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ON SOME GENERALIZED DIFFERENCE PARANORMED SEQUENCE SPACES ASSOCIATED WITH MULTIPLIER SEQUENCE DEFINED BY MODULUS FUNCTION 被引量:5
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作者 Binod Chandra Tripathy Prabhat Chandra 《Analysis in Theory and Applications》 2011年第1期21-27,共7页
In this article we introduce the paranormed sequence spaces (f,A, Am,p), c0(f,A,Am,p) and L00(f,A, Am,p), associated with the multiplier sequence ∧ = (hk), defined by a modulus function f. We study their diff... In this article we introduce the paranormed sequence spaces (f,A, Am,p), c0(f,A,Am,p) and L00(f,A, Am,p), associated with the multiplier sequence ∧ = (hk), defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results. 展开更多
关键词 paranorm solid space symmetric space difference sequence modulus function multiplier seuence
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SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m 被引量:5
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作者 Harun Polat Feyzi Basar 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期254-266,共13页
Kizmaz [13] studied the difference sequence spaces ∞(A), c(A), and co(A). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Alta... Kizmaz [13] studied the difference sequence spaces ∞(A), c(A), and co(A). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m))consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m)), and the Schauder basis of the spaces e0^r△^(m)), ec^r△^(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^(m)). 展开更多
关键词 Difference sequence spaces of order m Schauder basis the α- β- and γ-duals matrix mappings
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CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m 被引量:2
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作者 Ivana Djolovi Eberhard Malkowsky 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1465-1474,共10页
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ (... In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness. 展开更多
关键词 difference sequence spaces of order m matrix transformations compact operators Hausdorff measure of noncompactness
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SOME GEOMETRIC PROPERTIES OF A NEW DIFFERENCE SEQUENCE SPACE INVOLVING LACUNARY SEQUENCES 被引量:1
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作者 Murat KARAKAS Mikail ET Vatan KARAKAYA 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1711-1720,共10页
In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property (β) for this space and also show that it is not rotund where p = (pr)... In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property (β) for this space and also show that it is not rotund where p = (pr) is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N. 展开更多
关键词 difference sequence space lacunary sequence k-NUC property ROTUNDITY Luxemburg norm
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ON THE m^(th) ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS 被引量:1
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作者 Metin BASARIR Emrah Evren KARA 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期797-813,共17页
In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; △(m)), which consist of the sequences whose generalized weighted △(m)-di... In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; △(m)), which consist of the sequences whose generalized weighted △(m)-difference means are in the linear space l(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l(u, v, p, △(m)) to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp(U, v, △(m)) (1 ≤ p 〈 ∞). 展开更多
关键词 Paranormed sequence spaces difference sequence spaces weighted mean α- β γ-duals matrix mappings Hausdorff measure of noncompactness compactoperators
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SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI
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作者 Ayhan Esi Mehmet Aikgz 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期229-236,共8页
In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.
关键词 Fuzzy numbers paranorm difference sequences modulus function
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PROPERTIES OF SOME SETS OF SEQUENCES DEFINED BY A MODULUS FUNCTION
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作者 Yavuz Altin 《Acta Mathematica Scientia》 SCIE CSCD 2009年第2期427-434,共8页
In this article, the author introduces the generalized difference paranormed sequence spaces c (△v^m, f, p, q, s), c0 (△v^m, f, p, q, s), and l∞ (△v^m, f, p, q, s) defined over a seminormed sequence space (... In this article, the author introduces the generalized difference paranormed sequence spaces c (△v^m, f, p, q, s), c0 (△v^m, f, p, q, s), and l∞ (△v^m, f, p, q, s) defined over a seminormed sequence space (X, q). The author also studies their properties like completeness, solidity, symmetricitv, etc. 展开更多
关键词 Difference sequence modulus function SEMINORM
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On some difference sequence spaces defined by a sequence of Orlicz functions
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作者 ASMA BEKTA■ i■dem 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期2093-2096,共4页
The idea of difference sequence spaces was introduced in (Klzmaz, 1981) and this concept was generalized in (Et and Colak, 1995). In this paper we define some difference sequence spaces by a sequence of Orlicz fun... The idea of difference sequence spaces was introduced in (Klzmaz, 1981) and this concept was generalized in (Et and Colak, 1995). In this paper we define some difference sequence spaces by a sequence of Orlicz functions and establish some inclusion relations. 展开更多
关键词 Difference sequence Orlicz function sequence of Orlicz functions Strongly almost convergent
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Some new generalized difference sequence spaces defined by a sequence of moduli
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作者 Vakeel A Khan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第1期104-108,共5页
The idea of difference sequence sets X(△) = {x = (xk) : △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence sp... The idea of difference sequence sets X(△) = {x = (xk) : △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations. 展开更多
关键词 Difference sequence space sequence of moduli inclusion relation.
