Solutions - Science topic

We consider a minimizing movement scheme of Chambolle-type for the mean curvature flow equation with prescribed contact angle condition in a smooth bounded domain in R d (d ≥ 2). We prove that an approximate solution constructed by the proposed scheme converges to the level-set mean curvature flow with prescribed contact angle provided that the dom...

This article deals with the stability problem for a higher-order dispersive model governed by the so-called Kawahara equation. To do so, a damping mechanism is introduced, which contains a distributed memory term, and then proves that the solutions of the system are exponentially stable, provided that specific assumptions on the memory kernel are f...

We study in this paper the existence and uniqueness of solutions to initial value problems for semilinear differential equations involving ψ-Caputo differential derivatives of an arbitrary l ∈ (0, 1), using the fixed theorem. We do analyse further the M-L-U-H stability and the M-L-U-H-R stability. Then we conclude with an example to illustrate the...

We modify and generalize the basic theory of formal completion (I-adic completion) as in [3], [8] and [6] with using a general Zariskian filtration F R and replacing quiotient filtration F R I n ; n ∈ Z. We establish the exactness, finitness and flatness of formal completion. The formal microlocalization of R ∧I-module M ∧I represents the solution...

Cet ouvrage constitue une référence incontournable pour les professionnels de la logistique, les décideurs et les chercheurs soucieux de relever les défis posés par la complexité croissante des environnements opérationnels. En proposant des cadres d'analyse et des solutions pragmatiques dans un contexte de faible degré de certitude.

Decision-making is the process of systematically selecting the best option from a set of alternatives, considering criteria, constraints, and desired outcomes. Extensions of decision-making, such as HyperDecision-Making and SuperHyperDecision-Making, are well-known. Additionally, various decision-making frameworks have been developed, including Mul...

In this paper, we consider a class of p(x, ·)-integro-differential Kirchhoff-type problem with Dirichlet boundary conditions. Considering various variational methods, we establish the existence of multiple solutions taking into account the different situations concerning the non-linearity and growth conditions.

This paper we concern the solvability and uniqueness of higher-order Langevin fractional differential equations subject to integral boundary conditions. We establish the existence of solutions using Krasnoselskii's fixed point theorem, while uniqueness is demonstrated through the application of the Banach fixed point theorem. The obtained results o...

The aim of this paper is to study a class of anisotropic Robin elliptic equations with variable exponents where the nonlinearity may depend on the gradient of the solution. First, we demonstrate the existence of at least one weak solution using the surjectivity result of pseudomonotone operators. Moreover, under additional conditions on the data, w...

Retraction of ‘Color tuning of Bi³⁺-doped double-perovskite Ba2(Gd1−x,Lux)NbO6 (0 ≤ x ≤ 0.6) solid solution compounds via crystal field modulation for white LEDs’ by Xufang Tang et al., RSC Adv., 2020, 10, 25500–25508, https://doi.org/10.1039/D0RA03793A.

We consider the following higher-order Schrödinger equation involving supercritical growth and competing potentials: *\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\b...

We give a coordinate transformation in the extended configuration space that maps the trajectories of a free particle in two dimensions into the trajectories of a charged particle in a uniform magnetic field. We show that this coordinate transformation also relates the solutions of the Schrödinger equations for these two problems.

We present the complete solution to the classification problem regarding the variational symmetries of the generalized Brans-Dicke cosmological model in the presence of a second scalar field minimally coupled to gravity and the generalized Brans-Dicke scalar field theory. Through the symmetry analysis, we were able to specify the functional form of...

We experimentally demonstrate symmetry breaking, symmetry restoring, and intensity switching of counterpropagating Raman waves in a microresonator with symmetric intracavity waves at the pump frequency. Stationary symmetric and asymmetric states of Raman waves are theoretically found within a symmetric system of equations, and asymmetric branches o...

This article explores the International Council on Archives and its role in standardizing archival activities. It focuses on promoting collaboration among archives, improving document management, and preserving cultural heritage. The research analyzes proposed solutions to enhance efficiency in information management, providing valuable insights fo...

Let n ≥ 3 be a integer. In this paper, we study some generalized Fermat's equations of signature (2n, 2, 3) and (n, 2n, 2). More precisely we show that the Diophantine equation of type x 2n + 3y 2 = z 3 has no solution in non-zero coprime integers unknowns x, y, z. Using a combination of the modular approach (via Frey curves and Galois representati...

We continue the study of the Dirichlet boundary value problem of nonlinear wave equation with radial data in the exterior $\Omega = \mathbb{R}^3\backslash \bar{B}(0,1)$. We combine the distorted Fourier truncation method in \cite{Bourgain98:FTM}, the global-in-time (endpoint) Strichartz estimates in \cite{XuYang:NLW} with the energy method in \cite...

