Linear Equations Research Articles

Employing consumer knowledge to protect consumer rights

The research aims to measure the level of connection and impact of consumer knowledge in protecting consumer rights, and the sample consisted of (275) consumers in five markets (large retail markets in Baghdad) as they represent the research community of consumers who go to the markets to buy products. The data and hypotheses were analyzed and tested using appropriate statistical tools, including the arithmetic mean and standard deviation to measure the level of descriptive responses of the research sample, correlation coefficients (Pearson) to test the relationships between the research variables, and the simple and multiple linear regression equation to test the effect. The results showed the validity of the research hypotheses, and concluded with a number of Conclusions and recommendations.

Over the Past Decade, Preoperative Anemia Has Become a Greater Predictor of Transfusions after Total Knee Arthroplasty.

With advancements in perioperative blood management and the use of tranexamic acid, the rate of transfusions after total knee arthroplasty (TKA) has substantially decreased. As these principles are refined, other modifiable risk factors, such as preoperative anemia, may play an increasingly important role in transfusion risk for patients undergoing TKA. A multicenter, national database was utilized to identify patients undergoing TKA from 2010 to 2021. Anemia was defined by World Health Organization (WHO) definitions as < 12 g/dL for women and < 13 g/dL for men. A predictive model was created using backwards elimination logistic regression to predict transfusion risk, controlling for demographic and medical covariates. The coefficient of anemia was then analyzed for each year. The trend over time was fitted with a best-fit linear regression equation. There were 509,117 patients who underwent TKA, and had a mean age of 67 years (range, 18 to 89). There were 57,716 (11%) patients who were anemic preoperatively, and 15,426 (3%) of patients required a transfusion. Rate of transfusion decreased from 10.6% in 2010 to 0.6% in 2021. The OR (odds ratio) associated with anemia as a predictor of transfusion increased from 3.1 (95% CI [confidence interval]: 2.1 to 4.6) in 2010 to 14.0 (95% CI: 8.9 to 24) in 2021. The results of this study demonstrate that the importance of preoperative anemia as a predictor of transfusion has increased over the past decade as rates of transfusion have decreased. As perioperative blood management protocols improve, preoperative anemia should be considered an important focus of intervention to reduce the risk of transfusion prior to TKA.

Opportunities and Challenges of Implementing a Jigsaw Type Cooperative Learning Model on Two Variable Linear Equation System Material

This study aims to describe the opportunities and challenges of implementing Jigsaw-type cooperative learning on the material of Two Variable Linear Equation Systems. The subjects of this study were all 27 grade VIII students of Yedam Abepura Junior High School. Data collection techniques use data triangulation, namely by observation techniques, student worksheet data and interviews. The results of this study showed that the opportunity to apply Jigsaw-type cooperative learning to the material of the two-variable linear equation system received a positive response from all students, enthusiastic and enthusiastic students in doing tests on worksheets based on observations. The implementation process went well and smoothly and was completed on time. For satisfaction, teachers and students are quite satisfied with the results obtained. The challenge in implementing this Jigsaw type cooperative learning model is that there are differences in students' basic academic abilities or in other words, students' basic abilities, especially Mathematics learning, vary so that when learning the Jigsaw model cooperative model, students who do not understand need to get extra explanations with additional long time compared to students who already have a good academic ability foundation finish faster and wait queue of friends who have not moved from another group during explaining the material. Then the odd number of students also causes difficulty dividing in groups evenly.

Solving a non-local linear differential equation model of the Newtonian-type

Solving a non-local linear differential equation model of the Newtonian-type

Representation of solutions to fuzzy linear fractional differential equations with a piecewise constant argument

Abstract This study marks the first exploration of fuzzy linear fractional differential equations with a piecewise constant argument (FLFDEs-PCA), incorporating the concept of Caputo's type gH-differentiability with the order $\alpha \in (0,1]$. Such problems are noteworthy as they represent hybrid systems, blending the characteristics of continuous and discrete dynamical systems and integrating aspects from both differential and difference equations. The primary objective of this research is to establish a standardized framework for deriving explicit solution formulas for FLFDEs-PCA under various scenarios. Additionally, illustrative examples are provided to demonstrate the practical implications of our theoretical findings.

