Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Diversity and change in Australia's rangelands: a post-productivist transition with a difference?

Australia's rangelands are experiencing a post-productivist transition at a tempo comparable to Western Europe's, but in contexts that ensure marked divergence in impulses, actors, processes and outcomes. In Australia's most marginal lands, a flimsy mode of pastoral occupance is being displaced by renewed indigenous occupance, conservation and tourism, with significant changes in land ownership, property rights, investment sources and power relations, but also with structural problems arising from fugitive income streams. The sharp delineation between structurally coherent commodity-oriented regions and emerging amenity-oriented regions can provisionally be mapped at a national scale. A comparison of Australia with Western Europe indicates that three distinct but interconnected driving forces are propelling the rural transition, namely: agricultural overcapacity; the emergence of amenity-oriented uses; and changing societal values.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Living with 'difference': growing up Chinese in white Australia

This Article does not have an abstract.

Effects of physical exercise training in DNA damage and repair - could the difference be in hOGG1 Ser326Cys polymorphism?

Acute physical exercise is associated with increased oxygen consumption, which could result in an increased formation of reactive oxygen species (ROS). ROS can react with several organic structures, namely DNA, causing strand breaks and a variety of modified bases in DNA. Physical exercise training seems to decrease the incidence of oxidative stress-associated diseases, and is considered as a key component of a healthy lifestyle. This is a result of exercise-induced adaptation, which has been associated with the possible increase in antioxidant activity and in oxidative damage repair enzymes, leading to an improved physiological function and enhanced resistance to oxidative stress (Radak et al. 2008). Human 8-oxoguanine DNA glycosylase 1 (hOGG1) is involved in the base excision repair (BER) pathway and encodes an enzyme responsible for removing the most common product of oxidative damage in DNA, 8-hydroxyguanine (8-OH-G). The genetic polymorphism of hOGG1 at codon 326 results in a serine (Ser) to cysteine (Cys) amino acid substitution (Ser326Cys). It has been suggested that the carriers of at least one hOGG1Cys variant allele exhibit lower 8-OH-G excision activity than the wild-type (Wilson et al. 2011). The aim of this study was to investigate the possible influence of hOGG1 Ser326Cys polymorphism on DNA damage and repair activity in response to 16 weeks of combined physical exercise training, in thirty healthy Caucasian men. Comet assay was carried out using peripheral blood lymphocytes and enabled the evaluation of DNA damage, both strand breaks and FPG-sensitive sites, and DNA repair activity. Genotypes were determined by PCR-RFLP analysis. The subjects with Ser/Ser genotype were considered as wild-type group (n=20), Ser/Cys and Cys/Cys genotype were analyzed together as mutant group (n=10). Regarding differences between pre and post-training in the wild-type group, the results showed a significant decrease in DNA strand breaks (DNA SBs) (p=0.002) and also in FPG-sensitive sites (p=0.017). No significant differences were observed in weight (p=0.389) and in lipid peroxidation (MDA) (p=0.102). A significant increase in total antioxidant capacity (evaluated by ABTS) was observed (p=0.010). Regarding mutant group, the results showed a significant decrease in DNA SBs (p=0.008) and in weight (p=0.028). No significant differences were observed in FPG-sensitive sites (p=0.916), in ABTS (p=0.074) and in MDA (p=0.086). No significant changes in DNA repair activity were observed in both genotype groups. This preliminary study suggests the possibility of different responses in DNA damage to physical exercise training, considering the hOGG1 Ser326Cys polymorphism.

Portugal making a difference with children and families: the GADIF model

Portugal is a culture grounded in strong traditions and family. Yet, social changes like women returning to the workforce and a decreas ed national birth rate are impacting the traditional family structure and care giving environments of children. Female employment has been increasing steadily in P ortugal over the last three decades (Galego & Pereira, 2006) and the total fert ility rate decreasing from 4.1 to 2.8 (INE, 2006). Furthermore, extended family me mbers, like grandparents, no longer reside close by to their children and grandc hildren as in the past, because of a changing labor market. Many of the younger gen eration are leaving their rural communities to flock to urban areas because o f job opportunities, leaving behind older relatives who would have otherwise par ticipated in the daily care of children. Given these social and economic changes, children are spending more time in out-of-home care with non-familial caregive rs. Yet, government regulations and guidelines in early care and educat ion (ECCE) and early intervention (EI) are only just emerging; it contin ues to be a work in progress.

