EQUIVARIANT SELF EQUIVALENCES OF PRINCIPAL FIBRE BUNDLES

Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.

STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

EQUIVALENCES BETWEEN BLOCH TYPE SPACES AND BMO SPACES ON THE HYPERBOLIC DOmAINS IN C

For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.

ON REDUCIBILITY OF THE SELF-HOMOTOPY EQUIVALENCES OF WEDGE SPACES

Reducibility of the self-homotopy equivalences of wedge spaces is studied and some conditions implying the reducibility are obtained.

Approximate trace and singleton failures equivalences for transition systems

Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire met- ric, a generalized framework of transition system approximation is proposed by developing the notions of approximate language equivalence and approximate singleton failures （SF） equivalence. The framework takes the traditional exact equivalence as a special case. The approximate language equivalence is coarser than the approximate Slc equivalence, just like the hierarchy of the exact ones. The main conclusion is that the two approximate equiva- lences satisfy the transitive property, consequently, they can be successively used in transition system approximation.

LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS

In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.

INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type. First of all, we show that, if two finite-dimensional selfinjective k-algebras are stably equivalent of Morita type, then their orbit algebras are isomorphic. Secondly, it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type. As an application of this result, it is obtained that if an algebra is of finite representation type, then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally, we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type, their repetitive algebras are also stably equivalent of Morita tvDe under cert..in conditions.

The initial stages of Li_(2)O_(2) formation during oxygen reduction reaction in Li-O_(2) batteries:The significance of Li_(2)O_(2) in charge-transfer reactions within devices

Lithium-oxygen batteries are a promising technology because they can greatly surpass the energy density of lithium-ion batteries.However,this theoretical characteristic has not yet been converted into a real device with high cyclability.Problems with air contamination,metallic lithium reactivity,and complex discharge and charge reactions are the main issues for this technology.A fast and reversible oxygen reduction reaction(ORR)is crucial for good performance of secondary batteries',but the partial knowledge of its mechanisms,especially when devices are concerned,hinders further development.From this perspective,the present work uses operando Raman experiments and electrochemical impedance spectroscopy(EIS)to assess the first stages of the discharge processes in porous carbon electrodes,following their changes cycle by cycle at initial operation.A growth kinetic formation of the discharge product signal(Li_(2)O_(2))was observed with operando Raman,indicating a first-order reaction and enabling an analysis by a microkinetic model.The solution mechanism in the evaluated system was ascribed for an equivalent circuit with three time constants.While the time constant for the anode interface reveals to remain relatively constant after the first discharge,its surface seemed to be more non-uniform.The model indicated that the reaction occurs at the Li_(2)O_(2) surface,decreasing the associated resistance during the initial discharge phase.Furthermore,the growth of Li_(2)O_(2) forms a hetero-phase between Li_(2)O_(2)/electrolyte,while creating a more compact and homogeneous on the Li_(2)O_(2)/cathode surface.The methodology here described thus offers a way of directly probing changes in surface chemistry evolution during cycling from a device through EIS analysis.

Distribution and correlation of refractive parameters in children with different corneal curvatures in southeast China

AIM:To analyze the distribution of refractive status in school-age children with different corneal curvatures(CC)and the correlation between CC and refractive status.METHODS:A total of 2214 school-aged children of grade 4 in Hangzhou who were screened for school myopia were included.Uncorrected distance visual acuity(UCDVA),non-cycloplegic refraction,axial length(AL),horizontal and vertical corneal curvature(K1,K2)were measured and spherical equivalent(SE),corneal curvature radius(CCR)and axial length/corneal radius of curvature ratio(AL/CR)were calculated.UCDVA<5.0 and SE≤-0.50 D were classified as school-screening myopia.According to the different CCRs,the patients were divided into the lower corneal curvature(LCC)group(CCR≥7.92)and the higher corneal curvature(HCC)group(CCR<7.92).Each group was further divided into the normal AL subgroup and the long AL subgroup.The refractive parameters were compared to identify any differences between the two groups.RESULTS:Both SE and AL were greater in the LCC group(P=0.013,P<0.001).The prevalence of myopia was 38% in the LCC group and 44% in the HCC group(P<0.001).The proportion of children without screening myopia was higher in the LCC group(62%)than in the HCC group(56%).Among these children without screening myopia,the proportion of long AL in the LCC group(24%)was significantly higher than that in the HCC group(0.012%;P<0.001).The change of SE in the LCC group was less affected by the increase of AL than that in the HCC group.CONCLUSION:School-aged children in the LCC group have a lower incidence of screening myopia and longer AL.Low CC can mask SE reduction and AL growth to some extent,and the change of AL growth change more in children with low CC than high CC.Before the onset of myopia,its growth rate is even faster than that after the onset of myopia.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

