Correction to:Theoretical analysis of the double-differential cross-sections of neutron,proton,deuteron,^(3)He,and α for the p+^(6)Li reaction

Correction to:Nuclear Science and Techniques(2024)35:61 https://doi.org/10.1007/s41365-024-01421-5 In this article,the figures were wrongly numbered.The Fig.7 and 8 should have been Fig.11 and 12.The Fig.9,10,11,and 12 should have been 7,8,9 and 10.The original article has been corrected.

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.

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.

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.

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 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.

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.

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.

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.

EXPONENTIAL CONVERGENCE FOR NONLINEAR SPDES WITH DOUBLE REFLECTING WALLS

The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling,in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.

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.

Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.

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.

Influence of Heating Rate on Double Reversible Transformation in CuZnAlMnNi Shape Memory Alloy

The influence of heating rate on double reversible transformation in CuZnAlMnNi shape memory alloy was investigated by differential scanning calorimetry. It was found that rapid heating inhibits X -->M transformation but is favorable to the reverse martensite transformation, giving rise to the approach of the two transformation peaks. With the decrease of heating rate, the two transformation peaks separate gradually.

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.

Hidden Properties of Mathematical Physics Equations. Double Solutions. The Realization of Integrable Structures. Emergence of Physical Structures and Observable Formations

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

double-order Hilfer分数阶共振边值问题解的存在性

为了拓展分数阶微分方程边值问题的基本理论,研究了共振情形下double-order Hilfer分数阶微分方程在Riemann-Stieltjes积分边界条件下解的存在性。首先,构造2个合适的Banach空间;然后,在Banach空间中定义恰当的算子并使用Mawhin重合度理论,获得double-order Hilfer分数阶共振边值问题解的存在性;最后,通过例子验证结果的正确性。结果表明,在合适的Banach空间中,double-order Hilfer分数阶共振边值问题的解具有存在性。采用Mawhin重合度理论方法研究double-order Hilfer分数阶共振边值问题解的存在性,扩展了微分算子阶数的取值范围,丰富了分数阶微分方程的可解性理论,为微分方程在空气动力学、经济学、控制理论等领域的应用提供了理论参考。