This paper considers the stability problem of Lur’e type descriptor systems (LDS) with sector and slope restricted nonlinearities. The concepts of global index one and strongly absolute stability are firstly introduced. Then by using S-procedure and matrix inequality approach, two sufficient conditions for LDS to be strongly absolutely stable are derived. It is shown that such conditions also g...

Received: date / Revised version: date Abstract. We consider robust semi-definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sum-of-squares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxat...

We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on Rn, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly conve...

In this note, we consider a similar type of Gauss inequality for fuzzy integrals. More precisely, we show that the inequality x(S) ∫ ∞

Let G be a graph of order n and clique number !: For every x = (x1; : : : ; xn) 2 Rn and 1 s !; set fs (G;x) = X fxi1 : : : xis : fi1; : : : ; isg is an s-clique of Gg ; and let s (G;x) = fs (G;x) ! s 1 : We show that if x 0; then 1 (G;x) 1=2 2 (G;x) 1=! ! (G;x) : This extends the inequality of Maclaurin (G = Kn) and generalizes the inequality of Motzkin and Straus. In addition, if x > 0; for e...

We give a short and elementary proof of an inverse Bernsteintype inequality found by S. Khrushchev for the derivative of a polynomial having all its zeros on the unit circle . The inequality is used to show that equally-spaced points solve a min-max-min problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we s...

A generalization of Émery’s inequality for stochastic integrals is shown for convolution integrals of the form ( ∫ t 0 g(t − s)Y (s−) dZ(s))t>0, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. The function g is assumed to be absolutely continuous with a derivative that is continuous or of bounded variation or a sum of such functions. The function g may ...

We consider t-designs with *=1 (generalized Steiner systems) for which the block size is not necessarily constant. An inequality for the number of blocks is derived. For t=2, this inequality is the well known De Bruijn Erdo s inequality. For t>2 it has the same order of magnitude as the Wilson Petrenjuk inequality for Steiner systems with constant block size. The point of this note is that the ...

‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...

In the article, the complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis inequality, and an integral inequality due to R. P. Agarwal, P. Cerone, S. S. Dragomir and F. Qi. Mathematics subject classification (2010): 26D15, 33C75, 33E05.