We show that any càdlàg predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated ‘from below’ by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable ...

We show variational estimates for paraproducts, Theorems 1.2 and 1.3, which can be viewed as bilinear generalizations of Lépingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents, 1 < r ≤ 2.

A notion called Herbrand saturation is shown to provide the modeltheoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

An important question is the role of these results under mis-specification. It has been assumed thus far that the variables in the investigation are linked by a closed dynamic system of form (2.5), in which β has a structural interpretation. We should also know how to interpret regressions when some variables that appear in the long-run solution of (2.5) are missing from the data set. Of course...

The theory of structural reliability is widely applied in many fields, such as architectural design, and mechanical engineering. In this paper, the resident and the load of a structure are defined as uncertain variables and the reliability index is defined as as the uncertain measure of the event that the resident is larger than the load. Furthermore, the reliability of series and parallel stru...

It has been known for a long time that many mathematical objects can be naturally decomposed into a ‘pseudorandom’, chaotic part and/or a highly organized ‘periodic’ component. Theorems or heuristics of this type have been used in combinatorics, harmonic analysis, dynamical systems and other parts of mathematics for many years, but a number of results related to such ‘structural’ theorems emerg...

The purpose of this paper is to establish the methodology of complexity assessment for the innovation system, named as conception system. The article applies the theories and methods of mathematics, dynamics, information science, charting theories, relational mathematics, etc, to put forth the concepts, definitions, basic theorems and mathematical models of the information force, energy and str...

A set Y ⊆ R that intersects every convex set of volume 1 is called a Danzer set. It is not known whether there are Danzer sets in R with growth rate O(T ). We prove that natural candidates, such as discrete sets that arise from substitutions and from cut-and-project constructions, are not Danzer sets. For cut and project sets our proof relies on the dynamics of homogeneous flows. We consider a ...

Direct quotations from business leaders can communicate to the wider public the latent state of their organization as well as the beliefs of the organization’s leaders. Candid quotes from business leaders can have dramatic effects upon the share price of their organization. For example, Gerald Ratner in 1991 stated that his company’s products were crap and consequently his company (Ratners) los...

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive Voronovskaya-type asymptotic theorem for this type of operator. Then, local global theorems are obtained by using classical modulus continuity K-functional. Finally, rate convergence functions with a derivative bounded variation. The results show that new have g...