Search results for " function"

THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS

2018

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.

Fractional p-Laplacian evolution equations

2016

Abstract In this paper we study the fractional p-Laplacian evolution equation given by u t ( t , x ) = ∫ A 1 | x − y | N + s p | u ( t , y ) − u ( t , x ) | p − 2 ( u ( t , y ) − u ( t , x ) ) d y for  x ∈ Ω ,  t > 0 , 0 s 1 , p ≥ 1 . In a bounded domain Ω we deal with the Dirichlet problem by taking A = R N and u = 0 in R N ∖ Ω , and the Neumann problem by taking A = Ω . We include here the limit case p = 1 that has the extra difficulty of giving a meaning to u ( y ) − u ( x ) | u ( y ) − u ( x ) | when u ( y ) = u ( x ) . We also consider the Cauchy problem in the whole R N by taking A = Ω = R N . We find existence and uniqueness of strong solutions for each of the above mentioned problem…

A strongly degenerate quasilinear elliptic equation

2005

Abstract We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u - div a ( u , Du ) = v , where 0 ⩽ v ∈ L 1 ( R N ) ∩ L ∞ ( R N ) , a ( z , ξ ) = ∇ ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ∥ ξ ∥ → ∞ , satisfying other additional assumptions. In particular, this class of equations includes the elliptic problems associated to a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics, respectively. In a second part of this work, using Crandall–Liggett's iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the corresponding…

Explicit solutions for a system of coupled Lyapunov differential matrix equations

1987

This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [1…

Exact treatment of linear difference equations with noncommutative coefficients

2007

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

Effects of the modulation of epoxide hydrolase activity on the binding of benzo[a]pyrene metabolites to DNA in the intact nuclei.

1983

PARTICIPATION OF RAT LIVER NUCLEI IN MOVEMENTS OF SODIUM.

1964

In vitro investigations of movements of sodium with muscular tissue seem to have shown that the non-extracellular sodium belongs to more than one phase1. The existence of either a membranous and a cellular phase2 or of two cellular phases with different degrees of order3 has been discussed. We wish to present some experimental findings which may well contribute to the interpretation of sodium transfer processes in animal tissue.

ALS-linked FUS mutations confer loss and gain of function in the nucleus by promoting excessive formation of dysfunctional paraspeckles

2019

Mutations in the FUS gene cause amyotrophic lateral sclerosis (ALS-FUS). Mutant FUS is known to confer cytoplasmic gain of function but its effects in the nucleus are less understood. FUS is an essential component of paraspeckles, subnuclear bodies assembled on a lncRNA NEAT1. Paraspeckles may play a protective role specifically in degenerating spinal motor neurons. However it is still unknown how endogenous levels of mutant FUS would affect NEAT1/paraspeckles. Using novel cell lines with the FUS gene modified by CRISPR/Cas9 and human patient fibroblasts, we found that endogenous levels of mutant FUS cause accumulation of NEAT1 isoforms and paraspeckles. However, despite only mild cytoplasm…

Modeling Local Social Migrations: A Cellular Automata Approach

2015

In local social migrations, agents move from their initial location looking for a better local social environment. Social migrations processes do not change the number of social agents of a given type (i.e., the empirical distribution of the population) but their spatial location. Although cellular automata seems to appear as a natural approach to model of social migrations, the evolution of the configuration through a cellular automata might induce a new configuration wherein the number of agents of each type might be actually modified. This article provides a characterization of these cellular automata rules such that for any initial empirical distribution, the evolution of the configurat…

Axonal control of the adult neural stem cell niche.

2014

SummaryThe ventricular-subventricular zone (V-SVZ) is an extensive germinal niche containing neural stem cells (NSCs) in the walls of the lateral ventricles of the adult brain. How the adult brain’s neural activity influences the behavior of adult NSCs remains largely unknown. We show that serotonergic (5HT) axons originating from a small group of neurons in the raphe form an extensive plexus on most of the ventricular walls. Electron microscopy revealed intimate contacts between 5HT axons and NSCs (B1) or ependymal cells (E1) and these cells were labeled by a transsynaptic viral tracer injected into the raphe. B1 cells express the 5HT receptors 2C and 5A. Electrophysiology showed that acti…