Function Solution Method Research Articles

Clean affinity matrix learning with rank equality constraint for multi-view subspace clustering

The existing multi-view subspace clustering (MVSC) algorithm still has certain limitations. First, the affinity matrix obtained by them is not clean and robust enough since the original multi-view data usually contain noise. Second, they also have defects in exploring the consistency between views. To compensate for these two shortcomings, we propose a novel MVSC, i.e., clean affinity matrix learning with rank equality constraint (CAMR) for MVSC. By borrowing the idea from robust principal component analysis (RPCA), the representation matrix of each view obtained by low-rank representation (LRR) is first cleaned up to obtain a cleaner and more robust affinity matrix. In addition, the rank constraint is utilized to explore the same clustering properties between different views. An objective function solution method based on an augmented Lagrange multiplier (ALM) is designed and tested on four widely employed datasets to verify that CAMR has better clustering performance than certain state-of-the-art methods. We provide the code of CAMR at https://github.com/zhaojinbiao/CAMR.

Pressure-Transient Performances of Fractured Horizontal Wells in the Compartmentalized Heterogeneous Unconventional Reservoirs

In order to investigate pressure performance of multiple fractured horizontal wells (MFHWs) penetrating heterogeneous unconventional reservoir and avoid the high computational cost of numerical simulation, a semi-analytical model for MFHWs combining Green function solution and boundary element method has been obtained, where the reservoir is divided into different homogeneous substructures and coupled at interface boundaries by plane source function in a closed rectangular parallelepiped. Hydraulic fractures are assumed uniform flux and dual porosity model is used for natural fractures system. Then the model is validated by compared with analytical solution of MFHWs in a homogeneous reservoir and trilinear flow model, which shows that this model can achieve high accuracy even with a small interface discretization number, and it can consider the radial flow around each hydraulic fractures. Finally, the pressure responses with heterogeneous parameters of reservoirs are discussed including heterogeneous permeability, non-uniform block-length and fracture half-length distribution as well as dual porosity parameters like elastic storage ratio and crossflow ratio.

Irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function

The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR). The IR basis enables a compact representation of the Matsubara Green’s function and efficient calculations of quantum models. The IR basis functions are defined as the solution of an integral equation whose analytical solution is not available for this moment. The library consists of a database of pre-computed high-precision numerical solutions and computational code for evaluating the functions from the database. This paper describes technical details and demonstrates how to use the library. Program summaryProgram Title: irbasisProgram Files doi:http://dx.doi.org/10.17632/2fh88ynxm6.1Licensing provisions: MIT licenseProgramming language:C++, Python.External routines/libraries: numpy, scipy and h5py for Python library, HDF5 C library for C++ library.Nature of problem: Numerical orthogonal systems for Green’s functionSolution method: Galerkin method, piece-wise polynomial representation

Solvability of boundary value problems of nonlinear fractional differential equations

In this paper, we study the existence of multiple positive solutions for the nonlinear fractional differential equation boundary value problem $D^{\alpha}_{0^{+}}u(t)+f(t,u(t))=0 $ , $0< t<1$ , $u(0)=u(1)=u'(0)=0$ , where $2<\alpha\leq3$ is a real number, $D^{\alpha}_{0^{+}}$ is the Riemann-Liouville fractional derivative. By the properties of the Green’s function, the lower and upper solution method and the Leggett-Williams fixed point theorem, some new existence criteria are established. As applications, examples are presented to illustrate the main results.

Existence and uniqueness of positive solutions for integral boundary problems of nonlinear fractional differential equations with p -Laplacian operator

In this paper, we deal with the following integral boundary problem of nonlinear fractional differential equations with $p$-Laplacian operator \begin{displaymath} \begin{array}{lll} D_{0+}^{\gamma}(\phi_p(D_{0+}^{\alpha}u(t))) + f(t,u(t))=0, \quad 0 \lt t \lt 1, u(0) = u'(0)=0, \quad u'(1) = \int_0^\eta u(s)\,ds,\quad D_{0+}^{\alpha}u(t)|_{t=0}=0, \end{array} \end{displaymath} where $0 \lt \gamma \lt 1$, $2 \lt \alpha \lt 3$, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, $\phi_p(s)=|s|^{p-2}s, p>1$, $(\phi_p)^{-1}=\phi_q$, ${1}/{p}+{1}/{q}=1$. By the properties of the Green function, the lower and upper solution method and fixed-point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.

