Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative; Model-2 with the one-dimensional fractional Laplacian operator; and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions

Can Charisma Be Taught? Tests of Two Interventions

We tested whether we could teach individuals to behave more charismatically, andwhether changes in charisma affected leader outcomes. In Study 1, a mixed-design fieldexperiment, we randomly assigned 34 middle-level managers to a control or anexperimental group. Three months later, we reassessed the managers using theircoworker ratings (Time 1 raters = 343; Time 2 raters = 321). In Study 2, a within-subjectslaboratory experiment, we videotaped 41 MBA participants giving a speech. We thentaught them how to behave more charismatically, and they redelivered the speech6 weeks later. Independent assessors (n = 135) rated the speeches. Results from thestudies indicated that the training had significant effects on ratings of leader charisma(mean D = .62) and that charisma had significant effects on ratings of leaderprototypicality and emergence...............................................................................................................................

Cells activated for wound repair have the potential to direct collective invasion of an epithelium.

Mechanisms regulating how groups of cells are signaled to move collectively from their original site and invade surrounding matrix are poorly understood. Here we develop a clinically relevant ex vivo injury invasion model to determine whether cells involved in directing wound healing have invasive function and whether they can act as leader cells to direct movement of a wounded epithelium through a three-dimensional (3D) extracellular matrix (ECM) environment. Similar to cancer invasion, we found that the injured cells invade into the ECM as cords, involving heterotypical cell-cell interactions. Mesenchymal cells with properties of activated repair cells that typically locate to a wound edge are present in leader positions at the front of ZO-1-rich invading cords of cells, where they extend vimentin intermediate filament-enriched protrusions into the 3D ECM. Injury-induced invasion depends on both vimentin cytoskeletal function and MMP-2/9 matrix remodeling, because inhibiting either of these suppressed invasion. Potential push and pull forces at the tips of the invading cords were revealed by time-lapse imaging, which showed cells actively extending and retracting protrusions into the ECM. This 3D injury invasion model can be used to investigate mechanisms of leader cell-directed invasion and understand how mechanisms of wound healing are hijacked to cause disease

Anticholinergic burden in older women: not seeing the wood for the trees?

Objectives: To identify medicines contributing to and describe predictors of anticholinergic burden among community-dwelling older Australian women. Design, setting and participants: Retrospective longitudinal analysis of data from the Australian Longitudinal Study on Women's Health linked to Pharmaceutical Benefits Scheme medicines data from 1 January 2008 to 30 December 2010; for 3694 women born in 1921–1926. Main outcome measures: Anticholinergic burden calculated from Anticholinergic Drug Scale (ADS) scores derived from ADS levels (0 to 3) for all medicines used by each woman, summed over each 6-month period (semester), medicines commonly used by women with high semester ADS scores (defined as 75th percentile of scores). Results: 1126 women (59.9%) used at least one medicine with anticholinergic properties. The median ADS score was 4 or 5 across all semesters. Most anticholinergic medicines used by women who had a high anticholinergic burden (ADS score, = 9) had a low anticholinergic potency (ADS level 1). Increasing age, cardiovascular disease, and number of other medicines used were predictive of a higher anticholinergic burden. Conclusions: A high anticholinergic medicines burden in this group was driven by the use of multiple medicines with lower anticholinergic potency rather than the use of medicines with higher potency. This is a novel and important finding for clinical practice as doctors would readily identify the risk of a high anticholinergic burden for patients using high potency medicines, but may be less likely to identify this risk for users of multiple medicines with low anticholinergic potency

The International comparison of Systems of care and patient outcomes In minor Stroke and Tia (InSIST) study: A community-based cohort study

This is the author accepted manuscript. The final version is available from Sage Publications via the DOI in this record.Rationale: Rapid response by health-care systems for transient ischemic attack and minor stroke (TIA/mS) is recommended to maximize the impact of secondary prevention strategies. The applicability of this evidence to Australian non-hospital-based TIA/mS management is uncertain. Aims: Within an Australian community setting we seek to document processes of care, establish determinants of access to care, establish attack rates and determinants of recurrent vascular events and other clinical outcomes, establish the performance of ABC2-risk stratification, and compare the processes of care and outcomes to those in the UK and New Zealand for TIA/mS. Sample size estimates: Recruiting practices containing approximately 51 full-time-equivalent general practitioners to recruit 100 TIA/mS per year over a four-year study period will provide sufficient power for each of our outcomes. Methods and design: An inception cohort study of patients with possible TIA/mS recruited from 16 general practices in the Newcastle-Hunter Valley-Manning Valley region of Australia. Potential TIA/mS will be ascertained by multiple overlapping methods at general practices, after-hours collaborative, and hospital in-patient and outpatient services. Participants’ index and subsequent clinical events will be adjudicated as TIA/mS or mimics by an expert panel. Study outcomes: Process outcomes—whether the patient was referred for secondary care; time from event to first patient presentation to a health professional; time from event to specialist acute-access clinic appointment; time from event to brain and vascular imaging and relevant prescriptions. Clinical outcomes—recurrent stroke and major vascular events; and health-related quality of life. Discussion: Community management of TIA/mS will be informed by this study.Nationale Health and Medical Research Council (NHMRC

THE FORMATION OF THE NECESSARY COMPLEX MECHANICAL PROPERTIES OF METAL IN THE PRODUCTION CHAINS OF HIGH STRENGTH

В статье рассмотрено производство цепей из высокопрочной стали 30ХГСА. Исследовано влияние механических свойств стали на процесс гибки прутка в заготовку звена цепи. На основании полученных экспериментальных результатов предлагается технология термической обработки, которая обеспечивает необходимый комплекс механических свойств в производстве цепей высокой прочности.The article describes the production chains of high strength steel 30ХГСА(30KHGSA). The influence of the mechanical properties of steel for the bending of the rod in the procurement chain link. Based on the experimental results, it is proposed the technology of heat treatment, which ensures the required mechanical properties in the production chains of high strength