Hydrocephalic cerebrospinal fluid flowing rotationally with pulsatile boundaries:A mathematical simulation of the thermodynamical approach

To study the kinematics of flow rate and ventricular dilatation,an analytical perturbation approach of hydrocephalus has been devised.This research provides a comprehensive investigation of the characteristics of cerebrospinal fluid(CSF)flow and pressure in a hydrocephalic patient.The influence of hydrocephalic CSF,flowing rotationally with realistic dynamical characteristics on pulsatile boundaries of subarachnoid space,was demonstrated using a nonlinear controlling system of CSF.An analytical perturbation method of hydrocephalus has been developed to investigate the biomechanics of fluid flow rate and the ventricular enlargement.In this paper presents a detailed analysis of CSF flow and pressure dynamics in a hydrocephalic patient.It was elaborated with a nonlinear governing model of CSF to show the influence of hydrocephalic CSF,flowing rotationally with realistic dynamical behaviors on pulsatile boundaries of subarachnoid space.In accordance with the suggested model,the elasticity factor changes depending on how much a porous layer,in this case the brain parenchyma,is stretched.It was improved to include the relaxation of internal mechanical stresses for various perturbation orders,modelling the potential plasticity of brain tissue.The initial geometry that was utilised to create the framework of CSF with pathological disease hydrocephalus and indeed the output of simulations using this model were compared to the actual progression of ventricular dimensions and shapes in patients.According to this observation,the non-linear and elastic mechanical phenomena incorporated into the current model are probably true.Further modelling of ventricular dilation at a normal pressure may benefit from the existence of a valid model whose parameters approximate genuine mechanical characteristics of the cerebral cortex.

Quasi Controlled K-Metric Spaces over C^(*)-Algebras with an Application to Stochastic Integral Equations

Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.

Numerical Comparisons of Different Imaging Algorithms

Image processing is the set of operations performed to extract “information” from the image. An interesting problem in digital image processing is the restoration of degraded images. It often happens that the resulting image is different from the expected image. Our problem will therefore be to recover an image close to the original image from a poor quality image (that has been skewed by Gaussian and additive noise). There are several algorithms on how we can improve the broken image in better quality. We present in this paper our numerical results obtained with the models of Tikhonov regularization, ROF, Vese Osher, anisotropic and isotropic TV denoising algorithms.

The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

The multifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.

Improvement of groundwater resources potential by artificial recharge technique: A case study of Charf El Akab aquifer in the Tangier region, Morocco

In arid and semi-arid zones,water is the most vulnerable resource to climate change.In fact,various techniques such as artificial recharge are adopted to restore aquifers and to ensure aquifer sustainability in relation to the accelerated pace of exploitation.Morocco is a Mediterranean country highly vulnerable to climate change,many of its main aquifers are subjected to excessive drawdowns.This technique is practiced to increase potentiality of these aquifers.In the Northwestern area of Morocco,the significant development experienced by Tangier City in the industrial,tourism,and commercial sectors will lead to increased water requirements-up to 5 067 L/s(159.8 mm^3)by 2030.However,the Charf El Akab aquifer system,subject to artificial recharge,is the only groundwater resource of Tangier region;hence,a rational management context is needed to ensure aquifer sustainability,and optimized exploitation under the background of differing constraints,such as increased water requirements,and climate change impacts.This work aims to respond,for the first time,to the Charf El Akab aquifer overexploitation problem,and to evaluate the future scenarios of its exploitation in the event of failure of one of the superficial resources.This work also presents a synthesized hydrodynamic modeling based on the results of the numerical simulations carried out using Feflow software for 2004(date of cessation of injections)and 2011(date of resumption of these facilities),making it possible to evaluate the impact of the artificial recharge on the piezometric level of the aquifer on a spatiotemporal scale.Finally,the exploitation scenarios have shown that the aquifer of Charf El Akab will not adequatly provide for the region's water requirements on the future horizon,entailing an optimal management of water resources in the region and an intentionally increased recharge rate.

