Linear Equations Research Articles

Free radical fragmentation and oxidation in the polar part of lysophospholipids: Results of the study of blood serum of healthy donors and patients with acute surgical pathology.

The interaction of reactive oxygen species with cell membrane lipids is usually considered in the context of lipid peroxidation in the nonpolar component of the membrane. In this work, for the first time, data were obtained indicating that damage to human cell membranes can occur in the polar part of lysophospholipids at the interface with the aqueous environment due to free radical fragmentation (FRF) processes. FRF products, namely 1-hexadecanoyloxyacetone (PAc) and 1-octadecanoyloxyacetone (SAc), were identified in human serum, and a GC-MS method was developed to quantify PAc and SAc. The content of FRF products in serum samples of 52 healthy donors was found to be in the range of 1.98-4.75μmol/L. A linear regression equation, CPAc&SAc (μmol/L)=0.51+0.064 × years, was derived to describe the relationship between age and content of FRF products. In 70 patients with acute surgical pathology in comparison with the control group of healthy donors, two distinct clusters with different concentration levels of FRF products were revealed. The first cluster: groups of 43 patients with various localized inflammatory-destructive lesions of hollow organ walls and bacterial translocation (septic inflammation) of abdominal cavity organs. These patients showed a 1.5-1.9-fold (p=0.012) decrease in the total concentration of PAc and SAc in serum. In the second cluster: groups of 27 patients with ischemia-reperfusion tissue damage (aseptic inflammation), - a statistically significant increase in the concentration of FRF products was observed: in 2.2-4.0 times (p=0.0001). The obtained data allow us to further understand the role of free-radical processes in the damage of lipid molecules. FRF products can potentially be used as markers of the degree of free-radical damage of hydroxyl containing phospholipids.

VINNYTSIA REGION: STATUS AND TRENDS OF PRODUCTION, PROCESSING AND STORAGE OF GRAIN

The article is devoted to the study of the state of production, processing and storage of grain in the Vinnytsia region. The objectives of the research were to monitor the collected areas and gross harvests of the main crops in 2011-2021, establish the trends of their changes, analyze the capacities of transport and technological equipment and granaries of the region. The analysis was conducted on the basis of data from the State Statistics Service of Ukraine for 2011-2021. The analysis of harvested areas and gross harvests of grain of the main crops at agricultural enterprises of the region in 2011–2021 showed their tendency to increase. During this period, harvested areas increased by 1.42 times, and annual volumes of gross grain harvests had a wave-like growth pattern. Linear trend equations are proposed for forecasting harvested areas and gross grain harvests, which are characterized by coefficients of determination R2 of 0.79 and 0.65, respectively. The largest gross harvests were given by corn, wheat and sunflower, and smaller – by barley, soybeans and rapeseed. In 2018-2021, the gross harvest of these crops was within the following limits (thousand tons): corn 2015-2620, wheat 1200-1691, and sunflower 755-1001. 66 enterprises receive grain from vehicles, and 65 forward it. The average capacity of receiving grain is 3032.41 t/day, and forwarding 1183.61 t/day. There are 21 railway transport enterprises hiring, and 55 enterprises offering leave. The average capacity of receiving devices from the railway is 949.52 t/day, and the output capacity is 1448.69 t/day. 111 grain dryers from 11 producing countries are installed at the considered 53 enterprises of the region. Of them, 18.9% of enterprises have dryers of Ukrainian production only, 20.8% of enterprises have both domestic and foreign ones, but the majority of enterprises have dryers of foreign production only, which are 1.85 times more than the number of Ukrainian made dryers. It was established that 82 separators are used for grain cleaning at 37 elevators, most of which (63%) are domestically produced, which outnumber imported ones by 1.73 times. The total capacity of simultaneous storage of grain in 67 elevators of agricultural enterprises is 3554.35 thousand tons, of which 2449.41 thousand tons have harvesting elevators and 1104.94 thousand tons – production elevators. Their simultaneous storage capacity is less than the forecast values of gross grain harvests in 2022 – 6354.2 thousand tons, which requires the expansion of the elevator network of the Vinnytsia region.

Differential equations for Carrollian amplitudes

Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.

Generalization of conformal Hamada operators

AbstractThe six-derivative conformal scalar operator was originally found by Hamada in its critical dimension of spacetime, $$d=6$$ d = 6 . We generalize this construction to arbitrary dimensions d by adding new terms cubic in gravitational curvatures and by changing its coefficients of expansion in various curvature terms. The consequences of global scale-invariance and of infinitesimal local conformal transformations are derived for the form of this generalized operator. The system of linear equations for coefficients is solved giving explicitly the conformal Hamada operator in any d. Some singularities in construction for dimensions $$d=2$$ d = 2 and $$d=4$$ d = 4 are noticed. We also prove a general theorem that a scalar conformal operator with n derivatives in $$d=n-2$$ d = n - 2 dimensions is impossible to construct. Finally, we compare our explicit construction with the one that uses conformal covariant derivatives and conformal curvature tensors. We present new results for operators built with different orders of conformal covariant derivatives.

A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate.

Quantum Bernoulli noises approach to quantum master equations and applications to Ehrenfest-type theorems

This paper investigates the regularity properties of quantum master equations with unbounded coefficients within the space of square-integrable complex-valued Bernoulli functionals. Initially, we demonstrate the existence of a unique regular solution to the linear stochastic Schrödinger equation driven by cylindrical Brownian motions. Subsequently, we establish the existence of regular solutions for the autonomous linear quantum master equation and provide a probabilistic representation of this solution in terms of the stochastic Schrödinger equation. Finally, by taking the expectation of some observables with respect to the solution of the quantum master equation, we derive a system of differential equations that describe the evolution of the mean values of certain quantum observables.

Characterization of Graphite and ZrO2 Reinforced Aluminium Metal Matrix Composite For Enhanced Mechanical Properties in Electronics Applications

Abstract The objective of this work is to examine the wear properties of a hybrid Metal Matrix Composite (MMC) consisting of 92 weight percent (wt. %) Aluminium Alloy 6061 (AA6061), 2 wt. % Graphite (C), and 6 wt. % Zirconium Dioxide (ZrO2). It was previously determined that this composition was ideal for improved metallurgical and mechanical properties. Nine specimens of the same composition were fabricated for this continuation work and put through wear tests with different applied load, sliding velocity, and sliding distance settings. To evaluate the performance of the composite, measurements were made of the wear rate and Coefficient of Friction (COF). According to the results, the wear rate typically increased as the applied load and sliding velocity increased. At the lowest load (10 N) and velocity (2 m/s), the lowest wear rate (50.90 µg) and COF (0.197) were noted. Specimens with lower wear rates had smoother surfaces and less wear, as revealed by SEM analysis of the worn surfaces; specimens with higher wear rates showed more significant surface damage, such as deeper cuts and serrations. In specimens with less wear, XRD analysis verified the presence of crystalline aluminium, indicating a strong correlation between wear resistance and the crystalline structure of the composite. Linear regression equations were created to predict wear behavior under different conditions. According to the results, the composite's wear characteristics are greatly influenced by the sliding velocity and applied load. ZrO2 and C together have lubricating and strengthening properties that, under certain circumstances, reduce wear. The composite exhibits potential for usage in electronics applications, especially in components where wear resistance and mechanical durability are critical due to its favorable wear characteristics and mechanical properties.

Development and Analysis of novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Parametrically Driven Nonlinear System of Pseudo-Excitations on a Two-Leg Ladder Lattice

Following the main principles of developing the evolutionary nonlinear integrable systems on quasi-one-dimensional lattices, we suggest a novel nonlinear integrable system of parametrically driven pseudo-excitations on a regular two-leg ladder lattice. The initial (prototype) form of the system is derivable in the framework of semi-discrete zero-curvature equation with the spectral and evolution operators specified by the properly organized 3 × 3 square matrices. Although the lowest conserved local densities found via the direct recursive method do not prompt us the algebraic structure of system’s Hamiltonian function, but the heuristically substantiated search for the suitable two-stage transformation of prototype field functions to the physically motivated ones has allowed to disclose the physically meaningful nonlinear integrable system with time-dependent longitudinal and transverse inter-site coupling parameters. The time dependencies of inter-site coupling parameters in the transformed system are consistently defined in terms of the accompanying parametric driver formalized by the set of four homogeneous ordinary linear differential equations with the time-dependent coefficients. The physically meaningful parametrically driven nonlinear system permits its concise Hamiltonian formulation with the two pairs of field functions serving as the two pairs of canonically conjugated field amplitudes. The explicit example of oscillatory parametric drive is described in full mathematical details.

Investigation of the Effects of Creative Imagination on Academic Outcomes in Design Programs

Imagination as the key to the creative process is one of the key components of design education that affects students' problem-solving skills and innovation. The purpose of this research is to determine the impact of creative imagination on the academic performance of students enrolled in design courses. It intends to obtain a measure of the way creative imagination affects or influences students’ performance as well as their achievements. However, there is a lack of understanding regarding the correlation between creativity and performance among university students. The study collected data on creative imagination and academic performance through a survey of 350 participants drawn from five universities. Self-administered questionnaires were distributed to 350 participants, of which 320 were 176 males and 144 females. The research included quantitative techniques such as linear regression, correlation analysis, and structural equation modeling-partial least squares (SEM-PLS). Further, the result of the analysis showed that imagination level has the most significant impact on academic outcomes in design programs with a strong positive effect (β=0.35, p-value = 0.04). Higher creative imagination scores had a positive correlation with grades and students' involvement. This underscores the importance of forecasting to enhance students’ performance and engagement in design programs. The strategies used in education should be utilized to supplement creativity to raise the performance and satisfaction of students.

