Principal Part Research Articles

A nonlinear Dirichlet problem involving terms with logarithmic growth

We study existence and regularity of weak solutions for a class of boundary value problems, whose form is − div ( log ( 1 + | ∇ u | ) | ∇ u | m ( x ) ∇ u ) + u | ∇ u | log ( 1 + | ∇ u | ) = f ( x ) , in Ω u = 0 , on ∂ Ω where both the principal part and the lower order term have a logarithmic growth with respect to the gradient of the solutions. We prove that the solutions, due to the regularizing effect given by the lower order term, belong to the Orlicz–Sobolev space generated by the function s log ( 1 + | s | ) even for L 1 ( Ω ) data.

Anisotropic elliptic equations with gradient-dependent lower order terms and $ L^1 $ data

<abstract><p>We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $ \mathcal Au+\Phi(x, u, \nabla u) = \mathfrak{B}u+f $ in $ \Omega $, where $ \Omega $ is a bounded open subset of $ \mathbb R^N $ and $ f\in L^1(\Omega) $ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $ \mathcal A $, the prototype of which is $ \mathcal A u = -\sum_{j = 1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u) $ with $ p_j > 1 $ for all $ 1\leq j\leq N $ and $ \sum_{j = 1}^N (1/p_j) > 1 $. As a novelty in this paper, our lower order terms involve a new class of operators $ \mathfrak B $ such that $ \mathcal{A}-\mathfrak{B} $ is bounded, coercive and pseudo-monotone from $ W_0^{1, \overrightarrow{p}}(\Omega) $ into its dual, as well as a gradient-dependent nonlinearity $ \Phi $ with an "anisotropic natural growth" in the gradient and a good sign condition.</p></abstract>

Qualitative Properties of Solutions of Degenerate Parabolic Equations via Energy Approaches

We consider several problems for degenerate parabolic equations exhibiting nonlinearities of various kinds. For example the equations may contain superlinear sources, causing blow up of the solutions, or damping terms; the principal part of the operator is also nonlinear. We mention as unifying features the fact that the spatial domains have non-compact boundary, and the technical approach which is based on energy methods and a priori estimates. The issues investigated include existence under optimal assumptions on the data, asymptotic behavior of solutions, existence or non-existence of global in time solutions.

Null controllability of strongly degenerate parabolic equations

We consider linear one-dimensional strongly degenerate parabolic equations with measurable coefficients that may be degenerate or singular. Taking 0 as the point where the strong degeneracy occurs, we assume that the coefficient a = a(x) in the principal part of the parabolic equation is such that the function x → x/a(x) is in Lp(0,1) for some p > 1. After establishing some spectral estimates for the corresponding elliptic problem, we prove that the parabolic equation is null controllable in the energy space by using one boundary control.

An approximation approach for solving degenerated quasilinear problems

<p style='text-indent:20px;'>The present paper develops an approximation approach for solving a quasilinear Dirichlet boundary value problem that exhibits a degenerated <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian and full dependence on the solution and its gradient (convection term). The results establish that the solution set is nonempty and bounded. The principal part of the equation is driven by a <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian type operator containing a weight depending on the solution without any monotonicity assumption. The existence of a weak solution results through a limit process by means of approximate solutions arising from finite-dimensional problems. The a priori estimates are obtained in adequate Sobolev spaces with weights. An example provides an explicit illustration of the involved technique.</p>

A class of integral functionals with a $W^{1,1}_0$-minimum

In this paper, we study the minimization of the integral functionals of the type \int_{\Omega}\frac{|\nabla v|^2}{\big[1+B|v|\big]^{2}} + \frac12\int_{\Omega} a(x)|v|^2 - \frac1q\int_{\Omega} \rho(x)|v|^q, where 0<B , 0<a_0\leq a(x)\in L^1_{\mathrm{loc}}(\Omega) , 0\not\equiv\rho^+(x)\in L^{{\frac{2}{2-q}}}(\Omega) , and 0<q<2 . The degeneracy of the principal part of the functional implies that it is not coercive in W_{0}^{1,2}(\Omega) and pushes to set and solve the minimization problem in W_{0}^{1,1}(\Omega) instead of the space W_{0}^{1,2}(\Omega) . In addition, when the coefficients a(x) and \rho(x) are merely in L^1(\Omega) , but satisfy for some Q>0 the condition |\rho(x)|\leq Q a(x) , we show the existence of a minimum of the functional which belongs to W_{0}^{1,2}(\Omega){\cap L^\infty(\Omega)}\setminus\{0\} .

