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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Editorial
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 EDTInteractive Construction of Small Grammarshttp://projecteuclid.org/euclid.mjms/1418931953<strong>Jeffrey Clark</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 115--121.</p><p><strong>Abstract:</strong><br/>
An interactive approach to constructing small LR(1) grammars is presented. An
example involving parsing permutations is used to illustrate the approach.
</p>projecteuclid.org/euclid.mjms/1418931953_20141218144559Thu, 18 Dec 2014 14:45 ESTJordan Forms and $n$th Order Linear Recurrenceshttp://projecteuclid.org/euclid.mjms/1418931954<strong>Thomas McKenzie</strong>, <strong>Shannon Overbay</strong>, <strong>Robert Ray</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 122--133.</p><p><strong>Abstract:</strong><br/>
Let $p$ be a prime number with $p\neq 2$. We consider sequences generated by
$n$th order linear recurrence relations over the finite field $Z_p$. In the
first part of this paper we generalize some of the ideas in
[6] to $n$th order linear recurrences. We then consider
the case where the characteristic polynomial of the recurrence has one root in
$Z_p$ of multiplicity $n$. In this case, we show that the corresponding
recurrence can be generated by a relatively simple matrix.
</p>projecteuclid.org/euclid.mjms/1418931954_20141218144559Thu, 18 Dec 2014 14:45 ESTThe Converse of the Intermediate Value Theorem: From Conway to Cantor to Cosets
and Beyondhttp://projecteuclid.org/euclid.mjms/1418931955<strong>Greg Oman</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 134--150.</p><p><strong>Abstract:</strong><br/>
The classical Intermediate Value Theorem (IVT) states that if $f$ is a continuous
real-valued function on an interval $[a,b]\subseteq\mathbb{R}$ and if $y$ is a
real number strictly between $f(a)$ and $f(b)$, then there exists a real number
$x\in(a,b)$ such that $f(x)=y$. The standard counterexample showing that the
converse of the IVT is false is the function $f$ defined on $\mathbb{R}$ by
$f(x):=\sin(\frac{1}{x})$ for $x\neq 0$ and $f(0):=0$. However, this
counterexample is a bit weak as $f$ is discontinuous only at $0$. In this note,
we study a class of strong counterexamples to the converse of the IVT. In
particular, we present several constructions of functions $f \colon
\mathbb{R}\rightarrow\mathbb{R}$ such that $f[I]=\mathbb{R}$ for every nonempty
open interval $I$ of $\mathbb{R}$ ($f[I]:=\{f(x):x\in I\}$). Note that such an
$f$ clearly satisfies the conclusion of the IVT on every interval $[a,b]$ (and
then some), yet $f$ is necessarily nowhere continuous! This leads us to a more
general study of topological spaces $X=(X,\mathcal{T})$ with the property that
there exists a function $f \colon X\rightarrow X$ such that $f[O]=X$ for every
nonvoid open set $O\in\mathcal{T}$.
</p>projecteuclid.org/euclid.mjms/1418931955_20141218144559Thu, 18 Dec 2014 14:45 ESTZero-Divisor Graphs of $2 \times 2$ Upper Triangular Matrix Rings Over
$Z_n$http://projecteuclid.org/euclid.mjms/1418931956<strong>Todd Fenstermacher</strong>, <strong>Ethan Gegner</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 151--167.</p><p><strong>Abstract:</strong><br/>
Istvan Beck introduced the zero-divisor graph in 1988. We explore the directed
and undirected zero-divisor graphs of the rings of $2 \times 2$ upper triangular
matrices mod $n$, denoted by $\Gamma(T_2(n))$ and $\tilde{\Gamma}(T_2(n))$,
respectively. For prime $p$, we completely characterize the graph
$\Gamma(T_2(p))$ by partitioning $T_2(p)$, and prove several key properties of
the graphs using this approach. We establish additional properties of
$\Gamma(T_2(n))$ for arbitrary $n$. We prove that $\Gamma(T_2(n))$ is
Hamiltonian if and only if $n$ is prime, and we give explicit formulas for the
edge connectivity and clique number of $\Gamma(T_2(n))$ in terms of the prime
factorization of $n$.
</p>projecteuclid.org/euclid.mjms/1418931956_20141218144559Thu, 18 Dec 2014 14:45 ESTThe Linear Topology Associated with Weak Convergence of Probability
Measureshttp://projecteuclid.org/euclid.mjms/1418931957<strong>Liang Hong</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 168--172.</p><p><strong>Abstract:</strong><br/>
This expository note aims at illustrating weak convergence of probability
measures from a broader view than a previously published paper. Though the
results are standard for functional analysts, this approach is rarely known by
statisticians and our presentation gives an alternative view to most standard
probability textbooks. In particular, this functional approach clarifies the
underlying topological structure of weak convergence. We hope this short note is
helpful for those who are interested in weak convergence as well as instructors
of measure theoretic probability.
