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.

High-Order Spatial FDTD Solver of Maxwell’s Equations for Terahertz Radiation Production

We applied a spatial high-order finite-difference-time-domain (HO-FDTD) scheme to solve 2D Maxwell’s equations in order to develop a fluid model employed to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma. We examined the performance of the applied scheme, in this context, we implemented the developed model to study selected phenomena in terahertz radiation production, such as the excitation energy and conversion efficiency of the produced THz radiation, in addition to the influence of the pulse chirping on properties of the produced radiation. The obtained numerical results have clarified that the applied HO-FDTD scheme is precisely accurate to solve Maxwell’s equations and sufficiently valid to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma.

GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON R^(3)×T WITH CUBIC NONLINEARITIES

In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.

The establishment of a new deliverability equation considering threshold pressure gradient

The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.

Assessment of Relationship of Some Causal Factors Associated with Productivity of Longwall Mining Using Structured Equation Modeling

Enhancement of productivity optimization is steadily gaining the priority in mining companies especially in the underground coal mining industry which faces a daunting task to balance marginal profit generation with a comparatively high cost of production, volatile market price and rapid grade variation. This paper is aimed to analyze some of the causal factors both technical and site specific which are directly or indirectly impacting the productivity of the longwall coal mining system such as downtime of equipment system in longwall panel, overloading of conveyors and bin, preventive maintenance, gas management practices and injury severity rate. Structured Equation Modelling (SEM) was used to study the causal relationships between the above-mentioned factors and mine productivity. The equipment considered for analysis included shearer, armored face conveyor, crusher, bridge stage loader, chock supports, main gate drive, gate conveyor, hydraulic pumps and crusher. SEM was applied to relate the correlations existing among these causal variables in order to assess their direct or indirect impact on mining productivity. Based on the data extracted over a period of 10 months which included the extraction of 2 longwall panels, the study revealed a significant negative causal relationship between injury severity rate (p < 0.01) and equipment downtime (p = 0.001), with mine productivity. However, preventive maintenance delay time, gas management delay time and conveyor overloading delay time were found to have an insignificant direct influence on mine productivity but indirectly modify it through a significant mediator relationship with equipment downtime. This information would assist mine management to take proper preventive measures.

Coupling Relationship Analysis on Households′ Production Behaviors and Their Influencing Factors in Nature Reserves:A Structural Equation Model

A households′production behavior directly influences the quality of the environment and determines the successful development of nature reserves.Meanwhile,the households′production behaviors are complicated by interrelated factors,such as protection attitudes,resource endowment,and family wealth.This research evaluated households near the Crested Ibis National Nature Reserve in Shaanxi Province,acquiring data from 436 households around Yang County and Ningshan County in the south slope of Qinling Mountains,China.Based on the collected data,we developed a structural equation model to evaluate the coupling relationships among households′ protection attitudes,production behaviors,resource endowment,and family wealth.The results showed that:1) households with great resource endowment had more negative attitudes,probably due to their greater protection costs;2) the households with higher education levels had worse protection attitudes;3) the households with more family wealth were likely to use fewer fertilizers,pesticides,and firewood;4) the households with more resource endowment showed less production and management behaviors;5) the enhancement of households' attitudes improved production behaviors to protection the environment,but the effects were not statistically significant.Our results provide a basis for the government's protection policy making,exploring the effective management measures that are beneficial for both nature reserve management and community development.

Intuitionistic Menger inner product spaces and applications to integral equations

In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.

Two Dimensional Tensor Product B-Spline Wavelet Scaling Functions for the Solution of Two-Dimensional Unsteady Diffusion Equations

The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions,4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.

A New Method to Construct Integrable Coupling System for Burgers Equation Hierarchy by Kronecker Product

It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.

