In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c0(C(q)) c(C(q)) defined as domain q-Catalan in c0 c, respectively. We exhibit some topological properties, obtain Schauder bases determine ?-, ?-duals c(C(q)). Finally, characterize certain class mappings from to space ? = {??, c0, ?1} give necessary sufficient conditions for a operator be compact.

In asymptotic expansions of resolvent traces Tr(A(P − λ)) for classical pseudodifferential operators on closed manifolds, the coefficient C0(A,P ) of (−λ) is of special interest, since it is the first coefficient containing nonlocal elements from A; on the other hand if A = I and P = DD it gives part of the index of D. C0(A,P ) also equals the zeta function value at 0 when P is invertible. C0(A...

We describe a practical model-based testing tool developed at Microsoft Research called Spec Explorer. Spec Explorer enables modeling and automatic testing of concurrent object-oriented systems. These systems take inputs as well as provide outputs in form of spontaneous reactions, where inputs and outputs can be arbitrary data types, including objects. Spec Explorer is being used daily by sever...

Denote by [0, ω1) the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let C0[0, ω1) be the Banach space of scalar-valued, continuous functions which are defined on [0, ω1) and vanish eventually. We show that a weak ∗compact subset of the dual space of C0[0, ω1) is either uniformly Eberlein compact, or it contains a homeomorphic copy of...

We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c0 and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical `p-spaces into c0 and give other applications. We prove that if a Banach space embeds almost isometrical...

We study the ordinary differential equation εẍ+ ẋ+ εg(x) = εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0 ∈ R is such that g(c0) equals the average of f and g(c0) 6= 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c0 with frequency vector ω. We show that such a solution depends analytically on ε in...

We investigate long-range intensity correlations on both sides of the Anderson transition of classical waves in a three-dimensional disordered material. Our ultrasonic experiments are designed to unambiguously detect a recently predicted infinite-range C0 contribution, due to local density of states fluctuations near the source. We find that these C0 correlations, in addition to C2 and C3 contr...

In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using row stochastic (as a special case), define the relation < bdr on c0, which is said majorization. We also obtain some important properties of Pbdr, set all bounded linear operators T : c0 ? c0; preserve Further, it obtained necessary conditions for operator be preserver majorization bdr. Also...

Calmodulin (CaM) is the major Ca2+ sensor in eukaryotic cells. It consists of four EF-hand Ca2+ binding motifs, two in its N-terminal domain and two in its C-terminal domain. Through a negative feedback loop, CaM inhibits Ca2+ influx through N-methyl-D-aspartate-type glutamate receptors in neurons by binding to the C0 region in the cytosolic tail of the NR1 subunit. Ca2+ -depleted (apo)CaM is p...