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form Is = S2. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric i.e. the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac’s linear equation. It is proved that soliton-like solutions are absent.

Experimental Studies of Low-Pressure Plasma Jet by Means of Langmuir Probes and Emission Spectra

An investigation was made into the argon plasma jet that expanded in a low-pressurevacuum chamber.The spatial distributions of the parameters of the plasma jet with differentsupplied powers were measured using a ten-channel Langmuir probe array.The chemical speciesin the plasma jet were identified by emission spectroscopy.The electron excitation temperaturesat two positions,10 cm and 50 cm downstream from the nozzle exit were calculated,respectively,by the Boltzmann plot method.

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions.The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameterε.Firstly,the problem statement and variational formulation are formulated.We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameterε.Finally,we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

EXISTENCE AND BOUNDEDNESS OF SOLUTIONS FOR SYSTEMS OF QUASILINEAR ELLIPTIC EQUATIONS

This article sets forth results on the existence and boundedness of solutions for quasilinear elliptic systems involving p-Laplacian and q-Laplacian operators.The approach combines Schaefer's fixed point as well as Moser's iteration procedure.

Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences

Based on the role of the polynomial functions on the homogeneous Besov spaces,on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.

Taxpayers Fraudulent Behavior Modeling The Use of Datamining in Fiscal Fraud Detecting Moroccan Case

The fraudulent behavior of taxpayers impacts negatively the resources available to finance public services. It creates distortions of competition and inequality, harming honest taxpayers. Such behavior requires the government intervention to bring order and establish a fiscal justice. This study emphasizes the determination of the interactions linking taxpayers with tax authorities. We try to see how fiscal audit can influence taxpayers’ fraudulent behavior. First of all, we present a theoretical study of a model pre established by other authors. We have released some conditions of this model and we have introduced a new parameter reflecting the efficiency of tax control;we found that the efficiency of a fiscal control have an important effect on these interactions. Basing on the fact that the detection of fraudulent taxpayers is the most difficult step in fiscal control, We established a new approach using DATA MINING process in order to improve fiscal control efficiency. We found results that reflect fairly the conduct of taxpayers that we have tested based on actual statistics. The results are reliable.

Necessary and Sufficient Conditions for the Separability and the R-Separability of the Irrotational Stokes Equation and Applications

In the present manuscript, we formulate and prove rigorously, necessary and sufficient conditions for all kinds of separation of variables that a solution of the irrotational Stokes equation may exhibit, in any orthogonal axisymmetric system, namely: simple separation and R-separation. These conditions may serve as a road map for obtaining the corresponding solution space of the irrotational Stokes equation, in any orthogonal axisymmetric coordinate system. Additionally, we investigate how the inversion of the coordinate system, with respect to a sphere, affects the type of separation. Specifically, we prove that if the irrotational Stokes equation separates variables in an axisymmetric coordinate system, then it R-separates variables in the corresponding inverted coordinate system. This is a quite useful outcome since it allows the derivation of solutions for a problem, from the knowledge of the solution of the same problem in the inverted geometry and vice-versa. Furthermore, as an illustration, we derive the eigenfunctions of the irrotational Stokes equation governing the flow past oblate spheroid particles and inverted oblate spheroidal particles.

Portfolio Optimization under Cardinality Constraints: A Comparative Study

The Cardinality Constraint-Based Optimization problem is investigated in this note. In portfolio optimization problem, the cardinality constraint allows one to invest in assets out of a universe of N assets for a prespecified value of K. It is generally agreed that choosing a “small” value of K forces the implementation of diversification in small portfolios. However, the question of how small must be K has remained unanswered. In the present work, using a comparative approach we show computationally that optimal portfolio selection with a relatively small or large number of assets, K, may produce similar results with differentiated reliabilities.

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.

Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric

The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant <img src="Edit_f8bf864e-8dfd-42d9-82fc-76b8c18997cc.png" alt="" />. Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.