Related papers: Estimates for first-order homogeneous linear chara…
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
In a very general quasilinear setting, we show that the regularizing effect of a first order term causes the existence of energy solutions for problems involving the Hardy potential and $L^1$ data. In the same setting we study sharp (local…
We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
We present some new ideas to derive {\em a priori} second order estiamtes for a wide class of fully nonlinear parabolic equations. Our methods, which produce new existence results for the initial-boundary value problems in $\bfR^n$, are…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…
A priori estimates for finite-difference approximations for the first and second order derivatives are obtained for solutions of parabolic equations described in the title.
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…