Recursos de colección
Project Euclid (Hosted at Cornell University Library) (198.174 recursos)
Rocky Mountain Journal of Mathematics
Rocky Mountain Journal of Mathematics
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.
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.
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.
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.
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.
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.
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...
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...
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...
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...
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.
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.
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 $Pic _H^{\rho ^s}(A^s )$,...
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 $Pic _H^{\rho ^s}(A^s )$,...
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...
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...
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.
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.
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.
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.