Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures

In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant’s rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fisher information number (FIN), and cumulative past inaccuracy (CPI) are theoretically and numerically studied.

On the Existence of Independent [j,k]-Dominating Sets in the Generalized Corona of Graphs

In 2013 the concept of [j,k]-dominating sets in graphs have been introduced as an extension of [1,k]-dominating sets. Regarding studying [j,k]-dominating sets, the research is also interesting if the additional independence requirement is assumed, because the existence of independent [1,k]-dominating sets is an NP-complete problem in general case. Inspired by this topic, in this paper we study the problem of the existence of independent [j,k]-dominating sets in a special, multi-argument graph product. We give the complete characterization of the generalized corona G∘hn with an independent [j,k]-dominating set, for arbitrary positive integers j and k, which generalize the known result for a corona of two graphs.

Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19

It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.

Sharp Coefficient Bounds for a New Subclass of q-Starlike Functions Associated with q-Analogue of the Hyperbolic Tangent Function

In this study, by making the use of q-analogous of the hyperbolic tangent function and a Sălăgean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk U, especially the first three coefficient bounds, Fekete–Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore, some known corollaries are highlighted based on the unique choices of the involved parameters l and q.

Starlike Functions Associated with Secant Hyperbolic Function

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural formula, certain sharp radii results such as radius of starlikeness and convexity of order α. It also finds a radius for ratios of analytic functions associated with Euler numbers.

Fixed-Point Results for (α-ψ)-Fuzzy Contractive Mappings on Fuzzy Double-Controlled Metric Spaces

We introduce the novel concept of (α-ψ)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of fuzzy double-controlled metric spaces. Furthermore, we provide several examples and an application of our result on the existence of the solution to an integral equation.

Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family

In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.

Geometry and Application in Economics of Fixed Point

Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed point and study their geometry in a partial metric space by introducing some novel contractions and notions of a fixed ellipse-like curve and a common fixed ellipse-like curve which is symmetrical in shape but entirely different than that of an ellipse in a Euclidean space. We look at new hypotheses essential for the collection of nonunique fixed/common fixed points of some mathematical operators to incorporate an ellipse-like curve keeping in view the symmetry in fixed/common fixed points approaches. Appropriate nontrivial examples verify established conclusions. We conclude our work by applying our results to construct the mathematical model and solve the Production–Consumption Equilibrium problem of economics.

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet C5C7(a,b) is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding, non-bonding and antibonding Ruckel molecular orbitals. They are demonstrated to be immediately determinable from their topological characteristics. The effort of chemical and pharmaceutical researchers is significantly increased by the need to conduct numerous chemical experiments to ascertain the chemical characteristics of such a wide variety of novel chemicals. In order to generate novel cellular imaging techniques and to accomplish the regulation of certain cellular mechanisms, scientists have utilized the attributes of nanosheets such as their flexibility and simplicity of modification, out of which carbon nanosheets stand out for their remarkable strength, chemical stability, and electrical conductivity. With efficient tools like polynomials and functions that can forecast compound features, mathematical chemistry has a lot to offer. One such approach is the M-polynomial, a fundamental polynomial that can generate a significant number of degree-based topological indices. Among them, the neighborhood M-polynomial is useful in retrieving neighborhood degree sum-based topological indices that can help in carrying out physical, chemical, and biological experiments. This paper formulates the unique M-polynomial approach which is used to derive and compare a variety of neighborhood degree-based molecular descriptors and the corresponding entropy measures of two variations of pent-heptagonal carbon nanosheets. Furthermore, a regression analysis on these descriptors has also been carried out which can further help in the prediction of various properties of the molecule.

Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers

For the first time, we attempted to define two new sub-classes of bi-univalent functions in the open unit disc of the complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients of functions in these classes were obtained. Moreover, we also determined the Fekete–Szegö inequalities for function in these and several related corollaries.

