Mostrando recursos 1 - 20 de 58

  1. Remarks on the lifespan ofsolutions to wave equationswith a potential

    Zhang, Qidi
    In this paper, we show that the solution to the semilinear wave equation with a potential of quadratic type blows up in finite time. We also give an upper bound estimate for the lifespan of the solution.

  2. Remarks on the lifespan ofsolutions to wave equationswith a potential

    Zhang, Qidi
    In this paper, we show that the solution to the semilinear wave equation with a potential of quadratic type blows up in finite time. We also give an upper bound estimate for the lifespan of the solution.

  3. Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system

    Tian, Yu; Zhang, Yajing
    In this paper, we discuss the existence of multiple solutions to a second order anti-periodic boundary value problem \[ \ddot {x}(t)+M x(t)+\nabla F(t, x(t))=0\quad\mbox{almost every } t\in [0, T],\\ x(0)=-x(T) \qquad\qquad\qquad\ \, \dot {x}(0)=-\dot {x}(T) \] by using variational methods and critical point theory. Furthermore, we obtain the existence of periodic solutions for corresponding second-order differential systems.

  4. Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system

    Tian, Yu; Zhang, Yajing
    In this paper, we discuss the existence of multiple solutions to a second order anti-periodic boundary value problem \[ \ddot {x}(t)+M x(t)+\nabla F(t, x(t))=0\quad\mbox{almost every } t\in [0, T],\\ x(0)=-x(T) \qquad\qquad\qquad\ \, \dot {x}(0)=-\dot {x}(T) \] by using variational methods and critical point theory. Furthermore, we obtain the existence of periodic solutions for corresponding second-order differential systems.

  5. On three consecutive prime-gaps

    Spiro, Claudia A.
    We prove that the sequence of gaps in the sequence of prime numbers contains infinitely many runs of three terms, with the middle term exceeding both the first and third, provided that there is at least one integer $m$ exceeding $3$, and at least one set $A$ of $2^{m-2}$ integers, with infinitely many translations of this set $n+A$ such that they contain at least $m$ primes.

  6. On three consecutive prime-gaps

    Spiro, Claudia A.
    We prove that the sequence of gaps in the sequence of prime numbers contains infinitely many runs of three terms, with the middle term exceeding both the first and third, provided that there is at least one integer $m$ exceeding $3$, and at least one set $A$ of $2^{m-2}$ integers, with infinitely many translations of this set $n+A$ such that they contain at least $m$ primes.

  7. Certain K3 surfaces parametrized bythe Fibonacci sequenceviolate the Hasse principle

    Nguyen, Dong Quan Ngoc
    For a prime $p \equiv 5 \pmod {8}$ satisfying certain conditions, we show that there exist an infinitude of K3 surfaces parameterized by certain solutions to Pell's equation $X^2 - pY^2 = 4$ in the projective $5$-space that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these surfaces contain no zero-cycle of odd degree over~$\mathbb{Q} $. As an illustration for the main result, we show that the prime $p = 5$ satisfies all of the required conditions in the main theorem, and hence, there exist an infinitude of K3 surfaces parameterized by the Fibonacci sequence that...

  8. Certain K3 surfaces parametrized bythe Fibonacci sequenceviolate the Hasse principle

    Nguyen, Dong Quan Ngoc
    For a prime $p \equiv 5 \pmod {8}$ satisfying certain conditions, we show that there exist an infinitude of K3 surfaces parameterized by certain solutions to Pell's equation $X^2 - pY^2 = 4$ in the projective $5$-space that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these surfaces contain no zero-cycle of odd degree over~$\mathbb{Q} $. As an illustration for the main result, we show that the prime $p = 5$ satisfies all of the required conditions in the main theorem, and hence, there exist an infinitude of K3 surfaces parameterized by the Fibonacci sequence that...

  9. Fractional cone and hex splines

    Massopust, Peter R.; Fleet, Patrick J. Van
    We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain $s$-directional meshes and include as special cases the $3$-directional box splines~\cite {article:condat} and hex splines~\cite {article:vandeville} previously considered by Condat and Van De Ville, et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in~\cite {article:fbu, article:ub} and, e.g., investigated in~\cite {article:fm, article:mf}. Explicit time domain representations are de\-rived for these splines on $3$-directional meshes. We present some properties of these...

  10. Fractional cone and hex splines

    Massopust, Peter R.; Fleet, Patrick J. Van
    We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain $s$-directional meshes and include as special cases the $3$-directional box splines~\cite {article:condat} and hex splines~\cite {article:vandeville} previously considered by Condat and Van De Ville, et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in~\cite {article:fbu, article:ub} and, e.g., investigated in~\cite {article:fm, article:mf}. Explicit time domain representations are de\-rived for these splines on $3$-directional meshes. We present some properties of these...

  11. Rough singular integralsassociated to surfaces of revolutionon Triebel-Lizorkin spaces

    Liu, Feng
    In this paper, we establish the boundedness of rough singular integrals associated to surfaces of revolution generated by two polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces.

