Acta Mathematica Sinica-English Series最新文献

In this paper, we consider λ-translating solitons in ℝ³. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.

Cyclotomic multiple zeta values are generalizations of multiple zeta values. In this paper, we establish sum formulas for various kinds of cyclotomic multiple zeta values. As an interesting application, we show that the ℚ-algebra generated by Riemann zeta values are contained in the ℚ-algebra generated by unit cyclotomic multiple zeta values of level N for any N ≥ 2.

The main purpose of this article is to study the lattice structure of quantum logics by using the theory of partially order sets. The goal is achieved by constructing a natural embedding map from the quantum logic posets into the complete lattices. The embedding map needs to be dense (in the order sense) and such complete lattices are so-called extended logics which preserve all essential features of the quantum logic. We obtain that the extended logic is unique up to a lattice isomorphism.

In many practical applications, we need to recover block sparse signals. In this paper, we encounter the system model where joint sparse signals exhibit block structure. To reconstruct this category of signals, we propose a new algorithm called block signal subspace matching pursuit (BSSMP) for the block joint sparse recovery problem in compressed sensing, which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix. To begin with, we consider the case where block joint sparse matrix X has full column rank and any r nonzero row-blocks are linearly independent. Based on these assumptions, our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most (k - r + leftlceil {{r over L}} rightrceil) iterations if sensing matrix A satisfies the block restricted isometry property of order L(K − r) + r + 1 with ({delta _{{B_{L( {K - r}) + r + 1}}}}< max {{{{sqrt r} over {sqrt {K + {r over 4}} + sqrt {{r over 4}} }},{{sqrt L} over {sqrt {Kd} + sqrt L}}}}). This condition improves the existing result.

Regression models are often transformed into certain alternative forms in statistical inference theory. In this paper, we assume that a general linear model (GLM) is transformed into two different forms, and our aim is to study some comparison problems under the two transformed general linear models (TGLMs). We first construct a general vector composed of all unknown parameters under the two different TGLMs, derive exact expressions of best linear minimum bias predictors (BLMBPs) by solving a constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and describe a variety of mathematical and statistical properties and performances of the BLMBPs. We then approach some algebraic characterization problems concerning relationships between the BLMBPs under two different TGLMs. As applications, two specific cases are presented to illustrate the main contributions in the study.

We consider the following fractional prescribed curvature problem

where (s in (0,, {1 over 2})) for N = 3, s ∈ (0, 1) for N ≥ 4 and (2_{s}^{*}={2N over N-2s}) is the fractional critical Sobolev exponent, K(y) has a local maximum point in r ∈ (r₀ − δ, r₀ + δ). First, for any sufficient large k, we construct a 2k bubbling solution to (0.1) of some new type, which concentrates on an upper and lower surfaces of an oblate cylinder through the Lyapunov–Schmidt reduction method. Furthermore, a non-degeneracy result of the multi-bubbling solutions is proved by use of various Pohozaev identities, which is new in the study of the fractional problems.

For a piecewise monotone function F of height 1, an open question was raised: Does F have an iterative root f of order n ≤ N(F) + 1 if the ‘characteristic endpoints condition’ is not satisfied? This question was answered partly in the case that F is strictly increasing on its characteristic interval K(F) but f is strictly decreasing on K(F). In this paper we discuss the question for F increasing on K(F) in some remaining cases, giving the necessary and sufficient conditions for the existence of continuous iterative roots f decreasing on K(F) of order n = N(F) > 2 with H(f) = n − 1.

In this paper, complete convergence and complete moment convergence for maximal weighted sums of ρ⁻-mixing random variables are investigated, and some sufficient conditions for the convergence are provided. The relationships among the weights of the partial sums, boundary function and weight function are in a sense revealed. Additionally, a Marcinkiewicz–Zygmund type strong law of large numbers for maximal weighted sums of ρ⁻-mixing random variables is established. The results obtained extend the corresponding ones for random variables with independence structure and some dependence structures. As an application, the strong consistency for the tail-value-at-risk (TVaR) estimator in the financial and actuarial fields is established.

We study Berry–Esseen bounds and Cramér-type moderate deviations of a jump-type Cox–Ingersoll–Ross (CIR) process driven by a standard Wiener process and a subordinator. In the subcritical case, we obtain the best Berry–Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment. Under the Cramér condition, we establish the Cramér-type moderate deviations of the MLE of the growth rate. We first derive a Berry–Esseen bound, a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean. Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry–Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.

The main purpose of this article is using the elementary techniques and the properties of the character sums to study the computational problem of one kind products of Gauss sums, and give an interesting triplication formula for them.