Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

In this paper the authors study the boundedness for a large class of sublinear operators \({T_{\alpha}, \alpha \in [0,n)}\) generated by Calderón–Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces \({M_{p,\varphi}}\) . As an application of the above result, the boundeness of the commutator of sublinear operators \({T_{b,\alpha}, \alpha \in [0,n)}\) on generalized Morrey spaces is also obtained. In the case \({b \in BMO}\) and T _b,α is a sublinear operator, we find the sufficient conditions on the pair \({(\varphi_1,\varphi_2)}\) which ensures the boundedness of the operators \({T_{b,\alpha}, \alpha \in [0,n)}\) from one generalized Morrey space \({M_{p,\varphi_1}}\) to another \({M_{q,\varphi_2}}\) with 1/p ? 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on \({(\varphi_1,\varphi_2)}\) , which do not assume any assumption on monotonicity of \({\varphi_1, \, \varphi_2}\) in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.     

Comparison of morphology, stability and electrocatalytic properties of Ru0.3Ti0.7O2 and Ru0.3Ti0.4Ir0.3O2 coated titanium anodes

This paper presents the comparative study of two dimensionally stable anodes (DSA?) of nominal composition Ti/Ru_0.3Ti_0.7O₂ and Ti/Ru_0.3Ti_0.4Ir_0.3O₂, prepared by thermal decomposition of the chloride precursor mixtures at 450°C. The materials were studied by scanning electron microscopy (SEM), cyclic voltammetry and Tafel measurements to obtain information about their surface and electrocatalytic properties towards Cl₂ evolution reaction. The stability of the prepared anodes was investigated under accelerated conditions. It has been observed that the coating surface with 30% mole IrO₂ possesses more compact structure with less cracks. Furthermore, it had excellent electrocatalytic activity for the chlorine evolution. Accelerated stability tests showed long lifetime for Ti/Ru_0.3Ti_0.4Ir_0.3O₂ electrode. On the other hand, besides the excellent improvement of catalytic activity, the stability of the ternary oxide electrode increases compared to the binary oxide one. The deactivation rate appeared to be a consequence of the different morphology and synergetic effects of the prepared coatings.     

A new way to evaluate the Probability and Fresnel integrals

In this article, we show how Laplace Transform may be used to evaluate variety of nontrivial improper integrals, including Probability and Fresnel integrals. The algorithm we have developed here to evaluate Probability, Fresnel and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals into evaluation of improper integrals of the corresponding Laplace transform, which in many cases are much easier.     

Synthesis,Characterization and Ion Exchange Properties of a New Composite of Inorganic Ion Exchanger: Polyacrylonitrile Cerium(IV) Molybdophosphate

In this work, the synthesis of the composite of cerium(IV) molybdophosphate (CMP) and polyacrylonitrile (PAN) was reported (CMP‐PAN). The material has been characterized by elemental and spectral (FT‐IR), X‐ray and thermal (TGA) analysis. Also the size analysis of the composite was done by scanning electron microscopy (SEM). Its chemical stability in acidic, basic and saline solutions and radiation stability up to 100 kGy total expose dose were assessed. Whereas the synthesized composite has ion exchange properties, its ion exchange capacity and behavior toward several metal ions were also investigated. Further, the distribution coefficients of the metal ions were calculated. Finally, the ability of the synthesized CMP‐PAN composite for the decontamination of low level liquid waste (LLLW) was investigated.     

A perspective view of top‐down proteomics in snake venom research

The venom produced by snakes contains complex mixtures of pharmacologically active proteins and peptides which play a crucial role in the pathophysiology of snakebite diseases. The deep understanding of venom proteomes can help to improve the treatment of this “neglected tropical disease” (as expressed by the World Health Organization [WHO]) and to develop new drugs. The most widely used technique for venom analysis is liquid chromatography/tandem mass spectrometry (LC/MS/MS)‐based bottom‐up (BU) proteomics. Considering the fact that multiple multi‐locus gene families encode snake venom proteins, the major challenge for the BU proteomics is the limited sequence coverage and also the “protein inference problem” which result in a loss of information for the identification and characterization of toxin proteoforms (genetic variation, alternative mRNA splicing, single nucleotide polymorphism [SNP] and post‐translational modifications [PTMs]). In contrast, intact protein measurements with top‐down (TD) MS strategies cover almost complete protein sequences, and prove the ability to identify venom proteoforms and to localize their modifications and sequence variations.     

Solution of Poisson’s equation by analytical boundary element integration

The solution of Poisson’s equation is essential for many branches of science and engineering such as fluid-mechanics, geosciences, and electrostatics. Solution of two-dimensional Poisson’s equations is carried out by BEM based on Galerkin Vector Method in which the integrals that appear in the boundary element method are expressed by analytical integration. In this paper, the Galerkin vector method is developed for more general case than presented in the previous works. The integrals are computed for constant and linear elements in BEM. By employing analytical integration in BEM computation, the numerical schemes and coordinate transformations can be avoided. The presented method can also be used for the multiple domain case. The results of the analytical integration are employed in BEM code and the obtained analytical expression will be applied to several examples where the exact solution exists. The produced results are in good agreement with the exact solution.     

Novel and efficient synthesis of triazolobenzodiazepine analogues through the sequential Ugi 4CR-click-N-arylation reactions

An efficient approach for the synthesis of N-alkyl-2-aryl-2-(6-oxo-4H-benzo[f][1,2,3]triazolo[1,5-a][1,4]diazepin-5(6H)-yl)acetamides is described. The protocol involves Ugi four-component reaction of 2-bromobenzoic acid, propargylamine, aldehydes and isocyanides followed by in situ sequential click reaction of azide ion with triple bond and N-arylation reaction to afford desired products in good to excellent yields.     

On the structure of dithizone

The ¹³C NMR spectrum of dithizone, unlike that of its oxygen analogue, shows only five different types of carbon atom. The ¹³C chemical shift of the C?S group in dithizone is only 7 ppm to lower field of that of the C?O moiety in its analogous compound. The results can be rationalized by consideration of tautomeric equilibria which lead to C_2v time-averaged symmetry.     

An efficient four-component reaction for the synthesis of chromeno[4,3-<Emphasis Type="Italic">b</Emphasis>]quinolone derivatives

Chromenoquinolines have been prepared via an efficient one-pot, multi-component reaction of 4-hydroxy coumarin, aqueous ammonia, dimedone and different aldehydes.