Makespan minimization onm identical machines is a fundamental scheduling problem. The goal is to assign a sequence of jobs, each specified by a processing time, to parallel machines so as to minimize the maximum completion time of any job. Deterministic online algorithms achieve a competitive ratio of about 1.92. Due to this relatively high competitiveness and the lack of progress in the area o...

We prove that an n-valued function that is lower semi-continuous is also upper semi-continuous and therefore continuous, that is, an n-valued map. Several conditions are shown to be equivalent to continuity for n-valued functions, in particular the continuity of a corresponding singlevalued function to a configuration space. Consequently, splitting is related to braid groups to prove a Splittin...

We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique nontrivial homologies. We prove the following two results: if the center foliation is one dimensional, then the topological entropy is locally a constant; and if the center foliation is two dimensional, then the topological entropy is continuous on the set of a...

BACKGROUND The authors present the high-resolution computed tomography findings of an immunosuppressed patient with semi-invasive pulmonary aspergillosis. CASE PRESENTATION The main finding consisted of irregular, thick-walled cavity in the right upper lobe and a mass with soft-tissue attenuation within it and thickening of adjacent pleura. Additional findings were bronchial wall thickening a...

We consider a radially symmetric free boundary problem with logistic nonlinear term. The spatial environment is assumed to be asymptotically periodic at infinity in the radial direction. For such a free boundary problem, it is known from [7] that a spreading-vanishing dichotomy holds. However, when spreading occurs, only upper and lower bounds are obtained in [7] for the asymptotic spreading sp...

We show the existence of Banach spaces X, Y such that the set of strictly singular operators ᏿(X,Y) (resp., the set of strictly cosingular operators Ꮿ᏿(X,Y)) would be strictly included in F + (X,Y) (resp., F − (X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ + (X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ − ...

We identify a class of potentials for which the semiclassical estimate N (semi) = 1 π ∫ ∞ 0 dr √ −V (r)θ [−V (r)] of the number N of (S-wave) bound states provides a (rigorous) lower limit: N ≥ {{ N (semi) }} , where the double braces denote the integer part. Higher partial waves can be included via the standard replacement of the potential V (r) with the effective l-wave potential V (eff) l (r...

This paper is a survey of the upper bounds on the complexity of basic algebraic and geometric operations with Pfaffian and Noetherian functions, and with sets definable by these functions. Among other results, we consider bounds on Betti numbers of sub-Pfaffian sets, multiplicities of Pfaffian intersections, effective Lojasiewicz inequality for Pfaffian functions, computing frontier and closure...