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Derivations in disjointly complete commutative regular algebras Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Aleksey Ber, Vladimir Chilin, Fedor Sukochev
We show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense ...
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A rigid Riesz space Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 A.W. Wickstead
We give an example of an Archimedean Riesz space on which every automorphism is a strictly positive multiple of the identity.
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To the memory of W.A.J. Luxemburg and his mathematical legacy Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Koos Grobler, Sanne ter Host, Ben de Pagter, Anton R. Schep
Published in Quaestiones Mathematicae (Vol. 47, No. sup1, 2024)
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Generating functions in Riesz spaces Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Youssef Azouzi, Youssef Nasri
We 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 ...
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Truncated vector lattices: A Maeda-Ogasawara type representation Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Karim Boulabiar, Rawaa Hajji
Let 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 isomorph...
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The order bidual of C(X) for a realcompact space Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Marcel de Jeu, Jan Harm van der Walt
It 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...
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The modulus of a vector measure Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Ben de Pagter, Werner J. Ricker
It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measur...
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On the diagonal of Riesz operators on Banach lattices Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 R. Drnovšek, M. Kandić
This 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...
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Order boundedness and order continuity properties of positive operator semigroups Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Jochen Glück, Michael Kaplin
Relatively 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 se...
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Scaling and instantaneous blow up Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Gisèle Ruiz Goldstein, Jerome A. Goldstein, İsmail Kömbe, Abdelaziz Rhandi
The main result is a simple proof of the Baras-Goldstein (1984) instantaneous blow up result for the heat equation with the inverse square potential. The proof relies heavily, indeed mainly, on sca...
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Remarks on weak compactness criteria in variable exponent Lebesgue spaces Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Francisco L. Hernández, César Ruiz, Mauro Sanchiz
We give two weak compactness Andô type criteria in variable exponent Lebesgue spaces Lp(·) (Ω) on infinite measures. This extends some results of [13] given in the case of finite measures. Spaces L...
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A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Anke Kalauch, Wenchi Kuo, Bruce A. Watson
We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [B.A. Watson, An Andô-Douglas type theorem in Riesz spaces with a conditional expectation, Positivity, 13 (2009), 543–5...
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Towards a geometrical equivalence of norms Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Eder Kikianty
Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and t...
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Stone-Weierstrass approximation revisited Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Anatoly G. Kusraev, Semën S. Kutateladze
The 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 t...
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Weak and strong type inequalities for Orlicz spaces Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Louis Labuschagne
We revisit the generalisation of Calderon’s Transfer Principle as espoused in [7]. This principle is used to generate weak type maximal inequalities for ergodic operators in the setting of σ-compac...
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Generalized domination of ergodic elements in ordered Banach algebras Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 S. Mouton, A.D. Rabearivony
Let A be an ordered Banach algebra and a, b ∈ A such that 0 ≤ a ≤ b. The domination problem involves finding natural conditions under which properties of b will be inherited by a. In [12] this prob...
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Fubini’s theorem for a vector-valued Daniell integral Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Jacobus J. Grobler
We define the product integral for two Riesz space-valued Daniell integrals and prove Fubini’s theorem establishing the relation between product integrals and iterated integrals. The properties of ...
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The second nonlinear mixed bi-skew Lie triple derivations on factor von Neumann algebras Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Yuan Yang, Jianhua Zhang
Let be a factor von Neumann algebra with dim . In this paper, it is shown that if a map satisfies for all , then ϕ is an additive ∗-derivation, where .
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Complete convergence for the maximal partial sums without maximal inequalities Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Fakhreddine Boukhari, Nguyen Chi Dzung, Lê Vǎn Thaǹh
This 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 inequali...
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A comonadicity theorem for partial comodules Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Eliezer Batista, William Hautekiet, Joost Vercruysse
We show that the category of partial comodules over a Hopf algebra H is comonadic over Vectk and provide an explicit construction of this comonad using topological vector spaces. The case when H is...
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Optimal system and conservation laws for the generalized Fisher equation in cylindrical coordinates Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 A.H. Kara, Sonia Naseer, Ali Raza, F.D. Zaman
The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. In many practical situations, the physical domain of the problem is...
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Lattice characterization of extreme positive operators Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Jamel Jaber, Adnen Khalfaoui
We present a lattice-based characterization of extreme points whithin well-defined convex subsets of positive operators, operating between Banach lattices with quasi-interior points.
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On the solution of the Cauchy problem for a higher-order equation with the fractional Riemann-Liouville derivative Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 B.Yu. Irgashev
In this article, a representation of the solution of the Cauchy problem for an equation of high even order with a fractional derivative in the Riemann-Liouville sense of order greater than one is o...
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Exponential decay of solutions to an inertial model for a wave equation with viscoelastic damping and time varying delay Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Mohamed Berbiche
In the present work, we study the global existence and uniform decay rates of solutions to the initial-boundary value problem related to the dynamic behavior of evolution equations accounting for r...
