If $A_1,\ldots,A_N$ are real $d \times d$ matrices, then the $p$-radius, generalized Lyapunov exponent, or matrix pressure is defined to be asymptotic exponential growth rate of sum $\sum_{i_1,\ldots,i_n=1}^N \|A_{i_n}\cdots A_{i_1}\|^p$, where $p$ a parameter. Under its various names this quantity has been investigated for applications topics including wavelet regularity and refinement equatio...

A closed-form solution for deflections and stresses in an annular thin plate of radially functionally graded material under transverse uniform pressure loading is presented. The small displacement theory of elasticity is assumed in the present work. Young’s modulus of the material is taken in the form of a simple power law to vary in the radial direction with an arbitrary exponent showing heter...

The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the...

We study the spectral properties of and crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), unitary (GUE)] in correlated spin-chain systems, presence magnetic fields, scalar spin-chirality term, competing with usual isotropic time-reversal invariant Heisenberg term. have investigated these context level-spacing distribution ratio distribution. u...

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on restricted condition number of Hessian loss function, we establish an error bound to true non-strict critical points rank not more than that matrix. Then, F-norm factorized least squares its KL property exponent 1/2 global optimal s...

We carry out a finite-size scaling analysis of the jamming transition in frictionless bidisperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spa...

The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density matrix renormalization group. By analyzing the finite size scaling behavior of the low energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the ex...

The class of nilpotent groups of class c and prime exponent p> c with additional predicates Pc ⊆Pc−1 ⊆ . . . ⊆P1 for suitable subgroups has the amalgamation property. Hence the Fräıssé limit D of the finite groups of this class exists. 〈1〉⊆Pc(D)⊆ . . . ⊆P2(D)⊆P1(D)=D is the lower and the upper central series of D. In this extended language, D is ultrahomogeneous. The elementary theory of D allo...

It is known in thin-film deposition that the density of nucleated clusters N varies with the deposition rate F as a power law, N ∼ Fα. The exponent α is a function of the critical nucleus size i in a way that changes with the aggregation limiting process. We extend here the derivation of the analytical capture-zone distribution function Pβ(s) = aß ·sβ ·exp(-bβs2) of Pimpinelli and Einstein to g...