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Compactness in fuzzy function spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gunther JägerIn [3] we defined a notion of compactness in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. In their paper the latter also introduced a fuzzy convergence structure c-lim for fuzzy function spaces thus proving that... -
The quasi-metric of complexity convergence
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Salvador Romaguera Michel SchellekensFor any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤ d , the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) Xω , is... -
Compactness with Respect to a Convergence Structure
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Josef SlapalA convergence structure for a category is given by determining convergent nets and their limits for each object of this category under validity of some basic convergence axioms. The nets considered are obtained as a categorical generalization of the usual... -
Measures of affinity of a sequence for a number
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Fatih Nuray WilliamH. RuckleWe define strong and weak affinities of a number a for a sequence (xk ) denoted by L (a,(xk )) and U (a, (xk )) respectively. We show U (a,(xk )) > 0 if and only if the number a... -
Convergence of ray sequences of Padé approximants for 2 f 1(a, 1; c; z), (c > a > 0)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: K. Driver K. JordaanThe Padé table of 2 F 1(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n - 1 and c ∉ Z-, the denominator polynomial Q mn (z) in the [m/n]... -
Completion of Probabilistic Uniform Limit Spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Harald NusserIn this article completions of special probabilistic semiuniform convergence spaces are considered. It turns out that every probabilitic Cauchy space under a given t-norm T (triangular norm) has a completion which, in the special case of probabilistic Cauchy spaces with... -
Stratified L-uniform convergence spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G. Jäger M.H. BurtonWe define a supercategory of the category of stratified L-uniform spaces, where L is a complete Heyting algebra. Our category is topological over SET and cartesian closed. In the case where L is the two-point chain, it coincides with the... -
The m-convergence theory in fuzzy topological spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Qingguo LiIn this paper, the m-convergences of fuzzy nets and fuzzy filters are introduced in a fuzzy topological space. The relations between m-convergences of fuzzy nets and fuzzy filters are investigated as are the relations between Hausdorff fuzzy topology and m-convergences... -
The Coarsest Hausdorff Lebesgue Topology
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jurie ConradieIf a Riesz space E contains an order dense Riesz subspace which admits a Hausdorff Lebesgue (i.e. order continuous) topology, then there is a coarsest Hausdorff Lebesgue topology on E. This topology extends uniquely to a Hausdorff Lebesgue topology on... -
Order convergence structure on C(X)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Roumen Anguelov Jan Harm van der WaltThis paper brings together three concepts which have not been related so far, namely, the concept of order convergence, the concept of convergence space and the concept of Hausdorff continuous functions. The order convergence on a poset P, which is... -
On completeness in symmetric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: SeithutiP. MoshokoaIn the literature completeness for symmetric spaces is done through the classical Cauchy criterion for metric spaces. However, unlike the situation in metric spaces a convergent sequence in a symmetric space is not necessarily a Cauchy sequence. In the paper... -
Lattice-Valued Convergence Ring and Its Uniform Convergence Structure
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: T.M.G. Ahsanullah --- Department of Mathematics, Saudi ArabiaConsidering L a frame, we introduce the notion of stratified L-neighborhood topological ring, produce some characterization theorems including its Luniformizability. With the help of the notions of stratified convergence structures attributed to Gunther Jäger [10], we introduce and study various... -
Lattice-Valued Cauchy Spaces and Completion
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gunther Jäger --- Department of Statistics, South AfricaWe define lattice-valued Cauchy spaces. The category of these spaces is topological over SET and cartesian closed. Special examples are lattice-valued uniform convergence spaces and probabilistic Cauchy spaces. We further define completeness and give a completion for these spaces which... -
Vector integration
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: E.G.F. Thomas --- Johann Bernoulli Institute for Mathematics and Computer Science, The NetherlandsThis paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to... -
On convergence of homotopy analysis method and its application to fractional integro-differential equations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: S. Abbasbandy --- Department of Mathematics, Iran M.S. Hashemi --- Department of Mathematics and Computer Science, Engineering and Technical Faculty, Iran I. Hashim --- Centre for Modelling & Data Analysis, School of Mathematical Sciences, MalaysiaIn this paper, we have used the homotopy analysis method (HAM) to obtain approximate solution of fractional integro-differential equations (FIDEs). Convergence of HAM is considered for this kind of equations. Also some examples are given to illustrate the high efficiency... -
