Some Generalization for an Operator Which Preserving Inequalities Between Polynomials

For a polynomial p(z) of degree n which has no zeros in |z| 1, Dewan et al.,(K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363(2010), 38–41) established zp′(z) +nβ2p(z) ≤n2{( β2 + 1+β2)max|z|=1|p(z)|-( 1+β2- β2)min|z|=1|p(z)|},for any complex number β with |β|≤ 1 and |z| = 1. In this paper we consider the operator B, which carries a polynomial p(z) into B[ p(z)] := λ0p(z) + λ1(nz2)p′(z)1!+ λ2(nz2)2 p′′(z)2!,where λ0, λ1, and λ2are such that all the zeros of u(z) = λ0+c(n,1)λ1z+c(n,2)λ2z2lie in the half plane |z| ≤ |z-n/2|. By using the operator B, we present a generalization of result of Dewan. Our result generalizes certain well-known polynomial inequalities.     

LINEAR DILATATION OF QUASIREGULAR MAPPINGS IN SPACE

1 IntroductionIn this paPert we use the fOlowing notatioll for Euclidean n-space m and r = Rn U {oo}.Unit vectors in the directions of the rectangular coordinate axes in m are denoted by e1,', en.The open ball and sphere with center x and radius r > 0 are written as B"(x, r) and S"--'(x, r),respectively. We sometimes write Bn (r) = Bn (0, r), S"--'(r) = Sn-- 1 (0, r), Bn = B"(1), Sn-- 1 =sn-- '(1).Let f be a discrete and open maPping from a domain G of R" into R". Thenis called the l…     

二元Lagrange三角插值多项式在Orlicz空间内的逼近

研究了二元函数用一种组合型的三角插值多项式算子逼近的问题.借助连续模这一工具,给出了这类三角插值多项式在Orlicz空间内的逼近定理.     

MICROSTRUCTURE AND MECHANICAL PROPERTIES OF ALUMINA COATINGS PLASMA-SPRAYED AT DIFFERENT SUBSTRATE TEMPERATURES

Alumina coatings are prepared by atmospheric plasma spraying through controlling the substrate temperature during spraying. The changes in microstructure and mechanical properties of the coatings prepared at different substrate temperatures are examined. The hardness and the elastic modulus of the coatings are measured by indentation methods. The results show that interlamellar bonding in the coatings is significantly improved with increasing the substrate temperature. Moreover, long through-thickness colum...     

STANCU POLYNOMIALS BASED ON THE Q-INTEGERS

A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper.Moreover,the shape-preserving and convergence properties of these polynomials are also investigated.     

Clove essential oil emulsion-filled cellulose nanofiber hydrogel produced by high-intensity ultrasound technology for tissue engineering applications

High-intensity ultrasound (HIUS) was used to produce emulsion-filled cellulose nanofiber (CNF) hydrogel using clove essential oil (0.1, 0.5 and 1.0 wt%) as dispersed phase towards tissue engineering applications. The novel encapsulating systems obtained using HIUS specific energy at the levels of 0.10, 0.17, and 0.24 kJ/g were characterized by oil entrapment efficiency, microstructure, water retention value, color parameters, and viscoelastic properties. Freeze-dried emulsion-filled CNF hydrogels were characterized by porosity and swelling capacity. In addition, human gingival fibroblast cell cytocompatibility tests were performed to evaluate their potential applications as tissue engineering scaffold. The clove essential oil content strongly affected the oil entrapment efficiency, water retention value, color difference and whiteness of the prepared emulsion-filled CNF hydrogel. And, the HIUS energy only affected the yellowness of the emulsion-filled CNF hydrogel. Via HIUS processing, the CNF hydrogel successfully acted as a continuous phase in the emulsion-filled gel system with maximum oil entrapment efficiency of 34% when 0.5 wt% clove essential oil was added to the system. The encapsulating systems had predominantly gel-like property with maximum elastic modulus of 411 Pa. Furthermore, the emulsion-filled CNF hydrogels with the addition of clove essential oil up to 0.5 wt% indicated good cell viability rates (74–101%) to human gingival fibroblast cells. The newly developed clove essential oil emulsion-filled CNF hydrogel shows desirable cytocompatibility characteristics and can be considered as an alternative scaffold for tissue engineering applications.     