</p>projecteuclid.org/euclid.mjms/1418931957_20141218144559Thu, 18 Dec 2014 14:45 ESTEngineers Do It, Scientists Do It, Mathematicians?http://projecteuclid.org/euclid.mjms/1418931958<strong>Joe Santmyer</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 173--188.</p><p><strong>Abstract:</strong><br/>
There is a magnificent mathematical gem missing from most numerical analysis
curricula. A literature search of numerical analysis and mathematical modeling
texts indicates its absence. What is missing from the numerical analysis toolbox
and why isn't it there? The missing tool is the Kalman filter . The Kalman
filter requires a modest knowledge of statistics. Is this why it is missing from
the toolbox? Read and reach your own conclusion whether this piece of
mathematics should be part of a numerical analysis or mathematical modeling
curriculum.
</p>projecteuclid.org/euclid.mjms/1418931958_20141218144559Thu, 18 Dec 2014 14:45 ESTAnalysis of Batch Arrival Queue with Two Stages of Service and Phase
Vactionshttp://projecteuclid.org/euclid.mjms/1418931959<strong>S. Maragatha Sundari</strong>, <strong>S. Srinivasan</strong>, <strong>A. Ranjitham</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 26, Number 2, 189--205.</p><p><strong>Abstract:</strong><br/>
We study a batch arrival queueing system of phase vacation with two stages of
service based on a Bernoulli schedule. A single server provides essential
service to all arriving customers with service time following a general
distribution. After two stages of service completion, the server leaves for
phase one vacation of random length with probability $p$ or to continue staying
in the system with probability $1-p$. As soon as the completion of phase one
vacation, the server undergoes phase two vacation. On completion of two
heterogeneous phases of vacation the server returns back to the system. The
vacation times are assumed to be general. The server is interrupted and the
service interruption follows an exponential distribution. The arrivals follow a
Poisson distribution. Using supplementary variable technique, the Laplace
transforms of time dependent probabilities of system state are derived. From
this we deduce the steady state results. We also obtain the average queue size
and average waiting time.
</p>projecteuclid.org/euclid.mjms/1418931959_20141218144559Thu, 18 Dec 2014 14:45 ESTBook Thickness of Planar Zero Divisor Graphshttp://projecteuclid.org/euclid.mjms/1449161362<strong>Thomas McKenzie</strong>, <strong>Shannon Overbay</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 2--9.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a finite commutative ring with identity.
We form the zero divisor graph of $R$ by taking the nonzero zero divisors as the vertices and connecting two
vertices, $x$ and $y$, by an edge if and only if $xy=0$.
We establish that if the zero divisor graph of a finite commutative ring with identity is planar,
then the graph has a planar supergraph with a Hamiltonian cycle.
We also determine the book thickness of all planar zero divisor graphs.
</p>projecteuclid.org/euclid.mjms/1449161362_20151203114923Thu, 03 Dec 2015 11:49 ESTSmith Numbers From Primes with Small Digitshttp://projecteuclid.org/euclid.mjms/1449161363<strong>Patrick Costello</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 10--15.</p><p><strong>Abstract:</strong><br/>
We find three new ways to construct Smith numbers from primes
that contain small digits and a known digit sum. The resulting Smith numbers
may have a fairly large number of digits.
</p>projecteuclid.org/euclid.mjms/1449161363_20151203114923Thu, 03 Dec 2015 11:49 ESTCentralizers of Transitive Permutation Groups and Applications to Galois Theoryhttp://projecteuclid.org/euclid.mjms/1449161364<strong>Chad Awtrey</strong>, <strong>Nakhila Mistry</strong>, <strong>Nicole Soltz</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 16--32.</p><p><strong>Abstract:</strong><br/>
Let $f(x)$ be an irreducible polynomial of degree $n$ defined over a field $F$,
and let $G$ be the Galois group of $f$, identified as a transitive subgroup of $S_n$.
Let $K/F$ be the stem field of $f$. We show the automorphism group of $K/F$ is
isomorphic to the centralizer of $G$ in $S_n$.
We include two applications to computing Galois groups; one in the case $F$ is
the rational numbers, the other when $F$ is the 5-adic numbers.
