It is well established that systems of totally positive blending functions, such as the Bernstein and B-spline bases, preserve monotonicity and convexity and are generally ‘shape preserving’ [9 ]. In this paper we show that total positivity is equivalent to the preservation of all orders of convexity. By a system we understand a sequence of functions (u0, . . . , un) defined on an interval [a, ...

A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem un uxx -uyy + u =0 (t > 0 ; x, y e R). Smooth data functions of compact support are prescribed at t = 0. On any time interval [0, 7"], second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

Fuzzy relations are mappings from pairs of elements into the interval [0, 1]. As a replacement for the complement operation one can use the mapping that sends x to 1 − x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however,...

1 Some Homework Exercises In introductory automata theory, one can nd a wealth of entertaining automata-theoretic puzzles such as the classical rst halves problem: Show that if A is a regular set, then so is the set of all rst halves of strings in A: FirstHalves(A) = fx j 9y jyj = jxj and xy 2 Ag : Once students master the basic pebbling technique for solving such problems, they can move on to ...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

It’s widely recognized that compression is useful and even necessary for inductive learning, where a short description will capture the ‘regularities’. We introduce complexitypreserving functions that preserve these regularities of the concept. They are based on the universal information distance [Bennett et al. ‘97] and define for an instance a set of elements sharing the same complexity type....

We study measure-preserving functions between Lebesgue measurable subsets of the real line. We use particular bijections of the interval [0, 1), called shifts, to approximate from below the set of measure-preserving maps on [0, 1). This construction is similar to the method used in ergodic theory to obtain special transformations by cutting and stacking. In our approach we provide the set of sh...