Search results for "auch"
showing 10 items of 221 documents
Glucosylsphingosine (Lyso-Gb1) as a reliable biomarker in Gaucher disease: a narrative review
2023
Abstract Background Gaucher disease (GD) is a rare, inherited, autosomal recessive disorder caused by a deficiency of the lysosomal enzyme, acid β-glucosidase. Its diagnosis is achieved via measurements of acid β-glucosidase activity in either fresh peripheral blood leukocytes or dried blood spots, and confirmed by identifying characteristic mutations in the GBA1 gene. Currently, several biomarkers are available for disease monitoring. Chitotriosidase has been used over the last 20 years to assess the severity of GD, but lacks specificity in GD patients. Conversely, the deacylated form of glucosylceramide, glucosylsphingosine (also known as lyso-Gb1), represents a more reliable biomarker ch…
The finite element method for the mechanically based model of non-local continuum
2011
SUMMARY In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interac…
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.
Convergence in discrete Cauchy problems and applications to circle patterns
2005
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS
2010
We study the existence of integral solutions to a class of nonlinear evolution equations of the form [Formula: see text] where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and [Formula: see text] are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.
Existence and Regularity of Solutions of Cauchy Problems for Inhomogeneous Wave Equations with Interaction
1991
The main aim of this paper is a nonrecursive formula for the compatibility conditions ensuring the regularity of solutions of abstract inhomogeneous linear wave equations, which we derive using the theory of T. Kato [11]. We apply it to interaction problems for wave equations (cf. [3]), generalizing regularity results of Lions-Magenes [12].
On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms
2010
We study one class of nonlinear fluid dynamic models with impulse source terms. The model consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density and a linear evolution equation for the processing rate. We consider the case when influx-rates in the second equation take the form of impulse functions. Using the vanishing viscosity method and the so-called principle of fictitious controls, we show that entropy solutions to the original Cauchy problem can be approximated by optimal solutions of special optimization problems.
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…
The Cauchy problem in hybrid metric-Palatini f(X)-gravity
2013
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it \`{a} la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-…