格上Ising模型的临界失真估计

本文是我们先前工作「１」，「２」的继续，对格上Ｉｓｉｎｇ模型的临界失真ｄｃ的估计，Ｎｅｗｍａｎ和Ｂａｋｅｒ「６」证明了ｄｃ和Ｉｓｉｎｇ模型的Ｍａｙｅｒ级数之收敛半径Ｒ有以下关系：ｄｃ＝Ｒ／（１＋Ｒ），在「１」中匀提出了估计Ｒ及ｄｃ的新方法，并它计算了二维矩形格Ｚ＾２上Ｉｓｉｎｇ模型的临界失真ｄｃ，此文中我们继续应用此方法首次计算了定义在其它二维和三维格上Ｉｓｉｎｇ模型的临界失真ｄｃ，数值计算的结果     

边临界图的新下界

图$G$ 为简单的第二类连通图, 且对$G$ 的任意边$e$,有$\chi^{\prime}(G-e)<\chi^{\prime}(G)$, 则称 $G$是临界的.该文给出了阶为$n$ 边数为$m$的$\Delta$ -临界图的新下界, 即$m\geq(3\Delta+6)n/10$, 这里$1\leq\Delta\leq18$     

拓扑熵的一个下界估计

设Ｘ为局部闭路可缩的紧致空间，ｆ为Ｘ的自映射，ｈ（ｆ）为ｆ的拓扑熵，Ｒ∞（ｆ）为ｆ的渐近Ｒｅｉｄｅｍｅｉｓｔｅｒ数，则有ｈ（ｆ）≥ｌｏｇＲ∞（ｆ）．     

Fermat和的下界估计

Ｆｅｒｍａｔ和的下界估计吴跃生（中国计量学院基础部３１００３４）设Ｐ是△ＡＢＣ的Ｆｅｒｍａｔ－Ｔｏｒｒｉｃｅｌｌｉ点，点Ｐ到各顶点的距离和为ｌ（简称Ｆｅｒｍａｔ和），［１」考虑了Ｆｅｒｍａｔ和的上界估计：本文考虑Ｆｅｒｍａｔ和的下界估计．定理其中ｈａ...     

弱相依误差线性回归模型M-估计的弱相合性

本文考虑线性回归模型yi=xTiβ+ei,i=1,2,…,n,其中ei是(ε,ψ)-弱相依随机误差.在较一般的条件下,我们得到了M-估计弱相合性的统一结果,该结果推广了线性回归模型M-估计的相应结论,包括所有时间序列相依误差,如:高斯序列、相协序列、Bernoulli漂移、Markov链、一些广泛使用的线性或非线性时间...     

自由半群的估计熵和△-弱混合集

本文对自由半群作用的动力系统引入了估计熵和△-弱混合集的概念,得到一些性质.通过引入△-熊混沌集,给出了△-弱混合集的一个等价刻画.     

Roper-Suffridge算子上的偏差定理下界估计的简单证明

Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.     

功率放大器失真问题研究及预失真建模

电子器件中的功率放大器常常伴随着非线性失真效应.为解决此类非线性失真问题,通过研究无记忆和有记忆功放的失真特性,运用最小二乘法来构建多种形式的特性拟合函数,在选择了效果较好的特性拟合函数基础上,根据实际约束条件进行预失真模型的建立,使失真处理后的输出信号趋于线性,最后从信号的功率谱密度的角度出发检验预失真模型的补偿效果,证明模型具有较好的可行性和准确性.     

具有稠密临界轨道和预不动临界轨道的单峰映射的丰富性

证明了对于实二次族在参数空间存在正Ｌｅｂｅｓｇｕｅ测度集合Ｅ,使得Ｅ中几乎所有的参数,相应的映射在不变测度的支集上具有稠密的临界轨道;还证明了Ｅ中存在稠密集合使得相应映射的临界轨道进入它的反向不动点。     

A New Lower Bound For A Ramsey-Type Problem

Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph on s vertices. The main aim of this paper is to provide a new lower bound on the size of the maximum subset of G without a copy of complete graph K_r. Our results substantially improve previous bounds of Krivelevich and Bollobás and Hind. * Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting Microsoft Research.     

