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A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
We prove a global continuation result for $T$-periodic solutions of a $T$-periodic parametrized second order retarded functional differential equation on a boundaryless compact manifold with nonzero Euler-Poincare' characteristic. The…
Let $C$ be a closed cone with nonempty interior $C^\circ$ in a Banach space. Let $f:C^\circ \rightarrow C^\circ$ be an order-preserving subhomogeneous function with a fixed point in $C^\circ$. We introduce a condition which guarantees that…
Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. Well-posedness of differential equation problems thus involves…
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…
We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making…
The eigenvalue problem for a linear function L centers on solving the eigen-equation Lx = rx. This paper generalizes the eigenvalue problem from a single linear function to an iterated function system F consisting of possibly an infinite…
In this paper, we frame homogeneous-feature multi-task learning (MTL) as a hierarchical representation learning problem, with one task-agnostic and multiple task-specific latent representations. Drawing inspiration from the information…