Differential Conditions Research Articles

Two remarks on properties of functions of bounded variation

In terms of variations, a sufficient condition for the uniform convergence of sequences of continuous functions is proved. Using this result, we obtain an addition to the classical Helly theorem on the selection of convergent sequences of functions with uniformly bounded variations in the case when the limit function is continuous. Also, by using an example we show that the condition of continuous differentiability of a function, ensuring the differentiability of its variation with the variable upper limit, is in a certain sense sharp.

Deep Learning Evidence for Global Optimality of Gerver’s Sofa

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver’s 1992 solution, providing a lower bound of approximately 2.2195, is the best known, though its global optimality remains unproven. This paper leverages neural networks’ approximation power and recent advances in invexity optimization to explore global optimality. We propose two approaches supporting Gerver’s conjecture that his sofa is the unique global maximum. The first approach uses continuous function learning, discarding assumptions about the monotonicity, symmetry, and differentiability of sofa movements. The sofa area is computed as a differentiable function using our “waterfall” algorithm, with the loss function incorporating both differential terms and initial conditions based on physics-informed machine learning. Extensive training with diverse network initialization consistently converges to Gerver’s solution. The second approach applies discrete optimization to the Kallus–Romik upper bound, improving it from 2.37 to 2.3337 for five rotation angles. As the number of angles increases, our model asymptotically converges to Gerver’s area from above, indicating that no larger sofa exists.

Sportsman’s employment contract: problematic issues and prospects for their solution

Individual contractual regulation, which reflects the real needs of the development of relations between an employee-athlete and an employer-sports organization, plays an important role in regulating the labor activities of athletes. Thus, the employment contract concluded with an athlete contains a number of conditions that objectively and significantly individualize his work, i.e. conditions inherent only to this category of employees. Moreover, it enshrines differential conditions for each specifically defined employee­athlete. The purpose of the article is to consider the specifics of the labor contract concluded between an employee-athlete and an employer­sports organization. It was concluded that the labor relations of a professional athlete should be regulated precisely by the norms of labor law and a special law on professional sports, which regulates the entire complex of relations between the state and participants in professional sports, although today there are opinions that the work of professional athletes should be provided with the help of civil - legal regulation. It is noted that, as of today, the main national law in the field of sports - the Law «On physical culture and sports» dated 12.24.1993 concerns only the general foundations of activities in the field of physical culture and sports, at the same time, it does not even contain an acceptable definition of such a concept as «labor contract with a professional athlete». Therefore, it is proposed to supplement the specified Law with a norm to provide for the definition of an employment contract with a professional athlete. In particular, as an employment agreement between an employee­athlete and an employer-sports organization with all appendices, changes and additions, concluded in accordance with the legislation of Ukraine, on the basis of which labor relations arise regarding the preparation and participation of the athlete in competitions for a monetary reward paid by the club. At the same time, in addition to defining and enshrining at the legislative level the concept of an athlete’s employment contract, the proposal to develop a standard form of contract with athletes of various sports was supported, the development of which should be based on the main directions of the joint sports activities of the athlete and the sports organization, which directly consists in the preparation athlete to a successful performance at competitions.

Standardization of Protocol for Production of Synthetic Seed of Brahmi (Bacopa monnieri) and Assessment of their Longevity under Differential Storage Condition

