Idempotents and the multiplicative group of some totally bounded rings

In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2^ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.     

Nanocellulose: A Fundamental Material for Science and Technology Applications

Recently, considerable interest has been focused on developing greener and biodegradable materials due to growing environmental concerns. Owing to their low cost, biodegradability, and good mechanical properties, plant fibers have substituted synthetic fibers in the preparation of composites. However, the poor interfacial adhesion due to the hydrophilic nature and high-water absorption limits the use of plant fibers as a reinforcing agent in polymer matrices. The hydrophilic nature of the plant fibers can be overcome by chemical treatments. Cellulose the most abundant natural polymer obtained from sources such as plants, wood, and bacteria has gained wider attention these days. Different methods, such as mechanical, chemical, and chemical treatments in combination with mechanical treatments, have been adopted by researchers for the extraction of cellulose from plants, bacteria, algae, etc. Cellulose nanocrystals (CNC), cellulose nanofibrils (CNF), and microcrystalline cellulose (MCC) have been extracted and used for different applications such as food packaging, water purification, drug delivery, and in composites. In this review, updated information on the methods of isolation of nanocellulose, classification, characterization, and application of nanocellulose has been highlighted. The characteristics and the current status of cellulose-based fiber-reinforced polymer composites in the industry have also been discussed in detail.     

On Jacobi fields

We define curves on a Riemannian manifold as integrals of generalized Jacobi fields. We show that the force term that deviates the trajectory from the geodesic motion can be constructed as a functional of the metric tensor. These curves can be interpreted as particles (observers) coupled nonminimally with gravitation that can provide a class of residual observers for the inevitable singularity—as shown in the text.This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.     

On the coupling of MIXED-FEM and BEM for an exterior Helmholtz problem in the plane

Summary This paper deals with an elliptic boundary value problem posed in the plane, with variable coefficients, but whose restriction to the exterior of a bounded domain reduces to a Helmholtz equation. We consider a mixed variational formulation in a bounded domain that contains the heterogeneous medium, coupled with a boundary integral method applied to the Helmholtz equation in . We utilize suitable auxiliary problems, duality arguments, and Fredholm alternative to show that the resulting formulation of the problem is well posed. Then, we define a corresponding Galerkin scheme by using rotated Raviart-Thomas subspaces and spectral elements (on the interface). We show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates. Finally we illustrate our analysis with some results from computational experiments.     

Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation

In this paper, we consider the nonlinear viscoelastic equation

with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p>m, we prove that there are solutions with positive initial energy that blow up in finite time.     

A semiparametric test of independence in copula models for censored data

We propose a semiparametric test of independence in copula models for bivariate survival censored data. We give the limit laws of the estimate of the parameter and the proposed test statistic under the null hypothesis of independence.     

Global Existence,Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem

In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition. We establish a blow up result for large initial data and a decay result for small enough initial data.     

Power limitations in fiber-optic frequency-division multiplexed systems

Abstract

Launch power is limited to the milliwatt level by stimulated Brillouin scattering (SBS) in a single-channel, coherent fiber-optic network. Increasing the number of frequency-division multiplexed channels causes the power limit to decrease quickly to submilliwatt levels due to three-wave intermodulation to keep the signal-to-noise ratio from deteriorating significantly. As the number of channels increases, stimulated Raman scattering (SRS) begins to dominate. If a maximum of 0.5–dB depletion in the highest-frequency channel is allowed, SRS dominates when the number of multiplexed channels reaches about 300. Generally, the launch-power-limiting phenomenon is dependent on the number of channels being multiplexed.     

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.     

General decay of solutions of a viscoelastic equation

In this paper we consider the following viscoelastic equation: