Strong Law of Large Numbers for a 2-Dimensional Array of Pairwise Negatively Dependent Random Variables

In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Recent Advances in In-Memory Computing:Exploring Memristor and Memtransistor Arrays with 2D Materials

The conventional computing architecture faces substantial chal-lenges,including high latency and energy consumption between memory and processing units.In response,in-memory computing has emerged as a promising alternative architecture,enabling computing operations within memory arrays to overcome these limitations.Memristive devices have gained significant attention as key components for in-memory computing due to their high-density arrays,rapid response times,and ability to emulate biological synapses.Among these devices,two-dimensional(2D)material-based memristor and memtransistor arrays have emerged as particularly promising candidates for next-generation in-memory computing,thanks to their exceptional performance driven by the unique properties of 2D materials,such as layered structures,mechanical flexibility,and the capability to form heterojunctions.This review delves into the state-of-the-art research on 2D material-based memristive arrays,encompassing critical aspects such as material selection,device perfor-mance metrics,array structures,and potential applications.Furthermore,it provides a comprehensive overview of the current challenges and limitations associated with these arrays,along with potential solutions.The primary objective of this review is to serve as a significant milestone in realizing next-generation in-memory computing utilizing 2D materials and bridge the gap from single-device characterization to array-level and system-level implementations of neuromorphic computing,leveraging the potential of 2D material-based memristive devices.

A 27 GHz,simple 2-bit 1×8 phased array

This study demonstrates a simple 2-bit phased array operating at 27 GHz that supports one-dimensional beam scanning with left-handed circular polarization(LHCP).The antenna is constructed using a compact four-layer printed circuit board(PCB)structure,consisting of a 90°phase shifter layer with microstrip structures,a ground(GND)layer,a direct current(DC)control layer,and a circularly polarized annular radiation patch layer with 1-bit phase shifting.Based on the proposed unit structure,a 1×8 array with half-wavelength inter-element spacing was designed and validated.Experimental results show that the array achieves a peak gain of 10.23 dBi and is capable of beam scanning within±50°.

Design of 32-bit differential paired eFuse OTP memory in a form of two-dimensional array

A differential paired eFuse OTP(one-time programmable)memory cell which can be configured into a 2D(two-dimensional)eFuse cell array was proposed.The sensible resistance of a programmed eFuse link is a half smaller than that of the single-ended counterpart and BL datum can be sensed without a reference voltage.With this 2D array of differential paired eFuse OTP memory cells,we design a 32-bit eFuse OTP memory IP.We use a sense amplifier based D F/F circuit as the BL(bit-line)SA(sense amplifier)and design a sensing margin test circuit with a variable pull-up load.It is confirmed by the function test that the designed 32-bit OTP memory IP functions normally on 30 sample dies.

10 × 10 Ga_(2)O_(3)-based solar-blind UV detector array and imaging characteristic

A 10 × 10 solar-blind ultraviolet(UV) imaging array with double-layer wire structure was prepared based on Ga_(2)O_(3) film grown by atomic layer deposition. These single detection units in the array exhibit excellent performance at 3 V: photo-todark current ratio(PDCR) of 5.5 × 10^(5), responsivity(R) of 4.28 A/W, external quantum efficiency(EQE) of 2.1 × 10^(3)%, detectivity(D*) of 1.5 × 10^(14) Jones, and fast response time. The photodetector array shows high uniformity under different light intensity and low operating bias. The array also has good temperature stability. Under 300 ℃, it still presents clear imaging and keeps high R of 34.4 and 6.45 A/W at 5 and 1 V, respectively. This work provides a new insight for the large-scale array of Ga_(2)O_(3) solarblind UV detectors.