Indefinite q-integrals from a method using q-Riccati equations

AbstractIn an earlier work, a method was introduced for obtaining indefinite q-integrals of q-special functions from the second-order linear q-difference equations that define them. In this paper, we reformulate the method in terms of q-Riccati equations, which are nonlinear and first order. We derive q-integrals using fragments of these Riccati equations, and here only two specific fragment types are examined in detail. The results presented here are for the q-Airy function, the Ramanujan function, the discrete q-Hermite I and II polynomials, the q-hypergeometric functions, the q-Laguerre polynomials, the Stieltjes-Wigert polynomial, the little q-Legendre and the big q-Legendre polynomials.

The effectiveness of intervention in hepatitis C patients and improvement in their referral rate

Background To investigate the effectiveness of the intervention with critical value management and push short messaging service (SMS), and to determine improvement in the referral rate of patients with positive hepatitis C antibody (anti-HCV). Methods No intervention was done for patients with positive anti-HCV screening results from 1 January 2015 to 31 October 2021. Patients with positive anti-HCV results at our hospital from 1 November 2021 to 31 July 2022 were informed vide critical value management and push SMS. For inpatients, a competent physician was requested to liaise with the infectious disease physician for consultation, and patients seen in the OPD (outpatient department) were asked to visit the liver disease clinic. The Chi-square correlation test, one-sided two-ratio test and linear regression were used to test the relationship between intervention and referral rate. Results A total of 638,308 cases were tested for anti-hepatitis C virus (HCV) in our hospital and 5983 of them were positive. 51.8% of the referred patients were aged 18–59 years and 10.8% were aged ≥75 years. The result of Chi-square correlation test between intervention and referral was p = .0000, p < .05. One-sided two-ratio test was performed for statistics of pre-intervention referral rate (p1) and post-intervention referral rate (p2). Normal approximation and Fisher’s exact test for the results obtained were 0.000, p < .05, and the alternative hypothesis p1 − p 2 < 0 was accepted. The linear regression equation was referral = 0.1396 × intervention + 0.3743, and the result model p = 8.79e − 09, p < .05. The model was significant, and the coefficient of intervention was 0.1396. Conclusions The interventions of critical value management and push SMS were correlated with the referral rate of patients with positive anti-HCV.

Boundary element method for bending-extension coupling shear deformable laminated composite plates with multiple stiffeners

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations.

A study on approximate controllability of linear impulsive equations in Hilbert spaces

In this paper, we study an approximate controllability for the impulsive linear evolution equations in Hilbert spaces. We give a representation of solution in terms of semigroup and impulsive operators. We present the necessary and sufficient conditions for approximate controllability of linear impulsive evolution equation in terms of impulsive resolvent operator. An example is provided to illustrate the application of the obtained results.

Magnetic molecularly imprinted polymers are used to selectively extract cephalosporins from milk samples and analyze by LC-MS/MS

Cephalosporins were extracted from milk samples by using magnetic molecularly imprinted polymers (MMIP). To characterize the physical properties of MMIP, an experiment was conducted involving both static and dynamic adsorption. Samples were analyzed with LC-MS/MS to identify cephalosporin residues. The quantitative technique employed was the use of an isotope as an internal standard. Analysis was conducted using an Ascentis C8 column with a mobile phase consisting of a 0.1% aqueous solution of formic acid and acetonitrile. The determination coefficients varied between 0.9945 and 0.9995, as indicated by the linear equations. Cephalosporins exhibited a diverse spectrum of recovery rates, varying between 80.7% and 118.3%, accompanied by a range of relative standard deviations spanning from 3.8% to 13.5%. The detection limits for 9 kinds of cephalosporins in milk samples varied from 1 μg kg−1 to 20 μg kg−1, while the quantification limits ranged from 3 μg kg−1 to 60 μg kg−1. The successful implementation of the validated technique has been applied to detect 9 different kinds of cephalosporins in real milk products.

