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An incomplete block design for reducing competition between inbreds and hybrids in a diallel cross experiment
Item type: Journal Article • Journal: South African Journal of Plant and Soil • Authors: T. Hohls --- Department of Genetics, Republic of South Africa G. P.Y. Clarke --- Department of Statistics and Biometry, Republic of South AfricaInterplot competition in plant breeding experiments can substantially reduce the efficiency of plant selection. In diallel experiments on outcrossing species such as maize (Zea mays L.), competing stresses might result from differences in vigour between inbred and hybrid entries. A... -
Optimal implicational bases for finite modular lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Marcel WildEach finite closure system, whence each finite lattice, can be described in terms of "implicational bases" (called "covers of functional dependencies" in relational database theory). Although a NP - complete problem in general, it turns out that for modular lattices... -
AL- and AM-spaces of integrable scalar functions with respect to a Fréchet-valued measure
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Antonio Fernández Francisco NaranjoWe study the question of determining conditions for the space of R-valued integrable functions with respect to a vector measure taking its values in a real Fréchet space to be an AL- or an AM-space. -
Homomorphisms of complete distributive lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Pultr J. Sichler V. TrnkováThe category of all complete distributive lattices and their complete homomorphisms is universal, and this is also true for the category of all complete distributive lattices whose morphisms preserve complete joins, finite meets and an additional nullary operation. A survey... -
Natural Alternatives For One Dimensional Median Filtering
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: C.H. Rohwer M. WildFor practical purposes median smoothers have often been considered the basic components for the construction of simple non-linear smoothers for removing impulsive noise before any subsequent linear signal extraction from a sequence. Alternatives exist that are computationally convenient, conceptually simpler... -
On the Relationship Between Several Basic Categories in Fuzzy Topology
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Dexue ZhangIn this paper, a process, which associates with every fibre-small topo- logical category A and every completely distributive lattice L another topological category called the co-tower extension of A, is introduced to investigate the relationship between several basic categories in... -
Riesz Reasonable Cross Norms on Tensor Products of Banach Lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: C.C.A. LabuschagneIf E and F are Banach lattices and α is any reasonable cross norm on E ⊗ F, then there exists a reasonable cross norm | α | on E ⊗ F such that E ⊗ |α | F is... -
There is No Lattice Preserving Natural Tensor Norm
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Pérez-García Ignacio VillanuevaWe prove that for every natural tensor norm α, one can find a Banach lattice X such that the tensor product X ⊗ X endowed with the norm α does not have the Gordon-Lewis property and, therefore, cannot be isomorphic... -
Characterizing the one-sided tensor norms Δ P and T Δ P
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: C.C.A. Labuschagne. The Bochner norms Δ p for 1< p < ∞ on the vector valued L p -spaces are examples of reasonable cross norms which are not tensor norms. Using the order structure of L p (μ), a... -
A positive note on a counterexample by Arens
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gerard Buskes Robert PageIn his seminal paper [2], Arens gave an example of a positive bilinear map P : l 1 × l 1 → R that is not regular. In this note we show that for Banach lattices E such a bilinear... -
Binary trees equipped with semivaluations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: H. Pajoohesh M. SchellekensWe consider the set Tn of binary trees with n leaves. This set can be ordered by the so-called "imbalance" order, where two trees are related in the order iff the second is less "balanced" than the first. This order... -
A note on the M-norm of Chaney-Schaefer
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: StuartF. Cullender CoenraadC.A. LabuschagneWe give elementary proofs of known results concerning lattice and duality properties of the M-norm, introduced by Chaney and Schaefer, on the tensor product of a Banachspace and a Banach lattice. -
Categories of Dicompact bi-T 2 texture spaces and a Banach-Stone theorem
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Filiz Yildiz LawrenceM. BrownThe principal aim of this paper is to consider various aspects of the theory of dicompact bi-T 2 texture spaces, and place them in a categorical setting. It culminates in a version of the Banach-Stone theorem. On the way, a... -
Positive derivations on lattice ordered rings of matrices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Homeira PajooheshHere we consider a commutative ℓ-ring R with unit. We show that the only positive derivation on the ℓ-ring Mn (R) is 0 if and only if the only positive derivation on R is zero. Also, if the only positive... -
A vector lattice version of r˚ adström's embedding theorem
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: C.C.A. Labuschagne A.L. Pinchuck C.J. van AltenR˚ adström's embedding theorem for 'near vector spaces', which are essentially vector spaces without additive inverses, is extended to embeddings of 'near vector lattices', which are essentially vector lattices without additive inverses, into vector lattices. -
Ideals in Heyting Semilattices and Open Homomorphisms
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jorge Picado Aleš Pultr Anna TozziSubfitness and its relation to openness and completeness is studied in the context of Heyting semilattices. A formally weaker condition (c-subfitness) is shown to be necessary and sufficient for openness and completeness to coincide. For a large class of spatial... -
Fremlin tensor products of Banach lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Daniele PuglisiWe prove that the Fremlin tensor product of two Banach lattices with the Radon-Nikodym property, with one of them atomic, has the Radon-Nikodym property. -
IS THE CONSTRUCT OF L-TOPOLOGICAL SPACES A CO-TOWER EXTENSION OF SOME SIMPLER CONSTRUCT?