A feasible numerical computation based on matrix operations and collocation points to solve linear system of partial differential equations

In this work, a system of linear partial differential equations with constant and variable coefficients via Cauchy conditions is handled by applying the numerical algorithm based on operational matrices and equally-spaced collocation points. To demonstrate the applicability and efficiency of the method, four illustrative examples are tested along with absolute error, maximum absolute error, RMS error, and CPU times. The approximate solutions are compared with the analytical solutions and other numerical results in literature. The obtained numerical results are scrutinized by means of tables and graphics. These comparisons show accuracy and productivity of our method for the linear systems of partial differential equations. Besides, an algorithm is described that summarizes the formulation of the presented method. This algorithm can be adapted to well-known computer programs.

Event locations: Speeding up grid searches using quadratic interpolation

Summary The grid search method is a common approach to estimate the three spatial coordinates of event hypocenters. However, locating events in large search spaces with small grid spacings is computationally prohibitive. This study accelerates the grid searches over large search spaces using a quadratic interpolation technique. We start with the coarse-grid-estimated location, where we have the minimum value of the difference in the traveltimes between S- and P-waves summed over all receivers. Then, we select the neighbouring grid points and build a 3D quadratic function. The unknown coefficients of the 3D quadratic function are computed by solving a system of linear equations. After that, we interpolate the location by solving partial derivatives of the quadratic function. The quadratic interpolation technique performs well on both synthetic and real microseismic data examples, typically leading to similar event locations as those obtained using 10 times smaller grid spacings in all three directions, at a minor additional computational expense, and without the need to generate traveltimes at new spatial positions.

Weighted generalized core–EP inverse

To solve some systems of operator equations, we generalize the concepts of the W–weighted core–EP inverse, the W-gMP inverse, the generalized core–EP inverse and their duals and we define new kinds of generalized inverses which are called the weighted generalized core–EP inverse and its dual. Thus, these new inverses present wider classes of generalized inverses. We establish a number of characterizations and representations of the weighted generalized core–EP inverse and its dual. As applications of our new inverses, we solve several systems of linear equations and a minimization problem.

Toward a Mølmer Sørensen gate with .9999 fidelity

Abstract Realistic fault-tolerant quantum computing at reasonable overhead requires two-qubit gates with the highest possible fidelity. Typically, an infidelity of ≲ 10 − 4 is recommended in the literature. Focusing on the phase-sensitive architecture used in laboratories and by commercial companies to implement quantum computers, we show that even under noise-free, ideal conditions, neglecting the carrier term and linearizing the Lamb–Dicke term in the Hamiltonian used for control-pulse construction for generating Mølmer–Sørensen XX gates based on the Raman scheme are not justified if the goal is an infidelity target of < 10 − 4 . We obtain these results with a gate simulator code that, in addition to the computational space, explicitly takes the most relevant part of the phonon space into account. With the help of a Magnus expansion carried to the third order, keeping terms up to the fourth order in the Lamb–Dicke parameters, we identify the leading sources of coherent errors, which we show can be eliminated by adding a single linear equation to the phase-space closure conditions and subsequently adjusting the amplitude of the control pulse (calibration). This way, we obtain XX gates with infidelities < 10 − 4 .

An Observation About Weak Solutions of Linear Differential Equations in Hilbert Spaces

An Observation About Weak Solutions of Linear Differential Equations in Hilbert Spaces

Stability of KdV equation on a network with bounded and unbounded lengths

In this work, we studied the exponential stability of the nonlinear KdV equation posed on a finite star shaped network with finite number of branches. On each branch of the network we define a KdV equation posed on a finite domain [[EQUATION]] or the half-line [[EQUATION]]. We start by proving well-posedness and some regularity results. Then, we state the exponential stability of the linear KdV equation by acting with a damping term on some branches. The main idea is to prove a suitable observability inequality. In the nonlinear case, we obtain two kinds of results: The first result holds for small amplitude solutions, and is proved using a perturbation argument from the linear case but without acting on all edges. The second result is a semiglobal stability result, and it is obtained by proving an observability inequality directly for the nonlinear system, but we need to act with damping terms on all the branches. In this case, we are able to prove the stabilization in weighted spaces.

