In Ch], Cheeger proved the following general lower bound for the rst eigenvalue 1 of a closed Riemannian manifold: Theorem ((Ch]): 1 1 4 h 2 ; where h = inf N area(N) min(vol(A); vol(B)) where N runs over (possibly disconnected) hypersurfaces of M which divide M into two pieces A and B, and where area denotes (n ? 1)-dimensional volume, and vol denotes n-dimensional volume, where n = dim(M). h(...

In this paper, we give a new minimax theorem and two new existence theorems of solutions for generalized quasi–variational inequalities in H-spaces. Our results improve and develop some famous results.

A feedback controller design which guarantees both finite-time boundedness and H∞ attenuation for a class of nonlinear systems with conic type nonlinearities and additive disturbances is presented. Conditions which guarantee the existence of a robust state-feedback controller for maintaining a bound on the transient response and satisfying an H∞ bound in the steady state for this class of syste...

where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a...

Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H ;〈·,·〉), r,s > 0, p ∈ (0,s], D = {x ∈ H ,‖rx− sa‖ ≤ p}, x1,x2 ∈D−{0}, and αr,s = min{(r2‖x...

In the paper, we formulate some open problems related to best description of values exceptional sets in Wiman's inequality for entire functions and Erd\H{o}s-Macintyre type theorems multiple Dirichlet series. At same time, clarify statement one \v{I}.V. Ostrovskii problem on inequality. We also prove three propositions theorem. On hand, a rather special case, these results give possible set Erd...

The problem of delay-dependent robust H∞ control for uncertain singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm bounded. By establishing an integral inequality based on quadratic terms, a new delay-dependent bounded real lemma is derived and expressed in terms of linear matrix inequality(LMI). A suitable robust H∞ state feedback control ...

This paper presents a robust iterative learning control (ILC) for a class of two dimensional (2D) linear systems with parametric uncertainty and considerable disturbances. The proposed control law is iteratively updated to guarantees the robust stability. Based on H∞ setting, sufficient conditions for robust monotonic convergence of the proposed scheme are presented in terms of linear matrix in...

and Applied Analysis 3 ordinary differential inequality, next given the sufficient conditions of blow-up of the solution of 1.4 by the inequality. In 21 , Hao et al. considered the single-wave equation of the form utt − div ( g ( |∇u| ) ∇u ) h ut f u , x ∈ Ω, t > 0 1.5 with initial and Dirichlet boundary condition, where g satisfies condition 1.2 and g s ≥ b1 b2s, q ≥ 0. 1.6 The damping term ha...

The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinge...