Let L be a countable first-order language and M = (M, . . .) be an L-structure. “Definable set” means a subset of M which is L-definable in M with parameters. A set X ⊆ M is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, A∩X is immune. X is said to be totally non-immune if for every definable A, A...

The potential application of ultrasonic energy for ablation of atherosclerotic plaques was studied in human atherosclerotic arteries with continuous and pulsed delivery of energy. With a prototype ultrasonic wire probe (n=79 segments), there was gross reduction in vascular lesions as well as microscopic disruption of fibrous and calcified plaques. Normal portions of vessels appeared unaffected ...

Let A be a finite alphabet and let DcA * be a finite set of words to be labelled "dirty". Let {Xa: a E A} be commuting indeterminates. To every letter a E A we assign the weight Xa and the weight of a word is the product of the weights of its letters. For example, weight (13221) = X1X3X2X2X1 = XiX~X3. Given any set S of words we let weight (S) be the sum of the weights of the members of S. For ...

A locally small category E is totally distributive (as defined by Rosebrugh-Wood) if there exists a string of adjoint functors t ⊣ c ⊣ y, where y : E → Ê is the Yoneda embedding. Saying that E is lex totally distributive if, moreover, the left adjoint t preserves finite limits, we show that the lex totally distributive categories with a small set of generators are exactly the injective Grothend...

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . . , |V (G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total label...

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz. From the properties of the algebra generated by the local jump operators, we construct explicitly the hierarchy of operators that commute with the Markov operator. The transfer matrix, which is the generating function of these operators, is shown to represent a discrete Markov proce...

The papers [19], [9], [1], [4], [20], [2], [18], [13], [5], [8], [14], [21], [7], [15], [12], [11], [17], [6], [10], [16], and [3] provide the terminology and notation for this paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M , F is a family of subsets of the carrier of M , A, B are subsets of the carrier of M , f is a function, n, m, p, k ar...