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On the way to Frölicher bornology Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Ben Moditi Mahudu, Mukinayi Hermenegilde Tshilombo
In this work we introduce the concept of bornology on the theory of Frölicher spaces. A canonical bornology, called the functional bornology, is induced from structure functions, and bounded maps u...
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Planar polynomial of the graphs Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Behnaz Tolue, Alireza Doostabadi, Sayed Masih Ayat
In this paper, the planar polynomial of a graph is introduced and some of its properties are discussed. The planar polynomial of the graph G is real-rooted if and only if G is planar. This polynomi...
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Hereditarily projectable Archimedean lattice-ordered groups with unit Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 Anthony W. Hager, Brian Wynne
Let 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 pro...
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On a special Kapteyn series Quaest. Math. (IF 0.7) Pub Date : 2024-03-07 A.J.E.M. Janssen
We investigate the mathematical properties of the function , ϵ ∈ [−1, 1], which is a special Kapteyn series of the first kind. Unlike various other special Kapteyn series, the function T (ϵ) does n...
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The role of derivations in the nilpotence and semisimplicity of Lie triple systems Quaest. Math. (IF 0.7) Pub Date : 2024-03-06 Hani Abdelwahab, Antonio J. Calderón Martín, Moustafa Mahanna
We explore the role derivations of a Lie triple system play in the nilpotence and semisimplicity of T. In particular analogous to two theorems of Jacobson for Lie algebras, (by giving a sufficient...
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Orbit spaces of free involutions on the product of three spheres Quaest. Math. (IF 0.7) Pub Date : 2024-03-05 Dimpi, Hemant Kumar Singh
In this paper, we have determined the orbit spaces of free involutions on a finitistic space having mod 2 cohomology of the product of three spheres . This paper generalizes the results proved by D...
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Near universal property of a quadratic form of Hessian discriminant 4 Quaest. Math. (IF 0.7) Pub Date : 2024-02-29 Jesse Ira Deutsch
A quadratic form is universal if it represents all totally positive integers in a number field. In classical number theory over the rational integers there are some results where a quadratic form t...
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Correction Quaest. Math. (IF 0.7) Pub Date : 2023-12-13
Notice of duplicate publication: ‘EINSTEIN HALF LIGHTLIKE SUB-MANIFOLDS OF A LORENTZIAN SPACE FORM WITH A SEMI-SYMMETRIC METRIC CONNECTION’D.H. Jin and J.W. Lee, ‘EINSTEIN HALF LIGHTLIKE SUBMANIFOL...
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Local and 2-local automorphisms of solvable Leibniz algebras with abelian and model nilradicals Quaest. Math. (IF 0.7) Pub Date : 2023-12-04 Iqboljon Karimjanov, Sardorbek Umrzaqov, Bakhtiyor Yusupov
In the paper, we describe the automorphisms on the solvable Leibniz algebras with the model or abelian nilradicals, whose complementary spaces are equal to two and one, respectively. We show that a...
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On the difference graph of power graphs of finite groups Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Jitender Kumar, Ramesh Prasad Panda, Parveen
The power graph of a finite group G is the simple undirected graph with vertex set G whose two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group G is ...
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Oscillation results for nonlinear weakly canonical fourth-order delay differential equations via canonical transform Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Natarajan Prabaharan, Ethiraju Thandapani, Ercan Tunç
By using canonical transformation technique, we convert the nonlinear weakly canonical fourth-order delay differential equations into strongly canonical equations. Then we apply oscillation results ...
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On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Elgiz Bairamov, Kenan Tas, Ekin Uğurlu
In this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduc...
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Extension properties for monotone sublinear operators Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Sorin G. Gal
In this paper we obtain extension properties for monotone sublinear operators. The results obtained generalize those known for positive linear operators. Several examples illustrating the results o...
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Discrete selectivity, shrinking properties, and disjoint local π-bases Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Gary Gruenhage, Vladimir V. Tkachuk
Using binary function spaces, we give an example of a pseudocompact discretely selective topological group. We show that, under PFA, every compact space of countable tightness has a countable disjo...
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Spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Meiram Akhymbek, Kanat Tulenov, Gulnur Zaur
In this paper, we investigate the spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces over a finite interval and a half line, thereby extending Boyd’s and Leibowitz’s results fo...
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Generalized derivations with nilpotent values in semiprime rings Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Cheng-Kai Liu
Let R be a (semi-) prime ring with extended centroid C, let f(X1, … , Xk) be a multilinear polynomial over C in k noncommutative indeterminates which is not central-valued on R and let g be a gener...
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Argument estimates associated with meromorphic close-to-starlike and Bazilević functions Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Nak Eun Cho, Inhwa Kim, H.M. Srivastava
The object of the present paper is to derive some argument properties associated with meromorphic close-to-starlike and Bazilević functions in the punctured open unit disk. Furthermore, we investig...