An inverse problem for pseudoparabolic equation: existence, uniqueness, stability, and numerical analysis

In this paper, we study an inverse problem for a linear third-order pseudoparabolic equation. The investigated inverse problem consists of determining a space-dependent coefficient of the right-hand side of a pseudoparabolic equation. As an additional information a final overdetermination condition is considered. Under the suitable conditions on the data of the problem, the unique solvability of the considered inverse problem is established. The stability of solutions is also proved. The established results are also true for inverse problems for parabolic equations, which could be obtained as a regularization of the studied pseudoparabolic equation. In addition, the pseudoparabolic problem is discretized using the cubic B-spline functions and recast as a nonlinear least-squares minimization of the Tikhonov regularization function. Numerically, this is effectively solved using the MATLAB subroutine lsqnonlin. Both exact and noisy data are inverted. Numerical results for three benchmark test examples are presented and discussed. Moreover, the von Neumann stability analysis is also discussed.

Levels of melatonin and some indicators of angiogenesis, antioxidant system and lipid peroxidation in blood plasma in women with uterine leiomyoma

Uterine leiomyoma is one of the most common gynaecological diseases, which often leads to loss of fertility. It is known that in this pathology, damage to the tissues of the uterus is accompanied by oxidative stress, and the mechanisms of its compensation play a decisive role in the process of myometrial regeneration, especially when performing organ-preserving operations. The aim of the study was to determine the levels of melatonin, reproductive hormones and state of angiogenesis, antioxidant system and lipid peroxidation in women of reproductive age who were diagnosed with uterine leiomyoma. Material and methods. 60 women of reproductive age with uterine leiomyoma (study group) were examined. The control group consisted of 20 healthy women of the same age group. Melatonin levels in women's blood were determined once, on an empty stomach, at 8 a.m.; the concentrations of estradiol and progesterone in the follicular phase of the menstrual cycle were also measured. The state of the angiogenesis system was studied by examining the levels of vascular endothelial growth factor (VEGF) and the content of the final metabolites of nitric oxide NO in blood plasma. The activity of the antioxidant system was assessed by blood plasma concentrations of reduced glutathione, glutathione peroxidase, and glutathione transferase. Indicators of lipid peroxidation were investigated by the content of malondialdehyde (MDA) in blood plasma and erythrocytes. Results. It was found that in the patients of the study group with leiomyoma, there was a significantly lower level of melatonin in blood plasma (111.1 ± 18.5 ng/mL) compared to the control group (153.5 ± 8.5 ng/mL), while the concentration of estradiol was almost three times higher (107.4 ± 25.3 pg/mL) compared to the control group (36.2 ± 3.2 pg/mL), and the concentration of progesterone was 1.9 times higher (2.1 ± 0.4 ng/mL compared to 1.1 ± 0.5 ng/mL in the control group). The level of VEGF in blood plasma in women with uterine leiomyoma was also higher (90.4 ± 23.6 pg/mL) compared to the control group (35.1 ± 8.3 pg/mL), as well as the concentration of final metabolites of nitric oxide, which reached 25.3 ± 5.9 pg/mL compared to 9.9 ± 3.9 pg/mL in the control group. The reduced glutathione level in the blood plasma of women with uterine leiomyoma was significantly lower (0.77 ± 0.13 µmol/L) compared to healthy women (1.02 ± 0.14 µmol/L) in the control group, while the concentrations of glutathione-S-transferase and glutathione peroxidase enzymes were higher (161.3 ± 22.3 ng/mL and 235.7 ± 35.9 ng/mL, respectively), whereas in the control group these indicators were 118.9 ± 18.0 ng/mL and 105.3 ± 41.2 ng/mL, respectively. The MDA content in women of the study group was higher, measuring 5.2 ± 0.8 nmol/L in plasma and 10.8 ± 1.1 nmol/L in erythrocytes compared to 2.3 ± 0.8 nmol/L and 5.3 ± 0.8 nmol/L in the control group, respectively. Conclusions. The levels of melatonin and reduced glutathione in the blood plasma of women with uterine leiomyoma were significantly lower, while the concentrations of estradiol, progesterone, glutathione-S-transferase, glutathione peroxidase, VEGF, final metabolites of nitric oxide, as well as the average MDA content in plasma and erythrocytes, were significantly higher compared to healthy women. In the study group, the relationship between the level of progesterone in blood plasma and the content of malondialdehyde in erythrocytes was described using a linear regression equation, which, as we suggest, indicates an activating effect of progesterone on oxidative stress mechanisms in the myometrium. In our opinion, oxidative stress in uterine leiomyoma occurs due to inadequate activity of the antioxidant system, an integral part of which is melatonin, leading to enhanced angiogenesis against the background of estrogen-induced myometrial proliferation.