</p>projecteuclid.org/euclid.mjms/1449161364_20151203114923Thu, 03 Dec 2015 11:49 ESTA Note on OI Torsion Abelian Groupshttp://projecteuclid.org/euclid.mjms/1449161365<strong>John A. Lewallen</strong>, <strong>Noel Sagullo</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 33--36.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a commutative ring with unity and $M_R$ be a nonzero unital right $R$-module.
We say that $M$ is an OI $R$-module if for each $x \in R$, $Mx = M$ implies $x$ is invertible in $R$.
We give a characterization of OI torsion abelian groups in terms of their direct summands.
</p>projecteuclid.org/euclid.mjms/1449161365_20151203114923Thu, 03 Dec 2015 11:49 ESTFamilies of Values of the Excedent Function $\sigma (n) - 2n$http://projecteuclid.org/euclid.mjms/1449161366<strong>Raven Dean</strong>, <strong>Rick Erdman</strong>, <strong>Dominic Klyve</strong>, <strong>Emily Lycette</strong>, <strong>Melissa Pidde</strong>, <strong>Derek Wheel</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 37--46.</p><p><strong>Abstract:</strong><br/>
The excedent function, $e(n) := \sigma(n) - 2n$, measures the amount by
which the sum of the divisors of an
integer exceeds that integer. Despite having been in the mathematical consciousness
for more than $2000$ years, there are many unanswered questions concerning the function.
Of particular importance to us is the question of explaining and classifying values in the
image of $e(n)$ — especially in understanding the ``small'' values. We look at extensive
calculated data, and use them as inspiration for new results, generalizing theorems in the
literature, to better understand a family of values in this image.
</p>projecteuclid.org/euclid.mjms/1449161366_20151203114923Thu, 03 Dec 2015 11:49 ESTIntersection Theorems for Closed Convex Sets and Applicationshttp://projecteuclid.org/euclid.mjms/1449161367<strong>Hichem Ben-El-Mechaiekh</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 47--63.</p><p><strong>Abstract:</strong><br/>
A number of landmark existence theorems of nonlinear functional analysis
follow in a simple and direct way from the basic separation of convex closed
sets in finite dimension via elementary versions of the
Knaster-Kuratowski-Mazurkiewicz principle - which we extend to arbitrary
topological vector spaces - and a coincidence property for so-called von
Neumann relations. The method avoids the use of deeper results of
topological essence such as the Brouwer Fixed Point Theorem or the Sperner's Lemma and
underlines the crucial role played by convexity. It turns
out that the convex KKM Principle is equivalent to the Hahn-Banach Theorem,
the Markov-Kakutani Fixed Point Theorem, and the Sion-von Neumann Minimax Principle.
</p>projecteuclid.org/euclid.mjms/1449161367_20151203114923Thu, 03 Dec 2015 11:49 ESTGeneral Dorroh Extensionshttp://projecteuclid.org/euclid.mjms/1449161368<strong>I. Alhribat</strong>, <strong>P. Jara</strong>, <strong>I. M\'arquez</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 64--70.</p><p><strong>Abstract:</strong><br/>
In a recent paper G. A. Cannon and K. M. Neuerburg point out that if $A=\mathbb{Z}$ and $B$ is an
arbitrary ring with unity, then $\mathbb{Z}\star{B}$, the Dorroh extension of $B$, is isomorphic
to the direct product $\mathbb{Z}\times{B}$. Thus, the ideal structure of $\mathbb{Z}\star{B}$
can be completely described. The aim of this note is to point out that this result may be extended to
any pair $(A,B)$ in which $B$ is an $A$-algebra with unity, and to study the construction of
extensions of algebras without zero divisors and their behavior with respect to algebra maps.
</p>projecteuclid.org/euclid.mjms/1449161368_20151203114923Thu, 03 Dec 2015 11:49 ESTHermite-Hadamard Type Inequalities for the Product of $(\alpha, m)$-Convex Functionhttp://projecteuclid.org/euclid.mjms/1449161369<strong>Hong-Ping Yin</strong>, <strong>Feng Qi</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 71--79.</p><p><strong>Abstract:</strong><br/>
In the paper, the authors establish some Hermite-Hadamard type inequalities
for the product of two $(\alpha, m)$-convex functions.
</p>projecteuclid.org/euclid.mjms/1449161369_20151203114923Thu, 03 Dec 2015 11:49 ESTTT-Functionals and Martin-L\"of Randomness for Bernoulli Measureshttp://projecteuclid.org/euclid.mjms/1449161370<strong>Logan Axon</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 80--86.</p><p><strong>Abstract:</strong><br/>
For $r \in [0,1]$, the Bernoulli measure $\mu_r$ on the Cantor space $\cs$ assigns
measure $r$ to the set of sequences with $1$ at a fixed position.
