We defined the fractional maximal operators and found a control function related to the maximal operators. We obtain the boundedness of fractional maximal operators on homogeneous trees from the weak(1,1)type of maximal operators.

This paper primarily demonstrates that several classes of algebras possess the property of zero Lie product determinacy. Firstly, it provides some equivalent characterizations of zero product determinacy along with an application. Secondly, we prove that the triangular UHF algebras, countable dimensional locally matrix algebra, and algebras consisting of finite rank operators in J -subspace lattices are all zero Lie product determined. Furthermore, the paper explores the preservationof the zero product determinacy property under certain mappings and presents several counterexamples.

In four-dimensional Euclidean space, utilizing the definition of a waist curve, the structure functions of ruled surfaces is proposed, extending the non-developable ruled surfaces and their standard equations in three-dimensional Euclidean space to four-dimensional Euclidean space. By studing the properties of the surface itself through the structural function of the ruled surface, the relationships between the structural functions, directors, and waist curves of four types of special associated ruled surfaces are obtained, and these four kinds of ruled surfaces are classified. Finally, specific expressions for the structural functions are given when the director is a Mannheim curve and a skew helix of the third type, and the mean curvature vector field of the associated ruled surface in these cases is calculated.

In order to verify that capturing the uncertainty features of the probability distribution of financial time series based on different frequency domain scales can effectively improve the measurement accuracy of VaR model, the W-G-VaR model is constructed by combining wavelet multi-resolution analysis with nonlinear expectation theory for the first time. Standard & Poors 500 composite stock price index(S& P 500 Index)and Shanghai(securities)composite index are selected as samples for empirical analysis. The results show that, compared to the G-VaR model, the W-G-VaR model constructed from the dual perspectives of the time domain and the frequency domain has more accurate risk measurement results throughout the sample period, especially during the occurrence of major risks, and the size of the window when capturing uncertainties does not affect the superiority of the W-G-VaR model.

In order to ensure the integrity of decision information, we extend the Muirhead mean operator in the environment of interval hesitant trapezoidal fuzzy sets. The concepts of interval hesitant trapezoidal fuzzy Muirhead mean operator and interval hesitant trapezoidal fuzzy geometric Muirhead mean operator have been proposed. Their properties and theorems are given, and several degenerate forms of the operators are introduced. Considering that the Choquet integral can objectively calculate the weights of attributes, this paper introduces the Choquet integral into the above operators, and proposes the concepts of interval hesitant trapezoidal fuzzy Choquet Muirhead mean operator and interval hesitant trapezoidal fuzzy geometric Choquet Muirhead mean operator. Meanwhile, a multi-attribute decision making model based on interval hesitant trapezoidal fuzzy Choquet Muirhead mean operator is constructed. Finally, it was applied to the green battery supplier selection problem to analyze its feasibility and effectiveness.

The new inequality relationships between global Roman domination number and Roman domination number are obtained by using the graph parameters such as the order, the number of edges and degree.

For an undirected connected graph G(V,E), if there exists a single mapping f:V(G)∪E(G)→{1,2,…,|V|+|E|}, and conditions uv∈E(G) and d(u)=d(v) are satisfied, then there exists S(u)=S(v), where S(u)=f(u)+∑ holds. Let d(u) denote the degree of vertex u; thus, f is referred to as an adjacent vertex reducible total labeling(AVRTL)of G. This study combines genetic algorithms and particle swarm algorithms to design a heuristic search algorithm that can determine whether a random graph with a finite number of vertices contains an AVRTL. Through the analysis of experimental results, several theorems regarding linked graphs are summarized and proved. Finally, the following conclusion is drawn: if subgraphs G1 and G2 are AVRTL graphs, then the graph operation ↑ab exhibits closure, meaning the linked graph G1↑_abG2 is also an AVRTL graph.

The Mostar index M(G) of a connected graph G is defined as M(G)=∑_e=uv∈E(G)|n_u(e)-n_v(e)|, where n_u(e) and n_v(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. The lower bound of the Mostar index among all tricyclic graphs is established, and the extremal graphs that attained the lower bound are determined.

This paper studies the normal criterion of holomorphic functions involving exceptional functions and differential polynomials by using Pang-Zalcman lemma. A new normal criterion is obtained by extending the previous results through the method of proof by contradiction.

In this paper, the authors mainly discuss the boundedness of parametrized area integral μ^ρ_Ω,S and parametrized Littlewood-Paley g^*_λ-function μ^{*, ρ}_Ω,λ and their higher order commutators ［b^m, μ^ρ_Ω,S］ and ［b^m, μ^{*, ρ}_Ω,λ］ generated by b∈BMO and μ^ρ_Ω,S、 g^*_λ-function μ^{*, ρ}_Ω,λ on generalized Morrey spaces associated with ball quasi-Banach function spaces M_u(X).

The boundedness of the bilinear θ-type Calderón-Zygmund operator on the double-weight variable exponent Herz space is obtained by using the double-weight estimation and the function decomposition method, as well as the weighted boundedness on the product L^p(·) space.

In this paper, the existence of traveling wave solutions for a kind of discrete diffusion SEIR model with saturated recovery rate and bilinear occurrence rate is studied. Firstly, the existence of solutions for truncationproblem is proved by using the method of upper and lower solutions and the Schauder fixed point theorem; Secondly, it is proved by the limit method that when R0>1, c>c^*, the system has traveling wave solutions connecting the disease-free equilibrium point and the positive equilibrium point. Finally, the asymptotic behavior of traveling wave solution at infinity is proved.

In this paper, the Brusselator model with cross-diffusion and delay are studied. Firstly, by analyzing the distribution of the roots of the characterstic equation of the system using linearization method, the local asymptotic stability of the system and the existence of Hopf bifurcation at the unique positive equilibrium point are obtained. Then the effect of time delay parameters on the existence of Hopf bifurcation is analyzed. Finally, numerical simulation is carried out to support the theoretical results using MATLAB.

Self-similar solutions and approaches for analytically solving a class of(3+1)-dimensional macroscopic population balance(integro-partial differential)equations with homogeneous collision kernels are studied.(3+1)-dimensional integro-partial differential equation is successfully transformed into(2+1)-dimensional partial differential moment equations by use of the method of moments. The admitted scaling transformation groups, reduced(2+1)-dimensional integro-partial differential equations, reduced(1+1)-dimensional ordinary differential equations, self-similar solutions, explicit exact solutions of(3+1)-dimensional integro-partial differential equations and(2+1)-dimensional partial differential moment equations are presented by use of the method of scaling transformation analysis. The dynamic behaviour analysis of the obtained solutions are also given.

This paper studies a three-species predator-prey model in discrete patch environments, the existence of forced waves is obtained by using Schauders fixed point theorem and constructing appropriate upper-lower solutions.