Dynamic Economic Dispatch Solution Using Composite Cost Function

This paper proposes using the composite cost function to solve the dynamic economic dispatch problem in power system operation. The dynamic economic dispatch must not only satisfy the system load demand and the spinning reserve capacity, but some practical operation constraints of generators, such as ramp rate limits are also considered in practical generator operation. The feasibility of the proposed composite cost function solution method is demonstrated on sample power system and it is compared with other stochastic methods in terms of solution quality and computation efficiency. The numerical simulation results showed that the proposed method was indeed capable of obtaining the higher quality solutions efficiently in dynamic economic dispatch problems

Transmission loss analysis of single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) circular chamber mufflers by using Green’s function method

A Green’s function solution method is implemented to study sound attenuation in single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) circular chamber mufflers. The mufflers are modeled as piston driven rigid circular chambers containing a stationary fluid. The pistons are assumed to perform simple harmonic motion with uniform velocities. Velocity potential in the chamber is derived as a superposition of three dimensional velocity potential due to each piston. Pressure field in the chamber is calculated from the velocity potential through conservation of linear momentum equation. Acoustic pressure acting on each piston is calculated by averaging over the surface of the piston. Transmission loss (TL) is evaluated from incident and transmitted acoustic energy. TL curves for various inlet/outlet orientations derived from this method is validated with results obtained from the literature. The effect of locations of inlet/outlet on TL is studied.

Green’s Function Solution for the Dual-Phase-Lag Heat Equation

The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method. Also, the Green’s function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1-4].

Existence and uniqueness of positive solutions to nonlinear fractional differential equation with integral boundary conditions

In this paper, we consider the following nonlinear fractional three-point boundary-value problem: $$ \begin{array}{*{20}{c}} {D_{0 + }^\alpha u(t) + f\left( {t,u(t)} \right) = 0,\,\,\,\,0 < t < 1,} \\ {u(0) = u'(0) = 0,\,\,\,\,u'(1) = \int\limits_0^\eta {u(s){\text{d}}s,} } \\ \end{array} $$ whereD α 0+ is the standard Riemann-Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method, and fixed-point theorem in partially ordered sets, we establish some new results on the existence and uniqueness of positive solutions to the above boundary-value problem. As applications, examples are presented to illustrate the main results.

Communication Software Design of Remote Monitoring System for Motor Excitation Parameters Based on PSTN

Based on the remote maintenance of motor exciation, this paper discusses the function design and solution method of communication software which is used in remote monitoring system of motor exciation. It mainly introduces the process of data transmission founded on the Public Switched Telephone Network (PSTN) and key problems of the implementation of communication MSComm control in VC++.

Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation

In this paper, we consider the following nonlinear fractional m-point boundary value problem Open image in new window where \(D_{0+}^{\alpha}\) is the standard Riemann-Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method and fixed-point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.

The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations

In this paper, we study the existence on multiple positive solutions for the nonlinear fractional differential equation boundary value problem. D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ′ ( 0 ) = u ′ ( 1 ) = 0 , where 2 < α ⩽ 3 is a real number, D 0 + α is the Riemann–Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method and fixed point theorem, some new existence criteria for singular and nonsingular fractional differential equation boundary value problem are established. As applications, examples are presented to illustrate the main results.

PERFORMANCE IMPROVEMENT IN AMPLITUDE SYNTHESIS OF UNEQUALLY SPACED ARRAY USING LEAST MEAN SQUARE METHOD

In this paper, an efficient method to obtain the elements current distribution for a non uniformly spaced array is presented. For a given far field pattern, after sampling the array factor the proposed method uses the least mean square error technique to solve the system ofequations rather than solving the previously published Legendre function method. It's shown that the average side lob level obtained by this proposed method is some 5 dB lower in comparison with the existing Legendre function method ofsolution. Ifthe Legendre function method published in the literature is to be used to solve for the current distribution, in the final part ofthis paper, a criteria on how to choose suitable vectors that would result in a 3 dB lower side lobe level performance will be provided.

