相关论文: Omega results for the divisor and circle problems

We first consider a question raised by Alexander Eremenko and show that if $\Omega $ is an arbitrary connected open cone in ${\mathbb R}^d$, then any two positive harmonic functions in $\Omega $ that vanish on $\partial \Omega $ must be…

In this paper we consider the Navier-Stokes Equations in 3 dimensions in the vorticity formulation in the absence of the external forces. We derive upper bounds on L_{infinity} norm of omega and use them together with the Local Existence…

We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove…

In this paper we prove the uniqueness of the critical point for stable solutions of the Robin problem \[ \begin{cases} -\Delta u=f(u)&\text{in }\Omega\\ u>0&\text{in }\Omega\\ \partial_\nu u+\beta u=0&\text{on }\partial\Omega, \end{cases}…

I propose a notion of $(\omega_1,\beta)$-morass for the case $\omega_1 \leq \beta$.

We prove effective versions of Oppenheim's conjecture for generic inhomogeneous forms in the S-arithmetic setting. We prove an effective result for fixed rational shifts and generic forms and we also prove a result where both the quadratic…

In this paper, we consider the analogous of the obtacle problem in $H_0^1(\Omega)$, on the space $W^{1,p}_0(\Omega)$. We prove an existence and uniqueness of the result. In a second time, we define the optimal control problem associated.…

Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the projection from Delta to Delta/Omega and provide fast,…

We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…

We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential…

We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…

Lexicase and epsilon-lexicase selection are state of the art parent selection techniques for problems featuring multiple selection criteria. Originally, lexicase selection was developed for cases where these selection criteria are unlikely…

We present some new results in theory of classical theta-functions of Jacobi and sigma-functions of Weierstrass: ordinary differential equations (dynamical systems) and series expansions. The paper is basically organized as a stream of new…

Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions…

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…

The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.