Mathematical Equations for Reducing Water Pollution Problems among Poultry Production Clusters in Nong Khai Province, Thailand

Poultry production clusters (PPC) in Nong Khai raise layer chickens in the poultry houses constructed over fish ponds. Layer farmers use chicken manure to feed their fish. However, unbalance between chicken raising and the size of fish pond or number of fish results in low water quality, which affects fish production and the community’s public water resource. In this field study, data was collected from layer farms in three poultry production clusters in Nong Khai province in the northeast of Thailand (a total of 90 farms) between April and August 2013. Data collected consisted of observations of dissolved oxygen (DO) values of water in the fish ponds, the number of egg-laying chickens raised above the fish ponds, the number of fish and size of the fish ponds. When all of these four observations were analyzed, mathematical equations for calculating the number of chickens raised, the number of fish per one rai (1600 m2), and the size of pond suitable for the number of chickens and fish were obtained as follows: 1) number of fish/rai = 5796 + 1097(size of pond) (R2 = 0.71), 2) number of chicken/rai = 513 + 223(size of pond) (R2 = 0.48) and 3) size of pond =-0.328474 + 0.000262(Fish) + 0.00117(Chicken) (R2 = 0.40). When pond = desired pond size, fish = number of fish to be raised and chicken = number of chickens to be raised.

Tree Network Formation in Poisson Equation Models and the Implications for the Maximum Entropy Production Principle

This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable couplingsystem of soliton equation hierarchy in this paper.A direct application to the fractional cubic Volterra lattice spectralproblem leads to a novel integrable coupling system of soliton equation hierarchy.It is also indicated that the study ofdiscrete integrable couplings by using the Kronecker product is an efficient and straightforward method.This methodcan be used generally.

The Exact Solutions of Such Coupled Linear Matrix Fractional Differential Equations of Diagonal Unknown Matrices by Using Hadamard Product

In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.

On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

Calculation of Combustion Products by the New Iteration Method of Non-linear Equations

For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly nonlinear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, to be present the efficient numerical algorithms for. solving the combustion problem, to be used nonlinear equations based on the iteration method and high order of the Taylor series. The modified Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable, typical deviations from previous results are less than 0.05%.

Geologically controlling factors on coal bed methane （CBM） productivity in Liulin

It is of great significance to forecast high yield of CBM wells and analyze dynamic production by having an overall study on the characteristics of the produced CBM and determining the main factors influencing the productivity of CBM. With the test report and the related geological parameters of a single well, methods of combining the productivity data and typical production curves were used to analyze different geological factors and how to influence the capacity of a single layer. Then, the paper proposed a new understanding about capacity characteristics of the study area and geological control factors： First, the Shanxi formation production capacity characteristics was divided into two-stages, showing signs of gas and gas break- through for 100 days. Second, two parameters, which include potential of gas production and gas production capacity, were bet- ter than the single parameter, such as gas content, coal thickness, and penetration to analyze affecting factors of single well pro- duction. Finally, comprehensive analysis concluded that the ratio of critical desorption pressure to reservoir pressure has greater influence on the production of vertical CBM wells. Besides, the potential of gas production capacity has greater impact at stage of showing gas signs; the coal reservoir pressure and gas production capacity have greater impact at stage of gas breakthrough for 100 days. Thus, to seek the coal bed methane with high ratio of critical desorption pressure to reservoir pressure and high yield of gas will be important guarantee to the success of the coal bed methane exploration and development.

Movement Differential Equation of Seed Roller which Has Been Installed Stake Accelerator on the Roll Box of Gin Machine

In the article stake accelerator has proposed on the side of the roll box in order to increase the productivity of the gin machine. The effect to the raw material of the proposed stakes was studied. Movement differential equation of the seed roller was made up and necessary graphics were taken based on laws.

ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

We present results on approximate solutions to the biadditive equationf（x＋y,z-w）＋f（x-y,z＋w）=2f（x,z）-2f（y,w）on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately （in some sense） must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

On a Matrix Equation AX+XB=C over a Skew Field

In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.