LOCAL TOPOLOGICAL STRUCTURE OF THE PLANE CUBIC SYSTEM IN THE UNDETERMINED SIGN CASE

In this paper we discuss the topological structure near the singular point O (0,0) of the plane cubic system in the undetermined sign case, and give their coefficient conditions.

ANovel Non-Isolated Cubic DC-DC Converter with High Voltage Gain for Renewable Energy Power Generation System

In recent years,switched inductor(SL)technology,switched capacitor(SC)technology,and switched inductor-capacitor(SL-SC)technology have been widely applied to optimize and improve DC-DC boost converters,which can effectively enhance voltage gain and reduce device stress.To address the issue of low output voltage in current renewable energy power generation systems,this study proposes a novel non-isolated cubic high-gain DC-DC converter based on the traditional quadratic DC-DC boost converter by incorporating a SC and a SL-SC unit.Firstly,the proposed converter’s details are elaborated,including its topology structure,operating mode,voltage gain,device stress,and power loss.Subsequently,a comparative analysis is conducted on the voltage gain and device stress between the proposed converter and other high-gain converters.Then,a closed-loop simulation system is constructed to obtain simulation waveforms of various devices and explore the dynamic performance.Finally,an experimental prototype is built,experimental waveforms are obtained,and the experimental dynamic performance and conversion efficiency are analyzed.The theoretical analysis’s correctness is verified through simulation and experimental results.The proposed converter has advantages such as high voltage gain,low device stress,high conversion efficiency,simple control,and wide input voltage range,achieving a good balance between voltage gain,device stress,and power loss.The proposed converter is well-suited for renewable energy systems and holds theoretical significance and practical value in renewable energy applications.It provides an effective solution to the issue of low output voltage in renewable energy power generation systems.

1∶2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES

The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1 :2 internal resonance were derived by using the direct method of normal form. In the normal,forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.

Existence of Limit Cycles for a Cubic Kolmogorov System with a Hyperbolic Solution

This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.

Linear, Cubic and Quintic Coordinate-Dependent Forces and Kinematic Characteristics of a Spring-Mass System

By combining a pair of linear springs we devise a nonlinear vibrator. For a one dimensional scenario the nonlinear force is composed of a polynomial of odd powers of position-dependent variable greater than or equal three. For a chosen initial condition without compromising the generality of the problem we analyze the problem considering only the leading cubic term. We solve the equation of motion analytically leading to The Jacobi Elliptic Function. To avoid the complexity of the latter, we propose a practical, intuitive-based and easy to use alternative semi-analytic method producing the same result. We demonstrate that our method is intuitive and practical vs. the plug-in Jacobi function. According to the proposed procedure, higher order terms such as quintic and beyond easily may be included in the analysis. We also extend the application of our method considering a system of a three-linear spring. Mathematica [1] is being used throughout the investigation and proven to be an indispensable computational tool.

Limit Cycle Containing Nine Critical Points in its Interior for a Class of Cubic Systems

Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function(PSF)caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration.This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF.Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask.The system with the novel phase mask has better performance in the modulation transfer function(MTF)especially in low-and-medium spatial frequency region.The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect.The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.

Synthesizing active and durable cubic ceria catalysts(<6 nm)for fast dehydrogenation of bio-polyols to carboxylic acids coproducing green H_(2)

