Generalized Bessel functions: Theory and their applications

This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.     

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.     

Graphene domain boundaries on Pt(111) as nucleation sites for Pt nanocluster formation

The growth of Pt nanoclusters on a graphene layer on Pt(111) was studied with ultra high vacuum scanning tunneling microscopy. Different periodicities in the moiré patterns of the graphene layer are observed corresponding to different orientations with respect to the Pt(111) lattice. Various graphene orientations are possible because of a relatively weak graphene–Pt interaction. Following Pt deposition onto the graphene-covered surface, small Pt nanoclusters are observed to preferentially form along the moiré domain boundaries. The weak interaction of graphene with Pt(111) leads to a weak corrugation in the superlattice compared to other transition metals, such as Ru, but it is found even this weak corrugation is sufficient to serve as a template for the formation of mono-dispersed one-dimensional Pt nanocluster chains. These Pt nanoclusters are relatively stable and only undergo agglomeration at annealing temperatures above 600 K.     

A MILD METHOD FOR CONVERSION OF ALCOHOLS TO DIALKYL SULFITES BY USE OF Na2SO3/SOCl2

Alcohols are easily converted to their corresponding dialkyl sulfite under mild reaction conditions using Na₂SO₃/SOCl₂ in moderate to good isolated yields.     

A Comparison Between Full-COLD PCR/HRM and PCR Sequencing for Detection of Mutations in Exon 9 of PIK3CA in Breast Cancer Patients

Applied Biochemistry and Biotechnology - One of the most common somatic mutations in breast cancer is found in PIK3CA with a prevalence rate of 18–45%. Different variants of this gene are...     

Na 2 SO 3 /SOCl 2 , an Efficient Reagent for the Dehydration of Aldoximes to Nitriles

Aldoximes undergo rapid dehydration with sodium sulfite, thionyl chloride, under mild reaction condition to afford nitriles in excellent isolated yields. Dehydration reactions were performed in solvent and under solvent free conditions.