Recursos de colección
Project Euclid (Hosted at Cornell University Library) (198.174 recursos)
Missouri Journal of Mathematical Sciences
Missouri Journal of Mathematical Sciences
Ding, J.; Rhee, N. H.
In this article we prove that $A$ and $A^{-1}$ are stochastic if and only of $A$
is a permutation matrix. Then we extend this result to show that $A$ and
$A^{-1}$ are nonnegative if and only if it is a product of a diagonal matrix
with all positive diagonal entries and a permutation matrix.
Ding, J.; Rhee, N. H.
In this article we prove that $A$ and $A^{-1}$ are stochastic if and only of $A$
is a permutation matrix. Then we extend this result to show that $A$ and
$A^{-1}$ are nonnegative if and only if it is a product of a diagonal matrix
with all positive diagonal entries and a permutation matrix.
Coppin, Charles A.
We present a proof based on a 1905 paper by Henri Lebesgue that any continuous
function defined on an interval has an antiderivative {\em without first proving
the existence of the definite integral of the function}. We also demonstrate how
the definite integral is a byproduct of this proof. Instead of merely presenting
an efficient proof using modern techniques, we have chosen to present a more
instructive proof actually following the steps of Lebesgue in the spirit of Otto
Toeplitz's~\cite{Toeplitz} genetic approach.
Coppin, Charles A.
We present a proof based on a 1905 paper by Henri Lebesgue that any continuous
function defined on an interval has an antiderivative {\em without first proving
the existence of the definite integral of the function}. We also demonstrate how
the definite integral is a byproduct of this proof. Instead of merely presenting
an efficient proof using modern techniques, we have chosen to present a more
instructive proof actually following the steps of Lebesgue in the spirit of Otto
Toeplitz's~\cite{Toeplitz} genetic approach.
Aljarrah, H. H.; Noorani, M. S. M.; Noiri, T.
The aim of this paper is to introduce and study the class of $g\omega
\beta$-closed sets. This class of sets is finer than $g$-closed sets and $\omega
\beta- $closed sets. We study the fundamental properties of this class of sets.
Further, we introduce and study $g\omega \beta$-open sets, $g\omega
\beta$-neighborhoodsets, $g\omega \beta$-continuous functions, $g\omega
\beta$-irresolute functions and $g\omega \beta$-closed functions.
Aljarrah, H. H.; Noorani, M. S. M.; Noiri, T.
The aim of this paper is to introduce and study the class of $g\omega
\beta$-closed sets. This class of sets is finer than $g$-closed sets and $\omega
\beta- $closed sets. We study the fundamental properties of this class of sets.
Further, we introduce and study $g\omega \beta$-open sets, $g\omega
\beta$-neighborhoodsets, $g\omega \beta$-continuous functions, $g\omega
\beta$-irresolute functions and $g\omega \beta$-closed functions.
Ledford, Jeff
This article shows that continuous functions on compact intervals may be
approximated uniformly with scattered translates of the Poisson kernel
$(\alpha^2+x^2)^{-1}$, where $\alpha>0$ is a fixed real parameter.
Ledford, Jeff
This article shows that continuous functions on compact intervals may be
approximated uniformly with scattered translates of the Poisson kernel
$(\alpha^2+x^2)^{-1}$, where $\alpha>0$ is a fixed real parameter.
Derryberry, Dewayne; Bimali, Milan
With regard to the one sided hypothesis test, we propose a likelihood ratio that
might be viewed as a Bayes/Non-Bayes compromise in the spirit of I. J. Good
(1983). The influence of A. W. F. Edwards (1972) will also be apparent. Although
we will develop some general ideas, most of our effort will focus on tests of a
single unknown mean and the specific case of a sample from a normal population
with unknown mean and known variance.
Derryberry, Dewayne; Bimali, Milan
With regard to the one sided hypothesis test, we propose a likelihood ratio that
might be viewed as a Bayes/Non-Bayes compromise in the spirit of I. J. Good
(1983). The influence of A. W. F. Edwards (1972) will also be apparent. Although
we will develop some general ideas, most of our effort will focus on tests of a
single unknown mean and the specific case of a sample from a normal population
with unknown mean and known variance.
