This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher-order functions and inductive data types. The derived bounds are multivariate polynomials that are functions of data structures. Bound inference is enabled by local type rules that reduce type inference to linear constraint solving. The type system is based on the potential method of amortized analysis and extends automatic amortized resource analysis (AARA) for deterministic programs. A main innovation is that bounds can contain symbolic probabilities, which may appear in data structures and function arguments. Another contribution is a novel soundness proof that establishes the correctness of the derived bounds with respect to a distribution-based operational cost semantics that also includes nontrivial diverging behavior. For cost models like time, derived bounds imply termination with probability one. To highlight the novel ideas, the presentation focuses on linear potential and a core language. However, the analysis is implemented as an extension of Resource Aware ML and supports polynomial bounds and user defined data structures. The effectiveness of the technique is evaluated by analyzing the sample complexity of discrete distributions and with a novel average-case estimation for deterministic programs that combines expected cost analysis with statistical methods.

On rotating vectors, Jacobi elliptic functions and free vibration of the Duffing oscillator

The free vibration displacement of an undamped hardening Duffing oscillator is described in exact form by a Jacobi elliptic function. Unlike an undamped linear oscillator, whose displacement is described by a trigonometric function, a Jacobi elliptic function is difficult to interpret by a simple inspection of the function arguments. The displacement of a linear oscillator is often visualised as a rotating vector, which has two characteristics — a constant amplitude and a phase (or frequency). These parameters are readily related to the physical response of the system. In this paper, a similar approach is applied to the free vibration displacement of a Duffing oscillator. However, the rotating vector description of the motion is much more complicated than for a linear system. It still has two characteristics though — an amplitude and a phase, but in general both these quantities are dependent on the position of the vector, i.e., they are frequency modulated. It is shown that there is not a unique rotating vector representation of the cn Jacobi elliptic function. Indeed, there are an infinite number of elliptical loci bounded between an elliptical and a circular locus of the vector. There are two specific cases. One is where the amplitude of the vector is constant and the phase angle is frequency modulated (the circle), and the other is when the amplitude of the vector is frequency modulated and the angular velocity is constant. In all other cases, both the amplitude and the angular velocity of the rotating vector are frequency modulated. To aid in the visualisation of the rotating vectors that represent the free vibration solution of a highly nonlinear hardening Duffing oscillator, two animations are provided.

On integrals associated with the free particle wave packet

Abstract We discuss some properties of integrals associated with the free particle wave packet, ψ ⁢ ( x , t ) {\psi(x,t)} , which are solutions to the time-dependent Schrödinger equation for a free particle. Some noteworthy discussion is made in relation to integrals which have appeared in the literature. We also obtain formulas for half-integer arguments of the Riemann zeta function.

About Calculation Of Strength Of Reinforced Concrete Elements On Inclined Sections

The calculation model of the bearing capacity of reinforced concrete elements along an inclined section is based on empirical coefficients and the indefinite length of the projection of the inclined section onto the longitudinal axis. As a result of the analysis of numerous studies, the physical essence of empirical coefficients is revealed and the calculated values of the arguments of the strength function are justified. It is established that the numerical coefficients in the calculated function of the strength of inclined sections to the effect of shear force, parameter limitations and the slope of the calculated section depend on the ratio of concrete shear and tensile strength. It is proposed to normalize this ratio and use, when calculating, the assumption of equivalent strength of a normal section that collapses from a shear (shear), and an inclined section in an axial tension state. The improved model is tested on the experimental data previously obtained. The use of the proposed model with a clear physical meaning of the design parameters will help to clarify the assessment of the strength under the action of a transverse force when designing bent reinforced concrete elements.

