Related papers: Exponential lower bound for Berge-Ramsey problems
We prove an explicit version of Burgess' bound on character sums for composite moduli.
We give a uniform estimate and an inequality for solutions of an equation with Dirichlet boundary condition.
In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.
This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive real and complex solutions for the RBLSE problem by utilizing…
Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu$. Under the assumptions that $\mu$ has a finite exponential…
For a finite abelian group $G$, the generalized Erd\H{o}s--Ginzburg--Ziv constant $\mathsf s_{k}(G)$ is the smallest $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. If $n =…
A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…
Using cyclic graphs I give new lower bounds for two color and multicolor Ramsey numbers: R(4,16)>163, R(5,11)>170, R(5,12)>190, R(5,13)>212, R(5,14)>238, R(3,3,9)>117, R(3,3,10)>141 and R(3,3,11)>157. Improving the previous best known…
We prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.
We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described…
New error bounds for the linear complementarity problems are given respectively when the involved matrices are Nekrasov matrices and B-Nekrasov matrices. Numerical examples are given to show that new bounds are better respectively than…
We give a lower bound for the Gaussian curvature of convex level sets of minimal graphs and the solutions to semilinear elliptic equations with the norm of boundary gradient and the Gaussian curvature of the boundary.
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with…
We prove an upper bound for the least prime in an irrational Beatty sequence. This result may be compared with Linnik's theorem on the least prime in an arithmetic progression.
We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.
An exact Rosenthal-type inequality for the third absolute moments is given, as well as a number of related results. Such results are useful in applications to Berry--Esseen bounds.
In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy},…
We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.
We give a Hopf boundary point lemma for weak solutions of linear divergence form uniformly elliptic equations, with H$\ddot{\text{o}}$lder continuous top-order coefficients and lower-order coefficients in a Morrey space.