bluuebunny/crossref_metadata_2025_split huggingface dataset:
UNIQUENESS IN THE CAUCHY PROBLEM FOR PARABOLIC EQUATIONS
Authors: Ferretti Elisa 
Published: July 2003

AbstractWe discuss the problem of the uniqueness of the solution to the Cauchy problem for second-order, linear, uniformly parabolic differential equations. For most uniqueness theorems the solution must be uniformly bounded with respect to the time variable $t$, but some authors have shown an interest in relaxing the growth conditions in time.In 1997, Chung proved that, in the case of the heat equation, uniqueness holds under the restriction: $|u(x,t)|\leq C\exp[(a/t)^{\alpha}+a|x|^2]$, for some constants $C,a>0$, $0\lt\alpha\lt1$. The proof of Chung’s theorem is based on ultradistribution theory, in particular it relies heavily on the fact that the coefficients are constants and that the solution is smooth. Therefore, his method does not work for parabolic operators with arbitrary coefficients. In this paper we prove a uniqueness theorem for uniformly parabolic equations imposing the same growth condition as Chung on the solution $u(x,t)$. At the centre of the proof are the maximum principle, Gaussian-type estimates for short cylinders and a boot-strapping argument.AMS 2000 Mathematics subject classification: Primary 35K15
EPIMORPHISMS ONTO DERIVATION ALGEBRAS
Authors: Villena A. R. 
Published: July 2003

AbstractWe prove that the separating space of an epimorphism from a Lie–Banach algebra onto the (continuous) derivation algebra $\mathfrak{Der}(A)$ of a Banach algebra $A$ consists of derivations which map into the radical of $A$.AMS 2000 Mathematics subject classification: Primary 46H40; 46H70. Secondary 47B47; 47B48
THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS
Authors: Keyantuo Valentin , Müller Claus , Vieten Peter 
Published: July 2003

AbstractThe characterization theorem for the Banach-space-valued local Laplace transform established by Keyantuo, Müller and Vieten is used to obtain a real variable characterization of generators of local convoluted semigroups. The concept of local convoluted semigroups extends that of distribution as well as ultradistribution semigroups. Complete characterizations existed only for exponentially bounded semigroups integrated $\alpha$ times, whereas for the non-exponential case generation results had been obtained in terms of complex conditions only.AMS 2000 Mathematics subject classification: Primary 47D03; 47D06; 44A10
OPTIMAL EMBEDDINGS OF DISTRIBUTIONS INTO ALGEBRAS
Authors: Vernaeve H. 
Published: July 2003

AbstractLet $\varOmega$ be a convex, open subset of $\mathbb{R}^n$ and let $\mathcal{D}'(\varOmega)$ be the space of distributions on $\varOmega$. It is shown that there exist linear embeddings of $\mathcal{D}'(\varOmega)$ into a differential algebra that commute with partial derivatives and that embed $\mathcal{C}^{\infty}(\varOmega)$ as a subalgebra. This embedding appears to be the first one after Colombeau’s to possess these properties. We show that many nonlinear operations on distributions can be defined that are not definable in the Colombeau setting.AMS 2000 Mathematics subject classification: Primary 46F30. Secondary 13C11
STABILITY OF THE DEFICIENCY INDICES OF SYMMETRIC OPERATORS UNDER SELF-ADJOINT PERTURBATIONS
Authors: Kissin Edward 
Published: July 2003

