We study the concept of quadratic variation a continuous path along sequence partitions and its dependence with respect to choice partition sequence. introduce roughness show that for Hölder-continuous paths satisfying this condition, balanced is invariant Typical Brownian motion are shown satisfy property almost-surely any required step size condition. Using these results we derive formulation...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

<p style='text-indent:20px;'>We investigate existence of stationary solutions to an aggregation/diffusion system PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually proportional negative constant <inline-formula><tex-math id="M1">\begin{document}$ -\alpha $\end{document}</tex-math>&...

In this paper we study properties that the vacuum must possess in minimal extension to teleparallel equivalent of general relativity (TEGR) where action is supplemented with a quadratic torsion term. No assumption made about weakness term although weak-field regime validity our previously derived perturbative solution confirmed. Regarding exact nature vacuum, it found if center symmetry be regu...

We provide the modified TOV equations for hydrostatic equilibrium of charged compact stars within metric $f(R)$ gravitational background. adopt MIT bag model EoS dense matter and assume a charge distribution where electric density $\rho_{\rm ch}$ is proportional to standard energy $\rho$. Using Starobinsky model, we explore role $\alpha R^2$ term, $\alpha$ free constant $R$ Ricci scalar, on glo...

We study the two-dimensional stochastic nonlinear wave equation (SNLW) and heat (SNLH) with a quadratic nonlinearity, forced by fractional derivative (of order $\alpha > 0$) of space-time white noise. In particular, we show that well-posedness theory breaks at = \frac 12$ for SNLW 1$ SNLH. This provides first example showing behaves less favorably than (i) As SNLW, Deya (2020) essentially prove...

First-order optimization algorithms can be considered as a discretization of ordinary differential equations (ODEs) (Su et al. in Adv Neural Inf Process Syst 27, 2014). In this perspective, studying the properties corresponding trajectories may lead to convergence results which transfered numerical scheme. paper we analyse following ODE introduced by Attouch (J Differ Equ 261(10):5734–5783, 201...

An upper quasi-density on $\bf H$ (the integers or the non-negative integers) is a real-valued subadditive function $\mu^\ast$ defined whole power set of $\mathbf such that $\mu^\ast(X) \le \mu^\ast({\bf H}) = 1$ and $\mu^\ast(k \cdot X + h) \frac{1}{k}\, \mu^\ast(X)$ for all $X \subseteq \bf H$, $k \in {\bf N}^+$, $h N$, where := \{kx: x X\}$; an density non-decreasing with respect to inclusio...

Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of 2D spin-1/2 Heisenberg model with long-range interactions. With $1/r^{\alpha}$ ferromagnetic and staggered antiferromagnetic interactions, find explicit range in $\alpha$ for {\color{black} short-range Goldstone-type (gapless), anomalous (gapless) Higgs-type (gapped) spectra. Accompanied by sp...