Equal Coefficients Research Articles

Regularity for minimizers of a planar partitioning problem with cusps

We study the regularity of minimizers for a variant of the soap bubble cluster problem: min∑ℓ=0NcℓP(Sℓ),where cℓ>00$$\\end{document}]]>, among partitions {S0,⋯,SN,G} of R2 satisfying |G|≤δ and an area constraint on each Sℓ for 1≤ℓ≤N. If δ>00$$\\end{document}]]>, we prove that for any minimizer, each ∂Sℓ is C1,1 and consists of finitely many curves of constant curvature. Any such curve contained in ∂Sℓ∩∂Sm or ∂Sℓ∩∂G can only terminate at a point in ∂G∩∂Sℓ∩∂Sm at which G has a cusp. We also analyze a similar problem on the unit ball B with a trace constraint instead of an area constraint and obtain analogous regularity up to ∂B. Finally, in the case of equal coefficients cℓ, we completely characterize minimizers on the ball for small δ: they are perturbations of minimizers for δ=0 in which the triple junction singularities, including those possibly on ∂B, are “wetted”by G.

Equivalent spring-like system for two nonlinear springs in series: application in metastructure units design

The paper deals with the problem of design of unit in auxetic metastructure. The unit is modeled as a two-part spring-like system where each part is with individual stiffness. To overcome the problem of analyzing of each of parts separately, the equivalent spring is suggested to be introduced. In the paper, a method for obtaining the equivalent elastic force of the unit is developed. The method is the generalization of the procedure suggested for substitution of a hard and a soft spring in series with an equivalent one. The nonlinearity of original springs is of quadratic order. As a results, it is obtained that the equivalent elastic force for two equal springs remains of the same type as of the original springs (soft or hard). For two opposite type springs in series with equal coefficients, the equivalent force is soft. The method is applicable for any hard and soft nonlinear springs or spring-like systems. Thus the hexagonal auxetic unit which contains a soft and a hard part in series is analyzed. In the paper, a new analytic method for determination of the frequency of vibration for the unit under action of a constant compression force acting along the unit axis is introduced. The method is applied for units which contain two parts: hard–hard, soft–soft, hard–linear, soft–linear and opposite. The obtained approximate vibration results are compared with numerically obtained ones and show good agreement. The advantage of the method is its simplicity as it does not require the nonlinear equation of motion to be solved.

Основные особенности климатических условий зимнего сезона 2023/2024 гг. по данным мониторинга и прогнозов

The main results of the comprehensive analysis of the Northern Hemisphere large-scale atmospheric circulation features are presented for the 2023/2024 winter season. Skill scores of the consensus forecast for the 2023/2024 Northern Eurasia winter season are discussed in the context of reproducing the temperature and humidity regime. The qualitative analysis of the multimodel forecast from WMO’s Lead Center and the consensus forecast issued by NEACOF for seasonal anomalies in air temperature and precipitation for the winter of 2023/2024 resulted in the conclusion of the superior accuracy of the consensus forecast. This forecast was based on the data of three Russian models SL-AV, MGO, and INM with equal weighting coefficients.

Simultaneous confidence interval construction for many-to-one of proportion ratios of bilateral correlated data.

In ophthalmology and otolaryngology, data collected from paired body parts are typically reformatted into categorical bilateral data structures for subsequent research. This article applies Donner's equal correlation coefficient model and obtains nine simultaneous confidence intervals (SCI) of proportion ratios under three asymptotic statistical methods and three ways of multiplicity adjustment. The empirical coverage probability and mean interval width are evaluated through Monte Carlo simulations. A real example is used to demonstrate the proposed methods.

The effect of load-dependent tyre friction and aerodynamic cross-flow forces on the g-g maps and minimum-lap-time of motorcycles

A three-dimensional quasi-steady-state free-trajectory method based on semi-analytical g-g maps has been recently proposed to simulate the minimum-time manoeuvring of road vehicles. A number of assumptions, such as identical tyre-road friction coefficients on front and rear tyres and negligible aerodynamic cross-flow forces (i.e. downforces and sideforces), were enforced in the case of motorcycles to keep the g-g maps semi-analytical. Such assumptions are lifted in this work and their effect on the g-g maps of single-track vehicles is analysed, together with the consequences on the related minimum-lap-time simulations. The examples of application are carried out on the Mugello circuit and compared with previous findings in the literature. It is found that different friction coefficients on tyres call for different braking strategies to extract the maximum performance of the vehicle (when compared against the case with equal friction coefficients), while aerodynamic downforces can reduce stoppie and wheelie problems, improve acceleration and braking performance and increase the maximum lateral acceleration achievable. However, if the resulting cross-flow force lies on the plane of the bike the maximum lateral performance could be reduced, depending on tyre properties.

