负曲率流形上给定数量曲率的共形形变

本文研究具强负曲率Cartan－Hadamard流形M~n（n≥3）上给定数量曲率函数S的共形形变问题．利用上下解方法,并通过精心构造上解,我们获得了当完备的共形形变度量存在时,函数S在无穷远附近的最佳渐近性态．在较一般情况下,我们还给出了共形数量曲率方程解的渐近估计．     

IMAGE RESTORATION UNDER CAUCHY NOISE WITH SPARSE REPRESENTATION PRIOR AND TOTAL GENERALIZED VARIATION

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring.The model integrates a nonconvex data-fidelity term with two regularization terms,a sparse representation prior over dictionary learning and total generalized variation(TGV)regularization.The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns,while adequately denoising in homogeneous regions and contributing natural visual quality.TGV regularization further assists in effectively denoising in smooth regions while retaining edges.By adopting the penalty method and an alternating minimization approach,we present an efficient iterative algorithm to solve the proposed model.Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.     

组态相互作用中的特征波函数

提出了完全活性空间组态相互作用方法中对称化算符、本征基、特征矩阵、特征波函数等概念和将多电子波函救按空间与自旋对称分类的统一方法。按此法对称化算符并作用在特征波函数上,再按等价权空间求和即得全组态波函数。因对称性使组态函数中物理因子与几何因子完全分离,可消除了变分求解中多余的变量。特征基化学概念明确,直接对应给定的价键结构。     

Molecular and supramolecular helicity induction in trityl group-containing compounds: The case of chiral 3,3,3-triphenylpropionic acid derivatives

The process of dynamic chirality transmission from permanent chirality element to stereodynamic triphenylmethyl group placed in the distance of 4 bonds, has been studied for series of optically active 3,3,3-triphenylpropionic acid derivatives. Structural analysis, carried out with the use of complementary methods and supported by theoretical calculations, enabled us to determine the mechanism of chirality transmission. The observed chirality transfer phenomenon, demonstrated unequivocally as raising of non-zero Cotton effects in the region of UV absorption of trityl group, is a cascade process driven by weak intramolecular interactions. Despite the much larger inductor-effector distance, the sensitivity in chirogenesis is comparable to other stereodynamic probes reported so far. In the crystalline phase, the combination of trityl group with amino acid moiety results in the formation of helical superstructures, where individual molecules are held together by hydrogen bonding cascades. The proper combination of functionalities in the molecule skeleton allows, to some extent, the control over the association process and authorizes determination of the trityl group as the supramolecular synthon.     

Persistent currents and induced magnetization in presence of external magnetic field and transition probabilities in presence of combined laser pulse and external magnetic field for a confined hydrogen atom

In this work we propose to study an atom confined in a potential which consists of a Hulthén potential plus a ring-shaped potential. The atom is further subjected to a spherical confinement. The time-independent Schrödinger equation (TISE) of the system is solved numerically. Exact energy levels are obtained. The persistent current and induced magnetic field of such a confined atom is evaluated. Finally, the atomic system in this potential and confinement is subjected to short electromagnetic pulses, which are shown to induce enormous currents.     

Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field

We investigate the influence of an induced magnetic field on the peristaltic flow of an incompressible fourth grade fluid in a symmetric channel with heat transfer. Adopting long wavelength, low Reynolds number and small Deborah number assumptions we derive the solutions for stream function, pressure gradient, temperature, magnetic force function, induced magnetic field and current density. Qualitative agreement is demonstrated between the graphs and expected observations.     

闭模糊拟阵模糊圈的极值问题

本文主要方法是通过基本序列、导出拟阵序列和模糊集分解定理,将模糊圈的研究转化为对圈子集套和数组的研究。在闭模糊拟阵中,我们得出三个结论:以同一集合为支撑集的模糊圈的最大模糊圈总是存在;以同一子集串为圈子集套的模糊圈的最大模糊圈不一定存在。但是,找到了存在最大模糊圈的充要条件;以同一集合为支撑集的模糊圈的最小模糊圈,以同一子集串为圈子集套的模糊圈的最小模糊圈都是不存在的。但它们的最小模糊势是存在的,而且找出了计算最小模糊势的公式。我们构造了两个算法:一是构造支撑集最大模糊圈算法。通过这个算法可构造出支撑集最大模糊圈,同时计算出其最大模糊势;二是判断和构造圈子集套最大模糊圈算法。通过这个算法首先判断最大模糊圈是否存在,如果存在就可以找出圈子集套最大模糊圈同时计算出最大模糊势。     

On the sizes of large subgraphs of the binomial random graph

We consider the binomial random graph $G(n,p)$, where p is a constant, and answer the following two questions.First, given $e(k)=p\left(\begin{array}{c}k\\ 2\end{array}\right)+O(k)$, what is the maximum k such that a.a.s. the binomial random graph $G(n,p)$ has an induced subgraph with k vertices and $e(k)$ edges? We prove that this maximum is not concentrated in any finite set (in contrast to the case of a small $e(k)$). Moreover, for every constant $C>0$, with probability bounded away from 0, the size of the concentration set is bigger than $C\sqrt{n/\ln ?n}$, and, for every ${\omega }_n\to \infty$, a.a.s. it is smaller than ${\omega }_n\sqrt{n/\ln ?n}$.Second, given $k>\epsilon n$, what is the maximum μ such that a.a.s. the set of sizes of k-vertex subgraphs of $G(n,p)$ contains a full interval of length μ? The answer is $\mu =\mathrm{\Theta }\left(\sqrt{(n?k)n\ln ?\left(\begin{array}{c}n\\ k\end{array}\right)}\right)$.     

On the inducibility of oriented graphs on four vertices

We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for more than half of the graphs, and very close lower and upper bounds for all the remaining ones. It occurs that, for some graphs, the structure of extremal constructions maximizing density of its induced copies is very sophisticated and complex.