Heat transfer to flow through porous passages using extended weighted residuals method—a Green’s function solution

The Green’s function solution method is a direct and powerful tool for solving heat transfer problems associated with flow through passages. It is also an equally powerful tool when these passages are filled with saturated porous materials. The capability of the Green’s function solution is enhanced when it is used in conjunction with the method of weighted residuals extended for this type of application. This study discusses the calculation of heat transfer to fluids flowing through different porous passages by using this combined methodology. The numerical illustrations include the study of heat transfer in isosceles triangular passages. Also, this methodology is equally applicable when the boundary conditions are of the first, second, or third kind.

A NUMERICAL STUDY OF THE HEAT TRANSFER TO FLUID FLOW THROUGH CIRCULAR POROUS PASSAGES

A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating/cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.

Green's function solution of temperature field for flow in porous passages

Recently, the heat transfer in porous passages has received attention from many investigators. The Green's function solution method can serve as a powerful tool to accomplish this task of providing solutions to this type of problems with or without the effect of axial conduction. The study of heat transfer with emphasis on frictional heating, in the absence of axial conduction, is the subject of this presentation. As a simple example, consideration is given to the numerical study of the heat transfer in flow between two impermeable parallel plates. The individual effects of temperature change at the walls, frictional heating, and the combined effects are examined. The data shows that the combined effects can produce removable singularities under certain boundary conditions. To avoid the occurrence of singularities in these types of applications, certain heat transfer parameters are presented in different but basic forms.

Volterra integral equations solved in Fredholm form using Walsh functions

Recently Walsh function methods have been developed for the numerical solution of several classes of problems, mainly linear and nonlinear integral equations of both Volterra and Fredholm types. In addition, modifications of the basic approach have led to the solution of functional differential equations, variational problems and parameter estimation problems. Linear Volterra integral equations are re-written as Fredholm integral equations with appropriately modified kernels. In this Fredholm equation form, the Walsh function solution method is more efficient than directly solving the Volterra equation. Walsh function methods are spectral methods but they have a natural grid interpretation. Multigrid methods and a variation on the use of Richardson extrapolation are used on six well known Volterra test problems, re-written in Fredholm form, to illustrate that these methods provide effective and efficient solution methods.

A 2-D analytic model for the threshold-voltage of fully depleted short gate-length Si-SOI MESFETs

A two-zone Green's function solution method is proposed to analytically model the potential distribution in the silicon film of fully depleted SOI MESFETs, in which the exact solution of 2-D Poisson's equation is obtained by using the appropriate boundary conditions. From the derived analytic 2-D potential distribution, the bottom potential in the active silicon film is used to analyze the drain-induced barrier lowering effect and the threshold voltage is defined in terms of minimum channel potential barrier. The results of the developed analytic threshold-voltage model are compared with those of 2-D numerical simulation, and good agreements are obtained for the gate length down to 0.1 /spl mu/m with wide ranges of structure parameters and bias conditions.

Green's function solution for thermal wave equation in finite bodies

The classical diffusion theory is based on the assumption of local thermal equilibrium. For conduction in thin films or at low temperature, the classical theory of heat conduction breaks down. Various investigations have shown that a wave-type conduction equation adequately describes the thermal energy transport. This paper describes a general solution technique when the wave nature of thermal energy transport is dominant. The solution for temperature distribution is derived for finite bodies. The definition of Green's functions for a wave-type conduction equation is presented and a general form of the Green's function solution method for finite bodies is introduced.

Thermal Characteristics of Two-Layered Bodies With Embedded Thin-Film Heat Source

Exact series solutions for three-dimensional temperature distribution in two-layer bodies subject to various types of boundary conditions are presented. Special consideration is given to the case when one layer is a thin diamond film. The computation emphasizes the temperature effect of an embedded thin heat source of the type used in electronic devices. The mathematical formulation employs the Green’s function solution method. The solution is time partitioned in order to achieve a high degree of accuracy. Time partitioning greatly improves the convergence of three-dimensional heat conduction solutions. Time-partitioned series solutions with a reduced number of terms yield highly accurate temperature data. A two-layer model is chosen for simplicity of presentation; however, the method can be extended to more than two layers.