Alewine, J. Alan
A function $f \colon [0,1]\to {\mathbb R}$ is Riemann integrable if and only if
its Riemann sums $f(T)$ and $f(T')$ get closer to each other as $\delta\to 0$,
uniformly over all $\delta$-fine tagged divisions $T$ and $T'$. We show that
$\delta^{-1}|f(T)-f(T')|\asymp \mbox{Var}(f)$. We also give an example of a
function $f\notin \mbox{BV}$ with $|f(T)-f(T')|= {\mathcal O}(\delta|\ln
\delta|)$. As a lemma, we show that any $f\in\mbox{BV}$ can be approximated
uniformly by a step function $g$ with $\mbox{Var}(g)\approx\mbox{Var}(f)$.
Alewine, J. Alan
A function $f \colon [0,1]\to {\mathbb R}$ is Riemann integrable if and only if
its Riemann sums $f(T)$ and $f(T')$ get closer to each other as $\delta\to 0$,
uniformly over all $\delta$-fine tagged divisions $T$ and $T'$. We show that
$\delta^{-1}|f(T)-f(T')|\asymp \mbox{Var}(f)$. We also give an example of a
function $f\notin \mbox{BV}$ with $|f(T)-f(T')|= {\mathcal O}(\delta|\ln
\delta|)$. As a lemma, we show that any $f\in\mbox{BV}$ can be approximated
uniformly by a step function $g$ with $\mbox{Var}(g)\approx\mbox{Var}(f)$.
Al-Omeri, Wadei; Noorani, Mohd. Salmi Md.; Al-Omari, A.
In this paper, we apply the notion of $e$-$\I$-open sets \cite{Wadei6} in ideal
topological spaces to present and study new classes of functions called contra
$e$-$\I$-continuous functions, almost-$e$-$\I$-continuous, almost
contra-$e$-$\I$-continuous, and almost weakly-$e$-$\I$-continuous along with
their several properties, characterizations and mutual relationships.
Relationships between their new classes and other classes of functions are
established and some characterizations of their new classes of functions are
studied. Further, we introduce new types of graphs, called $e$-$\I$-closed,
contra-$e$-$\I$-closed, and strongly contra-$e$-$\I$-closed graphs via
$e$-$\I$-open sets. Several characterizations and properties of such notions are
investigated.
Al-Omeri, Wadei; Noorani, Mohd. Salmi Md.; Al-Omari, A.
In this paper, we apply the notion of $e$-$\I$-open sets \cite{Wadei6} in ideal
topological spaces to present and study new classes of functions called contra
$e$-$\I$-continuous functions, almost-$e$-$\I$-continuous, almost
contra-$e$-$\I$-continuous, and almost weakly-$e$-$\I$-continuous along with
their several properties, characterizations and mutual relationships.
Relationships between their new classes and other classes of functions are
established and some characterizations of their new classes of functions are
studied. Further, we introduce new types of graphs, called $e$-$\I$-closed,
contra-$e$-$\I$-closed, and strongly contra-$e$-$\I$-closed graphs via
$e$-$\I$-open sets. Several characterizations and properties of such notions are
investigated.
Nikolaev, Igor
Let $G_A$ be an $AF$-algebra given by a periodic Bratteli diagram with the
incidence matrix $A\in GL(n, {\Bbb Z})$. For a given polynomial $p(x)\in {\Bbb
Z}[x]$ we assign to $G_A$ a finite abelian group $Ab_{p(x)}(G_A)={\Bbb
Z}^n/p(A){\Bbb Z}^n$. It is shown that if $p(0)=\pm 1$ and ${\Bbb Z}[x]/\langle
p(x)\rangle$ is a principal ideal domain, then $Ab_{p(x)}(G_A)$ is an invariant
of the strong stable isomorphism class of $G_A$. For $n=2$ and $p(x)=x-1$ we
conjecture a formula linking values of the invariant and torsion subgroup of
elliptic curves with complex multiplication.
