For uniform systems of spin-less fermions in d spatial dimensions with d > 1, interacting through the isotropic two-body potential v(r − r), a celebrated theorem due to Luttinger (1961) states that under the assumption of validity of the many-body perturbation theory the self-energy Σ(k; ε), with 0 ≤ k∼3kF (where kF stands for the Fermi wavenumber), satisfies the following universal asymptotic ...

Let (M, g̃) be an N -dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation ε∆g̃u + (1− u)u = 0 in M, where ε is a small parameter. Let K ⊂M be an (N − 1)-dimensional smooth minimal submanifold that separatesM into two disjoint components. Assume that K is non-degenerate in the sense that it does not support non-trivial Jacobi fields, and that |AK...

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an ε-global minimizer is guaranteed. At each iteration k, the algorithm requires a (ρ(k),ε(k))-global minimizer of a bound constrained bi-objective subproblem, where as k→ ∞, ρ(k)→ 0 gives the constraint violation tolerance and ε(k)→ ε is the error bo...

We consider the k-Center problem and some generalizations. For k-Center a set of k center vertices needs to be found in a graph G with edge lengths, such that the distance from any vertex of G to its nearest center is minimized. This problem naturally occurs in transportation networks, and therefore we model the inputs as graphs with bounded highway dimension, as proposed by Abraham et al. [SOD...

providing clear evidence for a non-zero ε/ε value. The theoretical status is instead more debated (see ref. [2] for a brief review). One of the problems that had to be faced during the past years has been that, while CP violation is born at a scale say O(MW ), the observables that enter in the game have to be estimated at a scale of O(MK) (see fig. 1). Changing the order of magnitude of the sca...

and Applied Analysis 3 2. Preliminaries In this section, we complete notations and recall some known definitions. Let K X be the class of all nonempty and compact subset of X. If A ∈ K X we define the ε-neighbourhood of A as the set N A, ε {x ∈ X | d x,A < ε}, 2.1 where d x,A infa∈A‖x − a‖. The Hausdorff separation ρ A,B of A,B ∈ K X is defined by ρ A,B inf{ε > 0 | A ⊆ N B, ε }. 2.2 The Hausdor...

In this paper, effects of the cross shore and groyne wall slopes on flow parameters around an impermeable groyne were considered using a three-dimensional numerical CFD model (i.e., FLUENT). The k-ε turbulence model was used to evaluate the Reynolds stresses. The model was first applied to a vertical groyne on a flat bed and the model results were compared with the relevant experimental data. T...

Let {Rt, 0 ≤ t ≤ 1} be a symmetric α-stable Riemann-Liouville process with Hurst parameterH > 0. Consider a translation invariant, β-self-similar, and p-pseudo-additive functional semi-norm ||.||. We show that if H > β+1/p and γ = (H − β− 1/p), then lim ε↓0 ε logP [||R|| ≤ ε] = −K ∈ [−∞, 0), with K finite in the Gaussian case α = 2. If α < 2, we prove that K is finite when R is continuous and H...

Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lamé system) are determined by an asymptotic analysis as the thickness (2ε) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar model that depends on two parameters: the angular frequency k and the half-thickness ε. Optim...