In \cite{MR1078668} it is shown that for $r,s \in [0,1]$, $\mu_s$ is continuously reducible to
$\mu_r$ if any only if $r$ and $s$ satisfy certain purely number theoretic conditions (binomial
reduciblility).
We bring these results into the context of computability theory and Martin-L\"of randomness and
show that the continuous maps arising in \cite{MR1078668} are truth-table functionals
(tt-functionals) on $\cs$.
This allows us extend the characterization of continuous reductions between Bernoulli
measures to include tt-functionals.
It then follows from the conservation of randomness under tt-functionals that if $s$ is
binomially reducible to $r$, then there is a tt-functional that maps every Martin-L\"of random
sequence for $\mu_s$ to a Martin-L\"of random sequences for $\mu_r$.
We are also able to show using results in \cite{MR2974238} that the converse of this
statement is not true.
</p>projecteuclid.org/euclid.mjms/1449161370_20151203114923Thu, 03 Dec 2015 11:49 ESTContra-Somewhat Continuous Functionshttp://projecteuclid.org/euclid.mjms/1449161371<strong>C. W. Baker</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 87--94.</p><p><strong>Abstract:</strong><br/>
Two new forms of contra-somewhat continuity are introduced.
Characterizations and the basic properties of both forms investigated.
</p>projecteuclid.org/euclid.mjms/1449161371_20151203114923Thu, 03 Dec 2015 11:49 ESTAn Exceedingly Short Proof that the Harmonic Series Divergeshttp://projecteuclid.org/euclid.mjms/1449161372<strong>Richard L. Baker</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 27, Number 1, 95--96.</p><p><strong>Abstract:</strong><br/>
In this short note we give an exceedingly short proof that the
harmonic series diverges . The proof is virtually a one-liner.
</p>projecteuclid.org/euclid.mjms/1449161372_20151203114923Thu, 03 Dec 2015 11:49 ESTMinimizing Times Between Boundary Points on Rectangular Poolshttp://projecteuclid.org/euclid.mjms/1474295351<strong>Tonja Miick</strong>, <strong>Tom Richmond</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 2--14.</p><p><strong>Abstract:</strong><br/>
The well-known ``do dogs know calculus'' problem optimizes the travel time from
an onshore dog to an offshore stick, given different running and swimming speeds
and a straight coastline. Here, we optimize the travel time between two points
on the boundary of a rectangular swimming pool, assuming that running speed
along the edge differs from the swimming speed.
</p>projecteuclid.org/euclid.mjms/1474295351_20160919102916Mon, 19 Sep 2016 10:29 EDT$\mu$-Lindelöfness in Terms of a Hereditary Classhttp://projecteuclid.org/euclid.mjms/1474295352<strong>Abdo Qahis</strong>, <strong>Heyam Hussain AlJarrah</strong>, <strong>Takashi Noiri</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 15--24.</p><p><strong>Abstract:</strong><br/>
A hereditary class on a set $X$ is a nonempty collection of subsets of $X$ closed
under the hereditary property. In this paper, we define and study the notion of
Lindelöfness in generalized topological spaces with respect to a hereditary
class called, $\mu\mathcal{H}$-Lindelöf spaces and discuss their properties.
</p>projecteuclid.org/euclid.mjms/1474295352_20160919102916Mon, 19 Sep 2016 10:29 EDT$\omega$-Jointly Metrizable Spaceshttp://projecteuclid.org/euclid.mjms/1474295353<strong>M. A. Al Shumrani</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 25--30.</p><p><strong>Abstract:</strong><br/>
A topological space $X$ is $\omega$- jointly metrizable if for every
countable collection of metrizable subspaces of $X$, there exists a metric on
$X$ which metrizes every member of this collection. Although the Sorgenfrey line
is not jointly partially metrizable, we prove that it is $\omega$- jointly
metrizable .
We show that if $X$ is a regular first countable $T_{1}$-space such that $X$ is
the union of two subspaces one of which is separable and metrizable, and the
other is closed and discrete, then $X$ is $\omega$- jointly metrizable .
