Mathematica Slovaca (MATH SLOVACA)

Publications in this journal

• Article: Boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

  Ushangi Goginava, Karoly Nagy
  Mathematica Slovaca 01/2013;
• Article: Complete moment convergence of moving average processes under ρ-mixing assumption

  Xing-Cai Zhou, Jin-Guan Lin
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  ABSTRACT: Let {Y i : −∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, and {a i : −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper we prove the complete moment convergence for the partial sums of moving average processes { Xn = åi = - ¥¥ ai Yi + n, n \geqslant 1 } \{ X_n = \sum\limits_{i = - \infty }^\infty {a_i Y_{i + n,} n \geqslant 1} \} based on the sequence {Y i : −∞ < i < ∞} of ρ-mixing random variables under some suitable conditions. Keywordsmoving average– ρ-mixing–complete moment convergence
  Mathematica Slovaca 05/2012; 61(6):979-992.
• Article: Effect-like algebras induced by means of basic algebras

  Ivan Chajda
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  ABSTRACT: Having an MV-algebra, we can restrict its binary operation addition only to the pairs of orthogonal elements. The resulting structure is known as an effect algebra, precisely distributive lattice effect algebra. Basic algebras were introduced as a generalization of MV-algebras. Hence, there is a natural question what an effect-like algebra can be reached by the above mentioned construction if an MV-algebra is replaced by a basic algebra. This is answered in the paper and properties of these effect-like algebras are studied.
  Mathematica Slovaca 05/2012; 60(1):21-32.
• Article: On the existence of solutions for singular boundary value problem of third-order differential equations

  Feng Wang, Yujun Cui
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  ABSTRACT: The singular boundary value problems of third-order differential equations $ {*{20}c} { - u'''(t) = h(t)f(t,u(t)), t \in (0,1),} \\ {u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\ $ \begin{array}{*{20}c} { - u'''(t) = h(t)f(t,u(t)), t \in (0,1),} \\ {u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\ \end{array} are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(t) is allowed to be singular at both t = 0 and t = 1, and f is not necessary to be nonnegative. The existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory. Keywordssingular-nontrivial solutions-positive solutions-topology degree 2000 Mathematics Subject ClassificationPrimary 34B10, 34B18
  Mathematica Slovaca 05/2012; 60(4):485-494.
• Article: Perfect residuated lattice ordered monoids

  Jiří Rachůnek, Dana Šalounová
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  ABSTRACT: Bounded Rℓ-monoids form a large subclass of the class of residuated lattices which contains certain of algebras of fuzzy and intuitionistic logics, such as GMV-algebras (= pseudo-MV-algebras), pseudo-BL-algebras and Heyting algebras. Moreover, GMV-algebras and pseudo-BL-algebras can be recognized as special kinds of pseudo-MV-effect algebras and pseudo-weak MV-effect algebras, i.e., as algebras of some quantum logics. In the paper, bipartite, local and perfect Rℓ-monoids are investigated and it is shown that every good perfect Rℓ-monoid has a state (= an analogue of probability measure). Keywords Rℓ-monoid-pseudo BL-algebra-pseudo MV-algebra-local Rℓ-monoid-perfect Rℓ-monoid 2000 Mathematics Subject ClassificationPrimary 06D35, 06F05
  Mathematica Slovaca 05/2012; 60(6):823-838.
• Article: On estimations of dispersion of ratio block sequences

  József Bukor, Peter Csiba
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  ABSTRACT: Using new characteristics of an infinite subset of positive integers we give some estimations of the dispersion of the related block sequence.
  Mathematica Slovaca 05/2012; 59(3):283-290.
• Article: Deductive systems of a cone algebra — II: Isomorphism theorem

  N. V. Subrahmanyam
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  ABSTRACT: We prove that there is an isomorphism φ of the lattice of deductive systems of a cone algebra onto the lattice of convex ℓ-subgroups of a lattice ordered group (determined by the cone algebra) such that for any deductive system A of the cone algebra, A is respectively a prime, normal or polar if and only if φ(A) is a prime convex ℓ-subgroup, ℓ-ideal or polar subgroup of the ℓ-group, thus generalizing and extending the result of Rachůnek that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex ℓ-subgroups of a unital lattice ordered group.
  Mathematica Slovaca 05/2012; 58(6):671-684.
• Article: Weak MV-algebras

  Radomír Halaš, Luboš Plojhar
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  ABSTRACT: In a recent paper [CHAJDA, I.—KÜHR, J.: A non-associative generalization of MV-algebras, Math. Slovaca 57, (2007), 301–312], authors introduced and studied a non-associative generalization of MV-algebras called NMV-algebras. In contrast to MV-algebras, sections (i.e. principal filters) in NMV-algebras which are proper (i.e. are not MV-algebras), do not admit a structure of an NMV-algebra with respect to the operations defined in a natural way. The aim of the paper is to present a new class of algebras generalizing MV-algebras but sharing the above property.
  Mathematica Slovaca 05/2012; 58(3):253-262.
• Article: Geometry of isometric reflection vectors

  Francisco Javier García-Pacheco
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  ABSTRACT: In this paper we study the geometry of isometric reflection vectors. In particular, we generalize known results by proving that the minimal face that contains an isometric reflection vector must be an exposed face. We also solve an open question by showing that there are isometric reflection vectors in any two dimensional subspace that are not isometric reflection vectors in the whole space. Finally, we prove that the previous situation does not hold in smooth spaces, and study the orthogonality properties of isometric reflection vectors in those spaces. Keywordsisometric reflection vector–exposed point
  Mathematica Slovaca 05/2012; 61(5):807-816.
• Article: First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

  Xiao-Ming Zeng, Fuhua (Frank) Cheng
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  ABSTRACT: A sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators M n . This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators M n . The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible. Keywordsabsolute moment–Meyer-König and Zeller operators–approximation–absolutely continuous functions
  Mathematica Slovaca 05/2012; 61(4):635-644.
• Article: Higher degrees of distributivity in complete generalized MV-algebras

  Ján Jakubík
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  ABSTRACT: We apply the notion of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis. Let M be a complete GMV-algebra and let α be a cardinal. We prove that M is α-distributive if and only if it is (α, 2)-distributive. We deal with direct summands of M which are homogeneous with respect to higher degrees of distributivity. Keywordsgeneralized MV-algebra–completeness–higher degrees of distributivity–direct product
  Mathematica Slovaca 05/2012; 61(3):341-354.
• Article: On primitive for the GAP-integral

  D. K. Ganguly, Ranu Mukherjee
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  ABSTRACT: The concept of the GAP-integral was introduced by the authors. In this paper some results on primitive for the GAP-integral are presented. Keywordsapproximate full cover–density point–Δ-division–GAP-integral–Saks-Henstock lemma–nearly everywhere
  Mathematica Slovaca 05/2012; 61(4):665-673.
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  Article: Strongly almost (ω, λ, q)-summable sequences

  Mahmut Işik
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  ABSTRACT: The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (ω, λ, q)-summable with respect to a modulus function, then it is S(λ q )-statistically convergent. Keywords(ω, λ, q)-summability–statistical convergence–modulus function
  Mathematica Slovaca 05/2012; 61(5):779-788.
• Article: Absolutely continuous variational measures of Mawhin’s type

  Francesco Tulone, Yurij Zherebyov
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  ABSTRACT: In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F- and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodým theorem for these measures. Keywordsderivation basis–variational measure–Mawhin integral– F-integral– BV-integral–Radon-Nikodým derivative
  Mathematica Slovaca 05/2012; 61(5):747-768.
• Article: Neighborhoods and convergence with respect to a closure operator

  Josef Šlapal
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  ABSTRACT: We study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways. Keywordscategorical closure operator–neighborhood–separation–compactness–convergence
  Mathematica Slovaca 05/2012; 61(5):717-732.
• Article: Uniqueness and set sharing of derivatives of meromorphic functions

  Abhijit Banerjee, Pranab Bhattacharjee
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  ABSTRACT: We prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share two or three sets which will improve some existing results. Keywordsmeromorphic functions–uniqueness–weighted sharing–derivative–shared set
  Mathematica Slovaca 05/2012; 61(2):197-214.
• Article: Generalized difference sequence space defined by |, pk| summability and an Orlicz function in seminormed space

  Vinod K. Bhardwaj, Indu Bala
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  ABSTRACT: The object of this paper is to introduce a new difference sequence space which arise from the notions of |$ \bar N $ \bar N , p k | summability and an Orlicz function in seminormed complex linear space. Various algebraic and topological properties and certain inclusion relations involving this space have been discussed. This study generalizes results: [ALTIN, Y.—ET, M.—TRIPATHY, B. C.: The sequence space |$ \bar N_p $ \bar N_p |(M, r, q, s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423–430], [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$ \bar N $ \bar N , p n | summability, Demonstratio Math. 32 (1999), 539–546] and [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$ \bar N $ \bar N , p n | summability and an Orlicz function, Indian J. Pure Appl. Math. 31 (2000), 319–325]. Keywordsdifference sequence space-Orlicz function-summability-topological linear space 2000 Mathematics Subject ClassificationPrimary 40C05, 46A45
  Mathematica Slovaca 05/2012; 60(2):257-264.
• Article: Remark to an unambiguity of estimators in the universal linear statistical models with the type ii constraints

  Lubomír Kubáček
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  ABSTRACT: In the universal linear statistical model with the type II constraints, estimates of the unbiasedly estimable linear functions of the parameters of the mean value vector are given by special types of generalized matrix inverse. Since there exists many versions of such matrix inverse it is of some interest to check the unambiguity of obtained estimators. The aim of the paper is to find the best unbiased linear estimators of unbiasedly estimable functions and to show that they do not depend on the choice of the used generalized inverse of the matrices. Keywordsuniversal linear statistical model-type II constraints-unambiguity of estimators 2000 Mathematics Subject ClassificationPrimary 62J05
  Mathematica Slovaca 05/2012; 60(3):411-418.