Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

For positive integers s and k1, k2, . . . , ks, let w(k1, k2, . . . , ks) be the minimum integer n such that any s-coloring {1, 2, . . . , n} → {1, 2, . . . , s} admits a ki-term arithmetic progression of color i for some i, 1 ≤ i ≤ s. In the case when k1 = k2 = · · · = ks = k we simply write w(k; s). That such a minimum integer exists follows from van der Waerden’s theorem on arithmetic progre...

In 1950, C.A. Rogers introduced and studied the simultaneous packing and covering constants for a convex body and obtained the first general upper bound. Afterwards, they have attracted the interests of many authors such as L. Fejes Tóth, S.S. Rys̆kov, G.L. Butler, K. Böröczky, H. Horváth, J. Linhart and M. Henk since, besides their own geometric significance, they are closely related to the pac...

Recent interest in networked control systems (NCS) has instigated research in various areas of both communication networks and control. The analysis of NCS has often been performed either from the network, or the control point of view and not many papers exist were the analysis of both is done in the same context. Here a simple overall analysis is presented. In the paper the procedure of obtain...

In this research, flat rolling process of bonded sandwich sheets is investigated by the method of upper bound. A kinematically admissible velocity field is developed for a single layer sheet and is extended into the rolling of the symmetrical sandwich sheets. The internal, shear and frictional power terms are derived and they are used in the upper bound model. Through the analysis, the rolling ...

Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's method, which works when the Mordell-Weil ...

We prove new upper bound theorems on the consistency strengths of SPFA(θ), SPFA(θ-linked) and SPFA(θ-cc). Our results are in terms of (θ,Γ)-subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γ-indescribability. Our upper bound for SPFA(c-linked) has a corresponding lower bound, which is due to Neeman and appears in his follow-up to this paper....