Search results for "Linea"
showing 10 items of 7724 documents
Solution of a cauchy problem for an infinite chain of linear differential equations
2005
Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.
The cauchy problem for non-linear Klein-Gordon equations
1993
We consider in ℝ n+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the …
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.
Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems
2002
AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.
A shallow water model with eddy viscosity for basins with varying bottom topography
2001
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.
Analytic structure ofϕ4theory using light-by-light sum rules
2013
Abstract We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ 4 quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain …
Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions
2008
We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…
The stem cell concept in sponges (Porifera): Metazoan traits.
2006
Sponges are considered the oldest living animal group and provide important insights into the earliest evolutionary processes in the Metazoa. This paper reviews the evidence that sponge stem cells have essential roles in cellular specialization, embryogenesis and Bauplan formation. Data indicate that sponge archaeocytes not only represent germ cells but also totipotent stem cells. Marker genes have been identified which are expressed in totipotent stem cells and gemmule cells. Furthermore, genes are described for the three main cell lineages in sponge, which share a common origin from archaeocytes and result in the differentiation of skeletal, epithelial, and contractile cells.
The Embryonic Central Nervous System Lineages ofDrosophila melanogaster
1996
In Drosophila, central nervous system (CNS) formation starts with the delamination from the neuroectoderm of about 30 neuroblasts (NBs) per hemisegment. They give rise to approximately 350 neurons and 30 glial cells during embryonic development. Understanding the mechanisms leading to cell fate specification and differentiation in the CNS requires the identification of the NB lineages. The embryonic lineages derived from 17 NBs of the ventral part of the neuroectoderm have previously been described (Bossing et al., 1996). Here we present 13 lineages derived from the dorsal part of the neuroectoderm and we assign 12 of them to identified NBs. Together, the 13 lineages comprise approximately …
High-resolution mouse subventricular zone stem-cell niche transcriptome reveals features of lineage, anatomy, and aging
2020
Adult neural stem cells (NSC) serve as a reservoir for brain plasticity and origin for certain gliomas. Lineage tracing and genomic approaches have portrayed complex underlying heterogeneity within the major anatomical location for NSC, the subventricular zone (SVZ). To gain a comprehensive profile of NSC heterogeneity, we utilized a well-validated stem/progenitor-specific reporter transgene in concert with single-cell RNA sequencing to achieve unbiased analysis of SVZ cells from infancy to advanced age. The magnitude and high specificity of the resulting transcriptional datasets allow precise identification of the varied cell types embedded in the SVZ including specialized parenchymal cell…