Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets,Aggregation Operators and Basic Uncertainty Information Granule

Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.

Morphological and biochemical characteristics associated with autophagy in gastrointestinal diseases

Autophagy is a cellular catabolic process characterized by the formation of double-membrane autophagosomes.Transmission electron microscopy is the most rigorous method to clearly visualize autophagic engulfment and degradation.A large number of studies have shown that autophagy is closely related to the digestion,secretion,and regeneration of gastrointestinal(GI)cells.However,the role of autophagy in GI diseases remains controversial.This article focuses on the morphological and biochemical characteristics of autophagy in GI diseases,in order to provide new ideas for their diagnosis and treatment.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

Morphological comparison and molecular marker screening of three Skeletonema species found in Changjiang(Yangtze)River Basin

In our recent investigations of diatom diversity,we studied three species,namely,Skeletonema costatum,Skeletonema subsalsum,and Skeletonema potamos.Although they have been found frequently in Changjiang(Yangtze)River Basin,their morphological and molecular identification is difficult in taxonomy.Therefore,to integrate morphological and molecular biological approaches,we compared systematically their morphological characters and performed phylogenetic analysis.Twelve strains of Skeletonema were collected and isolated from Shanghai and Jiangsu,China,and their morphological characteristics were examined by light microscopy(LM)and the scanning electron microscopy(SEM).Based on morphological comparison,we determined that S.potamos is easy to distinguish from the other two species.The heavily silicified areolae,undulated or cleft distal ends of terminal fultoportula processes(TFPPs),absence of basal pores of fultoportula processes(FPPs),the rootlike protrusions of FPPs,and no interlocking connection are the stable characteristics that can be used to identify S.potamos.However,there are only two features that can distinguish S.costatum from S.subsalsum,namely the location of terminal rimoportulae(TRPs)and the distal shape of TFPPs.In addition,we amplified and sequenced nine common genetic markers from the strains,from which 101 sequences were obtained,constructed phylogenetic trees based on the nine genes and evaluated that seven genes can be used to identify S.potamos,and revealed that S.subsalsum is the closest known relative of S.costatum,and only ATP synthetase beta-subunit gene(atp B)is able to distinguish them from each other,which strongly support that it is an effective molecular marker for Skeletonema.This work provided a theoretical basis for the taxonomic study of Skeletonema.

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

Morphological and Molecular Characterizations of Country Bean (Lablab purpureus L.) Genotypes for Drought Tolerance

Country bean, Lablab purpureus (L.) is considered one of the most important leguminous crops, but their cultivation under drought stress condition encounters challenges. In this study, an experiment has been conducted among 30 genotypes under drought condition to explore morphological diversity of qualitative and quantitative, biochemical, molecular analysis. The study identified significant variations in eight traits among the genotypes examined, with phenotypic variance exceeding genotypic variance, indicating both genetic and environmental influences. High heritability and genetic advance were observed in primary, secondary, and tertiary branch lengths, suggesting these traits are likely controlled by additive gene effects, making them effective targets for selection. Principal component analysis identified three components that made a substantial contribution, accounting for approximately 73.06% of the overall quantitative variations. Among the quantitative traits, the highest coefficient of variation (CV%) has been found in number of flowers (55.05%). While number of primary branches, primary branch length, number of secondary branches, secondary branch length, number of tertiary branches, tertiary branch length has individually more than 20% of CV%. The genotypes have been grouped into three clusters based on quantitative traits. Analysis of protein reveals that the genotypes of DS28 and DS29 have higher protein content than other genotypes. Dehydrogenase responsive genotypes have been found on DS28 and DS29 from the molecular analysis. The results suggest that the genotypes DS28 and DS29 could contribute as genetic resource of high protein content and DREB responsive, and the eight quantitative traits of 30 genotypes could be used for further breeding programme.

Random Amplification Polymorphic DNA and Agro-Morphological Traits-Based Fingerprinting for Detection of Genetic Divergence in Indian Black Rice

In this study, 32 black rice genotypes spanning diverse geographies in India were evaluated at both phenotypic and DNA sequence levels to gain insights into their genetic makeup. Significant variations were observed for 14 agro-morphological traits, showing correlations among several yield-related traits.

An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

Morphological and molecular evidence for natural hybridization between Sorbus pohuashanensis and S. discolor (Rosaceae)

In overlapping distribution areas of Sorbus pohuashanensis and S.discolor in North China(Mount Tuoliang,Mount Xiling and Mount Baihua),Sorbus indi-viduals were found with pink fruit,which have never been recorded for the flora of China.Fourteen morphological characters combined with four chloroplast DNA markers and internal transcribed spacer(ITS)were used to analyze the origin of the Sorbus individuals with pink fruits and their relationship to S.pohuashanensis and S.discolor.PCA,SDA and one-way(taxon)ANOVA of morphological characters provided convincing evidence of the hybrid ori-gin of Sorbus individuals with pink fruits based on a novel morphological character and many intermediate characters.Haplotype analysis based on four cpDNA markers showed that either S.pohuashanensis or S.discolor were maternal parents of Sorbus individuals with pink fruits.Incongru-ence of the position of Sorbus individuals with pink fruits between cpDNA and ITS in cluster trees supported by DNA sequence comparative analysis,implying former hybridiza-tion events between S.pohuashanensis and S.discolor.Mul-tiple hybridization events between S.pohuashanensis and S.discolor might have contributed to the generation of Sorbus individuals with pink fruits.This study has provided insights into hybridization between species of the same genus in sympatric areas,which is of great significance for the study of interspecific hybridization.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Molecular phylogeny and taxonomy of Phlomoides(Lamiaceae subfamily Lamioideae)in China:Insights from molecular and morphological data