Athermal pulsational mode dynamics with negative ions

The stability dynamics of the pulsational mode of gravitational collapse (PMGC), excitable in athermal (nonthermal) spherical complex dust molecular clouds (DMCs) in the presence of active role of negative ions, is semi-analytically investigated. The adopted partially ionized DMC model consists of five constitutive plasma species, well-coupled via the gravito-electrostatic Poisson formalism, depicting the corresponding potential-density correlations. The nonthermal uncorrelated lighter (inertialess) species are electrons, positive ions, and negative ions. The thermal correlated heavier (inertial) species are neutral and charged dust grains. The application of a standard spherical wave analysis results in a generalized linear cubic dispersion equation involving a new set of multi-factorial dispersion coefficients dependent on diverse equilibrium plasma parameters. A numerical illustrative platform is broadly created to analyze the DMC stabilization and destabilization factors relative to the non-local inward Newtonian self-gravity. It is interestingly seen that the DMC stabilizing agents are the radial cloud size, dust charge, neutral dust viscoelastic relaxation time, Tribeche thermostatistical parameters, etc. In contrast, the dust mass and equilibrium neutral dust density show destabilizing effects, and so forth. The results systematically explored here are fairly consistent and reliably correlated with the previous results on structure formation mechanism in the DMCs as heretofore reported extensively in the literature.

The Influence of Pancasila and Citizenship Education Learning on Critical Thinking at Tandun 1 State High School

This research is motivated by the lack of student motivation to learn which is still low. The research results show that learning motivation is very important and can influence critical and creative thinking. This research aims to find out whether learning Pancasila education has an effect on the critical thinking skills of students at SMA Negeri 1 Tandun. This research was carried out using quantitative methods with a casual associative approach, and involved students of SMA Negeri 1 Tandun as research subjects. The data collection instrument used was conventional, and the IBM SPSS Version 22 application was used for data processing. Based on the results of the analysis, a simple linear regression equation was obtained, namely Ŷ= 14,245 + 0.629 Meanwhile, the results of the t test obtained t_count of 14.245 t_table of 2.00, which shows that so that Ho is rejected and Ha is accepted. So this research hypothesis is accepted that there is an influence of Civics Learning on Critical Thinking Ability.

Reactivities of acrylamide warheads toward cysteine targets: a QM/ML approach to covalent inhibitor design.

