Abstract. We investigate harmonic Bergman spaces bp = bp(Ω), 0 < p < ∞, where Ω = Rn \Zn and prove that bq ⊂ bp for n/(k + 1) ≤ q < p < n/k. In the planar case we prove that bp is non empty for all 0 < p < ∞. Further, for each 0 < p < ∞ there is a non-trivial f ∈ bp tending to zero at infinity at any prescribed rate.

Abstract. We prove that ωu(δ) ≤ Cωf(δ), where u: Ω → Rn is the harmonic extension of a continuous map f: ∂Ω → Rn, if u is a K-quasiregular map and Ω is bounded in Rn with C2 boundary. Here C is a constant depending only on n, ωf and K and ωh denotes the modulus of continuity of h. We also prove a version of this result for Λω-extension domains with c-uniformly perfect boundary and quasiconformal mappings.

The aim of this work was to establish the deformation behavior of two vanadium mic-roalloyed medium carbon steels with different contents of carbon and titanium by tensile testing at 77 K. Samples were reheated at 1250 C for 30 min and continuously cooled in still air. Beside acicular ferrite as the dominant morphology in both microstructures, the steel with lower content of carbon and negligible amount of titanium contains consi-derable fraction of grain boundary ferrite and pearlite. It was found that Ti-free steel exhibits a higher strain hardening rate and significantly lower elongation at 77 K than the fully acicular ferrite steel. The difference in tensile behavior at 77 K of the two steels has been associated with the influence of the pearlite, together with higher dislocation density of acicular ferrite.

The characteristics of composite materials are of high importance to engineering applications; therefore the increasing use as a substitute for conventional materials, especially in the field of aircraft and space industries. It is a known fact that researchers use finite element programs for the design and analysis of composite structures, use of symmetrical conditions especially in complicated structures, in the modeling and analysis phase of the design, to reduce processing time, memory size required, and simplifying complicated calculations, as well as considering the response of composite structures to different loading conditions to be identical to that of metallic structures. Finite element methods are a popular method used to analyze composite laminate structures. The design of laminated composite structures includes phases that do not exist in the design of traditional metallic structures, for instance, the choice of possible material combinations is huge and the mechanical properties of a composite structure, which are anisotropic by nature, are created in the design phase with the choice of the appropriate fiber orientations and stacking sequence. The use of finite element programs (conventional analysis usually applied in the case of orthotropic materials) to analysis composite structures especially those manufactured using angle ply laminate techniques or a combination of cross and angle ply techniques, as well considering the loading response of the composite structure to be identical to that of structures made of traditional materials, has made the use of, and the results obtained by using such analysis techniques and conditions questionable. Hence, the main objective of this paper is to highlight and present the results obtained when analyzing and modeling symmetrical conditions as applied to commercial materials and that applied to composite laminates. A comparison case study is carried out using cross-ply and angle-ply laminates which concluded that, if the composition of laminate structure is pure cross-ply, the FEA is well suited for predicting the mechanical response of composite structure using principle of symmetry condition. On the other hand that is not the case for angle-ply or mixed-ply laminate structure.

 In this paper, English language will be used as an instance of natural languages as we will be concerned with the set of all natural language texts. this research tries to employ a set of all synonyms as a way to hide secret message inside a natural language text. 

Abstract: This paper presenting the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tubes subjected to lateral compression load. A comprehensive experimental program has been carried out on three geometrically different types of composite tubes: radial corrugated composite tubes, cylindrical composite tubes, and corrugated surrounded by cylindrical tubes. The three structures are made of woven roving glass fibre/epoxy 600 g/sqm. All specimens fabricated under the same conditions with a fixed number of layers equal to six.