On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

3D‑Printed Carbon‑Based Conformal Electromagnetic Interference Shielding Module for Integrated Electronics

Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern electronics.However,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electronics,posing a major obstacle to the integra-tion of electronics.The innovation of integrating 3D-printed conformal shielding(c-SE)modules with packaging materials onto core electronics offers infinite possibilities to satisfy ideal SE func-tion without occupying additional space.Herein,the 3D printable carbon-based inks with various proportions of graphene and carbon nanotube nanoparticles are well-formulated by manipulating their rheological peculiarity.Accordingly,the free-constructed architectures with arbitrarily-customized structure and multifunctionality are created via 3D printing.In particular,the SE performance of 3D-printed frame is up to 61.4 dB,simultaneously accompanied with an ultralight architecture of 0.076 g cm^(-3) and a superhigh specific shielding of 802.4 dB cm3 g^(-1).Moreover,as a proof-of-concept,the 3D-printed c-SE module is in situ integrated into core electronics,successfully replacing the traditional metal-based module to afford multiple functions for electromagnetic compatibility and thermal dissipa-tion.Thus,this scientific innovation completely makes up the blank for assembling carbon-based c-SE modules and sheds a brilliant light on developing the next generation of high-performance shielding materials with arbitrarily-customized structure for integrated electronics.

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.

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.

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.

Double Integrable Couplings and Their Constructing Method

To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.

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.

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.

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].

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.

New Double Integrals Weighted Cebysev Type Inequalities

In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.

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.

双频DC-DC变换器的磁集成技术

双频Buck变换器由两个降压单元级联构成,具有动态响应快,开关损耗小等优势。然而不足的是磁件占据了整个系统的大部分体积与重量,降低了系统的功率密度。针对这一问题,提出一种三段式绕制磁集成技术,将磁件以解耦的方式集成在一副磁心中。该文首先建立集成磁件的磁路等效模型,通过抵消各绕组之间的耦合作用推导出解耦条件,并详细阐述了磁心的选取、匝数以及气隙的设计原则。其次,利用有限元仿真平台对所提集成磁件进行建模分析,与现有的集成方法相比,磁通密度分布更为均匀,磁心的利用率得到了有效提升。最后,搭建一台48 V/12 V、108 W的实验样机,体积和重量同分离磁件相比降低了31.2%和25.3%,提高了系统的功率密度,验证了该集成方法理论分析的正确性和可行性。

基于GaAs E/D PHEMT工艺的Ku波段双通道幅相控制多功能芯片

基于GaAs增强/耗尽型赝配高电子迁移率晶体管(E/D PHEMT)工艺设计了一款14~18 GHz的双通道多功能芯片。芯片集成了单刀双掷(SPDT)开关、6 bit数控移相器、4 bit数控衰减器和增益补偿放大器。采用正压控制开关以减小控制位数;优化移相、衰减和放大等电路拓扑结构,以获得良好的幅相特性;采用紧凑布局、双通道对称的版图设计,以实现小尺寸和高性能。测试结果表明,+5 V电压下,接收通道增益大于3 dB,1 dB压缩点输出功率大于8 dBm;发射通道增益大于1 dB,1 dB压缩点输出功率大于2 dBm;64态移相均方根误差小于2.5°,16态衰减均方根误差小于0.3 dB,芯片尺寸为3.90 mm×2.25 mm。该多功能芯片可实现对射频信号幅度和相位的高精度控制,可广泛应用于微波收发模块。

High-Performance and Flexible Co-Planar Integrated Microsystem of Carbon-Based All-Solid-State Micro-Supercapacitor and Real-Time Temperature Sensor

With the rapid development of flexible and portable microelectronics,the extreme demand for miniaturized,mechanically flexible,and integrated microsystems are strongly stimulated.Here,biomass-derived carbons(BDCs)are prepared by KOH activation using Qamgur precursor,exhibiting three-dimensional(3D)hierarchical porous structure.Benefiting from unobstructed 3D hierarchical porous structure,BDCs provide an excellent specific capacitance of 433 F g^(-1)and prominent cyclability without capacitance degradation after 50000 cycles at 50 A g^(-1).Furthermore,BDC-based planar micro-supercapacitors(MSCs)without metal collector,prepared by mask-assisted coating,exhibit outstanding areal-specific capacitance of 84 mF cm^(-2)and areal energy density of 10.6μWh cm^(-2),exceeding most of the previous carbon-based MSCs.Impressively,the MSCs disclose extraordinary flexibility with capacitance retention of almost 100%under extreme bending state.More importantly,a flexible planar integrated system composed of the MSC and temperature sensor is assembled to efficiently monitor the temperature variation,providing a feasible route for flexible MSC-based functional micro-devices.

Integral imaging-based tabletop light field 3D display with large viewing angle

Light field 3D display technology is considered a revolutionary technology to address the critical visual fatigue issues in the existing 3D displays.Tabletop light field 3D display provides a brand-new display form that satisfies multi-user shared viewing and collaborative works,and it is poised to become a potential alternative to the traditional wall and portable display forms.However,a large radial viewing angle and correct radial perspective and parallax are still out of reach for most current tabletop light field 3D displays due to the limited amount of spatial information.To address the viewing angle and perspective issues,a novel integral imaging-based tabletop light field 3D display with a simple flat-panel structure is proposed and developed by applying a compound lens array,two spliced 8K liquid crystal display panels,and a light shaping diffuser screen.The compound lens array is designed to be composed of multiple three-piece compound lens units by employing a reverse design scheme,which greatly extends the radial viewing angle in the case of a limited amount of spatial information and balances other important 3D display parameters.The proposed display has a radial viewing angle of 68.7°in a large display size of 43.5 inches,which is larger than the conventional tabletop light field 3D displays.The radial perspective and parallax are correct,and high-resolution 3D images can be reproduced in large radial viewing positions.We envision that this proposed display opens up possibility for redefining the display forms of consumer electronics.

DNA聚合酶θ:易错的多功能DNA末端修复分子

DNA聚合酶θ(DNA polymerase theta,Polθ)是一种广泛存在于动植物中的DNA修复酶。它在选择性末端连接(alternative end-joining,Alt-EJ)途径中发挥着关键作用,常参与DNA双链断裂(DNA double-strand breaks,DSB)损伤修复。在正常生理状态下,Polθ主要调控基因组稳定性。然而,在恶性肿瘤发生时,Polθ表现出异常高表达水平,并参与调控肿瘤细胞的恶性转变过程。研究表明,抑制Polθ活性可导致同源重组(homologous recombination,HR)缺陷的肿瘤细胞发生合成致死(synthetic lethality,SL)。因此,已经开发出多种针对Polθ的小分子抑制剂,可与其他化疗药物联合使用以抑制恶性肿瘤的发展。此外,敲除或抑制Polθ活性还能增加HR修复效率,从而提高外源基因靶向整合效果。本文综述了Polθ及其介导的Alt-EJ修复机制在生物学功能方面的最新研究进展,为靶向Polθ在肿瘤治疗和基因编辑方面的应用提供理论基础。

Constructing generalized Drinfel'd quantum double

Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.