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We establish that a Čech-complete space $$X$$ X must be subcompact if it has a dense subspace representable as the countable union of closed subcompact subspaces of $$X$$ X . In particular, if a Čech-complete space contains a dense $$\sigma $$ σ -compact subspace then it is subcompact. This result is new even for separable Čech-complete spaces. Furthermore, if $$X$$ ...
There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric...
Our purpose is to obtain a very effective and general method to prove that certain $$C_0$$ C 0 -semigroups admit invariant strongly mixing measures. More precisely, we show that the frequent hypercyclicity criterion for $$C_0$$ C 0 -semigroups ensures the existence of invariant strongly mixing measures with full support. We will provide several examples, that range from birth-and-death...
In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.
In this article, the strong law of large numbers for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables is obtained. Some sufficient conditions for the strong law of large numbers of random variables are presented. In addition, the results of the paper generalize and improve earlier ones of Chung (Am J Math 69:189–192, 1947) and Teicher (Proc Natl Acad Sci...
In this article, we consider the following $$N$$ N -Kirchhoff type problem $$\begin{aligned} \left\{ \begin{array}{ll} -M\left( \int \limits _{\Omega }|\nabla u|^N\,dx\right) \Delta _N u = \lambda f(x,u) +\mu g(x,u) \quad \text { in } \Omega ,\\ u =0 \quad \text { on } \partial \Omega , \end{array}\right. \end{aligned}$$ - M ∫ Ω | ∇ u | N d x Δ N u = λ f ( x , u...
We present an efficient procedure to simulate the dynamics of Libor Market Model that avoids the use of drift dependent paths in Monte Carlo simulation. We follow a drift-free simulation methodology by first simulating certain martingales and then obtaining the involved forward Libor rates in terms of them. More precisely, we propose a parameterization of those martingales so that the desired properties...
In this paper, the authors discuss the continuability and boundedness of solutions of a second order functional integro-differential equation with multiple delays. The proof involves the construction of a Lyapunov-Krasovskii type functional.
The rational de Casteljau algorithm for the evaluation of rational Bézier curves is extended to very general rational spaces. Many examples are included.
In this paper, we define random Lie $$C^*$$ C ∗ -algebras, then we apply a fixed point theorem to investigate some new stability results for $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -derivations on random Lie $$C^*$$ C ∗ -algebras associated with a generalized Cauchy–Jensen type additive functional equation.
We prove some existence (and sometimes also uniqueness) of solutions to some stationary equations associated to the complex Schrödinger operator under the presence of a singular nonlinear term. Among other new facts, with respect some previous results in the literature for such type of nonlinear potential terms, we include the case in which the spatial domain is possibly unbounded (something which...
Two rank $$n$$ n , integral quadratic forms $$f$$ f and $$g$$ g are said projectively equivalent if there exist nonzero rational numbers $$r$$ r and $$s$$ s such that $$rf$$ r f and $$sg$$ s g are rationally equivalent. Two odd dimensional, integral quadratic forms $$f$$ f and $$g$$ g are projectivelly...
Consider the nonparametric regression model with repeated measurements: $$Y^{(j)}(x_{ni})=g(x_{ni})+e^{(j)}(x_{ni})$$ Y ( j ) ( x n i ) = g ( x n i ) + e ( j ) ( x n i ) , where $$Y^{(j)}(x_{ni})$$ Y ( j ) ( x n i ) is the $$j$$ j th response at the point $$x_{ni}$$ x n i , $$x_{ni}$$ x n i ’s are known and nonrandom,...
We prove that normed unital complex (possibly non-associative) algebras with no non-zero left topological divisor of zero are isomorphic to the field $$\mathbb {C} $$ C of complex numbers. We also show the existence of a complete normed unital infinite-dimensional complex algebra with no non-zero two-sided topological divisor of zero.
The purpose of this paper is to present some new fixed point theorems for singlevalued operators in a generalized Kasahara space, starting from the results given by Kasahara (Math. Semin. Notes 5:29–35, 1977), Iseki (Math. Semin. Notes 3:193–202, 1975), and Rus (Sci. Math. Jpn. 72(1):101–110, 2010). As an application, an existence and uniqueness theorem for a Cauchy problem is given.
This paper is concerned with partial regularity of weak solutions to nonlinear sub-elliptic systems under sub-quadratic natural growth conditions. We begin with establishing a Sobolev-Poincaré type inequality associated with Hörmander’s vector fields for $$u\in HW^{1,m}(\Omega , \mathbb {R}^N)$$ u ∈ H W 1 , m ( Ω , R N ) with $$1<m<2$$ 1 < m < 2 . Then ...
Let $$E, G$$ E , G denote two Banach lattices, and let $$(T_n)$$ ( T n ) be a sequence of continuous linear operators $$E \rightarrow G$$ E → G . We prove that if $$(T_n)$$ ( T n ) satisfies the difference condition $$|T_n - T_m| x = |T_n x - T_m x|$$ | T n - T m | x = | T n x - T m x | for all $$x \in E^+$$ x ∈ E + ...
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