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On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences
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作者 Gan Shi-xin 1, Qiu De-hua 2 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 2. Department of Mathematics, Hengyang Teacher’s College, Hengyang 421008, Hunan, China 《Wuhan University Journal of Natural Sciences》 CAS 2002年第2期133-136,共4页
Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are ob... Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained. 展开更多
关键词 p-smoothable Banach space weighted partial sum martingale difference sequence strong law of large numbers
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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES
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作者 甘师信 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1021-1028,共8页
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen... We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions. 展开更多
关键词 Strong law of large number almost sure convergence Lp convergence weighted sums Banach space valued random element sequence Banach space martingale difference sequence
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Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications
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作者 WANG XUE-JUN SHEN YAN HU SHU-HE YANG WEN-ZHI 《Communications in Mathematical Research》 CSCD 2011年第1期6-16,共11页
In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences a... In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57(2002) and 78(2008). Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences. 展开更多
关键词 Hajek-Renyi-type inequality associated random variable sequence strongly positive dependent stochastic sequence martingale difference sequence
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Strong Limit Theorems for Arbitrary Fuzzy Stochastic Sequences
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作者 费为银 《Journal of Donghua University(English Edition)》 EI CAS 2008年第5期556-560,共5页
Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are ext... Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are extended. In order to prove results of this paper, the notion of fuzzy martingale difference sequences is also introduced. 展开更多
关键词 fuzzy random variables fuzzy conditional expectation strong law of large numbers fuzzy stochastic sequences fuzzy martingale difference sequences
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QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
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作者 郑惠萍 薛禹胜 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第9期1138-1145,共8页
Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based sta... Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare are determined. 展开更多
关键词 nonlinear rotor system BIFURCATION stability margin extended phase plane dynamic central point kinetic energy difference sequence
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A note on strong law of large numbers of random variables
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作者 LIN Zheng-yan SHEN Xin-mei 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第6期1088-1091,共4页
In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker tha... In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix. 展开更多
关键词 Strong law of large numbers (SLLN) Martingale difference sequence A-summable sequence
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Precise Synthesis of Acrylate Copolymer via RAFT Polymerization and Its Application
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作者 Lei Li Jinxing Song +4 位作者 Xin Yang Shengpeng Wang Zuguang Li Yingying Chen Aiyuan You 《Journal of Materials Science and Chemical Engineering》 2021年第6期59-67,共9页
<div style="text-align:justify;"> A series of different sequence structure containing stearyl acrylate (SA) and hydroxyethyl acrylate (HEA) copolymer were synthesized via reversible addition-fragmentat... <div style="text-align:justify;"> A series of different sequence structure containing stearyl acrylate (SA) and hydroxyethyl acrylate (HEA) copolymer were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization. The crystallization property of PHEA-<em>b</em>-PSA, PHEA-<em>b</em>-PSA-<em>b</em>-PHEA, PSA-<em>b</em>-PHEA-<em>b</em>-PSA, PHEA-<em>co</em>-PSA, and PHEA-<em>grad-b</em>-PSA were characterized by Differential Scanning Calorimetry (DSC). The condensed structure of different sequence copolymers were investigated using small-angle X-ray scattering (SAXS). A series of copolymers with different sequence structure were coated on the surface of polyester fabric, which can be found that PHEA-b-PSA-b-PHEA block copolymer has good water repellency. </div> 展开更多
