Missouri Journal of Mathematical Sciences Articles (Project Euclid)
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The latest articles from Missouri Journal of Mathematical Sciences on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2011 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Wed, 14 Sep 2011 16:37 EDTWed, 14 Sep 2011 16:37 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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http://projecteuclid.org/euclid.mjms/1312233177
<strong>Terry Goodman</strong><p><strong>Source: </strong>Missouri J. Math. Sci., Volume 23, Number 1, 1--2.</p>projecteuclid.org/euclid.mjms/1312233177_Wed, 14 Sep 2011 16:37 EDTWed, 14 Sep 2011 16:37 EDTSieving for the Primes to Prove Their Infinitudehttps://projecteuclid.org/euclid.mjms/1513306829<strong>Hunde Eba</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 176--183.</p><p><strong>Abstract:</strong><br/>
We prove the infinitude of prime numbers by the principle of contradiction, that is different from Euclid's proof in a way that it uses an explicit property of prime numbers. A sieve method that applies the inclusion-exclusion principle is used to give the property of the prime numbers in terms of the prime counting function.
</p>projecteuclid.org/euclid.mjms/1513306829_20171214220030Thu, 14 Dec 2017 22:00 ESTWeakly JU Ringshttps://projecteuclid.org/euclid.mjms/1513306830<strong>Peter V. Danchev</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 184--196.</p><p><strong>Abstract:</strong><br/>
We define and completely explore the so-called WJU rings . This class properly encompasses the class of JU rings, introduced and studied by the present author in detail in Toyama Math. J. (2016).
</p>projecteuclid.org/euclid.mjms/1513306830_20171214220030Thu, 14 Dec 2017 22:00 ESTOn $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy Soft $BCI$-algebrashttps://projecteuclid.org/euclid.mjms/1513306831<strong>Chiranjibe Jana</strong>, <strong>Madhumangal Pal</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 197--215.</p><p><strong>Abstract:</strong><br/>
Molodtsov initiated soft set theory which has provided a general mathematical framework for handling uncertainties that occur in various real life problems. The aim of this paper is to provide fuzzy soft algebraic tools in considering many problems that contain uncertainties. In this article, the notion of $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy soft $BCI$-subalgebra of $BCI$-algebra is introduced. Some operational properties on $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy soft $BCI$-subalgebras are discussed as well as lattice structures of this kind of fuzzy soft set on $BCI$-subalgebras are derived.
</p>projecteuclid.org/euclid.mjms/1513306831_20171214220030Thu, 14 Dec 2017 22:00 ESTOn a Problem of Hararyhttps://projecteuclid.org/euclid.mjms/1513306832<strong>Paul C. Kainen</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 216--218.</p><p><strong>Abstract:</strong><br/>
An exercise in Harary [1, p. 100] states that the product of the vertex independence number and the vertex covering number is an upper bound on the number of edges in a bipartite graph. In this note, we extend the bound to triangle-free graphs, and show that equality holds if and only if the graph is complete bipartite.
</p>projecteuclid.org/euclid.mjms/1513306832_20171214220030Thu, 14 Dec 2017 22:00 ESTSoccer Balls, Golf Balls, and the Euler Identityhttps://projecteuclid.org/euclid.mjms/1513306833<strong>Linda Lesniak</strong>, <strong>Arthur T. White</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 219--222.</p><p><strong>Abstract:</strong><br/>
We show, with simple combinatorics, that if the dimples on a golf ball are all 5-sided and 6-sided polygons, with three dimples at each “vertex”, then no matter how many dimples there are and no matter the sizes and distribution of the dimples, there will always be exactly twelve 5-sided dimples. Of course, the same is true of a soccer ball and its faces.
</p>projecteuclid.org/euclid.mjms/1513306833_20171214220030Thu, 14 Dec 2017 22:00 ESTAnnouncementshttps://projecteuclid.org/euclid.mjms/1513306834<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 223--224.</p>projecteuclid.org/euclid.mjms/1513306834_20171214220030Thu, 14 Dec 2017 22:00 ESTMunchausen Numbers Reduxhttps://projecteuclid.org/euclid.mjms/1534384947<strong>Devin Akman</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 1--4.</p><p><strong>Abstract:</strong><br/>
A Munchausen number is a mathematical curiosity: raise each digit to the power of itself, add them all up, and recover the original number. In the seminal paper on this topic, D. Van Berkel derived a bound on such numbers for any given radix, which means that they can be completely enumerated in principle. We present a simpler argument which yields a bound one half the size and show that a radically different approach would be required for further reductions.
</p>projecteuclid.org/euclid.mjms/1534384947_20180815220242Wed, 15 Aug 2018 22:02 EDTCubic Commutative Ideals of $BCK$-algebrashttps://projecteuclid.org/euclid.mjms/1534384948<strong>Tapan Senapati</strong>, <strong>K. P. Shum</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 5--19.</p><p><strong>Abstract:</strong><br/>
In this paper, we apply the concept of cubic set to commutative ideals of $BCK$-algebras, and then characterize their basic properties. We discuss relations among cubic commutative ideals, cubic subalgebras, and cubic ideals of $BCK$-algebras. We provide a condition for a cubic ideal to be a cubic commutative ideal. We define inverse images of cubic commutative ideals and establish how the inverse images of a cubic commutative ideal becomes a cubic commutative ideal. We introduce products of cubic $BCK$-algebras. Finally, we discuss the relationships between (cubic) commutative ideals, implicative ideals, and positive implicative ideals in $BCK/BCI$-algebras.
