Coefficient Functions Research Articles

An Ab-initio study on spin gapless semiconducting in novel quaternary heusler alloys RhCoVZ (Z = Al, Ga, and In): Insights into stability, electronic, magnetic, thermoelectric, and optical properties

The stability and half-metallic ferromagnetic properties of recently developed gapless semiconductor alloys, RhCoVZ (Z = Al, Ga, and In), were the subject of investigation in this research study. Three different non-equivalent structural configurations, namely type I, type II, and type III structures, have been examined. Among these compounds, Type I is characterized as the most stable phase in the ferromagnetic order, as opposed to the non-magnetic order. Through calculations of cohesive energies, formation energies, phonon dispersion curves, and elastic constants, we have demonstrated that RhCoVZ (Z = Al, Ga, and In) exhibits thermodynamic stability, as well as dynamic and mechanical. Using modified Becke-Johnson (mBJ) calculations, it has been revealed that RhCoVZ (Z = Al, Ga, and In) are spin gapless semiconductor half-metallic ferromagnets with an indirect bandgap. Additionally, it was observed that the electrons at the Fermi level (EF) are entirely spin-polarized. The total magnetic moment in all three compounds was determined to be an integer value of 2.00 µB per formula, in accordance with the Slater-Pauling rule (Mt = Zt - 24). All the calculations in this study were performed using density functional theory (DFT) based on the full-potential linearized augmented plane wave (FP-LAPW) method, which was implemented in the WIEN2k code. The effective mass of electrons/holes is (0.167/0.385) for RhCoVAl, (0.454/0.322) for RhCoVGa, and (0.604/0.242) for RhCoVIn. The thermoelectric properties of the three compounds were explored using the semi-classical Boltzmann transport theory. It was discovered that all three compounds exhibit high power factors and high Seebeck coefficients, with values reaching up to 1.5 mV/K for RhCoVAl and 1.25 mV/K for RhCoVGa. Based on the results, the highest observed ZT values for RhCoVZ (Z = Al, Ga, and In) are 0.95, 0.97, and 0.93, respectively. The study's findings indicate that these compounds possess stable characteristics, making them promising candidates for various device applications in fields like spintronics, thermoelectricity, shape memory, and spin filters. Furthermore, the investigation of their optical properties, including the dielectric function and absorption coefficient, suggests potential implications for optoelectronic applications. Overall, these materials exhibit diverse and valuable properties, opening up exciting opportunities for future technological advancements in multiple domains.

Model order reduction for optimality systems through empirical gramians

In the present article, optimal control problems for linear parabolic partial differential equations (PDEs) with time-dependent coefficient functions are considered. One of the common approach in literature is to derive the first-order sufficient optimality system and to apply a finite element (FE) discretization. This leads to a specific linear but high-dimensional time variant (LTV) dynamical system. To reduce the size of the LTV system, we apply a tailored reduced order modeling technique based on empirical gramians and derived directly from the first-order optimality system. For testing purpose, we focus on two specific examples: a multiobjective optimization and a closed-loop optimal control problem. Our proposed methodology results to be better performing than a standard proper orthogonal decomposition (POD) approach for the above mentioned examples.

Methods of periodically non-stationary random processes for vibrations monitoring of rolling bearing with damaged outer race

The vibrations of a rolling bearing with a damaged outer race are analyzed using a method based on periodically non-stationary random processes (PNRPs). PNRPs can be considered as a particular case of poly-periodically non-stationary random processes (PPNRs), which describe the interactions of vibration stochastic rhythms with different periods that are determined based on the characteristic bearing frequencies. A PNRP model for these vibrations is verified using methods for discovering the first- and second-order periodicities. By applying the least squares technique, it is shown that the mean function and variance are time periodic functions, and their basic frequencies are determined. This enables us to calculate the amplitude spectra for the deterministic oscillations and the time changes in the power for the stochastic part. It is shown that the dependencies of the Fourier coefficients for the covariance function on lag have the forms of slowly damped groups. Vibration covariance structures are compared for different fault widths; it is found that high-frequency modulations of the PNRP carrier modulations are narrow-band, and Rice representations are used to model them. The PRNP model of vibrations is then represented in the form of a superposition of the stationary high-frequency components that are jointly periodically non-stationary. The mutual periodical non-stationarity of these components results in variance time changes. Band-pass filtering of the vibration signal is conducted, and the influence of the filter bandwidth on the number and values of the amplitude of the variance harmonics is analyzed. It is shown that PNRP methods for time series processing enable fault detection in cases where the squared envelope and other familiar techniques are ineffective.

