Variable Coefficients Research Articles

Dynamics of the prey–predator model with variable coefficients and degenerate diffusion coefficients

Dynamics of the prey–predator model with variable coefficients and degenerate diffusion coefficients

Molecular cloud matching in CO and dust in M33. I. High-resolution hydrogen column density maps from Herschel

This study is aimed to contribute to a more comprehensive understanding of the molecular hydrogen distribution in the galaxy M33 by introducing novel methods for generating high angular resolution ($18.2''$, equivalent to $75\ pc $ for a distance of $847\ kpc $) column density maps of molecular hydrogen ($N_ H_2 $). M33 is a local group galaxy that has been observed with Herschel in the far-infrared (FIR) wavelength range from $70$ to $500\ Previous studies have presented total hydrogen column density maps ($N_ H $), using these FIR data (partly combined with mid-IR maps), employing various methods. We first performed a spectral energy distribution (SED) fit to the $160$, $250$, $350,$ and $500\ continuum data obtain $N_ H $, using a technique similar to one previously reported in the literature. We also use a second method which involves translating only the $250\ map into a $N_ H $ map at the same angular resolution of $18.2''$. An $N_ H_2 $ map via each method is then obtained by subtracting the component. Distinguishing our study from previous ones, we adopt a more versatile approach by considering a variable emissivity index, $ and dust absorption coefficient, $ This choice enables us to construct a $ map, thereby enhancing the depth and accuracy of our investigation of the hydrogen column density. We address the inherent biases and challenges within both methods (which give similar results) and compare them with existing maps available in the literature. Moreover, we calculate a map of the carbon monoxide $ CO(1-0) $-to-molecular hydrogen (htwo ) conversion factor ( factor), which shows a strong dispersion around an average value of $1.8 throughout the disk. We obtain column density probability distribution functions ($N$-PDFs) from the $N_ H $, $N_ H_2 $, and $N_ hi $ maps and discuss their shape, consisting of several log-normal and power-law tail components.

Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic–quintic nonlinear Schrödinger equations with self-steepening

Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic–quintic nonlinear Schrödinger equations with self-steepening

Study on Nonlinear Behavior of Variable Thickness Plates

The analysis of variable-thickness plates is much more complicated than that of uniform-thickness plates because variable coefficients occur in the equations. In reality, this analysis is of great interest in various engineering disciplines, such as civil engineering, aerospace engineering, machine design, and so on. Although there is extensive literature on analyses of plates with constant thickness, a rather limited amount of technical literature is available on the solutions to problems dealing with plates with nonuniform thickness. The reason is that the analytical solutions meet insurmountable difficulties. Besides, the nonlinear analysis process also faces more difficulties than the linear analysis of structures. For these reasons, the nonlinear behavior of variable-thickness plates based on a finite element procedure is presented in this study. Although the topic is not special, it will help the engineer have a specific view of the nonlinear bending of the plate with variable thickness. This survey will be based on the change in geometrical parameters. Numerical solutions are then presented to verify the simplicity of this proposed procedure.

Effect of the mitochondrial membrane potential on the absorbance of the reduced form of cytochrome c oxidase

The effect of mitochondrial membrane potential (ΔΨm) on the absorbance of the reduced cytochrome c oxidase (COX) was evaluated in isolated rabbit heart mitochondria using integrating sphere optical spectroscopy. Maximal reduction of the mitochondrial cytochromes was achieved by either blowing nitrogen to remove oxygen, or by adding cyanide. Gradual depolarization of ΔΨm by adding increasing concentrations of uncoupler resulted in an increase of up to 50 % in the absorbance of cytochrome aa3 under nitrogen saturation, and of 25 % with cyanide. Cytochrome aa3 absorbance increases were also observed in the presence of cyanide with apyrase (20 %) or oligomycin (12 %). The bL heme absorbance also decreased as expected from ΔΨm depolarization. A ~ 1 nm red shift in the peak wavelength of cytochrome aa3 was observed under anoxic conditions as ΔΨm was depolarized. Importantly, cytochrome c and c1 absorbances remained constant at levels corresponding to full reduction under all experimental manipulations of ΔΨm, especially with cyanide. These data suggest that ΔΨm-dependent changes in the absorbance of reduced COX were due to a variable extinction coefficient of heme a and/or a3 as a function of ΔΨm. A similar increase in the reduced cytochrome aa3 absorbance without changes in cytochrome c and c1 was observed in the perfused rabbit heart when decreasing ΔΨm with uncoupler. Our results imply that COX absorbance in its fully reduced state does not simply reflect the oxygen tension but also the ΔΨm. This may prove useful in monitoring ΔΨm under anoxic or ischemic conditions in intact tissue.

Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics-informed augmentation

This paper presents a positivity-preserving discontinuous Galerkin (DG) scheme for the linear hyperbolic problem with variable coefficients on structured Cartesian domains. The standard DG spaces are augmented with either polynomial or non-polynomial basis functions. The primary purpose of these augmented basis functions is to ensure that the cell average from the unmodulated DG scheme remains positive. We explicitly obtain suitable basis functions by inspecting the method of characteristics on an auxiliary problem. A key result is proved which demonstrates that the unmodulated augmented DG scheme will retain a positive cell average, provided that the inflow, source term, and variable coefficients are positive. A simple scaling limiter can then be leveraged to produce a high-order conservative positivity-preserving DG scheme. Numerical experiments demonstrate the scheme is able to retain high-order accuracy as well as robustness for variable coefficients. To improve efficiency, an inexact augmented basis function can be obtained rather than a analytic non-polynomial solution to the auxiliary problem from the method of characteristics.

Admissibility and Mean Hyperbolicity for Evolution Equations

Mean hyperbolic systems permit non-hyperbolic behavior at certain moments during the evolution process T(t,s), owing to non-fixed error hyperbolic degree ε(t,s). Despite the coexistence of compression and expansion behaviors in generalized stable and unstable subspaces, mean hyperbolic systems admit fixed average contraction and expansion rates measured at sufficiently long time. To discuss the relationship between admissibility and mean hyperbolicity for evolution equations, our main goal is to construct admissible function classes and invariant decomposition with generalized stable and unstable subspaces. As applications, the mean hyperbolicity of variable coefficient damped wave equation and the roughness of mean hyperbolicity are presented.

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

An innovative damping random walk algorithm with compulsive evolution for the synthesis of heat exchanger networks

Heat exchanger network synthesis in process system engineering poses a significant challenge, primarily because of the intricacies of stream matches and the nonlinear nature of continuous variables. Numerous heuristic methods are frequently trapped in local optima because of their greedy acceptance criteria, which limits their capacity to explore diverse solutions. This aspect of enhancing algorithms through acceptance Criterion has yet to be considered in previous studies. Hence, a damping strategy using damping perfect solutions is proposed and applied to the Random Walk Algorithm with Compulsive Evolution, which has recently received considerable attention. This strategy aims to prevent trapping in local optima and improve global search capabilities, thereby reducing the risk of premature convergence to the local optima. To address the impact of different damping coefficients within the strategy on the optimization process and structural variations in the algorithm, three damping strategies were designed: a fixed damping strategy with a constant damping coefficient, a variable damping strategy featuring variable damping coefficients at different optimization stages, and an adaptive damping strategy that tracks structural changes and selectively delays modifications driven by continuous variables to preserve those driven by integer variables. The results obtained from applying these strategies to three classical industrial HEN cases are 2,890,884 $/yr, 6,650,082 $/yr, and 1,709,205 $/yr, respectively. These results outperformed the optimal outcomes documented in the literature, demonstrating the effectiveness of the new method.

