Propagation of sound pulses in a semiinfinite stratified medium

We consider the propagation of sound pulses due to a line source in the inhomogeneous, semi-infinite mediumy ≥ 0 with the boundary conditionφ=0 or?φ/(?y)=0 aty=0, whereφ is the acoustic velocity potential. We suppose that the velocity of wave propagation,c, is given byc ^?2=p ?qe ^?ay , wherep, q, α are real and positive andp>q. The method of dual integral transformation is used. The solution in terms of pulse propagation modes yields the diffracted pulse and the method of steepest descents gives the geometrical acoustic field.     

Diffraction of sound pulses by a rigid cylinder in an inhomogeneous medium

We consider the problem of scattering of two-dimensional sound pulses by a rigid circular cylinder embedded in a cylindrically stratified inhomogeneous medium. The line source is parallel to the axis of the cylinder. It is assumed that the velocity of soundc is given byc ^?1=pr ^q, wherep andq are real constants andp>0. The method of dual integral transformation developed by Friedlander is used. The solution in terms of pulse propagation modes gives the diffracted pulse and the method of steepest descents yields the geometrical acoustic field.     

Preparation and photocatalytic properties of hybrid core–shell reusable CoFe2O4–ZnO nanospheres

Magnetically separable and reusable core–shell CoFe₂O₄–ZnO photocatalyst nanospheres were prepared by the hydrothermal synthesis technique using glucose derived carbon nanospheres as the template. The morphology and the phase of core–shell hybrid structure of CoFe₂O₄–ZnO were assessed via TEM, SEM and XRD. The magnetic composite showed high UV photocatalytic activity for the degradation of methylene blue in water. The photocatalytic activity was found to be ZnO shell thickness dependent. Thicker ZnO shells lead to higher rate of photocatalytic activity. Hybrid nanospheres recovered using an external magnetic field demonstrated good repeatability of photocatalytic activity. These results promise the reusability of the hybrid nanospheres for photocatalytic activity.     

Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

Growth mechanism and optical property of CdS nanoparticles synthesized using amino-acid histidine as chelating agent under sonochemical process

Using amino-acid histidine as chelating agent, CdS nanoparticles have been synthesized by sonochemical method. It is found that by varying the ultrasonic irradiation time, we can tune the band gap and particle size of CdS nanoparticles. The imidazole ring of histidine captures the Cd ions from the solution, and prevents the growth of the CdS nanoparticles. The deviation in the linear relation in between cube of radius of nanoparticles and ultrasonic irradiation time confirms the growth of CdS nanoparticles occur via two process; one is the diffusion process of the reactants as well as reaction at the surface of the crystallite. CdS nanoparticles synthesized using histidine as organic chelating agent have band edge emission at 481 nm and have greater photoluminescence intensity with blue-shift to higher energy due to typical quantum confinement effect.     

Hypersurfaces of a Finsler space with a special (<Emphasis Type="Italic">α</Emphasis>, <Emphasis Type="Italic">β</Emphasis>)-metric

In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient, one-pot synthesis of trithiocarbonates from the corresponding thiols using the Mitsunobu reagent

A novel Mitsunobu-based protocol has been developed for the synthesis of a variety of symmetrical and unsymmetrical trithiocarbonates from primary, secondary and tertiary thiols using carbon disulfide, in good to excellent yields. This protocol is mild and efficient compared to other reported methods.