Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Capping computation time and storage requirements for appearance-based localization with CAT-SLAM

Appearance-based localization is increasingly used for loop closure detection in metric SLAM systems. Since it relies only upon the appearance-based similarity between images from two locations, it can perform loop closure regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale linearly not only with the size of the environment but also with the operation time of the platform. These properties impose severe restrictions on longterm autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. We present a set of improvements to the appearance-based SLAM algorithm CAT-SLAM to constrain computation scaling and memory usage with minimal degradation in performance over time. The appearance-based comparison stage is accelerated by exploiting properties of the particle observation update, and nodes in the continuous trajectory map are removed according to minimal information loss criteria. We demonstrate constant time and space loop closure detection in a large urban environment with recall performance exceeding FAB-MAP by a factor of 3 at 100% precision, and investigate the minimum computational and memory requirements for maintaining mapping performance.

Clinical performance of a new silicone hydrogel contact lens over 6 months of extended wear

Purpose: Silicone hydrogel contact lenses (CLs) are becoming increasingly popular for daily wear (DW), extended wear (EW) and continuous wear (CW), due to their higher oxygen transmissibility compared to hydrogel CLs. The aim of this study was to investigate the clinical and subjective performance of asmofilcon A (Menicon Co., Ltd), a new surface treated silicone hydrogel CL, during 6-night EW over 6 months (M). Methods: A prospective, randomised, single-masked, monadic study was conducted. N=60 experienced DW soft CL wearers were randomly assigned to wear either asmofilcon A (test: Dk=129, water content (WC)=40%, Nanogloss surface treatment) or senofilcon A (control: Dk=103, WC=38%, PVP internal wetting agent, Vistakon, Johnson & Johnson Vision Care) CLs bilaterally for 6 M on an EW basis. A PHMB-preserved solution (Menicon Co., Ltd) was dispensed for CL care. Evaluations were conducted at CL delivery and after 1 week (W), 4 W, 3 M and 6 M of EW. At each visit, a range of objective and subjective clinical performance measures were assessed. Results: N=50 subjects (83%) successfully completed the study, with the majority of discontinuations due to loss to follow-up (n=3) or moving away/travel (n=5). N=2 subjects experienced adverse events; n=1 unilateral red eye with asmofilcon A and n=1 asymptomatic infiltrate with senofilcon A. There were no significant differences in high or low contrast distance visual acuity (HCDVA or LCDVA) between asmofilcon A and senofilcon A; however, LCDVA decreased significantly over time with both CL types (p<0.05). The two CL types did not vary significantly with respect to any of the objective and subjective measures assessed (p>0.05); CL fitting characteristics and CL surface measurements were very similar and mean bulbar and limbal redness measures were always less than grade 1.0. Superior palpebral conjunctival injection showed a statistically, but not clinically, significant increase over time with both CL types (p<0.05). Corneal staining did not vary significantly between asmofilcon A and senofilcon A (p>0.05), with low median gradings of less than 0.5 observed for all areas assessed. There were no solution-related staining reactions observed with either CL type. The asmofilcon A and senofilcon A CLs were both rated highly with respect to overall comfort, with medians of 14 or 15 hours of comfortable lens wearing time per day reported at each of the study visits (p>0.05). Conclusions: Over 6 months of EW, the asmofilcon A and senofilcon A CLs performed in a similar manner with respect to visual acuity, ocular health and CL performance measures. Some changes over time were observed with both CL types, including reduced LCDVA and increased superior palpebral injection, which warrant further investigation in longer-term EW studies. Asmofilcon A appeared to be equivalent in performance to senofilcon A.

The Moral Economy of Everyday Crime: Markets, Consumers and Citizens

Between the crimes in the suites and the crimes in the streets lies the mostly unexplored terrain within which we find crimes of ‘everyday life’. Not all of these are formally illegal, but all are generally seen as morally dubious. Most of the crimes of everyday life are committed in the contemporary marketplace, and by those who think of themselves (and are mostly considered by others) as respectable citizens. We contextualize normative orientations that are conducive to such types of behaviour using a framework that links E. P. Thompson’s (1963) concept of the ‘moral economy’ with Institutional Anomie Theory (Messner and Rosenfeld 1994, 2007). Findings from a comparative survey study in three economic change regions (England and Wales, Western and Eastern Germany) show that a syndrome of market anomie comprising distrust, fear and cynical attitudes toward law increases the willingness of respectable citizens to engage in illegal and unfair practices in the marketplace.

What health problems overcrowd hospital emergency departments in Queensland and has this changed over time? A case study of two hospitals in Queensland 2001 - 2009

Aim: to describe what health problems patients attending emergency department with and whether this changed over time. Methods: Electronic data was retrieved from EDIS (Emergency Department Information System) and HBCIS (Hospital Based Clinical Information System) in two hospitals in Queensland in the period 2001-2009. The ICD-10 code of patient's diagnosis was then extrapolated and then group into ICD-10 chapters, such that the health problem can be presented. Results: Among the specific health problems, Chapter XIX 'Injury and poisoning' ranked number one consistently (ranging from 22.1% to 31.2% of the total presentations) in both the urban and remote hospitals in Queensland. The top ten specific presenting health problems in both the urban and remote hospital include Chapter XI 'Digestive system', Chapter XIV 'Genitourinary system', Chapter IX 'Circulatory system', and Chapter XIII 'Musculoskeletal system and connective tissue'. Chapter X 'Respiratory system' made the top ten presenting Chapters in both hospitals, but ranked much higher (number four consistently for the eight years, ranging from 6.8% to 8.3%) in the remote hospital. Chapter XV 'Pregnancy childbirth and puerperium' made to the top ten in the urban hospital only while Chapter XII 'Skin and subcutaneous tissue', Chapter I 'Infectious and parasitic diseases' made the top ten in the remote hospital only. Conclusion: The number one health problem presenting to both the urban and remote hospitals in Queensland is Chapter XIX 'Injury and poisoning', and it did not change in the period 211 - 2009.