The Riesz convergence property on weighted Lorentz spaces and Orlicz-Lorentz spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Hongliang Li --- Department of Mathematics, P.R.ChinaIn this paper, we define new Orlicz-Lorentz spaces . We find the necessary condition and sufficient condition for quasi-normed weighted Lorentz spaces to have Riesz convergence property. Also, we find the similar result for quasi-normed Orlicz-Lorentz... -
Fischer's Diagonal Condition for Lattice-Valued Convergence Spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gunther JägerWe study a generalization of a diagonal condition which classically ensures that a convergence space is topological. We show that only under an additional condition, which classically is always true, the validity of this diagonal condition implies that a Heyting... -
Quotient Maps: Frame-Valued Spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: H. Boustique G. RichardsonIt is known that the category of frame-valued convergence spaces is topological, cartesian-closed and extensional. Properties of quotient maps between objects in this category are investigated here; in particular, it is shown that quotient maps are productive under arbitrary products. -
The Uniform Order Convergence Structure on ML (X)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: vanJ.H. der WaltThe aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the order completion method [18] for nonlinear Partial Differential Equations (PDEs). In this regard, we consider an appropriate space ML(X) of... -
Measure of compactness for filters in the approach setting
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Frédéric MynardNew explicit descriptions of the reflections of a convergence-approach space on pseudo-approach, pre-approach and approach spaces are given. A measure of compactness for filters is introduced in the context of convergence-approach spaces. It is shown that this measure generalizes all... -
On convergence completeness in symmetric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: SeithutiP. MoshokoaThe notion of a convergence complete symmetric space is introduced in [6]. In this paper we shall show that every symmetric space admits a weakly S-convergence complete symmetric space. As applications of convergence completeness, we present some fixed point results... -
Level spaces for lattice-valued uniform convergence spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gunther JägerWe define level structures for lattice-valued uniform spaces and lattice-valued uniform convergence spaces. We show that these structures characterize the spaces from which they are obtained and use them to show that the categories of probabilistic uniform convergence spaces, of... -
Frame valued stratified generalized convergence groups
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: T.M.G. Ahsanullah Jawaher Al-MufarrijFollowing the notion of stratified L-fuzzy convergence space of Gunther Jäger [Quaest. Math. 24 (2001), 501–517], we introduce the notion of a stratified L-generalized convergence group, and look into some other objects, namely, stratified L-Kent convergence groups, and stratified L-principal... -
Jordan homomorphisms between algebras of measurable operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Martin WeigtWe prove that every self-adjoint algebra homomorphism between algebras of measurable operators is continuous and can be expressed as a sum of a self-adjoint algebra homomorphism as well as a self-adjoint algebra anti-homomorphism. We also provide sufficient conditions under which... -
The completion of uniform convergence spaces and an application to nonlinear PDEs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jan Harm van der Walt --- Department of Mathematics and Applied Mathematics, South AfricaThis paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result for the mentioned systems of... -
DNA sequences from the Little Brown Bustard Eupodotis humilis suggest its close phylogenetic relationship to the Little Bustard Tetrax tetrax
Item type: Journal Article • Journal: Ostrich: Journal of African Ornithology • Authors: José Luis Horreo --- Museo Nacional de Ciencias Naturales, Spain Juan Carlos Alonso --- Museo Nacional de Ciencias Naturales, Spain Borja Milá --- Museo Nacional de Ciencias Naturales, SpainTaxonomic classification of birds based exclusively on morphology and plumage traits has often been found to be inconsistent with true evolutionary history when tested with molecular phylogenies based on neutrally evolving markers. Here we present cytochrome-b gene sequences for the... -
Convergence of Ishikawa iterations on noncompact sets
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Simba A. Mutangadura --- Department of Mathematics & Applied Mathematics, South AfricaRecall that Ishikawa's theorem [4] provides an iterative procedure that yields a sequence which converges to a fixed point of a Lipschitz pseudocontrative map T: C →C, where C is a compact convex subset of a Hilbert space X. The... -
Neurophysiological foundations of organ electrodermal diagnostics, acupuncture, TENS and other reflexive therapies
Item type: Journal Article • Journal: Southern African Journal of Anaesthesia and Analgesia • Authors: JZ Szopinski --- Pain Clinic, South Africa T Sierak --- Department of Medical Biophysics, Poland GP Lochner --- Department of Electronic Engineering, South AfricaThe nervous system is the primary computing system of the human body. The sensory nervous system detects any damage done to the body from both outside and inside and sends the information, at the earliest stage of pathology, to the... -
Economic growth and R&D expenditures in selected OECD countries: Is there any convergence?
