Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

GATA Factors Regulate Inner Ear Development and Midbrain Neurogenesis

The zinc-finger transcription factors GATA2 and GATA3 in vertebrates belong to the six-member family that are essential regulators in the development of various organs. The aim of this study was to gain new information of the roles of GATA2 and GATA3 in inner ear morphogenesis and of the function of GATA2 in neuronal fate specification in the midbrain using genetically modified mouse and chicken embryos as models. A century ago the stepwise process of inner ear epithelial morphogenesis was described, but the molecular players regulating the cellular differentiation of the otic epithelium are still not fully resolved. This study provided novel data on GATA factor roles in several developmental processes during otic development. The expression analysis in chicken suggested that GATA2 and GATA3 possess redundant roles during otic cup and vesicle formation, but complementary cell-type specific functions during vestibular and cochlear morphogenesis. The comparative analysis between mouse and chicken Gata2 and Gata3 expression revealed many conserved aspects, especially during later stages of inner ear development, while the expression was more divergent at early stages. Namely, expression of both Gata genes was initiated earlier in chicken than mouse otic epithelium relative to the morphogenetic stages. Likewise, important differences concerning Gata3 expression in the otic cup epithelium were detected between mouse and chicken, suggesting that distinct molecular mechanisms regulate otic vesicle closure in different vertebrate species. Temporally distinct Gata2 and Gata3 expression was also found during otic ganglion formation in mouse and chicken. Targeted inactivation of Gata3 in mouse embryos caused aberrant morphology of the otic vesicle that in severe cases was disrupted into two parts, a dorsal and a ventral vesicle. Detailed analyses of Gata3 mutant embryos unveiled a crucial role for GATA3 in the initial inner ear morphogenetic event, the invagination of the otic placode. A large-scale comparative expression analysis suggested that GATA3 could control cell adhesion and motility in otic epithelium, which could be important for early morphogenesis. GATA3 was also identified as the first factor to directly regulate Fgf10 expression in the otic epithelium and could thus influence the development of the semicircular ducts. Despite the serious problems in the early inner ear development, the otic sensory fate establishment and some vestibular hair cell differentiation was observable in pharmacologically rescued Gata3-/- embryos. Cochlear sensory differentiation was, however, completely blocked so that no auditory hair cells were detected. In contrast to the early morphogenetic phenotype in Gata3-/- mutants, conditional inactivation of Gata2 in mouse embryos resulted in a relatively late growth defect of the three semicircular ducts. GATA2 was required for the proliferation of the vestibular nonsensory epithelium to support growing of the three ducts. Concurrently, with the role in epithelial semicircular ducts, GATA2 was also required for the mesenchymal cell clearance from the vestibular perilymphatic region between the membranous labyrinth and bony capsule. The gamma-aminobutyric acid-secreting (GABAergic) neurons in the midbrain are clinically relevant since they contribute to fear, anxiety, and addiction regulation. The molecular mechanisms regulating the GABAergic neuronal development, however, are largely unknown. Using tissue-specific mutagenesis in mice, GATA2 was characterized as a critical determinant of the GABAergic neuronal fate in the midbrain. In Gata2-deficient mouse midbrain, GABAergic neurons were not produced, instead the Gata2-mutant cells acquired a glutamatergic neuronal phenotype. Gain-of-function experiments in chicken also revealed that GATA2 was sufficient to induce GABAergic differentiation in the midbrain.

On piercing (pseudo)lines and boxes

We say a family of geometric objects C has (l;k)-property if every subfamily C0C of cardinality at most lisk- piercable. In this paper we investigate the existence of g(k;d)such that if any family of objects C in Rd has the (g(k;d);k)-property, then C is k-piercable. Danzer and Gr̈ unbaum showed that g(k;d)is infinite for fami-lies of boxes and translates of centrally symmetric convex hexagons. In this paper we show that any family of pseudo-lines(lines) with (k2+k+ 1;k)-property is k-piercable and extend this result to certain families of objects with discrete intersections. This is the first positive result for arbitrary k for a general family of objects. We also pose a relaxed ver-sion of the above question and show that any family of boxes in Rd with (k2d;k)-property is 2dk- piercable.

An experimental study on the load carrying capacity of cold-formed steel studs and panels

A full-scale experimental study on the structural performance of load-bearing wall panels made of cold-formed steel frames and boards is presented. Six different types of C-channel stud, a total of 20 panels with one middle stud and 10 panels with two middle studs were tested under vertical compression until failure. For panels, the main variables considered are screw spacing (300 mm, 400 mm, or 600 mm) in the middle stud, board type (oriented strand board - OSB, cement particle board - CPB, or calcium silicate board - CSB), board number (no sheathing, one-side sheathing, or two-side sheathing), and loading type (1, 3, or 4-point loading). The measured load capacity of studs and panels agrees well with analytical prediction. Due to the restraint by rivet connections between stud and track, the effective length factor for the middle stud and the side stud in a frame (unsheathed panel) is reduced to 0.90 and 0.84, respectively. The load carrying capacity of a stud increases significantly whenever one- or two-side sheathing is used, although the latter is significantly more effective. It is also dependent upon the type of board used. Whereas panels with either OSB or CPB boards have nearly identical load carrying capacity, panels with CSB boards are considerably weaker. Screw spacing affects the load carrying capacity of a stud. When the screw spacing on the middle stud in panels with one-side sheathing is reduced from 600 mm to 300 mm, its load carrying capacity increases by 14.5 %, 20.6% and 94.2% for OSB, CPB and CSB, respectively.

Dynamics of Streptococcus pneumoniae Serotypes Causing Acute Otitis Media Isolated from Children with Spontaneous Middle-Ear Drainage over a 12-Year Period (1999–2010) in a Region of Northern Spain

10 p.