Abstract:
In a multicenter observational cohort of patients-admitted to intensive care units (ICU), we assessed whether creatinine elevation prior to dialysis initiation in acute kidney injury (AKI-D) further discriminates risk-adjusted mortality. AKI-D was categorized into four groups (Grp) based on creatinine elevation after ICU admission but before dialysis initiation: Grp I ？>？0.3？mg/dL to <2-fold increase, Grp II ≥2 times but <3 times increase, Grp III ≥3-fold increase in creatinine, and Grp IV none or <0.3？mg/dl increase. Standardized mortality rates (SMR) were calculated by using a validated risk-adjusted mortality model and expressed with 95% confidence intervals (CI). 2,744 patients developed AKI-D during ICU stay; 36.7%, 20.9%, 31.2%, and 11.2% belonged to groups I, II, III, and IV, respectively. SMR showed a graded increase in Grp I, II, and III (1.40 (95% CI, 1.29–1.42), 1.84 (1.66–2.04), and 2.25 (2.07–2.45)) and was 0.98 (0.78–1.20) in Grp IV. In ICU patients with AKI-D, degree of creatinine elevation prior to dialysis initiation is independently associated with hospital mortality. It is the lowest in those experiencing minor or no elevations in creatinine and may represent reversible fluid-electrolyte disturbances. 1. Introduction Acute kidney injury (AKI) requiring dialysis is a serious complication in critically ill patients, bringing increased morbidity, mortality, and costs of care [1–4]. AKI requiring dialysis is usually considered the most severe form of kidney injury, and these patients have been conventionally regarded as a relatively “homogenous” group of patients, either when describing epidemiological information or while conducting clinical trials [5, 6]. However, studies examining interventions in dialysis patients (e.g., dialysis modality or frequency have not demonstrated unequivocal survival benefits [7–9]. It is well recognized that small changes in creatinine (mild-to-moderate AKI) independently predict mortality [10, 11]; we also recently reported that patients with AKI requiring dialysis represent a wider spectrum of severity of kidney injury, contrary to the prevalent notion [12]. Thus, it can be hypothesized that the degree of elevation of creatinine prior to initiating dialysis may discriminate risk-adjusted mortality, similar to the observations in nondialysis requiring AKI. The Acute Kidney Injury Network (AKIN) has issued standard definitions of AKI; currently, in these criteria, AKI requiring dialysis is classified as stage III (or severe) AKI [13]. The consensus panel also proposed that the examination of natural history

Abstract:
The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that a domain does not have property (KS) provided the boundary contains at least three differrent irreducible algebraic hypersurfaces for which two of them have a common point.

Abstract:
The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that property (KS) for a domain $\Omega $ is equivalent to the surjectivity of a Fischer operator associated to the domain $\Omega .$

Abstract:
In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Pi\c{t}ul and P. Sablonni\`{e}re. It is shown that the rational Bernstein operators R_n converge to the identity operator if and only if \Delta_n, the maximal difference between two consecutive nodes of R_n, is converging to zero. Error estimates in terms of \Delta_n are provided. Moreover a Voronovskaja theorem is presented which is based on the explicit computation of higher order moments for the rational Bernstein operator.

Abstract:
We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such family arises as the family of languages accepted by N-automata where N is a simple or 0-simple monoid. A consequence is that every such family is either the class of regular languages, contains all the blind one-counter languages, or is the family of languages accepted by G-automata for G a non-locally-finite torsion group. We consider a natural extension of the usual definition which permits the automata to utilise more of the structure of each monoid, and also allows us to define S-automata for S an arbitrary semigroup. In the monoid case, the resulting automata are equivalent to the valence automata with rational target sets} which arise in the theory of regulated rewriting systems. We study the case that the register semigroup is completely simple or completely 0-simple, obtaining a complete characterisation of the classes of languages corresponding to such semigroups in terms of their maximal subgroups. In the process, we obtain a number of results about rational subsets of Rees matrix semigroups which may be of independent interest.

Abstract:
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally the corresponding truncated moment problem is discussed.

Abstract:
We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is, the bicyclic monoid), they accept a class of languages strictly including the partially blind one-counter languages. Key to the proof is a description of the rational subsets of polycyclic and bicyclic monoids, other consequences of which include the decidability of the rational subset membership problem for these monoids, and the closure of the class of rational subsets under intersection and complement.

Abstract:
Unlike the classical polynomial case there has not been invented up to very recently a tool similar to the Bernstein-Bezier representation which would allow us to control the behavior of the exponential polynomials. The exponential analog to the classical Bernstein polynomials has been introduced in a recent authors' paper which appeared in Constructive Approximations, and this analog retains all basic properties of the classical Bernstein polynomials. The main purpose of the present paper is to contribute in this direction, by proving some important properties of the "Bernstein exponential operator" which has been introduced. We also fix our attention upon some special type of exponential polynomials which are particularly important for the further development of theory of representation of Multivariate data.

Abstract:
Polyharmonic functions f of infinite order and type {\tau} on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients f_{k,l}(r) of a polyharmonic function f of infinite order and type 0 can be extended to analytic functions on the complex plane cut along the negative semiaxis. The second main result gives a constructive procedure via Fourier-Laplace series for the analytic extension of a polyharmonic function on annular region A(r_{0},r_{1}) of infinite order and type less than 1/2r_{1} to the kernel of the harmonicity hull of the annular region. The methods of proof depend on an extensive investigation of Taylor series with respect to linear differential operators with constant coefficients.

Abstract:
Let $u\left( t,y\right) $ be a polyharmonic function of order $N$ defined on the strip $\left( a,b\right) \times\mathbb{R}^{d}$ satisfying the growth condition $$ \sup_{t\in K}\left\vert u\left( t,y\right) \right\vert \leq o\left( \left\vert y\right\vert ^{\left( 1-d\right) /2}e^{\frac{\pi}{c}\left\vert y\right\vert }\right) $$ for $\left\vert y\right\vert \rightarrow\infty$ and any compact subinterval $K$ of $\left( a,b\right) $, and suppose that $u\left( t,y\right) $ vanishes on $2N-1$ equidistant hyperplanes of the form $\left\{ t_{j}\right\} \times\mathbb{R}^{d}$ for $t_{j}=t_{0}+jc\in\left( a,b\right) $ and $j=-\left( N-1\right) ,...,N-1.$ Then it is shown that $u\left( t,y\right) $ is odd at $t_{0},$ i.e. that $u\left( t_{0}+t,y\right) =-u\left( t_{0}-t,y\right) $ for $y\in\mathbb{R}^{d}$. The second main result states that $u$ is identically zero provided that $u$ satisfies the growth condition and vanishes on $2N$ equidistant hyperplanes with distance $c.$