Strong Single Frequency Jamming Detection Method based on Adaptive Equalization Coefficients

Abstract Serious jamming effect on the communication signal maybe comes from the result of single-frequency jamming which could concentrate energy applying into the transmitted spectra. Usually, the communication signal is covered by the jamming effect. In order to effectively detect the existence of single frequency interference signal or not, the paper presents a frequency domain abnormal phenomena detection method based on adaptive equalization coefficients. The proposed method directly transforms the calculated equalization coefficients into the frequency domain. Then, the existence of strong single-frequency interference signals can be directly detected online by observing the characteristics of the frequency domain. The simulation results show that this method has a good detection effect on strong single frequency jamming. The research shows that the mentioned detection method and the related anomaly recognition technology based on equalization coefficients can be used for jamming detection, and can provide a new technical approach for jamming detection.

Kraje Unii Europejskiej a ubóstwo, przed i po kryzysie COVID-19

The purpose of the paper is to evaluate and present the position of the European Union countries according to the poverty level before and after the COVID-19 crisis, combining five individual indicators. The GRA (Grey Relational Analysis) method was used to calculate the composite poverty indicator. To assess poverty, the study uses criteria from the official database of the European Commission and calculates the aggregate index for 2019 and 2022. All criteria in the model have the same relative importance because the method of equal weight coefficients is applied. The paper proved that the Czech Republic and Slovenia had the most favourable indicators of poverty in both periods, while Greece, Romania, Bulgaria, and Latvia occupied a critical position. In general, the countries of Southern Europe and the Baltic countries have poor poverty indicators. Compared to 2019, according to the country rankings, the poverty level is significantly higher in Finland, Germany, and Hungary, while after the pandemic, the following countries made considerable progress in reducing poverty: Poland, Belgium, Luxembourg, and Cyprus. The presented results can be useful to decision-makers at the macro level in the field of economic, social, and sustainable development policy.

Asymmetric Rectified Electric Fields for Symmetric Electrolytes.

In this paper, building upon the numerical discovery of asymmetric rectified electric fields (AREFs), we explore the generation of AREF by applying a sawtooth-like voltage to 1:1 electrolytes with equal diffusion coefficients confined between two planar blocking electrodes. This differs from an earlier approach based on a sinusoidal AC voltage applied to 1:1 electrolytes with unequal diffusion coefficients. By numerically solving the full Poisson-Nernst-Planck equations, we demonstrate that AREF can be generated by a slow rise and a fast drop of the potential (or vice versa), even for electrolytes with equal diffusion coefficients of the cations and anions. We employ an analytically constructed equivalent electric circuit to explain the underlying physical mechanism. Importantly, we find that the strength of AREF can be effectively tuned from zero to its maximal value by only manipulating the time dependence of the driving voltage, eliminating the necessity to modify the electrolyte composition between experiments. This provides valuable insights to control the manipulation of AREF, which facilitates enhanced applications in diverse electrochemical systems.

Robust, wide-range, and precise transmitter IQ impairment monitoring scheme for coherent digital subcarrier multiplexing systems.

In this Letter, we present a robust, wide-range, and precise monitoring scheme for transmitter (Tx) impairments in coherent digital subcarrier multiplexing (DSCM) systems. The proposed scheme employs frequency-domain pilot tones (FPTs) to compensate for frequency offset (FO), polarization aliasing, and carrier phase noise, thus isolating Tx impairments from channel distortions. It then implements 4 × 4 real-valued MIMO to compensate for Tx impairments by equalizing symmetric subcarriers. Tx impairment monitoring is derived from the equalizer coefficients. By considering the phase shift caused by Tx impairments, a wide-range and precise monitoring of Tx impairments including IQ skew, IQ phase, and gain imbalances is achieved. We experimentally validated our approach using a 48-GBaud, four-subcarrier, dual-polarization coherent DSCM system. The results confirm the method's capability for a wide-range, robust, and precise Tx impairment monitoring in coherent DSCM systems, maintaining performance even in the presence of ultra-fast polarization variation.

