We consider the following on-line scheduling problem. We have to schedule n independent jobs, where n is unknown, on m uniform parallel machines so as to minimize the makespan; preemption is allowed. Each job becomes available at its release date, and this release date is not known beforehand; its processing requirement becomes known at its arrival. We show that if only a finite number of preem...

In this paper, we study the stochastic nonlinear heat equations (SNLH) and wave (SNLW) on two-dimensional torus $${\mathbb {T}}^2 = ({\mathbb {R}}/2\pi {\mathbb {Z}})^2$$ driven by a subordinate cylindrical Brownian noise, which define time-derivative of motion subordinated to nondecreasing càdlàg process. To construct solution, introduce suitable renormalization similarly Da Prato Debussche (A...

Given a nondecreasing nonlinearity f , we prove uniqueness of large solutions to the equation (1) below, in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex.

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c 0 ∗ > such that for each c c∗ ≥ , the systems under consideration admit monotonic nondecreasing traveling waves.

For a nondecreasing score function having finitely many jump-discontinuities. a representation of M-estimators with the second order asymptotic distribution is established. and the result is also extended to one-step versions of M-estimators.

We give a Bennett-type factorization of the space ces(pn) for monotone nonincreasing sequence {pn}. If the sequence {pn} is nondecreasing and bounded then certain converse assertion is proved.

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P 2 (R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of " sticky " particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evol...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P 2 (R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of " sticky " particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evol...

This paper is devoted to the study of semi-stable radial solutions u ∈ H1(B1) of −∆u = g(u) in B1 \ {0}, where g ∈ C (R) is a general nonlinearity and B1 is the unit ball of R N . We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the semilinear ...