Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

FINITE RANGE SET WITH TRUNCATED MULTIPLICITY FOR MEROMORPHIC FUNCTIONS ON SOME COMPLEX DISC

In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.

A Hybrid Classification and Identification of Pneumonia Using African Buffalo Optimization and CNN from Chest X-Ray Images

An illness known as pneumonia causes inflammation in the lungs.Since there is so much information available fromvarious X-ray images,diagnosing pneumonia has typically proven challenging.To improve image quality and speed up the diagnosis of pneumonia,numerous approaches have been devised.To date,several methods have been employed to identify pneumonia.The Convolutional Neural Network(CNN)has achieved outstanding success in identifying and diagnosing diseases in the fields of medicine and radiology.However,these methods are complex,inefficient,and imprecise to analyze a big number of datasets.In this paper,a new hybrid method for the automatic classification and identification of Pneumonia from chest X-ray images is proposed.The proposed method(ABOCNN)utilized theAfrican BuffaloOptimization(ABO)algorithmto enhanceCNNperformance and accuracy.The Weinmed filter is employed for pre-processing to eliminate unwanted noises from chest X-ray images,followed by feature extraction using the Grey Level Co-Occurrence Matrix(GLCM)approach.Relevant features are then selected from the dataset using the ABO algorithm,and ultimately,high-performance deep learning using the CNN approach is introduced for the classification and identification of Pneumonia.Experimental results on various datasets showed that,when contrasted to other approaches,the ABO-CNN outperforms them all for the classification tasks.The proposed method exhibits superior values like 96.95%,88%,86%,and 86%for accuracy,precision,recall,and F1-score,respectively.

SwinVid:Enhancing Video Object Detection Using Swin Transformer

What causes object detection in video to be less accurate than it is in still images?Because some video frames have degraded in appearance from fast movement,out-of-focus camera shots,and changes in posture.These reasons have made video object detection(VID)a growing area of research in recent years.Video object detection can be used for various healthcare applications,such as detecting and tracking tumors in medical imaging,monitoring the movement of patients in hospitals and long-term care facilities,and analyzing videos of surgeries to improve technique and training.Additionally,it can be used in telemedicine to help diagnose and monitor patients remotely.Existing VID techniques are based on recurrent neural networks or optical flow for feature aggregation to produce reliable features which can be used for detection.Some of those methods aggregate features on the full-sequence level or from nearby frames.To create feature maps,existing VID techniques frequently use Convolutional Neural Networks(CNNs)as the backbone network.On the other hand,Vision Transformers have outperformed CNNs in various vision tasks,including object detection in still images and image classification.We propose in this research to use Swin-Transformer,a state-of-the-art Vision Transformer,as an alternative to CNN-based backbone networks for object detection in videos.The proposed architecture enhances the accuracy of existing VID methods.The ImageNet VID and EPIC KITCHENS datasets are used to evaluate the suggested methodology.We have demonstrated that our proposed method is efficient by achieving 84.3%mean average precision(mAP)on ImageNet VID using less memory in comparison to other leading VID techniques.The source code is available on the website https://github.com/amaharek/SwinVid.

紧黎曼曲面上锥度量的高斯博内公式

We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue integrable with respect to the area form of the metric.We also construct explicitly some conical metrics whose curvature is not integrable.

Effect of Sweptback Angle of a Delta Wing on Surface Pressure Distribution at Supersonic Mach Numbers

The purpose of this work is to shed light on the effect of the pivot position on the surface pressure distribution over a 3D wing in different flight conditions.The study is intended to support the design and development of aerospace vehicles where stability analysis,performance optimization,and aircraft design are of primary importance.The following parameters are considered:Mach numbers(M)of 1.3,1.8,2.3,2.8,3.3,and 3.8,angle of incidence(θ)in the range from 5°to 25°,pivot position from h=0.2 to 1.The results of the CFD numerical simulations match available analytical data,thereby providing evidence for the reliability of the used approach.The findings provide valuable insights into the relationship between the surface pressure distribution,the Mach number and the angle of incidence.

GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA

In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Feynman Path Integral Using Operator Integration in Banach Space

Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.

Pyroelectric Plate with Magnetoelectric Effect

In dynamic problems the electric and magnetic fields are inseparable. At the same time, a multitude of electrostatic and magnetostatic effects permit mutually independent description. This separation appears to be possible and thermodynamically consistent when the bulk energy density depends only on the polarization density or, alternatively, on the magnetization density. However, when the bulk energy density depends simultaneously on the both densities, then, the electrostatic and magnetostatic effects should be studied together. There appear interesting cross-effects;among those are the change of the internal electrostatic field inside a specimen under the influence of the external magnetic fields, and vice versa. Below, in the framework of thermodynamic approach the boundary value problem for magnetoelectric plate is formulated and analyzed. The exact solution is established for the isotropic pyroelectric plate.

Existence of Solutions of a Convolution Integral Equation

In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball Br belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.