The circuitry landscape of perovskite solar cells:An in-depth analysis

The extensive research and development in perovskite solar cells (PSCs) have rekindled the hopes of converting solar energy into electricity.An elusive understanding of underlying mechanisms is required for the development of efficient PSCs.Over the years,Impedance Spectroscopy (IS) characterization,along with complementary techniques,has proven to be an effective way to understand and analyze the charge transport and recombination at interface and bulk of PSCs.The IS of PSCs have been analyzed,interpreted,and improvised continuously,revealing intricate details about the work.However,there is a lack of centralized source of these details,which make it tougher to account for the generalized approach to understand the device properties.The present work is focused on compiling the research done on various PSC device architectures via IS to construct a comprehensive foundation of information on impedance plots,equivalent circuits,and associated processes.

Infiltration,runoff,and slope stability behaviors of infinite slope with macropores based on an improved Green–Ampt model

Infiltration–runoff–slope instability mechanism of macropore slope under heavy rainfall is unclear.This paper studied its instability mechanism with an improved Green–Ampt(GA)model considering the dual-porosity(i.e.,matrix and macropore)and ponding condition,and proposed the infiltration equations,infiltration–runoff coupled model,and safety factor calculation method.Results show that the infiltration processes of macropore slope can be divided into three stages,and the proposed model is rational by a comparative analysis.The wetting front depth of the traditional unsaturated slope is 17.2%larger than that of the macropore slope in the early rainfall stage and 27%smaller than that of the macropore slope in the late rainfall stage.Then,macropores benefit the slope stability in the early rainfall but not in the latter.Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration.The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow.Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain(ω_(f)),whereas promoted by increasing ratio of saturated permeability coefficients between the two domains(μ).The increasing trend of ponding depth is sharp at first and then grows slowly.Finally,when rainfall duration is less than 3 h,ωf andμhave no significant effect on the safety factor,whereas it decreases with increasingωf and increases with increasingμunder longer duration(≥3 h).With the increase ofω_(f),the slope maximum instability time advances by 10.5 h,and with the increase ofμ,the slope maximum instability time delays by 3.1 h.

Ultrahigh spatiotemporal resolution beam signal reconstruction with bunch phase compensation

Various electromagnetic signals are excited by the beam in the acceleration and beam-diagnostic elements of a particle accelerator.It is important to obtain time-domain waveforms of these signals with high temporal resolution for research,such as the study of beam–cavity interactions and bunch-by-bunch parameter measurements.Therefore,a signal reconstruction algorithm with ultrahigh spatiotemporal resolution and bunch phase compensation based on equivalent sampling is proposed in this paper.Compared with traditional equivalent sampling,the use of phase compensation and setting the bunch signal zero-crossing point as the time reference can construct a more accurate reconstructed signal.The basic principles of the method,simulation,and experimental comparison are also introduced.Based on the beam test platform of the Shanghai Synchrotron Radiation Facility(SSRF)and the method of experimental verification,the factors that affect the reconstructed signal quality are analyzed and discussed,including the depth of the sampled data,quantization noise of analog-to-digital converter,beam transverse oscillation,and longitudinal oscillation.The results of the beam experiments show that under the user operation conditions of the SSRF,a beam excitation signal with an amplitude uncertainty of 2%can be reconstructed.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

A compact X-band backward traveling-wave accelerating structure

Very high-energy electrons(VHEEs)are potential candidates for FLASH radiotherapy for deep-seated tumors.We proposed a compact VHEE facility based on an X-band high-gradient high-power technique.In this study,we investigated and realized the first X-band backward traveling-wave(BTW)accelerating structure as the buncher for a VHEE facility.A method for calculating the parameters of single cell from the field distribution was introduced to simplify the design of the BTW structure.Time-domain circuit equations were applied to calculate the transient beam parameters of the buncher in the unsteady state.A prototype of the BTW structure with a thermionic cathode-diode electron gun was designed,fabricated,and tested at high power at the Tsinghua X-band high-power test stand.The structure successfully operated with 5-MW microwave pulses from the pulse compressor and outputted electron bunches with an energy of 8 MeV and a pulsed current of 108 mA.

