On the rearrangement estimates and the boundedness of the generalized fractional integrals associated with the Laplace-Bessel differential operator

We introduce the generalized fractional integrals (generalized B-fractional integrals) generated by the Δ _B Laplace-Bessel differential operator and give some results for them. We obtain O’Neil type inequalities for the B-convolutions and give pointwise rearrangement estimates of the generalized B-fractional integrals. Then we get the L _p,γ -boundedness of the generalized B-convolution operator, the generalized B-Riesz potential and the generalized fractional B-maximal function. Finally, we prove a sharp pointwise estimate of the nonincreasing rearrangement of the generalized fractional B-maximal function. V. S. Guliyev was partially supported by the grant of INTAS (Nr. 05-1000008-8157). Z. V. Safarov was partially supported by INTAS YS Post Doctoral Fellowship (Nr. 05-113-4671).     

Synthesis of some 3‐aryl‐1H‐isochromene‐1‐thiones

A rapid microwave‐accelerated thionation of some 3‐substitued isocoumarins to corresponding 1‐thio‐isocoumarins was achieved employing Lawesson's reagent under solventless conditions.     

Preparation of 5‐bromo‐6‐phenylimidazo[2,1‐b][1,3,4]thiadiazol‐2‐ylamines

The reaction of primary or secondary amines with 2,5‐dibromo‐6‐phenylimidazo[2,1‐b][1,3,4]‐thiadiazole ( 5 ) leads to a chemoselective replacement of the 2‐Br substituent. The process represents a convenient route to the corresponding 2‐ylamines 7a‐d . Hydrazine reacts in an analogous fashion ( 5 → 7e ). The structure determinations are based on an X‐ray crystal structure analysis and on one‐ and two‐dimensional NMR measurements.     

Thermostability of Cromobacterium viscosum lipase in AOT/isooctane reverse micelle

The thermostability of Cromobacterium viscosum lipase (EC 3.1.1.3) entrapped in AOT (sodium bis-[2-ethylhexyl] sulfosuccinate) reverse micelles was increased by the addition of short-chain polyethylene glycol (PEG 400). Two different approaches were considered: (1) the determination of half-life time and (2) the mechanistic analysis of deactivation kinetics. The half-life of lipase entrapped in AOT/isooctane reverse micelles with PEG 400 at 60 degrees C was 28 h, ninefold higher than that in reverse micelles without PEG 400. The lipase entrapped in both reverse micellar systems followed a series-type deactivation mechanism involving two first-order steps. The deactivation constant for the first step at 60 degrees C in PEG containing reverse micelles was 0.055 h!1, 11-fold lower than that in reverse micelles without PEG, whereas it remained almost constant for the second step. The inactivation energy of the lipase entrapped in reverse micelles with and without PEG 400 was 88.12 and 21.97 kJ/mol, respectively.     

Free energy landscape of receptor-mediated cell adhesion

Receptor-mediated cell adhesion plays a critical role in cell migration, proliferation, signaling, and survival. A number of diseases, including cancer, show a strong correlation between integrin activation and metastasis. A better understanding of cell adhesion is highly desirable for not only therapeutic but also a number of tissue engineering applications. While a number of computational models and experimental studies have addressed the issue of cell adhesion to surfaces, no model or theory has adequately addressed cell adhesion at the molecular level. In this paper, the authors present a thermodynamic model that addresses receptor-mediated cell adhesion at the molecular level. By incorporating the entropic, conformational, solvation, and long- and short-range interactive components of receptors and the extracellular matrix molecules, they are able to predict adhesive free energy as a function of a number of key variables such as surface coverage, interaction distance, molecule size, and solvent conditions. Their method allows them to compute the free energy of adhesion in a multicomponent system where they can simultaneously study adhesion receptors and ligands of different sizes, chemical identities, and conformational properties. The authors' results not only provide a fundamental understanding of adhesion at the molecular level but also suggest possible strategies for designing novel biomaterials.     

Experimental study of ultrasmall-angle scattering of electron bremsstrahlung gamma-quanta (<Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis></Subscript> = 11.8 MeV)

The study of the angular distribution of electron bremsstrahlung γ-quanta scattered from the reflector surface through an angle of 166 μrad reveals the emergence of total internal reflection of γ quanta with an energy E _γ ≤ 300 keV.     

Microstructure and mechanical behavior of UFG copper processed by ECAP following different processing regimes

Commercially pure (99.9%) copper was severe plastically deformed by equal-channel angular pressing (ECAP) following route-Bc in three different processing regimes in order to obtain ultrafine-grained (UFG) microstructures leading to improved mechanical properties. In regime-1, the billets were processed at room temperature up to eight passes. The billets were processed at 200°C up to eight passes in regime-2. Regime-3 is a hybrid regime by which the billets were deformed at 200°C up to four passes first, and these billets were then processed at room temperature for one, two and four passes. In all regimes, the ECAP processing results in a refinement of the conventionally grained (CG) initial microstructure of copper down to sub-micron level leading to a great improvement in the strength as compared to CG copper. Among the regimes applied, regime-3 was found to be the best regime for improvement in strength along with adequate ductility. The samples showed more than eight times increases in yield strength after processing in regime-3 for 4?+?4 passes, from 47?MPa for CG copper to about 408?MPa for the UFG sample. Such improvement in strength was accompanied by a 16.9% total elongation and 6% uniform elongation. The processing in regime-2 resulted in the best elongation to failure of about 22% after eight passes, but it gave the lowest strength values among others.     

On holomorphic solutions of some boundary-value problems for second-order elliptic operator differential equations

In the class of holomorphic vector functions, we determine the conditions of solvability of the boundaryvalue problem for a class of second-order operator differential equations expressed in terms of the operator coefficients appearing both in the equation and in the boundary condition.     

Effect of monomer-treated inorganic fillers on mechanical,rheological, and thermal properties of LLDPE nanocomposites

This article discusses the role of nanoscale calcium carbonate (nCC) surface treatment in affecting the mechanical, rheological, and thermal properties of linear low-density polyethylene (LLDPE). The mechanical tests indicated that nCC could simultaneously reinforce and toughen LLDPE. In addition, the composite sample with methacrylic acid (MA)-treated nanoparticles shows further increased mechanical properties as compared to unmodified nanoparticles. In the presence of dicumyl peroxide (DCP), a small amount of MA could increase markedly the mechanical properties of LLDPE/nCC composites. The results of rheological property analysis indicated that the viscosity increased with increasing amount of the filler, especially at low shear rates, but showed a substantial reduction with increasing concentration of the reactive monomer. The thermal behavior of these materials is evaluated by differential scanning calorimetry and thermogravimetric analysis. The addition of a small amount of MA and DCP enhances the stabilization of the blends.     

Square-root dynamics of a giving up smoking model

The paper presents a new giving up smoking model for which interaction term is square root of potential and occasional smokers of model presented in Zaman (2011) [15]. First, we will show formulation of the model. Then we will discuss local and global stability of the model and its general solutions. The non-standard finite difference method (NSFD) is used to solve the new giving up smoking model. Both non-negativity and conservative law for differential equations system are discussed. Numerical results are presented graphically and compared well with those obtained by Runge–Kutta fourth-order method (RK4) and ODE45.