On expansion problems involving addition theorems and Kapteyn series

AbstractThe paper deals with general expansions which give as special cases new results involving the Bessel functions, Jacobi, ultraspherical, and Laguerre polynomials, where the degree of the function is incorporated in the argument. In fact, the theorems unify and extend the Neumann-Gegenbauer expansion and its generalization by Fields and Wimp, Cohen, and others, the Kapteyn expansion theory, and the Kapteyn expansion of the second kind. New expressions are given for the Neumann-type degenerate form of a Gegenbauer addition theorem, the Feldheim expansions for the Jacobi and ultraspherical polynomials, and other expressions. Also of interest is the new method of proof, involving differential and integral operators

Comparison of articulate brachiopod nuclear and mitochondrial gene trees leads to a clade-based redefinition of protostomes (Protostomozoa) and deuterostomes (Deuterostomozoa)

Nuclear and mtDNA sequences from selected short-looped terebratuloid (terebratulacean) articulate brachiopods yield congruent and genetically independent phylogenetic reconstructions by parsimony, neighbor-joining and maximum likelihood methods, suggesting that both sources of data are reliable guides to brachiopod species phylogeny. The present-day genealogical relationships and geographical distributions of the tested terebratuloid brachiopods are consistent with a tethyan dispersal and subsequent radiation. Concordance of nuclear and mitochondrial gene phylogenies reinforces previous indications that articulate brachiopods, inarticulate brachiopods, phoronids and ectoprocts cluster with other organisms generally regarded as protostomes. Since ontogeny and morphology in brachiopods, ectoprocts and phoronids depart in important respects from those features supposedly diagnostic of protostomes, this demonstrates that the operational definition of protostomy by the usual ontological characters must be misleading or unreliable. New, molecular, operational definitions are proposed to replace the traditional criteria for the recognition of protostomes and deuterostomes, and the clade-based terms 'Protostomozoa' and 'Deuterostomozoa' are proposed to replace the existing terms 'Protostomia' and 'Deuterostomia'

Transient domain walls and lepton asymmetry in the Left-Right symmetric model

It is shown that the dynamics of domain walls in Left-Right symmetric models, separating respective regions of unbroken SU(2)_L and SU(2)_R in the early universe, can give rise to baryogenesis via leptogenesis. Neutrinos have a spatially varying complex mass matrix due to CP-violating scalar condensates in the domain wall. The motion of the wall through the plasma generates a flux of lepton number across the wall which is converted to a lepton asymmetry by helicity-flipping scatterings. Subsequent processing of the lepton excess by sphalerons results in the observed baryon asymmetry, for a range of parameters in Left-Right symmetric models.Comment: v2 version accepted for publication in Phys. Rev. D. Discussion in Introduction and Conclusion sharpened. Equation (12) corrected. 16 pages, 3 figure files, RevTeX4 styl

First-principles study of stability and vibrational properties of tetragonal PbTiO_3

A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.Comment: 8 pages, two-column style with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ag_pbt

No turning,a Mouse Mutation Causing Left–Right and Axial Patterning Defects

AbstractPatterning along the left/right axes helps establish the orientation of visceral organ asymmetries, a process which is of fundamental importance to the viability of an organism. A linkage between left/right and axial patterning is indicated by the finding that a number of genes involved in left/right patterning also play a role in anteroposterior and dorsoventral patterning. We have recovered a spontaneous mouse mutation causing left/right patterning defects together with defects in anteroposterior and dorsoventral patterning. This mutation is recessive lethal and was namedno turning (nt)because the mutant embryos fail to undergo embryonic turning.ntembryos exhibit cranial neural tube closure defects and malformed somites and are caudally truncated. Development of the heart arrests at the looped heart tube stage, with cardiovascular defects indicated by ballooning of the pericardial sac and the pooling of blood in various regions of the embryo. Interestingly, inntembryos, the direction of heart looping was randomized.Nodalandlefty,two genes that are normally expressed only in the left lateral plate mesoderm, show expression in the right and left lateral plate mesoderm.Lefty,which is normally also expressed in the floorplate, is not found in the prospective floorplate ofntembryos. This suggests the possibility of notochordal defects. This was confirmed by histological analysis and the examination ofsonic hedgehog, Brachyury,andHNF-3βgene expression. These studies showed that the notochord is present in the earlyntembryo, but degenerates as development progresses. Overall, these findings support the hypothesis that the notochord plays an active role in left/right patterning. Our results suggest thatntmay participate in this process by modulating the notochordal expression ofHNF-3β

Towards the Theory of Cosmological Phase Transitions

We discuss recent progress (and controversies) in the theory of finite temperature phase transitions. This includes the structure of the effective potential at a finite temperature, the infrared problem in quantum statistics of gauge fields, the theory of formation of critical and subcritical bubbles and the theory of bubble wall propagation.Comment: 50 p

Ab-initio study of BaTiO3 surfaces

We have carried out first-principles total-energy calculations of (001) surfaces of the tetragonal and cubic phases of BaTiO3. Both BaO-terminated (type I) and TiO2-terminated (type II) surfaces are considered, and the atomic configurations have been fully relaxed. We found no deep-gap surface states for any of the surfaces, in agreement with previous theoretical studies. However, the gap is reduced for the type-II surface, especially in the cubic phase. The surface relaxation energies are found to be substantial, i.e., many times larger than the bulk ferroelectric well depth. Nevertheless, the influence of the surface upon the ferroelectric order parameter is modest; we find only a small enhancement of the ferroelectricity near the surface.Comment: 8 pages, two-column style with 4 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#pad_sur

Phase transitions in BaTiO3_3 from first principles

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultra-soft pseudopotential calculations. This approach is applied to BaTiO$_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder vs.\ displacive character of the transitions and the roles played by different interactions are discussed.Comment: 13 page

Electroweak Baryogenesis in Non-minimal Composite Higgs Models

We address electroweak baryogenesis in the context of composite Higgs models, pointing out that modifications to the Higgs and top quark sectors can play an important role in generating the baryon asymmetry. Our main observation is that composite Higgs models that include a light, gauge singlet scalar in the spectrum [as in the model based on the symmetry breaking pattern SO(6)/SO(5)], provide all necessary ingredients for viable baryogenesis. In particular, the singlet leads to a strongly first-order electroweak phase transition and introduces new sources of CP violation in dimension-five operators involving the top quark. We discuss the amount of baryon asymmetry produced and the experimental constraints on the model.Comment: 15 pages, 7 figure