It is known that, due to the fact that L1,∞ not a Banach space, if (Tj)j sequence of bounded operators so thatTj:L1⟶L1,∞, with norm less than or equal ||Tj|| and ∑j||Tj||<∞, nothing can be said about operator T=∑jTj. This origin many difficult open problems. However, we assume thatTj:L1(u)⟶L1,∞(u),∀u∈A1, φ(||u||A1)||Tj||, where φ nondecreasing function A1 Muckenhoupt class weights, then prove e...

It is usually difficult for prevalent negative co-location patterns to be mined and calculated. This paper proposes a join-based mining algorithm, which can quickly effectively mine all the in spatial data. Firstly, this verifies monotonic nondecreasing property of participation index (PI) value as size increases. Secondly, using property, it deduced that any pattern with n generated by connect...

In the standard setting of one-way ANOVA with normal errors, a new algorithm, called the Step Down Maximum Mean Selection Algorithm (SDMMSA), is proposed to estimate the treatment means under an assumption that the treatment mean is nondecreasing in the factor level. We prove that i) the SDMMSA and the Pooled Adjacent Violator Algorithm (PAVA), a widely used algorithm in many problems, generate...

W consider the optimal production and inventory control of an assemble-to-order system with m components, one end-product, and n customer classes. A control policy specifies when to produce each component and, whenever an order is placed, whether or not to satisfy it from on-hand inventory. We formulate the problem as a Markov decision process and characterize the structure of an optimal policy...

In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...

We introduce the concept of quasi-Lovász extension as being a mapping f : I → IR defined over a nonempty real interval I containing the origin, and which can be factorized as f(x1, . . . , xn) = L(φ(x1), . . . , φ(xn)), where L is the Lovász extension of a pseudo-Boolean function ψ : {0, 1} → IR (i.e., the function L : IR → IR whose restriction to each simplex of the standard triangulation of [...

We prove necessary and sufficient conditions for the almost sure convergence of the integrals ∫∞ 1 g(a(t)+Mt)df(t), ∫ 1 0 g(a(t)+Mt)df(t), and thus of ∫∞ 0 g(a(t)+Mt)df(t), where Mt = sup{|Xs| : s ≤ t} is the two-sided maximum process corresponding to a Lévy process (Xt)t≥0, a(·) is a nondecreasing function on [0,∞) with a(0) = 0, g(·) is a positive nonincreasing function on (0,∞), possibly wit...

In this paper we pose some important queuing problems, make some conjectures about their solution, and present some evidence in support of the conjectures. We consider the standard GI/G/s queueing model with s homogeneous servers in parallel, unlimited waiting room, the first-come first-served discipline and lid (independent and identically distributed) service times (with a general distributio...