Let Λ be a complete metric space, and let {Sλ(·) : λ ∈ Λ} be a parametrised family of semigroups with global attractors Aλ. We assume that there exists a fixed bounded set D such that Aλ ⊂ D for every λ ∈ Λ. By viewing the attractors as the limit as t → ∞ of the sets Sλ(t)D, we give simple proofs of the equivalence of ‘equi-attraction’ to continuity (when this convergence is uniform in λ) and s...

The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...

A topological algebra is a complex associative algebra which is also a Hausdorff topological vector space such that the multiplication is separately continuous. A locally convex algebra is a topological algebra whose topology is determined by a family of seminorms. A complete metrizable locally convex algebra is called a B0-algebra. The topology of a B0-algebra A may be given by a countable fam...

and Applied Analysis 3 Definition 2.2. Let f be any real-valued function and ν ∈ 0, 1 . The left discrete fractional difference and the right discrete fractional difference operators are, respectively, defined as tΔaf t ΔtΔ − 1−ν a f t 1 Γ 1 − ν Δ t ν−1 ∑ s a t − s − 1 −ν f s , t ≡ a − ν 1 mod1 , bΔt f t −ΔbΔ 1−ν t f t 1 Γ 1 − ν −Δ b ∑ s t 1−ν s − t − 1 −ν f s , t ≡ b ν − 1 mod1 . 2.2 Definitio...

String rewriting systems, also known as semi-Thue systems, consist of a set of rules l → r, specifying valid replacements of substrings of strings over a given alphabet. In the case of one single rule, it is an open problem whether there is a system that is neither terminating nor looping. Another open question is the decidability of termination. Difficulties arise especially for non-confluent ...

and Applied Analysis 3 The purpose of this paper is to generalize the above results using an ICS mapping T : X → X and involving some generalized weak contractions of Boyd-Wong-type 31 . Also, some examples are presented to show that our results are effective. 2. Main Result First, denote by Φ the set of functions φ : 0, ∞ → 0, ∞ satisfying a φ t < t for all t > 0, b φ is upper semicontinuous f...

Let K be a discrete valuation field with ring of integers OK . Let f :X → Y be a finite morphism of curves overK . In this article, we study some possible relationships between the models over OK of X and of Y . Three such relationships are listed below. Consider a Galois cover f :X→ Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-st...

SEMI-QUANTIFICATION OF FATTY DEGENERATION WITHIN SUPRASPINATUS MUSCLE BY USING 2-POINT DIXON TECHNIQUE AT 3.0-T MRI Taiki Nozaki, Junko Ochi, Chiharu Osakabe, Atsushi Tasaki, Yasuhito Kaneko, and Hiroshi Yoshioka Radiological Sciences, University of California, Irvine, Orange, California, United States, Radiology, St.Luke's International Hospital, Chuo-ku, Tokyo, Japan, Orthopedic Surgery, St.L...

In this paper, we propose a semi-supervised online graph labelling method that a↵ords early learning capability. We use mean field approximation for predicting the unknown labels of the vertices of the graph with high accuracy on the standard benchmark datasets. The minimum cut is the energy function of our probabilistic model that encodes the uncertainty about the labels of the vertices. Our m...

The two operations, deletion and contraction of an edge, on multigraphs directly lead to the Tutte polynomial which satisfies a universal problem. As observed by Brylawski [8] in terms of order relations, these operations may be interpreted as a particular instance of a general theory which involves universal invariants like the Tutte polynomial, and a universal group, called the Tutte-Grothend...