The exact solutions for the Riemann problem concerning the one‐dimensional triple‐pressure Euler equations with the Coulomb‐type frictional term are displayed in perfectly explicit forms, where both the rarefaction and shock waves are presented in parabolic shapes with equal curvature under the action of the Coulomb‐type frictional term. Specifical...

We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem -- the so-called landscape problem for the operator -- instead of refining based on the computed eigenpairs. Some...

In this paper, we will study the issue about the 1-$\Gamma$ inverse, where $\Gamma\in\{\dag, D, *\}$, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1-$\Gamma$ inverse is introduced. Equivalent conditions for a tensor to be a 1-$\Gamma$ inverse are established. Secondly, using the sin...

A family of single-parameter Atkinson–Shapley rules for TU-games is introduced. These rules are marginalist with a specific transformation of the marginal contributions depending on a parameter, which assesses how equality among payoffs fairly offsets inefficiency in the redistribution. This normative content is similar in spirit to that of Atkinso...

We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least one of the weight functions is very small. The basic idea is to replace the distributional derivative with a new...

In this paper, a combination of Galerkin's method and Dafermos' transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next, the existence of tempered random attractors for such equations is established in an appropriate space for the an...

We study the bifurcation phenomena between spherical and axisymmetric bosonic stars. By numerically solving for the zero-modes of spherical bosonic stars under specific axially symmetric perturbations, we discover that excited state spherical bosonic stars bifurcate into two types of axisymmetric bosonic stars under $\ell=2$ perturbations, with mat...

In this work, we give sufficient conditions to the existence and uniqueness for the heat equation involving the operator ∆ G = 1 2 ∆ x + |x| 2 ∆ y in Marcinkiewcz spaces. Furthermore, we give sufficient conditions to the existence of positive, symmetric and self-similar solutions.

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In this paper, we study a class of bi-nonlocal fourth-order discrete problems involving p(k)-Laplacian operator in a finite-dimensional Banach space. Using the variational method and the (S+) mapping theory, we investigate the existence and multiplicity of nontrivial solutions, subject to the condition that the parameters are sufficiently large.

When is it possible to project two sets of labeled points lying in a pair of projective planes to the same image on a projective line? We give a complete answer to this question and describe the loci of the projection centers that enable a common image. In particular, we find that there exists a solution to this problem if and only if these two set...

In this work, we explore the existence of solutions to an initial value problem for nonlinear neutral delay \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi$$\end{d...

We investigate the multidimensional stability of planar traveling waves in competitive–cooperative Lotka–Volterra system of three species in n-dimensional space. For planar traveling waves with speed c>c*, we establish their exponential stability in L∞(Rn), which is expressed as t−n2e−ετσt, where σ>0 is a constant and ετ∈(0,1) depends on the time d...

We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the case in which the dual dissipation potential is given by a sum of two functionals and show that solutions of the associated gradient-flow evolution equation with combined...

We present a method for constructing covariantly constant endomorphisms for the mod p equivariant quantum connection, using the quantum Steenrod power operations of Fukaya and Wilkins. The example of the cotangent bundle of the projective line is fully computed, and we discuss the relationship with the mod p solutions of trigonometric KZ equation r...

In this paper, we investigate multiplicity, existence, and nonexistence of periodic solutions to a fourth-order partial difference equation via linking theorem and saddle point theorem. Our obtained results significantly generalize and improve some existing ones. We also provide examples and numerical simulations to illustrate applications of our m...

The paper studies the existence of periodic solutions of a perturbed relativistic Kepler problem of the type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{alig...

Let \(\{P_{t}^{[\lambda]}\}_{t>0}\) be the Poisson semigroup associated with the Bessel operator \(\Delta_{\lambda}\) on \(\mathbb{R}_+:=(0,\infty)\), where \(\lambda>0\) and \(\Delta_{\lambda}:=-x^{-2\lambda}\frac{d}{dx}x^{2\lambda}\frac{d}{dx}\). In this paper, the authors show that a function \(u(y,t)\) on \(\mathbb{R}_{+}\times\mathbb{R}_{+}\),...

We study properties of !-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the omega-limit set of a trajectory is chain recurrent, applying this result to an evolution differential inclusion with upper semicontinous right-hand side. Second, we give conditions e...

In this work, we study the existence and nonexistence of solutions to fractional Dirichlet boundary value problems with ψ$$ \psi $$‐Hilfer fractional derivatives, p$$ p $$‐Laplacian, and Hardy‐type singularity term using variational methods.

In this paper, a class of controlled variational control models is studied by considering the notion of (q, w) − π-invexity. Our aim is to investigate a solution set in the considered interval-valued controlled models. To achieve this, we establish some characterization results of solutions in the controlled interval-valued variational models. More...

