Chain graphs are 2K2, C3, C5-free graphs. Balaban index and sum-Balaban index are two important topological indices. In this paper, we concentrate on the subclass of bicyclic connected chain graphs, identifying the extremal graphs that exhibit the minimum or maximum Balaban index and sum-Balaban index within this class. Moreover, we provide a systematic ordering of all bicyclic connected chain graphs according to the magnitude of their Balaban index and sum-Balaban index.
Currently, researchers worldwide are conducting theoretical and experimental studies to understand the significance of nanofluids in heat transfer processes. These fluids are created by dispersing nanoparticles in a base fluid. Experiments have demonstrated that nanofluids exhibit superior and more attractive thermal properties compared to conventional fluids. In this current study, we discuss about the heat transfer enhancement of unsteady incompressible laminar couple stress nanofluid flow with Magnetohydrodynamics (MHD) between parallel plates. Prescribed temperature boundary conditions of the surface are employed on the porous surface and it is assumed that the temperature changes periodically over time on the plates. The flow is provoked by periodic suction as well as injection at the plates. With the aid of similarity variables, the system of governing transport equations is transformed into a nonlinear system of ordinary differential equations which is subsequently solved using shooting method along with Runge-Kutta fourth order scheme. The obtained results are shown graphically and explained for the non-dimensional velocity, heat profiles with diverse fluid parameters as well as geometric parameters. Nusselt number is calculated at the lower and upper plates. It is found that temperature component of the fluid is augmenting with suction-injection parameter, whereas it is decreasing in nature with respect to Reynolds number.
In this paper, we study a predator-prey model with additional food for predator. By using white noise to perturb the natural growth rates and introduce a jump process, we model the corresponding stochastic differential equations. The effect of fear and prey refuge on population dynamics is also considered. First, we use Itô’s formula to prove the existence and uniqueness of a global positive solution and its boundedness. Next, sufficient conditions for the extinction and persistence of both species have been given. Then the stochastic permanence of our system is investigated under some conditions. Our main results demonstrate that sufficiently large white noise could drive both species to extinction. However, Lévy noise enhances the survival of both prey and predator species. Our analytical derivations are justified through numerical simulations which show the reliability of the model from the ecological point of view. In addition, we have investigated the impact of fear effect, prey refuge and the additional food biomass on this model by numerical simulation.
With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the independent one, using balance equations in which the counts (aggregation-reduction) are of the multiplicative type. We enter the context of the “differential” equations typical of non-Newtonian calculations, such as geometric calculus, bi-geometric calculus, or the lesser-known logarithmic calculus, when we take the step to the limit. In these new possibilities of dynamic laws, we highlight the interpretive aspects. A particular case is to review the equivalents of the logistic equation of the standard calculation in the new accounting calculations, where we make graphical and semantic comparisons. Finally, the construction of a geometric type equation is exemplified, with applications inherent to the financial mathematics.
HIV infection continues to pose a significant global health challenge, with sub-Saharan Africa bearing a disproportionate burden. The replication cycle of HIV is fundamentally driven by intricate molecular interactions. This study investigates the competitive biochemical interplay between reverse transcriptase (RT) and integrase (IN) enzymes, employing a fractional calculus framework to model their mutual inhibitory effects. Through the application of fixed-point theory and Picard stability analysis, the existence, uniqueness, and stability of the fractional-order system are rigorously established. The role of RT-IN enzymatic competition in influencing HIV replication dynamics is elucidated through global sensitivity analysis using Latin Hypercube Sampling. Furthermore, the model incorporates memory-dependent characteristics by examining three distinct fractional operators, namely, the Caputo, Caputo-Fabrizio, and Atangana-Baleanu operators in the Caputo sense, thereby elucidating their respective influences on system behavior. The Atangana-Baleanu operator, in particular, demonstrates an enhanced capacity to capture the complex, synergistic processes underpinning HIV progression. This research provides a critical nexus between molecular virology and applied mathematics, offering foundational insights for the advancement of more precise and targeted therapeutic strategies against HIV.
An efficient scheme is applied to generate a nonisospectral Botie-Pempinelli-Tu (BPT) integrable hierarchy under the case where λ_t = ∑_j=0^n k_j(t)λ^-j . Based on an expanding higher-dimensional Lie algebra, we obtain a nonisospectral BPT integrable coupling hieararchy. It follws that some new nonisospectral nonlinear systems are obtained by reducing these two non-isospectral BPT hierarchies. Actually, these nonisospectral integrable models that we obtained can enrich the existing integrable models and possibly describe new nonlinear phenomena.
In this paper, a class of discontinuous Cohen-Grossberg neural networks with time-varying delays is considered. Firstly, under the extended Filippov differential inclusions framework, the problem of periodic solutions of the considered neural networks with more relaxed conditions imposed on the amplification functions is analyzed by using set-valued mapping and Kakutani’s fixed point theorem, which has rarely been used to study such problem. Secondly, the fixed-time synchronization of the error system of the considered neural networks is also investigated by designing a novel control strategy, which can improve not only the previous ones with sign function greatly, but also can reduce the chattering phenomenon. Finally, two numerical examples are presented to further illustrate the validity of the obtained results.
In Minkowski 3-space, we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature, geodesic or asymptotic curve. Moreover, the conditions are examined for the ruled surface to be developable. And we support our conclusion with some examples.
In this study, we introduce the sequence space ℓμ(p, Δm) with a fractional order μ. Furthermore, we give some topological properties of this space. Also we introduce α–, β–, and γ–duals of ℓμ(p, Δm) and its some matrix mappings.