A novel least squares approach generating approximations orthogonal to the null space of the operator

We introduce a novel least squares functional specifically formulated to solve linear partial differential equations with operators that have a nonempty null space. Our method involves projecting the solution onto the orthogonal complement of the operator's null space to overcome challenges encountered by conventional numerical methods when nonzero null components are present. We describe the theoretical framework of the proposed method and validate it through numerical examples that show improved accuracy and usability in cases where traditional methods are less effective due to significant null space components. Overall, this approach provides a practical and reliable solution for partial differential equations with substantial null space components.

Ethno-Science, Technology, Engineering, and Mathematics (EthnoSTEM) Ideas in the Sama Mat-Weaving

Mat weaving has been culturally and economically significant among the Sama ethnolinguistic group since time immemorial. This study sought to find concepts and processes of ethnoscience, ethnotechnology, ethnoengineering, and ethnomathematics (ethnoSTEM) present in weaving tepo, a hand-woven mat of the Sama, made from indigenously processed leaves of pandan or screw pine (Pandanus tectorius). To determine ethnoSTEM ideas, concepts, and processes in tepo weaving, an ethnography was conducted involving five female mat weavers in a coastal village in Tawi-Tawi’s major producer of tepo, the Municipality of Tandubas. Data were gathered primarily through observations during a monthlong community immersion. Results revealed that Ethnotechnology tools were in the form of bolo, pandan-presser, pandan slitter, traditional stove, bamboo scalp scratcher, and other local cooking tools, with each tool exhibiting unique characteristics and functions needed for weaving. Ethnoengineering was evident in preparing pandan strips to create, bleach, and dye pandan strips for weaving and fastening the tepo. Ethnomathematics comprised primitive length measurement, arithmetic calculations, ratio and proportion, linear and quadratic equations, sinusoidal functions, basic geometric concepts, circles, symmetries, and isometries. Ethnoscience was observed in the processes determining the dyeability of pandan strips, as well as in the procedures employed in its softening and bleaching. It is concluded that the concepts and ideas of ethnoSTEM found in Sama weaving of tepo are loaded with scientific affluence that should be preserved to preclude them from fading to oblivion.

Control problems in the coefficients and the domain for linear elliptic equations

In the present work we are interested in an optimal design problem for a linear elliptic state equation with a homogeneous boundary Dirichlet condition. The control variables correspond to the coefficients of the diffusion term and the open set where the equation is posed. From the application point of view these variables represent the layout of the materials composing the corresponding domain and its shape. We obtain a relaxed formulation of the problem, the optimality conditions, and we provide a numerical algorithm to solve it. Some numerical simulations are also carried out.

Maximum temperature of steel bridges due to multiple under-bridge fire sources

In this study, an analytical model was developed and predictive equations were proposed to estimate the maximum temperature of steel bridges in the event of a fire originating from complex facilities beneath the bridge. Based on statistical data, a representative shape of steel bridges in South Korea was selected. A representative Heat Release Rate (HRR) curve for the complex facility was selected, and a parametric study was conducted, including variables such as Heat Release Rate Per Unit Area (HRRPUA), fully developed time, vertical clearance, and the area of the complex facility. Through correlation analysis, key parameters influencing the maximum temperature in steel bridges were examined. Based on the results, both linear and non-linear temperature prediction equations were suggested. The non-linear equation demonstrated higher predictive performance than the linear equation. This study provides foundational data for enhancing the accuracy of fire analysis methods and temperature prediction models for steel bridges.

Confirmatory Study on Prediction of Maximal Oxygen Uptake by Ensemble Learning Algorithm

Objective: The prediction model of maximal oxygen uptake (VO2max) was established by different ensemble learning methods. Compared with multiple linear regression, a common prediction method of VO2max, the effectiveness of the ensemble learning model is verified, and screen out the optimal VO2max prediction model. Methods: A total of 84 male college students, were recruited, informed of the purpose and procedure of the experiment, and passed the PAR-Q questionnaire screening. Cardiopulmonary Exercise Test (CPET), lung function, body composition test, VO2max, minute ventilation volume (VE), tidal volume (Vt), weight, and other related indicators. After the correlation analysis of the experimental results, a VO2max multiple linear regression model and an ensemble learning prediction model are computed. Results: The indicators that finally enter the multiple linear regression equation include: weight, Vt, VE. The regression equation is: VO2max (ml/kg/min) = 52.455+0.005×VT (ml/min) + 0.111×VE (L/min)-0.441×weight (kg), and the regression coefficient test results is extremely significant (P<0.01). The VO2max prediction model is computed by using the ensemble learning algorithm and among the five prediction models, it is found that Weighted average (R^2=0.7715) has the best effect, and higher than multiple regression model, there is no significant difference between the actual value and the predicted value VO2max (P>0.05). Conclusion: In the case of a small sample size, the weighted average model predicts VO2max the most accurately, compared with multiple regression models, the ensemble learning model can include more basic indicators, the evaluation of VO2max in the body is more comprehensive, and the prediction results are more accurate.