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Horst Herrlich --- Fachbereich 3, Mathematik, University of Bremen, Bremen, Germany, Dexue Zhang --- Department of Mathematics, Sichuan University, Chengdu, China,In an earlier paper, the second author associated with any fibre-small topological construct A and any completely distributive lattice L, an extension of A, called the (L-)-co-tower extension of A. He demonstrated that many familiar constructs in fuzzy topology can... -
Banach-Stone-like theorems for lattices of uniformly continuous functions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. Hušek --- , A. Pulgarín --- Avda. Universidad s/n, SpainNew couples of uniform spaces X, Y are found out for which a lattice isomorphism between U(X) and U(Y) implies a uniform homeomorphism between X and Y. -
Lattices of uniformly continuous functions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. Hušek --- , Czech Republic A. Pulgarín --- , SpainWe obtain an internal characterization of the lattice U (X) of real-valued uniformly continuous functions on a uniform space X. -
The class of b-AM-compact operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Belmesnaoui Aqzzouz --- Juridiques et Sociales, Département d'Economie, Morocco Jawad H'Michane --- Département de Mathématiques, MoroccoWe introduce and study a new class of operators that we call b-AM compact operators, and we establish necessary and sufficient conditions on the duality property for this class of operators. As interesting consequences, we obtain some characterizations of discrete... -
A Description of the Space of Banach Space-valued Absolutely p-summable Sequences
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: StuartF. Cullender CoenraadC.A. LabuschagneConradie and Swart described the sequence space l p strong(X) of Banach space-valued absolutely p-summable sequences as the Banach space of cone absolutely summing operators (1-concave operators) from c 0 to X for p = 1, or l... -
Functorial relationships between lattice-valued topology and topological systems
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: J.T. Denniston S.E. RodabaughThis paper investigates functorial relationships between lattice-valued topology (arising from fuzzy sets and fuzzy logic) and topological systems (arising from topological and localic aspects of domains and finite observational logic in computer science). Two such relationships are embeddings from TopSys... -
Symmetric bi-derivations of lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Yılmaz ÇevenIn this paper, we introduced the notion of symmetric bi-derivation on lattices and investigated some related properties. We characterized the distributive and modular lattices by symmetric bi-derivations. -
Permuting tri-derivations in lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mehmet Ali Öztürk --- Faculty of Arts and Sciences, Department of Mathematics, Turkey Hasret Yazarli --- Faculty of Arts and Sciences, Department of Mathematics, Turkey Kyung Ho Kim --- Department of Mathematics, KoreaThe aim of this paper is to introduce the notion of permuting triderivations in lattices and to study some properties of permuting tri-derivations. -
Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-II
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Qingying Bu* --- Department of Mathematics, USA Michelle Craddock --- Department of Mathematics, USA Donghai Ji --- Department of Mathematics, P.R. ChinaLet ϕ be an Orlicz function such that ϕ and its complementary function ϕ* satisfy the Δ2-condition, let ℓϕ be an Orlicz sequence space associated to ϕ, and let X be a Banach lattice. Then ℓϕ ⊗F X (respectively, ℓϕ... -
Structural matrix algebras related to finite distributive lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: E. Akkurt --- Gebze Institute of Technology, Turkey M. Akkurt --- Gebze Institute of Technology, Turkey G.P. Barker --- University of Missouri, Kansas City, USAIn this paper, we investigate the relation between a structural matrix algebra and the lattice properties of its lattice of invariant subspaces, and reprove known results in a fresh and an explanatory way. Moreover, we also prove the theorem which... -
The number of symmetric colorings of the dihedral group D3
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Iryna Kashuba --- Institute of Mathematics, University of S̃ao Paulo, Brazil Yuliya Zelenyuk --- School of Mathematics, South AfricaWe compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the dihedral group D3. -
Spatial modelling of cumulative human pressure in the tropical coastscape of Zanzibar, Tanzania
