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Can we admit the way in which $\sin(x)$ is typically defined?
I review some facts which the usual sen(x) and cos(x) definitions are based on. The purpose of this paper is to show that this facts can be proved if we assume some basic ideas of elementary geometry. Read More >
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Zeta functions and asymptotic additive bases with some unusual sets of primes
Fix $\delta\in(0,1]$, $\sigma_0\in[0,1)$ and a real-valued function $\varepsilon(x)$ for which $\limsup_{x\to\infty}\varepsilon(x)\le 0$. For every set of primes ${\mathcal P}$ whose counting function $\pi_{\mathcal P}(x)$ satis ... Read More >
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Compressed Cliques Graphs, Clique Coverings and Positive Zero Forcing
Zero forcing parameters, associated with graphs, have been studied for over a decade, and have gained popularity as the number of related applications grows. In particular, it is well-known that such parameters are related to ce ... Read More >
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On the trace of random walks on random graphs
We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any $\varepsilon>0$ there exists $C>1$ such that the trace of the simple random walk of length $(1+\varepsilon)n\ln{n}$ on the ... Read More >
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Improved bounds in Weaver and Feichtinger Conjectures
We sharpen the constant in the $KS_2$ conjecture of Weaver \cite{We}, which was validated by Marcus, Spielman, and Srivastava \cite{MSS} in their solution of the Kadison--Singer problem. We then apply this result to prove optima ... Read More >
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Collocation Method using Compactly Supported Radial Basis Function for Solving V ...
In this paper, indirect collocation approach based on compactly supported radial basis function is applied for solving Volterras population model. The method reduces the solution of this problem to the solution of a system of al ... Read More >
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Application of Meshfree Method Based on Compactly Supported Radial Basis Functio ...
In this paper, we have applied the Meshless method based compactly supported radial basis function collocation for obtaining the numerical solution of unsteady gas equation. The unsteady gas equation is a second order non-linear ... Read More >
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Numerical Study of Astrophysics Equations by Meshless Collocation Method Based o ...
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite d ... Read More >
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Bilevel parameter learning for higher-order total variation regularisation model ...
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and ana ... Read More >
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Polyhedral studies of vertex coloring problems: The asymmetric representatives f ...
Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between \emph{optimization} ... Read More >