Robust multimodulus blind equalization algorithm for multilevel QAM signals in impulsive noise

Robust multimodulus blind equalization algorithm for multilevel QAM signals in impulsive noise

Anisotropic media with singular slowness surfaces

It is proved that if an anisotropic medium has an open set of singular directions, then this medium has two slowness surfaces that completely coincide. The coinciding slowness surfaces form one double singular slowness surface. The corresponding anisotropic medium is an elliptical orthorhombic (ORT) medium with equal stiffness coefficients c44=c55=c66 rotated to an arbitrary coordinate system. Based on the representation of the Christoffel matrix as a uniaxial tensor and considering that the elements of the Christoffel matrix are quadratic forms in the components of the slowness vector, a system of homogeneous polynomial equations was derived. Then, the identical equalities between homogeneous polynomials are replaced by the equalities between their coefficients. As a result, a new system of equations is obtained, the solution of which is the values of the reduced (density normalized) stiffness coefficients in a medium with a singular surface. Conditions for the positive definite of the obtained stiffness matrix are studied. For the defined medium, the Christoffel equations and equations of group velocity surfaces are derived. The orthogonal rotation matrix that transforms the medium with a singular surface into an elliptic ORT medium in the canonical coordinate system is determined. In the canonical coordinate system, the slowness surfaces S1 and S2 waves coincide and are given by a sphere with a radius . The slowness surface of qP waves in the canonical coordinate system is an ellipsoid with semi-axes , , . The polarization vectors of S1 and S2 waves can be arbitrarily selected in the plane orthogonal to the polarization vector of the qP wave. However, the qP wave polarization vector can be significantly different from the wave vector. This feature should be taken into account in the joint processing and modelling of S and qP waves. The results are illustrated in one example of an elliptical ORT medium.

Equalizer Parameters’ Adjustment Based on an Oversampled Channel Model for OFDM Modulation Systems

A physical model of a wireless transmission channel in the time domain usually consists of the main propagation path and only a few reflections. The reasonable assumptions made about the channel model can improve its parameters’ estimation by a greedy OFDM (Orthogonal Frequency Division Multiplexing) equalizer. The equalizer works flawlessly if delays between propagation paths are in the sampling grid. Otherwise, the channel impulse response loses its compressible characteristic and the number of coefficients to find increases. It is possible to get back to the simple channel model by data oversampling. The paper describes how the above idea helps the OMP (Orthogonal Matching Pursuit) algorithm estimate channel coefficients. The authors analyze the oversampling algorithm on the one hand to assess the influence of filtering function and signal resolution on the quality of the channel impulse response reconstruction. On the other hand, the abilities of the OMP algorithm are analyzed to distinguish components of the oversampled signal. Based on these analyses, we proposed modifications to the compressible channel’s impulse response reconstruction algorithm to minimize the number of transmission errors. A distinction was made between the filters used in the OMP search and channel reconstruction stages before calculating equalizer coefficients. Additionally, the results of the search stage were considered as elements within the groups.

Running-Time Analysis of Brain Storm Optimization Based on Average Gain Model.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O(n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U-12,12 mutation operator are approximately twice those of BSOs with the U(-1,1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.

Economic tolerance design of the P2 raceway based on the quasi-static model of aerospace ball bearings

This study focused on designing the raceway tolerance of high-precision rolling bearings. After the tolerance error equivalence relationship is defined, the application of the rolling bearing error equalization effect in tolerance design is studied. First, a five-degree of freedom quasi-static model was established for angular contact ball bearings. The waviness was included in the manufacturing error, and the radial and axial runouts of the bearing inner ring were calculated. Second, the error homogenization effect of the rolling bearing was studied, and the error homogenization coefficient was defined. The results of the study demonstrated that the bearing rotary accuracy was higher than the raceway error by an order of magnitude. Third, the manufacturing error range of each precision grade of the rolling bearing raceway was obtained by investigating errors of the equalization coefficient. Finally, the specific value of the raceway tolerance of P2 rolling bearings was obtained.

