Numerical Methods for Solving Fractional Differential Equations

Department of Mathematical SciencesIn this thesis, several efficient numerical methods are proposed to solve initial value problems and boundary value problems of fractional di???erential equations. For fractional initial value problems, we propose a new type of the predictorevaluate-corrector-evaluate method based on the Caputo fractional derivative operator. Furthermore, we propose a new type of the Caputo fractional derivative operator that does not have a di???erential form of a solution. However, with some fractional orders, there are problems that a solution blows up and the scheme has a low convergence. Thus, we identify new treatments for these values. Then, we can expect a significant improvement for all fractional orders. The advantages and improvements are shown by testing various numerical examples. For fractional BVPs, we propose an explicit method that dramatically reduces the computational time for solving a dense matrix system. Moreover, by adopting high-order predictor-corrector methods which have uniform convergence rates O(h2) or O(h3) for all fractional orders [8], we propose a second-order method and a third-order method by using the Newton???s method and the Halley method, respectively. We show its advantage by testing various numerical examples.clos

I feel better naked: Communal naked activity increases body appreciation by reducing social physique anxiety.

Positive body image predicts several measures of happiness, well-being, and sexual functioning. Prior research has suggested a link between communal naked activity and positive body image, but has thus far not clarified either the direction or mechanisms of this relationship. This was the first randomised controlled trail of the effects of nakedness on body image. Two potential explanatory mediators of this effect were also investigated. Fifty-one participants were randomly assigned to one of two groups in which they interacted with other people either naked (naked condition) or clothed (control condition). All participants completed measures of body appreciation before and after the intervention, as well as measures of the relative perceived attractiveness of others and social physique anxiety immediately after the intervention. Perceived attractiveness of others was neither affected by the manipulation nor corelated with body appreciation. However, as expected, participants in the naked condition reported more body appreciation, an effect that was mediated by reductions in social physique anxiety. This research provides initial evidence that naked activity can lead to improvements in body image and evidence of a specific explanatory mechanism. Theoretical and practical implications are discussed

Effectiveness Of Ghana\u27s Decenctralized Administraiton In Matters Of Physical Development: The Case Of The Wa District Assembly

The topic concerns evaluating the effectiveness of a decentralized administration in matters of physical development, using the Wa District Assembly in the Upper West Region, Ghana, as its case study. The paper attempts to do this my examining 5 sets of District implemented projects, and determine their overall level of success, which is defined in terms of both the project\u27s efficiency and the degree to which it responds to the real needs of its benefactors. The paper then isolates three District activities whose functions directly contributes to the success of development projects, and uses the data drawn from the project histories to evaluate the District\u27s level of effectiveness in performing these activities. From the analysis, the write attempts to illustrate the effectiveness of the District in matters of development, so long as the actual activity of the District is decentralized to a large enough degree, and this is reflected in his recommendations for further decentralization

A British Reflection: the Relationship between Dante’s Comedy and the Italian Fascist Movement and Regime during the 1920s and 1930s with references to the Risorgimento

This thesis considers the relationship that Dante’s Comedy had with Italian Fascism during the 1920s and 1930s via the mediation of Britain. Whilst previous studies have engaged in a debate that focuses mostly on a possible, or otherwise unlikely, use of Dante’s masterpiece during what came to be known as the Ventennio, the twenty years of fascist rule of Italy, in this dissertation, I argue that the appropriation that there was of the Comedy on behalf of the Fascist Movement and Regime happened, albeit not exclusively, thanks to a centuries-long British interest in Italian affairs. It was in London that the Comedy truly started its astonishing meteoritic ascension to notoriety outside the more restrictive academic circles, and it was in England that Dante began, and then continued, to influence Italian thought. In other words, the cognitive reshaping, or in some cases forming, of Italian identity owed the British a great deal more than currently accepted in present historiography. In short, it was, by and large, an English Dante he who was then translated into Fascism and absorbed into their ideological apparatus. Therefore, the interaction between the various systems at play is not framed exclusively within a narrative of endorsement that indicated the Fascist Regime (and Movement) as the sole beneficiary of such association, but extended to embrace collateral agents who might have had an overt or otherwise concealed interest in Dante’s masterpiece and its relationship with Fascism. Gellner (1983), Anderson (1983), and others helped to establish the theoretical framework for this study that thus benefitted from different methodological approaches drawn from various fields, in line with a long-standing intellectual history tradition as expressed as early as 1912 by J. H. Robinson. The results of this investigation have delivered a complex picture of dictatorship, financial interests, international powers, and secrecy that intersect along the trajectory of the Comedy, and the consequences of which should be further questioned and explored in future studies

Investigating the Solvation, Binding Mode, and Free Energy of a Minor Groove DNA Complex Using Atomistic Computer Simulations