AbstractLet $S$ and $T$ be symmetric unbounded operators. Denote by $\overline{S+T}$ the closure of the symmetric operator $S+T$. In general, the deficiency indices of $\overline{S+T}$ are not determined by the deficiency indices of $S$ and $T$. The paper studies some sufficient conditions for the stability of the deficiency indices of a symmetric operator $S$ under self-adjoint perturbations $T$. One can associate with $S$ the largest closed $^*$-derivation $\delta_{S}$ implemented by $S$. We prove that if the unitary operators $\exp(\ri tT)$, for $t\in\mathbb{R}$, belong to the domain of $\delta_{S}$ and $\delta_{S}(\exp(\ri tT))\rightarrow0$ in the strong operator topology as $t\rightarrow0$, then the deficiency indices of $S$ and $\overline{S+T}$ coincide. In particular, this holds if $S$ and $\exp(\ri tT)$ commute or satisfy the infinitesimal Weyl relation.We also study the case when $S$ and $T$ anticommute: $\exp(-\ri tT)S\subseteq S\exp(\ri tT)$, for $t\in\mathbb{R}$. We show that if the deficiency indices of $S$ are equal, or if the group $\{\exp(\ri tT):t\in\mathbb{R}\}$ of unitary operators has no stationary points in the deficiency space of $S$, then $S$ has a self-adjoint extension which anticommutes with $T$, the operator $S+T$ is closed and the deficiency indices of $S$ and $S+T$ coincide.AMS 2000 Mathematics subject classification: Primary 47B25
BOUNDARY-CHAOTIC BEHAVIOUR OF CONTINUOUS FUNCTIONS UNDER THE ACTION OF OPERATORS
Authors: Bernal-González Luis , Calderón-Moreno María del Carmen 
Published: July 2003

AbstractIn this paper we introduce two classes of operators on spaces of continuous functions with values in $F$-spaces under the action of which many functions behave chaotically near the boundary. Several examples—including onto linear operators, left and right composition operators, multiplication operators, and operators with pointwise dense range or with some stability property—are given. This new theory extends one recently developed on spaces of holomorphic functions.AMS 2000 Mathematics subject classification: Primary 47B38. Secondary 30D40; 46E10; 54D45
QUANTUM CHANNELS, WAVELETS, DILATIONS AND REPRESENTATIONS OF $\mathcal{O}_{n}$
Authors: Kribs David W. 
Published: July 2003

AbstractWe show that the representations of the Cuntz $C^*$-algebras $\mathcal{O}_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this analysis, we find an application in quantum information theory; namely, a structure theorem for the fixed-point set of a unital quantum channel. We also include some open problems motivated by this work.AMS 2000 Mathematics subject classification: Primary 46L45; 47A20; 46L60; 42C40; 81P15
INDECOMPOSABLE NON-HOLONOMIC $\mathcal{D}$-MODULES IN DIMENSION $2$
Authors: Coutinho S. C. 
Published: July 2003

AbstractA module of a ring of differential operators $\mathcal{D}$ over a smooth surface has order $1$ if it is isomorphic to a factor module of $\mathcal{D}$ by a cyclic ideal generated by an operator of order $1$. Let $k$ be a positive integer. We give conditions under which an indecomposable $\mathcal{D}$-module of order $1$ is GK-critical of length $k$. We also give examples of indecomposable, non-critical, $\mathcal{D}$-modules whose subfactors have order $1$.AMS 2000 Mathematics subject classification: Primary 16S32. Secondary 37F75
FINITE AND LOCAL LAPLACE TRANSFORMS IN BANACH SPACES
Authors: Keyantuo Valentin , Müller Claus , Vieten Peter 
Published: July 2003

AbstractWe establish two characterizations of local Laplace transforms in Banach spaces. The first result follows the classic approach of Widder, while the second is in terms of vector-valued moment sequences. As a consequence, we derive characterizations of nilpotent semigroups.AMS 2000 Mathematics subject classification: Primary 44A10; 47D03
HILBERT MODULAR PSEUDODIFFERENTIAL OPERATORS OF MIXED WEIGHT
Authors: Lee Min Ho , Myung Hyo Chul 
Published: July 2003

AbstractWe introduce an action of a discrete subgroup $\varGamma$ of $SL(2,\mathbb{R})^n$ on the space of pseudodifferential operators of $n$ variables, and construct a map from the space of Hilbert modular forms for $\varGamma$ to the space of pseudodifferential operators invariant under such a $\varGamma$-action, which is a lifting of the symbol map of pseudodifferential operators. We also obtain a necessary and sufficient condition for a certain type of pseudodifferential operator to be $\varGamma$-invariant.AMS 2000 Mathematics subject classification: Primary 11F41; 35S05
ON FACTORIZATION IN BLOCK MONOIDS FORMED BY $\{\bar{1},\bar{a}\}$ IN $\mathbb{Z}_{n}$
Authors: Chapman Scott T. , Smith William W. 
Published: July 2003