Brahmi [Bacopa monnieri (L) Pennel] is an important medicinal small succulent, medicinal herb belongs to the family ‘Scrophulariaceae’ which is commonly known as Jala Brahmi or Nira-Brahmi. National Medicinal Plants Board (NMPB), estimated an annual demand of Bacopa in 2004-2005 was 6621.8 tonnes, with a 7% annual growth rate. Micropropagation techniques and production of synthetic seeds can be a breakthrough to overcome the low availability of Brahmi propagating materials. So, the present study was conducted to standardize the protocol for preparation of synthetic seeds of Brahmi using nodal segment. The experiment was conducted with five treatments by using combinations of different concentrations of sodium alginate and calcium chloride and preparing two types of synthetic seeds (single layer and double layer). Further the longevity of both single layer and double layered synthetic seeds was studied under two different storage temperatures at 25°C (ambient condition) and 4°C (refrigerator) up to 40 days by inoculating them in two different types of media. The result showed no significant effect of concentrations of gelling agent and complexing agent on the germination percentage of synthetic seeds. The number of shoots per synthetic seed varied from 22.00 to 29.35 with 100% germination and maximum shoots/synthetic seed and shoot length was obtained by using T5 (single layered with MS media, 3% sodium alginate and 2.5% calcium chloride). Maximum number of days of storage can be observed in the single layer synthetic seeds when stored at 4°C along with media followed by double layer synthetic seeds when stored at 4°C along with media. However, seeds stored on vermiculite got dried up in the initial days of storage. Germination was found to be higher in seeds stored at 4°C when compared to seeds stored at 25°C. The study as a whole elucidated the opportunity for the use of synthetic seed as an alternative to traditional propagation system for Brahmi.

Systemic Juvenile Idiopathic Arthritis and arthralgia - can it be diagnosed early within the window period? – An observation of serum biomarkers and analysis with other differential conditions in children

Background: Systemic juvenile idiopathic arthritis (sJIA)is a cause of persisting arthralgia which is often missed. Diagnosing sJIA can be challenging, especially when overt arthritis is absent at presentation, highlighting the need for a diagnostic biomarker. Few recent studies have assessed potential biomarkers for sJIA, however, there is no consensus in detecting early. We conducted a study evaluating serum IL-1, IL-6, IL-18, S100A8, and S100A9 as potential diagnostic markers to distinguish sJIA from other conditions presenting as joint pain in children. Methods: A prospective study was conducted in our institute from May-2019 to October-2020 in children under 16 years, who had persisting arthralgia. Serum concentrations of IL-1, IL-6, IL-18, S100A9, and S100A8 were determined using ELISA kits. Receiver operating curve (ROC) analysis was used to determine the cut-off values for IL-1, IL-6, IL-18, S100A8, and S100A9 for differentiating sJIA from other causes of joint pain and fever. Results- Out of 47 children who presented with joint pain and fever 19 of them were eventually diagnosed with sJIA. In the other 28 children, arthralgia and fever was attributed to conditions other than sJIA (non-sJIA). The non-sJIA group comprised children with acute lymphoblastic leukemia, hemophagocytic histiocytosis, systemic lupus erythematosus, Kawasaki disease, Kikuchi disease, and inflammatory bowel disease. Serum levels of IL-18, S100A8, and S100A9 were significantly higher in patients with sJIA compared to the non-sJIA group (p<0.05). The area under the curve (AUC) was significant for IL-18(77.9%), S100A8 (74.9%), and S100A9(71.2%). A serum IL-18 cut-off level of > 2030.45 pg/ml was useful for differentiating between sJIA and other diseases with a sensitivity of 66.67% and specificity of 75.86% for the diagnosis of sJIA. Conclusion- Serum IL-18, S100A8, and S100A9 can be useful in differentiating sJIA early from other causes of persisting arthralgia in children provided with appropriate identification of symptomatology and suspicion.

Mathematical Methods for Control Systems in Electrical Engineering

Control frameworks are exceptionally imperative in electrical building since they make it conceivable to absolutely control and move forward complicated gadgets and forms. This unique talks almost essential scientific procedures that are required to get it and construct control frameworks within the field of electrical designing. Through science structures, it appears vital thoughts like criticism control, soundness examination, and framework optimization. Differential conditions, which depict how energetic frameworks carry on, are the building squares of control frameworks. These conditions appear how framework variables are associated to each other and how quick they alter over time. They are utilized to ponder how frameworks move and remain steady. These forms decide how electric circuits, engines, generators, and other critical parts of advanced innovation foundation work in electrical building employments. The thought of control gives us ways to form these frameworks more steady, controlled, and successful. Differential conditions can be effectively interpreted into the recurrence space utilizing strategies like Laplace changes. This makes it simpler to think about how frameworks react to distinctive inputs and changes. This alter makes it less demanding to figure out framework exchange capacities, which makes a difference when making controls that alter how frameworks carry on to meet execution objectives. Steadiness investigation too makes beyond any doubt that controlled frameworks work reliably and typically indeed when conditions alter. Strategies like root locus, Nyquist measure, and Bode plots offer assistance us get it the limits of a system's steadiness and how it reacts, which is vital for making beyond any doubt it works well and anticipating undesirable variances or insecurity.

