Solution of the Matrix Second Semi-Tensor Product Equation A ∘ l X ∘ l B=C

In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time, the compatibility conditions, the sufficient and necessary conditions and the specific solution methods for the matrix solution are given. Secondly, we further consider the solvability of the second semi-tensor product equation of the matrix. For each part, several examples are given to illustrate the validity of the results.

Growth performance and physiological parameters of the second generation selected and control groups of Pinctada martensii

In May of 2007,the second generation selected （SS） and control （SC） groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals （60.0–75.0 mm at shell length） were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 （P 0.05）.The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group （P 0.05）.At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant （P 0.05）.At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group （P 0.05）.At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups （P 0.05）.The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.

ON NEWMAN-TYPE RATIONAL INTERPOLATION TO |x| AT THE CHEBYSHEV NODES OF THE SECOND KIND

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）

An Equation of Stirling Numbers of the Second Kind

In this paper, We propose and prove the following equation, where {3^n} is a stirling number of the second kind, when n ≥ 3 is given.

The second Eshelby problem and its solvability

It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities （cracks, pores, foreign particles）. From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomo- geneity. In this paper, we point out the impossibility to trans- form this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed

Grain growth simulation with the second phase particle pinning for heat-affected zone of microalloyed steel welds

The second phase particle dispersed in microalloyed steel has different effects on grain growth depending on their size and volume fiaction of the second phase particles which will change during welding thermal cycles. The particle coarsening and dissolution kinetics model was analyzed for continuous heating and cooling. In addition, based on experimental data, the coupled equation of grain growth was established by introducing limited size of grain growth with the consideration of the second phase particles pinning effects. Using Monte Carlo method based on experimental data model, the grain growth simulation for heat-affected zone of microalloyed steel welds was achieved. The calculating results were well in agreement with that of experiments.

Some Identities of the Higher-Order Type 2 Bernoulli Numbers and Polynomials of the Second Kind

We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.

The Lifting Scheme Based on the Second Generation Wavelets

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.

2014 The Second International Conference on Advanced Cloud and Big Data(CBD 2014)

Organizing ＆ Program CommitteesGeneral Conference Co-Chairs - Yi Pan, Geot,gta State umversity, USA - You Chin Fuh, IBM

THE SECOND RECIPROCAL DERIVATIVE POTENTIOMETRIC STRIPPING ANALYSIS

A theory of the second reciprocal derivative potentiometric stripping analysis with a mercury thin-film electrode is reported.

THE SECOND RECIPROCAL DERIVATIVE CHRONOPOTENTIOMETRY ANALYSIS

Theories of the second reciprocal derivative chronopotentiometry analysis were deduced and experimentally verificated.Results in this study show that chronopotentiometry is significantly developed in both sensitivity and resolution for signals treated by the second reciprocal derivative.

CRITICAL DAMPING OF THE SECOND-ORDERPENDULUM-LIKE SYSTEMS

First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.

USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE

The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.

The Second mKdV Equation and Its Hereditary Symmetry and Hamiltonian Structure

The isospectral problem of the second mKdV equation is found out firstly. It follows that the strong hereditary symmetry and the Hamiltonian structure of the second mKdV equation are presented.

Some Properties of Degenerate r-Dowling Polynomials and Numbers of the Second Kind

The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics.In recent years,some mathematicians have studied degenerate version of them and obtained many interesting results.With this in mind,in this paper,we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind.We derive many interesting properties and identities for them including generating functions,Dobinski-like formula,integral representations,recurrence relations,differential equation and various explicit expressions.In addition,we explore some expressions for them that can be derived from repeated applications of certain operators to the exponential functions,the derivatives of them and some identities involving them.

The Second International Conference on HSLA Steels

GENERAL INFORMATIONThe Chinese Society of Metals is pleased to announcethat The Second International Conference on HSLASteels(HSEA’90)will be held in Beijing,China inOctober 1990.Much progress in research and devel-opment of HSLA steels has been achieved by theworld’s metallurgical and materials community sincethe previous International Conference HSLA Steels’85 was held in Beijing,The aim of the conference isto review and to consolidate the scientific,metallurgical,and economical results and to assessthe future trend of development in the fields.

THE 6TH INTERNATIONAL CONFERENCE ON RARE EARTH DEVELOPMENT AND APPLICATIONS ICRE'2010(The Second Circular)

Beijing / China August 2-6, 2010 Organized by The Chinese Society of Rare Earths (CSRE) Co-Organized by Peking University (PKU), Roskill Information Services Ltd., Metallurgical Council