AbstractWe consider the factorization properties of block monoids on $\mathbb{Z}_n$ determined by subsets of the form $S_a=\{\bar{1},\bar{a}\}$. We denote such a block monoid by $\mathcal{B}_a(n)$. In §2, we provide a method based on the division algorithm for determining the irreducible elements of $\mathcal{B}_a(n)$. Section 3 offers a method to determine the elasticity of $\mathcal{B}_a(n)$ based solely on the cross number. Section 4 applies the results of §3 to investigate the complete set of elasticities of Krull monoids with divisor class group $\mathbb{Z}_n$.AMS 2000 Mathematics subject classification: Primary 20M14; 20D60; 13F05
EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS
Authors: Ma Ruyun 
Published: July 2003

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15
INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS
Authors: Alías Luis J. , Brasil Aldir , Gervasio Colares A. 
Published: July 2003

AbstractIn this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their $r$-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their $r$-mean curvatures are linearly related or one of them is constant.AMS 2000 Mathematics subject classification: Primary 53C42. Secondary 53B30; 53C50; 53Z05; 83C99
NUMERICAL INDEX AND THE DAUGAVET PROPERTY FOR $L_\infty(\mu,X)$
Authors: Martín Miguel , Villena Armando R. 
Published: July 2003

AbstractWe prove that the space $L_\infty(\mu,X)$ has the same numerical index as the Banach space $X$ for every $\sigma$-finite measure $\mu$. We also show that $L_\infty(\mu,X)$ has the Daugavet property if and only if $X$ has or $\mu$ is atomless.AMS 2000 Mathematics subject classification: Primary 46B20; 47A12
A SHOCK LAYER IN PARABOLIC PERTURBATIONS OF A SCALAR CONSERVATION LAW
Authors: Shelukhin Vladimir 
Published: July 2003

AbstractA definition of a shock layer of thickness $\delta$ is proposed when a parabolic perturbation is applied to a scalar conservation law. The asymptotic equality $\delta\asymp\sqrt{\varepsilon}$ is established, where $\varepsilon$ denotes viscosity. This equality is proved to be optimal. Nevertheless, the equality $\delta\asymp\varepsilon$ is also proved to be valid for a class of shocks in accordance with the Mises conjecture.AMS 2000 Mathematics subject classification: Primary 35L67. Secondary 35K65
STEIN EMBEDDING THEOREM FOR $\mathbb{B}$-MANIFOLDS
Authors: Gadea P. M. , Grifone J. , Muñoz Masqué J. 
Published: July 2003

AbstractAn analogue of the Stein embedding theorem for $C^\infty$ manifolds endowed with two equidimensional supplementary foliations is proved.AMS 2000 Mathematics subject classification: Primary 30G35. Secondary 16P10; 26E05; 32E10; 53C12; 57R30.
POINCARÉ SERIES FOR SEVERAL PLANE DIVISORIAL VALUATIONS
Authors: Delgado F. , Gusein-Zade S. M. 
Published: July 2003

AbstractWe compute the (generalized) Poincaré series of the multi-index filtration defined by a finite collection of divisorial valuations on the ring $\mathcal{O}_{\mathbb{C}^2,0}$ of germs of functions of two variables. We use the method initially elaborated by the authors and Campillo for computing the similar Poincaré series for the valuations defined by the irreducible components of a plane curve singularity. The method is essentially based on the notions of the so-called extended semigroup and of the integral with respect to the Euler characteristic over the projectivization of the space of germs of functions of two variables. The last notion is similar to (and inspired by) the notion of the motivic integration.AMS 2000 Mathematics subject classification: Primary 14B05; 16W70
A UNIQUENESS THEOREM FOR AN INVERSE ELECTROMAGNETIC SCATTERING PROBLEM IN INHOMOGENEOUS ANISOTROPIC MEDIA
Authors: Cakoni Fioralba , Colton David 
Published: July 2003

