A virtual element formulation for general element shapes

The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.

BIBLICAL PHRASEOLOGICAL UNITS IN BULGARIAN AND POLISH (A COMPARATIVE ANALYSIS IN THE AREA OF NON-PREDICATIVE EXPRESSIONS)

The paper presents a short contrastive analysis of phraseological units in the Bulgarian and the Polish language, which have Biblical origin. The text is focused on non-predicative expressions (i.e., it deals with semantic, formal and stylistic features of expressions with no verbal component) and observes their variation of the meaning following as a context their contribution in Bulgarian and Polish resources. In this respect, the first part of the article represents the similarities between Bulgarian and Polish Biblical Phraseological Units. The units under observation here are grouped in pairs, depending on the general element they contain. Mainly, that is an onomastic element with symbolic meaning and it is a kind of reference to the Old or New Testament. In the second part of the present text, Biblical expressions share one and the same symbolic element, but they have different semantics and structure. The compared constructions are based on different aspects of the symbol and they have different connotative potential. That part has a main function to highlight that both – Bulgarian and Polish language, using the same Biblical element could make completely different phraseological units. Despite the genetic relations of the two Slavic languages, the cited constructions are formed by Bulgarian and Polish cultural and religious experience.

Trigonal Deformations of Rank One and Jacobians

We study the infinitesimal deformations of a trigonal curve that preserve the trigonal series and such that the associate infinitesimal variation of Hodge structure is of rank $1.$ We show that if $g\geq 8$ or $g=6,7$ and the curve is Maroni general, this locus is zero dimensional. Moreover, we complete the result [10, Theorem 1.6]. We show in fact that if $g\geq 6$, the hyperelliptic locus ${{\mathcal{M}}}^1_{g,2}$ is the only $2g-1$-dimensional sub-locus ${{\mathcal{Y}}}$ of the moduli space ${{\mathcal{M}}}_g$ of curves of genus $g$, such that for the general element $[C]\in{{\mathcal{Y}}}$, its Jacobian $J(C)$ is dominated by a hyperelliptic Jacobian of genus $g^{\prime}\geq g$.

Polish economic clusters and their efforts to protect the environment – selected examples

This paper presents the benefits they can obtain business which aim to protect the environment. The environment protection has found its place and affects the process of systemic change of the Polish economy. This article assumes that building a competitive economy and enterprise development based on the principle of sustainable development requires the development of mechanisms for mutual benefits. These will be the economic mechanisms, technical and technological, and social. All these mechanisms are concentrated in clusters. Pursue sustainable development policies, an emphasis on environmental protection will be the general element for them a competitive advantage. Sustainable development will in this case be both the agent and the goal of economic and entrepreneurship development. Basing on the assumption that economic development is possible through the achievement of competitive advantage, sustainable development should be treated as its source.

A question of commitment

This paper addresses certain restrictions on the use of declaratives as questions in English. Declaratives are taken to express commitment by the speaker, even in a questioning use. The analysis traces the restrictions to two distinct contextual factors: (i) a general principle requiring that a commitment have a recognized source, i.e., a discourse agent who plausibly has independent evidence supporting the content committed to; (ii) specific to a questioning interpretation, the need for the context to support the inference that the speaker’s commitment depends upon the addressee’s anticipated confirmation. Rising intonation contributes a very general element of meaning, indicating that the utterance it marks is contingent upon some discourse condition obtaining; the specific conditions required for a questioning interpretation instantiate one such type of contingency. The proposals are modeled via elaboration of standard contextual structures in a possible-worlds framework.

Expression for a general element of anSO(n)matrix

We derive the expression for a general element of anSO(n)matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing Lyapunov exponents.