</p>projecteuclid.org/euclid.mjms/1534384948_20180815220242Wed, 15 Aug 2018 22:02 EDTStrong Forms of $\mu$-Lindelöfness with Respect to Hereditary Classeshttps://projecteuclid.org/euclid.mjms/1534384949<strong>Abdo Qahis</strong>, <strong>Heyam Hussain AlJarrah</strong>, <strong>Takashi Noiri</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 20--31.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to introduce and study strong forms of $\mu$-Lindelöfness in generalized topological spaces with a hereditary class, called $\mathcal{S} \mu\mathcal{H}$-Lindelöfness and $\mathbf{S}-\mathcal{S}\mu\mathcal{H}$-Lindelöfness. Interesting characterizations of these spaces are presented. Several effects of various types of functions on them are studied.
</p>projecteuclid.org/euclid.mjms/1534384949_20180815220242Wed, 15 Aug 2018 22:02 EDTSome Connections Between Bunke-Schick Differential K-theory and Topological $\mathbb{Z}/k\mathbb{Z}$ K-theoryhttps://projecteuclid.org/euclid.mjms/1534384951<strong>Adnane Elmrabty</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 32--44.</p><p><strong>Abstract:</strong><br/>
The purpose of this note is to prove some results in Bunke-Schick differential K-theory and topological $\mathbb{Z}/k\mathbb{Z}$ K-theory. The first one is an index theorem for the odd-dimensional geometric families of $\mathbb{Z}/k\mathbb{Z}$-manifolds. The second one is an alternative proof of the Freed-Melrose $\mathbb{Z}/k\mathbb{Z}$-index theorem in the framework of differential K-theory.
</p>projecteuclid.org/euclid.mjms/1534384951_20180815220242Wed, 15 Aug 2018 22:02 EDTNew Type of Simultaneous Remotal Sets in Certain Banach Spaceshttps://projecteuclid.org/euclid.mjms/1534384952<strong>Sh. Al-Sharif</strong>, <strong>A. Awad</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 45--53.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce a new concept of simultaneous remotal sets and farthest points in Banach spaces and we present various characterizations of such points in certain Banach spaces.
</p>projecteuclid.org/euclid.mjms/1534384952_20180815220242Wed, 15 Aug 2018 22:02 EDTMagnifying Elements in a Semigroup of Transformations with Restricted Rangehttps://projecteuclid.org/euclid.mjms/1534384954<strong>Ronnason Chinram</strong>, <strong>Samruam Baupradist</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 54--58.</p><p><strong>Abstract:</strong><br/>
Let $Y$ be a nonempty subset of a set $X$ and let $T(X,Y)$ be the semigroup (under composition) of all functions $X\rightarrow X$ whose range is a subset of $Y$. We give necessary and sufficient conditions for elements in $T(X,Y)$ to be left and right magnifying.
</p>projecteuclid.org/euclid.mjms/1534384954_20180815220242Wed, 15 Aug 2018 22:02 EDTSome Operators in Ideal Topological Spaceshttps://projecteuclid.org/euclid.mjms/1534384955<strong>H. Al-Saadi</strong>, <strong>A. Al-Omari</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 59--71.</p><p><strong>Abstract:</strong><br/>
In this paper, we give an extensive study of ideal topological spaces and introduce some new types of sets with the help of a local function. Several characterizations of these sets will also be discussed through this paper. Moreover, we obtain characterizations of $\Psi_{\omega}$-operator and $\omega$-codense.
</p>projecteuclid.org/euclid.mjms/1534384955_20180815220242Wed, 15 Aug 2018 22:02 EDTArbitrarily High Hausdorff Dimensions of Continuahttps://projecteuclid.org/euclid.mjms/1534384956<strong>R. Patrick Vernon</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 72--76.</p><p><strong>Abstract:</strong><br/>
It is well-known that Hausdorff dimension is not a topological invariant; that is, that two homeomorphic continua can have different Hausdorff dimension, although their topological dimension will be equal. We show that it is possible to take any continuum embeddable in $\mathbb{R}^n$ and embed it in such a way that its Hausdorff dimension is $n$. In doing so, we can obtain an arbitrarily high Hausdorff dimension for any nondegenerate continuum. As an example, we will give different embeddings of an arc whose Hausdorff dimension is any real number between $1$ and $\infty$, including an arc of infinite Hausdorff dimension.
</p>projecteuclid.org/euclid.mjms/1534384956_20180815220242Wed, 15 Aug 2018 22:02 EDTOn Constructing Chaotic Maps with a Prescribed Probability Distributionhttps://projecteuclid.org/euclid.mjms/1534384957<strong>Peter M. Uhl</strong>, <strong>Hannah Bohn</strong>, <strong>Noah H. Rhee</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 77--84.</p><p><strong>Abstract:</strong><br/>
In this paper we discuss how to construct piecewise linear chaotic maps with a prescribed probability distribution on a finite number of open intervals of equal length that form a partition of the unit interval. The idea and method of how to find such a map are given in [3]. But a formal proof is not given. In this paper we provide a formal proof.
</p>projecteuclid.org/euclid.mjms/1534384957_20180815220242Wed, 15 Aug 2018 22:02 EDTThe Smallest Self-dual Embeddable Graphs in a Pseudosurfacehttps://projecteuclid.org/euclid.mjms/1534384958<strong>Ethan Rarity</strong>, <strong>Steven Schluchter</strong>, <strong>J. Z. Schroeder</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 85--92.</p><p><strong>Abstract:</strong><br/>
A proper embedding of a graph $G$ in a pseudosurface $P$ is an embedding in which the regions of the complement of $G$ in $P$ are homeomorphic to discs and a vertex of $G$ appears at each pinchpoint of $P$; we say that a proper embedding of $G$ in $P$ is self dual if there exists an isomorphism from $G$ to its topological dual. We determine five possible graphs with 7 vertices and 13 edges that could be self-dual embeddable in the pinched sphere, and we establish, by way of computer-powered methods, that such a self-embedding exists for exactly two of these five graphs.