  12. Rough singular integralsassociated to surfaces of revolutionon Triebel-Lizorkin spaces

    Liu, Feng
    In this paper, we establish the boundedness of rough singular integrals associated to surfaces of revolution generated by two polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces.

  13. Equivariant Picard groups of$C^*$-algebras with finite dimensional$C^*$-Hopf algebra coactions

    Kodaka, Kazunori
    Let $A$ be a $C^*$-algebra and $H$ a finite dimensional $C^*$-Hopf algebra with its dual $C^*$-Hopf algebra $H^0$. Let $(\rho , u)$ be a twisted coaction of $H^0$ on $A$. We shall define the $(\rho , u, H)$-equivariant Picard group of $A$, which is denoted by $Pic _H^{\rho , u}(A)$, and discuss the basic properties of $Pic _H^{\rho , u}(A)$. Also, we suppose that $(\rho , u)$ is the coaction of $H^0$ on the unital $C^*$-algebra $A$, that is, $u=1\otimes 1^0$. We investigate the relation between $Pic (A^s )$, the ordinary Picard group of $A^s$, and $Pic _H^{\rho ^s}(A^s )$,...

  14. Equivariant Picard groups of$C^*$-algebras with finite dimensional$C^*$-Hopf algebra coactions

    Kodaka, Kazunori
    Let $A$ be a $C^*$-algebra and $H$ a finite dimensional $C^*$-Hopf algebra with its dual $C^*$-Hopf algebra $H^0$. Let $(\rho , u)$ be a twisted coaction of $H^0$ on $A$. We shall define the $(\rho , u, H)$-equivariant Picard group of $A$, which is denoted by $Pic _H^{\rho , u}(A)$, and discuss the basic properties of $Pic _H^{\rho , u}(A)$. Also, we suppose that $(\rho , u)$ is the coaction of $H^0$ on the unital $C^*$-algebra $A$, that is, $u=1\otimes 1^0$. We investigate the relation between $Pic (A^s )$, the ordinary Picard group of $A^s$, and $Pic _H^{\rho ^s}(A^s )$,...

  15. A generalization of the classof principally lifting modules

    Hosseinpour, M.; Ungor, B.; Talebi, Y.; Harmanci, A.
    Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module. In this paper, we introduce a class of modules which is analogous to that of Goldie$^*$-lifting and principally Goldie$^*$-lifting modules. The module~$M$ is called \textit {principally} $\mathcal {G}^*$-\nobreak $\delta $-\textit {lifting} if, for any $m\in M$, there exists a direct summand $N$ of $M$ such that $mR$ is $\beta ^*_{\delta }$-equivalent to $N$. We also introduce a generalization of Goldie$^*$-supplemented modules, namely, a module $M$ is said to be \textit {principally} $\mathcal {G}^*$-$\delta $-\textit {supplemented} if, for any $m\in M$, there exists a $\delta $-supplement~$N$ in~$M$ such...

  16. A generalization of the classof principally lifting modules

    Hosseinpour, M.; Ungor, B.; Talebi, Y.; Harmanci, A.
    Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module. In this paper, we introduce a class of modules which is analogous to that of Goldie$^*$-lifting and principally Goldie$^*$-lifting modules. The module~$M$ is called \textit {principally} $\mathcal {G}^*$-\nobreak $\delta $-\textit {lifting} if, for any $m\in M$, there exists a direct summand $N$ of $M$ such that $mR$ is $\beta ^*_{\delta }$-equivalent to $N$. We also introduce a generalization of Goldie$^*$-supplemented modules, namely, a module $M$ is said to be \textit {principally} $\mathcal {G}^*$-$\delta $-\textit {supplemented} if, for any $m\in M$, there exists a $\delta $-supplement~$N$ in~$M$ such...

  17. On the irrationality of infinite series of reciprocals of square roots

    Hančl, Jaroslav; Nair, Radhakrishnan
    This paper gives sufficient conditions on the sequence $\{a_n\}_{n=1}^\infty $ of positive integers to ensure that the number $\sum _{n=1}^\infty 1/{\sqrt {a_n}}$ is irrational.

  18. On the irrationality of infinite series of reciprocals of square roots

    Hančl, Jaroslav; Nair, Radhakrishnan
    This paper gives sufficient conditions on the sequence $\{a_n\}_{n=1}^\infty $ of positive integers to ensure that the number $\sum _{n=1}^\infty 1/{\sqrt {a_n}}$ is irrational.

  19. Oscillatory criteria forthe systems of two first-orderlinear differential equations

    Grigorian, G.A.
    A definition of strict oscillation of the system of two first-order linear ordinary differential equations is given. It is shown that oscillation follows from strict oscillation of its system, but strict oscillation does not follow. Sturm-type theorems are proven. Oscillatory and strict oscillatory criteria in terms of coefficients of the system are obtained.

  20. Oscillatory criteria forthe systems of two first-orderlinear differential equations

    Grigorian, G.A.
    A definition of strict oscillation of the system of two first-order linear ordinary differential equations is given. It is shown that oscillation follows from strict oscillation of its system, but strict oscillation does not follow. Sturm-type theorems are proven. Oscillatory and strict oscillatory criteria in terms of coefficients of the system are obtained.

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