A subgradient-based neurodynamic algorithm to constrained nonsmooth nonconvex interval-valued optimization

In this paper, a subgradient-based neurodynamic algorithm is presented to solve the nonsmooth nonconvex interval-valued optimization problem with both partial order and linear equality constraints, where the interval-valued objective function is nonconvex, and interval-valued partial order constraint functions are convex. The designed neurodynamic system is constructed by a differential inclusion with upper semicontinuous right-hand side, whose calculation load is reduced by relieving penalty parameters estimation and complex matrix inversion. Based on nonsmooth analysis and the extension theorem of the solution of differential inclusion, it is obtained that the global existence and boundedness of state solution of neurodynamic system, as well as the asymptotic convergence of state solution to the feasible region and the set of LU-critical points of interval-valued nonconvex optimization problem. Several numerical experiments and the applications to emergency supplies distribution and nondeterministic fractional continuous static games are solved to illustrate the applicability of the proposed neurodynamic algorithm.

Structure Fault Tolerance of Bubble-Sort Star Graphs

As two significant performance indicators, structure connectivity and substructure connectivity have been widely studied, and they are used to judge a network’s fault tolerance properties from the perspective of the structure becoming faulty. An n-dimensional bubble-sort star graph BSn is a popular interconnection network with many good properties. We find the upper bounds of κ(BSn;K1,3) and κs(BSn;K1,3) in this paper. Furthermore, we establish κ(BSn;H) and κs(BSn;H) of BSn, where H∈{K1,K1,1,K1,2}.

Viral dynamics with immune responses: effects of distributed delays and Filippov antiretroviral therapy

In this paper, we propose a general viral infection model to incorporate two infection modes (virus-to-cell mode and cell-to-cell mode), the CTL immune response, and the distributed intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We investigate the existence, the uniqueness, and the global stability of three equilibria: infection-free equilibrium [Formula: see text], immune-inactivated equilibrium [Formula: see text] and immune-activated equilibrium [Formula: see text], respectively. We prove that the viral dynamics are determined by two threshold parameters: the basic reproduction number for infection [Formula: see text] and the basic reproduction number for immune response [Formula: see text]. We also numerically explore the viral dynamics beyond stability. We use bifurcation diagrams to show that increasing the delay in CTL immune cell recruitment can induce a switch in viral load from a stable constant level to sustained oscillations, and then back to a stable equilibrium. We also compare the contributions of the two infection modes to the total infection level and identify the key parameters that would affect the percentages of virus-to-cell infection and cell-to-cell infection. Finally, we explore how Filippov control can be applied in antiretroviral therapy to reduce the viral loads.

On General Class of Z-Contractions with Applications to Spring Mass Problem

One of the latest techniques in metric fixed point theory is the interpolation approach. This notion has so far been examined using standard functional equations. A hybrid form of this concept is yet to be uncovered by observing the available literature. With this background information, and based on the symmetry and rectangular properties of generalized metric spaces, this paper introduces a novel and unified hybrid concept under the name interpolative Y-Hardy–Rogers–Suzuki-type Z-contraction and establishes sufficient conditions for the existence of fixed points for such contractions. As an application, one of the obtained results was employed to examine new criteria for the existence of a solution to a boundary valued problem arising in the oscillation of a spring. The ideas proposed herein advance some recently announced important results in the corresponding literature. A comparative example was constructed to justify the abstractions and pre-eminence of our obtained results.

The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function

In this paper, we give sharp bounds of the Hankel determinant H 2 ( 3 ) ( f ) for the coefficients of functions in the class of starlike functions related to a domain that is like three leaves. We also give sharp bounds for the Hankel determinants H 3 ( 1 ) ( f ) and H 2 ( 3 ) ( f ) for the coefficients of functions in the class of convex functions related to the three-leaf-like domain.

Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network.

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

A multiple-scale perturbation analysis is presented to analyse the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid flowing between two parallel plates filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation in its own plane moving with a constant velocity, and the periodic pressure gradient. Mei’s homogenization technique is used to find the concentration distribution up to third order, complemented with the dispersion coefficients for four different situations, namely, steady, pulsatile, oscillatory and the combined effect of all these. We observe that when the flow is under the combined effect of wall oscillation and pressure pulsation, then the respective frequency (Womersley number) and amplitude parameters oppose each other while influencing the dispersion coefficient. Our analysis reveals that for a fixed amplitude of oscillation and pulsation, the frequency of pressure pulsation has a stronger effect on the dispersion coefficient compared with the wall oscillation. On the other hand, when the Womersley number is kept fixed, amplitude of the wall oscillation dominates the pressure pulsation. This behaviour is more prominent for higher values of the Darcy number. The transverse concentration distribution and its dependency on porous medium parameters are also discussed in detail.

Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling "shock and kill" strategy

Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy ("shock and kill") to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of "shock and kill" strategy with VIP. We derive the basic reproduction number R₀ of the model and show that R₀ completely determines the dynamics of the model: if R₀<1, the disease-free equilibrium is globally asymptotically stable; if R₀>1, the system is uniformly persistent. Numerical simulations suggest that the "shock and kill" strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.

Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds

Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e., it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. The curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for a dimension of at least seven) as a conformal invariant to obtain these properties and to construct an explicit example in relation to the obtained results.

Neighbourhood Sum Degree-Based Indices and Entropy Measures for Certain Family of Graphene Molecules

A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties, chemical reactivity and biological activity. Several kinds of TIs have been defined and studied for different molecular structures. Graphene is the thinnest material known to man and is also extremely strong while being a good conductor of heat and electricity. With such unique features, graphene and its derivatives have found commercial uses and have also fascinated theoretical chemists. In this article, the neighbourhood sum degree-based M-polynomial and entropy measures have been computed for graphene, graphyne and graphdiyne structures. The proper analytical expressions for these indices are derived. The obtained results will enable theoretical chemists to study these exciting structures further from a structural perspective.

The extreme vertices of the power graph of a group

For a fixed finite group G, the power graph of G was defined to be the simple graph Γ ( G ) whose vertex set V ( Γ ( G ) ) = G , and edge set E ( Γ ( G ) ) = { x y :  either  x = y n  or  y = x n  for some integer  n } . In this paper the extreme vertices of the power graph of abelian groups, dihedral groups and dicyclic groups have been characterized.

The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs

Topological invariants are numerical parameters of graphs or hypergraphs that indicate its topology and are known as graph or hypergraph invariants. In this paper, topological indices of hypergraphs such as Wiener index, degree distance index and Gutman index are considered. A g-composite hypergraphs is a hypergraphs that is obtained by the union of g hypergraphs with every hypergraph has exactly one vertex in common. In this article, results of above said indices for g-composite hypergraphs, where g ≥ 2 , are calculated. Further these results are used to find the Wiener index, degree distance index and Gutman index of sunflower hypergraphs and linear uniform hyper-paths.

Solving a Boundary Value Problem via Fixed-Point Theorem on ®-Metric Space

In this paper, we prove the fixed-point theorem for rational contractive mapping on ®-metric space. Additionally, an Euclidean metric space with a binary relation example and an application to the first-order boundary value problem are given. Moreover, the obtained results generalize and extend some of the well-known results in the literature.

On ve-Degree Irregularity Index of Graphs and Its Applications as Molecular Descriptor

Most of the molecular graphs in the area of mathematical chemistry are irregular. Therefore, irregularity measure is a crucial parameter in chemical graph theory. One such measure that has recently been proposed is the ve-degree irregularity index (irrve). Quantitative structure property relationship (QSPR) analysis explores the capability of an index to model numerous properties of molecules. We investigate the usefulness of the irrve index in predicting different physico-chemical properties by carrying out QSPR analysis. It is established that the irrve index is efficient to explain the acentric factor and boiling point of molecules with powerful accuracy. An upper bound of irrve for the class of all trees is computed with identifying extremal graphs. We noticed that the result is not correct. In this report, we provide a counter example to justify our argument and determine the correct outcome.

Mapping Properties of Associate Laguerre Polynomials in Leminiscate, Exponential and Nephroid Domain

The function PL(z)=1+z maps the unit disc D={z∈C:|z|<1} to a leminscate which is symmetric about the x-axis. The conditions on the parameters α and n, for which the associated Laguerre polynomial (ALP) Lnα maps unit disc into the leminscate domain, are deduced in this article. We also establish the condition under which a function involving Lnα maps D to a domain subordinated by ϕNe(z)=1−z+z3/3, ϕe(z)=ez, and ϕA(z)=1+Az, A∈(0,1]. We provide several graphical presentations for a clear view of some of the obtained results. The possibilities for the improvements of the results are also highlighted.