Item type: Journal Article • Journal: African Journal of Marine Science • Authors: ZA Khamis --- Department of Geography and Geology, Finland R Kalliola --- Department of Geography and Geology, Finland N Käyhkö --- Department of Geography and Geology, FinlandCoastal landscapes and seascapes (‘coastscapes’) are under immense anthropogenic pressures emanating from multiple human activities. We applied spatial modelling to characterise the cumulative pressures in the coastscape of Zanzibar’s main island Unguja (hereafter Zanzibar), in the western Indian Ocean. We... -
Some notes on orthogonally additive polynomials
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: C. Schwanke --- University of Pretoria, South AfricaWe provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is... -
Weak limited sets and operators on Banach lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Farid Afkir --- Moulay Ismaïl University, Morocco Aziz Elbour --- Moulay Ismaïl University, MoroccoIn this paper, we prove that an operator T : E → F , between two Banach lattices, maps order intervals onto weak limited sets if and only if the modulus |ST| exists and is Dunford-Pettis for every Dunford-Pettis operator... -
Net convergence structures with applications to vector lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. O’Brien --- University of Alberta, Canada V.G. Troitsky --- University of Alberta, Canada J.H. van der Walt --- University of Pretoria, South AfricaConvergence is a fundamental topic in analysis that is most commonly modeled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable functions and order convergence... -
On minimum proper essential extensions in a category
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anthony W. Hager --- Wesleyan University, USA Brian Wynne --- Lehman College, CUNY, USAIn a concrete category A satisfying certain natural conditions, we investigate minimum proper essential extenstions (A-mpee’s) and how this relates to atoms in the complete lattice hoA of hull operators on A (if A # is the category with... -
On bases of closure operators on complete lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Josef Šlapal --- Brno University of Technology, Institute of Mathematics, Czech RepublicWe study closure operators on complete lattices and define for them the concepts of closed and open bases as well as that of a neighborhood base. Some properties of these concepts are studied including relationships between them. In particular, we... -
Embedding of a truncated vector lattice into its universal completion
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Karim Boulabiar --- Université de Tunis El Manar, Tunisia Rawaa Hajji --- Université de Tunis El Manar, TunisiaWe prove in a purely algebraic way that if L is an Archimedean truncated vector lattice then there exists a positive element e in the universal completion Lu of L such that the truncation of L is provided by meet... -
Universal specialization semilattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Paolo Lipparini --- Università di Roma “Tor Vergata”, ItalyA specialization semilattice is a structure which can be embedded into , where X is a topological space, x ⊑ y means x ⊆ Ky, for x, y ⊆ X, and K is closure in X. Specialization semilattices and posets... -
Haagerup property of semigroup crossed products
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Qing Meng --- Qufu Normal University, ChinaIn this paper, we study the Haagerup property of semigroup crossed products for lattice ordered groups. Let G be a lattice ordered group. We show that the reduced semigroup C*-algebra C*r (G +) has the Haagerup property if and only... -
Epimorphisms and closure operators of categories of semilattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: D. Dikranjan --- Università degli Studi di Udine, Italy A. Giordano Bruno --- Università degli Studi di Udine, Italy N. Zava --- Institute of Science and Technology Austria (ISTA),Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLatt O of join semilattices with bottom element. In particular, we show that there are only finitely many... -
Some properties of conjunctivity (subfitness) in generalized settings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. Andrew Moshier --- CECAT, Chapman University, USA Jorge Picado --- University of Coimbra, Portugal Aleš Pultr --- Charles University, Czech RepublicThe property of subfitness used in point-free topology (roughly speaking) to replace the slightly stronger T 1-separation, appeared (as disjunctivity) already in the pioneering Wallman’s [16], then practically disappeared to reappear again (conjunctivity, subfitness), until it was in the recent... -
Some questions on partially ordered rings – a survey
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jingjing Ma --- University of Houston-Clear Lake, USAThis survey provides a brief overview and new developments on some questions in the area of partially ordered and lattice-ordered rings and algebras. -
Quasilattices and complex concept analysis
