The Lower Orders of Dirichlet and Random Dirichlet Series

The formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of the coefficients. Corresponding results are obtained for some random Dirichlet series.

THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES

The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.

Theoretical Explanation for Lower Order Harmonic Resonance Phenomenon of Three-Ring Gear Transmissions

Dynamic investigations revealed that lower order harmonic resonance phenomenon exists in the three ring gear transmission. That is, when the input speed is close to 1/3, 1/6, 1/9,…, 1/3 n of the primary natural frequency of the transmission, the loads on the bearings and gears are especially high. This paper explained this phenomenon from the viewpoint of parametric resonance in terms of perturbation technique. A conclusion was drawn that the basic reason for this phenomenon is the primary resonance caused by forcing excitation and parametric resonance caused by parametric change.

THE GENERALIZED LOWER ORDER OF DIRICHLET SERIES

In this paper,we study the generalized lower order of entire functions defined by Dirichlet series.By constructing the Newton polygon based on Knopp-Kojima’s formula,we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.

The Lower Order and Type of Solutions of Second Order Differential Equation

The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0,where A(z)is a polynomial.In the case of A(z)=a_dz^d,the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to(d+2)/2 and(2(|a_d|)^(1/2))/(d+2)respectively.In the case of A(z)=a_dz^d+a_(d-1)z^(d-1)+…a_1z+a_0,a_d>0,a_(d-1)>0,…,a_1≥0,a_0≥0,the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is(d+2)/2.

Construction of Split-Plot Designs with General Minimum Lower Order Confounding

Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.

DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.

New blind estimation method of evoked potentials based on minimum dispersion criterion and fractional lower order statistics

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Tra-ditional EP analysis methods are developed under the condition that the background noises in EP are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noises than Gaussian distribution in biomedical signal proc-essing. Conventional blind separation and es-timation method of evoked potentials is based on second order statistics or high order Statis-tics. Conventional blind separation and estima-tion method of evoked potentials is based on second order statistics (SOS). In this paper, we propose a new algorithm based on minimum dispersion criterion and fractional lower order statistics. The simulation experiments show that the proposed new algorithm is more robust than the conventional algorithm.

Some Results on Entire Functions of Finite Lower Order

Let f（z） be an entire function of order λ and of finite lower order μ. If the zeros of f（z） accumulate in the vicinity of a finite number of rays, then （a） λ is finite; （b） for every arbitrary number k1】1, there exists k2】1 such that T（k1r, f）≤k2T（r, f） for all r≥r0. Applying the above results, we prove that if f（z） is extremal for Yang’s inequality p=g/2, then （c） every deficient value of f（z） is also its asymptotic value; （d） every asymptotic value of f（z） is also its deficient value; （e） λ=μ; （f） ∑a≠∞δ5（a, f）≤1-k（μ）.

A theory on constructing blocked two-level designs with general minimum lower order confounding

Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.

Lower Approximation Reduction in Ordered Information System with Fuzzy Decision

Attribute reduction is one of the most important problems in rough set theory. This paper introduces the concept of lower approximation reduction in ordered information systems with fuzzy decision. Moreover, the judgment theorem and discernable matrix are obtained, in which case an approach to attribute reduction in ordered information system with fuzzy decision is constructed. As an application of lower approximation reduction, some examples are applied to examine the validity of works obtained in our works..

Direction finding of bistatic MIMO radar in strong impulse noise

For bistatic multiple-input multiple-output(MIMO)radar,this paper presents a robust and direction finding method in strong impulse noise environment.By means of a new lower order covariance,the method is effective in suppressing impulse noise and achieving superior direction finding performance using the maximum likelihood(ML)estimation method.A quantum equilibrium optimizer algorithm(QEOA)is devised to resolve the corresponding objective function for efficient and accurate direc-tion finding.The results of simulation reveal the capability of the presented method in success rate and root mean square error over existing direction-finding methods in different application situations,e.g.,locating coherent signal sources with very few snapshots in strong impulse noise.Other than that,the Cramér-Rao bound(CRB)under impulse noise environment has been drawn to test the capability of the presented method.