Mathematical Modeling of Electrical Power Systems for Fault Detection

Control networks are critical offices that have to be exceptionally solid and productive. Finding issues in these frameworks is exceptionally imperative for keeping them steady, keeping gear from breaking, and maintaining a strategic distance from long power blackouts. It has gotten to be clear that scientific modeling may be a awesome way to think about and discover issues in control frameworks. Taking after this strategy requires making a scientific show of the control framework, which incorporates motors, transformers, transmission lines, and loads. A few physical laws, like Ohm's Law and Kirchhoff's laws, are frequently utilized within the models to accurately show how electrical circuits work when they are working legitimately and when they aren't. On the off chance that you need to discover issues, you'll utilize numerical models to form flaws like brief circuits, open circuits, and ground deficiencies appear genuine. Through examining how the framework responds to these fake issues, engineers can make programs that can discover genuine flaws and tell where they are when they happen. These calculations frequently utilize strategies like evaluating the state, evaluating the parameters, and recognizing designs. Utilizing real-time information to figure the current state of the framework is what state estimation is all approximately. On the other hand, parameter estimation is all almost finding changes in framework parameters that might cruel there is a problem. Design acknowledgment employments past information and machine learning to discover peculiarities and sort diverse sorts of flaws. Differential conditions, framework polynomial math, and numerical strategies are fair some of the progressed science instruments that are frequently utilized to unravel the complicated conditions that depict how the power framework works. Putting these models beside unused computer innovations like high-performance computing and real-time simulations makes issue location strategies more exact and quicker. As green vitality sources and shrewd network advances are included to control frameworks, they will continue to alter. Mathematical modeling will become more and more important to make sure they work safely and efficiently. It talks about how to mathematically model electrical power systems to find faults, what they can be used for, and what the future holds for this field.

Computational Mathematics for Electromagnetic Field Simulation

Computational science could be a key portion of making reenactments and investigations of electromagnetic areas superior, which is critical for numerous ranges, from restorative imaging to broadcast communications. This theoretical talks around the essential thoughts, computer methods, and fundamental issues that come up when utilizing scientific models to form precise considers of electromagnetic areas. Maxwell's conditions portray how electric and attractive areas carry on in space and time and are utilized to recreate electromagnetic areas. Since real-life circumstances are so complicated and distinctive, these conditions, which are made up of differential conditions with fractional subordinates, got to be fathomed numerically. Utilizing procedures like finite difference, limited component, and boundary component strategies, computational science breaks these issues down into shapes that can be fathomed. Limited contrast strategies utilize a framework to induce near to subordinates, whereas finite element strategies break the space up into littler pieces to accurately illuminate complicated geometries. Boundary component strategies center on fundamentally details along the domain's edges, giving fast answers for problems within the exterior world. Each strategy strikes a adjust between exactness, the speed of calculations, and the capacity to work with distinctive electromagnetic occasions. Overseeing the complexity of the coding system, accurately speaking to the highlights of the fabric, and dealing with nonlinearities within the conditions are a few of the issues that come up in computational electromagnetic field reenactment. To create simulations more exact and productive, analysts are continuously looking into unused math calculations, concurrent computer methods, and optimization methodologies.

Histopathology reveals environmental stress in dusky flounder Syacium papillosum of the Yucatan Peninsula continental shelf

The histological changes in the liver, kidney, spleen, and gills of Syacium papillosum from the continental shelf of the Yucatan Peninsula, Gulf of Mexico, and their statistical associations with environmental conditions and pollutants were assessed in 2010, 2011, and 2012. We evaluated the extension and severity of the lesions through a degree of tissue change (DTC), and, with the sum of the number of lesion types within each of their DTC stages, we determined the histological alteration index (HAI). The liver and kidney were the most affected organs, with HAI values > 100. Fish with the most severe damage were observed on the Campeche Bank and the Caribbean Sea, contrasting with those collected from the northern Yucatan continental shelf. The presence of foci cellular alteration and abundant melanomacrophage centers indicated that these flatfishes were chronically exposed to environmental stress factors. Redundancy analyses showed strong associations between HAI values and hydrocarbon and heavy metal concentrations in muscle. Our results provide evidence for the first time of a differential health condition of the Yucatan shelf through the histopathology shown in S. papillosum, establishing the baseline for future monitoring programs in the region.Graphical abstract

