Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Workplace Discrimination Climate and Team Effectiveness: The Mediating Role of Collective Value Congruence, Team Cohesion, and Collective Affective Commitment

This study explored the relationship between workplace discrimination climate on team effectiveness through three serial mediators: collective value congruence, team cohesion, and collective affective commitment. As more individuals of marginalized groups diversify the workforce and as more organizations move toward team-based work (Cannon-Bowers & Bowers, 2010), it is imperative to understand how employees perceive their organization’s discriminatory climate as well as its effect on teams. An archival dataset consisting of 6,824 respondents was used, resulting in 332 work teams with five or more members in each. The data were collected as part of an employee climate survey administered in 2011 throughout the United States’ Department of Defense. The results revealed that the indirect effect through M1 (collective value congruence) and M2 (team cohesion) best accounted for the relationship between workplace discrimination climate (X) and team effectiveness (Y). Meaning, on average, teams that reported a greater climate for workplace discrimination also reported less collective value congruence with their organization (a1 = -1.07, p < .001). With less shared perceptions of value congruence, there is less team cohesion (d21 = .45, p < .001), and with less team cohesion there is less team effectiveness (b2 = .57, p < .001). In addition, because of theoretical overlap, this study makes the case for studying workplace discrimination under the broader construct of workplace aggression within the I/O psychology literature. Exploratory and confirmatory factor analysis found that workplace discrimination based on five types of marginalized groups: race/ethnicity, gender, religion, age, and disability was best explained by a three-factor model, including: career obstruction based on age and disability bias (CO), verbal aggression based on multiple types of bias (VA), and differential treatment based on racial/ethnic bias (DT). There was initial support to claim that workplace discrimination items covary not only based on type, but also based on form (i.e., nonviolent aggressive behaviors). Therefore, the form of workplace discrimination is just as important as the type when studying climate perceptions and team-level effects. Theoretical and organizational implications are also discussed.

Conservation value, biodiversity value and methods of assessment in regenerating and human disturbed tropical forest

Although the value of primary forests for biodiversity conservation is well known, the potential biodiversity and conservation value of regenerating forests remains controversial. Many factors likely contribute to this, including: 1. the variable ages of regenerating forests being studied (often dominated by relatively young regenerating forests); 2. the potential for confounding on-going human disturbance (such as logging and hunting); 3. the relatively low number of multi-taxa studies; 4. the lack of studies that directly compare different historic disturbances within the same location; 5. contrasting patterns from different survey methodologies and the paucity of knowledge on the impacts across different vertical levels of rainforest biodiversity (often due to a lack of suitable methodologies available to assess them). We also know relatively little as to how biodiversity is affected by major current impacts, such as unmarked rainforest roads, which contribute to this degradation of habitat and fragmentation. This thesis explores the potential biodiversity value of regenerating rainforests under the best of scenarios and seeks to understand more about the impact of current human disturbance to biodiversity; data comes from case studies from the Manu and Sumaco Biosphere Reserves in the Western Amazon. Specifically, I compare overall biodiversity and conservation value of a best case regenerating rainforest site with a selection of well-studied primary forest sites and with predicted species lists for the region; including a focus on species of key conservation concern. I then investigate the biodiversity of the same study site in reference to different types of historic anthropogenic disturbance. Following this I investigate the impacts to biodiversity from an unmarked rainforest road. In order to understand more about the differential effects of habitat disturbance on arboreal diversity I directly assess how patterns of butterfly biodiversity vary between three vertical strata. Although assessments within the canopy have been made for birds, invertebrates and bats, very few studies have successfully targeted arboreal mammals. I therefore investigate the potential of camera traps for inventorying arboreal mammal species in comparison with traditional methodologies. Finally, in order to investigate the possibility that different survey methodologies might identify different biodiversity patterns in habitat disturbance assessments, I investigate whether two different but commonly used survey methodologies used to assess amphibians, indicate the same or different responses of amphibian biodiversity to historic habitat change by people. The regenerating rainforest study site contained high levels of species richness; both in terms of alpha diversity found in nearby primary forest areas (87% ±3.5) and in terms of predicted primary forest diversity from the region (83% ±6.7). This included 89% (39 out of 44) of the species of high conservation concern predicted for the Manu region. Faunal species richness in once completely cleared regenerating forest was on average 13% (±9.8) lower than historically selectively logged forest. The presence of the small unmarked road significantly altered levels of faunal biodiversity for three taxa, up to and potentially beyond 350m into the forest interior. Most notably, the impact on biodiversity extended to at least 32% of the whole reserve area. The assessment of butterflies across strata showed that different vertical zones within the same rainforest responded differently in areas with different historic human disturbance. A comparison between forest regenerating after selective logging and forest regenerating after complete clearance, showed that there was a 17% greater reduction in canopy species richness in the historically cleared forest compared with the terrestrial community. Comparing arboreal camera traps with traditional ground-based techniques suggests that camera traps are an effective tool for inventorying secretive arboreal rainforest mammal communities and detect a higher number of cryptic species. Finally, the two survey methodologies used to assess amphibian communities identified contrasting biodiversity patterns in a human modified rainforest; one indicated biodiversity differences between forests with different human disturbance histories, whereas the other suggested no differences between forest disturbance types. Overall, in this thesis I find that the conservation and biodiversity value of regenerating and human disturbed tropical forest can potentially contribute to rainforest biodiversity conservation, particularly in the best of circumstances. I also highlight the importance of utilising appropriate study methodologies that to investigate these three-dimensional habitats, and contribute to the development of methodologies to do so. However, care should be taken when using different survey methodologies, which can provide contrasting biodiversity patterns in response to human disturbance.