Interaction of 3-(1H-tetrazol-5-yl) Coumarin With Bovine Serum Albumin and Calf Thymus DNA: Deciphering the Mode of Binding by In Vitro Studies

Background: Coumarins comprise a large family of heterocyclic compounds with a benzo-a-pyrone moiety. Objectives: This study aimed to analyze the binding affinity of 3-(1H-tetrazol-5-yl) coumarin to bovine serum albumin (BSA) and calf thymus DNA (Ct-DNA) using fluorescence spectroscopy. The quenching of fluorescence was recognized during the interaction between 3-(1H-tetrazol-5-yl) coumarin and BSA, followed by a static mechanism. Methods: The hydrogen bonds, hydrophobic interactions, and Vander Waals forces were regarded as the principal part in the 3-(1H-tetrazol-5-yl) coumarin and BSA complexation process. The fluorescence spectral characteristics demonstrated an enhancement in fluorescence intensity of the 3-(1H-tetrazol-5-yl) coumarin in the presence of ct-DNA solution. Results: The experimental results indicated that the 3-(1H-tetrazol-5-yl) coumarin binds to DNA via interjection, hydrogen bonds, and Vander Waals forces. This work illustrated that BSA fluorescence was quenched by 3-(1H-tetrazol-5-yl) coumarin via a static mechanism and the ct-DNA fluorescence enhancement by 3-(1H-tetrazol-5-yl) coumarin was a static process. The secondary structure of proteins changed upon drug binding. Conclusion: It is deduced that 3-(1H-tetrazol-5-yl) coumarin represents a higher binding affinity to DNA compared to BSA. This finding can be useful in designing more effective new drugs with fewer side effects.

Nonhomogeneous Dirichlet Problems with Unbounded Coefficient in the Principal Part

The main result of the paper establishes the existence of a bounded weak solution for a nonlinear Dirichlet problem exhibiting full dependence on the solution u and its gradient ∇u in the reaction term, which is driven by a p-Laplacian-type operator with a coefficient G(u) that can be unbounded. Through a special Moser iteration procedure, it is shown that the solution set is uniformly bounded. A truncated problem is formulated that drops that G(u) be unbounded. The existence of a bounded weak solution to the truncated problem is proven via the theory of pseudomonotone operators. It is noted that the bound of the solution for the truncated problem coincides with the uniform bound of the original problem. This estimate allows us to deduce that for an appropriate choice of truncation, one actually resolves the original problem.

Contact problems for a transversely isotropic layer

Two spatial, one axisymmetric and two plane contact problems are considered for a transversely isotropic elastic layer with one face subjected to sliding support. In the spatial and plane contact problems, the planes of isotropy may be either parallel or perpendicular to the layer faces. In the case of axial symmetry, the planes of isotropy are parallel to the layer faces. By using Fourier integral transforms, the contact problems are reduced to integral equations with respect to the contact pressure, the limiting cases of which are the well-known equations of the corresponding problems for an isotropic layer. For solving the spatial problems with unknown contact domains, the nonlinear boundary integral equations method is used, which make it possible to determine the contact pressure and the contact domain simultaneously. To extract the kernel principal part of the spatial problem integral equation when the isotropy planes are perpendicular to the layer faces, it is used the kernel of the integral equation of the corresponding contact problem for a transversely isotropic half-space obtained earlier without quadratures. The integral equation of the axially symmetric problem is reduced to a Fredholm integral equation of the second kind with the help of the method of pair equations, and the method of mechanical quadratures is used for numerical solutions. Plane problems are solved in a closed form based on special approximations of the kernel symbols. The approximations accuracy grows as anisotropy increases. Here, the anisotropy level can be characterized by the difference between ratio of a characteristic equation roots and unit because the unit value corresponds to the isotropic case. Mechanical characteristics as well as errors of the approximations are calculated for well-known transversely isotropic materials.

Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients

In this work, we are interested in an inverse potential problem for a semilinear generalized fractional diffusion equation with a time-dependent principal part. The missing time-dependent potential is reconstructed from an additional integral measured data over the domain. Due to the nonlinearity of the equation and arising of a space-time dependent principal part operator in the model, such a nonlinear inverse problem is novel and significant. The well-posedness of the forward problem is firstly investigated by using the well known Rothe’s method. Then the existence and uniqueness of the inverse problem are obtained by employing the Arzelà–Ascoli theorem, a coerciveness of the fractional derivative and Gronwall’s inequality, as well as the regularities of the direct problem. Also, the ill-posedness of the inverse problem is proved by analyzing the properties of the forward operator. Finally a modified non-stationary iterative Tikhonov regularization method is used to find a stable approximate solution for the potential term. Numerical examples in one- and two-dimensional cases are provided to illustrate the efficiency and robustness of the proposed algorithm.

The Improvement of Artificial Neural Network Accuracy Using Principle Component Analysis Approach

An important problem in a classification system is how to get good accuracy results. A way to increase the accuracy of a classifier system is to improve the number of input data attributes. Improving the number of input data attributes can be done using the Principal Component Analysis (PCA) method. The aim of this research is to reduce the number of input data attributes to increase the accuracy in a mushroom classification system. The research method used in this study started from collecting datasets from Kaggle.com related to mushroom-classification, then the data visualization process was carried out using pie charts then a dimension reduction process was carried out to reduce the number of variables using the PCA method. The next step is the training and testing of the artificial neural network. The architecture of artificial neural network used is backward error propagation with the number of hidden layers as much as 2 layers with the number of cells as many as 3 and 2. The training data used is 80%, while the testing data is 20%. Based on the test results, obtained an accuracy of 100% with 150,000 iterations and using 11 input variables from 22 existing input variables. By adding Principal Component Analysis part of the development that can improve the accuracy and performance of Artificial Neural Networks

THE FORMAL-SYNTACTIC STRUCTURE OF SENTENCES WITH PREDICATES OF PRESENCE / ABSENCE

The article deals with the comprehensive analysis of the formal-syntactic structure of simple sentences with verbal predicates of presence / absence which state or deny the fact of subject’s presence, existence and organize existential sentences. The analysis of sentences with verbal predicates of presence / absence shows that their semantic structure mainly consists of existential predicate and subject which are represented by the principal parts of the sentence – the grammatical predicate and subject at the formal-syntactic sentence level. The relations between the semantic and formal-syntactic structure of sentences with the predicates of presence / absence are represented by the correlative and non-correlative types of relations.

Battery Lifetime Prediction via Neural Networks with Discharge Capacity and State of Health

The market share of electric vehicles (EVs) has grown exponentially in recent years to reduce air pollution and greenhouse gas emissions. The principal part of an EV is the energy storage system, which is usually the batteries. Thus, the accurate estimation of the remaining useful life (RUL) of the batteries, for an optimal health management and a decision-making policy, still remains a challenge for automakers. In this paper, the problem of battery RUL prediction is studied from a new perspective. Unlike other estimation strategies existing in the literature, the proposed technique uses an intelligent prediction of the lifespan of lithium–iron–phosphate (LFP) batteries via a modified version of neural networks. It uses a data-driven life estimation approach and optimization method and does not require any prior comprehension and initialization of any parameters of the battery model. To validate and verify the proposed technique, we use LFP battery data sets, and the experimental results showed that the proposed methodology can well learn the characteristic relationship of battery discharge capacities as well as its state of health (SOH), where the battery life cycle changes as the battery ages with time and cycles.

Design and Development of Turn Insulation Automatic Wrapping System for CRAFT TF

A principal part of the Comprehensive Research Facility for Fusion Technology (CRAFT) is the toroidal field (TF) coil project, which aims at fabricating a prototype TF coil for China Fusion Engineering Test Reactor (CFETR). The TF coil is composed of 3-D-shaped subwinding packs (sub-WPs) enclosed in a stainless coil case, and the conductor core of medium and high field sub-WPs is Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn, following the “Winding & Reaction” manufacturing process. After heat treatment of the conductor, turn insulation will be automatically wrapped. Strictly restricted by the brittleness of the heat-treated Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn, the strain must be controlled during the wrapping process. Presented in this article is a description of the CRAFT TF coil and its turn insulation structure, followed by descriptions of the structural design of the wrapping unit and mathematical models about wrapping control of the wrapping machine. Turn insulation wrapping trials are performed with one-fourth part of the wrapping unit, and tapes with a fixed width and a uniform steel tube are used as specimens, verifying the correctness of the structure and models. The one-fourth part of the wrapping unit has been fabricated in March 2022 and it is foreseen that the fabrication will be finished in June 2022.

