Ultrastructural description of spermiogenesis within the Mediterranean Gecko, Hemidactylus turcicus (Squamata: Gekkonidae)

We studied spermiogenesis in the Mediterranean Gecko, Hemidactylus turcicus, at the electron microscope level and compared to what is known within other Lepidosaurs. In H. turcicus germ cells are connected via cytoplasmic bridges where organelle and cytoplasm sharing is observed. The acrosome develops from merging transport vesicles that arise from the Golgi and subsequently partition into an acrosomal cap containing an acrosomal cortex, acrosomal medulla, perforatorium, and subacrosomal cone. Condensation of DNA occurs in a spiral fashion and elongation is aided by microtubules of the manchette. A nuclear rostrum extends into the subacrosomal cone and is capped by an epinuclear lucent zone. Mitochondria and rough endoplasmic reticulum migrate to the posterior portion of the developing germ cell during the cytoplasmic shift and the flagellum elongates. Mitochondria surround the midpiece as the anlage of the annulus forms. The fibrous sheath begins at mitochondrial tier 3 and continues into the principal piece. Peripheral fibers associated with microtubule doublets 3 and 8 are grossly enlarged. During the final stages of germ cell development spermatids are wrapped with a series of Sertoli cell processes, which exhibit ectoplasmic specializations and differing cytoplasmic consistencies. The results observed here corroborate previous studies, which show the conservative nature of sperm morphology. However, ultrastructural character combinations specific to sperm and spermiogenesis seem to differ among taxa. Further studies into sperm morphology are needed in order to judge the relevance of the ontogenic changes recorded here and to determine their role in future studies on amniote evolution.     

Approximation of some Feller semigroups associated with a modification of Szász–Mirakjan–Kantorovich operators

We deepen the study of a sequence (C _n ) _n≧1 of positive linear operators, first introduced in [4], that generalize the classical Szász–Mirakjan–Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the C ₀-semigroups generated by the second order differential operator $$V_l(u)(x)=xu''(x)+\frac{l}{2} u'(x)\quad (x \geqq 0,\ l \in [0, 2]) $$ on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C _n ’s.     

Seed oil triglyceride profiling of thirty-two hybrid grape varieties

Triglyceride profile of seed oil samples from 32 hybrid grape varieties not studied before was investigated. A new method for the analysis of triacylglycerols (TAGs) has been developed based on the direct infusion in the electrospray ionization (ESI) source and employing tetrahydrofuran/methanol/water (85:10:5 v|v|v) as solvent; the formation of [M?+?Na](+) ions in high yield has been observed. TAGs were identified by ESI-tandem mass spectrometry analysis, and the matrix-assisted-laser-desorption-ionization and time-of-flight profile of samples was determined. Six were the principal TAGs identified in seed oil: trilinolein (LLL) was the most abundant (43%), followed by dilinoleoyl-oleoylglycerol (LOL, 23%), and dilinoleoyl-palmitoylglycerol (LPL, 15%). Compounds present in lower concentration were LSL and LOO (11%), LOP (6%), and LSP (2%). Compared with seed oils produced from V. Vinifera grapes, some significant differences in the relative abundances of TAGs were found, in particular hybrid grape seed oils showed higher LOL and lower LPL content, respectively. Among the samples studied, a particularly high content of LLL (rich in unsaturated fatty acids) was found in seed oils from two red varieties. Copyright ? 2012 John Wiley & Sons, Ltd.     

Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any <Emphasis Type="Italic">κ</Emphasis>-value

The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.     

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = $ \tilde l $ = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.     

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schr?dinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.      

On the jumping conics of a semistable rank two vector bundle on P2

Stromme (see [S], (1.7)) introduced the notion of jumping conic of a normalized semistable rank two vector bundle E on ℙ² and he remarked that the locus of jumping conics of E has codimension ≤3+2c₁(E), with equality for general E. Here we introduce a concept of jumping conic of a semistable rank two vector bundle on ℙ² (see (I.1)) by generalizing the notion of jumping line of the second kind introduced by Hulek in [H]. Our definition agrees with Stromme's for c₁=−1, but not for c₁=0. In contrast with the case of jumping lines, where we have a different behaviour in the case c₁ even or c₁ odd, the set of jumping conics according to our definition is always a divisor (possibly empty) in the ℙ⁵ of all conics of ℙ² (see th. (I.8)), whose degree depends on c₂(E).     

On a superadditivity property of Gram’s determinant

Summary Some superadditivity properties are given for Gram determinants involving inner products on a linear space.     

Hyperbolic systems of conservation laws with some special invariance properties

The Euler equations of fluid dynamics are an example of a very special class of nonlinear, hyperbolic systems of conservation laws, in particular those satisfying conditions of reflection and Galilean invariance. These invariance properties are directly responsible for several of the attractive structural features of this system.