</p>projecteuclid.org/euclid.mjms/1534384958_20180815220242Wed, 15 Aug 2018 22:02 EDTGenerating Stern-Brocot Type Rational Numbers with Mediantshttps://projecteuclid.org/euclid.mjms/1534384959<strong>Harold Reiter</strong>, <strong>Arthur Holshouser</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 93--104.</p><p><strong>Abstract:</strong><br/>
The Stern–Brocot tree is a method of generating or organizing all fractions in the interval \((0,1)\) by starting with the endpoints \(\frac{0}{1} \) and \(\frac{1}{1}\) and repeatedly applying the mediant operation: \(m\left( \frac{a}{b},\frac{c}{d} \right) =\frac{a+c}{b+d}\). A recent paper of Aiylam considers two generalizations: one is to apply the mediant operation starting with an arbitrary interval \(\left( \frac{a}{b},\frac{c}{d} \right)\) (the fractions must be non-negative), and the other is to allow arbitrary reduction of generated fractions to lower terms. In the present paper, we give simpler proofs of some of Aiylam's results, and we give a simpler method of generating just the portion of the tree that leads to a given fraction.
</p>projecteuclid.org/euclid.mjms/1534384959_20180815220242Wed, 15 Aug 2018 22:02 EDTAnnouncementshttps://projecteuclid.org/euclid.mjms/1534384960<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 1, 105--106.</p>projecteuclid.org/euclid.mjms/1534384960_20180815220242Wed, 15 Aug 2018 22:02 EDTGuassian Amicable Pairshttps://projecteuclid.org/euclid.mjms/1544151688<strong>Patrick Costello</strong>, <strong>Ranthony A. C. Edmonds</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 107--116.</p><p><strong>Abstract:</strong><br/>
This article defines amicable pairs in the complex numbers and finds that some amicable pairs in the natural numbers are also amicable in the complex numbers. Unlike the case in the natural numbers, it is proved that no $(2,1)$ pairs made up of natural numbers where the common factor is a power of $2$ exist as Gaussian amicable pairs. Many pairs are found with complex parts using the DivisorSigma function in Mathematica . The factorizations into primes is given so that the type of pair might be determined.
</p>projecteuclid.org/euclid.mjms/1544151688_20181206220136Thu, 06 Dec 2018 22:01 ESTMozes' Game of Numbers on Directed Graphshttps://projecteuclid.org/euclid.mjms/1544151689<strong>Rohan Hemasinha</strong>, <strong>Avinash J. Dalal</strong>, <strong>Donald McGinn</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 117--131.</p><p><strong>Abstract:</strong><br/>
In 1986, the contestants of the $27$th International Mathematical Olympiad were given a game of numbers played on a pentagon. In 1987, Mozes generalized this game to an arbitrary undirected, weighted, connected graph. The convergence properties and total number of moves of any convergent game have been resolved by Mozes using Weyl groups. Eriksson provided an alternate proof using matrix theory and graph theory. In this paper, we briefly discuss the results of Mozes and Eriksson on undirected graphs. Then we generalize this game to arbitrary directed, strongly connected graphs and investigate the convergence properties of the game of numbers.
</p>projecteuclid.org/euclid.mjms/1544151689_20181206220136Thu, 06 Dec 2018 22:01 ESTHyper Dice Backgammon of Finite Sizehttps://projecteuclid.org/euclid.mjms/1544151690<strong>Amir M. Rahimi</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 132--139.</p><p><strong>Abstract:</strong><br/>
In this note, we extend the notion of standard backgammon to a more general setting and call it hyper dice backgammon (or HD-gammon for short) of size $n \geq 6$ (a positive even integer) by extending the regular die to a hyper die (i.e., hyper cube) with $n$ faces and the board from 24 pips to $4n$ pips, where $n = 2k \geq 6$ and there are $4k+3$ checkers for each player. The rules of the game are similar to the rules of standard backgammon when $n = 2k = 6$ and the number of the $n$-sided dice depends on $n$. Finally, we include a list of references related to some theoretical studies on standard backgammon.
</p>projecteuclid.org/euclid.mjms/1544151690_20181206220136Thu, 06 Dec 2018 22:01 ESTTranslational Surfaceshttps://projecteuclid.org/euclid.mjms/1544151691<strong>Andrew Crutcher</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 140--149.</p><p><strong>Abstract:</strong><br/>
A translational surface is a rational surface generated from two rational space curves by translating one curve along the other curve. In this paper, we utilize matrices to represent translational surfaces, and give necessary and sufficient conditions for a real rational surface to be a translational surface.
</p>projecteuclid.org/euclid.mjms/1544151691_20181206220136Thu, 06 Dec 2018 22:01 ESTIsoperimetry in Surfaces of Revolution with Densityhttps://projecteuclid.org/euclid.mjms/1544151692<strong>Eliot Bongiovanni</strong>, <strong>Alejandro Diaz</strong>, <strong>Arjun Kakkar</strong>, <strong>Nat Sothanaphan</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 150--165.</p><p><strong>Abstract:</strong><br/>
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on $\mathbb{R}^n$, the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two different densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric.
</p>projecteuclid.org/euclid.mjms/1544151692_20181206220136Thu, 06 Dec 2018 22:01 ESTDouble Bubbles on the Line with Log-Convex Density $f$ with $(\log f)'$ Boundedhttps://projecteuclid.org/euclid.mjms/1544151693<strong>Nat Sothanaphan</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 166--175.</p><p><strong>Abstract:</strong><br/>
We extend results of Bongiovanni et al. [1] on double bubbles on the line with log-convex density to the case where the derivative of the log of the density is bounded. We show that the tie function between the double interval and the triple interval still exists, but may blow up to infinity in finite time. For the first time, a density is presented for which the blowup time is positive and finite.
