In 1932 F. Severi claimed, with an incorrect proof, that every smooth minimal pro-jective surface S such that the bundle Ω 1 S is generically generated by global sections satisfies the topological inequality 2c 2 1 (S) ≥ c2(S). According to Enriques-Kodaira classification, the above inequality is easily verified when the Kodaira dimension of the surface is ≤ 1, while for surfaces of general typ...

We also proved a softer version of statement 2 as cheeger’s inequality i.e. Cheeger’s Inequality: 1−λ2 2 ≤ h(G) ≤ √ 2(1− λ2) Note:The same results also hold for a weighted graph which is not d regular.In that case we define define a matrix of degrees D,with Dii=degree of vertex i= ∑ j w(i, j) and Dij = 0∀i 6= j.Then M is given by L=D−1/2AD−1/2.It may be noted that M = A d for a d-regular graph....

In order to estimate traffic densities in a large-scale urban freeway network in an accurate and timely fashion when traffic sensors do not cover the freeway network completely and thus only local measurement data can be utilized, this paper proposes a decentralized state observer approach based on a macroscopic traffic flow model. Firstly, by using the well-known cell transmission model (CTM),...

in this paper we consider contact cr-warped product submanifolds of the type $m = n_ttimes_f n_perp$, of a nearly kenmotsu generalized sasakian space form $bar m(f_1‎, ‎f_2‎, ‎f_3)$ and by use of hopf's lemma we show that $m$ is simply contact cr-product under certain condition‎. ‎finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case i...

For any set S let ∣ ∣ seq1-1(S) ∣ ∣ denote the cardinality of the set of all finite one-to-one sequences that can be formed from S, and for positive integers a let ∣ ∣a ∣ ∣ denote the cardinality of all functions from S to a. Using a result from combinatorial number theory, Halbeisen and Shelah have shown that even in the absence of the axiom of choice, for infinite sets S one always has ∣ ∣ se...

We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f 2 C 0; 1], by polynomials. For the sake of completeness as well as in order to strengthen some existing results, we discuss brieey the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory es...

This paper is concerned with the H∞ and generalized H2 estimation problems for a class of continuoustime piecewise linear systems. We present a linear matrix inequality (LMI) based approach to the design of generalized H2 and H∞ estimators. Our approach employs S-procedure and partition-dependent slack variables to reduce design conservatism. Examples demonstrate the advantages and good estimat...

In this paper, we design a tracking controller which satisfies transient response specifications and maintains tracking error within a tolerable limit for the uncertain track-following system of an optical disk drive. To this end, a robust H1 control problem with regional stability constraints and sinusoidal disturbance rejection is considered. The internal model principle is used for rejecting...

For n ∈ N, let Sn be the smallest number S > 0 satisfying the inequality

We remove the hypothesis “S is finite” from the BKR inequality for product measures on Sd, which raises some issues related to descriptive set theory. We also discuss the extension of the BKR operator and inequality, from 2 events to 2 or more events, and we remove, in one sense, the hypothesis that d be finite.