Investigation of Airfoil Design and Analysis

Abstract: In this project “Aerofoil Design and Analysis” an attempt has made to make a complete study on lift and drag coefficient of various aerofoil sections using CFD. The primary goal of this project is to learn and analyse the aerodynamic performance of wings. The objective of this study is to improve aerofoil design using the software CATIA, And Fluent Analysis using the software ANSYS. Aerofoil is a principal part of any airplane construction. How much lift force and drag force is sufficient to balance the weight of the plane is decided by the aerofoil. Aerofoils are basically divided into two categories - they are Asymmetrical and Symmetrical aerofoils. Based on their drag and lift coefficient’s variation with angle of attack, stall angle of attack and magnitude of the coefficients they are divided. Here the NACA aerofoil is modified by adding dimples on the upper half of the wing and compared with the simple one. The comparison is made on different speed and pressure on the wing and the coefficient of lift and drag.

On the Separation Principle in Dynamic Output Controller Design for Uncertain Linear Systems

In this paper, the problem of designing the improper dynamic output controllers for uncertain linear multi-input/multi-output continuous-time systems is considered. In the principal part, the system state coordinate transform is outlined and matrix variable structures are found, defining the solution based on the structured linear matrix inequalities and linear matrix equality. Of principal novelty is the framework related to the system uncertainties with newly introduced inequality structures and their partial factorization. The main results are shown in detail by the example to characterize potential application of the method for quadratic stabilization of uncertain linear systems by the improper dynamic output controllers.

Sperm Dysfunction in the Testes and Epididymides due to Overweight and Obesity Is Not Caused by Oxidative Stress.

Obesity is a condition that has been linked to male infertility. The current hypothesis regarding the cause of infertility is that sperm are highly sensitive to reactive oxygen species (ROS) during spermatogenesis in the testes and transit through the epididymides, so the increase in ROS brought on by obesity could cause oxidative stress. The aim of this study was to evaluate whether the activity of the enzymes catalase (CAT), superoxide dismutase (SOD), and glutathione peroxidase (GPX) is capable of counteracting oxidative stress in sperm. The male Wistar rat was used as an overweight and obesity model, and analysis of fertility in these groups was carried out including the control group. Serum testosterone levels were determined, and the scrotal fat, testes, and epididymides were extracted. The epididymides were separated ini0 3 principal parts (caput, corpus, and cauda) before evaluating sperm viability, sperm morphology, damage to desoxyribonucleic acid of the sperm, and ROS production. The protein content and specific activity of the three enzymes mentioned above were evaluated. Results showed a gain in body weight and scrotal fat in the overweight and obese groups with decreased parameters for serum testosterone levels and sperm viability and morphology. Fertility was not greatly affected and no DNA integrity damage was found, although ROS in the epididymal sperm increased markedly and Raman spectroscopy showed a disulfide bridge collapse associated with DNA. The specific activities of CAT and GPX increased in the overweight and obesity groups, but those of SOD did not change. The amounts of proteins in the testes and epididymides decreased. These findings confirm that overweight and obesity decrease concentrations of free testosterone and seem to decrease protein content, causing poor sperm quality. Implications. An increase in scrotal fat in these conditions fosters an increase of ROS, but the increase of GPX and CAT activity seems to avoid oxidative stress increase in the sperm without damaging your DNA.