</p>projecteuclid.org/euclid.mjms/1474295353_20160919102916Mon, 19 Sep 2016 10:29 EDTI'm Thinking of a Number $\ldots$http://projecteuclid.org/euclid.mjms/1474295354<strong>Adam Hammett</strong>, <strong>Greg Oman</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 31--48.</p><p><strong>Abstract:</strong><br/>
Consider the following game: Player A chooses an integer $\alpha$ between $1$ and
$n$ for some integer $n\geq1$, but does not reveal $\alpha$ to Player B. Player B
then asks Player A a yes/no question about which number Player A chose, after
which Player A responds truthfully with either ``yes'' or ``no.'' After a
predetermined number $m$ of questions have been asked ($m\geq 1$), Player B must
attempt to guess the number chosen by Player A. Player B wins if she guesses
$\alpha$. The purpose of this note is to find, for every $m\geq 1$, all canonical
$m$-question algorithms which maximize the probability of Player B winning the
game (the notion of ``canonical algorithm'' will be made precise in Section 3).
</p>projecteuclid.org/euclid.mjms/1474295354_20160919102916Mon, 19 Sep 2016 10:29 EDTAn Interesting Infinite Series and Its Implications to Operator Theoryhttp://projecteuclid.org/euclid.mjms/1474295355<strong>Melanie Henthorn-Baker</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 49--61.</p><p><strong>Abstract:</strong><br/>
The following is a discussion regarding a specific class of operators acting on
the space of entire functions, denoted $H(\mathbb{C})$. A diagonal operator $D$ on $H(\mathbb{C})$
is defined to be a continuous linear map, sending $H(\mathbb{C})$ into $H(\mathbb{C})$, that has the
monomials $z^n$ as its eigenvectors and $\{\lambda_n\}$ as the corresponding
eigenvalues. A closed subspace $M$ is invariant for $D$ if $Df\in M$ for all
$f\in M$. The study of invariant subspaces is a popular topic in modern operator
theory. We observe that the closed linear span of the orbit, which we write
$\overline{\mbox{span}}\{D^kf:k\geq0\}=\overline{\mbox{span}}\{\sum^{\infty}_{n=0}a_n\lambda_n^kz^n:k\geq0\}$,
is the smallest closed invariant subspace for $D$ containing $f$. If every
invariant subspace for a diagonal operator $D$ on $H(\mathbb{C})$ can be expressed as a
closed linear span of some subset of the eigenvectors of $D$, we say that $D$
admits spectral synthesis on $H(\mathbb{C})$. Until recently, it was not known whether or
not every diagonal operator on $H(\mathbb{C})$ admitted spectral synthesis. This article
focuses on using techniques from calculus and linear algebra to construct a
class of operators which fail spectral synthesis on $H(\mathbb{C})$. If the reader is not
familiar with the operator theory definitions provided in the background, he or
she can still appreciate the construction of an interesting infinite series
relying on properties of logarithms, various convergence tests, and Cramer's
Rule.
</p>projecteuclid.org/euclid.mjms/1474295355_20160919102916Mon, 19 Sep 2016 10:29 EDTCompact Weighted Composition Operators Between Generalized Fock Spaceshttp://projecteuclid.org/euclid.mjms/1474295356<strong>Waleed Al-Rawashdeh</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 62--75.</p><p><strong>Abstract:</strong><br/>
Let $\psi$ be an entire self-map of the $n$-dimensional Euclidean complex space
$\mathbb{C}^n$ and $u$ be an entire function on $\mathbb{C}^n$. A weighted
composition operator induced by $\psi$ with weight $u$ is given by
$(uC_{\psi}f)(z)= u(z)f(\psi(z))$, for $z \in \mathbb{C}^n$ and $f$ is the
entire function on $\mathbb{C}^n$. In this paper, we study weighted composition
operators acting between generalized Fock-types spaces. We characterize the
boundedness and compactness of these operators act between
$\mathcal{F}_{\phi}^{p}(\mathbb{C}^n)$ and
$\mathcal{F}_{\phi}^{q}(\mathbb{C}^n)$ for $0\lt p, q\leq\infty$. Moreover, we
give estimates for the Fock-norm of $uC_{\psi}:
\mathcal{F}_{\phi}^{p}\rightarrow \mathcal{F}_{\phi}^{q}$ when $0\lt p, q\lt
\infty$, and also when $p=\infty$ and $0\lt q\lt \infty$.
</p>projecteuclid.org/euclid.mjms/1474295356_20160919102916Mon, 19 Sep 2016 10:29 EDTIdentifying Outlying Observations in Regression Treeshttp://projecteuclid.org/euclid.mjms/1474295357<strong>Nicholas Granered</strong>, <strong>Samantha C. Bates Prins</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 76--87.</p><p><strong>Abstract:</strong><br/>
Regression trees are an alternative to classical linear regression models that
seek to fit a piecewise linear model to data. The structure of regression trees
makes them well-suited to the modeling of data containing outliers. We propose
an algorithm that takes advantage of this feature in order to automatically
detect outliers. This new algorithm performs well on the four test datasets
[7] that are considered to be necessary for a valid outlier
detection algorithm in a linear regression context, even though regression trees
lack the global linearity assumption. We also show the practical use of this
approach in detecting outliers in an ecological dataset collected in the
Shenandoah Valley.