Item type: Journal Article • Journal: African Journal of Science, Technology, Innovation and Development • Authors: Deepika Chawla --- Department of Economics, Patiala, IndiaThe economic growth of nations is strongly associated with rising R&D expenditures. The present study therefore endeavours to examine the stylized patterns of evolution of R&D expenditures (R&D expenditures as a share of GDP) along the development course in 18... -
Digging adaptations evolved independently in two lineages of Psammophiid snake: evidence from cranial morphology
Item type: Journal Article • Journal: African Journal of Herpetology • Authors: Nick Sekits --- Whitman College, United States Walter Tunnell-Wilson --- Whitman College, United States Kate Jackson --- Whitman College, United StatesThe Beaked Snakes (Rhamphiophis) are semi-fossorial snakes with reinforced snouts adapted for digging. The Skaapstekers (Psammophylax) are generalist terrestrial snakes. Both belong to the family, Psammophiidae. The Striped Beaked Snake (Kladirostratus acutus) was originally assigned to the genus Rhamphiophis, because... -
The category of residuated lattice valued filter spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lin Zhang --- School of Mathematics and Statistics, Beijing Institute of Technology, China Bin Pang --- School of Mathematics and Statistics, Beijing Institute of Technology, ChinaConsidering L as a complete residuated lattice, some further investigations on L-filter spaces are made. Firstly, it is shown that the category L-Fil of L-filter spaces is monoidal closed. Secondly, it is proved that the categories of L-Cauchy spaces and... -
Multidimensional Kantorovich modifications of exponential sampling series
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Tuncer Acar --- Selcuk University, Turkey Sadettin Kursun --- Selcuk University, Turkey Metin Turgay --- Selcuk University, TurkeyThis paper is devoted to construction of multidimensional Kantorovich modifications of exponential sampling series, which allows to approximate suitable measurable functions by considering their mean values on just one section of the function involved. Approximation behaviour of newly constructed operators... -
Sustainability of energy transition on output growth and carbon emission abatement in sub-Saharan Africa
Item type: Journal Article • Journal: African Journal of Science, Technology, Innovation and Development • Authors: Ikechukwu Sebastine Asogwa --- Michael Okpara University of Agriculture, Nigeria Charles Nnamdi Anumudu --- Michael Okpara University of Agriculture, NigeriaThis study examined the effects of renewable energy use on the output growth convergence, as well as the impacts of renewable energy use for an alternative to carbon emission (CO2) abatement in sub-Saharan Africa (SSA). The dual purpose followed the... -
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... -
Some properties of the Walsh-Nörlund means
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Ushangi Goginava --- United Arab Emirates University, UAE Károly Nagy --- Institute of Mathematics and Computer Sciences, University of Nyíregyháza, Nyíregyháza, HungaryIn the present paper we give a necessary and sufficient condition on monotone weights, which guaranties the Nörlund means of Walsh-Fourier series converge in L 1 norm and CW norm. We also discuss the almost everywhere summability by Nörlund means... -
Some further remarks on characterized subgroups generated by modular simple density
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Ayan Ghosh --- Jadavpur University, IndiaIn this short note we have constructed an uncountable tower of characterized subgroups using the notion of modular simple density [8] which subsequently gives the solution of Problem 2.15 [7] in a more general setting. -
A strong law of large numbers for non identically distributed Pettis integrable random sets in a general Banach space
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. El Allali --- University Sidi Mohamed Ben Abdellah, FSTF, Morocco F. Ezzaki --- University Sidi Mohamed Ben Abdellah, FSTF, MoroccoA multivalued version of Cesàro mean convergence theorem is established. As a consequence, various convergence results of strong law of large numbers for pairwise independent Pettis integrable random sets in a Banach space without any additional geometric condition on the... -
On uniform f −statistical convergence of sequences of functions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M.C. Listán-García --- Universidad de Cádiz, SpainWe introduce the notions of uniform f −statistical convergence of sequences and uniform f −statistical Cauchy sequences of functions. The natural equivalence between these two notions, in Banach spaces, is proved. In doing so, we generalize and improve results of... -
Order boundedness and order continuity properties of positive operator semigroups
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jochen Glück --- University of Wuppertal, School of Mathematics and Natural Sciences, Germany Michael Kaplin --- Institute of Mathematics, SlovenijaRelatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandic, Kramar-Fijavž, and the second-named author, in order to make the theory of one-parameter operator semigroups available in the setting of vector lattices, where no norm is present in... -
Generating functions in Riesz spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Youssef Azouzi --- Tunis-El Manar University, Tunisia Youssef Nasri --- Tunis-El Manar University, TunisiaWe introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectation operator. This allows us to study discrete processes in a free-measure setting. In particular we improve a... -
On the extension of the Voronin universality theorem for the Riemann zeta-function
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Antanas Laurinčikas --- Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, LithuaniaIn the paper, we prove a general universality theorem for the Riemann zeta-function ζ (s) on approximation of a class of analytic functions by generalized shifts ζ (s + ia(τ)). Here a(τ) is a real-valued continuous increasing to +∞ function,... -
Complete convergence for the maximal partial sums without maximal inequalities
