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Abstract: In this paper, the authors define the homology of sets, which comes from and contains the ideas of path homology and embedded homology. Moreover, A Künneth formula for sets associated to the homology of sets is given. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0292-3

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Abstract: The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in ℂn with a unified method. Especially the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of order α. The obtained results unify and generalize the corresponding results in some prior literatures. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0297-y

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Abstract: Torus orbifolds are topological generalizations of symplectic toric orbifolds. The authours give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using a toric topological method. As a result, they show that any orientable locally standard torus orbifold is equivariantly cobordant to some copies of orbifold complex projective spaces. They also discuss some further equivariant cobordism results including the cases when torus orbifolds are actually torus manifolds. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0295-0

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Abstract: The authors consider the short time existence for Ricci-Bourguignon flow on manifolds with boundary. If the initial metric has constant mean curvature and satisfies some compatibility conditions, they show the short time existence of the Ricci-Bourguignon flow with constant mean curvature on the boundary. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0299-9

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Abstract: This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponent γ ∈ (1, 3]. Given some small BV perturbations of the initial state, the author employs a modified wave front tracking method, constructs a new Glimm functional, and proves its monotone decreasing based on the possible local wave interaction estimates, then establishes the global stability of the multi-wave configurations, consisting of a strong 1-shock wave, a strong 2-contact discontinuity, and a strong 3-shock wave, without restrictions on their strengths. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0298-x

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Abstract: In this paper, the authors study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. They adopt the frequency domain method to prove that the system with smooth initial data is logarithmically stable, provided that the coupling domain and the damping domain intersect each other. Moreover, they show, by an example, that this geometric assumption of the intersection is necessary for 1-D case. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0293-8

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Abstract: In this paper, the author focuses on the joint effects of diffusion and advection on the dynamics of a classical two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. For comparison purposes, the two species are assumed to have identical competition abilities throughout this paper. The results explore the condition on the diffusion and advection rates for the stability of former species. Meanwhile, an asymptotic behavior of the stable coexistence steady states is obtained. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0296-z

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Abstract: Consider the heterogeneity (e.g., heterogeneous social behaviour, heterogeneity due to different geography, contrasting contact patterns and different numbers of sexual partners etc.) of host population, in this paper, the authors propose an infection age multi-group SEIR epidemic model. The model system also incorporates the feedback variables, where the infectivity of infected individuals may depend on the infection age. In the direction of mathematical analysis of model, the basic reproduction number R0 has been computed. The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R0. More precisely, for R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and for R0 > 1, they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method. By considering a numerical example, they investigate the effects of infection age and feedback on the prevalence of the disease. Their result shows that feedback parameters have different and even opposite effects on different groups. However, by choosing an appropriate value of feedback parameters, the disease could be eradicated or maintained at endemic level. Besides, the infection age of infected individuals may also change the behaviour of the disease, global stable to damped oscillations or damped oscillations to global stable. PubDate: 2021-11-01 DOI: 10.1007/s11401-021-0294-1

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Abstract: Let Z2 denote a cyclic group of 2 order and Z 2 2 = Z2 × Z2 the direct product of groups. Suppose that (M, Φ) is a closed and smooth manifold M with a smooth Z 2 2 -action whose fixed point set is the disjoint union of two real projective spaces with the same dimension. In this paper, the authors give a sufficient condition on the fixed data of the action for (M, Φ) bounding equivariantly. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0288-z

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Abstract: The authors give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology In addition, they give a shorter proof of a well known criterion on this subject. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0290-5

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Abstract: In this paper, the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0286-1

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Abstract: In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary (null) controllability and the exact boundary observability for first order hyperbolic systems. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0284-3

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Abstract: Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties intersecting moving hypersurfaces targets. The main purpose of this paper is to give some interesting improvements of Ru’s second main theorem for moving hypersurfaces targets located in subgeneral position with index. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0289-y

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Abstract: Let \({\mathbb{F}_q}\) be a finite field with order q and D2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the finite dihedral group algebras \({\mathbb{F}_q}[{D_{2n}}]\) . Some numerical examples are also presented to illustrate the main results. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0291-4

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Abstract: For the iteration of spherical average (A1)N and the Laplace operator Δ, we consider the boundedness of the operator Δ(A1)N on the α-modulation spaces \(M_{p,q}^{s,\alpha }\) . The authors obtain some sufficient and necessary conditions to ensure the boundedness on the α-modulation spaces. The main theorems significantly improve some known results. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0287-0

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Abstract: A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T − λ) = {0} or ker(T − λ)* = {0} for each λ ∈ ℂ. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property. Moreover, they study the stability of these properties under small compact perturbations. PubDate: 2021-09-01 DOI: 10.1007/s11401-021-0285-2

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Abstract: In this paper, the author solves the Dirichlet problem for Hermitian-Poisson metric equation \(\sqrt { - 1} {\Lambda _\omega }{G_H} = \lambda {\rm{Id}}\) and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds. When λ = 0, the Hermitian-Poisson metric is a Hermitian harmonic metric. PubDate: 2021-07-01 DOI: 10.1007/s11401-021-0279-0

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Abstract: The author shows that if a locally conformal Kähler metric is Hermitian Yang-Mills with respect to itself with Einstein constant c ≤ 0, then it is a Kahler-Einstein metric. In the case of c > 0, some identities on torsions and an inequality on the second Chern number are derived. PubDate: 2021-07-01 DOI: 10.1007/s11401-021-0274-5

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Abstract: Let F be a graph. A hypergraph \({\cal H}\) is Berge-F if there is a bijection \(f:E(F) \rightarrow E({\cal H})\) such that e ⊂ f(e) for every e ∈ E(F). A hypergraph is Berge-F-free if it does not contain a subhypergraph isomorphic to a Berge-F hypergraph. The authors denote the maximum number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by exr (n, Berge-F). A (k, p)-fan, denoted by Fk,p, is a graph on k(p − 1) + 1 vertices consisting of k cliques with p vertices that intersect in exactly one common vertex. In this paper they determine the bounds of exr(n, Berge-F) when F is a (k, p)-fan for k ≥ 2, p ≥ 3 and r ≥ 3. PubDate: 2021-07-01 DOI: 10.1007/s11401-021-0272-7

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Abstract: In this paper, the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space. They show that if the initial velocity satisfies some condition on the integral J in the “isolated mass group” (see (1.13)), then there will be finite time blow-up of regular solutions to the Euler system with J ≤ 0 (n ≥ 1) and to the Euler-Boltzmann system with J < 0 (n ≥ 1) and J = 0 (n ≥ 2), no matter how small and smooth the initial data are. It is worth mentioning that these blow-up results imply the following: The radiation is not strong enough to prevent the formation of singularities caused by the appearance of vacuum, with the only possible exception in the case J = 0 and n = 1 since the radiation behaves differently on this occasion. PubDate: 2021-07-01 DOI: 10.1007/s11401-021-0273-6