</p>projecteuclid.org/euclid.mjms/1474295357_20160919102916Mon, 19 Sep 2016 10:29 EDTAn Alternate Cayley-Dickson Producthttp://projecteuclid.org/euclid.mjms/1474295358<strong>John W. Bales</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 88--96.</p><p><strong>Abstract:</strong><br/>
Although the Cayley-Dickson algebras are twisted group algebras, little
attention has been paid to the nature of the Cayley-Dickson twist. One reason is
that the twist appears to be highly chaotic and there are other interesting
things about the algebras to focus attention upon. However, if one uses a
doubling product for the algebras different from yet equivalent to the ones
commonly used, and if one uses a numbering of the basis vectors different from
the standard basis a quite beautiful and highly periodic twist emerges. This
leads easily to a simple closed form equation for the product of any two basis
vectors of a Cayley-Dickson algebra.
</p>projecteuclid.org/euclid.mjms/1474295358_20160919102916Mon, 19 Sep 2016 10:29 EDTOuterplanar Coarseness of Planar Graphshttp://projecteuclid.org/euclid.mjms/1474295359<strong>Paul C. Kainen</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 28, Number 1, 97--98.</p><p><strong>Abstract:</strong><br/>
The (outer) planar coarseness of a graph is the largest number of
pairwise-edge-disjoint non-(outer)planar subgraphs. It is shown that the maximum
outerplanar coarseness, over all $n$-vertex planar graphs, lies in the interval
$\;\big [\lfloor (n-2)/3 \rfloor, \lfloor (n-2)/2 \rfloor \big ]$.
</p>projecteuclid.org/euclid.mjms/1474295359_20160919102916Mon, 19 Sep 2016 10:29 EDTEditorialhttp://projecteuclid.org/euclid.mjms/1488423695<strong>Sam Creswell</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 1--1.</p>projecteuclid.org/euclid.mjms/1488423695_20170301220243Wed, 01 Mar 2017 22:02 ESTCenters and Generalized Centers of Nearrings Without Identityhttp://projecteuclid.org/euclid.mjms/1488423696<strong>G. Alan Cannon</strong>, <strong>Vincent Glorioso</strong>, <strong>Brad Bailey Hall</strong>, <strong>Taylor Triche</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 2--11.</p><p><strong>Abstract:</strong><br/>
The center of a nearring $N$, in general, is not a subnearring of $N$. The center,
however, is contained in a related structure, the generalized center, which is always a subnearring.
We give three constructions of nearrings without multiplicative identity and characterize their centers
and generalized centers. We find that the centers of these nearrings are always subnearrings.
</p>projecteuclid.org/euclid.mjms/1488423696_20170301220243Wed, 01 Mar 2017 22:02 ESTSolving Sudoku: Structures and Strategieshttp://projecteuclid.org/euclid.mjms/1488423697<strong>Hang Chen</strong>, <strong>Curtis Cooper</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 12--18.</p><p><strong>Abstract:</strong><br/>
We intend to solve Sudoku puzzles using various rules based on the structures and
properties of the puzzle. In this paper, we shall present several structures related to either one
potential solution or two potential solutions.
</p>projecteuclid.org/euclid.mjms/1488423697_20170301220243Wed, 01 Mar 2017 22:02 ESTReal Preimages of Duplication on Elliptic Curveshttp://projecteuclid.org/euclid.mjms/1488423698<strong>John Cullinan</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 19--26.</p><p><strong>Abstract:</strong><br/>
Let $E$ be an elliptic curve defined over the real numbers $R$ and let $P \in E(R)$. In
this note we give an elementary proof of necessary and sufficient conditions for the preimages
of $P$ under duplication to be real-valued.
</p>projecteuclid.org/euclid.mjms/1488423698_20170301220243Wed, 01 Mar 2017 22:02 ESTInteger Invariants of an Incidence Matrix Related to Rota's Basis Conjecturehttp://projecteuclid.org/euclid.mjms/1488423699<strong>Stephanie Bittner</strong>, <strong>Joshua Ducey</strong>, <strong>Xuyi Guo</strong>, <strong>Minah Oh</strong>, <strong>Adam Zweber</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 27--32.</p><p><strong>Abstract:</strong><br/>
We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a
combinatorial object closely related to the $n$-dimensional case of Rota's basis conjecture.
