We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = (V,E) with a maximum edge size f . Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the demands of the edge...

Let G be a graph of order n, maximum degree ∆ and minimum degree δ. Let P (G,λ) be the chromatic polynomial of G. It is known that the multiplicity of zero ‘0’ of P (G,λ) is one if G is connected; and the multiplicity of zero ‘1’ of P (G,λ) is one if G is 2-connected. Is the multiplicity of zero ‘2’ of P (G,λ) at most one if G is 3-connected? In this paper, we first construct an infinite family...

We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These are solutions to an inhomogeneous semilinear elliptic PDE that give rise diffuse objects (varifolds) limit hypersurfaces, possibly singularities, whose is determined by "prescribed curvature" function and limiting multiplicity. establish upper bounds for eigenvalues problem, as well more sub...

Evolutionary considerations suggest aging is caused not by active gene programming but by evolved limitations in somatic maintenance, resulting in a build-up of damage. Ecological factors such as hazard rates and food availability influence the trade-offs between investing in growth, reproduction, and somatic survival, explaining why species evolved different life spans and why aging rate can s...

We explore the consequences of the structure of the discrete automorphic spectrum of the split orthogonal group SO(5) for holomorphic Siegel modular forms of degree 2. In particular, the combination of the local and global packet structure with the local paramodular newform theory for GSp(4) leads to a strong multiplicity one theorem for paramodular cusp forms.

Let D1,2(RN ) denote the closure of C∞ 0 (R N ) in the norm ‖u‖2 D1,2(RN ) = ∫ RN |∇u|2. Let N ≥ 3 and define the constants αN = N(N − 2) and CN = (N(N − 2)) N−2 4 . Let K ∈ C2(RN ). We consider the following problem for ε ≥ 0 : (Pε) ⎪⎨⎪⎩ Find u ∈ D1,2(RN ) solving : −∆u = αN (1 + εK(x))u N+2 N−2 , u > 0 } in RN . We show an exact multiplicity result for (Pε) for all small ε > 0.

We consider a class of partial differential equations with characteristics of constant multiplicity m ≥ 4. We prove for these equations a result of hypoellipticity and Gevrey hypoellipticity, by using classical Fourier integral operators and Sm ρ,δ arguments.

In a recent paper Królak and Beem (1998 J. Math. Phys. at press) have shown differentiability of Cauchy horizons at all points of multiplicity one. In this note we give a simpler proof of this result. PACS numbers: 0420C, 0420G