We consider linearized 5-d gravity in the Randall-Sundrum brane world. The class of static solutions for linearized Einstein equations is found. Also we obtaine wave solutions describing radiation from an imaginary point source located at the Planck distance from the brane. We analyze the fields asymptotic behavior and peculiarities of matter sources.

In this note we have revisited some of of the results of Trachtenberg [9], which are directly related with the number of solutions of some special linearized polynomials over finite fields. In some cases we give improvements. Also, we give some results on the exact number of solutions of certain linearized equations depending on the coefficients of that equation.

The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the H-gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding di...

The null exact controllability of Predator-prey model with homogeneous Neumann boundary conditions is studied.A carleman type estimate for adjoint linearized system is firstly established.Then we get the controllability of the linearized system. Finally, null exact controlla-bility for the nonlinear problem is obtained using the Kakutani's fixed point theorem.

The alternating direction method of multipliers (ADMM) is being widely used for various convex minimization models with separable structures arising in a variety of areas. In the literature, the proximal version of ADMM which allows ADMM’s subproblems to be proximally regularized has been well studied. Particularly the linearized version of ADMM can be yielded when the proximal terms are approp...

The goal of the study was to compare pulse responses with sinusoidal temporal responsivity. The response of macaque ganglion cells was measured to brief luminance and chromatic pulses and to luminance or chromatic sinusoidal modulation. To make both positive and negative lobes of the pulse response visible, responses to pulses of opposite polarity were combined to yield a linearized pulse respo...

Method for water vapor profile retrievals by means of minimizing difference between estimated and actual brightness temperatures derived from AIRS data and radiative transfer model is proposed. Initial value is determined by linearized radiative transfer equation. It is found that this initial value determination method makes improvement of estimation accuracy together with reducing convergence...