Two helical (alpha and beta) strands form DNA. The DNA structural background provides grooves which may act as a binding site. The major groove is 22 Å wide whereas the minor groove is 12 Å wide. The minor groove of the double-stranded DNA can interact with many different classes of ligands in a sequence specific fashion. Netropsin is an oligopeptide with antibiotic and antiviral activity that binds tightly to an adenine-rich sequence of DNA. Atomic resolution x-ray crystal structures of the DNA-netropsin complex have been solved and many experiments have been carried out over the year to understand the thermodynamics and kinetics of netropsin binding. However, the experimental biophysics community disagrees on the exact nature of the different binding modes in solution and the role water molecules play in the recognition. Here, we carried out molecular dynamics simulations on the free DNA, free netropsin, and DNA-netropsin complex in explicit water, in order to gain insights on the subtleties of the DNA-netropsin complex at atomistic detail. We have studied the different conformational states of netropsin in the minor groove of the DNA. We have also analyzed the population and dynamics of the water molecules upon complex formation and calculated the free energy of binding. Results show an affinity for holding water molecules in the binding site rather than on the surface of DNA or complex. These results provide atomistic insights into DNA minor groove recognition that will be beneficial in the development of novel drug candidates

AMPA experimental communications systems

The program was conducted to demonstrate the satellite communication advantages of Adaptive Phased Array Technology. A laboratory based experiment was designed and implemented to demonstrate a low earth orbit satellite communications system. Using a 32 element, L-band phased array augmented with 4 sets of weights (2 for reception and 2 for transmission) a high speed digital processing system and operating against multiple user terminals and interferers, the AMPA system demonstrated: communications with austere user terminals, frequency reuse, communications in the face of interference, and geolocation. The program and experiment objectives are described, the system hardware and software/firmware are defined, and the test performed and the resultant test data are presented

Distinct patterns of cortical thickness predict rTMS treatment response

INTRODUCTION Major depressive disorder (MDD) affects approximately 15% of adolescents, and is linked with impairment in social, family and academic functioning. Current treatment options are limited. Repetitive transcranial magnetic stimulation (rTMS) represents a novel avenue for treatment of depression; utilizing magnetic pulses to stimulate specific brain regions thought to underlie MDD. However, beneficial response to rTMS is not universal. Identifying baseline biomarkers that correlate to treatment response will allow professionals to apply a more personalized and effective treatment program and will be more cost-effective for the health care system. Therefore, the aim of this project is to investigate cortical thickness as a baseline structural predictor of rTMS treatment response in MDD children and youth. METHODS Participants (n=15, age range 16 - 21; mean 18.43 ± 1.41) were recruited using advertisement and referral. Inclusion criterion included resistance to antidepressants for at least 8 weeks. Exclusion criteria were additional neurological or psychiatric diagnoses, previous seizures or epilepsy, hypertension, left handedness, pregnancy or braces. The Hamilton Rating Scale for Depression (Ham-D) was used to measure depression severity. A cut-off of a 30% post-treatment reduction in HAM-D was used to distinguish between responders and non-responders. 10 responders and 5 non-responders were not significantly different into terms of sex, age, IQ or baseline HAM-D. The rTMS treatment was applied for 5 days a week for 3 weeks. Participants underwent a baseline MRI scan. Cortical thickness was analyzed using FreeSurfer software. RESULTS We observed increased thickness in the left Broca’s Area, left frontal pole, and right lateral orbitofrontal gyrus in non-responders versus responders. Conversely, the left caudal anterior cingulate cortex was thicker in responders versus non-responders (Table 1). DISCUSSION AND CONCLUSIONS Our current findings match our previous studies showing a thicker anterior cingulate and frontal in MDD versus controls [1,2]. Other studies have indicated structural differences in lateral orbitofrontal gyrus in MDD [3]. This preliminary data suggests that these regions may act as baseline structural biomarkers for rTMS treatment responders, and may influence future MDD treatment protocols. FUTURE DIRECTIONS To further validate these results, a study should be conducted with a larger sample size, especially for rTMS non-responders. Identifying baseline biomarkers for the use of rTMS will enable professional to maximize the potential of this novel therapy in treating MDD and other mental health disorders in children and youth

A nudity-based intervention to improve body image, self-esteem, and life satisfaction

An individual’s body image has profound implications for their self-esteem and overall life-satisfaction, and is a significant predictor of the onset of eating disorders. Recent research suggested that nude activities improved body image, self-esteem, and life-satisfaction among participants who were predisposed to take part in such activities. This current research investigated whether a nudity-based intervention can have similar positive effects among non-nudist participants with low levels of positive body-image, and whether those effects endure. Fifteen participants completed measures of body-image, self-esteem, and life-satisfaction before, immediately after, and one month after participating in a 4-day, nudity-based intervention. Participants reported substantial improvements in all three outcomes that remained one month after the intervention’s completion. Results suggest that nudity-based interventions can meaningfully and enduringly improve body image and related outcomes, even among non-nudists

IIRSA and Energy Connectivity in the Amazon: Can infrastructure solve energy poverty in the region?

About 85 percent (EIA 2010) of Brazil’s electricity comes from hydropower plants. Recent efforts are expanding the use of hydropower throughout the country and across its Amazonian region. Major programs, both private and in the government, are financing expansion of dams, as well as other transportation infrastructure. The largest infrastructure group in South America, the Initiative For the Integration of Regional Infrastructure in South America (IIRSA), defines its purpose as an aim to strengthen transport, energy, and communications infrastructure under a regional prospective (IIRSA 2011). Thus presumptuously expanded and new infrastructure is essential to providing a better quality of life. This may be particularly in beneficial South America, where more infrastructure has the ability to provide greater connectivity throughout areas, and expand sources of energy to those without access. This study will analyze these endeavors to suggest whether expanded development achieves its goal in establishing better connectivity and access to energy. Paper prepared for the Environmental Studies Senior Seminar/Geography Capstone