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

Research on Outcrop Sequence Stratigraphy of Permian in Middle-Lower Yangtze Region

According to the latest International Chronostratigraphic Scheme (ICS, 2000), the Permian in the Middle Lower Yangtze region of South China can be divided into three series and nine stages relevant to the traditional six stages of South China. From Assellian to Changxingian of Permian, 44 Ma in age range, the strata are composed of 14 third order sequences, each of which is 3.14 Ma in average age range. There is one third order sequence of Zisongian, equivalent to middle and upper Chuanshan Formation or equal to Asselian and two thirds of Sakmarian. There are two third order sequences, corresponding to Liang shan Formation or Zhenjiang Formation and upper Chuanshan Formation, which are assigned to Longlingian, coinciding with Artinskian and one third of Sakmarian. In addition, three third order sequences, equal to Qixia Formation, are attributed to Chihsian, corresponding to Kubergandian and one third of Roadian. Four third order sequences, comprising Gufeng, Maokou, Yanqiao, Yinping and Wuxue formations, are assigned to Maokouan, equivalent to two thirds of Roadian, Wordian and Capitanian. Two third order sequences, equal to Longtan Formation or Wujiaping Formation, are included in Wuchiapingian. Other two third order sequences, corresponding to Changxing Formation or Dalong Formation, are assigned to Changhsingian. In brief, these above third order sequences can be incorporated into 4 sequences sets.

Existence of Positive Solutions for A Fourth-order Boundary Value Problems with p-Laplacian Operators

This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory.

三水平逆耶茨序设计的低阶混杂性质

在三水平正规设计中,低阶成分效应的混杂信息对选择最优设计至关重要.本文研究一类三水平逆耶茨序设计Dq(n),其中q为独立列个数,n为因子个数,得到设计Dq(n)在三种情况下低阶混杂信息的结果:(i)q<n<3q-1,n=2k,k∈N;(ii)q<n<3q-1;n=2k+1;k∈N;(iii)3q-1≤n<(3q-1)/2.通过实例来演示上述结果.

Existence of Solutions to the Higher Order Nonlinear Differential Equations

This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 >0 and c～2+d～2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.

极限下限分析的区域光滑径向点插值法

极限分析的高效数值计算方法在结构设计和安全评定中具有非常重要的作用.为了更加有效地求解极限分析问题,将区域光滑径向点插值法与二阶锥规划相结合,提出了理想弹塑性结构极限下限分析的一种新方法.将问题域离散为简单的三角形背景单元,每个单元进一步划分成若干个光滑域.为了将复杂的域积分转化为简单的边界积分,并且避免计算形函数的导数,采用广义梯度光滑技术对每个光滑域进行应变光滑处理.由于径向点插值法构造的形函数满足Kronecker delta性质,本质边界条件可以直接施加.依据下限定理,在满足以等效积分弱形式表达的自平衡应力场平衡条件的基础上,用二阶锥规划成功构建了极限分析下限法的计算模型,从而可方便地通过基于原始-对偶内点法的数学规划求解器MOSEK直接求解该问题.数值算例结果表明,本文所提方法有效地克服了维数障碍问题,具有较高的计算精度,并且计算结果对网格畸变十分不敏感.

灾后应急配送中心选址问题的降阶回溯算法

近年来自然灾害频发,提高灾后应急物资的配送效率一直以来都是性命攸关的大事,因此文章基于灾后应急配送中心选址问题的精确算法进行研究。首先,建立该问题的数学模型并对该问题中的数学性质进行研究和证明;其次,在这些数学性质的基础上,设计上下界子算法和降阶子算法,这些子算法能够有效减少解空间,提高算法的效率,使该算法能够更有效地处理规模更大的问题;再次,提出降阶回溯子算法,通过剪枝和局部降阶进一步缩小问题的搜索规模,并能得到最优解;最后,通过分析和解决一个案例来更清楚地说明算法的原理和操作步骤。

奖励-收集Steiner树问题的精确算法

奖励-收集Steiner树问题是图的Steiner最小树问题的衍生,同时也是组合优化中的NP-hard问题。首先,提出该问题的数学性质并给出证明,利用数学性质能降低该问题的规模;其次,基于该问题的数学性质设计出上下界子算法、降阶子算法和回溯子算法,通过上下界子算法和降阶子算法可以降低该问题解空间的规模,从而缩短回溯子算法的搜索时间,进而降低求解该问题最优解的时间;最后,应用案例分析、算例分析以及算法分析与对比表明,所设计的算法不仅可以求出该问题的最优解,而且比没有考虑该问题数学性质的一般回溯算法的时间复杂度更低。