Three essays on corporate taxation : financial reporting, value, and firm creation

Doutoramento em Gestão

Measurement of the inclusive and differential t/t cross sections at 13 TeV in the all-jets boosted regime with CMS

The t/t production cross section is measured with the CMS detector in the all-jets channel in $pp$ collisions at the centre-of-mass energy of 13 TeV. The analysis is based on the study of t/t events in the boosted topology, namely events in which decay products of the quark top have a high Lorentz boost and are thus reconstructed in the detector as a single, wide jet. The data sample used in this analysis corresponds to an integrated luminosity of 2.53 fb-1. The inclusive cross section is found to be sigma(t/t) = 727 +- 46 (stat.) +115-112 (sys.) +- 20~(lumi.) pb, a value which is consistent with the theoretical predictions. The differential, detector-level cross section is measured as a function of the transverse momentum of the leading jet and compared to the QCD theoretical predictions. Finally, the differential, parton-level cross section is reported, measured as a function of the transverse momentum of the leading parton, extrapolated to the full phase space and compared to the QCD predictions.

Contextual effects of power differentials: Construct validation and concurrent validity of the Power Differential Scale

Power distance can produce contextual effects that surpass the cultural level of analysis, allowing predicting how the assimilation of these cultural values impacts individuals motivations to attain power positions and behaviors towards authorities. Power distance value can be conceived both at a micro and macro level of analysis. However existing measures used at a cultural level have been the object of several critics, and others applied at the individual level need further study in terms of their psychometric properties. This article presents the main psychometric properties of the Earley and Erez (1997) Power Differential Scale. This scale measures the acceptability of power and status differences both at micro and macro level. Two studies analyse the scale’s construct validity and its factorial invariance across groups of participants (Study 1); and its predictive validity at an individual level (Study 2). The results obtained support the proposed unidimensionality of the scale. Furthermore, it demonstrated predictive power by showing the role of power distance in the prediction of individual motivations to attain power and to respond to power situations using withdrawal or confrontational strategies. Future research is discussed, specifically the impact of power differential construct in individual attitudes and behavior.

The Value Of The 2005 International Society Of Urological Pathology (isup) Modified Gleason Grading System As A Predictor Of Biochemical Recurrence After Radical Prostatectomy.