Analysis of optimization methods for nonparametric estimation of probability density in large volume samples

A method is proposed for selecting the blurriness coefficient of kernel functions for nonparametric estimation of the probability density of a one-dimensional random variable with large volumes of statistical data, for example, obtained by remote sensing of natural objects. In the proposed method for selecting the blurriness coefficient, a regression estimate of the probability density is used. A method for synthesizing a regression probability density estimate is presented. The synthesis of the estimate is based on compression of the initial sample by decomposition of the range of values of a random variable. To decompose the range of values of a random variable, the Heinhold-Gaede rule and the formula for optimal selection of the number of sampling intervals are applied. Two approaches to the selection of the blurriness coefficient of the regression estimation of probability density using the traditional and proposed by the authors optimization methods of nonparametric estimation of probability density are considered. The traditional method of optimizing nonparametric estimation of probability density is based on minimizing its mean square deviation. In the proposed method, the selection of the blurriness coefficients of the kernel functions is based on the conditions of the minimum error of approximation of the regression estimate of the desired probability density. The approximation properties of the regression estimation of probability density using two methods of its optimization are analyzed. The conditions of their competence in estimating the probability densities of random variables with a lognormal distribution law are established. The results obtained allow for development when optimizing a regression estimate of the probability density of a multidimensional random variable.

Modifikasi Metode Big-M dan Analisis Sensitivitasnya untuk Optimasi Produksi Usaha Kecil Menengah

UKM (Small and Medium Enterprises) X is a business that produces various types of peanut brittle. Rempeyek is suitable as a snack and is popular with children and adults. The production process of UKM X is related to the quantity of demand and availability of raw materials. Therefore, optimal production planning is needed for UKM X to meet customer demand and obtain maximum profits. The problem of production is modeled into linear programming with the method used, namely, the method of Big M. The Big-M method is used because, on the function of the barrier on the production target, there is an equation , so artificial variables must be added to its solution. In this study, a modification of the Big-M method is made, and at the completion stage, it uses iteration with the determinant algorithm of the order of two matrices. The calculation results obtained the maximum profit of UKM X in a week of Rs5.455.775 by producing 56 kg of peanuts, 20 kg of seeds, 16 kg of spinach, 23 kg of tempe, and 60 kg of shrimp to meet customer requirements and utilize the availability of raw materials. Subsequently, sensitivity analysis is performed on the target function coefficient and the right street constants of the barrier to determine how the change affects the optimal solution. The results show that the solution remains optimal when profits are in the interval obtained, but the maximum profit value changes with constant production. Based on the calculation results, raw material supplies remain optimal when the change value is within the interval obtained.

On a Coefficient Inequality for Carathéodory Functions

In the paper we consider a general inequality |pn-1pn+1-pn2|≤4-|p1|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|p_{n-1}p_{n+1}-p_n{}^2|\\le 4-|p_1|^2$$\\end{document} involving coefficients of functions with a positive real part. We prove this inequality for n=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=2$$\\end{document} and n=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=3$$\\end{document}. Consequently, the relative inequalities involving coefficients of Schwarz functions are obtained. As an application, the two sharp estimates of the Hankel determinants H3,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{3,1}$$\\end{document} and H2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{2,3}$$\\end{document} are proved for functions in S∗(1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal S}^*(1/2)$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document}, respectively.

