Related papers: Sur les estimations du type sup+inf et sup*inf
We establish derivative estimates of solution of elliptic system in narrow regions.
We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of…
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for this quantity, in which the dependence upon the…
We present new infinite arctangent sums and infinite sums of products of arctangents. Many previously known evaluations appear as special cases of the general results derived in this paper.
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…
Under various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the…
We obtain some results related to Romanoff's theorem.
In this short note we present some new results concerning cotype and absolutely summing multilinear operators.
We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
In this paper we prove new upper bounds for the sum $\sum_{n=a+1}^{a+N}f(n)$, for a certain class of arithmetic functions $f$. Our results improve the previous results of G. Bachman and L. Rachakonda.
In this paper, we define indexed type theories which are related to indexed ($\infty$-)categories in the same way as (homotopy) type theories are related to ($\infty$-)categories. We define several standard constructions for such theories…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
This short note contains elementary evaluations of some Euler sums.
We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. Especially we recover some known results.
We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.
We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ together with a sequence of independent, identically distributed $X$-space valued random variables $\xi_1,\dots,\xi_n$ and give a good estimate on the…