Recent Progress of TGV Technology for High Performance Semiconductor Packaging

In recent semiconductor packaging, the adoption of through silicon via (TSV) technology has become crucial for the integration of 2.5 and 3D Si chips, and interposers. The TSV offers significant advantages including high interconnect density, shortened signal pathways, and improved electrical performance. However, challenges such as electrical loss, substrate warpage, and high manufacturing costs are associated with TSV implementation. In contrast, glass-based through-glass vias (TGVs) exhibit promising characteristics such as excellent insulation properties, cost-effectiveness, and variable coefficient of thermal expansion (CTE) values that mitigate warpage in stacked devices. Moreover, they facilitate miniaturization and support high-frequency applications. This paper provides an overview of recent advancements in glass substrate, TGV drilling techniques, functional layer depositions, and Cu-filling processes in semiconductor packaging evolution.

Exact Solutions for the Modified Burgers Equation with Additional Time-dependent Variable Coefficient

In this article, we investigated new travelling wave solutions for the modified Burgers equation with additional time-dependent variable coefficient via the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions. All solutions of this equation have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena. This method presents a wider applicability for handling nonlinear wave equations.

Pengaruh Inovasi Pada Aplikasi Access by KAI Terhadap Kualitas Pelayanan

Innovation in the Access by KAI application aims to provide better services to the public. However, this innovation encounters several issues such as limited technological access by the public, policy non-inclusivity, and lack of effectiveness in socialization efforts. Therefore, this study aims to investigate the impact of innovation in the Access by KAI application on service quality. Additionally, it aims to determine the effective contribution of innovation dimensions in the Access by KAI application to service quality. This research utilizes an associative method with a quantitative approach. Data was collected through observation and questionnaire results, while data analysis employed robust M-estimation regression. The results indicate that the quality of public service innovation is very high, and the quality of m-service is high. Furthermore, public service innovation obtains significant variable coefficient values at a significant level (α=0.05). This is indicated by the p-value of the public service innovation variable being 0.000<0.05, showing the influence of public service innovation on m-service quality in the Access by KAI application. The effective contribution of each dimension of public service innovation to m-service quality is as follows: relative advantage dimension 0.48%, compatibility dimension 29.03%, complexity dimension 14.22%, testability dimension 9.83%, and observability dimension 8.39%.

Dust magnetoacoustic waves in an inhomogeneous cylindrical four-component dusty plasma in the presence of polarization force

Abstract Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.

Low-complexity reconfigurable FIR lowpass equalizers for polynomial channel models

This paper introduces realizations of a reconfigurable finite-impulse-response (FIR) filter for simultaneous equalization and lowpass filtering. The main advantage of the proposed solutions is computational complexity reduction compared to existing solutions for a given performance, which leads to reduced hardware complexity. The proposed structures employ properties of both a variable bandwidth (VBW) filter and a variable equalizer (VE) with variable coefficients. The overall transfer function of the proposed reconfigurable lowpass equalizer (RLPE) is a weighted linear combination of fixed subfilters where the weights are directly determined by the bandwidth and one or several parameters of the channel needed to be equalized. The paper provides design procedures based on minimax optimization and introduces a fast design method for the filter with several variable parameters that can substantially decrease the design time. Filter order estimation expressions as well as complexity expressions are presented for all proposed realizations. Design examples include comparison of the RLPE structures and a common approach of using a regular FIR equalization filter requiring online redesign when the bandwidth or channel characteristics are changed. It is shown that the number of general multiplications can be reduced up to 91% using the proposed RLPE.

