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An analytical expression for the Unit Step Function
In this paper, the author obtains an analytical exact form of the Unit Step Function (or Heaviside Step Function) which evidently constitutes a...
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The Gradient Projection Method for a Supporting Function on the Unit Sphere and Its Applications
AbstractWe consider minimization of the supporting function of a convex compact set on the unit sphere. In essence, this is the problem of projecting...
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Green’s Function of the Riquier–Neumann Problem for the Polyharmonic Equation in the Unit Ball
AbstractThe Green’s function of the Riquier–Neumann problem for the polyharmonic equation in the unit ball is constructed, and an integral...
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Impulse and Step Response of Linear Systems
In this chapter you will learn how to draw the response of linear systems to Dirac delta (unit impulse) function and Heaviside (unit) step functions....
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Characterization and algorithm for bivariate multi-unit assignment valuations
A multi-unit assignment valuation is a function represented by a weighted bipartite graph. In this paper, we provide a characterization of such a...
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A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step procedure, defined over...
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Schwarz–Pick Estimates of the Real Unit Ball for Harmonic Map**s
In this paper, Schwarz–Pick estimates are obtained for harmonic map**s from the unit ball of ℝ n into origin-symmetric bounded convex domains Ω ⊂ ℝ m ,...
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The Guaranteeing Estimation Method to Calibrate a Gyro Unit
AbstractThis paper is devoted to the guaranteeing estimation method with application to the calibration problem of a gyro unit. Mathematical models...
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Bernstein-Type Operators on the Unit Disk
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study...
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The density of planar sets avoiding unit distances
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set...
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On Some Non-Rigid Unit Distance Patterns
A recent generalization of the Erdős Unit Distance Problem, proposed by Palsson, Senger, and Sheffer, asks for the maximum number of unit distance...
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An away-step Frank–Wolfe algorithm for constrained multiobjective optimization
In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We...
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Stochastic algorithms with geometric step decay converge linearly on sharp functions
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size...
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On the Toeplitz Algebra in the Case of All Entire Functions and All Functions Holomorphic in the Unit Disc
We study the algebra generated by all Toeplitz operators on the Fréchet space of all entire functions and all functions holomorphic in the unit disk....
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Function spaces
This chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.
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A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
We multiply both sides of the complex symmetric linear system Ax = b by 1 − i ω to obtain a new equivalent linear system, then a dual-parameter...
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Availability Investigation and Optimization of Crystallizer Unit of Sugar Mill Using Markov Approach and Cuckoo Search Algorithm
AbstractThe prominent objective of the present study is to investigate and optimize the availability of the crystallizer unit of the sugar power...
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On Multi-step Partially Randomized Extended Kaczmarz Method for Solving Large Sparse Inconsistent Linear Systems
To enhance the computational performance of the partially randomized extended Kaczmarz (PREK) method, we propose the multi-step PREK (MPREK) method....
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A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere
The one-bit compressed sensing problem is of fundamental importance in many areas, such as wireless communication, statistics, and so on. However,...