Controlling Problem within a Class of Two-Level Positive Maps

This paper aims to define the set of unital positive maps on M2(C) by means of quantum Lotka–Volterra operators which are quantum analogues of the classical Lotka–Volterra operators. Furthermore, a quantum control problem within the class of quantum Lotka–Volterra operators are studied. The proposed approach will lead to the understanding of the behavior of the classical Lotka–Volterra systems within a quantum framework.

Online and Connected Online Ramsey Numbers of a Matching versus a Path

The (G1,G2)-online Ramsey game is a two-player turn-based game between a builder and a painter. Starting from an empty graph with infinite vertices, the builder adds a new edge in each round, and the painter colors it red or blue. The builder aims to force either a red copy of G1 or a blue copy of G2 in as few rounds as possible, while the painter’s aim is the opposite. The online Ramsey number r˜(G1,G2) is the minimum number of edges that the builder needs to win the (G1,G2)-online Ramsey game, regardless of the painter’s strategy. Furthermore, we initiate the study of connected online Ramsey game, which is identical to the usual one, except that at any time the graph induced by all edges should be connected. In this paper, we show a general bound of the online Ramsey number of a matching versus a path and determine its exact value when the path has an order of three or four. For the connected version, we obtain all connected online Ramsey numbers of a matching versus a path.

Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions

In this paper, we define certain families SE*(ϑ) and CE(ϑ) of holomorphic and bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö type inequalities for functions in these families.

Correlation between the Quality of Talent Training and Regional Economic Development Based on Multivariate Statistical Analysis Model

Entering the era of knowledge economy, the economic value of talent education is more and more emphasized, and it contributes more and more to the local economy and injects new vitality into local economic development. However, there are still some difficulties in the synergistic development of talent education and local economy, such as the low degree of integration of "industry, profession, and employment" and the lack of synergy between schools and enterprises, which affects the high-quality development of talent education and restricts the long-term development of regional economy. This paper incorporates machine learning algorithms to construct a multivariate statistics analysis model based on the correlation analysis model between talent training quality and regional economic development. Based on the multi-variate statistical analysis theory and method, the qualitative analysis and quantitative analysis are closely combined to scientifically pick up the main indicators affecting the comprehensive quality of talent cultivation and overcome the drawbacks of artificial subjective assignment of values. Through the judicious selection of evaluation indexes, a scientific and fair evaluation model is established, and the targets of talent cultivation are combined with regional economic development, in a comprehensive analysis, which provides a new means for the development of the regional economy.

Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays

This paper investigates the bifurcation issue of fractional-order four-neuron recurrent neural network with multiple delays. First, the stability and Hopf bifurcation of the system are studied by analyzing the associated characteristic equations. It is shown that the dynamics of delayed fractional-order neural networks not only depend heavily on the communication delay but also significantly affects the applications with different delays. Second, we numerically demonstrate the effect of the order on the Hopf bifurcation. Two numerical examples illustrate the validity of the theoretical results at the end.

On Topological Properties for Benzenoid Planar Octahedron Networks

Chemical descriptors are numeric numbers that capture the whole graph structure and comprise a basic chemical structure. As a topological descriptor, it correlates with certain physical aspects in addition to its chemical representation of underlying chemical substances. In the modelling and design of any chemical network, the graph is important. A number of chemical indices have been developed in theoretical chemistry, including the Wiener index, the Randić index, and many others. In this paper, we look at the benzenoid networks and calculate the exact topological indices based on the degrees of the end vertices.

Qualitative Analysis of the Transmission Dynamics of Dengue with the Effect of Memory, Reinfection, and Vaccination