</p>projecteuclid.org/euclid.mjms/1544151693_20181206220136Thu, 06 Dec 2018 22:01 ESTIndicators of Pointed Hopf Algebras of Dimensions $pq$ Over Characteristic $p$https://projecteuclid.org/euclid.mjms/1544151694<strong>Si Chen</strong>, <strong>Tiantian Liu</strong>, <strong>Linhong Wang</strong>, <strong>Xingting Wang</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 176--184.</p><p><strong>Abstract:</strong><br/>
Let $p$, $q$ be two distinct primes. We consider pointed Hopf algebras of dimension $pq$ over an algebraically closed field of characteristic $p$. We compute higher Frobenius-Schur indicators of these Hopf algebras through the associated graded Hopf algebras with respect to their coradical filtrations. The resulting indicators are gauge invariants for the monoidal representation categories of these algebras.
</p>projecteuclid.org/euclid.mjms/1544151694_20181206220136Thu, 06 Dec 2018 22:01 ESTA Note on Class $Q(N)$ Operatorshttps://projecteuclid.org/euclid.mjms/1544151695<strong>Shqipe Lohaj</strong>, <strong>Valdete Rexhëbeqaj Hamiti</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 185--196.</p><p><strong>Abstract:</strong><br/>
Let $T$ be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. In this paper we introduce two new classes of operators: class $Q(N)$ and class $Q^*(N)$. An operator $T\in \mathcal{L}(\mathcal{H})$ is of class $Q(N)$ for a fixed real number $N\geq 1$, if $T$ satisfies $N\|Tx\|^{2} \leq \| T^2 x\|^{2}+ \| x\|^{2}$ for all $x\in \mathcal{H}$. And an operator $T\in \mathcal{L}(\mathcal{H})$ is of class $Q^*(N)$ for a fixed real number $N\geq 1$, if $T$ satisfies $N\|T^*x\|^{2} \leq \| T^2 x\|^{2}+ \| x\|^{2}$ for all $x\in \mathcal{H}$. We prove the basic properties of these classes of operators.
</p>projecteuclid.org/euclid.mjms/1544151695_20181206220136Thu, 06 Dec 2018 22:01 ESTPolynomials in Base $x$ and the Prime-Irreducible Affintyhttps://projecteuclid.org/euclid.mjms/1544151696<strong>Fusun Akman</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 197--217.</p><p><strong>Abstract:</strong><br/>
Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready to spill two of their secrets: (i) There exists a unique “base-$x$” representation of such polynomials that makes the ring $\mathbb{Z}[x]$ into an ordered domain; and (ii) There is a 1-1 correspondence between positive rational primes $p$ and certain infinite sets of irreducible polynomials $f(x)$ that attain the value $p$ at sufficiently large $x$, each generated in finitely many steps from the $p$th cyclotomic polynomial. The base-$x$ representation provides practical conversion methods among numeric bases (not to mention a polynomial factorization algorithm), while the prime-irreducible correspondence puts a new angle on the Bouniakowsky Conjecture, a generalization of Dirichlet's Theorem on Primes in Arithmetic Progressions.
</p>projecteuclid.org/euclid.mjms/1544151696_20181206220136Thu, 06 Dec 2018 22:01 ESTAnnouncementshttps://projecteuclid.org/euclid.mjms/1544151697<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 30, Number 2, 218--219.</p>projecteuclid.org/euclid.mjms/1544151697_20181206220136Thu, 06 Dec 2018 22:01 ESTAn Application of Infinite Sums and Products Relating to Spectral Synthesishttps://projecteuclid.org/euclid.mjms/1559181622<strong>Melanie Henthorn-Baker</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 1--13.</p><p><strong>Abstract:</strong><br/>
The following is a discussion regarding a specific set of operators acting on the space of functions analytic on the unit disk. A diagonal operator is said to admit spectral synthesis if all of its invariant subspaces can be expressed as a closed linear span of a subset of its eigenvectors. This article employs various techniques for verifying the convergence of infinite products and infinite sums as a means of demonstrating that a certain class of operators fail to admit spectral synthesis.
</p>projecteuclid.org/euclid.mjms/1559181622_20190529220033Wed, 29 May 2019 22:00 EDTComputation of Inverse 1-Center Location Problem on the Weighted Trapezoid Graphshttps://projecteuclid.org/euclid.mjms/1559181623<strong>Biswanath Jana</strong>, <strong>Sukumar Mondal</strong>, <strong>Madhumangal Pal</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 14--35.</p><p><strong>Abstract:</strong><br/>
Let $T_{TRP}$ be the tree corresponding to the weighted trapezoid graph $G=(V,E)$. The eccentricity $e(v)$ of the vertex $v$ is defined as the sum of the weights of the vertices from $v$ to the vertex farthest from $v \in T_{TRP}$. A vertex with minimum eccentricity in the tree $T_{TRP}$ is called the 1-center of that tree. In an inverse 1-center location problem, the parameter of the tree $T_{TRP}$ corresponding to the weighted trapezoid graph $G=(V,E)$, like vertex weights, have to be modified at minimum total cost such that a pre-specified vertex $s \in V$ becomes the 1-center of the trapezoid graph $G$. In this paper, we present an optimal algorithm to find an inverse 1-center location on the weighted tree $T_{TRP}$ corresponding to the weighted trapezoid graph $G=(V,E)$, where the vertex weights can be changed within certain bounds. The time complexity of our proposed algorithm is $O(n)$, where $n$ is the number of vertices of the trapezoid graph $G$.
</p>projecteuclid.org/euclid.mjms/1559181623_20190529220033Wed, 29 May 2019 22:00 EDTShift Up-Filters and Decompositions of Up-Filters in Up-Algebrashttps://projecteuclid.org/euclid.mjms/1559181624<strong>Young Bae Jun</strong>, <strong>Aiyared Iampan</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 36--45.</p><p><strong>Abstract:</strong><br/>
The decomposition of a UP-filter is first discussed, and then the notion of a shift UP-filter is introduced, and several properties are investigated. Relations between a UP-filter, a comparative UP-filter, and a shift UP-filter are considered. Conditions for a UP-filter to be a shift UP-filter, and for a comparative UP-filter to be a shift UP-filter are provided. Characterizations of a shift UP-filter are considered, and an extension property for a shift UP-filter is established.
