Results 81 to 90 of about 1,525 (223)

Nuclear Spaces of Generalized Test Functions

, 1973
It is well known that a large proportion of the locally convex spaces encountered in distribution theory are nuclear (Grothendieck [4], Treves [10], Schaeffer [8].) In [1] Beurling introduced spaces of test functions more general than those previously ...
H. Millington
core   +1 more source

Spatiotemporal cellular dynamics of the notochord shape intervertebral disc morphogenesis in the mouse embryo through apoptosis and proliferation

Developmental Dynamics, EarlyView.
Abstract Background The notochord is a midline structure essential for vertebrate embryogenesis, contributing to the development of the nervous system, digestive tract, and vertebral column. In particular, notochord signaling is indispensable for proper patterning and coordinated development of alternating vertebrae and intervertebral discs (IVDs ...
Julie Warin, Estelle Balissat, Pauline Colombier, Lily Paillat, Maeva Dutilleul, Anne Camus   +5 more
wiley   +1 more source

Scaling of Short‐Duration, Summer Rainfall Event Temporal Profiles With Warming Over Great Britain

International Journal of Climatology, EarlyView.
Temperature scaling has been used to analyse the temporal profiles of short‐duration, summer rainfall events in Great Britain, for sub‐hourly observed and convection‐permitting climate model (CPM) data. Results show an increase with dewpoint temperature of event total rainfall depth, maximum intensity, concentration and front‐loading.
Alexandra Seawell, Hayley J. Fowler, Stephen Blenkinsop, Caspar J. M. Hewett, Roberto Villalobos Herrera, Marie Hundhausen, Haider Ali   +6 more
wiley   +1 more source

Managing the meniscus part I—Anatomy, biomechanics, and treatment strategies for the atraumatic meniscus tear

Knee Surgery, Sports Traumatology, Arthroscopy, EarlyView.
Abstract Purpose The purpose of this article is to serve as the first of a two‐part review on the meniscus; in this review, we will establish the background on anatomy and pathogenesis of the meniscus, as well as the effect of the meniscus on native knee kinematics and function.
Ehab M. Nazzal, Jonathan D. Hughes, Armin Runer, Matthew P. Kolevar, Jorge Chahla, Robert G. Marx, James J. Irrgang, Roman Seil, Berte Bøe, David Parker, Ryosuke Kuroda, Eric H. Senorski, Sachin Tapasvi, Volker Musahl   +13 more
wiley   +1 more source

Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information.
Zhenfeng Zhang, Calogero Vetro, Tianqing An   +2 more
wiley   +1 more source

Some new classes of topological vector spaces with closed graph theorems [PDF]

, 1991
summary:In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces.
Rodrigues, Brian
core  

Differential calculus over general base fields and rings

, 2004
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is
Glöckner, Helge, Gloeckner, Helge, Glöckner, H., Neeb, Karl-Hermann, Bertram, W., Neeb, K.-H., Bertram, Wolfgang   +6 more
core   +1 more source

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley   +1 more source

Shape Derivatives of the Eigenvalues of the de Rham Complex for Lipschitz Deformations and Variable Coefficients: Part II

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the differentiability of eigenvalues with respect to perturbations of the involved parameters. As a byproduct,
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Linear Toroidal‐Inertial Waves on A Differentially Rotating Sphere with Application to Helioseismology: Modeling, Forward and Inverse Problems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen, Damien Fournier, Laurent Gizon, Thorsten Hohage   +3 more
wiley   +1 more source