Acta Mathematica Sinica-English Series最新文献

In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type B given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.

The paper considers the Cauchy problem with small initial values for semilinear wave equations with weighted nonlinear terms. Similar to Strauss exponent p₀(n) which is the positive root of the quadratic equation (1+{1over 2}(n+1)p-{1over 2}(n-1)p^{2}=0), we get smaller critical exponents p_m(n),p ^*_m (n) and have global existence in time when p>p_m(n) or p>p ^*_m (n). In addition, for the blow-up case, the introduction of the spacial weight shows the optimality of new upper and lower bound.

In this paper, we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions. By letting weight functions be probability density functions of a class of special distributions, the proposed test statistics have simple closed forms and do not require moment conditions on the random vectors. Moreover, we derive the asymptotic distributions of the test statistics under the null hypothesis. The proposed testing method is computationally feasible and easy to implement. Based on a data-driven bandwidth selection method, Monte Carlo simulation studies indicate that our tests have a relatively good performance compared with the competitors. A real data example is also presented to illustrate the application of our tests.

We study the topology of closed, simply-connected, 6-dimensional Riemannian manifolds of positive sectional curvature which admit isometric actions by SU(2) or SO(3). We show that their Euler characteristic agrees with that of the known examples, i.e., S⁶, (mathbb{CP}^{3}), the Wallach space SU(3)/T² and the biquotient SU(3)//T². We also classify, up to equivariant diffeomorphism, certain actions without exceptional orbits and show that there are strong restrictions on the exceptional strata.

Given a simple graph G and a proper total-k-coloring φ from V (G) ∪ E(G) to {1, 2,…,k}. Let f(v) = φ(v)Π_uv∈E(G)φ(uv). The coloring φ is neighbor product distinguishing if f(u) ≠ f(v) for each edge uv ∈ E(G). The neighbor product distinguishing total chromatic number of G, denoted by (chi_{Pi}^{primeprime}(G)), is the smallest integer k such that G admits a k-neighbor product distinguishing total coloring. Li et al. conjectured that (chi_{Pi}^{primeprime}(G)leq Delta(G)+3) for any graph with at least two vertices. Dong et al. showed that conjecture holds for planar graphs with maximum degree at least 10. By using the famous Combinatorial Nullstellensatz, we prove that if G is a planar graph without 5-cycles, then (chi_{Pi}^{primeprime}(G)leq max{Delta(G)+2,12}).

This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and maximum, which can be applied into the high-dimensional testing problems. By combining the sum-type test and the max-type test, we propose the Fisher’s combination tests for the one-sample mean test and two-sample mean test. Under this novel general framework, several strong assumptions in existing literature have been relaxed. Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.

Let λ > 0 and (Delta_{lambda} := -{{d^2} over {dx^{2}}} - {{2lambda} over x} {{d} over {dx}}) be the Bessel operator on ℝ₊:= (0, ∞). In this paper, the authors introduce and characterize the space VMO(ℝ₊, dm_λ) in terms of the Hankel translation, the Hankel convolution and a John–Nirenberg inequality, and obtain a sufficient condition of Fefferman–Stein type for functions f ∈ VMO(ℝ₊, dm_λ) using ({tilde R}_{{Delta}_lambda}), the adjoint of the Riesz transform ({R}_{{Delta}_lambda}). Furthermore, we obtain the characterization of CMO(ℝ₊, dm_λ) in terms of the John–Nirenberg inequality which is new even for the classical CMO(ℝⁿ) and a sufficient condition of Fefferman–Stein type for functions f ∈ CMO(ℝ₊, dm_λ).

In multiple heterogeneous networks, developing a model that considers both individual and shared structures is crucial for improving estimation efficiency and interpretability. In this paper, we introduce a semi-parametric individual network autoregressive model. We allow autoregression and regression coefficients to vary across networks with subgroup structure, and integrate both covariates and node relationships into network dependence using a single-index structure with unknown links. To estimate all individual and commonly shared parameters and functions, we introduce a novel penalized semiparametric approach based on the generalized method of moments. Theoretically, our proposed semiparametric estimator for heterogeneous networks exhibits estimation and selection consistency under regular conditions. Numerical experiments are conducted to illustrate the effectiveness of the proposed estimator. The proposed method is applied to analyze patient distribution in hospitals to further demonstrate its utility.

We introduce null surfaces (or nullcone fronts) of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space. These surfaces are formed by the light rays emitted from points on anti-de Sitter spacelike framed curves. We then classify singularities of the nullcone front of a pseudo-spherical spacelike framed curve and show how these singularities are related to the singularities of the associated framed curve. We also define a family of functions called the Anti-de Sitter distance-squared functions to explain the nullcone front of a pseudo-spherical spacelike framed curve as a wavefront from the viewpoint of the Legendrian singularity theory. We finally provide some examples to illustrate the results of this paper.

Let G be a graph and d_i denote the degree of a vertex v_i in G, and let f(x,y) be a real symmetric function. Then one can get an edge-weighted graph in such a way that for each edge v_iv_j of G, the weight of v_iv_j is assigned by the value f(d_i,d_j). Hence, we have a weighted adjacency matrix (mathcal{A}_{f}(G)) of G, in which the ij-entry is equal to f(d_i,d_j) if v_iv_j ∈ E(G) and 0 otherwise. This paper attempts to unify the study of spectral properties for the weighted adjacency matrix (mathcal{A}_{f}(G)) of graphs with a degree-based edge-weight function f(x,y). Some lower and upper bounds of the largest weighted adjacency eigenvalue λ₁ are given, and the corresponding extremal graphs are characterized. Bounds of the energy (mathcal{E}_{f}(G)) for the weighted adjacency matrix (mathcal{A}_{f}(G)) are also obtained. By virtue of the unified method, this makes many earlier results become special cases of our results.