</p>projecteuclid.org/euclid.mjms/1488423699_20170301220243Wed, 01 Mar 2017 22:02 ESTLocal Separation Axioms Between Kolmogorov and Fr\'{e}chet Spaceshttp://projecteuclid.org/euclid.mjms/1488423700<strong>Raghu Gompa</strong>, <strong>Vijaya L. Gompa</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 33--42.</p><p><strong>Abstract:</strong><br/>
Several separation axioms on topological spaces are described between Kolmogorov and Fréchet
spaces as properties of the space at a particular point. After describing various equivalent descriptions,
implications are established. Various examples are studied in order to show that the implications are strict.
</p>projecteuclid.org/euclid.mjms/1488423700_20170301220243Wed, 01 Mar 2017 22:02 ESTStrongly Generalized Neighborhood Systemshttp://projecteuclid.org/euclid.mjms/1488423701<strong>Murad Arar</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 43--49.</p><p><strong>Abstract:</strong><br/>
In this paper we define strongly generalized neighborhood systems (in brief strongly $GNS$) and
study their properties. It's proved that every generalized topology $\mu$ on $X$ gives a unique strongly $GNS$
$\psi_{\mu}:X\rightarrow \exp{(\exp{X})}$. We prove that if a generalized topology $\mu$ is given, then
$\mu_{\psi_{\mu}}=\mu$; and if a strongly $GNS $ $\psi$ is given, then $\psi_{\mu_{\psi}}=\psi$.
Strongly $(\psi_{1},\psi_{2})$-continuity is defined. We prove that $f:X\rightarrow Y$ is
strongly $(\psi_{1},\psi_{2})$-continuous if and only if it is $(\mu_{\psi_{1}},\mu_{\psi_{2}})$-continuous.
</p>projecteuclid.org/euclid.mjms/1488423701_20170301220243Wed, 01 Mar 2017 22:02 ESTA Simple Pure Water Oscillatorhttp://projecteuclid.org/euclid.mjms/1488423702<strong>S. Lakshmivarahan</strong>, <strong>N. Trung</strong>, <strong>Barry Ruddick</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 50--79.</p><p><strong>Abstract:</strong><br/>
In this paper we analyze the properties of a pure water oscillator by
considering the pure water lake as a well mixed two layered system.
While there is heating of and evaporation from the shallow top layer,
the temperature of the deep bottom layer is assumed to be constant. By
exploiting the nonlinear dependence of the density of pure water on
temperature, we describe two complementary mathematical models to
capture the vertical instability resulting from the variation of the
density of the top layer with temperature.
</p>projecteuclid.org/euclid.mjms/1488423702_20170301220243Wed, 01 Mar 2017 22:02 ESTOn Nano Resolvable Spaceshttp://projecteuclid.org/euclid.mjms/1488423703<strong>M. Lellis Thivagar</strong>, <strong>J. Kavitha</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 80--91.</p><p><strong>Abstract:</strong><br/>
This paper introduces nano resolvable spaces and nano irresolvable spaces. Also, a new form
of nano subspace topology is established. Several new characterizations of nano strongly irresolvable
spaces are found and precise relationships are noted between nano strongly irresolvability and nano
irresolvable space. Some weaker forms related to nano irresolvable are discussed. Also, comparisons
between them are given.
</p>projecteuclid.org/euclid.mjms/1488423703_20170301220243Wed, 01 Mar 2017 22:02 ESTAtanassov's Intuitionistic Fuzzy Bi-Normed KU-Subalgebras of a KU-Algebrahttp://projecteuclid.org/euclid.mjms/1488423704<strong>Tapan Senapati</strong>, <strong>K. P. Shum</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 92--112.</p><p><strong>Abstract:</strong><br/>
In this paper, by using the $t$-norm $T$ and $t$-conorm $S$, we introduce the intuitionistic
fuzzy bi-normed $KU$-subalgebras of
a $KU$-algebra. Some properties of intuitionistic fuzzy bi-normed $KU$-subalgebras of a
$KU$-algebra under the homomorphism are discussed.
The direct product and the $(T,S)$-product of intuitionistic fuzzy bi-normed
$KU$-subalgebras are particularly investigated.
