The main purpose of this paper is to study the mean value properties of thesecond Smarandache pseudo-odd number sequence and pseudo-even number sequence, andgive some interesting asymptotic formula for them.
We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new ...We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.展开更多
In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^...In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.展开更多
Molecular profiling of gene expression is important for determining signatures in cancer progression and diagnosis.For this purpose,polymerase chain reactionbased techniques are preferentially used as a feasible and s...Molecular profiling of gene expression is important for determining signatures in cancer progression and diagnosis.For this purpose,polymerase chain reactionbased techniques are preferentially used as a feasible and sensitive approach.Nevertheless,when relative quantitative analyses are performed on gene expression,the interpretation of mathematical equations must be carefully done.This letter to the editor is focused on recently published gene expression data in World Journal of Gastroenterology by Ozmen et al demonstrating increased levels of LYVE-1,VEGFR-3 and CD44 genes in gastric cancer samples compared to nonneoplastic gastric tissues.However,there are major concerns about misinterpretation of the gene expression data obtained with the 2-ΔΔCt relative quantitative method.In the study,2-ΔΔCt values calculated for many samples were smaller than 1(2-ΔΔCt < 1) which indicate decreased levels of LYVE-1,VEGFR-3 and CD44 gene expression in the gastric cancer tissues.This unfortunate mistake is an important example showing how a simple error in the interpretation of relative-quantitative gene expression data may result in misleading scientific conclusions.In this letter,a brief explanation of the 2-ΔΔCt method is given.In addition,the importance of technical quality and interpretation in gene expression studies is discussed.展开更多
In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for t...In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.展开更多
In this work, a new model reduction technique is introduced. The proposed technique is derived using the matrix reducibility concept. The eigenvalues of the reduced model are preserved; that is, the reduced model eige...In this work, a new model reduction technique is introduced. The proposed technique is derived using the matrix reducibility concept. The eigenvalues of the reduced model are preserved; that is, the reduced model eigenvalues are a subset of the full order model eigenvalues. This preservation of the eigenvalues makes the mathematical model closer to the physical model. Finally, the outcomes of this method are fully illustrated using simulations of two numeric examples.展开更多
Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1t...Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1tdt for x∈[0,1] if and only if α＋β≥1.This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.展开更多
In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.
In this note, the author find an upper bound formula for the number of the p × p normalized Latin Square,the first row and column of which are both standard order 1, 2,…p.
In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y...In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.展开更多
Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e...Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.展开更多
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary m...Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.展开更多
This paper gives and verifies a mathematical model with only one argument which determines the movement parameters of any point in a plane four-bar linkage on the basis of the analysis of mining machinery linkages. C ...This paper gives and verifies a mathematical model with only one argument which determines the movement parameters of any point in a plane four-bar linkage on the basis of the analysis of mining machinery linkages. C A A (computer aided analysis) based on the mathemetical model can be used to make not only the quick and accurate analysis and design of mining machinery linkages but also the movement analysis and optimization design of any other plane four-bar linkage.展开更多
Problems, which are studied in the paper, concern to theoretical aspects of interpolation theory. As is known, interpolation is one of the methods for approximate representation or recovery of functions on the basis o...Problems, which are studied in the paper, concern to theoretical aspects of interpolation theory. As is known, interpolation is one of the methods for approximate representation or recovery of functions on the basis of their given values at points of a grid. Interpolating functions can be chosen by many various ways. In the paper the authors are interested in interpolating functions, for which the Laplace operator, applied to them, has a minimal norm. The authors interpolate infinite bounded sequences at the knots of the square grid in Euclidian space. The considered problem is formulated as an extremal one. The main result of the paper is the theorem, in which certain estimates for the uniform norm of the Laplace operator applied to smooth interpolating functions of two real variables are established for the class of all bounded （in the corresponding discrete norm） interpolated sequences. Also connections of the considered interpolation problem with other problems and with embeddings of the Sobolev classes into the space of continuous functions are discussed. In the final part of the main section of the paper, the authors formulate some open problems in this area and sketch possible approaches to the search of solutions. In order to prove the main results, the authors use methods of classical mathematical analysis and the theory of polynomial splines of one variable with equidistant knots.展开更多
This document reviews the development of adult education towards Hong Kong, Macao and the Overseas over the past 30 years in Jinan University, and puts forward ideas for the development under the background of＂The Be...This document reviews the development of adult education towards Hong Kong, Macao and the Overseas over the past 30 years in Jinan University, and puts forward ideas for the development under the background of＂The Belt and Road＂. Such as： Increase policy support and enhance the level of management services; Based on big data analytics, optimize the mode of talent training; Develop short-term training projects and promote online education; Establish brand awareness and improve teaching quality monitoring mechanisms.展开更多
In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then c...In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.展开更多
A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for ...A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.展开更多
Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is： when does composition commute wi...Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is： when does composition commute with λ-Grobner basis computation？ We shall answer better the above question. This has a natural application in the computation of λ-Grobner bases.展开更多
Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued fu...Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.展开更多
文摘The main purpose of this paper is to study the mean value properties of thesecond Smarandache pseudo-odd number sequence and pseudo-even number sequence, andgive some interesting asymptotic formula for them.