Phlomoides,with 150-170 species,is the second largest and perhaps most taxonomically challenging genus within the subfamily Lamioideae(Lamiaceae).With about 60 species,China is one of three major biodiversity centers of Phlomoides.Although some Phlomoides species from China have been included in previous molecular phylogenetic studies,a robust and broad phylogeny of this lineage has yet to be completed.Moreover,given the myriad new additions to the genus,the existing infrageneric classification needs to be evaluated and revised.Here,we combine molecular and morphological data to investigate relationships within Phlomoides,with a focus on Chinese species.We observed that plastid DNA sequences can resolve relationships within Phlomoides better than nuclear ribosomal internal and external transcribed spacer regions(nrITS and nrETS).Molecular phylogenetic analyses confirm the monophyly of Phlomoides,but most previously defined infrageneric groups are not monophyletic.In addition,morphological analysis demonstrates the significant taxonomic value of eight characters to the genus.Based on our molecular phylogenetic analyses and morphological data,we establish a novel section Notochaete within Phlomoides,and propose three new combinations as well as three new synonyms.This study presents the first molecular phylogenetic analyses of Phlomoides in which taxa representative of the entire genus are included,and highlights the phylogenetic and taxonomic value of several morphological characters from species of Phlomoides from China.Our study suggests that a taxonomic revision and reclassification for the entire genus is necessary in the future.

Locally purified density operators for noisy quantum circuits

Open quantum system simulations are essential for exploring novel quantum phenomena and evaluating noisy quantum circuits.In this Letter,we investigate whether mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators(LPDOs).We map an LPDO of N qubits to a pure state of size 2×N defined on a ladder and introduce a unified method for managing virtual and Kraus bonds.We numerically simulate noisy random quantum circuits with depths of up to d=40 using fidelity and entanglement entropy as accuracy measures.The LPDO representation is effective in describing mixed states in both the quantum and classical regions;however,it encounters significant challenges at the quantum-classical critical point,restricting its applicability to the quantum region.In contrast,matrix product operators(MPO)successfully characterize the entanglement trend throughout the simulation,while the truncation in MPOs breaks the positivity condition required for a physical density matrix.This work advances our understanding of efficient mixed-state representations in open quantum systems and provides insights into the entanglement structure of noisy quantum circuits.

Appropriate Combination of Crossover Operator and Mutation Operator in Genetic Algorithms for the Travelling Salesman Problem

Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes.It uses a crossover operator to create better offspring chromosomes and thus,converges the population.Also,it uses a mutation operator to explore the unexplored areas by the crossover operator,and thus,diversifies the GA search space.A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution.However,appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem.In this present paper,we aim to study the benchmark traveling salesman problem(TSP).We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances.The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem.The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances.

Glacier area change (1993-2019) and its relationship to debris cover, proglacial lakes, and morphological parameters in the Chandra-Bhaga Basin, Western Himalaya, India

Glacier inventories serve as critical baseline data for understanding the impacts of climate change on glaciers.The present study maps the outlines of glaciers in the Chandra-Bhaga Basin(western Himalaya)for the years 1993,2000,2010,and 2019 using Landsat Thematic Mapper(TM),Enhanced Thematic Mapper(ETM),and Operational Land Imager(OLI)datasets.A total of 251 glaciers,each having an area above 0.5 km^(2),were identified,which include 216 clean-ice and 35 debris-covered glaciers.Area changes are estimated for three periods:1993-2000,2000-2010,and 2010-2019.The total glacierized area was 996±62 km^(2) in 1993,which decreased to 973±70 km^(2) in 2019.The mean rate of glacier area loss was higher in the recent decade(2010-2019),at 0.036 km^(2),compared to previous decades(0.029 km^(2) in 2000-2010 and 0.025 km^(2) in 1993-2000).Supraglacial debris cover changes are also mapped over the period of 1993 and 2019.It is found that the supraglacial debris cover increased by 14.12±2.54 km^(2)(15.2%)during 1993-2019.Extensive field surveys on Chhota Shigri,Panchi II,Patsio,Hamtah,Mulkila,and Yoche Lungpa glaciers were carried out to validate the glacier outlines and supraglacial debris cover estimated using satellite datasets.Controls of various morphological parameters on retreat were also analyzed.It is observed that small,clean ice,south oriented glaciers,and glaciers with proglacial lakes are losing area at faster rates than other glaciers in the basin.