Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Attitudes toward sport psychology consulting of adult athletes from the United States, United Kingdom, and Germany

The purpose of this study was to explore attitudes about sport psychology consulting of athletes living in the United States, United Kingdom and Germany. The Sport Psychology Attitudes - Revised form (SPA-R; Martin, Kellmann, Lavallee, & Page, 2002) was administered to 404 athletes from the United States, 147 athletes from the United Kingdom, and 260 athletes from Germany. A 2 (Gender) x 3 (Nationality: American, British and German) x 2 (Type of Sport: physical contact and physical non-contact) MANCOVA was conducted with past sport psychology conducting experience as a covariant and attitudes about sport psychology as dependent variables. Follow-up univariate and discriminant function analyses were then performed to identify the attitiudes that maximized differences related to gender, nationality, and type of sport. Results revealed that attitudes about sport psychology services might be influenced by gender, nationality, and type of sport. Sport psychology practitioners must be sensitive to how personal characteristics and past experiences influence athletes' expectations and attitudes toward sport psychology consulting to improve the services they offer

Less Anterior Knee Pain with a Mobile-bearing Prosthesis Compared with a Fixed-bearing Prosthesis

Anterior knee pain is one of the major short-term complaints after TKA. Since the introduction of the mobile-bearing TKA, numerous studies have attempted to confirm the theoretical advantages of a mobile-bearing TKA over a fixed-bearing TKA but most show little or no actual benefits. The concept of self-alignment for the mobile bearing suggests the posterior-stabilized mobile-bearing TKA would provide a lower incidence of anterior knee pain compared with a fixed-bearing TKA. We therefore asked whether the posterior-stabilized mobile-bearing knee would in fact reduce anterior knee pain. We randomized 103 patients scheduled for cemented three-component TKA for osteoarthrosis in a prospective, double-blind clinical trial. With a 1-year followup, more patients experienced persistent anterior knee pain in the posterior-stabilized fixed-bearing group (10 of 53, 18.9%) than in the posterior-stabilized mobile-bearing group (two of 47, 4.3%). No differences were observed for range of motion, visual analog scale for pain, Oxford 12-item questionnaire, SF-36, or the American Knee Society score. The posterior-stabilized mobile-bearing knee therefore seems to provide a short-term advantage compared with the posterior-stabilized fixed-bearing knee

Green Pathways for the Enzymatic Synthesis of Furan-Based Polyesters and Polyamides

The attention towards the utilization of sustainable feedstocks for polymer synthesis has grown exponentially in recent years. One of the spotlighted monomers derived from renewable resources is 2,5-furandicarboxylic acid (FDCA), one of the most promising bio-based monomers, due to its resemblance to petroleum-based terephthalic acid. Very interesting synthetic routes using this monomer have been reported in the last two decades. Combining the use of bio-based monomers and non-toxic chemicals via enzymatic polymerizations can lead to a robust and favorable approach towards a greener technology of bio-based polymer production. In this chapter, a brief introduction to FDCA-based monomers and enzymatic polymerizations is given, particularly focusing on furan-based polymers and their polymerization. In addition, an outline of the recent developments in the field of enzymatic polymerizations is discussed. </p

Pharmacologic prophylaxis for atrial fibrillation following cardiac surgery: a systematic review

Atrial Fibrillation (AF) is the most common arrhythmia occurring after cardiac surgery. Its incidence varies depending on type of surgery. Postoperative AF may cause hemodynamic deterioration, predispose to stroke and increase mortality. Effective treatment for prophylaxis of postoperative AF is vital as reduces hospitalization and overall morbidity. Beta - blockers, have been proved to prevent effectively atrial fibrillation following cardiac surgery and should be routinely used if there are no contraindications. Sotalol may be more effective than standard b-blockers for the prevention of AF without causing an excess of side effects. Amiodarone is useful when beta-blocker therapy is not possible or as additional prophylaxis in high risk patients. Other agents such as magnesium, calcium channels blocker or non-antiarrhythmic drugs as glycose-insulin - potassium, non-steroidal anti-inflammatory drugs, corticosteroids, N-acetylcysteine and statins have been studied as alternative treatment for postoperative AF prophylaxis