The Problem of Heat and Mass Transfer of a Half-Space with an Air Flow with Periodic Changes in Air Temperature

A system of differential equations, boundary and initial conditions for calculating temperature and moisture content fields in a homogeneous halfspace, the boundary of which is blown by an air flow, is formulated. The heat exchange of the boundary with the air medium occurs according to the Newtonian law, and mass transfer — according to the Dalton evaporation law. In the initial state, the air and the material have the same temperature, and water vapor, both near the surface of the material and outside the boundary layer, is in a saturation state, so there is no exchange of heat and moisture between the air and the material. At some point, the air temperature begins to produce small harmonic fluctuations near its initial value. For a mathematical model of heat and mass transfer, in which the movement of moisture to the surface is considered to be caused only by a drop in moisture content, i.e. the phenomenon of thermal diffusion is neglected, an asymptotic time view of the temperature and moisture content fields is obtained. The moisture content field has the form of a damped harmonic wave, and the temperature field is represented by the superposition of two waves of the same type, which have the same frequency, but different attenuation coefficients and phase velocities. The calculation of the basic wave parameters for a material with clay characteristics is carried out, and the results obtained are compared with experimental data. The constructed solution is a generalization of the Fourier formulas known in the literature, which are valid only in a situation when the material does not contain moisture, and according to the harmonic law, not the air temperature changes, but the surface temperature. The results obtained in the article will be used in geocryology as a theoretical tool in the study of seasonal fluctuations in the thermal and physical state of the soil, which is an important task in planning economic activities in the field of the distribution of frozen rocks.

Vibration Characteristics of Magnetostrictive Composite Cantilever Resonator with Nonlocal Effect.

Taking the nonlocal effect into account, the vibration governing differential equation and boundary conditions of a magnetostrictive composite cantilever resonator were established based on the Euler magnetoelastic beam theory. The frequency equation and vibration mode function of the composite cantilever were obtained by means of the separation of variables method and the analytic solution of ordinary differential equations. The lateral deflection, vibration governing equations, and boundary conditions were nondimensionalized. Furthermore, the natural frequency and modal function of the composite beam were quantitatively analyzed with different nonlocal parameters and transverse geometry dimensions using numerical examples. Compared with the results without considering the nonlocal effect, the influence of the nonlocal effect on the vibration characteristics was analyzed. The numerical results show that the frequency shift and frequency band narrowing of the magnetostrictive cantilever resonator are induced by nonlocal effects. In particular, the high-frequency vibration characteristics, such as vibration amplitude and modal node of the composite beam, are significantly affected. These analysis results can provide a reference for the functional design and optimization of magnetostrictive resonators.

Evaluating single multiplicative neuron models in physics-informed neural networks for differential equations

Machine learning is a prominent and highly effective field of study, renowned for its ability to yield favorable outcomes in estimation and classification tasks. Within this domain, artificial neural networks (ANNs) have emerged as one of the most powerful methodologies. Physics-informed neural networks (PINNs) have proven particularly adept at solving physics problems formulated as differential equations, incorporating boundary and initial conditions into the ANN’s loss function. However, a critical challenge in ANNs lies in determining the optimal architecture, encompassing the selection of the appropriate number of neurons and layers. Traditionally, the Single Multiplicative Neuron Model (SMNM) has been explored as a solution to this issue, utilizing a single neuron with a multiplication function in the hidden layer to enhance computational efficiency. This study initially aimed to apply the SMNM within the PINNs framework, targeting the differential equation y′-y=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y'-y=0$$\\end{document} with boundary conditions y(0)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y(0) = 1$$\\end{document} and y(1)=e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y(1) = e$$\\end{document}. Upon implementation, however, it was discovered that while the conventional SMNM approach was theorized to offer significant advantages, multiplicative aggregate function led to a failure in convergence. Consequently, we introduced a “mimic single multiplicative neuron model (mimic-SMNM)” employing an architecture with a single neuron, designed to simulate the SMNM’s conceptual advantages while ensuring convergence and computational efficiency. Comparative analysis revealed that the real-PINNs accurately solved the equation, the true SMNM failed to converge, and the mimic model was highlighted for its architectural simplicity and computational feasibility, directly implying it is faster and more efficient than real PINNs for the solution of simple differential equations. Furthermore, our findings demonstrated that our proposed mimic-SMNM model achieves a five-times increase in computational speed compared to real PINNs after 30,000 epochs.

Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions

This paper delves into a novel category of nonlocal boundary value problems concerning nonlinear sequential fractional differential equations, coupled with a unique form of generalized Riemann–Liouville fractional differential integral boundary conditions. For single-valued maps, we employ a transformation technique to convert the provided system into an equivalent fixed-point problem, which we then address using standard fixed-point theorems. Following this, we evaluate the stability of these solutions utilizing the Ulam–Hyres stability method. To elucidate the derived findings, we present constructed examples.

Optimal drift rate control and two-sided impulse control for a Brownian system with the long-run average criterion

Abstract In this paper, we consider a joint drift rate control and two-sided impulse control problem in which the system manager adjusts the drift rate as well as the instantaneous relocation for a Brownian motion, with the objective of minimizing the total average state-related cost and control cost. The system state can be negative. Assuming that instantaneous upward and downward relocations take a different cost structure, which consists of both a setup cost and a variable cost, we prove that the optimal control policy takes an $\left\{ {\!\left( {{s^{\ast}},{q^{\ast}},{Q^{\ast}},{S^{\ast}}} \right),\!\left\{ {{\mu ^{\ast}}(x)\,:\,x \in [ {{s^{\ast}},{S^{\ast}}}]} \right\}} \right\}$ form. Specifically, the optimal impulse control policy is characterized by a quadruple $\left( {{s^{\ast}},{q^{\ast}},{Q^{\ast}},{S^{\ast}}} \right)$ , under which the system state will be immediately relocated upwardly to ${q^{\ast}}$ once it drops to ${s^{\ast}}$ and be immediately relocated downwardly to ${Q^{\ast}}$ once it rises to ${S^{\ast}}$ ; the optimal drift rate control policy will depend solely on the current system state, which is characterized by a function ${\mu ^{\ast}}\!\left( \cdot \right)$ for the system state staying in $[ {{s^{\ast}},{S^{\ast}}}]$ . By analyzing an associated free boundary problem consisting of an ordinary differential equation and several free boundary conditions, we obtain these optimal policy parameters and show the optimality of the proposed policy using a lower-bound approach. Finally, we investigate the effect of the system parameters on the optimal policy parameters as well as the optimal system’s long-run average cost numerically.

Fault structure and earthquake clustering in Aswan region (Egypt) revealed by high-precision earthquake location from 35 years of recorded natural and induced seismicity

Starting from an initial catalogue of 7833 natural and reservoir-induced seismic events collected in Aswan region (south Egypt) from 1982 to 2016, we investigate the fault structure and triggering mechanisms by determining high-resolution hypocenters for 2562 earthquakes. Despite the complex network of intersecting fractures, high-precision earthquake locations reveal numerous discrete fault strands (some not mapped yet), whose kinematics have been determined from the focal mechanisms of Ml ≥ 2.5 earthquakes. Furthermore, the analysis of the space-time evolution of seismicity indicates an eastward migration of earthquakes and a progressive activation of different faults. This process could reflect fluid migration in the Wadi Kalabsha embayment likely controlled by permeability barriers at depth acting as seals, and the subsequent build-up of the pore pressure as the dominant driving mechanism of the observed seismicity in the region. A strong spatio-temporal earthquake clustering is observed in the region characterized by seismic sequences, repeated earthquakes, and long-lasting swarms. High variability of b-value in correspondence of the occurrence of mainshock-aftershock sequences also suggests the activation of faults and fractures within their respective fault zones under lower differential stress conditions due to fluids. The projection of earthquake hypocenters on an E-W vertical depth section of the study area shows a seismic gap with an approximate length of about 11 km along the Kalabsha fault, which suggests the presence of a locked fault patch that may generate a Mw 5.9 earthquake if this segment were to break in a single rupture episode.