In this paper, we study the local behavior of positive solutions near the boundary singularity to the fourth order Lane–Emden equations. By a blow-up analysis and the Liouville theorem, we derive an upper bound and the boundary Harnack inequality. Then we establish a generalized Bôcher theorem and give a classification of the boundary isolated sing...

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these boundary conditions not being well-posed for large times and/or data, we obtain wellposedness of the optimal control...

In this note, we investigate the existence and asymptotic property of positive periodic solutions to non-autonomous predator-prey system with stage-structured predator on time scales. Via Schauder’s fixed theorem, easily verifiable sufficient existence conditions of positive periodic solutions for the considered system are obtained. We also study a...

This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized solutions and entropy solutions to the equation is proved. To address the significant challenges encountered du...

Assuming a modular version of Schanuel’s conjecture and the modular Zilber–Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular j function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety...

Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd di...

Challenges and Solutions for Protection in Power Systems with Inverter-based Resources (IBR) Title: Challenges and Solutions for Protection in Power Systems with Inverter-based Resources (IBR) Conference: IDEAS 2025 IEEE International Decentralized Energy Access Solutions(IDEAS) Conference. Bali, Indonesia, January 7-9, 2025. VIDEO: https://youtu...

this paper shows one solution of the GZK paradox and how cosmic rays can be more energetic than model predicts .

The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is stablished, comparing classical results with the general situation of moment differentiation.

In the present paper, we study the Krasnoselskii-Mann method in order to obtain approximate solutions of a common coincidence problem in a metric space with a hyperbolic structure.

The aim of this paper is to study the oscillatory behavior of solutions of second-order noncanonical dynamical equations with a sublinear and superlinear neutral terms. Using the process of linearization, we obtain some new easily verifiable criteria for the oscillation of the aforementioned equation. The results are illustrated by three examples....

A swarm intelligence algorithm usually iterates many times to approximate the optimum to obtain the solution of a problem. The maximum iteration is influenced by many factors such as the algorithm itself, problem types, as well as dimensions and search space sizes of decision variables. There are few existing studies on efficient maximum iterations...

In this article, we prove the uniqueness of viscosity solutions to $\mathcal{L}_{\infty} u =f$ in $\Omega$, where $\mathcal{L}_{\infty}$ denotes the nonlocal infinity Laplace operator, $\Omega$ a bounded domain, and $f$ a continuous functions such that $f \leq 0$. Uniqueness is established through a comparison principle.

The present work examines the solvability of a tripled system of fractional Langevin differential equations with cyclic antiperiodic boundary conditions. The Krasnoselskii fixed point theorem, the Banach contraction mapping theorem, and specific properties of the Mittag-Leffler functions are employed to establish sufficient conditions for the exist...

We consider the problem of computing the optimal solution and objective of a linear program under linearly changing linear constraints. More specifically, we want to compute the optimal solution of a linear optimization where the constraint matrix linearly depends on a paramater that can take p different values. Based on the information given by a...

We prove a Liouville theorem for ancient solutions to the supercritical Fujita equation \[\partial_tu-\Delta u=|u|^{p-1}u, \quad -\infty <t<0, \quad p>\frac{n+2}{n-2},\] which says if $u$ is close to the ODE solution $u_0(t):=(p-1)^{-\frac{1}{p-1}}(-t)^{-\frac{1}{p-1}}$ at large scales, then it is an ODE solution (i.e. it depends only on $t$). This...

We give estimates for positive solutions for the Schr\"odinger equation $(\Delta_\mu+W)u=0$ on a wide class of parabolic weighted manifolds $(M, d\mu)$ when $W$ decays to zero at infinity faster than quadratically. These can be combined with results of Grigor'yan to give matching upper and lower bounds for the heat kernel of the corresponding Schr\...

Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any weak solution to the Smoluchowski equation looses mass in finite time. The class of kernels we consider is essentially the same as the one of Andreis-...

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The purpose of this paper is to study the boundedness of solutions of the Chern-Simons-Higgs equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \p...

Solutions to special Lagrangian equations near infinity, with supercritical phases or with semiconvexity on solutions, are known to be asymptotic to quadratic polynomials for dimension $n\ge 3$, with an extra logarithmic term for $n=2$. Via modified Kelvin transforms, we characterize remainders in the asymptotic expansions by a single function near...

In this paper we investigate the behaviour of massless fermions in the black string spacetime by computing the eigenvalues and eigenfunctions of the Weyl equations. These solutions allowed us to study the behaviour of such massless fermions in terms of the cosmological constant, the black string's mass and the radial distance of the particle from t...

