Research
Research
Research
Research
456+ open-access research outputs.
Semiclassical analysis and noncommutative geometry are two pillars of quantum theory. It's only recently that bridges between them have been emerging. In this monograph, we combine various techniques …
We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contri…
In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family o…
This article aims to present a unified framework for ranking-based voting rules based on the use of depth functions on permutations, as a counterpart of deepest voting rules on evaluation introduced i…
Degradation prognosis for lithium-ion cells requires forecasting the state-of-health (SOH) trajectory over future cycles. Existing data-driven approaches can produce trajectory outputs through direct …
In this work, we investigate the existence and uniqueness of solutions to the following 2D and 3D convective Brinkman-Forchheimer extended Darcy equations defined on a bounded smooth domain $\Omega\su…
This work studies the following doubly degenerate parabolic-elliptic nutrient taxis system $$ \begin{cases} u_t = (uvu_x)_x -(u^2 vv_x)_x + uv, \\[1.5 ex] \hspace{0.2 cm}0 = v_{xx} - uv + f(x,t), …
Recently, product states have been identified as simple-structured eigenstates of XXZ Heisenberg spin models in arbitrary dimensions, occurring at anisotropy values corresponding to certain roots of u…
Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or tho…
For general set-valued mappings, the Aubin property is ultimately tied to limiting coderivatives by the Mordukhovich criterion. Likewise, the existence of single-valued Lipschitzian localizations is r…
The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemic…
In this study, we investigate the incompressible generalised Navier-Stokes-Voigt equations within a bounded domain $\Omega \subset \mathbb{R}^d$, where $d \geq 2$. The governing momentum equation is e…
In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological algebra setting. Then,…
We study an optimal boundary control problem associated to the boundary obstacle problem for the couple conformal Laplacian and conformal Robin operator on n-dimensional compact Riemannian manifolds w…
In this paper, we investigate a multi-dimensional nonlocal degenerate diffusion-aggregation equation with a diffusion exponent $m$ in the intermediate range $\frac{2d}{2d-\gamma}<m<\frac{d+\gamma}{d}$…
We show that any toric asymptotically conical shrinking gradient K\"ahler-Ricci soliton on an anti-canonically polarised resolution of a K\"ahler cone satisfies a complex Monge-Amp\`ere equation. We t…
This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order variational function, s…
We consider the ground states of the nonlinear Schr{\"o}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate their behaviors at bo…
In this paper, we consider the Donaldson gauge functional and the twisted Aubin functionals on almost K\"ahler manifolds. As in K\"ahler geometry, we generalize the inequality between Aubin functional…
Multiplicity in pre-main-sequence (PMS) systems shapes circumstellar and circumbinary disks, often producing features such as inner cavities, spiral arms, and gas streamers that facilitate mass transf…
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