Incident component extraction from disturbed waves around large fixed cylindrical structures

The parameters of incident waves are critical for real-time wave load estimation of structures in service. Nonetheless, it is challenging to characterize incident waves accurately using the measured wave surface elevation around large fixed cylindrical structures due to the interaction with the structure in the wave field. To provide a better understanding of incident waves, which are usually buried in directly measured waves, a new time-domain method for the extraction of first-order and second-order incident waves around large fixed cylindrical structures is proposed. In contrast to most existing separation methods that are suitable for structures with equal reflection coefficients, the amplitude and phase changes of near-field waves around cylindrical structures can be determined by considering the significant diffraction effect, and then the time-frequency characteristic of the wavelet transform is employed, which enables the extraction of incident waves in the time domain. The accuracy of the proposed method is studied using several examples with known incident waves which are generated with the OpenFOAM. The numerical results show that the deviations between the exact and extracted incident waves change from 6.16% to 16.77% for different wave conditions. To further investigate the performance of the proposed method, an experimental study on waves around a mono-pile offshore wind turbine (OWT) is conducted in the laboratory of the Ocean University of China. The predicted results basically agree well with the target waves in terms of amplitude and phase. The deviations between predicted waves using the proposed method and target waves are 110% smaller than those between directly experimental measured waves and target waves for all tested conditions. Finally, 48 h of measured wave data were obtained during calm and typhoon periods around a mono-pile OWT located near Rudong County, Jiangsu Province, in the Yellow Sea of China. There are almost 150% and 30% differences between the extraction results and measured data in the time series and statistical wave heights, respectively, which means that employing disturbed wave data as the input for calculating real-time wave loads leads to deviations that cannot be ignored.

CNN neural network temporal feature storage structure fusion for the visible channel equalization algorithm

The visible light communication channel has time-varying characteristics and is difficult to predict. This paper proposes an equalization algorithm based on the structure of a convolutional neural network (CNN), combining time series feature length and long short-term memory (LSTM), and adding a residual structure. It can be seen that the equalization coefficient vector of the optical channel is a time series, which can reflect the noise characteristics of the channel and has storage characteristics. The equalizer algorithm can accurately learn the complex channel characteristics and calculate the compensation coefficient according to the channel characteristics. It can also restore the original transmission signal. At the same time, this paper also examines the compensation method of the receiver in the mobile state. The long-term memory parameters of LSTM are used to represent the sequence causality in the memory channel, and CNN and residual structure are used to refine the results and improve the accuracy of the reconstruction. The simulation results show that the algorithm can effectively eliminate the influence of the fading characteristics of the visible optical channel, improve the bit error rate performance of system transmission, solve the overall problem of channel corruption, and precisely restore the original transmission signal with fast convergence speed. In addition, this method can achieve a better balance between performance and complexity compared to the traditional contention balancing method, which proves the potential and effectiveness of the proposed channel balancing method.

Toward Full Passive Internet of Things: Symbiotic Localization and Ambient Backscatter Communication

In this paper, we proposed a symbiotic localization and ambient backscatter communication (SLABC) architecture, which uses existing ambient backscatter communication (AmBC) hardware and received signals to help Internet of Things (IoT) localize target objects. The SLABC can be viewed as a specific realization of integrated passive/symbiotic sensing and communication, which has two mutually beneficial stages: 1) sensing stage with generalized Prony with homologous matching (GPHM) method; 2) communication stage with multi-source constant modulus algorithm (MSCMA) method. To formulate SLABC, we propose a unified TMSC signal model to characterize the complex multi-source, multi-path and multi-reflection symbiotic communication (TMSC) and facilitate the key information extraction. Utilizing the frequency domain expression of the unified signal model and the similarity between multi-path channel coefficients and tap coefficients of equalizers, our proposed GPHM and MSCMA methods are efficient to mitigate the TMSC interference and retrieve the interested information to locate targets and communicate. The proposed SLABC concept updates the symbiotic AmBC IoT with the least cost and reduces the dependence on hardware stacking. The simulation results show that: 1) information extracted by GPHM and MSCMA can help localization achieve high accuracy and reduce the complexity of multi-path interference mitigation; 2) both of the two methods have a positive influence on each other.