</p>projecteuclid.org/euclid.mjms/1559181624_20190529220033Wed, 29 May 2019 22:00 EDTDirect Proofs of the Fundamental Theorem of Calculus for the Omega Integralhttps://projecteuclid.org/euclid.mjms/1559181625<strong>C. Bryan Dawson</strong>, <strong>Matthew Dawson</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 46--55.</p><p><strong>Abstract:</strong><br/>
When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow immediately, a much more satisfying approach would be to provide direct proofs not relying on the Riemann integral. This note provides those proofs.
</p>projecteuclid.org/euclid.mjms/1559181625_20190529220033Wed, 29 May 2019 22:00 EDTCommutative Ideals of BCK-Algebras Based on Uni-Hesitant Fuzzy Set Theoryhttps://projecteuclid.org/euclid.mjms/1559181626<strong>Shuaa Aldhafeeri</strong>, <strong>G. Muhiuddin</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 56--65.</p><p><strong>Abstract:</strong><br/>
The notion of uni-hesitant fuzzy commutative ideals in BCK-algebras is introduced, and related properties are investigated. Relations between uni-hesitant fuzzy commutative ideals and uni-hesitant fuzzy ideals are discussed. Characterizations of uni-hesitant fuzzy commutative ideals are considered. Conditions for a uni-hesitant fuzzy ideal to be a uni-hesitant fuzzy commutative ideal are provided. Extension property for a uni-hesitant fuzzy commutative ideal is established.
</p>projecteuclid.org/euclid.mjms/1559181626_20190529220033Wed, 29 May 2019 22:00 EDTSums of Powers of Integershttps://projecteuclid.org/euclid.mjms/1559181627<strong>Hunde Eba</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 66--78.</p><p><strong>Abstract:</strong><br/>
We present different methods to generalize sums of powers of positive integers in terms of recurrence relations using the Taylor series, and in closed form using a finite difference method and an integral method. The result gained through the integral method is similar to Bernoulli's sum formula, but it is expressed in terms of a certain recursive sequence $H_i$.
</p>projecteuclid.org/euclid.mjms/1559181627_20190529220033Wed, 29 May 2019 22:00 EDTOn the Kauffman-Jones Polynomial for Virtual Singular Linkshttps://projecteuclid.org/euclid.mjms/1559181628<strong>Carmen Caprau</strong>, <strong>Kelsey Friesen</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 79--104.</p><p><strong>Abstract:</strong><br/>
We extend the Kamada-Miyazawa polynomial to virtual singular links, which is valued in $\mathbb{Z}[A^2, A^{-2}, h]$. The decomposition of the resulting polynomial into two components, one in $\mathbb{Z}[A^2, A^{-2}]$ and the other in $\mathbb{Z}[A^2, A^{-2}]h$ yields the decomposition of the Kauffman-Jones polynomial of virtual singular links into two components, one in $\mathbb{Z}[A^2, A^{-2}]$ and the other in $\mathbb{Z}[A^2, A^{-2}]A^2$, where both components are invariants for virtual singular links.
</p>projecteuclid.org/euclid.mjms/1559181628_20190529220033Wed, 29 May 2019 22:00 EDTAnnouncementshttps://projecteuclid.org/euclid.mjms/1559181629<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 1, 105--106.</p>projecteuclid.org/euclid.mjms/1559181629_20190529220033Wed, 29 May 2019 22:00 EDTPower Series Extensions of Certain Functions of a Real Variablehttps://projecteuclid.org/euclid.mjms/1573873221<strong>Scott H. Demsky</strong>, <strong>Alex Opritsa</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 107--112.</p><p><strong>Abstract:</strong><br/>
The domain of the function $ f(x)=\cos \sqrt{x} $ is the set of all nonnegative real numbers. In this article, we will show how to use power series to extend this function to an analytic function defined on the entire real line. We will then show how this analytic extension of $ f(x) $ makes it easier and quicker for calculus students to compute derivatives of $ f(x) $ at the origin. We will moreover describe the process of extending the domain of any function of the form $ g(\sqrt{x}) $ for a given even analytic function $ g(x) $.
</p>projecteuclid.org/euclid.mjms/1573873221_20191115220042Fri, 15 Nov 2019 22:00 ESTUniqueness of the Common Invariant Density and the Convergence of the Fixed Point Iterationhttps://projecteuclid.org/euclid.mjms/1573873222<strong>Peter M. Uhl</strong>, <strong>Hannah Bohn</strong>, <strong>Noah H. Rhee</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 113--120.</p><p><strong>Abstract:</strong><br/>
In [6] we have shown that the Frobenius-Perron operators associated with a one parameter family of piecewise linear chaotic maps have a common invariant (fixed) density map. In this paper we show the uniqueness of the common invariant density map and analyze the corresponding fixed point algorithm.
</p>projecteuclid.org/euclid.mjms/1573873222_20191115220042Fri, 15 Nov 2019 22:00 ESTOn Homomorphisms of $AB$-algebrashttps://projecteuclid.org/euclid.mjms/1573873225<strong>Restituto D. Bejarasco</strong>, <strong>Narciso C. Gonzaga, Jr.</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 121--129.</p><p><strong>Abstract:</strong><br/>
In this study, the notion of $AB$-homomorphism of an $AB$-algebra is introduced and some of its properties are obtained. Moreover, the first and third isomorphism theorems for $AB$-algebras are investigated.
