Related papers: When is P such that l_0-minimization Equals to l_p…

We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2)^{1/p}\le((A^q+B^q)/2)^{1/q}$ holds for every pair of matrices $A,B>0$ are indeed best possible. The proof…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…

We prove the convergence of the solutions $u_{m,p}$ of the equation $u_t+(u^m)_x=-u^p$ in $\R\times (0,\infty)$, $u(x,0)=u_0(x)\ge 0$ in $\R$, as $m\to\infty$ for any $p>1$ and $u_0\in L^1(\R)\cap L^{\infty}(\R)$ or as $p\to\infty$ for any…

The main purpose of this paper is to show that there exists a positive number $\lambda_{1}$, the first eigenvalue, such that some $p(x)$-Laplace equation admits a solution if $\lambda=\lambda_{1}$ and that $\lambda_{1}$ is simple, i.e.,…

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space $X$ having a minimal separating function set in $C_p(X)$ is equivalent to having a minimal…

Let $p$ be a prime and let $A$ be a subset of $\mathbb{F}_p$ with $A=-A$ and $|A\setminus\{0\}| \leq 2\log_3(p)$. Then there is an element of $\mathbb{F}_p$ which has a unique representation as a difference of two elements of $A$.

We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…

Let A and B be two finite subsets of a field F. In this paper we provide a nontrivial lower bound for |{a+b: a in A, b in B, and P(a,b) not=0}| where $P(x,y)\in F[x,y]$.

Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…

We draw attention to simplifications in the theory of a N\"orlund summation method $(N, p)$ that arise when the series $\sum_{n \geqslant 0} p_n$ is convergent.

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…

Nontrivial $p$-polygonal equalities impose certain conditions on the geometry of a metric space $(X,d)$ and so it is of interest to be able to identify the values of $p \in [0,\infty)$ for which such equalities exist. Following work of Li…

We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem,…

We present a new elementary proof of the existence of the least and the greatest solutions to initial value problems in the conditions of Peano's existence theorem. Our proof is based on a modification of Perron's method which allows us to…

The main result is that the only non trivial closed ideal in the Banach algebra $L(L^p)$ of bounded linear operators on $L^p(0,1)$, $1\le p < \infty$, that has a left approximate identity is the ideal of compact operators. The algebra…

We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\ell_p$ and $L_p$, $1 \leq p <2$. More…

By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$-Laplace equation in $\mathbb{R}^n$, with $n\geq 3$, and whose infimum over a ball…

Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).

Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…

In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1},…