On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equations.Our purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of FCDLT.We obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace approach.We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

Double Differential Cross-Section for the Ionization of Hydrogenic 2S Metastable State

Double differential cross-sections of first Born estimation for ionization of hydrogenic 2S state by electrons are assessed for various kinematics situations in the asymmetric coplanar geometry. A final state wave function of multiple scattering theory is followed in this study. The present outcomes are compared with those of hydrogenic ground state, 2P state and ground state experimental results. Obtained findings show a good qualitative agreement with existing results.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations

In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.

Computation of one—dimensional consolidation of double layered ground using differential quadrature method

The authors give the solution to the problem of one-dimensional consolidation of double-layered ground with the use of the differential quadrature meahod.Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution;and that in the computationsl re-sults for the interface of soil lwyer also agreed with those of the analytical solution except for the small discrep-ancies during shortly after the start of computation.The advantages of the solution presented in this paper are that compared with the analytical solution,it avoids the cumbersome work in solving the transcendental equation for eigenvalues,and in the case of the Laplace transform solution,it can resolve the precision prob-lem in the numerical solution of long time inverse Laplace transform.Because of the matrix form of the solution in this paper,it is convenient for formulation computational program for engineering practice.The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils.

Use of Double Differential-mode Current Injection Method Equivalent to High Level Illumination for Susceptibility Testing

To achieve the electric field strength and the induced currents in equivalence in susceptibility tests with the high-level field radiation above 400 MHz,a double differential-mode(DM) current injection method based on directional couplers is proposed.Two cascaded symmetrical directional couplers compose a coupling device to inject the DM currents.When the coupling device is used,two devices are necessary to achieve the equivalence between radiation and injection,i.e.the equivalence between the injected voltages and the field strength,which is linear,regardless of the characteristics of the equipment under test(EUT).The results are verified by experiments using typical coaxial cables and nonlinear devices,where the equivalence between the nonlinear EUT responses induced by radiation and injection at both ends is achieved by using two coupling devices.At a frequency up to 1.75 GHz,the maximal experimental error is only 3.39%.The experimental results confirm the accuracy of the proposed method even both the EUTs work in the nonlinear region.The proposed method is applicable for radiated susceptibility(RS) testing of interconnected systems in the microwave frequency band.

Double-Differential Cross Section of ^5He Emission

The probability of 5He particle emission has been affirmed theoretically [J.S. Zhang, Science in China G47 (2004) 137]. In order to describe the 5He emission, the theoretical formula of the double-differential cross section of emitted 5He is to be established. Based on the pick-up mechanism, used for calculating the formula of d, t, 3He, α emissions, the theoretical formula of double-differential cross section of 5 He is obtained, which is expressed in the form of Legendre coefficients. In the case of low incident energies, the configuration [J.S. Zhang, Science in China G47 (2004)137; J.S. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 83] is the dominant part in the reaction processes.The calculated result indicates that the forward peaked angular distribution of the composite particle emission is weaker than that of the emitted single nucleon due to pick-up nucleon from the Fermi sea. As an example, the reactions of n + 14N have been calculated, and the Legendre coefficients of d, t, 3He, α, 5He emissions are obtained respectively.The results show that the forward tendency is decided by the average momentum per nucleon in the emitted composite particles. The larger the average momentum is, the stronger the forward tendency is.

Research on double differential pressure dynamic flowmeter

When testing an electrohydraulic proportional valve,it is necessary to test the high frequency dynamic flow with bias.Because of the limitation of the piston stroke,a no-load hydraulic cylinder is only suitable for a reciprocating symmetrical dynamic flow test.Since the traditional differential pressure flowmeter is affected by viscosity and inertia of the fluid,it is only suitable for measuring steady flow.Therefore,a new type of double pressure differential dynamic flowmeter is designed to improve the traditional differential pressure flowmeter.The influence of fluid viscosity and inertia in the flow process are negated by subtracting the differential pressure in section expansion from the differential pressure in section contraction.The double differential pressure flowmeter is modeled and a flow meter prototype is designed.Then,the flow coefficients are identified and corrected by a practical test.Finally,the dynamic performance and steady-state precision of the flowmeter are verified by comparing with the test results of the no-load hydraulic cylinder.The double differential pressure dynamic flowmeter is proven to measure dynamic flow accurately,especially at higher dynamic frequencies.

Liquid Level Measurement in Oil Tanks Based on Double-differential Pressure Technique

The system principle and configuration of the double differential pressure method for measuring oil tank level are presented. The fundamental method and circuit of fiber optic transmission are analyzed .The accuracy and security of level measurement in the oil tanks have been greatly improved.