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Uniformly S-Noetherian rings Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Mingzhao Chen, Hwankoo Kim, Wei Qi, Fanggui Wang, Wei Zhao
Let R be a ring and S be a multiplicative subset of R. Then R is called a uniformly S-Noetherian ring if there exists s ∈ S such that, for any ideal I of R, sI ⊆ K for some finitely generated subid...
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Maps preserving maximal numerical range of operator products Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 K. Dhifaoui, M. Mabrouk
Let be a complex Hilbert space and denote by the algebra of all linear bounded operators on . For any , denote by V0(T) its maximal numerical range. We prove that if is a surjective map such tha...
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The number of distinguishing colorings of a Cartesian product graph Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Saeid Alikhani, Mohammad H. Shekarriz
A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold θ(G) of a graph G is the minimum number of colors k required t...
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The solution set to the nonlinear operator equation XAX = BX on Hilbert spaces Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Hua Wang, Jingsong Wu
We present the representation of solution sets of the operator equation XAX = BX on Hilbert spaces by taking advantage of the invariant subspace of B, including solution sets of nonzero solutions, ...
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Remote sublocales Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Mbekezeli Nxumalo
We use the notion of a remote collection of a Tychonoff space to define a remote sublocale of any locale. Our definition is conservative, in the sense that, a subset is remote if and only if the sub...
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Generating functions of multiple t-star values Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Zhonghua Li, Lu Yan
In this paper, we study the generating functions of multiple t-star values with an arbitrary number of blocks of twos, which are based on the results of the corresponding generating functions of mu...
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Inverse problem of determining the coefficient in a sixth order Boussinesq equation with additional nonlocal integral condition Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 A.S. Farajov, M.J. Huntul, Yashar T. Mehraliyev
The work is devoted to the study of the solvability of the inverse boundary value problem with an unknown time depended coefficient for a sixth-order Boussinesq equation with an additional integral...
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Super-skewsymmetric super-biderivations on the N = 1 super Heisenberg-Virasoro algebra Quaest. Math. (IF 0.7) Pub Date : 2023-11-30 Jinlu Li, Jiancai Sun
In this paper, the super-skewsymmetric super-biderivations on the N = 1 super Heisenberg-Virasoro algebra are completely determined. Furthermore, we find that every super-skewsymmetric super-bideri...
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Topogenous orders and related families of morphisms Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 David Holgate, Minani Iragi
In a category with a proper ()-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow simu...
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Epimorphisms and closure operators of categories of semilattices Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 D. Dikranjan, A. Giordano Bruno, N. Zava
Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particu...
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Some properties of conjunctivity (subfitness) in generalized settings Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 M. Andrew Moshier, Jorge Picado, Aleš Pultr
The property of subfitness used in point-free topology (roughly speaking) to replace the slightly stronger T1-separation, appeared (as disjunctivity) already in the pioneering Wallman’s [16], then ...
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Horst Herrlich – A deep and enduring contribution to South African mathematics Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 David Holgate
Published in Quaestiones Mathematicae (Vol. 46, No. sup1, 2023)
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Special Issue Dedicated to the Memory of Professor Horst Herrlich Guest Editors’ Introduction Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 Klaas Pieter Hart, Mirek Hušek, Jan van Mill
Published in Quaestiones Mathematicae (Vol. 46, No. sup1, 2023)
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Some concepts of topology and questions in topological algebra Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 A.V. Arhangel’skii
This paper has features of mixed nature. It contains new results, in particular, on semitopological groups. We also pose some problems, introduce new definitions and describe in details certain tec...
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The ℓp-metrization of functors with finite supports Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 Taras Banakh, Viktoria Brydun, Lesia Karchevska, Mykhailo Zarichnyi
Let p ∈ [1, ∞] and F : Set → Set be a functor with finite supports in the category Set of sets. Given a non-empty metric space (X, dX), we introduce the distance on the functor-space FX as the lar...
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The monoidal nature of the Feistel-Toffoli construction Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 Hans-E. Porst
The Feistel-Toffoli construction of a bijective Boolean function out of an arbitrary one, a fundamental tool in reversible computing and in cryptography, has recently been analyzed (see [12]) to be...
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Lax comma categories of ordered sets Quaest. Math. (IF 0.7) Pub Date : 2023-11-01 Maria Manuel Clementino, Fernando Lucatelli Nunes
Let Ord be the category of (pre)ordered sets. Unlike Ord/X , whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category Ord//X . In this paper we show tha...
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Some curvature properties of perfect fluid spacetimes Quaest. Math. (IF 0.7) Pub Date : 2023-10-16 Krishnendu De, Uday Chand De, Ljubica S. Velimirovic
In this paper we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we invest...
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Congruences modulo powers of 5 for the crank parity function Quaest. Math. (IF 0.7) Pub Date : 2023-10-05 Dazhao Tang
In 1988, Andrews and Garvan introduced the partition statistic “crank” in order to give combinatorial interpretation for Ramanujan’s celebrated partition congruence modulo 11. In 2009, Choi, Kang a...