点传递图有向连通度的下界

本文研究点传递有向图与定向留连通度的下界，对达到此下界的Ｃｈｙｌｅｙ有向图与定向图进行了刻划。     

Mixing Times of Critical Two‐Dimensional Potts Models

We study dynamical aspects of the q‐state Potts model on an n × n box at its critical β_c(q). Heat‐bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that circumvent low‐temperature bottlenecks) are all expected to undergo “critical slowdowns” in the presence of periodic boundary conditions: the inverse spectral gap, which in the subcritical regime is O(1), should at criticality be polynomial in n for 1 < q ≤ 4, and exponential in n for q > 4 in accordance with the predicted discontinuous phase transition. This was confirmed for q = 2 (the Ising model) by the second author and Sly, and for sufficiently large q by Borgs et al. Here we show that the following holds for the critical Potts model on the torus: for q=3, the inverse gap of Glauber dynamics is n^O(1); for q = 4, it is at most n^{O(log n)}; and for every q > 4 in the phase‐coexistence regime, the inverse gaps of both Glauber dynamics and Swendsen‐Wang dynamics are exponential in n. For free or monochromatic boundary conditions and large q, we show that the dynamics at criticality is faster than on the torus (unlike the Ising model where free/periodic boundary conditions induce similar dynamical behavior at all temperatures): the inverse gap of Swendsen‐Wang dynamics is exp(n^o(1)). © 2017 Wiley Periodicals, Inc.     

A Lower Bound on the Distortion of Embedding Planar Metrics into Euclidean Space

We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than

An Inverse-Ackermann Type Lower Bound For Online Minimum Spanning Tree Verification*

Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST(G). A celebrated result of Komlós shows that this problem can be solved with a linear number of comparisons. Somewhat unexpectedly, MST verification turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to wonder whether a more flexible version of MST verification could be used to derive a faster deterministic minimum spanning tree algorithm. In this paper we consider the online MST verification problem in which we are given a sequence of queries of the form “Is e in the MST of T ∪{e}?”, where the tree T is fixed. We prove that there are no linear-time solutions to the online MST verification problem, and in particular, that answering m queries requires Ω(mα(m,n)) time, where α(m,n) is the inverse-Ackermann function and n is the size of the tree. On the other hand, we show that if the weights of T are permuted randomly there is a simple data structure that preprocesses the tree in expected linear time and answers queries in constant time. * A preliminary version of this paper appeared in the proceedings of the 43rd IEEE Symposium on Foundations of Computer Science (FOCS 2002), pages 155–163. † This work was supported by Texas Advanced Research Program Grant 003658-0029-1999, NSF Grant CCR-9988160, and an MCD Graduate Fellowship.     

A Lower Bound On The Integrality Gap For Minimum Multicut In Directed Networks

Given a directed edge-weighted graph and k source-sink pairs, the Minimum Directed Multicut Problem is to find an edge subset with minimal weight, that separates each source-sink pair. Determining the minimum multicut in directed or undirected graphs is NP-hard. The fractional version of the minimum multicut problem is dual to the maximum multicommodity flow problem. The integrality gap for an instance of this problem is the ratio of the minimum weight multicut to the minimum weight fractional multicut; trivially this gap is always at least 1 and it is easy to show that it is at most k. In the analogous problem for undirected graphs this upper bound was improved to O(log k).In this paper, for each k an explicit family of examples is presented each with k source-sink pairs for which the integrality gap can be made arbitrarily close to k. This shows that for directed graphs, the trivial upper bound of k can not be improved.* This work was supported in part by NSF grant CCR-9700239 and by DIMACS. This work was done while a postdoctoral fellow at DIMACS.     

Thermodynamical Averages For The Ising Model And Spectral Invariants Of Toeplitz Matrices

We derive a general formula giving a representation of the partition function of the one-dimensional Ising model of a system of N particles in the form of an explicitly defined functional of the spectral invariants of finite submatrices of a certain infinite Toeplitz matrix. We obtain an asymptotic representation of the partition function for large N, which can be a base for explicitly calculating some thermodynamic averages, for example, the specific free energy, in the case of a general translation-invariant spin interaction (not necessarily only between nearest neighbors). We estimate the partition function from above and below in the plane of the complex variable β (β is the inverse temperature) and consider the conditions under which these estimates are asymptotically equivalent as N → ∞

     

几类非线性微分系统极限环的存在性和唯一性

给出系统(E1),(E2)和(E3)等非线性微分系统存在闭轨的一些新的判定条件,推广了非线性微分系统极限环的存在性和唯一性许多这方面研究的结果,并大大改进了它们的某些条件．在这个基础上,还给出了系统(E1)和(E2)恰有一个极限环的一组充分条件．