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.

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].

Double Position Servo Synchronous Drive System Based on Cross-Coupling Integrated Feedforward Control for Broacher

Synchronization errors directly deteriorate the machining accuracy of metal parts and the existed method cannot keep high synchronization precision because of external disturbances. A new double position servo synchronous driving scheme based on semi-closed-loop cross- coupling integrated feedforward control is proposed. The scheme comprises a position error cross-coupling feedfor-ward control and a load torque identification with feed- forward control. A digital integrated simulation system for the dual servo synchronous drive system is established. Using a 20 t servo broacher, performance analysis of the scheme is conducted based on this simulation system and the simulation results show that systems with traditional parallel or single control have problems when the work- table works with an unbalanced load. However, the system with proposed scheme shows good synchronous perfor- mance and positional accuracy. Broaching tests are performed and the experimental results show that the maximum dual axis synchronization error of the system is only 8μm during acceleration and deceleration processes and the error between the actual running position and the given position is almost zero. A double position servo synchronous driving scheme is presented based on crosscoupled integrated feedforward compensation control, which can improve the synchronization precision.

A G-band terahertz monolithic integrated amplifier in 0.5-μm InP double heterojunction bipolar transistor technology

Design and characterization of a G-band（140–220 GHz） terahertz monolithic integrated circuit（TMIC） amplifier in eight-stage common-emitter topology are performed based on the 0.5-μm In Ga As/In P double heterojunction bipolar transistor（DHBT）. An inverted microstrip line is implemented to avoid a parasitic mode between the ground plane and the In P substrate. The on-wafer measurement results show that peak gains are 20 dB at 140 GHz and more than 15-dB gain at 140–190 GHz respectively. The saturation output powers are-2.688 dBm at 210 GHz and-2.88 dBm at 220 GHz,respectively. It is the first report on an amplifier operating at the G-band based on 0.5-μm InP DHBT technology. Compared with the hybrid integrated circuit of vacuum electronic devices, the monolithic integrated circuit has the advantage of reliability and consistency. This TMIC demonstrates the feasibility of the 0.5-μm InGaAs/InP DHBT amplifier in G-band frequencies applications.

AN ENDPOINT ESTIMATE FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH NON DOUBLING MEASURES

A weak type endpoint estimate is established for commutators of the Calderon-Zygmund singular integrals on Rd with non doubling measures.

Integrated Nanostructural Electrodes Based on Layered Double Hydroxides

Layered double hydroxides(LDHs), as a class of typical two-dimensional materials, have sparked increasing interest in the field of energy storage and conversion. In the last few years, the research about LDHs as electrode active materials has seen much progress in terms of structure designing, material synthesis, properties tailoring, and applications. In this review, we focus on the integrated nanostructural electrodes(INEs) construction using LDH materials, including pristine LDH-INEs, hybrid LDH-INEs, and LDH derivativeINEs, as well as the performance advantages and applications of LDH-INEs.Moreover, in the final section, the insights about challenges and prospective in this promising research field were concluded, especially in regulation of intrinsic activity and uncovering of structure–activity relationship, which would push forward the development of this fast-growing field.

Double Integrable Couplings and Their Constructing Method

扩大 integrable couplings 的学习范围，两倍 integrable couplings 的观点在纸被建议。在在纸造的构造方法出现的零个弯曲方程由被使用不安方法获得的新环代数学的元素组成。因此，在纸给的途径有广泛的适用的价值，也就是说，它适用调查进化方程的已知的 integrable 层次的很多双 integrable couplings。至于在纸建议的方法的明确的应用， AKNS 层次和 KN 层次的双 integrable couplings 分别地被得出。

BOUNDEDNESS OF FRACTIONAL INTEGRALS IN HARDY SPACES WITH NON-DOUBLING MEASURE—In Memory of Professor Sun Yongsheng

Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed n with 0 〈 n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H^1（μ）.

The Role of Mathematics in STEAM Education under the“Double Reduction”Policy

This essay delves into the pivotal role of mathematics within the context of STEAM(science,technology,engineering,arts,and mathematics)education under China’s“Double Reduction”policy.Amidst a shifting global education landscape that emphasizes holistic growth,policies such as the“Double Reduction”strategy underscore the significance of well-rounded development alongside academic excellence.By advocating for a balanced approach to education,the policy resonates with the principles of STEAM education,which seeks to cultivate versatile and innovative individuals.Mathematics,acting as a unifying force,connects disparate STEAM disciplines,fostering interdisciplinary collaboration and preparing students to thrive in a rapidly evolving,technology-driven world.This essay provides an in-depth exploration of the multifaceted role of mathematics in STEAM education,drawing on specific cases and scholarly references to highlight its contributions to creativity,critical thinking,and holistic development.

Boundedness for Multilinear Commutators of Marcinkiewicz Integral on Morrey-Herz Spaces with Non Doubling Measures

In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO（μ） function on homogeneous Morrey-Herz spaces with non doubling measures.