Ice-Induced Vibrational Response of Single-Pile Offshore Wind-Turbine Foundations

Important challenges must be addressed to make wind turbines sustainable renewable energy sources.A typical problem concerns the design of the foundation.If the pile diameter is larger than that of the jacket platform,traditional mechanical models cannot be used.In this study,relying on the seabed soil data of an offshore wind farm,the m-method and the equivalent embedded method are used to address the single-pile wind turbine foundation problem for different pile diameters.An approach to determine the equivalent pile length is also proposed accordingly.The results provide evidence for the effectiveness and reliability of the model based on the equivalent embedded method.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

An improved positioning model of deep-seafloor datum point at large incidence angle

The inhomogeneous sound speed in seawater causes refraction of sound waves,and the elimination of the refraction effect is essential to the accuracy of underwater acoustic positioning.The raytracing method is an indispensable tool for effectively handling problems.However,this method has a conflict between localization accuracy and computational quantity.The equivalent sound speed profile(ESSP)method uses a simple sound speed profile(SSP)instead of the actual complex SSP,which can improve positioning precision but with residual error.The residual error is especially non-negligible in deep water and at large beam incidence angles.By analyzing the residual error of the ESSP method through a simulation,an empirical formula of error is presented.The data collected in the sailing circle mode(large incidence angle)of the South China Sea are used for verification.The experiments show that compared to the ESSP method,the improved algorithm has higher positioning precision and is more efficient than the ray-tracing method.

Assessing the Efficacy of Wheat-Soybean Based Intercropping System at Different Plant Densities in Bambili, Cameroon

Wheat is one of the most important cereals in the world, serving as a staple for millions globally. In the wake of the geopolitical crisis between Russia and Ukraine, it has become incumbent for many countries to invest in wheat production. Improving cropping systems for wheat production is paramount. Intercropping cereals with legumes has tremendous advantages. Therefore, this study was designed to optimize wheat production by intercropping it with soybean at different densities. Between March and August 2023, a randomized complete block design trial was conducted in Bambili, North West of Cameroon with treatments T1 (wheat monocrop at 200,000 plants ha−1), T2 (soybean monocrop at 250,000 plants ha−1), T3 (200,000 wheat and 125,000 soybean ha−1), T4 (100,000 wheat and 250,000 soybean ha−1), T5 (200,000 wheat and 250,000 soybean ha−1) and T6 (100,000 wheat and 125,000 soybean ha−1). Results revealed that growth parameters of wheat were not significantly influenced by monocrop or intercrop. The yield of wheat was significantly higher in the monocrop than the intercrop treatments, with slight variation amongst the intercrop treatments. Soybean yield was higher in the monocrop than in the intercrop, with no variations amongst the intercrop treatments. Only the land equivalence ratio (LER) for T5 was greater than 1.0. The competitive ratio for T5 was 0.54 for wheat and 1.90 for soybean, comparatively lower than the other monocrop treatments. Intercropping wheat and soybean at 200,000:250,000 ratio is recommended.

Hybrid Multi-Infeed Interaction Factor Calculation Method Considering Voltage Regulation Control Characteristics of Voltage Source Converter

Voltage source converter based high voltage direct current(VSC-HVDC)can participate in voltage regulation by flexible control to help maintain the voltage stability of the power grid.In order to quantitatively evaluate its influence on the voltage interaction between VSC-HVDC and line commutated converter based high voltage direct current(LCC-HVDC),this paper proposes a hybrid multi-infeed interaction factor(HMIIF)calculation method considering the voltage regulation control characteristics of VSC-HVDC.Firstly,for a hybrid multi-infeed high voltage direct current system,an additional equivalent operating admittance matrix is constructed to characterize HVDC equipment characteristics under small disturbance.Secondly,based on the characteristic curve between the reactive power and the voltage of a certain VSC-HVDC project,the additional equivalent operating admittance of VSC-HVDC is derived.The additional equivalent operating admittance matrix calculation method is proposed.Thirdly,the equivalent bus impedance matrix is obtained by modifying the alternating current(AC)system admittance matrix with the additional equivalent operating admittance matrix.On this basis,the HMIIF calculation method based on the equivalent bus impedance ratio is proposed.Finally,the effectiveness of the proposed method is verified in a hybrid dual-infeed high voltage direct current system constructed in Power Systems Computer Aided Design(PSCAD),and the influence of voltage regulation control on HMIIF is analyzed.