## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Missouri Journal of Mathematical Sciences

1. #### When a Matrix and Its Inverse Are Nonnegative

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.

2. #### When a Matrix and Its Inverse Are Nonnegative

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.

3. #### Lebesgue's Remarkable Result

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.

4. #### Lebesgue's Remarkable Result

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.

5. #### On Generalized $\omega \beta$-Closed Sets

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.

6. #### On Generalized $\omega \beta$-Closed Sets

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.

7. #### Approximating Continuous Functions with Scattered Translates of the Poisson Kernel

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.

8. #### Approximating Continuous Functions with Scattered Translates of the Poisson Kernel

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.

9. #### Extending Edwards Likelihood Ratios to Simple One Sided Hypothesis Tests

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.

10. #### Extending Edwards Likelihood Ratios to Simple One Sided Hypothesis Tests

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.

11. #### Rates of Uniform Convergence for Riemann Integrals

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 $\mbox{Var}(g)\approx\mbox{Var}(f)$.

12. #### Rates of Uniform Convergence for Riemann Integrals

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 $\mbox{Var}(g)\approx\mbox{Var}(f)$.

13. #### New Forms of Contra-Continuity in Ideal Topology Spaces

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.

14. #### New Forms of Contra-Continuity in Ideal Topology Spaces

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.

15. #### Invariants of Stationary AF-Algebras and Torsion Subgroups 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.

16. #### Invariants of Stationary AF-Algebras and Torsion Subgroups 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.

17. #### Composition Operators on Generalized Weighted Nevanlinna Class

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...

18. #### Composition Operators on Generalized Weighted Nevanlinna Class

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...