</p>projecteuclid.org/euclid.mjms/1573873225_20191115220042Fri, 15 Nov 2019 22:00 ESTTopological Folding on the Chaotic Projective Spaces and Their Fundamental Grouphttps://projecteuclid.org/euclid.mjms/1573873226<strong>M. Abu-Saleem</strong>, <strong>W. Faris. Al-Omeri</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 130--135.</p><p><strong>Abstract:</strong><br/>
In this article we will introduce different types of topological foldings on chaotic projective space. The limit of topological foldings on the fundamental group of the real projective plane will be obtained. The chain of folding on the chaotic projective spaces will induce a chain of fundamental groups. The relations between these chains will be achieved.
</p>projecteuclid.org/euclid.mjms/1573873226_20191115220042Fri, 15 Nov 2019 22:00 ESTGenerating Pythagorean Triples of a Given Heighthttps://projecteuclid.org/euclid.mjms/1573873229<strong>Jathan Austin</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 136--145.</p><p><strong>Abstract:</strong><br/>
The height of a Pythagorean triple $(a,b,c)$ is defined as the difference $c - b$. In this paper, building on the Height-Excess Enumeration Theorem, we show how to generate primitive Pythagorean triples of a given height using powers of a single matrix. Then, we briefly discuss other matrices that both map any Pythagorean triple to another and also preserve a triple's height. We also note how Pythagorean triples with a given leg difference can be generated using matrices.
</p>projecteuclid.org/euclid.mjms/1573873229_20191115220042Fri, 15 Nov 2019 22:00 ESTVertex and Edge Padmakar-Ivan Indices of Unitary Cayley Graphshttps://projecteuclid.org/euclid.mjms/1573873230<strong>Roshan Sara Philipose</strong>, <strong>Sarasija Perurkada Balakrishnan</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 146--151.</p><p><strong>Abstract:</strong><br/>
In graph theory, many topological indices based on vertex and edge distances are utilized in theoretical chemistry. Even though there are many such indices, we restrict our attention in this paper to the vertex Padmakar-Ivan index $PI_v(G)$ and the edge Padmakar-Ivan index $PI_e(G)$ of a simple connected graph $G$ without directed edges. We shall emphasize the computation of the vertex and edge Padmakar-Ivan indices of unitary Cayley graphs, $X_n$.
</p>projecteuclid.org/euclid.mjms/1573873230_20191115220042Fri, 15 Nov 2019 22:00 ESTInt-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebrashttps://projecteuclid.org/euclid.mjms/1573873231<strong>Rajab Ali Borzooei</strong>, <strong>Xiao Long Xin</strong>, <strong>Eun Hwan Roh</strong>, <strong>Young Bae Jun</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 152--163.</p><p><strong>Abstract:</strong><br/>
The notion of an int-soft (weak) implicative hyper BCK-ideal is introduced, and related properties are investigated. Relations between an int-soft weak implicative hyper BCK-ideal, an int-soft implicative hyper BCK-ideal, an int-soft hyper BCK-ideal, and an int-soft strong hyper BCK-ideal are considered, and characterizations of an int-soft weak implicative hyper BCK-ideal are discussed. Conditions for an int-soft hyper BCK-ideal to be an int-soft weak implicative hyper BCK-ideal are provided. Using an int-soft weak implicative hyper BCK-ideal, a new int-soft weak implicative hyper BCK-ideal is established. Finally, we show the hyper homomorphic preimage of an int-soft implicative hyper BCK-ideal is also an int-soft implicative hyper BCK-ideal.
</p>projecteuclid.org/euclid.mjms/1573873231_20191115220042Fri, 15 Nov 2019 22:00 ESTThe Minimum Completions and Covers of Symmetric, Hankel Symmetric, and Centrosymmetric Doubly Substochastic Matriceshttps://projecteuclid.org/euclid.mjms/1573873232<strong>Jinze Song</strong>, <strong>Huili Liu</strong>, <strong>Hao Rong</strong>, <strong>Zhentao Xie</strong>, <strong>Xu Yan</strong>, <strong>Huilan Li</strong>, <strong>Zhi Chen</strong>, <strong>Lei Cao</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 164--173.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate and describe all the minimal completions and covers of the symmetric, Hankel symmetric, and centrosymmetric doubly substochastic matrices, respectively.
</p>projecteuclid.org/euclid.mjms/1573873232_20191115220042Fri, 15 Nov 2019 22:00 EST$\mathcal{I}_\mathbf{g}^*$-closed Sets via Ideal Topological Spaceshttps://projecteuclid.org/euclid.mjms/1573873233<strong>Wadei Al-Omeri</strong>, <strong>M. Abu-Saleem</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 174--191.</p><p><strong>Abstract:</strong><br/>
In this paper, aspects of generalized continuity and generalized closedness are explored. The standard material on the notions of $*g$-open, $\mathbf{g}$-open sets and some definitions and results that are needed are presented first. Then the class of $\mathcal{I}_\mathbf{g}^*$-closed sets is introduced and its fundamental properties are studied. Also, $\mathcal{I}_\mathbf{g}^*$-regular, $^*$-additive, $^*$-multiplicative, $\mathcal{I}_\mathbf{g}^*$-additive, and $\mathcal{I}_\mathbf{g}^*$-multiplicative spaces are introduced and their properties are investigated.
