A business process often shows different variations in a large organisation, due to different legal requirements in different countries, deviations in the IT infrastructure, or organisational differences. These variants are documented in separate independent process models. Management of these variants imposes various challenges. Invariant behaviour needs to be identified and redundancies among...

We study the solutions to Klein–Gordon equation for massive scalar field in universal covering space of a two-dimensional anti-de Sitter space. For certain values mass parameter, we impose suitable set boundary conditions, which make spatial component operator self-adjoint. This makes time-evolution classical well defined. Then, use transformation properties under isometry group theory, namely,...

We use modiied Tsirelson's spaces 3] to prove that there is no nite basis for turbulent Polish group actions. This answers a question of 1. Introduction One of the trends in Descriptive Set Theory during the last decade or so concerns the study of classiiability of Borel equivalence relations. Particularly well-studied are the orbit equivalence relations of Polish group actions (see 7, 10, 11, ...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

L. Kauffman introduced a graphical link invariant which is the normalized Jones polynomial [4][5]. It is well-known that the polynomial is derived from the fundamental representation of the quantum group Uq(sl2). Further, G. Kuperberg constructed a graphical link invariant associated with the fundamental representation of the quantum group Uq(sl3) [10]. H. Murakami, T. Ohtsuki and S. Yamada int...

Bollobás and Riordan introduce a Tutte polynomial for coloured graphs and matroids in [3]. We observe that this polynomial has an expansion as a sum indexed by the subsets of the ground-set of a coloured matroid, generalizing the subset expansion of the Tutte polynomial. We also discuss similar expansions of other contraction–deletion invariants of graphs and matroids. 1. The coloured Tutte pol...

Prove that any strictly monotone sequence (Uα)α<γ of open subsets of X has countable length, i.e. γ is countable. Hint: Use the same idea as in the proof of (a). (c) Show that every monotone sequence (Uα)α<ω1 open subsets of X eventually stabilizes, i.e. there is γ < ω1 such that for all α < ω1 with α ≥ γ, we have Uα = Uγ. Hint: Use the regularity of ω1. (d) Conclude that parts (a), (b) and (c)...

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...

Here we develop a technique of computing the invariants of n−ary forms and systems of forms using the discriminants of corresponding multilinear forms buit of their partial derivatives, which should be cosidered as generalizations of classical discriminants and resultants for binary forms. 0 Introduction Let f(y0, y1, ..., yn) = ∑ α1≤...≤αd cα1...αdyα1 ...yαd be an n + 1−ary form of degree d, w...