Role of compressive and tensile strains and spin-orbit coupling on structure and behaviors of cubic FAPbI3 perovskites: A first-principles prediction

Organic-inorganic perovskite materials have attracted significant attention in solar technologies due to their extraordinary structural, electrical, and optical features. This study extensively examined the impacts of bidirectional tensile and compressive strains and spin-orbit coupling (SOC) on the structural, electronic and optical characteristics of formamidinium lead iodide perovskite (FAPbI3) structures. The investigation was performed using the first-principles density-functional theory (DFT). The electronic band structures of FAPbI3 without SOC revealed that the perovskite structure possesses the characteristics of a semiconductor, explicitly featuring a direct bandgap. The application of compressive strains resulted in dwindling the electronic bandgap while tensile strains upsurged the bandgaps, except at +6 % strains. The incorporation of the SOC subjugated a notable decrease in the bandgap, causing a transition of the perovskite structure from a direct bandgap to an indirect bandgap state. The real dielectric constant suggested that the system maintains its semiconducting character under the exposure of both compressive and tensile strains. The imaginary part of the dielectric function, loss spectrum, and absorption coefficient peaks of FAPbI3 perovskites exhibited a blueshift when subjected to compressive strains. However, the application of tensile strains eventuated in a redshift. The electronic and optical characteristics indicated that FAPbI3 perovskites have great potential for optoelectronic devices, including LEDs, LCD backlights, solar cells, lasers, and light detectors.

Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses

This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete data. Second, we present an adjusted estimator of the stochastic error variance by employing the Nadaraya–Watson kernel estimation technique. Third, we apply the inverse probability-weighted method and instrumental variable adjustment technique to construct the adaptive-weighted adjusted estimators for unknown parameters and smooth functional coefficients. The asymptotic properties of our proposed estimators are established under some regularity conditions. Finally, numerous simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed estimators.

Detecting active latitudes of Sun-like stars using asteroseismic a-coefficients

Aims. We introduce a framework to measure the asphericity of Sun-like stars using a1, a2, and a4 coefficients and constrain their latitudes of magnetic activity. Methods. We evaluated systematic errors on the inferred coefficients in function of key physical and seismic parameters (inclination of rotation axis, average rotation, height-to-noise ratio of peaks in power spectrum). The measured a-coefficients account for rotational oblateness and the effect of surface magnetic activity. We used a simple model that assumes a single latitudinal band of activity. Results. Using solar SOHO, VIRGO, and SPM data, we demonstrate the capability of the method to detect the mean active latitude and its intensity changes between 1999 and 2002 (maximum of activity) and 2006 and 2009 (minimum of activity). We further applied the method to study the solar-analogue stars 16 Cyg A and B using Kepler observations. In 16 Cyg A, we detected an equatorial band of activity exhibiting an intensity that could be comparable to that of the Sun. However, 16 Cyg B exhibits a bimodality in a4 that is challenging to explain. We suggest that this could be a manifestation of the transition between a quiet and an active phase of activity. Validating or invalidating this hypothesis may require new observations.

The method of constant terms and k-colored generalized Frobenius partitions

In his 1984 AMS memoir, Andrews introduced the family of k-colored generalized Frobenius partition functions. For any positive integer k, let cϕk(n) denote the number of k-colored generalized Frobenius partitions of n. Among many other things, Andrews proved that for any n≥0, cϕ2(5n+3)≡0(mod5). Since then, many scholars subsequently considered congruence properties of various k-colored generalized Frobenius partition functions, typically with a small number of colors.In 2019, Chan, Wang and Yang systematically studied arithmetic properties of CΦk(q) with 2≤k≤17 by employing the theory of modular forms, where CΦk(q) denotes the generating function of cϕk(n). We notice that many coefficients in the expressions of CΦk(q) are not integers. In this paper, we first observe that CΦk(q) is related to the constant term of a family of bivariable functions, then establish a general symmetric and recurrence relation on the coefficients of these bivariable functions. Based on this relation, we next derive many bivariable identities. By extracting and computing the constant terms of these bivariable identities, we establish the expressions of CΦk(q) with integral coefficients. As an immediate consequence, we prove some infinite families of congruences satisfied by cϕk(n), where k is allowed to grow arbitrary large.

A Note on the Confusion Coefficient of Boolean Functions

Low confusion coefficient values can make side-channel attacks harder for vector Boolean functions in Block cipher. In this paper, we give new results of confusion coefficient for f ⊞ g, f ⊡ g, f ⊕ g and fg for different Boolean functions f and g, respectively. And we deduce a relationship on the sum-of-squares of the confusion coefficient between one n-variable function and two (n - 1)-variable decomposition functions. Finally, we find that the confusion coefficient of vector Boolean functions is affine invariant.