Modeling and Control for Beam Pumping Units: An Overview

Beam pumping units play a key role in oil extraction. There is an increasing demand for optimal oil-extracting performance as operational environments are becoming more challenging and complex. Therefore, it is vital to create an acceptable mathematical model and develop robust control mechanisms. In the past decades, researchers have achieved fruitful results regarding modeling and control methods in this field. This article provides a comprehensive review of the research on modeling and control methods for beam pumping units, including mathematical models based on differential equations and boundary conditions, as well as the control strategies designed. Finally, future perspectives and recommendations are presented.

A new approach to problems of thermoelasticity in stresses

It is known that the plane problems of the theory of elasticity and thermoelasticity are usually reduced to solving the biharmonic equation with respect to the Airy stress function. Solutions to spatial problems can also be defined using the Maxwell and Morera stress functions, etc. In this work, for solving a spatial thermoelastic problem, in the framework of the Beltrami-Michell equations, Poisson-type differential equations are found for each component of the stress tensor. In this case, the right-hand sides of these equations depend on temperature and elastic constants. The boundary conditions consist of the usual surface forces and “additional” boundary conditions derived from the equilibrium equations. The differential equations and boundary conditions of the plane problem of thermoelasticity in stresses are discussed in more detail. Grid equations for plane and spatial problems of thermoelasticity were compiled by the finite-difference method and solved by the iterative method. The problems of a thermoelastic rectangle and a parallelepiped located in a given temperature field are solved numerically. The validity of the formulated boundary value problems and the reliability of the results obtained are substantiated by comparing the numerical results with the solutions of the problems of a thermoelastic plate and a parallelepiped known in the literature.

Discrete inverse problem for a hyperbolic equation, properties of the solution to a discrete direct and auxiliary discrete problems

This paper considers the formulation of a discrete inverse problem for a hyperbolic equation. First, the continuous inverse problem is reduced to a convenient form for research. In the inverse problem, the required function is considered even. Since the Dirac delta function is present in the problem data, the structure of a generalized solution to the Cauchy problem for a hyperbolic equation is determined. The solution to the Cauchy problem for a hyperbolic equation is determined only for positive values in time, therefore the solution to the Cauchy problem for negative values in time is determined using odd continuation. After some transformations, the formulation of the continuous inverse problem is reduced to a form convenient for research. A grid domain is introduced, and for all functions in the problem statement the corresponding grid functions and a discrete analogue of the Dirac delta function are determined. Differential operators, initial conditions and additional data of the inverse problem are approximated by finite differences. Assuming that a solution to the discrete inverse problem exists, we prove the data lemma of the discrete inverse problem. In order to study the discrete inverse problem for a hyperbolic equation, a theorem on the existence and uniqueness of the discrete direct problem is proved, as well as on the properties of the solution to this discrete problem. In the course of proving the theorem, a discrete analogue of d'Alembert's formula for solving the Cauchy problem for a hyperbolic equation was obtained. The theorem on the existence of a unique solution to the auxiliary discrete problem and its properties is proved.

On a Method for Calculating Bending and Shear Vibrations of a Porous Piezoelement in the Low-Frequency Region

