These are expanded notes from four introductory lectures on Ergodic Theory, given at the Minerva summer school Flows on homogeneous spaces at the Technion, Haifa, Israel, in September 2012. 1. Dynamics on a compact metrizable space Given a compact metrizable space X, denote by C(X) the space of continuous functions f : X → C with the uniform norm ‖f‖u = max x∈X |f(x)|. This is a separable Banac...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

Recent studies have demonstrated that miRNAs can play important roles in osteoblast differentiation and bone formation. However, the function of miRNAs in bone loss induced by microgravity remains unclear. In this study, we investigated the differentially expressed miRNAs in both the femur tissues of hindlimb unloading rats and primary rat osteoblasts (prOB) exposed to simulated microgravity. S...

a r t i c l e i n f o a b s t r a c t Article history: Available online xxxx Description Logics (DLs) are a well-established family of knowledge representation formalisms. One of its members, the DL ELOR has been successfully used for representing knowledge from the bio-medical sciences, and is the basis for the OWL 2 EL profile of the standard ontology language for the Semantic Web. Reasoning ...

s/hermes.html [Wald and Sorenson(1984)] Wald, J.A., Sorenson, P.G.: Resolving the query inference prob-lem using Steiner trees. ACM Transactions on Database Systems 9(3), 348–368 (1984)

(define (problem macs-prob) (:domain macs-example) (:objects region1_left region2_left region1_right region switchRegion switchRegion doorRegionLeft doorRegionRight doorRegion rightRoom room leftRoom switchRoom ) (:init (inRoom region1_left leftRoom) ... (robotAt region1_left) (liftable region1_left) (switch-triggerable switchRegion)) (:goal (robotAt doorRegionRight))) Problem Definition

The probability that a number in many naturally occurring tables of numerical data has first significant digit (i.e., first non-zero digit) d is predicted by Benford’s Law Prob (d) = log 10 (

The B-method, as well as its offspring Event-B, are both formal methods used for the development of critical computer systems whose correctness has to be formally established. Event-B now spurs the RODIN platform, which is based on Eclipse and can be extended via plug-ins. In this paper, we present two such plug-ins; one for animation and one for interactive proof support, called a disprover. B...