Spectrum Analysis for Fully Connected Neural Networks.

This article studies the meaning of parameters of fully connected neural networks with single hidden layer from the perspective of spectrum. Under the constraints of numerical range, the corresponding relationship between parameters and the spectrum of network function can be established by the Fourier series coefficients of the activation function, which is truncated and periodically extended. This work is substantiated on the Mixed National Institute of Standards and Technology (MNIST) handwritten dataset and two illustrative examples with certain spectra. The simulations complete the conversion between spectrum and parameters with high precision and give the significance of hidden nodes to the spectrum of network function. Some algorithms derived from these properties, such as the parameter initialization method using spectrum and the pruning method by sorting amplification weights, are also presented to introduce how spectrum analysis affects neural network decision-making. Thus, spectrum analysis has great potential in network interpretation.

Kinematic power corrections in TMD factorization theorem

This work is dedicated to the study of power expansion in the transverse momentum dependent (TMD) factorization theorem. Each genuine term in this expansion gives rise to a series of kinematic power corrections (KPCs). All terms of this series exhibit the same properties as the leading term and share the same nonperturbative content. Among various power corrections, KPCs are especially important since they restore charge conservation and frame invariance, which are violated at a fixed power order. I derive and sum a series of KPCs associated with the leading-power term of the TMD factorization theorem. The resulting expression resembles a hadronic tensor computed with free massless quarks while still satisfying a proven factorization statement. Additionally, I provide an explicit check of this novel form of factorization theorem at the next-to-leading order (NLO) and demonstrate the restoration of the frame-invariant argument of the leading-power coefficient function. Numerical estimations show that incorporating the summed KPCs into the cross-section leads to an almost constant shift, which may help to explain the observed challenges in the TMD phenomenology.

Flow field characteristics and energy loss model of the effective upstream flow region of orifice in liquid jet

Orifice jets commonly adhere to the thick-walled orifice jet mechanism or the thin-walled one, where the difference between the two orifice jet mechanisms is generally considered to be caused after the fluid enters the orifice. However, ignoring the energy loss before entering the orifice could be inaccurate and even misleading. Therefore, we studied the flow behavior in the upstream flow region of thick-walled orifices (small orifices) and thin-walled ones (large ones). Firstly, the concept of the effective upstream flow region of orifice was proposed based on the film theory. It can be simplified into an approximate hemispherical multi-channel parallel contractive flow field. Then, the experiments of the effective upstream flow region were conducted by the streamlined contractive orifices with equivalent energy loss. The proportion of the energy loss before the fluid enters the orifice to the total energy loss was obtained. In addition, the maximum impact range of the effective upstream flow region was remarked by theoretical derivation, and local resistance coefficient functions were established based on the CFD simulation results. Finally, a semi-theoretical model of energy loss in this region was developed. It can quantitatively measure the proportion of increased energy consumption caused by the sucked air inside orifice, well verifying the eddy energy consumption, which provides a scientific exclusion method for predicting the complex form resistance.

Statistical inference of travelers’ route choice preferences with system-level data

Traditional network models encapsulate travel behavior among all origin–destination pairs based on a simplified and generic travelers’ utility function. Typically, the utility function consists of travel time solely, and its coefficients are equated to estimates obtained from discrete choice models and stated preference data. While this modeling strategy is reasonable, the inherent sampling bias in individual-level experimental data may be further amplified over network flow aggregation, leading to inaccurate flow estimates. In addition, individual-level data must be collected from surveys or travel diaries, which may be labor-intensive, costly, and limited to a small time horizon. To address these limitations, this study extends classical bi-level formulations to estimate travelers’ utility functions with multiple attributes using system-level data. This data tends to be less subject to sampling bias than individual-level data, it is cheaper to collect and it has become increasingly diverse and available. To leverage system-level data, we formulate a methodology grounded on non-linear least squares to statistically infer travelers’ utility function in the network context using traffic counts, traffic speeds, the number of traffic incidents, and sociodemographic information obtained from the US Census, among other attributes. The analysis of the mathematical properties of the optimization problem and its pseudo-convexity motivates the use of normalized gradient descent, an algorithm developed in the machine learning community that is suitable for pseudo-convex programs. More importantly, we develop a hypothesis test framework to examine the statistical properties of coefficients attached to utility terms and to perform attribute selection. Experiments on synthetic data show that the travelers’ utility function coefficients can be consistently recovered and that hypothesis tests are reliable statistics to identify which attributes are determinants of travelers’ route choices. Besides, a series of Monte-Carlo experiments showed that statistical inference is robust to various levels of sensor coverage and to noises in the Origin-Destination matrix and the traffic count measurements. The methodology is also deployed at a large scale using real-world multi-source data in Fresno, CA, collected before and during the COVID-19 outbreak.