AbstractWe show that the support of a (possibly) coated anisotropic medium is uniquely determined by the electric far-field patterns corresponding to incident time-harmonic electromagnetic plane waves with arbitrary polarization and direction. Our proof avoids the use of a fundamental solution to Maxwell’s equations in an anisotropic medium and instead relies on the well-posedness and regularity properties of solutions to an interior transmission problem for Maxwell’s equations.AMS 2000 Mathematics subject classification: Primary 35R30; 35Q60. Secondary 35P25; 78A45
PROJECTIVE DESCRIPTION OF WEIGHTED (LF)-SPACES OF HOLOMORPHIC FUNCTIONS ON THE DISC
Authors: Bierstedt Klaus D. , Bonet José 
Published: July 2003

AbstractThe topology of certain weighted inductive limits of Fréchet spaces of holomorphic functions on the unit disc can be described by means of weighted sup-seminorms in case the weights are radial and satisfy certain natural assumptions due to Lusky; in the sense of Shields and Williams the weights have to be normal. It turns out that no assumption on the (double) sequence of normal weights is necessary for the topological projective description in the case of o-growth conditions. For O-growth conditions, we give a necessary and sufficient condition (in terms of associated weights) for projective description in the case of (LB)-spaces and normal weights. This last result is related to a theorem of Mattila, Saksman and Taskinen.AMS 2000 Mathematics subject classification: Primary 46E10. Secondary 30H05; 46A13; 46M40
Social Exclusion and Transport in the UK: A Role for Virtual Accessibility in the Alleviation of Mobility-Related Social Exclusion?
Authors: KENYON SUSAN , RAFFERTY JACKIE , LYONS GLENN 
Published: July 2003

This paper reports findings from research into the possibility that mobility-related social exclusion could be affected by an increase in access to virtual mobility – access to opportunities, services and social networks, via the Internet – amongst populations that experience exclusion. Transport is starting to be recognised as a key component of social policy, particularly in light of a number of recent studies, which have highlighted the link between transport and social exclusion, suggesting that low access to mobility can reduce the opportunity to participate in society – a finding with which this research concurs. Following the identification of this causal link, the majority of studies suggest that an increase in access to adequate physical mobility can provide a viable solution to mobility-related aspects of social exclusion.This paper questions the likelihood that increased physical mobility can, by itself, provide a fully viable or sustainable solution to mobility-related aspects of social exclusion. Findings from both a desk study and public consultation suggest that virtual mobility is already fulfilling an accessibility role, both substituting for and supplementing physical mobility, working to alleviate some aspects of mobility-related social exclusion in some sectors of society. The paper incorporates an analysis of the barriers to and problems with an increase in virtual mobility in society, and concludes that virtual mobility could be a valuable tool in both social and transport policy.
The jockey and his horse
Authors: Blaisdell Bob 
Published: July 2003

It is told, that in the art of education he performed wonders; and a formidable list is given of the authors, Greek and Latin, that were read in Aldersgate-street, by youth between ten and fifteen or sixteen years of age. Those who tell or receive these stories should consider that nobody can be taught faster than he can learn. The speed of the horseman must be limited by the power of his horse. Every man that has ever undertaken to instruct others, can tell what slow advances he has been able to make, and how much patience it requires to recall vagrant inattention, to stimulate sluggish indifference, and to rectify absurd misapprehension.Samuel Johnson, “John Milton”The greatest man of letters in English continually reminds us in his essays and in Boswell's Life that we need to expect an awful lot of resistance to learning, and that he himself, Dr. Samuel Johnson (who had single-handedly composed a dictionary in seven years) lived full of “vagrant inattention” and “sluggish indifference” – though not of “absurd misapprehension”.
Soluble inflammatory markers in coronary sinus and peripheral blood of heart transplant recipients
Authors: Hsu Ron‐Bin , Tsay Yeou‐Guang , Lee Chii‐Ming , Chen Robert J , Wang Shoei‐Shen , Chu Shu‐Hsun 
Published: July 2003