Multi-hazard susceptibility model based on high spatial resolution data-a case study of Sali settlement (Dugi otok, Croatia).

The world has been facing an increase in various natural hazards. The coastal regions are recognized as one of the most vulnerable due to high population pressure and climate change intensity. Mediterranean countries have one of the most burnable ecosystems in the world, one of the most exposed to pluvial floods, and have the highest erosion rates within the EU. Therefore, the aim of this study was to develop the first multihazard susceptibility model in Croatia for the Sali settlement (island of Dugi otok). The creation of a multi-hazard susceptibility model (MHSM) combined the application of geospatial technology (GST) with a local perception survey. The methodology consisted of two main steps: (1) creating individual hazard susceptibility models (soil erosion, wildfires, pluvial floods), and (2) overall hazard susceptibility modeling. Multicriterial GIS analyses and the Analytical Hierarchy Process were used to create individual hazard models. Criteria used (32) to create models are derived from very-high-resolution (VHR) models. Two versions of MHSM are created: 1) all criteria with equal weighting coefficients and 2) weight coefficients determined based on public perception. According to MHSM 1, most of the research (58%) area is moderately susceptible to multiple hazards. Highly and very highly susceptible areas are 27% of the drainage basin and are mostly located near roads and houses. MHSM 2 reveals similar results to MHSM 1. The public perceives that the research area is the most susceptible to wildfires. The wildfire ignition risk is ranked as moderate (3.00) with a standard deviation of 1.16. Pluvial flood risk is ranked low (2.78), with a standard deviation of 1.15. The risk of soil is most inferior (2.24) with a standard deviation of 0.91. The the most significant difference between public perception and the GIS-MCDA model of hazard susceptibility is related to soil erosion. However, the accuracy of the soil erosion model was confirmed by ROC curves based on recent traces of soil erosion in the research area. The proposed methodological framework of multi-hazard susceptibility modeling can be applied, with minor modifications, to other Mediterranean countries.

Loss Imbalance Effect on Inter-Core Crosstalk in Bidirectional Uncoupled Multi-Core Fiber Transmission

The effect of core loss imbalance on inter-core crosstalk (XT) is studied theoretically and numerically in long-haul bidirectional uncoupled multi-core fiber transmission. The coupled power equations are solved for two cores with imbalance of loss coefficients, and the solution is used to obtain expressions for direct, indirect, backscattered and bidirectional XT powers. These expressions generalize expressions reported by other authors to arbitrary loss coefficients. It is shown that, in the range of the loss coefficient imbalance from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-0.04$</tex-math></inline-formula> dB/km to 0.04 dB/km, the XT powers in decibel show approximately a linear dependence on the loss coefficient imbalance. In that range, differences of the indirect XT power of nearly 1.2 dB relative to the indirect XT power with equal loss coefficients can occur for the larger loss coefficient imbalance; for the direct and backscattered XT powers, the differences are even larger, reaching around 2 dB. These values of 1.2 and 2 dB of difference translate directly to the bidirectional XT power of long-haul 2-core fiber links, in case of dominance of indirect and backscattered XT, respectively.

Adaptive Equalization for UWB communication System based on ANFIS

Ultra-wideband (UWB) communication systems cover enormous bandwidths that have strongly low-power spectral densities. At UWB communication system with high data rate, owing to multipath propagation, the spread delay in inter symbol interference (ISI) will raise the bit error rate (BER) considerably. ISI which is formed via the UWB channels can be removed by equalization, which is one of the most significant signal processing techniques. Furthermore, LMS algorithm represents a very efficient tool for determining adaptive equalizer coefficients values in communication systems, in spite of that, the LMS adaptive equalizer encounters response diminishing besides slow convergence rate. The current paper adopts an adaptive equalizer based adaptive neuron-fuzzy inference system (ANFIS). The simulation outcomes reveal that the convergence rates as well as accuracy of identification of ANFIS based algorithm are surpass the traditional LMS algorithm, moreover, simulation outcomes prove that ISI is effectively limited and the performance of the system is clearly improved.