Global Predefined Time and Accuracy Adaptive Neural Network Control for Uncertain Strict-Feedback Systems With Output Constraint and Dead Zone

This article proposes a global adaptive neural network tracking control method for uncertain strict-feedback nonlinear system with output constraint and dead zone to achieve predefined-time convergence of the tracking error to predefined accuracy. First, an integral-type Barrier Lyapunov function (BLF) is constructed to handle output constraint. Next, radial basis function neural network (RBFNN) control and robust control are used to tackle unknown nonlinear function. The continuous switching function is designed to switch RBFNN control to robust control when the arguments of the unknown function exceed the active region of neural network. Utilizing the property of radial basis function, we derive the upper bound of the term containing the unknown nonlinear function and design adaptive laws to determine the derived upper bound and robust control gain. Then, the predefined time virtual control inputs are obtained and their derivatives are estimated by finite time differentiator. Finally, we use the dead zone inverse technique to obtain the actual control input. Stability analysis shows the presented control scheme achieves global convergence of the errors to predefined accuracy within predefined time. The simulation results verify the effectiveness of the presented control scheme.

Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments

In this study, a method for numerically solving Riccatti type differential equations with functional arguments under the mixed condition is presented. For the method, Legendre polynomials, the solution forms and the required expressions are written in the matrix form and the collocation points are defined. Then, by using the obtained matrix relations and the collocation points, the Riccati problem is reduced to a system of nonlinear algebraic equations. The condition in the problem is written in the matrix form and a new system of the nonlinear algebraic equations is found with the aid of the obtained matrix relation. This system is solved and thus the coefficient matrix is detected. This coefficient matrix is written in the solution form and hence approximate solution is obtained. In addition, by defining the residual function, an error problem is established and approximate solutions which give better numerical results are obtained. To demonstrate that the method is trustworthy and convenient, the presented method and error estimation technique are explicated by numerical examples. Consequently, the numerical results are shown more clearly with the aid of the tables and graphs and also the results are compared with the results of other methods.

A bijective enumeration of tiered trees

Tiered trees were introduced by Dugan–Glennon–Gunnells–Steingrímsson as a generalization of intransitive trees that were introduced by Postnikov, the latter of which have exactly two tiers. Tiered trees arise naturally in counting the absolutely indecomposable representations of certain quivers, and enumerating torus orbits on certain homogeneous varieties over finite fields. By employing generating function arguments and geometric results, Dugan et al. derived an elegant formula concerning the enumeration of tiered trees, which is a generalization of Postnikov’s formula for intransitive trees. In this paper, we provide a bijective proof of this formula by establishing a bijection between tiered trees and certain rooted labeled trees. As an application, our bijection also enables us to derive a refinement of the enumeration of tiered trees with respect to level of the node 1.

Wavelet representation of light-front quantum field theory

A formally exact discrete multi-resolution representation of quantum field theory on a light front is presented. The formulation uses an orthonormal basis of compactly supported wavelets to expand the fields restricted to a light front. The representation has a number of useful properties. First, light front preserving Poincar\'e transformations can be computed by transforming the arguments of the basis functions. The discrete field operators, which are defined by integrating the product of the field and the basis functions over the light front, represent localized degrees of freedom on the light-front hyperplane. These discrete fields are irreducible and the vacuum is formally trivial. The light-front Hamiltonian and all of the Poincar\'e generators are linear combinations of normal ordered products of the discrete field operators with analytically computable constant coefficients. The representation is discrete and has natural resolution and volume truncations like lattice formulations. Because it is formally exact it is possible to systematically compute corrections for eliminated degrees of freedom.

The Best of Both Worlds or the Worst of Both Worlds? Multilateral Development Banks, Immunities and Accountability to Rights-Holders

Multilateral development banks (MDBs) are accorded immunities and privileges as agents of their member states as justified by functionalist arguments. They are also operationally hybrid: they are actors in their own right in addition to being functional agents. Navigating the functionalist imagery and relying on the argument that they are delegated purely economic pursuits (i.e. financing economic development), MDBs are able to eschew accountability to rights-holders that are affected by their decisions and operations. Although administrative law approaches have succeeded in increasing transparency, instilling self-regulatory frameworks and providing for independent review, the absence of external oversight of such review mechanisms and the broad immunities to suit enjoyed by MDBs have impeded true accountability to rights-holders. This article argues that, in so far as they engage in private sector financing operations, MDBs and their constituent arms share the form, function and relationships of an economic corporation to a large extent. Consequently, their immunities should be limited to render them bound—like ordinary corporations- by the domestic norms with respect to rule of law and human rights of the home and host countries in which they operate in order to make them accountable to rights-holders and to provide recourse for wrongdoings.