Discrete-Time Quantum Walk on Multilayer Networks.

A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.

Coefficient Estimates for Quasi-Subordination Classes Connected with the Combination of q-Convolution and Error Function

We utilize quasi-subordination to analyze and introduce several new classes, and we construct a new operator by combining the error function and q-convolution. Additionally, we obtain estimates for the Fekete Szego functional and the Taylor–Maclaurin coefficients for functions in c2 and c3 new classes. Moreover, we discuss some applications of the operator.

Functional coefficient cointegration models with Box–Cox transformation

This paper considers a functional coefficient cointegration model where the dependent variable is subject to a Box–Cox transformation. A profile method is proposed to estimate the Box–Cox transformation parameter β0. We first approximate the functional coefficients by sieve method assuming that β0 is known. Then an extremum estimator of β0 is proposed based on a loss function which measures the relative variation of the regression residual compared to the variation in the transformed dependent variable. Finally, a plug-in estimator of the functional coefficients is obtained. Asymptotic properties of the proposed estimators are developed. Numerical results demonstrate the nice performance of the estimators and corroborate the theoretical development.

Equivalence between the energy decay of fractional damped Klein–Gordon equations and geometric conditions for damping coefficients

We consider damped s s -fractional Klein–Gordon equations on R d \mathbb {R}^d , where s s denotes the order of the fractional Laplacian. In the one-dimensional case d = 1 d = 1 , Green (2020) established that the exponential decay for s ≥ 2 s \geq 2 and the polynomial decay of order s / ( 4 − 2 s ) s/(4-2s) hold if and only if the damping coefficient function satisfies the so-called geometric control condition. In this note, we show that the o ( 1 ) o(1) energy decay is also equivalent to these conditions in the case d = 1 d=1 . Furthermore, we extend this result to the higher-dimensional case: the logarithmic decay, the o ( 1 ) o(1) decay, and the thickness of the damping coefficient are equivalent for s ≥ 2 s \geq 2 . In addition, we also prove that the exponential decay holds for 0 > s > 2 0 > s > 2 if and only if the damping coefficient function has a positive lower bound, so in particular, we cannot expect the exponential decay under the geometric control condition.

Growth kinetics of Lactococcus lactis and Lactobacillus casei in liquid culture medium containing as prebiotics inulin or fructose.

Predictive microbiology is a tool that allows us to evaluate the behavior of the concentration of biomass and estimated cells under extrinsic conditions, providing scientific and industrial benefits. In the present study, the growth of L. lactis and L. casei combined with inulin and fructose was modeled using the Gompertz sigmoidal growth functions and plotted using data obtained from batch culture in relation to biomass and cell concentration expressed as estimates in ln N (OD600nm and cells mL-1 ) as a function of time. The results of the kinetic modeling indicated that (T1) A1B1 = L. lactis + fructose and (T4) A2B2 = L. casei + inulin presented the best function coefficients and best fits in most cases compared to the rest. The specific growth rate of the maximum acceleration was from 0.364 to 0.473 h-1 and 0.100 to 0.129 h-1 , the concentration of bacterial cells (A) was from 0.556 to 0.713 and 0.425 to 0.548 respectively and the time where (μ) occurred with a greater magnitude (L) fluctuated between 0.854 and 0.802 and when this time in (L) is very fast, it presents values of ≤0.072 to ≤0.092. Its coefficient of determination and/or multiple regression (R2 ) obtained in the two adjustments was 0.97. It was possible to predict the influence of the carbon source on the behavior of maximum growth rates, higher consumption due to nutrient affinity and shorter growth time. © 2023 Society of Chemical Industry.