</p>projecteuclid.org/euclid.mjms/1573873233_20191115220042Fri, 15 Nov 2019 22:00 ESTThe Isoperimetric Deficit of Equichordal Curves in $\mathbb{R}^2$https://projecteuclid.org/euclid.mjms/1573873234<strong>Zhenyi Wang</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 192--200.</p><p><strong>Abstract:</strong><br/>
We study lower and upper bounds of the isoperimetric deficit of equichordal curves in $\mathbb{R}^2$. An equichordal curve is defined by its polar radius $r(t)=p(t)+c$ with $t\in \mathbb{R}$, constant $c$, and $p(t)+p(t+\pi)=0$, such that chords through the origin are always of length $2c$. In the convex case, the isoperimetric deficit of equichordal curves has a non-attained constant upper bound. Otherwise, non-convex equichordal curves have an unbounded deficit. However, we prove that for any sufficiently regular equichordal curves $r(t)$, even non-convex, we can find associated curves of same enclosed area whose isoperimetric deficits bound from above and below the isoperimetric deficit of the equichordal curve $$0<L_{y_0}^2-4\pi A_{y_0} < L_r^2-4\pi A \leq L_{y_{max}}^2-4\pi A_{y_{max}} ,$$ where $L_{y_0}$ and $L_{y_{max}}$ refer to lengths of curves with radii $y_0(t)=\sqrt{p(t)^2+c^2}$ and, respectively, $y_{max}(t)=\sqrt{p(t)^2+c^2+\frac{p_m^2+c^2}{p_m}p(t)}$ with $p_m=\max\ |p|$.
</p>projecteuclid.org/euclid.mjms/1573873234_20191115220042Fri, 15 Nov 2019 22:00 ESTConeat Injective Moduleshttps://projecteuclid.org/euclid.mjms/1573873235<strong>Mohanad Farhan Hamid</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 201--211.</p><p><strong>Abstract:</strong><br/>
A module is called coneat injective if it is injective with respect to all coneat exact sequences. The class of such modules is enveloping and falls properly between injectives and pure injectives. Generalizations of coneat injectivity, like relative coneat injectivity and full invariance of a module in its coneat injective envelope, are studied. Using properties of such classes of modules, we characterize certain types of rings like von Neumann regular and right SF-rings. For instance, $R$ is a right SF-ring if and only if every coneat injective left $R$-module is injective.
</p>projecteuclid.org/euclid.mjms/1573873235_20191115220042Fri, 15 Nov 2019 22:00 ESTAnnouncementshttps://projecteuclid.org/euclid.mjms/1573873236<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 31, Number 2, 212--213.</p>projecteuclid.org/euclid.mjms/1573873236_20191115220042Fri, 15 Nov 2019 22:00 ESTVarious Types of Supra Pre-compact and Supra Pre-Lindelöf Spaceshttps://projecteuclid.org/euclid.mjms/1593655212<strong>T. M. Al-Shami</strong>, <strong>B. A. Asaad</strong>, <strong>M. A. El-Gayar</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 1--20.</p><p><strong>Abstract:</strong><br/>
The purpose of this article is to introduce three types of supra compactness and three types of supra Lindelöfness via supra topological spaces based on the supra pre-open sets. With the help of examples, we illustrate the relationships among them and show their relationships with some kinds of supra compactness and supra Lindelöfness given in [3]. We characterize each type of space and investigate the image of them under pre-irresolute mappings. Also, we prove that these spaces are preserved under the finite product spaces, and give a sufficient condition for the equivalence among supra compact, almost supra compact and supra pre-compact spaces. At the end of each section, we provide some examples to demonstrate that the spaces studied and their counterparts, introduced in [9], are independent of each other.
</p>projecteuclid.org/euclid.mjms/1593655212_20200701220026Wed, 01 Jul 2020 22:00 EDT$\mu$-Paracompactness via Hereditary Classeshttps://projecteuclid.org/euclid.mjms/1593655216<strong>Abdo Qahis</strong>, <strong>Takashi Noiri</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 21--31.</p><p><strong>Abstract:</strong><br/>
The notion of paracompactness in generalized topology is introduced and studied in [5]. In this paper, we introduce and investigate the notion of $\mu$-paracompact spaces with respect to a hereditary class $\mathcal{H}$, which is a generalization of the notion of $\mu$-paracompact spaces. We study characterizations, subsets, and subspaces of $\mu\mathcal{H}$-paracompact spaces. Also, we investigate the invariants of $\mu\mathcal{H}$-paracompact spaces by functions.
</p>projecteuclid.org/euclid.mjms/1593655216_20200701220026Wed, 01 Jul 2020 22:00 EDTArithmetic Sequences and Blocks of Powers of Two in the Collatz Arrayhttps://projecteuclid.org/euclid.mjms/1593655217<strong>Shaun V. Ault</strong>, <strong>Matthew Cliatt</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 32--38.</p><p><strong>Abstract:</strong><br/>
In this short paper, we examine a curious feature of the Collatz function. When the sequences generated by the Collatz function on consecutive integer initial points are arranged into an array, certain arithmetic sequences show up with common differences given by products of twos and threes. The common differences themselves are further related by a formula that depends on even versus odd input. While we do not solve the Collatz Conjecture by this observation, we present our findings as interesting mathematical results in their own rights.
</p>projecteuclid.org/euclid.mjms/1593655217_20200701220026Wed, 01 Jul 2020 22:00 EDTOn the Log-Concavity Density Function: A Case of Exponential Power Distribution and its Applicationhttps://projecteuclid.org/euclid.mjms/1593655218<strong>A. A. Olosunde</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 39--48.</p><p><strong>Abstract:</strong><br/>
Log-concavity of probability density functions has played an important role in many applications in economics, reliability studies, and many more. Several authors have studied log-concavity of many distribution such as the normal, logistic, exponential, etc., but no attention has been paid to exponential power distributions, a family of elliptical distributions which generalize the normal, double exponential, and Kotz distribution. This distribution has been found to be very useful in applications, especially when flexibility of the tails (heavier or thinner than the normal distribution) are required in modeling of natural phenomenon. This paper was written to fill this void in the literature.