Dehydrogenation is considered as one of the most important industrial applications for renewable energy.Cubic ceria-based catalysts are known to display promising dehydrogenation performances in this area.Large particle size(>20 nm)and less surface defects,however,hinder further application of ceria materials.Herein,an alternative strategy involving lactic acid(LA)assisted hydrothermal method was developed to synthesize active,selective and durable cubic ceria of<6 nm for dehydrogenation reactions.Detailed studies of growth mechanism revealed that,the carboxyl and hydroxyl groups in LA molecule synergistically manipulate the morphological evolution of ceria precursors.Carboxyl groups determine the cubic shape and particle size,while hydroxyl groups promote compositional transformation of ceria precursors into CeO_(2) phases.Moreover,enhanced oxygen vacancies(Vo)on the surface of CeO_(2) were obtained owing to continuous removal of O species under reductive atmosphere.Cubic CeO_(2) catalysts synthesized by the LA-assisted method,immobilized with bimetallic PtCo clusters,exhibit a record high activity(TOF:29,241 h^(-1))and Vo-dependent synergism for dehydrogenation of bio-derived polyols at 200℃.We also found that quenching Vo defects at air atmosphere causes activity loss of PtCo/CeO_(2) catalysts.To regenerate Vo defects,a simple strategy was developed by irradiating deactivated catalysts using hernia lamp.The outcome of this work will provide new insights into manufacturing durable catalyst materials for aqueous phase dehydrogenation applications.

Metastable face-centered cubic ruthenium-based binary alloy for efficient alkaline hydrogen oxidation electrocatalysis

Metastable nanostructured electrocatalyst with a completely different surface environment compared to conventional phase-based electrocatalyst often shows distinctive catalytic property.Although Ru-based electrocatalysts have been widely investigated toward hydrogen oxidation reaction(HOR)under alkaline electrolytes,these studies are mostly limited to conventional hexagonal-close-packed(hcp)phase,mainly arising from the lack of sufficient synthesis strategies.In this study,we report the precise synthesis of metastable binary RuW alloy with face-centered-cubic(fcc)phase.We find that the introduction of W can serve as fcc phase seeds and reduce the formation energy of metastable fcc-RuW alloy.Impressively,fcc-RuW exhibits remarkable alkaline HOR performance and stability with the activity of 0.67 mA cm_(Ru)^(-2)which is almost five and three times higher than that of hcp-Ru and commercial Pt/C,respectively,which is attributed to the optimized binding strength of adsorbed hydroxide intermediate derived from tailored electronic structure through W doping and phase engineering.Moreover,this strategy can also be applied to synthesize other metastable fcc-RuCr and fcc-RuMo alloys with enhanced HOR performances.

A novel rapid cooling assembly design in a high-pressure cubic press apparatus

In traditional high-pressure–temperature assembly design, priority has been given to temperature insulation and retention at high pressures.This limits the efficiency of cooling of samples at the end of experiments, with a negative impact on many studies in high-pressure Earth andplanetary science. Inefficient cooling of experiments containing molten phases at high temperature leads to the formation of quench textures,which makes it impossible to quantify key compositional parameters of the original molten phase, such as their volatile contents. Here,we present a new low-cost experimental assembly for rapid cooling in a six-anvil cubic press. This assembly not only retains high heatingefficiency and thermal insulation, but also enables a very high cooling rate (∼600 ℃/s from 1900 ℃ to the glass transition temperature).Without using expensive materials or external modification of the press, the cooling rate in an assembly (∼600 ℃/s) with cube lengths of38.5 mm is about ten times faster than that in the traditional assembly (∼60 ℃/s). Experiments yielding inhomogeneous quenched melttextures when the traditional assembly is used are shown to yield homogeneous silicate glass without quench textures when the rapid coolingassembly is used.

A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.

Invariant measure for cubic Fibonacci-like polynomials

A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.

High-Quality and Wafer-Scale Cubic Silicon Carbide Single Crystals

Cubic silicon carbide(3C-SiC)has superior mobility and thermal conduction over that of widely applied hexagonal 4H-SiC.Moreover,much lower concentration of interfacial traps between insulating oxide gate and 3C-SiC helps fabricate reliable and long-life devices like metal-oxidesemiconductor field effect transistors.However,the growth of high-quality and wafer-scale 3C-SiC crystals has remained a big challenge up to now despite decades-long efforts by researchers because of its easy transformation into other polytypes during growth,limiting the development of 3C-SiC-based devices.Herein,we report that 3C-SiC can be made thermodynamically favored from nucleation to growth on a 4H-SiC substrate by top-seeded solution growth technique,beyond what is expected by classical nucleation theory.This enables the steady growth of high-quality and large-size 3C-SiC crystals(2-4-inch in diameter and 4.0-10.0 mm in thickness)sustainable.The as-grown 3C-SiC crystals are free of other polytypes and have high-crystalline quality.Our findings broaden the mechanism of hetero-seed crystal growth and provide a feasible route to mass production of 3C-SiC crystals,offering new opportunities to develop power electronic devices potentially with better performances than those based on 4H-SiC.

Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

Effect of Size and Initial Water Content on the Effective Diffusion Coefficient during Convective Drying of Sweet Potato Cut into Cubic and Cylindrical Shapes

In this article, we investigated the influence of size and initial water content on the effective diffusion coefficient of sweet potatoes samples cut into cubic and cylindrical shapes. The sizes of the cubic samples are 0.5, 1, 1.5, 1.75, 2, 2.5 and 3 cm edge with a respective initial water content of 2.7, 3.76, 3.48, 2.68, 3.28, 2.17 and 2.29 kg/kgms. For cylindrical samples, the radius is set at 0.5 cm and sample heights are 1, 1.5, 2, 2.5, 3, 3.5 and 4 cm with respective water contents of 2.2, 3.19, 2.85, 2.1, 2.17, 2.39 and 2.03 kg/kgms. The effective diffusion coefficients of cubic samples are of the order of 10−10 and 10−9 m2∙s−1 grew with sample edge. As for the cylindrical samples, the effective diffusion coefficients were of the order of 10−9 m2∙s−1 and there was no linear correlation between cylinder height and their effective diffusion coefficient. As for the examination of the initial water content on the effective diffusion coefficient, it turned out that the initial water content had no influence on the effective diffusion coefficient of the sweet potato samples.

Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.

双正交Hermite Cubics的对称预滤波设计

将多小波预滤波器设计的"超函数"法推广到了双正交系统,得到使联合滤波器具有m阶平衡的条件,并针对双正交Hermite Cubics,分别设计了使系统具有2阶平衡与4阶平衡的对称预滤波器.

Application of face centred cubic TiB powder as conductive filler for electrically conductive adhesives

Face centred cubic（FCC） TiB ceramic powder synthesized by Ti-boronizing method was used as conductive filler to make ceramic electrically conductive adhesives（ECAs） with the polymer matrix.Electrically conductive properties of the ceramic ECAs were studied.The bulk electrical resistivity varied with the powder content of the FCC-TiB in ECAs.The FCC-TiB filled ECAs also showed the percolation behavior that usually occurred for the metal-filled ECAs,the percolation threshold was located at the content of 60%FCC-TiB.A minimum value of 0.1 Ω·cm was obtained at a content of 75%FCC-TiB.In order to check the reliability of mechanical property,tensile test was done to measure the shear strength,and the shear strength dropped with increasing the content of FCC-TiB powders.It is about 12.26 MPa at the content of 70%TiB powders.The Cu filled ECAs were also prepared for comparison.The properties of the oxidation resistance of the two ECAs were evaluated.The results show that the ceramic ECAs have excellent oxidation resistance and better stability compared with the Cu filled ECAs.

Growth of Cubic GaN by MOCVD at High Temperature

High quality cubic GaN (c GaN) is grown by metalorganic vapor deposition (MOCVD) at an increased growth temperature of 900℃,with the growth rate of 1 6μm/h.The full width at half maximum (FWHM) of room temperature photoluminescence (PL) for the high temperature grown GaN film is 48meV.It is smaller than that of the sample grown at 830℃.In X ray diffraction (XRD) measurement,the high temperature grown GaN shows a (002) peak at 20° with a FWHM of 21′.It can be concluded that,although c GaN is of metastable phase,high growth temperature is still beneficial to the improvement in its crystal quality.The relationship between the growth rate and growth temperature is also discussed.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.