This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems (TSVIP). The existence of solutions to the TSVIP is discussed, and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.

A B-spline adaptive sampling (B-SAS) method is proposed for three-dimensional freeform surface measurements using a laser differential confocal sensor (LDCS). High-precision focusing on optical freeform surfaces was achieved by axial scanning using the LDCS. The B-SAS method, based on the arc length and curvature uniformity, was introduced to enabl...

The Pseudo-Boolean problem deals with linear or polynomial constraints with integer coefficients over Boolean variables. The objective lies in optimizing a linear objective function, or finding a feasible solution, or finding a solution that satisfies as many constraints as possible. In the 2024 Pseudo-Boolean competition, solvers incorporating the...

Gurumukhani et al. (CCC'24) proposed the local enumeration problem Enum(k, t) as an approach to break the Super Strong Exponential Time Hypothesis (SSETH): for a natural number $k$ and a parameter $t$, given an $n$-variate $k$-CNF with no satisfying assignment of Hamming weight less than $t(n)$, enumerate all satisfying assignments of Hamming weigh...

This research used the genetic algorithm to solve non-zero-sum and non-cooperative games within the framework of game theory. It was noted that the genetic algorithm has a great ability to find optimal solutions to complex problems that require simultaneous optimization of several objectives. In this research, a model based on the genetic algorithm...

The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reformulation is that it's possible to find a 6-cycle 4-cover. In this paper we discuss the oriented version (o6c4c) of the latter statement, pose it as a conjecture and prove...

This paper presents a new insight into the epipole from four given image point correspondences in two calibrated views. Firstly, we propose an algebraic constraint on the relation between the epipole and a plane-induced homography. Secondly, we show a novel algorithm for determining the 10-degree curve about possible epipoles from four image point...

In this paper, we consider a bilevel problem: Variational inequalities over the solution set of a general split inverse problem consists of a monotone variational inclusion problem. We propose a relaxed inertial forward‐backward‐forward splitting algorithm with a new step size rule for finding an approximate solution of this problem in real Hilbert...

In this paper, we demonstrate that any asymptotically flat manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M^{n+1}, g)$$\end{document} with \documentclass[12p...

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In this paper, we consider the existence of normalized solutions for the following fourth‐order Schrödinger equation with saturated nonlinearity: Δ2u−Δu+λu=μI(x)+u21+I(x)+u2u,x∈ℝN∫ℝN|u|2dx=a2$$ \left\{\begin{array}{l}{\Delta}^2u-\Delta u+\lambda u=\mu \frac{I(x)+{u}^2}{1+I(x)+{u}^2}u,\kern1em x\in {\mathbb{R}}^N\\ {}{\int}_{{\mathbb{R}}^N}{\left|u\...

Our team is exploring innovative ways to enhance the efficiency of flotation processes, based on a deep understanding of the physicochemical characteristics of these ongoing processes.

This paper provides a formalism for an important class of causal inference problems inspired by user-advertiser interaction in online advertiser. Then this formalism is specialized to an extension of temporal marked point processes and the neural point processes are suggested as practical solutions to some interesting special cases.

Solutions to p-Laplace equations are not, in general, of class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document}. The study of Sobolev regularity of t...

In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Firstly, the error estimation between smoothed penalty function, non-smooth penalty function and original function is investigated. By using these new smooth penalty functions, nonline...

An extended (3+1)-dimensional Bogoyavl-ensky-Konopelchenko equation is the main focus of this study. We formulate the Nth-order Pfaffian solutions using a combination of the Hirota method and Pfaffian technique, where N is a positive integer. The Nth-order Pfaffian solutions are employed to determine the multi-soliton, multi-breather and hybrid sol...

This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution of the boundary value problems for DAEs have been found. The technique of constructing the asymptotic solutions...

We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained with brute-force methods require exponentially many computation steps and thus are infeasible for any graph of re...

The commented paper was found when explicitly looking for papers on fractal models for thermal conductivity, on which my experience learns that they are often flawed. This "review" paper offered me the opportunity to bundle a number of concerns on a number of papers on the topic, concerns that had not made it into the literature yet, typically beca...

In this paper, we investigate the Diophantine equation (2 k − 1)(3 k − 1) = x n and prove that it has no solutions in positive integers k, x, n > 2.

Using fibrations over K3 orbisurfaces we construct new smooth solutions to the Hull-Strominger system. In particular, we prove that, for $4 \leq k \leq 22$ and $5 \leq r\leq 22$, the smooth manifolds $S^1\times \sharp_k(S^2\times S^3)$ and $\sharp_r (S^2 \times S^4) \sharp_{r+1} (S^3 \times S^3)$, have a complex structure with trivial canonical bun...