</p>projecteuclid.org/euclid.mjms/1593655218_20200701220026Wed, 01 Jul 2020 22:00 EDTConditional Correctness of the Internal Boundary Value Problem of the Pseudoparabolic Equation with a Changing Time Directionhttps://projecteuclid.org/euclid.mjms/1593655219<strong>Kudratillo Sadridinovich Fayazov</strong>, <strong>Zamira Shamshaddinovna Abdullayeva</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 49--60.</p><p><strong>Abstract:</strong><br/>
We consider data and boundary conditions and data within the regularity domain of a pseudoparabolic equation with varying time direction. This problem cannot be solved in the sense of J. Hadamard. Based on A. N. Tikhonov's approach, this problem is investigated for conditional correctness, the uniqueness theorem is proved, and the evaluation of conditional stability on the set of correctness is established. This study uses methods of functional analysis and methods of the theory of functions of a complex variable.
</p>projecteuclid.org/euclid.mjms/1593655219_20200701220026Wed, 01 Jul 2020 22:00 EDTA Pascal Triangle Type Calculation for a Particular Infinite Serieshttps://projecteuclid.org/euclid.mjms/1593655220<strong>Simon Aloff</strong>, <strong>Michael Miniere (Deceased)</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 61--70.</p><p><strong>Abstract:</strong><br/>
In general, finding the sum of an infinite series is not always possible. However, there are infinite series whose sums can be computed. In our earlier paper, we derived a formula for computing the sum of a type of polylogarithm series involving multinomial coefficients. In this paper, we show that the formula leads to an elementary computation for the series $\sum_{k=1}^{\infty}\frac{k^n}{a^k}$ involving numbers obtained by a method similar to Pascal's triangle. We also show that our result is the number of ways of distributing $n$ distinct objects in $n$ or fewer distinct nonempty cells.
</p>projecteuclid.org/euclid.mjms/1593655220_20200701220026Wed, 01 Jul 2020 22:00 EDTA Hypergroup Dual Space Can be Unboundedhttps://projecteuclid.org/euclid.mjms/1593655221<strong>Adam Parr</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 71--79.</p><p><strong>Abstract:</strong><br/>
Unlike topological groups, hypergroups are not closed under duality. While it has long been known that a hypergroup dual space might be signed , the boundedness of such dual spaces has been an open question. In this paper it is shown that a hypergroup dual space may fail to be bounded. An example will be given of an infinite direct product of finite hypergroups whose dual space is a semi-bounded , but not bounded, generalized hypergroup.
</p>projecteuclid.org/euclid.mjms/1593655221_20200701220026Wed, 01 Jul 2020 22:00 EDTOn Almost $\alpha$-Topological Vector Spaceshttps://projecteuclid.org/euclid.mjms/1593655222<strong>Shallu Sharma</strong>, <strong>Sahil Billawria</strong>, <strong>Tsering Landol</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 80--87.</p><p><strong>Abstract:</strong><br/>
The main objective of this paper is to introduce a new generalized form of topological vector spaces, namely, almost $\alpha$-topological vector spaces by using the concepts of $\alpha$-open sets, regular open sets, and almost $\alpha$-continuous mappings. In the present paper, some important examples of almost $\alpha$-topological vector spaces with basic properties are characterized.
</p>projecteuclid.org/euclid.mjms/1593655222_20200701220026Wed, 01 Jul 2020 22:00 EDTFinitely Generated Submoduloids and Prime Submoduloids on a Nexushttps://projecteuclid.org/euclid.mjms/1593655223<strong>R. Kamrani</strong>, <strong>A. Hasankhani</strong>, <strong>M. Bolourian</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 88--109.</p><p><strong>Abstract:</strong><br/>
The concept of $\mathbb{N^{\infty}}$-submoduloid has been introduced in [5]. In this paper, the notions of a generating submoduloid, an additive absorption set, a prime $\mathbb{N^{\infty}}$-submoduloid, and an additive $\mathbb{N^{\infty}}$-submoduloid of an $\mathbb{N^{\infty}}$-moduloid are defined and some related results are investigated.
</p>projecteuclid.org/euclid.mjms/1593655223_20200701220026Wed, 01 Jul 2020 22:00 EDTStrongly Fully Stable Acts Relative to an Idealhttps://projecteuclid.org/euclid.mjms/1593655224<strong>A. K. Mutashar</strong>, <strong>H. R. Baanoon</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 110--117.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to introduce and investigate strongly fully stable acts relative to an ideal as a concept generalizing strongly fully stable modules relative to an ideal, but is stronger than that of fully stable acts. In this study, we consider some properties and characterizations of the class of strongly fully stable acts relative to an ideal, as well as the relations between this class and other classes. Among these classes are quasi-injective acts, strongly quasi-injective acts, acts which satisfy Baer's criterion, acts satisfying the strongly Baer's criterion, and duo acts. The product of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. The coproduct of any family of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. Also, we have that strongly fully stable acts relative to an ideal are equivalent to an $S$-act that satisfies the strongly Baer's criterion relative to an ideal $I$ for cyclic subacts. The strongly fully stable act relative to $I$ is equivalent to the strongly quasi-injective act relative to the ideal $I$ and duo act with a commutative monoid.
</p>projecteuclid.org/euclid.mjms/1593655224_20200701220026Wed, 01 Jul 2020 22:00 EDTA Retractionhttps://projecteuclid.org/euclid.mjms/1593655225<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 118--118.</p><p><strong>Abstract:</strong><br/>
An Alternate Cayley-Dickson Algebra , Volume 28, Issue 1 (2016), has been retracted by the author. He has discovered that the doubling product, which is the primary subject of the paper, does not generate a Cayley-Dickson algebra beyond the second doubling. As the paper cannot be repaired, he has asked for the paper's retraction.
</p>projecteuclid.org/euclid.mjms/1593655225_20200701220026Wed, 01 Jul 2020 22:00 EDTAnnouncementshttps://projecteuclid.org/euclid.mjms/1593655226<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 32, Number 1, 119--120.</p>projecteuclid.org/euclid.mjms/1593655226_20200701220026Wed, 01 Jul 2020 22:00 EDT