where x ∈ R is the vector of decision variables, c ∈ R is a linear objective function and S ⊂ R is the set of feasible solutions of (1). Because S is generally hard to deal with, a possible approach for tackling (1) is to optimize the objective function over a suitable relaxation (i.e., easy to solve) P ⊇ S. Let x be the optimal solution over P . If x ∈ S the problem is solved. Otherwise, one c...

Let Ω be a domain in R d with boundary Γ, Γ the Euclidean distance to and H = − div ( C ∇ ) an elliptic operator c k l > 0 where are real, bounded, Lipschitz functions. We assume that ∼ δ I as → sense of asymptotic analysis is strictly positive, function ≥ . also there r b , such weighted Hardy inequality ∫ | ψ 2 valid for all ∈ ∞ { x : < } then prove condition / sufficient essential self-adjoi...

In [H4], Hamilton determined a sharp tensor Harnack inequality for complete solutions of the Ricci flow with non-negative curvature operator. This Harnack inequality is of critical importance to the understanding of singularities of the Ricci flow, as is evident from its numerous applications in [H3], [H5], [H6], and [H7]. Moreover, according to Hamilton, the discovery of a Harnack inequality i...

DEFINITION A bi-temporal index is a data structure that supports both temporal time dimensions, namely, transactiontime (the time when a fact is stored in the database) and valid-time (the time when a fact becomes valid in reality). The characteristics of the time dimensions supported imply various properties that the bi-temporal index should have to be efficient. As traditional indices, the pe...

Access control is one of the most important technologies to guarantee computer security. A new model with support for valid time and usage constraint is described based on full analysis of flaws in existing models. In the new model, authorization rules can express access control policies completely and access constraints are necessary conditions to prevent authorization abuse. To solve the prob...

Induction of transplantation tolerance remains the ideal long-term clinical and logistic solution to the current challenges facing the management of renal allograft recipients. In this review, we describe the recent studies and advances made in identifying biomarkers of renal transplant tolerance, from study inceptions, to the lessons learned and their implications for current and future studie...

By supporting the valid and transaction time dimensions, bitemporal databases represent reality more accurately than conventional databases. In this paper, we examine the issues involved in designing efficient access methods for bitemporal databases, and propose the partial-persistence and the double-tree methodologies. The partial-persistence methodology reduces bitemporal queries to partial p...

The presented data model is a novel approach for integrating temporal concepts into a multimedia database system. Multimedia objects are extended with the traditional time dimensions valid time and transaction time. In addition a new time dimension specifically tailored for multimedia data types is presented with semantics that are completely orthogonal to the already established time dimension...