Partitioning taxon, phylogenetic and functional beta diversity into replacement and richness difference components

Copyright © 2013 John Wiley & Sons Ltd.

The invisible factors that can make the difference. Language management and knowledge transfer in multinational sites

The knowledge-based society we live in has stressed the importance of human capital and brought talent to the top of most wanted skills, especially to companies who want to succeed in turbulent environments worldwide. In fact, streams, sequences of decisions and resource commitments characterize the day-to-day of multinational companies (MNCs). Such decision-making activities encompass major strategic moves like internationalization and new market entries or diversification and acquisitions. In most companies, these strategic decisions are extensively discussed and debated and are generally framed, formulated, and articulated in specialized language often developed by the best minds in the company. Yet the language used in such deliberations, in detailing and enacting the implementation strategy is usually taken for granted and receives little if any explicit attention (Brannen & Doz, 2012) an can still be a “forgotten factor” (Marschan et al. 1997). Literature on language management and international business refers to lack of awareness of business managers of the impact that language can have not only in communication effectiveness but especially in knowledge transfer and knowledge management in business environments. In the context of MNCs, management is, for many different reasons, more complex and demanding than that of a national company, mainly because of diversity factors inherent to internationalization, namely geographical and cultural spaces, i.e, varied mindsets. Moreover, the way of functioning, and managing language, of the MNC depends on its vision, its values and its internationalization model, i.e on in the way the MNE adapts to and controls the new markets, which can vary essentially from a more ethnocentric to a more pluricentric focus. Regardless of the internationalization model followed by the MNC, communication between different business units is essential to achieve unity in diversity and business sustainability. For the business flow and prosperity, inter-subsidiary, intra-company and company-client (customers, suppliers, governments, municipalities, etc..) communication must work in various directions and levels of the organization. If not well managed, this diversity can be a barrier to global coordination and create turbulent environments, even if a good technological support is available (Feely et al., 2002: 4). According to Marchan-Piekkari (1999) the tongue can be both (i) a barrier, (ii) a facilitator and (iii) a source of power. Moreover, the lack of preparation for the barriers of linguistic diversity can lead to various costs, including negotiations’ failure and failure on internationalization.. On the other hand, communication and language fluency is not just a message transfer procedure, but above all a knowledge transfer process, which requires extra-linguistic skills (persuasion, assertiveness …) in order to promote credibility of both parties. For this reason, MNCs need a common code to communicate and trade information inside and outside the company, which will require one or more strategies, in order to overcome possible barriers and organization distortions.

Do Spirituality and Faith Make a Difference? Report from the Southern European Psycho-Oncology Study Group

OBJECTIVE: In the last decade, some attention has been given to spirituality and faith and their role in cancer patients' coping. Few data are available about spirituality among cancer patients in Southern European countries, which have a big tradition of spirituality, namely, the Catholic religion. As part of a more general investigation (Southern European Psycho-Oncology Study--SEPOS), the aim of this study was to examine the effect of spirituality in molding psychosocial implications in Southern European cancer patients. METHOD: A convenience sample of 323 outpatients with a diagnosis of cancer between 6 to 18 months, a good performance status (Karnofsky Performance Status > 80), and no cognitive deficits or central nervous system (CNS) involvement by disease were approached in university and affiliated cancer centers in Italy, Spain, Portugal, and Switzerland (Italian speaking area). Each patient was evaluated for spirituality (Visual Analog Scale 0-10), psychological morbidity (Hospital Anxiety and Depression Scale--HADS), coping strategies (Mini-Mental Adjustment to Cancer--Mini-MAC) and concerns about illness (Cancer Worries Inventory--CWI). RESULTS. The majority of patients (79.3%) referred to being supported by their spirituality/faith throughout their illness. Significant differences were found between the spirituality and non-spirituality groups (p ≤ 0.01) in terms of education, coping styles, and psychological morbidity. Spirituality was significantly correlated with fighting spirit (r = -0.27), fatalism (r = 0.50), and avoidance (r = 0.23) coping styles and negatively correlated with education (r = -0.25), depression (r = -0.22) and HAD total (r = -0.17). SIGNIFICANCE OF RESULTS: Spirituality is frequent among Southern European cancer patients with lower education and seems to play some protective role towards psychological morbidity, specifically depression. Further studies should examine this trend in Southern European cancer patients.