We provide new estimates on the best constant of Lieb-Thirring inequality for sum negative eigenvalues Schr\odinger operators, which significantly improve so far existing bounds.

Abstract: In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B1(h, k), which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y(h, k) and the sum C1(h, k). By using the Fibonacci numbers and two-term polynomial relation, we wi...

We present a tight bound on the exact maximum complexity of Minkowski sums of polytopes in R. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2, . . . ,mk facets respectively is bounded from above by

The subject of this thesis is the theory of nonholomorphic modular forms of non-integral weight, and its applications to arithmetical functions involving Dedekind sums and Kloosterman sums. As was discovered by Andre Weil, automorphic forms of non-integral weight correspond to invariant funtions on Metaplectic groups. We thus give an explicit description of Meptaplectic groups corresponding to ...

Focusing on the 311 Chinese firms listed in global markets from 2008 to 2019, based trade-off theory and resource slack theory, using panel vector autoregressive model threshold model, this paper explores impact of fulfilling ESG responsibility firm performance. The study reveals that short run, presents a “Substitution Effect,” whereas, long it “Promotional Effect.” On other hand, improvement ...

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...