相关论文: A general proof of the Dybvig-Ingersoll-Ross-Theor…

In this paper we show the convergence of the long-term return $t^{-\mu}\int_0^tX(s)\d s$ for some $\mu\geq1$, where $X$ is the short-term interest rate which follows an extension of Cox-Ingersoll-Ross type model with jumps and memory, and,…

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition.…

In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

We prove versions of Khintchine's Theorem (1924) for approximations by rational numbers whose numerators lie in randomly chosen sets of integers, and we explore the extent to which the monotonicity assumption can be removed. Roughly…

Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…

In this paper we establish properties of independence for the continued fraction expansions of two algebraic numbers. Roughly speaking, if the continued fraction expansions of two irrational algebraic numbers have the same long sub-word,…

The notion of a $\delta$-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each $\delta < {\omega}_{2}$, any $\delta$-generic sequence of P-points can be extended to an…

In this paper, we prove the converse of the dynamical Mordell--Lang conjecture in positive characteristic: For every subset $S \subseteq \mathbb{N}_0$ which is a union of finitely many arithmetic progressions along with finitely many…

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…

We study the existence of monotone wavefronts for a general family of bistable reaction-diffusion equations with delayed reaction term $g$. Differently from previous works, we do not assume the monotonicity of $g(u,v)$ with respect to the…

Well-posedness of a reversible variant of the Gray-Scott model is shown, along with the convergence of each trajectory to one of the two spatially homogeneous steady states. The principle of linearized stability provides the local…

We prove convergence rates of monotone schemes for conservation laws for H\"older continuous initial data with unbounded total variation, provided that the H\"older exponent of the initial data is greater than $1/2$. For strictly…

Let $[a_1(x),a_2(x),\ldots, a_n(x), \ldots]$ be the continued fraction expansion of an irrational number $x\in (0, 1)$. The study of the growth rate of the product of consecutive partial quotients $a_n(x)a_{n+1}(x)$ is associated with the…

The Generalized Riemann Hypothesis implies that at least 50% of the central values $L \left( \frac{1}{2},\chi\right)$ are non-vanishing as $\chi$ ranges over primitive characters modulo $q$. We show that one may unconditionally go beyond…

We present a collection of eight data sets, from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range $R_\lambda…

This paper establishes the asymptotic uniqueness of long-term probability forecasts in the following form. Consider two forecasters who repeatedly issue probability forecasts for the infinite future. The main result of the paper says that…

While one can in principle augment gravity theory with torsion, it is generally thought that any such torsion affects would be too small to be of consequence. Here we show that this cannot in general be the case. We show that the limit of…

This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed L\'evy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations.…

We derive a generalization of the Perron-Frobenius theorem to time-varying row-stochastic matrices as follows: using Kolmogorov's concept of absolute probability sequences, which are time-varying analogs of principal eigenvectors, we…