Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Attributes reduct and decision rules optimization based on maximal tolerance classification in incomplete information systems with fuzzy decisions

A new approach to knowledge acquisition in incomplete information system with fuzzy decisions is proposed. In such incomplete information system, the universe of discourse is classified by the maximal tolerance classes, and fuzzy approximations are defined based on them. Three types of relative reducts of maximal tolerance classes are then proposed, and three types of fuzzy decision rules based on the proposed attribute description are defined. The judgment theorems and approximation discernibility functions with respect to them are presented to compute the relative reduct by using Boolean reasoning techniques, from which we can derive optimal fuzzy decision rules from the systems. At last, three types of relative reducts of the system and their computing methods are given.

Boundeness of a Class of Maximal Operators on H^p Spaces on Compact Lie Groups

In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.

MAXIMAL ELEMENTS AND EQUILIBRIUM OF ABSTRACT ECONOMY

economy and qualitative game in which the constraint or preference correspondences are Q θ-majorized are obtained in locally convex topological vector spaces.

MAXIMAL ELEMENTS AND EQUILIBRIUM OF ABSTRACT ECONOMY

An existence theorem of maximal elements for a new type of preference correspondences which are Q(0)-majorized is given. Then some existence theorems of equilibrium for abstract economy and qualitative game in which the constraint or preference correspondences are Q(0)-majorized are obtained in locally convex topological vector spaces.

Finite p-groups with abelian maximal subgroups generated by two elements

Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an M_(n)-group.For p=2,M_(2)-groups have been classified.For odd prime p,this paper provides the isomorphism classification of M_(2)-groups,thereby achieving a complete classification of M_(2)-groups.

On the Wielandt Subgroup in a p-Group of Maximal Class

The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.

Finite p-groups all of whose maximal abelian subgroups are soft

A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4.

Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p

The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko.

p-Capitulation over Number Fields with p-Class Rank Two

Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K) of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the second p-class group G=Gal(Fp2K∣K) of K, complementary techniques are deve- loped for finding the nilpotency class and coclass of . An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(τ (K),ù(K)) of all 34631 real quadratic fields K=Q(√d) with discriminants 0d<108 and 3-class group of type (3, 3). The results admit extensive statistics of the second 3-class groups G=Gal(F32K∣K) and the 3-class field tower groups G=Gal(F3∞K∣K).

Successive Approximation of p-Class Towers

Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.

子载波信道模型盲均衡非合作水声正交频分复用类内调制识别

针对水声多径信道下传统正交频分复用(OFDM)类内调制识别特征稳健性不足导致识别方法失效的问题,提出了基于子载波信道模型盲均衡的水声OFDM类内调制识别方法,可识别类内调制方式包括BPSK、QPSK、8PSK及16QAM。首先,提出一种针对OFDM子载波映射符号的分块策略提高盲均衡的性能。然后,利用期望最大化(EM)算法,在该分块策略下对每个分块内的子载波映射符号进行处理,估计出信道衰落系数和噪声功率;进一步利用K均值聚类(K-means)算法得到该分块映射符号对应的信道衰落系数,并将该信道衰落系数作为EM算法的初始值,使EM算法能够快速收敛。最后,利用最大似然(ML)分类器实现OFDM类内调制识别。仿真和实验结果表明,提出的EM-Block-ML方法实现了水声多径信道下高可靠的OFDM类内调制识别,验证了所提识别方法的有效性。

极大类p群的非线性非忠实不可约特征标个数

利用极大类p群的性质以及有限群的特征标理论探究了极大类p群G的非线性非忠实不可约特征标的个数.证明了p^(n)阶的极大类p群G的非线性非忠实不可约特征标的个数等于p^(n-1)阶的极大类p群G/Z(G)的非线性不可约特征标的个数.特别地,分析了只有3个非线性非忠实不可约特征标的有限p群的性质.

FINITE GROUPS WITH AT MOST TWO SAME ORDER CLASSES OF MAXIMAL SUBGROUPS

S. Adnan has proved the fallowing theorem: Let G be a finite group. If G has exactly 2 conjugacy classes of maximal subgroups, then G is solvable. We extend the conjugacy classes to isomorphic classes, and further generalize them to same order classes of maximal subgroups. We obtain the following results.

Bogomolov Multipliers for Some p-groups of Nilpotency Class 2

The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.

Finite p-groups whose nonnormal subgroups are metacyclic

For an odd prime p,we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic,and based on the criterion,the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism.This solves a problem proposed by Berkovich.

2维Otsu自适应阈值的快速算法

Otsu自适应阈值法作为图像阈值分割的经典算法,在图像处理领域得到了广泛的应用,在其基础上发展起来的2维Otsu阈值法却因为计算时间长而制约了其应用。针对2维Otsu自适应阈值方法计算复杂度高的缺点,通过改变2维直方图上的区域划分,将2维阈值转换为1维阈值,从而提高了2维自适应阈值算法的计算速度。实验结果表明,该算法的计算时间远远小于原始2维Otsu算法,分割效果和原始算法基本一致。

区间值信息系统的知识约简

知识约简是粗糙集理论的重要研究内容之一.传统的知识约简主要针对单值信息系统,但在许多实际问题中,信息系统中的数据往往以区间值的形式存在,因此,区间值信息系统的知识约简研究具有重要意义.现有工作中,论域的分类结果存在冗余度大、误分率高等问题.针对上述问题,在区间值信息系统中引入了α-极大相容类的概念,并提出了新的粗糙上下近似算子,α-极大相容类的采用有效地提高了分类和粗糙近似精度.最后,给出了区间值信息系统知识约简的定义和相应区分函数的计算方法,为区间值信息系统的知识获取提供了一条新的途径.

多方位结构元素路面裂缝图像边缘检测算法

在数学形态学基础上,针对路面图像中噪声和裂缝类病害不同的像素分布特点,提出了多方位结构元素形态学边缘检测算法。该算法利用类间最大距离法确定路面裂缝图像中发生梯度变化的点,后对其采用多方位结构元素腐蚀操作,提取出路面裂缝边缘像素点并滤除噪声。实验结果表明:较传统的边缘检测算法,该算法在准确地检测路面裂缝边缘的同时有效地抑制了噪声干扰,检测效果良好,运算速度快。