Abstract: Cardiac allograft rejection is a focal inflammation and soluble markers are released into coronary sinus (CS). We investigated whether plasma‐soluble markers in CS is better to predict the clinical status of transplant recipients than in peripheral blood (PB). Between February 1998 and January 2001, 51 patients admitted for endomyocardial biopsy were included. The clinical events of the transplant recipient were recorded as: early post‐transplant, long‐term uneventful status, infection, acute rejection and transplant coronary artery disease. The plasma levels of interleukin‐2 (IL‐2), tumor necrosis factor‐α (TNF‐α), ICAM‐1, P‐selectin, high‐sensitive C‐reactive protein (CRP) and troponin‐I of CS and PB were determined. There were 71 blood samples. In patients within 1 month after heart transplant, there was a higher level of P‐selectin, ICAM‐1, CRP and troponin‐I in CS and PB. In patients with infection, there was a higher level of all soluble markers except IL‐2 in CS and PB. Patients with a long‐term uneventful status had a lower level of CRP in PB but not in CS. Patients with acute rejection had a higher level of IL‐2 in PB but not in CS. Patients with transplant coronary artery disease had a higher level of TNF‐α in PB but not in CS. Soluble markers in CS failed to predict the occurrence of acute or chronic rejections.
Intramucosal pH monitoring during liver transplantation
Authors: Mándli Tamás , Gondos Tibor 
Published: July 2003

Abstract: Purpose: To apply tonometry as a quick estimation of the early liver graft function.Patients and methods: Forty‐five liver‐transplanted patients were examined. Data were collected prospectively and analysed retrospectively. According to the early graft function, patients were classified into two groups: in group 1 (n = 28) adequate graft function, in group 2 (n = 17) deteriorated graft function was detected in the early post‐operative period. Complete conventional and volumetric haemodynamic monitoring and intramucosal pH (pHi), regional CO2 tension (PrCO2) measurements were performed during surgery and until the 36 hours post‐operatively.Results: In group 2 the packed blood cell, fresh frozen plasma consumption intraoperatively, and the time of hepatectomy were significantly higher; ICU treatment days, respiration time was longer and mortality rate was higher. Almost the whole examination period pHi was mostly below 7.3 and PrCO2 above 50 mmHg in group 2. There were significant differences in pHi between the groups from the preparation phase until the 24th post‐operative hour. In group 2, there were significantly lower values in cardiac output in the whole examination period and in the mean arterial pressure values in the revascularization phase. In group 1, the oxygen delivery values were significantly higher in the preparation phase and oxygen consumption values after revascularization phase. With regression analysis there were no significant correlations between pHi, PrCO2 and global haemodynamic parameters.Conclusion: Regional parameters were completely different from global haemodynamic parameters, therefore pHi and PrCO2 can be a good indicator of the early liver graft dysfunction.
Gastroesophageal reflux disease in lung transplant recipients
Authors: Hadjiliadis Denis , Duane Davis R , Steele Mark P , Messier Robert H , Lau Christine L , Eubanks Steve S , Palmer Scott M 
Published: July 2003

Abstract: Background: Chronic allograft dysfunction after lung transplantation contributes to poor long‐term survival. A link between gastric aspiration and post‐transplant lung dysfunction has been suggested, but little is known about the significance of gastroesophageal reflux disease (GERD) after lung transplantation.Methods: A retrospective study was performed to determine the prevalence of GERD in lung transplant recipients. Patients who underwent lung transplantation at Duke University, survived at least 6 months and had post‐transplant 24‐h pH studies were included in the analysis. Antireflux medications were discontinued prior to the pH study. Demographic data, pH study date and results, FEV1 at the time of the pH study, confirmed acute rejection episodes, and current medications were collected. The FEV1 ratio was calculated at the time of pH study (current FEV1/best post‐transplant FEV1).Results: Forty‐three patients met entry criteria. Studies were performed at a median of 558 d post‐transplant. Thirty of forty‐three (69.8%) patients tested had abnormal total acid contact times (normal: <5%). The mean acid contact times for all patients were 10% total, 11.8% upright and 7.9% supine. A negative correlation was found between total or upright acid reflux and FEV1 ratio at the time of studies (−0.341 and −0.419; p = 0.025 and p = 0.005, respectively). The effect of acid reflux on FEV1 ratio remained significant after multivariable analysis.Conclusions: There is a high prevalence of GERD among selected lung transplant recipients who had pH studies performed and its presence is associated with worse pulmonary function. Future studies are needed to assess whether GERD contributes to the pathogenesis of bronchiolitis obliterans syndrome (BOS).