SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.

Electrical conductivities for four ternary electrolyte aqueous solutions with one or two ionic liquid components at ambient temperatures and pressure

This work provides a method to explore the transport property of the electrolyte aqueous solutions with one or two ionic liquids, especially focus on their electrical conductivity. The conductivities were measured for the ternary systems Na Cl–[C6mim][Cl](1-hexyl-3-methylimidazolium chloride)–H2O, [C6mim][BF4]–[C6mim][Cl]–H2O,Na NO3–[C6mim][BF4](1-hexyl-3-methylimidazolium tetrafluoroborate)–H2O, and [C4mim][BF4](1-butyl-3-methylimidazolium tetrafluoroborate)–[C6mim][BF4]–H2O, and their binary subsystems NaN O3–H2O, NaC l–H2O,[C6mim][BF4]–H2O, [C6mim][Cl]–H2O, and [C4mim][BF4]–H2O, respectively. The conductivities of the ternary systems were also determined using generalized Young's rule and semi-ideal solution theory in terms of the data of their binary solutions. The comparison showed that the two simple equations provide good predictions for conductivity of mixed electrolyte solutions and the mixed ionic liquid solutions based on the conductivity of their binary subsystems.

ANALYTICAL SOLUTION OF FILLING AND EXHAUSTING PROCESS IN PNEUMATIC SYSTEM

The filling and exhausting processes in a pneumatic system are involved with many factors, and numerical solutions of many partial differential equations are always adapted in the study of those processes, which have been proved to be troublesome and less intuitive. Analytical solutions based on loss-less tube model and average friction tube model are found respectively by using fluid net theory, and they fit the experimental results well. The research work shows that： Fluid net theory can be used to solve the analytical solution of filling and exhausting processes of pneumatic system, and the result of loss-less tube model is close to that of average friction model, so loss-less tube model is recommended since it is simpler, and the difference between filling time and exhausting time is determined by initial and final pressures, the volume of container and the section area of tube, and has nothing to do with the length of the tube.

Exact 3D Thermoelastic Solutions for a Penny-Shaped Crack in an Infinite Magnetoelectric Medium

Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.

The Transference Number

The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion(often a cation)is transported from one electrode to the other.The cation transference number is an important transport parameter that affects this rate.The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number.We emphasize the fact that this parameter is dependent on the reference frame used in the analysis;care must be taken when comparing values obtained from different sources to account for differences in reference frames.We present data obtained from a well-characterized electrolyte.We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method.We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery。

Fuzzy TOPSIS method to primary crusher selection for Golegohar Iron Mine(Iran)

Selection of the crusher required a great deal of design regarding to the mine planning. Selection of suitable primary crusher from all of available primary crushers is a multi-criterion decision making(MCDM) problem. The present work explores the use of technique for order performance by similarity to ideal solution(TOPSIS) with fuzzy set theory to select best primary crusher for Golegohar Iron Mine in Iran. Gyratory, double toggle jaw, single toggle jaw, high speed roll crusher, low speed sizer, impact crusher, hammer mill and feeder breaker crushers have been considered as alternatives. Also, the capacity, feed size, product size, rock compressive strength, abrasion index and application of primary crusher for mobile plants were considered as criteria for solution of this MCDM problem. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution(FPIS) and fuzzy negative ideal solution(FNIS). Results of our work based on fuzzy TOPSIS method show that the gyratory is the best primary crusher for the studied mine.

ON THE SOLUTIONS OF NAVIER-STOKES EQUATIONS AND THE THEORY OF HOMOGENEOUS ISOTROPIC TURBULENCE

The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed to obtain the axinlly symmetrical solution of theNavier-Stokes equations of motion in the form of an infinite set of nonlinear partial differen-tial equations of the second order. For the present we solve the zeroth order approximation.By using the method of Fourier transform, we get a nonlinear nitegro-differential equationfor the amplitude function in the wave number space.It is also the dynamical equation forthe energy spectrum. By choosing a suitable initial condition, we solve this equation numerically. The energyspectrum function and the energy transfer spectrum function thus calculated satisfy the spec-trum form of the karman-Howarth equation exactly. We Lave computed the energy spectrumfunction, the energy transfer function the decay of turbulent energy, the integral scale, Taylormicroscale, the double and triple velocity correlations on the whole range from the initialperiod to the final period of decay. As a whole all these calculated statistical physicalquantities agree with experiments very wall except a few cases with small discrepancies at largeseparations.

New applications of a generalized Hooke's law for second gradient materials

We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the author, following a previous suggestion of delrlsola et al. （2009）. The motivation was to find benchmark analytical solutions that can serve to grasp the physical foundations of second gradient elasticity laws for heterogeneous materials. The analytical solution of the circular beam problem presents the additional advantage to establish some nice properties on the unknown second gradient elastic moduli introduced by Enakoutsa （2014） model and the classical elasticity constants for both incompressible and compressible heterogeneous elastic materials. A framework to find the elastic moduli of the new model is also proposed.

SOLUTION TO A PARAMETRIC EQUATION IN TRANSPORT THEORY

In 1976, Ronen et al. raised the question of how to solve the new integrodifferential parameter equation with transport theory. So far there have only been some approximate calculations and numerical analyses about this question. Using functional analysis, this note discusses this question in a strict mathematical way, gives the parameter distribution in L^p space (1≤p≤+∞) with which the

RECIPROCAL THEOREM METHOD FOR SOLVING THE PROBLEMS OFBENDING OF THICK RECTANGULAR PLATES

In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner’s theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate withthree clamped edges and one free edge under umiformly distributed load is found byRTM, finally, we analyze numerical results of the sohution.

Large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations

We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM(Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general convergence result for viscosity solutions and adherence of the graph as t →∞.

Assumed stress quasi-conforming triangular element for couple stress theory

In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.

Quasi-periodic Solutions for the Derivative Nonlinear Schrdinger Equation with Finitely Differentiable Nonlinearities

The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.

FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRA-LEVIN EQUATIONS

In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.

Viscosities of ternary systems Y(NO_3)_3+La(NO_3)_3+H_2O,La(NO_3)_3+Ce(NO_3)_3+H_2O,La(NO_3)_3+Nd(NO_3)_3+H_2O and their binary subsystems at different temperatures

Viscosities were measured for the ternary systems Y（NO3）3＋La（NO3）3＋H2O, La（NO3）3＋Ce（NO3）3＋H2O, and La（NO3）3＋Nd（NO3）3＋ H2O and their binary subsystems Y（NO3）3＋H2O, La（NO3）3＋H2O, Ce（NO3）3＋H2O, and Nd（NO3）3＋H2O at 293.15, 298.15 and 308.15 K. The results were used to test the applicability of simple equations for the viscosity of the mixed solutions. The predictions agreed well with measured values, implying that the viscosities of the examined electrolyte solutions could be related to those of their constituent binary solutions using these simple equations.

EFFECT OF FRACTIONAL ORDER PARAMETER ON THERMOELASTIC BEHAVIORS IN INFINITE ELASTIC MEDIUM WITH A CYLINDRICAL CAVITY

The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement, temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.