Pre-service Early Childhood Teachers’ Attitude Towards Mathematics: A Jamaican Inquiry

The purpose of the study was to evaluate Jamaican early childhood pre-service teachers’attitudes towards mathematics.The study is designed according to the quantitative survey model in the descriptive type.In this study,a modified version of the Fennema-Sherman mathematics attitude scale was used to measure the mathematics attitude of 144 early childhood pre-service teachers in four different categories of the attitude scale(mathematics usefulness,confidence in learning mathematics,mathematics anxiety,and mathematics motivation).The data were collected from participants in the five teachers’colleges that offer the early childhood education program in Jamaica.The findings revealed that Jamaican early childhood pre-service teachers generally have a more positive attitude towards mathematics.A comparison among the different year groups revealed that a significantly greater percentage of the Year two group of participants possessed a more positive mathematics attitude than the other year groups.A significantly higher percentage of the Year three group indicated that they do not want to teach the subject in the future.The findings have implications for the teaching and learning of mathematics in the early childhood education program in Jamaica and,by extension,the teaching and learning of mathematics at the early childhood level of the education system.

Mathematics Knowledge of Proof in Geometry： Pre-Service Teachers＇ Perspectives

This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.

Filter and Embedded Feature Selection Methods to Meet Big Data Visualization Challenges

This study focuses on meeting the challenges of big data visualization by using of data reduction methods based the feature selection methods.To reduce the volume of big data and minimize model training time(Tt)while maintaining data quality.We contributed to meeting the challenges of big data visualization using the embedded method based“Select from model(SFM)”method by using“Random forest Importance algorithm(RFI)”and comparing it with the filter method by using“Select percentile(SP)”method based chi square“Chi2”tool for selecting the most important features,which are then fed into a classification process using the logistic regression(LR)algorithm and the k-nearest neighbor(KNN)algorithm.Thus,the classification accuracy(AC)performance of LRis also compared to theKNN approach in python on eight data sets to see which method produces the best rating when feature selection methods are applied.Consequently,the study concluded that the feature selection methods have a significant impact on the analysis and visualization of the data after removing the repetitive data and the data that do not affect the goal.After making several comparisons,the study suggests(SFMLR)using SFM based on RFI algorithm for feature selection,with LR algorithm for data classify.The proposal proved its efficacy by comparing its results with recent literature.

A Novel Meta-Heuristic Optimization Algorithm in White Blood Cells Classification

Some human diseases are recognized through of each type of White Blood Cell(WBC)count,so detecting and classifying each type is important for human healthcare.The main aim of this paper is to propose a computer-aided WBCs utility analysis tool designed,developed,and evaluated to classify WBCs into five types namely neutrophils,eosinophils,lymphocytes,monocytes,and basophils.Using a computer-artificial model reduces resource and time consumption.Various pre-trained deep learning models have been used to extract features,including AlexNet,Visual Geometry Group(VGG),Residual Network(ResNet),which belong to different taxonomy types of deep learning architectures.Also,Binary Border Collie Optimization(BBCO)is introduced as an updated version of Border Collie Optimization(BCO)for feature reduction based on maximizing classification accuracy.The proposed computer aid diagnosis tool merges transfer deep learning ResNet101,BBCO feature reduction,and Support Vector Machine(SVM)classifier to forma hybridmodelResNet101-BBCO-SVM an accurate and fast model for classifying WBCs.As a result,the ResNet101-BBCO-SVM scores the best accuracy at 99.21%,compared to recent studies in the benchmark.The model showed that the addition of the BBCO algorithm increased the detection accuracy,and at the same time,decreased the classification time consumption.The effectiveness of the ResNet101-BBCO-SVM model has been demonstrated and beaten in reasonable ratios in recent literary studies and end-to-end transfer learning of pre-trained models.

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Optical dromions for complex Ginzburg Landau model with nonlinear media

This manuscript studies the optical dromions with beta derivative(BD)applied to the Complex Ginzburg Landau equation(CGLE)with Kerr law,parabolic law,cubic quintic septic law and quadratic cubic law.We obtain bright dromians by using the sine-cosine method(SCM).We will also obtain domain walls with the assistance of Bernoulli equation approach(BEA).Constraint conditions are also listed.

Optimization of the Placement and Size of Photovoltaic Source

This paper presents a new optimization study of the placement and size of a photovoltaic source(PVS)in a distribution grid,based on annual records of meteorological parameters(irradiance,temperature).Based on the recorded data,the production output as well as the daily average power(24-h vector)of the PVS is extracted over the year.When a power vector is available,it can be used as an input when searching for the optimal size of the PVS.This allows to take into account the constraint of the variation of the power generated by this source considering the variation of the power consumed by the electrical loads during the whole day.A multi-objective fitness function has been considered.The latter minimizes the active losses and maximizes the voltage stability index during the day,while considering the constraints of the system,that is,the security,technical,geographical,and meteorological constraints.This problem was solved using the Non-dominated Sorting Genetic Algorithm NSGA-II optimization technique under MATLAB 2021.It was applied to the distribution network of Ghardaïa of 59 nodes.