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION

Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Numerical study on THz radiation of two-dimensional plasmon resonance of GaN HEMT array

The Ga N high electron mobility transistor(HEMT)has been considered as a potential terahertz(THz)radiation source,yet the low radiation power level restricts their applications.The HEMT array is thought to improve the coupling efficiency between two-dimensional(2D)plasmons and THz radiation.In this work,we investigate the plasma oscillation,electromagnetic radiation,and the integration characteristics of Ga N HEMT targeting at a high THz radiation power source.The quantitative radiation power and directivity are obtained for integrated Ga N HEMT array with different array periods and element numbers.With the same initial plasma oscillation phase among the HEMT units,the radiation power of the two-element HEMT array can achieve 4 times as the single HEMT radiation power when the array period is shorter than 1/8electromagnetic wavelength.In addition,the radiation power of the HEMT array varies almost linearly with the element number,the smaller array period can lead to the greater radiation power.It shows that increasing the array period could narrow the main radiated lobe width while weaken the radiation power.Increasing the element number can improve both the radiation directivity and power.We also synchronize the plasma wave phases in the HEMT array by adopting an external Gaussian plane wave with central frequency the same as the plasmon resonant frequency,which solves the problem of the radiation power reduction caused by the asynchronous plasma oscillation phases among the elements.The study of the radiation power amplification of the one-dimensional(1D)Ga N HEMT array provides useful guidance for the research of compact high-power solid-state terahertz sources.

Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.

Three-dimensional hierarchical MoS_2/CoS_2 heterostructure arrays for highly efficient electrocatalytic hydrogen evolution

Developing non-expensive, highly active and highly stable electrocatalysts for hydrogen evolution has aroused extensive attention, owing to the necessity of novel clean and sustainable energy carriers. In this paper, we report a synthesis of free-standing three-dimensional hierarchical MoS_2/CoS_2 heterostructure arrays through a convenient process. The investigation of electrocatalytic HER performance suggests that the MoS_2/CoS_2 hybrid catalyst exhibits significant enhancement in HER(onsetpotential and potential at a current density of 100 mA cm^(-2) are 20 mV and125 mV, respectively) and superior durability(no shift of current density is observed after a continuous scanning of 3000 times) compared with individual CoS_2 and MoS_2. The superior HER performance was attributed to the formation of the interface between CoS_2 and MoS_2 through the electrochemical characterization, Raman, XPS analysis, and the control experiment. The lower onsetpotential, higher current density, excellent durability, and the free-standing structure of the three-dimensional hierarchical MoS_2/CoS_2 heterostructure array make it a promising cathode catalyst suitable for widespread application.

Investigation of photoelectrocatalytic degradation mechanism of methylene blue by a-Fe_(2)O_(3) nanorods array

Efficiently and thoroughly degrading organic dyes in wastewater is of great importance and challenge.Herein,vertically oriented mesoporous a-Fe_(2)O_(3)nanorods array(a-Fe_(2)O_(3)-NA)is directly grown on fluorine-doped tin oxide(FTO)glass and employed as the photoanode for photoelectrocatalytic degradation of methylene blue simulated dye wastewater.The Ovsites on the a-Fe_(2)O_(3)-NA surface are the active sites for methylene blue(MB)adsorption.Electrons transfer from the adsorbed MB to Fe-O is detected.Compared with electrocatalytic and photocatalytic degradation processes,the photoelectrocatalytic(PEC)process exhibited the best degrading performance and the largest kinetic constant.Hydroxyl,superoxide free radicals,and photo-generated holes play a jointly leading role in the PEC degradation.A possible degrading pathway is suggested by liquid chromatography-mass spectroscopy analysis.This work demonstrates that photoelectrocatalysis by a-Fe_(2)O_(3)-NA has a remarkable superiority over photocatalysis and electrocatalysis in MB degradation.The in-depth investigation of photoelectrocatalytic degradation mechanism in this study is meaningful for organic wastewater treatment.

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.

Role of 2-dimensional Doppler echo-cardiography in screening portopulmonary hypertension in portal hypertension patients

BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

A New Rational Algebraic Approach to Find Exact Analytical Solutions to a （2＋1）-Dimensional System

In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.

New Exact Solutions for （2＋1）-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.