Related papers: Critical length: an alternative approach
We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where…
This paper describes a linear-time algorithm that finds the longest stretch in a sequence of real numbers (``scores'') in which the sum exceeds an input parameter. The algorithm also solves the problem of finding the longest interval in…
We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials.
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
In this article we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding the corresponding integral kernels, we exploit the…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the…
With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…
In this paper we will study the numerical solution of a discontinuous differential system by a Rosenbrock method. We will also focus on one-sided approach in the context of Rosenbrock schemes, and we will suggest a technique based on the…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
We consider $2p\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by gaps. We define the Lyapunov function,…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…