</p>projecteuclid.org/euclid.mjms/1488423704_20170301220243Wed, 01 Mar 2017 22:02 ESTAnnouncementshttp://projecteuclid.org/euclid.mjms/1488423705<p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 1, 113--114.</p>projecteuclid.org/euclid.mjms/1488423705_20170301220243Wed, 01 Mar 2017 22:02 ESTAn Elementary Approach to the Diophantine Equation $ax^m + by^n = z^r$ Using Center of Masshttps://projecteuclid.org/euclid.mjms/1513306825<strong>Amir M. Rahimi</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 115--124.</p><p><strong>Abstract:</strong><br/>
This paper takes an interesting approach to conceptualize some power sum inequalities and uses them to develop limits on possible solutions to some Diophantine equations. In this work, we introduce how to apply center of mass of a $k$-mass-system to discuss a class of Diophantine equations (with fixed positive coefficients) and a class of equations related to Fermat's Last Theorem. By a constructive method, we find a lower bound for all positive integers that are not the solution for these type of equations. Also, we find an upper bound for any possible integral solution for these type of equations. We write an alternative expression of Fermat's Last Theorem for positive integers in terms of the product of the centers of masses of the systems of two fixed points (positive integers) with different masses. Finally, by assuming the validity of Beal's conjecture, we find an upper bound for any common divisor of $x$, $y$, and $z$ in the expression $ax^m+by^n = z^r$ in terms of $a, b, m({\rm or} ~n), r$, and the center of mass of the $k$-mass-system of $x$ and $y$.
</p>projecteuclid.org/euclid.mjms/1513306825_20171214220030Thu, 14 Dec 2017 22:00 ESTCubic Implicative Ideals of $BCK$-algebrashttps://projecteuclid.org/euclid.mjms/1513306826<strong>Tapan Senapati</strong>, <strong>K. P. Shum</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 125--138.</p><p><strong>Abstract:</strong><br/>
In this paper, we apply the concept of cubic sets to implicative ideals of $BCK$-algebras, and then characterize their basic properties. We discuss relations among cubic implicative ideals, cubic subalgebras and cubic ideals of $BCK$-algebras. We provide a condition for a cubic ideal to be a cubic implicative ideal. We define inverse images of cubic implicative ideals and establish how the inverse images of a cubic implicative ideal become a cubic implicative ideal. Finally we introduce products of cubic $BCK$-algebras.
</p>projecteuclid.org/euclid.mjms/1513306826_20171214220030Thu, 14 Dec 2017 22:00 EST$(\in,\in\vee q)$-bipolar Fuzzy $BCK/BCI$-algebrashttps://projecteuclid.org/euclid.mjms/1513306827<strong>Chiranjibe Jana</strong>, <strong>Madhumangal Pal</strong>, <strong>Arsham Borumand Saied</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 139--160.</p><p><strong>Abstract:</strong><br/>
In this paper, the concept of quasi-coincidence of a bipolar fuzzy point within a bipolar fuzzy set is introduced. The notion of $(\in,\in\vee q)$-bipolar fuzzy subalgebras and ideals of $BCK/BCI$-algebras are introduced and their related properties are investigated by some examples. We study bipolar fuzzy $BCK/BCI$-subalgebras and bipolar fuzzy $BCK/BCI$-ideals by their level subalgebras and level ideals. We also provide the relationship between $(\in,\in\vee q)$-bipolar fuzzy $BCK/BCI$-subalgebras and bipolar fuzzy $BCK/BCI$-subalgebras, and $(\in,\in\vee q)$-bipolar fuzzy $BCK/BCI$-ideals and bipolar fuzzy $BCK/BCI$-ideals by counter examples.
</p>projecteuclid.org/euclid.mjms/1513306827_20171214220030Thu, 14 Dec 2017 22:00 ESTGeometry of Polynomials with Three Rootshttps://projecteuclid.org/euclid.mjms/1513306828<strong>Christopher Frayer</strong>. <p><strong>Source: </strong>Missouri Journal of Mathematical Sciences, Volume 29, Number 2, 161--175.</p><p><strong>Abstract:</strong><br/>
Given a complex-valued polynomial of the form $p(z) = (z-1)^k(z-r_1)^m(z-r_2)^n$ with $|r_1|=|r_2|=1$; $k,m,n \in \mathbb{N}$ and $m \neq n$, where are the critical points? The Gauss-Lucas Theorem guarantees that the critical points of such a polynomial will lie within the unit disk. This paper further explores the location and structure of these critical points. Surprisingly, the unit disk contains two ‘desert’ regions in which critical points cannot occur, and each $c$ inside the unit disk and outside of the desert regions is the critical point of exactly two such polynomials.
</p>projecteuclid.org/euclid.mjms/1513306828_20171214220030Thu, 14 Dec 2017 22:00 ESTSieving 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 EDT