We develop a general model of edge spaces in order to generalize, unify, and simplify previous work on cycle spaces of infinite graphs. We give simple topological criteria to show that the fundamental cycles of a (generalization of a) spanning tree generate the cycle space in a connected, compact, weakly Hausdorff edge space. Furthermore, in such a space, the orthogonal complement of the bond s...

We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...

Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate function J (·, ·) and whose cumulative process satisfies the LDP with rate function I (·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of a cumulative renewal process it is demonst...

Optimal linear prediction (aka. kriging) of a random field {Z(x)}x?X indexed by compact metric space (X,dX) can be obtained if the mean value function m:X?R and covariance ?:X×X?R Z are known. We consider problem predicting Z(x?) at some location x??X based on observations locations {xj}j=1n, which accumulate x? as n?? (or, more generally, ?(Z) {?j(Z)}j=1n for functionals ?,?1,…,?n). Our main r...

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...

We determine the dark matter pair-wise relative velocity distribution in a set of Milky Way-like halos Auriga and APOSTLE simulations. Focusing on smooth halo component, is well-described by Maxwell-Boltzmann over nearly all radii halo. explore implications for velocity-dependent annihilation, focusing four models which scale as different powers velocity: Sommerfeld, s-wave, p-wave, d-wave mode...

Let X be a reflexive Banach space such that for any x 6= 0 the set {x∗ ∈ X∗ : ‖x∗‖ = 1 and x∗(x) = ‖x‖} is compact. We prove that any unrestricted product of of a finite number of (W ) contractions on X converges weakly. Recall a (bounded) linear operator on a Banach space X is said to be contraction if ‖Tx‖ ≤ ‖x‖ for all x ∈ X . T is said to satisfy condition (W ) if {xn} is bounded and ‖xn‖ −...

Let $$\mathscr {F}$$ be a holomorphic foliation by curves defined in neighborhood of 0 $$\mathbb {C}^n$$ ( $$n\ge 2$$ ) having as weakly hyperbolic singularity. T positive $${dd^c}$$ -closed current directed which does not give mass to any the n coordinate invariant hyperplanes $$\{z_j=0\}$$ for $$1\le j\le n.$$ Then we show that Lelong number at vanishes. Moreover, an application this local re...

Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(· , ·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstr...

The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station­ ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...