关键词 RAFT Polymerization Different sequence Structure Crystallization Prop-erty Water Repellency
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The stability of E protein gene of the Japanese encephalitis live attenuated vaccine virus SA_(14)-14-2
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作者 XING LIANG FAN YONG XIN YU DE FU LI LI LI JIA 《Journal of Microbiology and Immunology》 2005年第3期206-210,共5页
The purpose of this study was to understand the stability and possibility of back mutation of Japanese encephalitis (JE) attenuated vaccine virus strain SA14-14-2 HKs on molecular level. The E genes of the SA14-14-2... The purpose of this study was to understand the stability and possibility of back mutation of Japanese encephalitis (JE) attenuated vaccine virus strain SA14-14-2 HKs on molecular level. The E genes of the SA14-14-2 HKs vaccine virus and its PHK cells passaged virus (SA14-14-2 HK17 ), its mouse brain passaged virus (SA14-14-2 SM1 ) were sequenced and compared with the E gene of parental SAI4 virus. The total RNA was extracted from infected Vero cells and amplified by RT-PCR. The RT-PCR products were purified and cloned into T-vector. Positive clones were screened, identified and sequenced. There were twelve nucleotides and eight amino acids substitutions between SA14 parent virus and SA14-34-2 PHKs vaccine virus. The SA14-14-2 PHK17 virus showed two additional mutations (E-331 and E-398) which were not back mutations. Although five additional mutations were found in SA14-34-2 SMt virus, only one (E-307) was back mutation. Genetic characteristics of the attenuated vaccine virus SA14- 34-2 were stable when it was passaged 37 times on PHK cells or one time in mouse brains. 展开更多
关键词 Japanese encephalitis attenuated virus Viruses of different passages E gene sequence
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Statistically Convergent Difference Double Sequence Spaces 被引量:4
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作者 Binod Chandra TRIPATHY Bipul SARMA Mathematical Sciences Division,Institute of Advanced Study in Science and Technology,Paschim Boragaon Garchuk +1 位作者 Guwahati- 781 035 India 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第5期737-742,共6页
In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces 2l∞(△, q), 2c(△, q), 2cB(△, q), 2cR(△, q), 2cBR(△,q) etc. being symmetric, soli... In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces 2l∞(△, q), 2c(△, q), 2cB(△, q), 2cR(△, q), 2cBR(△,q) etc. being symmetric, solid, monotone, etc. We prove some inclusion results too. 展开更多
关键词 difference sequence statistical convergence COMPLETENESS solid space SYMMETRIC
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The Dual Spaces of Sets of Difference Sequences of Order m and Matrix Transformations 被引量:4
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作者 Eberhard MALKOWSKY M.MURSALEEN Suthep SUANTAI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第3期521-532,共12页
Let p = (pk)k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = (xk)k=0^∞ is any sequence of complex numbers we write Δ(m)x for the sequence of the m th order dif... Let p = (pk)k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = (xk)k=0^∞ is any sequence of complex numbers we write Δ(m)x for the sequence of the m th order differences of x and Δu^(m)X = {x=(x)k=0^∞ uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^(m)X for X=co(p),c(p),l∞(p) and characterize some matrix transformations between these spaces Δ^(m)X. 展开更多
关键词 difference sequences dual spaces matrix transformations
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On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions 被引量:3
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作者 Binod Chandra Tripathy Sabita Mahanta 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第2期231-238,共8页
In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞ using m^(th)- difference.We study their properties like completeness,solidness,symm... In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞ using m^(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞ and the Cesàro summable and strongly Cesàro summable sequences. 展开更多
关键词 Orlicz function lacunary sequence strong convergence difference sequence space
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