Introduction. Devices for collecting and storing energy from the external environment are low-power sources of electric energy that are actively used. The autonomous devices for monitoring the damaged condition of various structures include them as well. The working element of these devices is a piezoelectric generator (PEG) — a converter of mechanical energy into electrical energy. The design of PEG is associated with the preliminary construction of their mathematical and computer models, with the help of which the calculation and optimization of structures is carried out. One of the ways to model and calculate PEG is to develop approximate calculation methods based on applied theories. The applied theories for calculating bending vibrations of multilayer piezoactive plates are known and previously developed in the literature. However, in the scientific literature there is not enough information about bending and shear vibrations as a tool for improving the efficiency of engineering calculations of the described structures. The objective of this work was to develop an applied method for calculating bending and shear vibrations of piezoceramic plates, including porous ones.Materials and Methods. Piezoceramics PZT-4, including porous ones, were used as the piezoactive material of the plate. When using porous ceramics, the rigidity of the structure decreased to a greater extent than the piezoelectric modules, which made it possible to obtain a more effective PEG under mechanical action. The mathematical formulation was carried out within the framework of the linear theory of electroelasticity with plate polarization in thickness. The sides of the plate were electrodated, the right side was fixed, and a smooth contact in the vertical wall was set on the left side. Steady-state vibrations of the plate were caused by pressure on the front surfaces of the plate or the difference in electrical potentials at the electrodes. To calculate the characteristics of PEG, the authors proposed an applied theory based on hypotheses about the distribution of characteristics of the stress-strain state and the electric field.Results. Transverse vibrations of a piezoceramic plate in the low-frequency region (below the first bending-shear resonance) were studied. Due to the fact that the mathematical formulation was considered within the framework of the linear theory of elasticity, the problem was divided into the sum of two. The first one took into account the mechanical effect: a distributed load and a transverse force at the left end acted on the front surfaces of the plate, and the potentials at the electrodes were zero. In the second task, there were no mechanical loads, but the potential difference was set at the electrodes. Based on hypotheses about the distribution of deformations, mechanical stresses and electric potential, both problems were reduced to a system of ordinary differential equations and boundary conditions. Comparison with the results of calculations by the finite element method in the ACELAN package showed the adequacy of the proposed applied theory in the low-frequency region.Discussion and Conclusion. Since the formulation of the problem was considered in the linear theory of electroelasticity, and the low-frequency region was studied, the work succeeded in dividing the problem of bending-shear vibrations of a porous piezoceramic plate into two: bending — with mechanical action at zero potentials, and shear — when setting the potential difference and zero mechanical action. The corresponding hypotheses about bending and shear were used. Two systems of ordinary differential equations and boundary conditions, which were solved analytically without the use of “heavy” finite element packages, were constructed. To compare the results and confirm the adequacy of the proposed method, the finite element modeling of such tasks was carried out in a specialized ACELAN package. The comparison showed that the error in determining displacements and electric potential when using this approach, in the case of setting mechanical loads and potential differences, did not exceed 6%. The method developed in the paper can be applied in the design of piezoelectric generators for energy storage in the low-frequency region.

Evidence of oxidative stress responses of green turtles (Chelonia mydas) to differential habitat conditions in the Mexican Caribbean

Important foraging and nesting habitats for Caribbean green sea turtles (Chelonia mydas) exist within the Mesoamerican Reef System in the Mexican Caribbean. During the last 25 years, urban development and touristic activities have drastically increased in Quintana Roo, Mexico. Moreover, in the last decade, massive pelagic sargasso blooms have also afflicted this region; however, information about the biochemical responses of Caribbean green turtles to these inputs is absent. This study aimed to assess if the oxidative stress indicators in the red blood cells of green turtles are valuable biomarkers of the extent of the anthropic impact in this region. Persistent organic pollutants (POPs) were also measured in the plasma of free-living green turtles during 2015–2018 to characterize these habitats further. As biochemical biomarkers, the production rate of superoxide radical (O2•-), carbonylated protein content, and lipid peroxidation (TBARS) levels, and the activities of superoxide dismutase, glutathione S-transferase (GST), catalase, glutathione peroxidase were measured in erythrocytes. A 15 % occurrence of fibropapillomatosis (FP) was revealed, with tumor size being positively correlated with CAT activity in the affected individuals. A multivariate analysis embracing all oxidative stress markers discriminated green turtles between years of capture (p < 0.001), with those sampled during 2015 presenting the highest production of O2•- (p = 0.001), activities of GST (p < 0.001), levels of TBARS (p < 0.001) and carbonylated proteins (p = 0.02). These local and temporal biochemical responses coincided with the first massive Sargassum spp. bloom reported in the region. The results of this study corroborate the utility of the oxidative stress indicators as biomarkers of environmental conditions (sargasso blooms and POPs) in the green turtle as sentinel species.