Analysis of High-Order Bright–Dark Rogue Waves in (2+1)-D Variable-Coefficient Zakharov Equation via Self-Similar and Darboux Transformations

This paper conducts an in-depth study on the self-similar transformation, Darboux transformation, and the excitation and propagation characteristics of high-order bright–dark rogue wave solutions in the (2+1)-dimensional variable-coefficient Zakharov equation. The Zakharov equation is instrumental for studying complex nonlinear interactions in these areas, with specific implications for energy transfer processes in plasma and nonlinear wave propagation systems. By analyzing bright–dark rogue wave solutions—phenomena that are critical in understanding high-energy events in optical and fluid environments—this research elucidates the intricate dynamics of energy concentration and dissipation. Using the self-similar transformation method, we map the (2+1)-dimensional equation to a more tractable (1+1)-dimensional nonlinear Schrödinger equation form. Through the Lax pair and Darboux transformation, we successfully construct high-order solutions that reveal how variable coefficients influence rogue wave features, such as shape, amplitude, and dynamics. Numerical simulations demonstrate the evolution of these rogue waves, offering novel perspectives for predicting and mitigating extreme wave events in engineering applications.This paper crucially advances the practical understanding and manipulation of nonlinear wave phenomena in variable environments, providing significant insights for applications in optical fibers, atmospheric physics, and marine engineering.

Novel FR4‐based low loss reconfigurable filter with four operating modes using movable transmission lines

AbstractIn the letter, a novel reconfigurable filter using movable transmission lines is proposed. The filter is based on substrate‐integrated‐suspended‐line structure with two inner layers, fabricated on low‐cost FR4 substrate. The suspension line and the cavity are completely covered by copper. The suspension line could be freely moved in the air cavity. In the novel structure, the coupled lines have a variable coupling coefficient. With the movements of two transmission lines, the filter has four operating modes and can be tuned, with low insertion loss of less than 0.45 dB, showing promising properties.

Periodic solitons of generalized coupled nonlinear Schrödinger equations with variable coefficients

Periodic solitons of generalized coupled nonlinear Schrödinger equations with variable coefficients

Axially Non-Uniform Properties Effected Electro-Elastic Fields in Bended Piezoelectric Semiconductor Beams

This paper studied the effects of axially non-uniform material and non-uniform doping on the electro-elastic fields in bent piezoelectric semiconductor beams. The mathematical model is established based on the phenomenological theory of piezoelectric semiconductor and Euler’s beam theory. To solve the governing equations with variable coefficients, the differential quadrature method is adopted. As two representative structures, the pure bending beam and cantilever beam are studied, respectively. From the calculated results, it can be found the varied material properties changed the effective stiffness, as a result, all the field quantities are altered. Meanwhile, the symmetry of all field quantities in a pure bending beam is broken. Considering different Gaussian doping parameters [Formula: see text] and [Formula: see text], it can be observed that the distribution rule of perturbation carrier density becomes complex. The increment of [Formula: see text] broadens the width of optimum range-producing carriers, however, the increment of [Formula: see text] describes the moving of the optimum range from left to right. Importantly, the introduction of non-uniform doping breaks the limitation of perturbation carrier density in a cantilever beam with uniform material properties, the maximum value of perturbation carrier density does not appear at the fixed end only. The obtained results could be the guidance in designing high-performance electric devices.

Global well-posedness for the inhomogeneous incompressible MHD equations with variable viscosity coefficient and electrical conductivity

In this paper, we study the Cauchy problem for the inhomogeneous incompressible MHD system with variable viscosity coefficient and electrical conductivity. It is shown that the 3-D inhomogeneous incompressible MHD system has unique global solutions with small initial data conditions. Furthermore, we establish the global well-posedness of the two-dimensional MHD equations in critical spaces, given certain conditions on the density.

A principal-weighted penalized regression model and its application in economic modeling

This paper introduces a novel Principal-Weighted Penalized (PWP) regression model, designed for dimensionality reduction in large datasets without sacrificing essential information. This new model retains the favorable features of the principal component analysis (PCA) technique and penalized regression models. It weighs the variables in a large data set based on their contributions to principal components identified by PCA, enhancing its capacity to uncover crucial hidden variables. The PWP model also efficiently performs variable selection and estimates regression coefficients through regularization. An application of the proposed model on high-dimensional economic data is studied. The results of comparative studies in simulations and a real example in economic modeling demonstrate its superior fitting and predictive abilities. The resulting model excels in accuracy and interpretability, outperforming existing methods.