Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.     

Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.     

Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.     

Selective nucleophilic additions to poly(methacrylate)s containing isothiocyanate moieties in the side chains and their application in cross‐linking

Reactivity of isothiocynate moieties in the side chain of polymethacrylate with amine, alcohol, or thiol was investigated, and the reactions were applied to preparation of networked polymers. Isothiocyanate of polymer side chain rapidly reacted with amines without a catalyst, to give the corresponding thioureas. However, it did not react with alcohols or thiols under the same conditions. Using 1,8‐diazabicyclo[5.4.0]undec‐7‐ene (DBU) as a catalyst, addition of alcohols or thiols to the isothiocyanate proceeded smoothly. Addition of amines, alcohols, and thiols to isothiocyanates moiety contained in the side chain of polymethacrylate also proceeded readily with or without the catalyst, respectively, to effectively give the corresponding side chain modified polymers. Occurrence of these additions was confirmed by ¹H NMR and IR measurements. Glass transition temperatures and thermal decomposition temperatures of the obtained polymers were investigated by differential scanning calorimetry and thermogravimetric analysis. Networked polymers were easily prepared by addition of 1,6‐hexamethylenediamine or hexamethylene glycol to the polymethacrylate having isothiocyanato groups. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1832–1842     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

A Bertini type theorem for pencils over finite fields

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.