To compare time and risk to biochemical recurrence (BR) after radical prostatectomy of two chronologically different groups of patients using the standard and the modified Gleason system (MGS). Cohort 1 comprised biopsies of 197 patients graded according to the standard Gleason system (SGS) in the period 1997/2004, and cohort 2, 176 biopsies graded according to the modified system in the period 2005/2011. Time to BR was analyzed with the Kaplan-Meier product-limit analysis and prediction of shorter time to recurrence using univariate and multivariate Cox proportional hazards model. Patients in cohort 2 reflected time-related changes: striking increase in clinical stage T1c, systematic use of extended biopsies, and lower percentage of total length of cancer in millimeter in all cores. The MGS used in cohort 2 showed fewer biopsies with Gleason score ≤ 6 and more biopsies of the intermediate Gleason score 7. Time to BR using the Kaplan-Meier curves showed statistical significance using the MGS in cohort 2, but not the SGS in cohort 1. Only the MGS predicted shorter time to BR on univariate analysis and on multivariate analysis was an independent predictor. The results favor that the 2005 International Society of Urological Pathology modified system is a refinement of the Gleason grading and valuable for contemporary clinical practice.

Prognostic Value Of Dna And Mrna E6/e7 Of Human Papillomavirus In The Evolution Of Cervical Intraepithelial Neoplasia Grade 2.

This study aimed at evaluating whether human papillomavirus (HPV) groups and E6/E7 mRNA of HPV 16, 18, 31, 33, and 45 are prognostic of cervical intraepithelial neoplasia (CIN) 2 outcome in women with a cervical smear showing a low-grade squamous intraepithelial lesion (LSIL). This cohort study included women with biopsy-confirmed CIN 2 who were followed up for 12 months, with cervical smear and colposcopy performed every three months. Women with a negative or low-risk HPV status showed 100% CIN 2 regression. The CIN 2 regression rates at the 12-month follow-up were 69.4% for women with alpha-9 HPV versus 91.7% for other HPV species or HPV-negative status (P < 0.05). For women with HPV 16, the CIN 2 regression rate at the 12-month follow-up was 61.4% versus 89.5% for other HPV types or HPV-negative status (P < 0.05). The CIN 2 regression rate was 68.3% for women who tested positive for HPV E6/E7 mRNA versus 82.0% for the negative results, but this difference was not statistically significant. The expectant management for women with biopsy-confirmed CIN 2 and previous cytological tests showing LSIL exhibited a very high rate of spontaneous regression. HPV 16 is associated with a higher CIN 2 progression rate than other HPV infections. HPV E6/E7 mRNA is not a prognostic marker of the CIN 2 clinical outcome, although this analysis cannot be considered conclusive. Given the small sample size, this study could be considered a pilot for future larger studies on the role of predictive markers of CIN 2 evolution.

Predictive Value Of Phase I Trials For Safety In Later Trials And Final Approved Dose: Analysis Of 61 Approved Cancer Drugs.

Phase I trials use a small number of patients to define a maximum tolerated dose (MTD) and the safety of new agents. We compared data from phase I and registration trials to determine whether early trials predicted later safety and final dose. We searched the U.S. Food and Drug Administration (FDA) website for drugs approved in nonpediatric cancers (January 1990-October 2012). The recommended phase II dose (R2PD) and toxicities from phase I were compared with doses and safety in later trials. In 62 of 85 (73%) matched trials, the dose from the later trial was within 20% of the RP2D. In a multivariable analysis, phase I trials of targeted agents were less predictive of the final approved dose (OR, 0.2 for adopting ± 20% of the RP2D for targeted vs. other classes; P = 0.025). Of the 530 clinically relevant toxicities in later trials, 70% (n = 374) were described in phase I. A significant relationship (P = 0.0032) between increasing the number of patients in phase I (up to 60) and the ability to describe future clinically relevant toxicities was observed. Among 28,505 patients in later trials, the death rate that was related to drug was 1.41%. In conclusion, dosing based on phase I trials was associated with a low toxicity-related death rate in later trials. The ability to predict relevant toxicities correlates with the number of patients on the initial phase I trial. The final dose approved was within 20% of the RP2D in 73% of assessed trials.