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Fakhreddine Boukhari --- Abou Bekr Belkaid University, Algeria Nguyen Chi Dzung --- Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam Lê Vǎn Thaǹh --- Vinh University, VietnamThis work provides the necessary and sufficient conditions for complete convergence for the maximal partial sums of dependent random variables. The results are proved without using maximal inequalities. The main theorems can be applied to sequences of (i) m-pairwise negatively... -
A fully discrete scheme on piecewise-equidistant mesh for singularly perturbed delay integro-differential equations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Musa Cakir --- Van Yuzuncu Yil University, Turkey Baransel Gunes --- Van Yuzuncu Yil University, TurkeyThis paper chiefly takes into account the singularly perturbed delay Volterra-Fredholm integro-differential equations by numerically. In this context, firstly, priori estimates are given and a new discretization is constructed on piecewise-equidistant mesh by using interpolating quadrature rules [2] and composite... -
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... -
A convex combination of improved Fletcher-Reeves and Rivaie-Mustafa-Ismail-Leong conjugate gradient methods for unconstrained optimization problems and applications
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: T. Diphofu --- University of Botswana, Botswana P. Kaelo --- University of Botswana, Botswana S. Kooepile-Reikeletseng --- University of Botswana, Botswana M. Koorapetse --- University of Botswana, Botswana C.R. Sam --- University of Botswana, BotswanaConjugate gradient methods are probably the most used methods in solving large scale unconstrained optimization problems. They have become popular because of their simplicity and low memory requirements. In this paper, we propose a hybrid conjugate gradient method based on... -
On a weak law of large numbers and Lp -convergence for general random variables
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Qi Gao --- Henan Normal University, China Yu Miao --- Henan Normal University, ChinaIn the present paper, we consider a sequence of the general random variables, which include the sequences of martingale differences, and establish the weak law of large numbers and the convergence in Lp under some weaker conditions. -
Adaptive grid based moving mesh algorithms for singularly perturbed second-order Volterra integro differential equations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Sushree Priyadarshana --- Centre for Data Science, Institute of Technical Education and Research, SOA Deemed to be University, India Ajaya Padhan --- National Institute of Technology Rourkela, India Jugal Mohapatra --- National Institute of Technology Rourkela, IndiaRobust adaptive grid-based moving mesh algorithms are discussed for singularly perturbed second-order convection-diffusion type Volterra integro differential equations. Two different kinds of monitor functions are used to establish the numerical schemes. A well-studied first-order monitor function is used to construct... -
f-rough Cauchy sequences
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Tamim Aziz --- University of North Bengal, India Sanjoy Ghosal --- University of North Bengal, IndiaIn this article, we narrated the new notion of rough f-statistical convergence and rough f-statistical Cauchy sequences, successively becoming a more generalized version of rough statistical convergence and rough statistical Cauchy sequences. Consecutively, compare the following important theorems with those... -
Umbilicity of complete linear Weingarten hypersurfaces immersed in certain Einstein manifolds
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Henrique F. de Lima --- Universidade Federal de Campina Grande, Brazil Lucas S. Rocha --- Universidade Federal de Campina Grande, Brazil Marco Antonio L. Velásquez --- Universidade Federal de Campina Grande, BrazilIn this paper, we present some sets of geometric conditions that ensure the umbilicity of linear Weingarten hypersurfaces immersed in an Einstein manifold satisfying standard curvature constraints which, in particular, are verified by a Riemannian space with constant sectional curvature... -
A hybrid regularization method for simultaneous inversion of source term and initial value in a time-fractional diffusion equation
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jin Wen --- Northwest Normal University, P.R. China Yong-Ping Wang --- Northwest Normal University, P.R. China Li-Ming Huang --- Northwest Normal University, P.R. China Donal O’Regan --- University of Galway, IrelandThis paper considers an inverse problem to find the space-dependent source term and initial data simultaneously in a time-fractional diffusion equation. This inverse problem is usually ill-posed, that is, small errors in the measurement typically lead to large errors in... -
Acoustic, perceptual and social analyses of speech convergence of black and white people in Nigeria
Item type: Journal Article • Journal: South African Journal of African Languages • Authors: Joy Oluchi Uguru --- University of Nigeria, Nigeria Nkechi Mgbodichinma Ukaegbu --- University of Nigeria, NigeriaThis study assesses speech convergence between white American English (AE) speakers and black Nigerian English (NE) speakers. Most studies base convergence on speech shadowing, but this study investigates convergence in real-life conversations. Eighty utterances were analysed with PRAAT. The utterances... -
Exploring the factors behind digitalization convergence and revealing Africa’s digital transformation journeys
Item type: Journal Article • Journal: African Journal of Science, Technology, Innovation and Development • Authors: Thapelo Chauke --- North-West University, South Africa Oladipo Olalekan David --- North-West University, South Africa Afees Oluwashina Noah --- North-West University, South AfricaGlobal economies are transitioning from traditional agrarian models to technology-driven ones, focusing on sustainable growth. Historically, Africa has been slow to adopt digital technologies, lagging behind other regions. However, since the late 1990s, the continent has experienced significant growth in...