Dengue fever has a huge impact on people’s physical, social, and economic lives in low-income locations worldwide. Researchers use epidemic models to better understand the transmission patterns of dengue fever in order to recommend effective preventative measures and give data for vaccine and treatment development. We use fractional calculus to organise the transmission phenomena of dengue fever, including immunisation, reinfection, therapy, and asymptotic carriers. In addition, we focused our study on the dynamical behavior and qualitative approach of dengue infection. The existence and uniqueness of the solution of the suggested dengue dynamics are inspected through the fixed point theorems of Schaefer and Banach. The Ulam-Hyers stability of the suggested dengue model is established. To illustrate the contribution of the input factors on the system of dengue infection, the solution paths are studied using the Laplace Adomian decomposition approach. Furthermore, numerical simulations are used to show the effects of fractional-order, immunity loss, vaccination, asymptotic fraction, biting rate, and therapy. We have established that asymptomatic carriers, bite rates, and immunity loss rates are all important factors that might make controlling more challenging. The intensity of dengue fever may be controlled by reducing mosquito bite rates, whereas the asymptotic fraction is risky and can transmit the illness to noninfected regions. Vaccination, fractional order, index of memory, and medication can be employed as proper control parameters.

Hosoya Polynomials of Power Graphs of Certain Finite Groups

Assume that G is a finite group. The power graph P(G) of G is a graph in which G is its node set, where two different elements are connected by an edge whenever one of them is a power of the other. A topological index is a number generated from a molecular structure that indicates important structural properties of the proposed molecule. Indeed, it is a numerical quantity connected with the chemical composition that is used to correlate chemical structures with various physical characteristics, chemical reactivity, and biological activity. This information is important for identifying well-known chemical descriptors based on distance dependence. In this paper, we study Hosoya properties, such as the Hosoya polynomial and the reciprocal status Hosoya polynomial of power graphs of various finite cyclic and non-cyclic groups of order pq and pqr, where p,q and r(p≥q≥r) are prime numbers.

Certain Topological Indices of Non-Commuting Graphs for Finite Non-Abelian Groups

A topological index is a number derived from a molecular structure (i.e., a graph) that represents the fundamental structural characteristics of a suggested molecule. Various topological indices, including the atom-bond connectivity index, the geometric–arithmetic index, and the Randić index, can be utilized to determine various characteristics, such as physicochemical activity, chemical activity, and thermodynamic properties. Meanwhile, the non-commuting graph ΓG of a finite group G is a graph where non-central elements of G are its vertex set, while two different elements are edge connected when they do not commute in G. In this article, we investigate several topological properties of non-commuting graphs of finite groups, such as the Harary index, the harmonic index, the Randić index, reciprocal Wiener index, atomic-bond connectivity index, and the geometric–arithmetic index. In addition, we analyze the Hosoya characteristics, such as the Hosoya polynomial and the reciprocal status Hosoya polynomial of the non-commuting graphs over finite subgroups of SL(2,C). We then calculate the Hosoya index for non-commuting graphs of binary dihedral groups.

Optimization of Residential Landscape Design and Supply Chain System Using Intelligent Fuzzy Cognitive Map and Genetic Algorithm

This work intends to optimize residential landscape design and Supply Chain (SC) network systems. First, Fuzzy Cognitive Map (FCM) intelligent assistance and genetic algorithm (GA) are used to study residential landscape design and its integration with SC deeply. Weight matrix interactions are employed to implement iterative inference for FCM. The functions are transformed to unify variables of different scopes. Subsequently, a weighting method is proposed to deal with the disadvantage of the simple average method being too general. In addition, the Hebbian learning algorithm is used to adjust the state nodes and the connection weights. Finally, according to the fitness function of the GA and logistic regression (LR) model, residential landscape design and SC are combined. The simulation experiment results show that the causal relationship analysis between SC networks under fuzzy cognition shows that the state errors of each specific situation are 0.21, 0.16, and 0.24, respectively. The total average error is 0.21 in the case of multiple iterations. The average error of the result vector under fuzzy cognition and the operation of the actual result is 0.20, 0.15, and 0.24, respectively, and the error value is much reduced. The simulation accuracy of the GA-LR method for residential landscape design is improved from 77% to 84.7%. The “kappa coefficient” is also improved to 82.3%. The conclusion shows that the weight matrix is used to analyze the high-quality performance of landscape design according to the specific situation of SC. For each specific case, FCM is effective in reducing errors over multiple iterations. Under the GA-LR method, fewer geographic location types and larger accuracy deviations can improve the simulation accuracy.

Dynamic Hardy–Copson-Type Inequalities via (γ,a)-Nabla-Conformable Derivatives on Time Scales

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales. When γ=1, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous and discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.