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Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles due to differences in transcription time, degradation rate and RNA processing kinetics. Recent studies have shown that a…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm…
Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…
H\"older estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.
The aim of this study is to find asymptotic expressions of eigenvalues and eigenfunctions of a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition. Applications of…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions…
The present research paper is devoted to investigate the existence, uniqueness of mild solutions for impulsive delay integrodifferential equations with integral impulses in Banach spaces. We also investigate the dependence of solutions on…
Despite the fact that we have some proposals for the quantum theory of gravity like string theory or loop quantum gravity, we do not have any experimental evidence supporting any of these theories. Actually, we do not have experimental…
A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…
Let X be a hermitian manifold and let L^k be a high power of a hermitian line bundle over X. Local versions of Demailly's holomorphic Morse inequalities are presented - after integration they yield the usual inequalities. The local weak…
This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of…
In this paper we study Coifman type estimates and weighted norm inequalities for singular integral operators $T$ and its commutators, given by the convolution with a vector valued kernel $K$. We define a weaker H\"ormander type condition…
This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…
A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…
The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…
The concept of phase and dwell times used in tunneling is extended to quantum collisions to derive a relation between the phase and dwell time delays in scattering. This relation can be used to remove the near threshold s-wave singularities…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…