基金National Natural Science Foundation of China under Grant No.10675065
文摘We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.
基金the National Natural Science Foundation of China(10671056)
文摘In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.
文摘Molecular profiling of gene expression is important for determining signatures in cancer progression and diagnosis.For this purpose,polymerase chain reactionbased techniques are preferentially used as a feasible and sensitive approach.Nevertheless,when relative quantitative analyses are performed on gene expression,the interpretation of mathematical equations must be carefully done.This letter to the editor is focused on recently published gene expression data in World Journal of Gastroenterology by Ozmen et al demonstrating increased levels of LYVE-1,VEGFR-3 and CD44 genes in gastric cancer samples compared to nonneoplastic gastric tissues.However,there are major concerns about misinterpretation of the gene expression data obtained with the 2-ΔΔCt relative quantitative method.In the study,2-ΔΔCt values calculated for many samples were smaller than 1(2-ΔΔCt < 1) which indicate decreased levels of LYVE-1,VEGFR-3 and CD44 gene expression in the gastric cancer tissues.This unfortunate mistake is an important example showing how a simple error in the interpretation of relative-quantitative gene expression data may result in misleading scientific conclusions.In this letter,a brief explanation of the 2-ΔΔCt method is given.In addition,the importance of technical quality and interpretation in gene expression studies is discussed.
基金Foundation item： Supported by the Scientific Research Common Program of Beijing Municipal Commission of Education of China（Km200611417009） Suppoted by the Natural Science Foundation of Fujian Province Education Department of China（JA05324）
文摘In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.
文摘In this work, a new model reduction technique is introduced. The proposed technique is derived using the matrix reducibility concept. The eigenvalues of the reduced model are preserved; that is, the reduced model eigenvalues are a subset of the full order model eigenvalues. This preservation of the eigenvalues makes the mathematical model closer to the physical model. Finally, the outcomes of this method are fully illustrated using simulations of two numeric examples.
文摘Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1tdt for x∈[0,1] if and only if α＋β≥1.This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.
基金Project supported by the Youth Science Foundation of Shanghai Municipal Commission of Education(Grant No.214511)the Research Grants Council of the Hong Kong SAR,China(Grant No.HKU7016/07)
文摘In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.
文摘In this note, the author find an upper bound formula for the number of the p × p normalized Latin Square,the first row and column of which are both standard order 1, 2,…p.
文摘In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.
基金the Young Foundation of Sichuan Province(06ZQ026-037) the Education Department Foundation of Sichuan Province(2005A1212006A084)
文摘Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
基金The authors would like to thank Prof. Y.D. Zhang for selfless helps and valuable discussions.
文摘Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.
文摘This paper gives and verifies a mathematical model with only one argument which determines the movement parameters of any point in a plane four-bar linkage on the basis of the analysis of mining machinery linkages. C A A (computer aided analysis) based on the mathemetical model can be used to make not only the quick and accurate analysis and design of mining machinery linkages but also the movement analysis and optimization design of any other plane four-bar linkage.
文摘Problems, which are studied in the paper, concern to theoretical aspects of interpolation theory. As is known, interpolation is one of the methods for approximate representation or recovery of functions on the basis of their given values at points of a grid. Interpolating functions can be chosen by many various ways. In the paper the authors are interested in interpolating functions, for which the Laplace operator, applied to them, has a minimal norm. The authors interpolate infinite bounded sequences at the knots of the square grid in Euclidian space. The considered problem is formulated as an extremal one. The main result of the paper is the theorem, in which certain estimates for the uniform norm of the Laplace operator applied to smooth interpolating functions of two real variables are established for the class of all bounded （in the corresponding discrete norm） interpolated sequences. Also connections of the considered interpolation problem with other problems and with embeddings of the Sobolev classes into the space of continuous functions are discussed. In the final part of the main section of the paper, the authors formulate some open problems in this area and sketch possible approaches to the search of solutions. In order to prove the main results, the authors use methods of classical mathematical analysis and the theory of polynomial splines of one variable with equidistant knots.
文摘This document reviews the development of adult education towards Hong Kong, Macao and the Overseas over the past 30 years in Jinan University, and puts forward ideas for the development under the background of＂The Belt and Road＂. Such as： Increase policy support and enhance the level of management services; Based on big data analytics, optimize the mode of talent training; Develop short-term training projects and promote online education; Establish brand awareness and improve teaching quality monitoring mechanisms.
基金The research is supported by the National Natural Science Foundation under Grant No. 10471130 and the Zhejiang Province Science Foundation under Grant No. Y604003. Acknowledgements The author thanks the referees for giving valuable comments on this paper which make him rewrite this paper in a better form.
文摘In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.
文摘A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.
基金The research is supported by the National Natural Science Foundation of China under Grant No. 10771058, Hunan Provincial Natural Science Foundation of China under Grant No. o6jj20053, and Scientific Research Fund of Hunan Provincial Education Department under Grant No. 06A017.
文摘Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is： when does composition commute with λ-Grobner basis computation？ We shall answer better the above question. This has a natural application in the computation of λ-Grobner bases.
基金the National Natural Science Foundation of China （No. 10771171） the Scientific Research Item of Gansu Education Department （No. 0601-20）.
文摘Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.
