Acta Mathematicae Applicatae Sinica, English Series最新文献

Recurrent event data with a terminal event are commonly encountered in longitudinal follow-up studies. In this paper, we investigate regression analysis of the weighted composite endpoint of recurrent and terminal events with a semiparametric mixed model. Particularly, the weighted composite endpoint is constructed by the severity of all events while leaving the dependence structure among the recurrent and terminal events unspecified. The semiparametric mixed model is flexible since it allows the covariate effects on the rate function of the weighted composite endpoint to be proportional or convergent. For inference on the model parameters, the estimating equation approach and the inverse probability weighting technique are developed. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed procedure is evaluated through Monte Carlo simulation studies. We apply the proposed method to a real data set on a medical cost study of chronic heart failure patients for illustration.

A non-increasing sequence π = (d₁, ⋯, d_n) of nonnegative integers is said to be a graphic sequence if it is realizable by a simple graph G on n vertices. In this case, G is referred to as a realization of π. In terms of graphic sequences, the Loebl-Komlós-Sós conjecture states that for any integers k and n, if π = (d₁, ⋯, d_n) is a graphic sequence with ({d_{leftlceil {{n over 2}} rightrceil}} ge k), then every realization of π contains all trees with k edges as subgraphs. This problem can be viewed as a forcible degree sequence problem. In this paper, we consider a potential degree sequence problem of the Loebl-Komlós-Sós conjecture, that is, we prove that for any integers k and n, if π = {d₁, ⋯, d_n) is a graphic sequence with ({d_{leftlceil {{n over 2}} rightrceil}} ge k), then there is a realization of π containing all trees with k edges as subgraphs.

Given a forbidden graph H and a function f(n), the Ramsey-Turán number RT (n, H, f (n)) is the maximum number of edges of an H-free graph on n vertices with independence number less than f (n). For graphs G and H, the Ramsey number R(G, H) is the minimum integer N such that any red/blue edge coloring of the complete graph K_N contains either a red G or a blue H. Denote G + H by the join graph obtained from disjoint G and H by adding all edges between them completely. We first show that for any fixed graph H, if there are two constants p:= p(H) > 0 and q:= q(H) > 1 such that (R({H,{K_n}}) le {{p{n^q}} over {{{({log n})}^{q - 1}}}}), then (mathbf{RT}({n,{K_2} + H,o({{n^{{1 over q}}}{{({log n})}^{1 - {1 over q}}}})}) = o({{n^2}})), which extends several previous results. Moreover, we show that for any fixed forest F of order k ≥ 3, and for any 0 < δ < 1 and sufficiently large n

As a corollary, we have an upper bound for RT(n, K_2,2,2, n^δ) for any 0 < δ < 1.

In the paper, by exploring Stampacchia truncation method, some comparison techniques and variational approaches, we study the existence and regularity of positive solutions for a boundary value problem involving the fractional p-Laplacian, where the nonlinear term satisfies some growth conditions but without the Ambrosetti and Rabinowitz condition.

A general model of insider trading on a dynamic asset in a finite time interval is proposed, in which an insider possesses the whole information on the dynamic values, noise traders without any information submit orders randomly as a martingale with volatility following a stochastic process, and market makers observe partial information when setting price in a semi-strong efficient way. With the help of filtering theory, BSDE method and dynamic programming principle, we establish a market equilibrium consisting of linear insider trading strategy and linear pricing rule, with the later characterized by price pressure on market orders and price pressure on asset observations. It shows that in the equilibrium, all the information on the risky asset is incorporated into the market price at the end of the transaction, and price pressure on market orders is a submartingale while market depth process is a martingale. Furthermore, as market makers’ information precision on the asset tends to zero, the equilibrium with partial observation of market makers on the risky asset converges to the one without partial observation of market makers, while when market makers observe almost all of information on the asset, the expected profit earned by the insider makes almost zero, which is in accord with our economic intuition. Our results cover some classical results about continuous-time insider trading on a static asset.

In this article, the maximum likelihood estimators (MLEs) of the scale and shape parameters β and λ from the Exponential-Poisson distribution will be considered in moving extremes ranked set sampling (MERSS). These MLEs will be compared in terms of asymptotic efficiencies. The numerical results show that the MLEs obtained via MERSS can serve as effective alternatives to those derived from simple random sampling.

In this paper, we develop a robust variable selection procedure based on the exponential squared loss (ESL) function for the varying coefficient partially nonlinear model. Under certain conditions, some asymptotic properties of the proposed penalized ESL estimator are established. Meanwhile, the proposed procedure can automatically eliminate the irrelevant covariates, and simultaneously estimate the nonzero regression coefficients. Furthermore, we apply the local quadratic approximation (LQA) and minorization–maximization (MM) algorithm to calculate the estimates of non-parametric and parametric parts, and introduce a data-driven method to select the tuning parameters. Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset. Finally, we apply the proposed procedure to analyze the Boston housing price data. The results reveal that the proposed method has a better prediction ability.

In this paper, by using the concentration-compactness principle and a version of symmetry mountain pass theorem, we establish the existence and multiplicity of solutions to the following p-biharmonic problem with critical nonlinearity:

where Ω is a bounded domain in ℝ^N (N ≥ 3) with smooth boundary, (Delta_{p}^{2}u=Delta({vert Delta u vert}^{p-2} Delta u ), 1 < p < {N over 2}, p^{*}={N_{p}over N-2p}, {partial u over partial nu}) is the outer normal derivative, μ is a positive parameter and f: Ω × ℝ → ℝ is a Carathéodory function.

The biased random walk on supercritical Galton–Watson trees is known to exhibit a multiscale phenomenon in the slow regime: the maximal displacement of the walk in the first n steps is of order (log n)³, whereas the typical displacement of the walk at the n-th step is of order (log n)². Our main result reveals another multiscale property of biased walks: the maximal potential energy of the biased walks is of order (log n)² in contrast with its typical size, which is of order log n. The proof relies on analyzing the intricate multiscale structure of the potential energy.

Given a simple graph G = (V, E) and its (proper) total coloring ϕ with elements of the set {1, 2, ⋯, k}, let w_ϕ(v) denote the sum of the color of v and the colors of all edges incident with v. If for each edge uv ∈ E, w_ϕ(u) ≠ w_ϕ(v), we call ϕ a neighbor sum distinguishing total coloring of G. Let L = {L_x ∣ x ∈ V ⋃ E} be a set of lists of real numbers, each of size k. The neighbor sum distinguishing total choosability of G is the smallest k for which for any specified collection of such lists, there exists a neighbor sum distinguishing total coloring using colors from L_x for each x ∈ V ⋃ E, and we denote it by (text{ch}_{sum}^{primeprime}(G)). The known results of neighbor sum distinguishing total choosability are mainly about planar graphs. In this paper, we focus on 1-planar graphs. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. We prove that (text{ch}_{sum}^{primeprime}(G)leqDelta+4) for any 1-planar graph G with Δ ≥ 15, where Δ is the maximum degree of G.