Theoretical Analysis of Neutron Double-Differential Cross Section of n ＋^19F at 14.2 MeV

一个新轻原子反应模型被开发了， 1p 壳原子核的 thedouble 微分的大小成功地被分析了。现在，这个模型的应用程序被扩展到 ~(19 ) 2s-1d 壳原子核的 F。为 n +~(19 ) 的全部的出去的中子的 double-differentialcross 节在 E_n = 的 F 反应 14.2 兆电子伏被计算了并且分析，它与试验性的大小相当同意很好。在这篇论文，对双 differential 十字节的来自不同反应隧道的贡献详细被分析了。只要相关水平计划能足够地被提供，计算显示这个轻原子反应模型也能被用于 2s-1d 壳原子核。

Double Lipschitz Stability for Nonlinearly Perturbed Differential Systems with Multiple Delay

In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.

Research on the Equivalence Between Double Differential- mode Current Injection and Radiation Test Method

There are the application scope limits for single differential-mode current injection test method, so in order to carry out injection susceptibility test for two-pieces equipment interconnected with both ends of a cable simultaneously, a double differential-mode current in- jection test method (DDMCI) is proposed. The method adopted the equivalence source wave theorem and Baum-Liu-Tesche(BLT) equation as its theory foundation. The equivalent corresponding relation between injection voltage and radiation electric field intensity is derived, and the phase relation between the two injection voltage sources is confirmed. The results indicate that the amplitude and phase of the equivalent injection voltage source is closely related to the S parameter of directional coupling device, the transmission line length, and the source vector in BLT equation, but has nothing to do with the reflection coefficient between the two equipment pieces. Therefore, by choosing the right amplitude and phase of the double injection voltage sources, the DDMCI test is equivalent to the radiation test for two interconnected equipment of a system.

Double differential cross sections for ionization of H by 75 keV proton impact:Assessing the role of correlated wave functions

The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.

Measurement of Double Differential Cross Section for ^(93)Nb(n,xp) Reaction at E_n=14.6 MeV

-The energy spectrum and angular distributions of protons from 93Nb（n,xp）reactions are measured by means of the USTC（University of Science and Technologyof China）multitelescope system.The total proton production cross sections are in fairagreement with the results of other groups.The energy spectrum is well explained by thesum of the spectra calculated on the basis of the preequilibrium and the H-F theories.Deviations from the previous measurement at the high energy end of the angle-inte-grated proton spectrum are found.The angular distributions which show a stronglyenergy-dependent forward-backward asymmetry are in fair agreement with thephenomenological model of Kalbach-Mann.

Theoretical Analysis of Neutron Double-Differential Cross Sections of n ＋^9Be Reactions

由为轻原子核使用原子反应模型，从 n +9Be 反应的出去的中子的双 differential 十字节的计算被执行。全部的出去的中子仅仅被来从(n， 2n ) 2 反应隧道。(n， 2n ) 2 反应隧道通过六条不同反应途径被完成，它在这份报纸被说明。计算结果与测量数据同意很好在在 = 7.1， 8.09， 8.17， 9.09， 9.97 和 10.26 兆电子伏，因为更新的水平与 n 有关策划 +9Be，反应在这被采用了计算。

Output Speed and Torque of Differential Double-Stator Swing Hydraulic Multimotors

A new type of differential double-stator swing hydraulic motor,based on double stator structure,was introduced.Compared with the traditional swing hydraulic motors,it could provide various kinds of rotational speeds and torques under the same conditions of input flow rate and pressure.The operating principle and graphic symbols were described.The output speed and torque characters in multifarious connection modes were analyzed through single-acting differential double-stator swing hydraulic multi-motors.Then the differential connection modes and differential principles of differential double-stator swing hydraulic multi-motors were stated.Furthermore,the output speed and torque characters of doubleacting and triple-acting ones in multifarious connection modes were gotten.The interaction between output torque and the displacement ratio was studied.Finally,the internal leakage that influenced the volumetric efficiency was researched.The theoretical and experimental researches show that the differential double-stator swing hydraulic multi-motors can provide various kinds of rotational speeds and torques.Predictably,this new kind of swing hydraulic multi-motors has broad application prospects in machine tool equipments,engineering machineries,and simulation turntables.

A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY

Using Hartogs’fundamental theorem for analytic functions in several complex variables and q-partial differential equations,we establish a multiple q-exponential differential formula for analytic functions in several variables.With this identity,we give new proofs of a variety of important classical formulas including Bailey’s 6ψ6 series summation formula and the Atakishiyev integral.A new transformation formula for a double q-series with several interesting special cases is given.A new transformation formula for a 3ψ3 series is proved.

A simple approach to solving double sinh–Gordon equation

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation abundant types of explicit and exact solutions for the double sinh-Gordon equation are derived in a simple manner.

Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.