Spring-network model of red blood cell: From membrane mechanics to validation

Red blood cell membrane is highly elastic and proper modeling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. Inseparable and often some of the most difficult parts of modeling process are verification and validation. In this work, we present a revised model, which uses a spring network to represent the cell membrane immersed in a fluid and has been successfully used in blood flow simulations. We demonstrate the validation steps by first deriving the theoretical relations between the bulk properties of elastic membranes—shear modulus and area compressibility modulus—and parameters of the model that enter the nonlinear stretching and local area conservation computational moduli. We verify the theoretically derived relations using computer simulations of deformable triangular mesh. We calibrate the model by performing a computational version of the optical tweezers experiment. And finally, we validate the modeled cell behavior by investigating the cell rotation frequency when it is subjected to shear flow and cell deformation in narrow channels. The supplementary material contains an extensive dataset that can be used for setting different elastic properties for each cell in simulations of dense suspensions, while still conforming to the biological data. This work contains a complete model development process: From modelling of basic mechanical concepts (the spring network) and advanced biomechanical concepts (such as elasticity of the membrane), through calibration process towards the final stage of model validation.     

Effects of water freezing on the mechanical properties of nafion membranes

Most of the research efforts on Nafion have been devoted to the study of the perfluorinated ionomer membranes at optimal conditions for the desired applications, such as high temperature and low relative humidity for polymer electrolyte membrane fuel cells (PEM FC). In view of the possible changes induced by the freezing of water in the structure of Nafion and considering that in cold start conditions of a PEM FC device, Nafion needs to work also below 273 K, we measured the Young's modulus (Y) and the elastic energy dissipation (tan δ) in the temperature range between 90 and 470 K and the stress–strain curves between 300 and 173 K. The measurements reported here indicate that the mechanical properties of wet Nafion membrane change dramatically with temperature, that is, from a rubber‐like behavior at room temperature to a brittle behavior below 180 K. Moreover, we observed that the freezing of the nanoconfined water is complete only below 180 K, as indicated by a large increase of the Young's modulus. Between 180 and 300 K, the large values of tan δ suggest the occurrence of friction between the liquid water bound to the walls of the hydrophilic domains and the solid ice residing in the center of channels. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Mesoscopic superelasticity,superplasticity,and superrigidity

Atomic-undercoordination-induced local bond contraction,bond strength gain,and the associated temperature （T）-dependent atomic-cohesive-energy and binding-energy-density are shown to originate intrinsically the exotic paradox of superplasticity,superelasticity,and superrigidity demonstrated by solid sizing from monatomic chain to mesoscopic grain.The paradox follows these relationships:（ε（K,T）y（K,T）σ（K,T））∝(exp(B/△T_mk),(η₁△T_mk)d～（-3）,[1+AK～（-2/2）exp(△T_mk/T)]△T_mkd～（-3）),（Plastic strain）（Elastic modulus）（Yield stress,IHPR）where A,B,η1,d and△T_mk=Tm（K） Tare size （K）-dependent physical parameters.Tm （K） is the melting point.Mechanical work hardening during compressing and self-heating during stretching modulate the measured outcome extrinsically.Superplasticity dominates in the solid-quasimolten-liquid transition state.The competition between the accumulation and annihilation of dislocations activates the inverse Hall-Petch relationship.Therefore,it is essential for one to discriminate the intrinsic competition between the local bond energy density gain and the atomic cohesive energy loss from the extrinsic factors of pressure and temperature in dealing with atomistic mechano-thermo dynamics.