We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)· 2n(1−μ) for – μ = Ω( 1 c ) and polynomial space solving MAX-SAT and MAX-kSAT, – μ = Ω( 1 √ c ) and exponential space solving MAX-SAT and MAX-kSAT, – μ = Ω( 1 ck2 ) and polynomial space solving MAX-k-...

∂ 2 u ∂t 2 (x, t) − ∂ 2 u ∂x 2 (x, t) = 0, x ∈ IR, t > 0, u(x, 0) = u 0 (x), x ∈ IR, ∂u ∂t (x, 0) = u 1 (x), x ∈ IR. On suppose que les données initiales sont suffisamment régulières pour que le problème de Cauchy (1) admette une solution unique u(x, t) d'énergie finie et au moins de classe C 2 en temps. On note A l'opérateur −∆. 1 Etude du problème continu 1.1 Notion d'onde plane harmonique Un...

Given V a finite set, a self–adjoint operator on C(V ), K, is called elliptic if it is positive semi–definite and its lowest eigenvalue is simple. Therefore, there exists a unique, up to sign, unitary function ω ∈ C(V ) satisfying K(ω) = λω and then K is named (λ, ω)–elliptic. Clearly, a (λ, ω)–elliptic operator is singular iff λ = 0. Examples of elliptic operators are the so–called Schrödinger...

Cohesive subgraph identification is a fundamental problem in bipartite graph analysis. In real applications, to better represent the co-relationship between entities, edges are usually associated with weights or frequencies, which neglected by most existing research. To fill gap, we propose new cohesive model, (k,ω)-core, considering both cohesiveness and frequency for weighted graphs. Specific...

Let Ω be a bounded, weakly convex domain in C, n ≥ 2, having real-analytic boundary. A(Ω) is the algebra of all functions holomorphic in Ω and continuous upto the boundary. A submanifold M ⊂ ∂Ω is said to be complex-tangential if Tp(M) lies in the maximal complex subspace of Tp(∂Ω) for each p ∈ M. We show that for real-analytic submanifolds M ⊂ ∂Ω, if M is complex-tangential, then every compact...

Let (X, [ω]) be a compact Kähler manifold with a fixed Kähler class [ω]. Let K ω be the set of all Kähler metrics on X whose Kähler class equals [ω]. In this paper we investigate the critical points of the functional g ∈ K ω → Q(g) = v g T 0 (X, g) 1/2 , where v is a fixed nonzero vector of the determinant line λ(X) associated to H * (X) and T 0 (X, g) is the Ray-Singer analytic torsion. For a ...

It is known [6], [14], [19] that if Ω⊂Rd belongs to a class of k-tiling domains when translated by lattice Λ, there exists Riesz basis exponentials for L2(Ω) constructed using k translates the dual Λ⁎. In this paper, we give an explicit construction corresponding biorthogonal basis. We also extend iterative reconstruction algorithm introduced in [11] setting.

This paper studies the generalizations of the Stirling numbers of both kinds and the Lah numbers in association with the normal ordering problem in the Weyl algebra W = 〈x,D|Dx − xD = 1〉. Any word ω ∈ W with m x’s and n D’s can be expressed in the normally ordered form ω = xm−n ∑ k>0 { ω k } xkDk, where { ω k } is known as the Stirling number of the second kind for the word ω. This study consid...

We consider the equation (1) ε∆u = (u− a(x))(u − 1) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R, ν the outer unit normal to ∂Ω, and a a smooth function satisfying −1 < a(x) < 1 in Ω. We set K, Ω+ and Ω− to be respectively the zero-level set of a, {a > 0} and {a < 0}. Assuming ∇a 6= 0 on K and a 6= 0 on ∂Ω, we show that there exists a sequence εj → 0 such that equation (1)...