Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN

In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.

Monte Carlo Simulations of Doping Properties of a Spin-3/2 Ising Nanotube

The effect of spin-1 impurities doping on the magnetic properties of a spin-3/2 Ising nanotube is investigated using Monte Carlo simulations within the Blume-Emery-Griffiths model in the presence of an external magnetic field. The thermal behaviors of the order parameters and different macroscopic instabilities as well as the hysteretic behavior of the material are examined in great detail as a function of the dopant density. It is found that the impurities concentration affects all the system magnetic properties generating for some specific values, compensation points and multi-cycle hysteresis. Doping conditions where the saturation/remanent magnetization and coercive field of the investigated material can be modified for permanent or soft magnets synthesis purpose are discussed.

Multiverse/Hyperverse Models: (4 + 1)-Dimensional Landscape (Black Saturns, Bousso-Hawking Nucleation, Gogberashvili Multiverses, Schwarzschild-De Sitter Nurseries) and a (3 + 1)-Dimensional Model for Dark Energy

We consider the Hyperverse as a collection of multiverses in a (4 + 1)-dimensional spacetime with gravitational constant G. Multiverses in our model are bouquets of thin shells (with synchronized intrinsic times). If gis the gravitational constant of a shell Sand εits thickness, then G~εg. The physical universe is supposed to be one of those thin shells inside the local bouquet called Local Multiverse. Other remarkable objects of the Hyperverse are supposed to be black holes, black lenses, black rings and (generalized) Black Saturns. In addition, Schwarzschild-de Sitter multiversal nurseries can be hidden inside those Black Saturns, leading to their Bousso-Hawking nucleation. It also suggests that black holes in our physical universe might harbor embedded (2 + 1)-dimensional multiverses. This is compatible with outstanding ideas and results of Bekenstein, Hawking-Vaz and Corda about “black holes as atoms” and the condensation of matter on “apparent horizons”. It allows us to formulate conjecture 12.1 about the origin of the Local Multiverse. As an alternative model, we examine spacetime warping of our universe by external universes. It gives data for the accelerated expansion and the cosmological constant Λ, which are in agreement with observation, thus opening a possibility for verification of the multiverse model.

Photocatalytic Decoloration of Methyl Orange by TiO2 in Slurry

The problem of water depollution is gaining importance, especially as regulatory standards concerning drinking water are increasingly strict. The different industries (textile industries) generate chemically stable pollutants such as methyl orange which make their degradation difficult. It is therefore necessary to find new, more effective techniques for the treatment of these discharges. Among the different solutions proposed to deal with this problem, we find advanced oxidation processes (POAs) which are clean and promising technologies in the field of wastewater depollution. In this regard, heterogeneous photocatalysis was used in an aqueous suspension of titanium oxide (TiO2) using a ultraviolet (UV) lamp as artificial radiation. The objective of this work is to study the influence of some operating parameters such as: the catalyst mass, the initial pollutant concentration, the volume of the solution and the pH of the solution, were examined. The results obtained showed that this photocatalyst made it possible to degrade 99.85% of the initial concentration of methyl orange (10 ppm), after 240 min of irradiation with an optimal mass of 0.50 g of TiO2 for a volume of 200 mL of methyl orange solution at pH = 3.0.

A New Multiobjective Particle Swarm Optimization Using Local Displacement and Local Guides

This paper introduces a novel variant of particle swarm optimization that leverages local displacements through attractors for addressing multiobjective optimization problems. The method incorporates a square root distance mechanism into the external archives to enhance the diversity. We evaluate the performance of the proposed approach on a set of constrained and unconstrained multiobjective test functions, establishing a benchmark for comparison. In order to gauge its effectiveness relative to established techniques, we conduct a comprehensive comparison with well-known approaches such as SMPSO, NSGA2 and SPEA2. The numerical results demonstrate that our method not only achieves efficiency but also exhibits competitiveness when compared to evolutionary algorithms. Particularly noteworthy is its superior performance in terms of convergence and diversification, surpassing the capabilities of its predecessors.

Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation

Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management.

A Hybrid Learning Algorithm for Breast Cancer Diagnosis

In many fields, particularly that of health, the diagnosis of diseases is a very difficult task to carry out. Therefore, early detection of diseases using artificial intelligence tools can be of paramount importance in the medical field. In this study, we proposed an intelligent system capable of performing diagnoses for radiologists. The support system is designed to evaluate mammographic images, thereby classifying normal and abnormal patients. The proposed method (DiagBC for Breast Cancer Diagnosis) combines two (2) intelligent unsupervised learning algorithms (the C-Means clustering algorithm and the Gaussian Mixture Model) for the segmentation of medical images and an algorithm for supervised learning (a modified DenseNet) for the diagnosis of breast images. Ultimately, a prototype of the proposed system was implemented for the Magori Polyclinic in Niamey (Niger) making it possible to diagnose (or classify) breast cancer into two (2) classes: the normal class and the abnormal class.

Isometric Immersions of Lightlike Warped Product Manifolds

In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.

Optimized Adsorption of Small and Medium Molecules by a Biosorbent Based on Hevea Hulls

In the context of the recovery of agricultural waste, many researches have focused on the preparation of adsorbents from natural waste from fruit trees, egg shells, palm waste or sawdust. This work aims to optimize the preparation of a biosorbent from rubber hulls by studying its ability to adsorb small and medium molecules. The influence of parameters such as drying temperature (X1), particle size (X2), stirring time (X3) and sodium hypochloride mass (X4) was studied. The results indicate that the model used for biosorbent optimization on methylene blue and iodine index is significant. In addition, this model has greater adsorption capabilities on small molecules than with large molecules. Statistical analysis of the data shows that temperature is the most influential factor in the adsorption of small molecules. On the other hand, particle size has a significant influence on the adsorption of large molecules. The optimum biosorbent preparation values are 1.0 for drying temperature (X1), −1.0 for biosorbent grain size (X2), 1.0 for stirring time (X3) and 1.0 for sodium hypochloride mass (X4).