Nikolaev, Igor
Let $G_A$ be an $AF$-algebra given by a periodic Bratteli diagram with the
incidence matrix $A\in GL(n, {\Bbb Z})$. For a given polynomial $p(x)\in {\Bbb
Z}[x]$ we assign to $G_A$ a finite abelian group $Ab_{p(x)}(G_A)={\Bbb
Z}^n/p(A){\Bbb Z}^n$. It is shown that if $p(0)=\pm 1$ and ${\Bbb Z}[x]/\langle
p(x)\rangle$ is a principal ideal domain, then $Ab_{p(x)}(G_A)$ is an invariant
of the strong stable isomorphism class of $G_A$. For $n=2$ and $p(x)=x-1$ we
conjecture a formula linking values of the invariant and torsion subgroup of
elliptic curves with complex multiplication.
Al-Rawashdeh, Waleed
Let $\varphi$ be an analytic self-map of open unit disk $\mathbb{D}$. The
operator given by $(C_{\varphi}f)(z)=f(\varphi(z))$, for $z \in \mathbb{D}$ and
$f$ analytic on $\mathbb{D}$ is called a composition operator. Let $\omega$ be a
weight function such that $\omega\in L^{1}(\mathbb{D}, dA)$. The space we
consider is a generalized weighted Nevanlinna class $\mathcal{N}_{\omega}$,
which consists of all analytic functions $f$ on $\mathbb{D}$ such that
$\displaystyle \|f\|_{\omega}=\int_{\mathbb{D}}\log^{+}(|f(z)|) \omega(z) dA(z)$
is finite; that is, $\mathcal{N}_{\omega}$ is the space of all analytic
functions belong to $L_{\log^+}(\mathbb{D}, \omega dA)$. In this paper we
investigate, in terms of function-theoretic, composition operators on the space
$\mathcal{N}_{\omega}$. We give sufficient conditions for the boundedness and
compactness of these composition...
Al-Rawashdeh, Waleed
Let $\varphi$ be an analytic self-map of open unit disk $\mathbb{D}$. The
operator given by $(C_{\varphi}f)(z)=f(\varphi(z))$, for $z \in \mathbb{D}$ and
$f$ analytic on $\mathbb{D}$ is called a composition operator. Let $\omega$ be a
weight function such that $\omega\in L^{1}(\mathbb{D}, dA)$. The space we
consider is a generalized weighted Nevanlinna class $\mathcal{N}_{\omega}$,
which consists of all analytic functions $f$ on $\mathbb{D}$ such that
$\displaystyle \|f\|_{\omega}=\int_{\mathbb{D}}\log^{+}(|f(z)|) \omega(z) dA(z)$
is finite; that is, $\mathcal{N}_{\omega}$ is the space of all analytic
functions belong to $L_{\log^+}(\mathbb{D}, \omega dA)$. In this paper we
investigate, in terms of function-theoretic, composition operators on the space
$\mathcal{N}_{\omega}$. We give sufficient conditions for the boundedness and
compactness of these composition...
Wiley, Chad; Gray, Jeffrey
In knot theory, a common task is to take a given knot diagram and generate from
it a polynomial. One method for accomplishing this is to employ a skein relation
to convert the knot into a type of labeled binary tree and from this tree derive
a two-variable polynomial. The purpose of this paper is to determine, in a
simplified setting, which polynomials can be generated from labeled binary
trees. We give necessary and sufficient conditions for a polynomial to be
constructible in this fashion and we will provide a method for reconstructing
the generating tree from such a polynomial. We conclude with an application of
this theorem...
Wiley, Chad; Gray, Jeffrey
In knot theory, a common task is to take a given knot diagram and generate from
it a polynomial. One method for accomplishing this is to employ a skein relation
to convert the knot into a type of labeled binary tree and from this tree derive
a two-variable polynomial. The purpose of this paper is to determine, in a
simplified setting, which polynomials can be generated from labeled binary
trees. We give necessary and sufficient conditions for a polynomial to be
constructible in this fashion and we will provide a method for reconstructing
the generating tree from such a polynomial. We conclude with an application of
this theorem...