We study a class of nonlinear elliptic equations with nonstandard growth condition.The main feature is that two lower order terms,a non-coercive divergence term divΦ(x,u)and a gradient term H(x,u,▽u)with no growth r...We study a class of nonlinear elliptic equations with nonstandard growth condition.The main feature is that two lower order terms,a non-coercive divergence term divΦ(x,u)and a gradient term H(x,u,▽u)with no growth restriction on u,appear simultaneously in the variable exponents setting.These characteristics prevent us from directly obtaining the existence of solutions by employing the classical theory on existence results.By choosing some appropriate test functions in the perturbed problem,some a priori estimates are obtained under the variable exponent framework.Based on these estimates,we prove the almost everywhere convergence of the gradient sequence{▽u^(ε)}_(ε),which helps to pass to the limit to find a weak solution.展开更多
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 t...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.展开更多
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...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.展开更多
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 frequ...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.展开更多
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 t...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.展开更多
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 ...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.展开更多
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 attracti...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.展开更多
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 ...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.展开更多
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. A...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.展开更多
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 k<...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 k<sub>1</sub>】1, there exists k<sub>2</sub>】1 such that T（k<sub>1</sub>r, f）≤k<sub>2</sub>T（r, f） for all r≥r<sub>0</sub>. 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）.展开更多
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 ex...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.展开更多
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 judgm...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..展开更多
The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorp...The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorphic coefficients, and ci, i = 0,..., n being distinct complex numbers,where there is only one dominant coefficient.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)the University-Level Research Fund Project in Guizhou University of Finance and Economics(Grant No.2022KYYB01)。
文摘We study a class of nonlinear elliptic equations with nonstandard growth condition.The main feature is that two lower order terms,a non-coercive divergence term divΦ(x,u)and a gradient term H(x,u,▽u)with no growth restriction on u,appear simultaneously in the variable exponents setting.These characteristics prevent us from directly obtaining the existence of solutions by employing the classical theory on existence results.By choosing some appropriate test functions in the perturbed problem,some a priori estimates are obtained under the variable exponent framework.Based on these estimates,we prove the almost everywhere convergence of the gradient sequence{▽u^(ε)}_(ε),which helps to pass to the limit to find a weak solution.
文摘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.
基金supported by the National Natural Sci-ence Foundation of China(11501127)Natural Science Foundation of Guangdong Province(2016A030313686)+1 种基金the Training Program for Outstanding Young Teachers in University of Guangdong Province(312XCQ14564)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2013LYM0027,2014KQNCX068)
文摘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.
基金Partly supported by the Open Fund of theState Key Lab.of Mechanical TransmissionChongqing U niv
文摘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.
基金the National Natural Science Foundation of China(11501127)Natural Science Foundation of Guangdong Province(2018A030313954).
文摘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.
基金Foundation item： Supported by the NNSF of China（11201395） Supported by the Science Foundation of Educational Commission of Hubei Province（Q20132801）
文摘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.
文摘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.
基金supported in part by the National Natural Science Foundation of China(61301228,61371091)the Fundamental Research Funds for the Central Universities(3132014212)
文摘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.
文摘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.
文摘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 k<sub>1</sub>】1, there exists k<sub>2</sub>】1 such that T（k<sub>1</sub>r, f）≤k<sub>2</sub>T（r, f） for all r≥r<sub>0</sub>. 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）.
文摘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.
文摘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..
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123311171119)+1 种基金the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211002)the Youth Science Foundation of Education Bureau of Jiangxi Province(Grant No.GJJ14271)
文摘The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorphic coefficients, and ci, i = 0,..., n being distinct complex numbers,where there is only one dominant coefficient.
