Research
Research
Research
Research
111,116+ open-access research outputs.
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its …
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applic…
We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace tr…
We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle …
This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze…
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in t…
The Etzion-Silberstein conjecture asserts that, for any finite field $\mathbb F$, Ferrers diagram $\mathcal D$, and integer $d$, there exists a linear matrix code supported on $\mathcal D$ with minimu…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph t…
Let $X_1,\ldots,X_n$ be independent random points in the closed unit ball of $\mathbb{R}^d$. Assume that each $X_i$ has a beta distribution with parameter $\beta_i \ge -1$: if $\beta_i>-1$, then $X_i$…
The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a K\"ahler manifold with boundary…
We consider the problem of finding the (unique) minimal Walrasian equilibrium price in multi-item, multi-unit auction models: there are multiple indivisible items for sale, with several units of each …
We introduce G\r{a}rding polynomials, a class of real multivariate polynomials defined via positivity regions invariant under translation by positive directions and closed under strictly positive affi…
High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscos…
As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variational features of seve…
Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote…
We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates div…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The…
\indent In this paper, we study a class of parabolic-elliptic Keller-Segel systems with diffusion sensitivity dependent on spatial position, given by type \begin{equation} \left\{ \begin{array}{ll…
We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where $H$ is a nonlinear lower order term sati…
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