Covalent inhibition offers many advantages over non-covalent inhibition, but covalent warhead reactivity must be carefully balanced to maintain potency while avoiding unwanted side effects. While warhead reactivities are commonly measured with assays, a computational model to predict warhead reactivities could be useful for several aspects of the covalent inhibitor design process. Studies have shown correlations between covalent warhead reactivities and quantum mechanic (QM) properties that describe important aspects of the covalent reaction mechanism. However, the models from these studies are often linear regression equations and can have limitations associated with their usage. Applications of machine learning (ML) models to predict covalent warhead reactivities with QM descriptors are not extensively seen in the literature. This study uses QM descriptors, calculated at different levels of theory, to train ML models to predict reactivities of covalent acrylamide warheads. The QM/ML models are compared with linear regression models built upon the same QM descriptors and with ML models trained on structure-based features like Morgan fingerprints and RDKit descriptors. Experiments show that the QM/ML models outperform the linear regression models and the structure-based ML models, and literature test sets demonstrate the power of the QM/ML models to predict reactivities of unseen acrylamide warhead scaffolds. Ultimately, these QM/ML models are effective, computationally feasible tools that can expedite the design of new covalent inhibitors.

Virtual Power Plant and Microgrid Control Integration for Campus Environments with Wind Solar Pumped Hydro and Biomass Energy

This paper provides a comprehensive exploration of integrating renewable energy sources, focusing on wind, solar, Pumped Hydro and biogas, into power systems. Virtual Power Plants (VPPs) with an Energy Management System (EMS) offer a promising solution for managing these distributed resources. The VPP model, utilizing mixed integer linear programming (MILP) in GAMS and solved with CPLEX, optimizes net daily profit within a 24-hour interval. This approach efficiently allocates resources, maximizes profitability, and ensures stable energy supply, addressing the challenges posed by variable renewable energy outputs. The MILP model is formulated using linear equations and inequalities within GAMS, with the CPLEX solver being effective for handling large-scale linear programming tasks. The model is based on real-world data, including market variability, weather forecasts, and demand patterns, and can be optimized for better decision-making in VPP operations, ultimately maximizing profits while ensuring a stable and sustainable power supply.   

Flocking dynamics of agents moving with a constant speed and a randomly switching topology

Abstract In this paper, we present a sufficient framework to exhibit the sample path-wise asymptotic flocking dynamics of the Cucker–Smale model with unit-speed constraint and the randomly switching network topology. We employ a matrix formulation of the given equation, which allows us to evaluate the diameter of velocities with respect to the adjacency matrix of the network. Unlike the previous result on the randomly switching Cucker–Smale model, the unit-speed constraint disallows the system to be considered as a nonautonomous linear ordinary differential equation on velocity vector, which forces us to get a weaker form of the flocking estimate than the result for the original Cucker–Smale model.

Circular dichroism in nonlinear topological Weyl semimetals

In recent years, the field of topological photonics has emerged as a promising area of research due to its potential for the development of new photonic devices with unique properties. Topological Weyl semimetals (TWSs), which are characterized by the presence of Weyl points in their electronic band structure, are one such example of a material with interesting topological properties. In this study, Kerr and Faraday rotations were used to determine the nonlinear characteristics of TWSs. We focused on surfaces where no Fermi arcs are involved, so that Maxwell’s equations would contain some peculiar topological terms. In Weyl semimetals with a specific topology, the distance between Weyl nodes aligned along the z-direction functions as a magnet. This results in a significant polar Kerr/Faraday rotation effect that is proportional to the separation distance, when light is directed onto the surface of the TWS that lacks Fermi arc states. Conversely, when the light is directed onto a surface with Fermi arc states, the Voigt effect is quadratically proportional to the separation distance. We considered electromagnetic wave propagation in a nonlinear Kerr-type medium. We have derived and solved the linear and nonlinear Helmholtz equations for TWSs using the tanh method. Our findings reveal that wave solutions could have some potentially significant implications for the design and optimization of photonic devices based on TWSs.

Revivals, or the Talbot effect, for the Airy equation

AbstractWe study Dirichlet‐type problems for the simplest third‐order linear dispersive partial differential equations (PDE), often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the spatial operator. Our specific interest is to determine whether the peculiar phenomenon of revivals, also known as Talbot effect, is supported by these boundary conditions, which for third‐order problems are not reducible to periodic ones. We prove that this is the case only for a very special choice of the boundary conditions, for which a new type of weak cusp revival phenomenon has been recently discovered. We also give some new results on the functional class of the solution for other cases.

Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.