Bounded solutions for quasilinear modified Schrödinger equations

In this paper we establish a new existence result for the quasilinear elliptic problem \[ -{\rm div}(A(x,u)|\nabla u|^{p-2}\nabla u) +\frac1p A_t(x,u)|\nabla u|^p + V(x)|u|^{p-2} u = g(x,u)\quad\mbox{ in } \mathbb{R}^N, \] with $N\ge 2$, $p>1$ and $V:\mathbb{R}^N\to\mathbb{R}$ suitable measurable positive function, which generalizes the modified Schr\"odinger equation. Here, we suppose that $A:\mathbb{R}^N\times\mathbb{R}\rightarrow\mathbb{R}$ is a $\mathcal{C}^{1}$-Carath\'eodory function such that $A_t(x,t) = \frac{\partial A}{\partial t} (x,t)$ and a given Carath\'eodory function $g:\mathbb{R}^N\times\mathbb{R}\rightarrow\mathbb{R}$ has a subcritical growth and satisfies the Ambrosetti-Rabinowitz condition. Since the coefficient of the principal part depends also on the solution itself, we study the interaction of two different norms in a suitable Banach space so to obtain a "good" variational approach. Thus, by means of approximation arguments on bounded sets we can state the existence of a nontrivial weak bounded solution.

Critical appraisal skills training to undergraduate medical students: A Randomized Control Study.

Introduction: Critical appraisal skills are presumed to perform a principal part in evidence-based health education and practice methods. This study aimed to design an educational intervention around critical appraisal in this context, evaluate the efficacy of the teaching methods, and investigate critical appraisal skills training to undergraduate medical students.Methods: In this prospective Randomized Control Trial (RCT), 256 sixth-year undergraduate medical students from Shiraz University of Medical Science, Shiraz, Iran, participated. 124 of the students were not taught critical thinking methods as a control group, and 132 participants were taught critical thinking methods by multi-media and attended an online Critical Appraisal Skills (CAS) training workshop as an intervention group. We used the Critical Appraisal Skills Programme (CASP) questionnaire to evaluate students' knowledge, attitude, confidence, and appraisal skills. This questionnaire was translated into Persian for the first time in Iran by Shokooh Varai, et al. They investigated its validity and reliability, the reliability of the questionnaire being obtained by the Richardson Index (0.75), and the validity being confirmed by some faculty members of Tehran Nursing and Midwifery School. To compare both control and intervention groups, we used an independent t-test and a Chi-Square test at a significance level of 5%, and to analyze the demographic information, we applied some descriptive statistics: frequency, frequency percentage, mean and standard deviation. All of the statistical approaches were analyzed, using SPSS 22.Results: In all dimensions of the critical appraisal skills, medical students who completed the critical appraisal multi-media training and workshop performed better than those who did not (control group), and this difference was statistically significant (p<0.05). Moreover, the Chi-Square test results showed no statistical relationship between the groups regarding the demographic variables (p>0.05). Also, the Cohen's D effect size values in the knowledge and confidence dimensions were greater than 0.5; this meant a large effect. Regarding the attitude and appraises Skill dimensions, the effect size was between 0.2 and 0.5, which meant a medium effect.Conclusions: Teaching critical appraisal skills through multi-media and CAS online workshops to medical students effectively improves the students' knowledge and confidence in appraising articles. This teaching also indicated a medium effect on students' attitudes and behavior. Our findings can justify implementing critical appraisal skills teaching modules in the undergraduate medical education curriculum.

Контактная задача об осесимметричном кручении упругого слоя посредством цилиндрического штампа

The paper studies the axis-symmetric contact problem between an elastic layer and a rigid cylindrical circular stamp under torque. The stamp adheres to the upper boundary of the layer whereas the lower boundary of the layer is rigidly fastened. With the application of Hankel integral transform solving the problem reduces to solving the first kind Fredholm integral equation (IE) with symmetrical kernel, represented as a sum of its principal part, Weber-Sonin integral, and the regular kernel. It is estimated that once its height attains a certain level, the layer actually deforms as a semi-space. In the process, through Abel IE method, the solution of the well-known Reissner-Sagoci problem is obtained once again and the original first kind Fredholm IE is reduced to the second kind Fredholm IE. Concurrently, using the collocation method combined with Gauss type quadrature formulas for integral estimation, the original IE reduces to a finite system of linear algebraic equations. To obtain this quadrature formula, properties of Gegenbauer and Chebyshev orthogonal polynomials are used. In the enough wide range of change of characteristic elastic and geometrical parameters of the problem numerical analysis is performed and patterns of changes of tangential contact stresses under the stamp as well as the angle of twist of the stamp are identified.