The dynamical instability of many-body systems is best characterized through the time-dependent local Lyapunov spectrum [lambda(j)], its associated comoving eigenvectors [delta(j)], and the "global" time-averaged spectrum []. We study the fluctuations of the local spectra as well as the convergence rates and correlation functions associated with the delta vectors as functions of j an...

Building upon recent results of Dubédat [7] on the convergence topological correlators in double-dimer model considered Temperleyan approximations $\Omega^\delta$ to a simply connected domain $\Omega\subset\mathbb C$ we prove probabilities cylindrical events for loop ensembles as $\delta\to 0$. More precisely, let $\lambda_1,\dots,\lambda_n\in\Omega$ and $L$ be macroscopic lamination $\Omega\se...

NURBS-based isogeometric analysis (IGA) has currently been applied as a new numerical method in a considerable range of engineering problems. Due to non-interpolatory characteristic of NURBS basis functions, the properties of Kronecker Delta are not satisfied in IGA, and as a consequence, the imposition of essential boundary condition needs special treatment. The main contribution of this study...

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large devi...

Abstract Various leaning method of neural networks including supervised and unsupervised methods are presented and illustrated with examples. General learning rule as a function of the incoming signals is discussed. Other learning rules such as Hebbian learning, perceptron learning, LMS Least Mean Square learning, delta learning, WTA – Winner Take All learning, and PCA Principal Component Analy...

Although evidence suggests that delta-beta coupling may provide a useful index of trait level cortico-subcortical cross talk in baseline contexts, there has been little work done to clarify the role of delta-beta coupling across contexts and in association with other physiological markers of emotion processing. We examined whether individual differences in coupling were visible across both posi...

Parabolic equations with unbounded coefficients and even generalized functions (in particular Dirac–delta functions) model large–scale of problems in the heat–mass transfer. This paper provides estimates for the convergence rate of difference scheme in discrete Sobolev like norms, compatible with the smoothness of the differential problems solutions, i.e with the smoothness of the input data.