Identities for the Widder transform and transforms with Bessel function kernels

In the present paper, we consider the classical Widder transform, the H_ν-transform, the K_ν-transform, and the Y_ν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms.     

A general criterion to determine the number of change-points

A general criterion is proposed to determine the number K of the change-points in a parametric nonlinear multi-response model. Schwarz criterion is a particular case. The change-points depend on regressor values and not on instant of measure. We prove that the proposed estimator for K is consistent. Simulation results, using Monte Carlo technique, for nonlinear models which have numerous applications, support the relevance of the theory.     

Design and analysis of nano-deep corrugated waveguide grating-based dual-resonant filters in visible and infra-red regions

A theoretical analysis of nano-deep corrugated long-period waveguide gratings on a SU-8 polymer-based channel waveguide with NOA61 optical epoxy coated upper- and lower cladding is presented. The transmission spectra of the gratings show strong rejection bands both at visible (at wavelength region of 450?460 nm) and infra-red (at wavelength region of 1530?1540 nm) regions when a grating period of ?68 μm with optimized grating tooth height is considered. Phase-matching graphs are studied to find the relationship between resonance wavelength and grating period. These results show that the grating parameters significantly affect the characteristics of transmission spectra as well as the resonance wavelength of the grating. Long-period waveguide grating-based band pass filter made by use of same polymer materials are also designed and analyzed. These types of waveguide grating-based filters can widely be used for visible and infra-red wavelength sensing applications.     

Diophantine approximation in characteristiep

We study diophantine approximations to algebraic functions in characteristicp. We improve a theorem of Osgood, and give two classes of examples showing that this result is nearly sharp. One of these classes exhibits a new phenomenon.     

beta-Barrel transmembrane proteins: Geometric modelling, detection of transmembrane region, and structural properties

The location of the membrane lipid bilayer relative to a transmembrane protein structure is important in protein engineering. Since it is not present on the determined structures, it is essential to automatically define the membrane embedded protein region in order to test mutation effects or to design potential drugs. beta-Barrel transmembrane proteins, present in nature as outer membrane proteins (OMPs), comprise one of the two transmembrane protein fold classes. Lately, the number of their determined structures has increased and this enables the implementation and evaluation of structure-based annotation methods and their more comprehensive study. In this paper, we propose two new algorithms for (i) the geometric modelling of beta-barrels and (ii) the detection of the transmembrane region of a beta-barrel transmembrane protein. The geometric modelling algorithm combines a non-linear least square minimization method and a genetic algorithm in order to find the characteristics (axis, radius) of a shape with axial symmetry which best models a beta-barrel. The transmembrane region is detected by profiling the external residues of the beta-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. TbB-Tool implements these algorithms and is available in . A non-redundant set of 22 OMPs is used in order to evaluate the algorithms implemented and the results are very satisfying. In addition, we quantify the abundance of all amino acids and the average hydrophobicity for external and internal beta-stranded residues along the axis of beta-barrel, thus confirming and extending other researchers' results.     

Classification of solutions of elliptic equations arising from a gravitational O(3) gauge field model

In this paper, we study an elliptic equation arising from the self-dual Maxwell gauged $O(3)$ sigma model coupled with gravity. When the parameter τ equals 1 and there is only one singular source, we consider radially symmetric solutions. There appear three important constants: a positive parameter a representing a scaled gravitational constant, a nonnegative integer $N_1$ representing the total string number, and a nonnegative integer $N_2$ representing the total anti-string number. The values of the products $a{N}_1,a{N}_2\in [0,\infty )$ play a crucial role in classifying radial solutions. By using the decay rates of solutions at infinity, we provide a complete classification of solutions for all possible values of $a{N}_1$ and $a{N}_2$. This improves previously known results.     

On the Hénon equation with a Neumann boundary condition: Asymptotic profile of ground states

Consider the Hénon equation with the homogeneous Neumann boundary condition

$?\mathrm{\Delta }u+u=|x{|}^{\alpha }{u}^p,u>0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{ on }?\mathrm{\Omega },$

where $\mathrm{\Omega }?B(0,1)?{\mathbb{R}}^N,N\ge 2$ and $?\mathrm{\Omega }\cap ?B(0,1)\ne ?$. We are concerned on the asymptotic behavior of ground state solutions as the parameter $\alpha \to \infty$. As $\alpha \to \infty$, the non-autonomous term $|x{|}^{\alpha }$ is getting singular near $|x|=1$. The singular behavior of $|x{|}^{\alpha }$ for large $\alpha >0$ forces the solution to blow up. Depending subtly on the $(N?1)?$dimensional measure $|?\mathrm{\Omega }\cap ?B(0,1){|}_{N?1}$ and the nonlinear growth rate p, there are many different types of limiting profiles. To catch the asymptotic profiles, we take different types of renormalization depending on p and $|?\mathrm{\Omega }\cap ?B(0,1){|}_{N?1}$. In particular, the critical exponent $2_{?}=\frac{2(N?1)}{N?2}$ for the Sobolev trace embedding plays a crucial role in the renormalization process. This is quite contrasted with the case of Dirichlet problems, where there is only one type of limiting profile for any $p\in (1,2^{?}?1)$ and a smooth domain Ω.     

A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth.As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schr¨odinger equations.