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Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…

Numerical Analysis · Mathematics 2014-01-31 A. A. Alikhanov

Discrete Dirac type self-adjoint system is equivalent to the block Szeg\"o recurrence. Representation of the fundamental solution is obtained, inverse problems on the interval and semi-axis are solved. A Borg-Marchenko type result is…

Classical Analysis and ODEs · Mathematics 2011-04-05 B. Fritzsche , B. Kirstein , I. Ya. Roitberg , A. L. Sakhnovich

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…

Probability · Mathematics 2014-01-23 Ewa Damek , Thomas Mikosch , Jan Rosinski , Gennady Samorodnitsky

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines,…

Machine Learning · Computer Science 2024-12-24 Vijay Prakash S

In this paper we study the Dirichlet problem for systems of mean value equations on a regular tree. We deal both with the directed case (the equations verified by the components of the system at a node in the tree only involve values of the…

Analysis of PDEs · Mathematics 2025-03-19 Alfredo Miranda , Carolina A. Mosquera , Julio D. Rossi

To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifractal spectrum by means of a number theoretical free energy…

Number Theory · Mathematics 2010-06-30 Johannes Jaerisch , Marc Kesseböhmer

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

Analysis of PDEs · Mathematics 2016-05-24 Luciano Abadías , Marta de León-Contreras , José L. Torrea

We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point.…

Spectral Theory · Mathematics 2007-05-23 C. Mason

Many combinatorial numbers can be placed in the following generalized triangular array $[T_{n,k}]_{n,k\ge 0}$ satisfying the recurrence relation: \begin{equation*}…

Combinatorics · Mathematics 2021-06-02 Bao-Xuan Zhu

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms…

Spectral Theory · Mathematics 2007-05-23 Alexander Sakhnovich

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

Number Theory · Mathematics 2023-06-22 S. Mennou , A. Chillali , A. Kacha

This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide…

Probability · Mathematics 2011-03-15 Jeffrey F. Collamore , Anand N. Vidyashankar

A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…

Analysis of PDEs · Mathematics 2021-06-01 B. Irgashev

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on…

Algebraic Geometry · Mathematics 2015-11-03 Ravi Vakil , Melanie Matchett Wood

We study the continued fractions with bounded odd/even-order partial quotients. In particular, we investigate the sizes of the sets of continued fractions whose odd-order partial quotients are equal to 1. We demonstrate that the sum and the…

Number Theory · Mathematics 2025-07-22 Yuefeng Tang

Rational approximations to a square root $\sqrt{k}$ can be produced by iterating the transformation $f(x) = (dx+k)/(x+d)$ starting from $\infty$ for any positive integer $d$. We show that these approximations coincide infinitely often with…

Number Theory · Mathematics 2022-09-22 Evan O'Dorney

We investigate the qualitative properties of solution to the Zaremba type problem in unbounded domain for the non-divergence elliptic equation with possible degeneration at infinity. The main result is Phragm\'en-Lindel\"of type principle…

Analysis of PDEs · Mathematics 2018-01-03 Dat Cao , Akif Ibraguimov , Alexander I. Nazarov

We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…

Rings and Algebras · Mathematics 2013-12-17 Erhard Neher , Arturo Pianzola

We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type $|D^\sigma u|\leq g$, involving the distributional fractional Riesz gradient $D^\sigma$, $0<\sigma <1$, extending previous results on the…

Analysis of PDEs · Mathematics 2022-02-08 A. Azevedo , J. F. Rodrigues , L. Santos

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

Algebraic Geometry · Mathematics 2015-05-14 William D. Simmons