Mostrando recursos 1 - 20 de 89

  1. Announcements


  2. Atanassov's Intuitionistic Fuzzy Bi-Normed KU-Subalgebras of a KU-Algebra

    Senapati, Tapan; Shum, K. P.
    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.

  3. On Nano Resolvable Spaces

    Thivagar, M. Lellis; Kavitha, J.
    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.

  4. A Simple Pure Water Oscillator

    Lakshmivarahan, S.; Trung, N.; Ruddick, Barry
    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.

  5. Strongly Generalized Neighborhood Systems

    Arar, Murad
    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.

  6. Local Separation Axioms Between Kolmogorov and Fr\'{e}chet Spaces

    Gompa, Raghu; Gompa, Vijaya L.
    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.

  7. Integer Invariants of an Incidence Matrix Related to Rota's Basis Conjecture

    Bittner, Stephanie; Ducey, Joshua; Guo, Xuyi; Oh, Minah; Zweber, Adam
    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.

  8. Real Preimages of Duplication on Elliptic Curves

    Cullinan, John
    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.

  9. Solving Sudoku: Structures and Strategies

    Chen, Hang; Cooper, Curtis
    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.

  10. Centers and Generalized Centers of Nearrings Without Identity

    Cannon, G. Alan; Glorioso, Vincent; Hall, Brad Bailey; Triche, Taylor
    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.

  11. Editorial

    Creswell, Sam

  12. Outerplanar Coarseness of Planar Graphs

    Kainen, Paul C.
    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 $\;\big [\lfloor (n-2)/3 \rfloor, \lfloor (n-2)/2 \rfloor \big ]$.

  13. An Alternate Cayley-Dickson Product

    Bales, John W.
    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.

  14. Identifying Outlying Observations in Regression Trees

    Granered, Nicholas; Bates Prins, Samantha C.
    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.

  15. Compact Weighted Composition Operators Between Generalized Fock Spaces

    Al-Rawashdeh, Waleed
    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 $0\lt q\lt \infty$.

  16. An Interesting Infinite Series and Its Implications to Operator Theory

    Henthorn-Baker, Melanie
    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...

  17. I'm Thinking of a Number $\ldots$

    Hammett, Adam; Oman, Greg
    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...

  18. $\omega$-Jointly Metrizable Spaces

    Al Shumrani, M. A.
    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.

  19. $\mu$-Lindelöfness in Terms of a Hereditary Class

    Qahis, Abdo; AlJarrah, Heyam Hussain; Noiri, Takashi
    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.

  20. Minimizing Times Between Boundary Points on Rectangular Pools

    Miick, Tonja; Richmond, Tom
    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.

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