This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions (namely, the Dirichlet, Neumann, and Robin boundary conditions). Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained. The test function technique is performed in the proofs. It is worth observing that our results in Theorem 1.1 in this article contain the results in [6] as a special case when θ = 0. To the best of our knowledge, the results in Theorems 1.1–1.2 are new.
A tournament is an orientation of the edges of a complete graph. An arc in a digraph D is pancyclic if it is contained in a cycle of length k for every 3 ≤ k ≤ ∣V(D)∣. An arc uv in a digraph D is k-anticyclic if there is a path from u to v of length k − 1 in D. If for every 3 ≤ k ≤ ∣V(D)∣, an arc uv is k-anticyclic, then we say that uv is anti-pancyclic in D. It has been proved in Discrete Appl. Math. 79 (1997) 127–135 that every arc of a 3-strong and arc-3-cyclic tournament T is k-anticyclic for each k ≥ 4, unless T is isomorphic to two tournaments, each of which has exactly 8 vertices. In J. Combin. Inform. System Sci. 19 (1994) 207–214, Moon showed that every strong tournament contains at least three pancyclic arcs and characterized the tournaments that attain this lower bound. In this paper we investigate the number of antipancyclic arcs in strong tournaments and show that every strong tournament with order n ≥ 6 contains at least four anti-pancyclic arcs unless it is isomorphic to five tournaments, each of which has exactly 6 vertices. Consequently, every strong tournament with order n ≥ 7 contains at least four anti-pancyclic arcs.
A model for dynamic frictionless contact between a viscoelastic body and foundation is considered. The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition. We obtain the well-posedness using nonlinear semigroup theory arguments. Moreover, the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
This paper deals with homogeneous Dirichlet boundary value problem to a class of porous medium equations with viscoelastic term ∂ u∂ t - Δu^m + ∫_0^t g(t - s)Δu^m(x,s)ds = u^p, x ∈Ω , t ≥ 0, where p > m (m > 0). We prove that the weak solutions of the above problem blow up in finite time when the initial energy is positive and the function g satisfies suitable conditions. Our result generalizes that of S.A. Messaoudi in [1].
This paper surveys the literature for the optimization problems in both discrete and continuous time models in macroeconomics, and provides an overview over some related computational methods to solve the models linearly and nonlinearly, and to compute the transition dynamics and the impulse response functions. Also, the introduction of the financial sectors, the continuous time analysis, and the advanced mathematical tools into the general equilibrium framework expands greatly the scope of the interdisciplinary research to mathematics, statistics and econometrics, and creates further space for exploration and collaboration. Finally, some future research issues related to this topic are highlighted.
The manuscript’s authors examine some Milne-type inequalities for various function classes. Firstly, some Milne-type inequalities are established for differentiable convex functions by using Riemann-Liouville integrals. Secondly, we provide some fractional Milne-type inequalities for bounded functions by fractional integrals. Afterwards, we offer several Milne-type inequalities for Lipschitzian functions. Likewise, we offers Milne-type inequalities by fractional integrals of bounded variation. Finally, we demonstrate the correctness of our results by using special cases and examples of the obtained theorems.
Toric patch is a kind of rational multisided patch, which is associated with a finite integer lattice points set A . A set of weights is defined which depend on a parameter according to regular decomposition of A . When all weights of the patch tend to infinity, we obtain the limiting form of toric patch which is called its regular control surface. The different weights may induce the different regular control surfaces of the same toric patch. It prompts us to consider that how many regular control surfaces of a toric patch. In this paper, we study the regular decompositions of A by using integer programming method firstly, and then provide the relationship between all regular decompositions of A and corresponding state polytope. Moreover, we present that the number of regular control surfaces of a toric patch associated with A is equal to the number of regular decompositions of A . An algorithm to calculate the number of regular control surfaces of toric patch is provided. The algorithm also presents a method to construct all of the regular control surfaces of a toric patch. At last, the application of proposed result in shape deformation is demonstrated by several examples.
We study the global dynamics of a rational difference equation with higher order, which includes many rational difference equations as its special cases. By some complicate computations and mathematical skills, we show that its unique nonnegative fixed point is globally attractive. As application, our results not only improve many known ones, but also solve several “Open Problems and Conjectures” given by Professors Ladas and Camouzis, et al.
We investigate a sufficient condition, in terms of the azimuthal component ωθ of ω = curl u in cylindrical coordinates, for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations. More precisely, we prove that if ∫_0^T ω ^θ(·,t) _Ḃ^0_p,2p 3^q dt < ∞ with 2 q + 3 p = 2, 3 2 < p ≤∞. then the weak solution u is actually a regular solution. Similar regularity criterion still holds in the homogeneous Triebel-Lizorkin spaces.
In this paper, we give some properties for the so-called ε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator. Some sufficient conditions on the entries of an unbounded 2 × 2 block operator matrix L_0 ensuring its ε-pseudo weak demicompactness are provided. In addition, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of essential pseudospectra of L_0 . The results are formulated in terms of some denseness conditions on the topological dual space.
In this paper, we used higher order Haar wavelet method (HOHWM), introduced by Majak et al. [1], for approximate solution of second order integro-differential equations (IDEs) of second-kind. It is improvement of long-established Haar wavelet collocation method (HWCM) which has been much popular among researchers and has many applications in literature. Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM, depending on parameter λ for values 1 and 2, respectively. Several problems available in the literature of both, Volterra and Fredholm type of IDEs, are tested and compared with HWCM to illustrate the performance of our proposed method.