Cameroon Climate Predictions Using the SARIMA-LSTM Machine Learning Model: Adjustment of a Climate Model for the Sudano-Sahelian Zone of Cameroon

It is acknowledged today within the scientific community that two types of actions must be considered to limit global warming: mitigation actions by reducing GHG emissions, to contain the rate of global warming, and adaptation actions to adapt societies to Climate Change, to limit losses and damages [1] [2]. As far as adaptation actions are concerned, numerical simulation, due to its results, its costs which require less investment than tests carried out on complex mechanical structures, and its implementation facilities, appears to be a major step in the design and prediction of complex mechanical systems. However, despite the quality of the results obtained, biases and inaccuracies related to the structure of the models do exist. Therefore, there is a need to validate the results of this SARIMA-LSTM-digital learning model adjusted by a matching approach, “calculating-test”, in order to assess the quality of the results and the performance of the model. The methodology consists of exploiting two climatic databases (temperature and precipitation), one of which is in-situ and the other spatial, all derived from grid points. Data from the dot grids are processed and stored in specific formats and, through machine learning approaches, complex mathematical equations are worked out and interconnections within the climate system established. Through this mathematical approach, it is possible to predict the future climate of the Sudano-Sahelian zone of Cameroon and to propose adaptation strategies.

Theoretical and Experimental Quantification of Solar Radiation through a Tracking System

This work deals with the estimation of solar radiation through a solar tracker aimed at evaluating the effect of solar tracking on the solar deposit in Burkina Faso. Using a two-axis solar tracking system, we experimentally measured solar radiation at our Joseph KI-ZERBO University site and compared it with that obtained by a numerical simulation run using Fortran programming software based on a mathematical model by Brichambaut. The results obtained from the mathematical and experimental studies show that, with a solar tracker, on a clear-sky day, solar irradiation is between 800 W·m−2 and 1000 W·m−2 between about 8 a.m. and 4 p.m., i.e. a duration of 8 hours of insolation. Analysis of the numerical and experimental results shows very good quantitative and qualitative agreement, with an average relative error of 18%.

A Branch and Cut Algorithm for Two-Echelon Inventory Routing Problem with End-of-Tour Replenishment Policy

This study presents a two-echelon inventory routing problem (2E-IRP) with an end-of-tour replenishment (ETR) policy whose distribution network consists of a supplier, several distribution centers (DCs) and several retailers on a multi-period planning horizon. A formulation of the problem based on vehicle indices is proposed in the form of a mixed integer linear program (MILP). The mathematical model of the problem is solved using a branch and cut (B&C) algorithm. The results of the tests are compared to the results of a branch and price (B&P) algorithm from the literature on 2E-IRP with a classical distribution policy. The results of the tests show that the B&C algorithm solves 197 out of 200 instances (98.5%). The comparison of the B&C and B&P results shows that 185 best solutions are obtained with the B&C algorithm on 197 instances (93.9%). Overall, the B&C algorithm achieves cost reductions ranging from 0.26% to 41.44% compared to the classic 2E-IRP results solved with the B&P algorithm, with an overall average reduction of 18.08%.

Study of the Influence of Clay in the Degradation of Methylene Blue by Photo-Fenton Process

Industrial effluents from textile, tannery or printing activities often have a significant pollutant load composed of dyes that are difficult to biodegrade. These dyes pose a threat to the environment. To overcome this problem, various processes have been developed to eliminate these dyes in wastewater before their release into nature. Conventional biological or physical processes most often prove to be ineffective and expensive. It is therefore necessary to resort to other processes such as advanced oxidation processes (POA). This work therefore focuses on the study of the influence of clay in the degradation of Methylene Blue by the photo-Fenton process which is one of the advanced oxidation processes (POA), with the source of irradiation, natural light. To do this, two clays from Côte d’Ivoire referenced AB and Aga were the subject of a physicochemical and mineralogical characterization. The results showed that Aga clay is composed of 75.43% quartz, 12.72% kaolinite, 8.75% illite and 3.12% goethite and AB clay consists of 61, 36% kaolinite, 28.6% quartz and 10.10% illite. Under natural light irradiation the optimal amounts of Fenton reagents (iron: 10 mg;H2O2: 0.1 mL) were determined. Finally, the addition of clay to the photo-Fenton process made it possible to improve the degradation of the pollutant (Methylene Blue). Indeed, the yield increased from 92% for the photo-Fenton process to 98.43% with the addition of AB clay and 98.13% for the addition of Aga clay. The results of the degradation kinetics clearly show that the degradation follows the pseudo-second order kinetics with correlation coefficients greater than 0.99.

GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.

ON A BI-HARMONIC EQUATION INVOLVING CRITICAL EXPONENT: EXISTENCE AND MULTIPLICITY RESULTS

In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.

Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials

A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

We consider first order quasilinear hyperbolic systems with vertical characteristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on the equations corresponding to zero eigenvalues. In this paper, we will establish the exact controllability only by means of physically meaningfnl internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.

A CHARACTERIZATION OF SCHECHTER'S ESSENTIAL SPECTRUM BY MEAN OF MEASURE OF NON-STRICT-SINGULARITY AND APPLICATION TO MATRIX OPERATOR

In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.

Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems Via a Sequence of Penalized Equations

We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.