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G.N. Nop --- Iowa State University, USA J.D.H. Smith --- Iowa State University, USAQuasilattices are algebraic structures that comprise a semilattice-ordered system of lattices. In this paper, certain quasilattices (that are characterized abstractly by a local completeness property) provide an extension of Wille's concept analysis to the study of complex systems that function... -
Truncated vector lattices: A Maeda-Ogasawara type representation
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Karim Boulabiar --- Université de Tunis El Manar, Tunisia Rawaa Hajji --- Université de Tunis El Manar, TunisiaLet L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorphic with a truncated vector... -
The order bidual of C(X) for a realcompact space
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Marcel de Jeu --- Mathematical Institute, Leiden University, the Netherlands Jan Harm van der Walt --- University of Pretoria, South AfricaIt is well known that the bidual of C(X) for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to for some compact space . The space is unique up to homeomorphism. We... -
On the diagonal of Riesz operators on Banach lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: R. Drnovšek --- University of Ljubljana, Slovenia M. Kandić --- University of Ljubljana, SloveniaThis paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on... -
Hereditarily projectable Archimedean lattice-ordered groups with unit
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anthony W. Hager --- Wesleyan University, USA Brian Wynne --- , USALet W be the category of Archimedean lattice-ordered groups with distinguished weak unit and unit-preserving ℓ-group homomorphisms. We denote by P, wP, Loc, HA, respectively, the collections of projectable, weakly projectable, local, and hyperarchimedean W-objects. For any C ⊆ W,... -
Stone-Weierstrass approximation revisited
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anatoly G. Kusraev --- Southern Mathematical Institute of the Vladikavkaz Science Center of the Russian Academy of Sciences, Russia Semën S. Kutateladze --- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, RussiaThe aim of the present article is to extend the Stone-Weierstrass theorem to functions ranging in a lattice normed space and admitting order rather than topological approximation. We proceed with the machinery of Boolean-valued transfer from lattice normed space to... -
Lattice characterization of extreme positive operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jamel Jaber --- Tunis-El Manar University, Tunis Adnen Khalfaoui --- Tunis-El Manar University, TunisWe present a lattice-based characterization of extreme points whithin well-defined convex subsets of positive operators, operating between Banach lattices with quasi-interior points. -
Notes on sublocales and dissolution
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jorge Picado --- University of Coimbra, Portugal Aleš Pultr --- Charles University, Czech RepublicThe dissolution (introduced by Isbell in [3], discussed by Johnstone in [5] and later exploited by Plewe in [12, 13]) is here viewed as the relation of the geometry of L with that of the more dispersed T(L) = S(L)op... -
Norm and relative uniform convergence
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Zili Chen --- Southwest Jiaotong University, China Fu Zhang --- Southwest Jiaotong University, ChinaIn this paper, we show that if H is a Dedekind complete normed Riesz space with the local Egoroff property, then H is lattice isomorphic to an ideal of an AM-space if and only if for any order bounded norm... -
Local complementation in Banach spaces and its preservation under free constructions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Antonio Avilés --- Universidad de Murcia, Spain Gonzalo Martínez-Cervantes --- Universidad de Murcia, Spain Abraham Rueda Zoca --- Universidad de Granada, SpainIn this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed equivalent to the classical notion of local complementation of Banach spaces. As an application, we... -
A note on the U-Dunford-Pettis operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Farid Afkir --- Moulay Ismail University of Meknes, Morocco Aziz Elbour --- Moulay Ismail University of Meknes, MoroccoThe purpose of this note is to give a correct proof of the theorem that concerns the domination property of the class of U-Dunford-Pettis operators obtained by O. Aboutafail, K. El Fahri, J. H’Michane and L. Zraoula [On the class... -
Operators whose adjoints and second adjoints are almost Dunford-Pettis
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Geraldo Botelho --- Universidade Federal de Uberlândia, Brazil Luis Alberto Garcia --- Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, BrazilFirst we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend some known results concerning conditions on the Banach lattices E and...