DNA Double-Strand Breaks,Potential Targets for HBV Integration

Hepatitis B virus(HBV)-induced hepatocellular carcinoma(HCC) is one of the most fre-quently occurring cancers.Hepadnaviral DNA integrations are considered to be essential agents which can promote the process of the hepatocarcinogenesis.More and more researches were designed to find the relationship of the two.In this study,we investigated whether HBV DNA integration occurred at sites of DNA double-strand breaks(DSBs),one of the most detrimental DNA damage.An 18-bp I-SceI homing endonuclease recognition site was introduced into the DNA of HepG2 cell line by stable DNA transfection,then cells were incubated in patients’ serum with high HBV DNA copies and at the same time,DSBs were induced by transient expression of I-SceI after transfection of an I-SceI expression vector.By using nest PCR,the viral DNA was detected at the sites of the break.It appeared that integra-tion occurred between part of HBV x gene and the I-SceI induced breaks.The results suggested that DSBs,as the DNA damages,may serve as potential targets for hepadnaviral DNA insertion and the integrants would lead to widespread host genome changes necessarily.It provided a new site to investi-gate the integration.

Enhancement of Solar PV Panel Efficiency Using Double Integral Sliding Mode MPPT Control

The extraction of maximum power from the solar panels,using the sliding mode control scheme,becomes popular for partial weather atmospheric conditions due to its effective dynamic duty cycle ratio.However,the sliding mode control scheme was sophisticated with single integral and double integral sliding mode control scheme,which offer enhanced maximum power extraction and support enhanced solar panel efficiency in partial weather conditions.The operation of the sliding mode control scheme depends on the selection of a sliding surface selection based on the atmospheric weather condition,which enables the effective sliding duty cycle ratio operation for the DC/DC boost converter.The duty cycle ratio of the sliding mode control resembles the usual dynamic behavior to achieve enhanced efficiency compared to the various maximum power point tracking(MPPT)schemes.The major limitation of the sliding mode control scheme is to achieve the steady state voltage error of the solar panel in minimum settling time duration.The single integral sliding mode control scheme achieves the expected steady state voltage error limit but fails to achieve minimum settling time duration.Hence,the single integral sliding mode control is extended to a double integral sliding mode control scheme to achieve both steady state voltage error limits within the minimum settling time duration.This double integral sliding mode control scheme allows us to obtain the higher sliding surface duty cycle ratio which acts as the input signal to the boost converter.This activates the enhanced stable and reliable system operation,and nullifies the lacuna of maximum solar panel efficiency under partial weather conditions.Hence,this paper aims to present the design and performance operation of the double integral sliding mode(DISM)MPPT control scheme.To validate the performance analysis of the proposed DISM MPPT control scheme,the MATLAB/Simulink model is designed and verified.Also,the performance analysis of the proposed DISM MPPT control scheme is compared with the sliding mode controller(SMC)scheme and single integral sliding mode controller(SiSMC)scheme.The performance analysis of the proposed double integral sliding mode controller(DISMC)scheme attains 99.10%of efficiency and a very less setting time of 0.035s when compared to other existingmethods.

Calaulation of Time-Optimal Control Law for Double Integrator System with Complex Constraints: Endpoint Backward Method

An endpoint backward method is proposed to calculate the time-optimal control law of double integrator system. First, the time intervals between the switch points and the endpoints are calculated. Then, the positions of switch points are decided according to the motion equation, and the switch line is formed. Theoretical analysis shows that this method can be used to solve the double integrator system with functional constraint target set and deal with the second order oscillation system.

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.

Consensus problems in multi-agent systems with double integrator model

In this paper, we consider multi-agent consensus problems in a decentralised fashion. The interconnection topology graph among the agents is switching and undirected. The agent dynamics is expressed in the form of a double integrator model. Two different cases are considered in this study. One is the leader-following case and the other is leaderless case. Based on graph theory and common Lyapunov function method, some sufficient conditions are obtained for the consensus stability of the considered systems with the neighbour-based feedback laws in both leader-following case and leaderless case respectively. Finally, two numerical examples are given to illustrate the obtained results.

Optimal predication of double-star position/SINS based on discrete integration

Aiming at Double-Star positioning system's shortcomings of delayed position information and easy exposition of the user as well as the error increase of the SINS with the accumulation of time, the integration of Double-Star positioning system and the SINS is one of the developing directions for an integrated navigation system. This paper puts forward an optimal predication method of Double-Star/SINS integrated system based on discrete integration, which can make use of the delayed position information of Double-Star positioning system to optimally predicate the integrated system, and then corrects the SINS. The experimental results show that this method can increase the user's concealment under the condition of assuring the system's accuracy.

Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

A New Inversion Method of Sedimentary Strata For Deriving Double Parameters and Its Applications

The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.

二重积分integral from n=a to b(dx) integral from n=c to d (f(x,y)dy)的柯特斯公式及其误差分析

重积分是高等数学的主要内容之一。柯特斯公式是定积分数值算法的一种重要方法,其具有误差精度高的优点,误差精度可达到6阶,将结合定积分柯特斯公式与二重积分的特点,将柯特斯公式推广到二重积分的情形。首先,给出了柯特斯公式的表达式及其误差公式;然后,将定积分的柯特斯公式推广到二重积分的情形,并结合积分中值定理推出其误差表达式。误差结果表明,推广到二重积分后的柯特斯公式仍具有6阶精度。