Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

On the nature of the FBS blue stellar objects and the completeness of the Bright Quasar Survey. II

In Paper I (Mickaelian et al. 1999), we compared the surface density of QSOs in the Bright Quasar Survey (BQS) and in the First Byurakan Survey (FBS) and concluded that the completeness of the BQS is of the order of 70% rather than 30-50% as suggested by several authors. A number of new observations recently became available, allowing a re-evaluation of this completeness. We now obtain a surface density of QSOs brighter than B = 16.16 in a subarea of the FBS covering ~2250 deg^2, equal to 0.012 deg^-2 (26 QSOs), implying a completeness of 53+/-10%.Comment: LaTeX 2e, 11 pages, 3 tables and 3 figures (included in text). To appear in Astrophysics. Uses a modified aaspp4.sty (my_aaspp4.sty), included in packag

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

Spanish medical students’ attitudes and views towards Mental Health and Psychiatry: a multicentric cross-sectional study.

Objective The aim of this study is to investigate the attitudes towards mental illness and psychiatry among fifth year Spanish medical students. Methods The study included 171 students from three medical schools located in different areas of Spain: Cádiz; UCA (n= 113), Madrid; San Pablo-CEU (n=22), and Barcelona; UAB (n=36). They responded, prior to their undergraduate medical course in psychiatry, to the AMI questionnaire to measure the attitudes towards mental illness and to Balon’s adapted questionnaire to investigate their view towards psychiatry. Results The students (93.4 %) had a positive attitude towards mental illness (AMI). Attitudes towards psychiatry were fairly positive with a few negative views, specifically regarding the role of psychiatrists (items 11 and 13) and the prestige of the specialty (item 16). There were some statistically significant differences between the three medical schools in the perception of psychiatry as a medical discipline. A better attitude towards mental illness was associated with a better view of the overall merits of psychiatry. Conclusions Findings suggest that Spanish medical students do not have a negative attitude towards mental illness and they have a good perception of psychiatry, although there are still some misconceptions about this specialty. These student’s attitudes could favor an appropriate management of patients suffering from mental illness

Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica

Role of OH variability in the stalling of the global atmospheric CH4 growth rate from 1999 to 2006

The growth in atmospheric methane (CH4) concentrations over the past two decades has shown large variability on a timescale of several years. Prior to 1999 the globally averaged CH4 concentration was increasing at a rate of 6.0 ppb/yr, but during a stagnation period from 1999 to 2006 this growth rate slowed to 0.6 ppb/yr. From 2007 to 2009 the growth rate again increased to 4.9 ppb/yr. These changes in growth rate are usually ascribed to variations in CH4 emissions. We have used a 3-D global chemical transport model, driven by meteorological reanalyses and variations in global mean hydroxyl (OH) concentrations derived from CH3CCl3 observations from two independent networks, to investigate these CH4 growth variations. The model shows that between 1999 and 2006, changes in the CH4 atmospheric loss contributed significantly to the suppression in global CH4 concentrations relative to the pre-1999 trend. The largest factor in this is relatively small variations in global mean OH on a timescale of a few years, with minor contributions of atmospheric transport of CH4 to its sink region and of atmospheric temperature. Although changes in emissions may be important during the stagnation period, these results imply a smaller variation is required to explain the observed CH4 trends. The contribution of OH variations to the renewed CH4 growth after 2007 cannot be determined with data currently available

Flexible parameter-sparse global temperature time-profiles that stabilise at 1.5C and 2.0C

The meeting of the United Nations Framework Convention on Climate Change (UNFCCC) in December 2015 committed parties to the Convention to hold the rise in global average temperature to well below 2.0 C above pre-industrial levels. It also committed the parties to pursue efforts to limit warming to 1.5 C. This leads to two key questions. First,what extent of emission reductions will achieve either target? Second, what is the benefit of the reduced climate impacts by keeping warming at or below 1.5 C? To provide answers, climate model simulations need to follow trajectories consistent with these global temperature limits. It is useful to operate models in an inverse mode to make model-specific estimates of greenhouse gas (GHG) concentration pathways consistent with the prescribed temperature profiles. Further inversion derives related emissions pathways for these concentrations. For this to happen, and to enable climate research centres to compare GHG concentrations and emissions estimates, common temperature trajectory scenarios are required. Here we define algebraic curves which asymptote to a stabilised limit, while also matching the magnitude and gradient of recent warming levels. The curves are deliberately parameter-sparse, needing prescription of just two parameters plus the final temperature. Yet despite this simplicity, they can allow for temperature overshoot and for generational changes where more effort to decelerate warming change is needed by future generations. The curves capture temperature profiles from the existing Representative Concentration Pathway (RCP2.6) scenario projections by a range of different earth system models (ESMs), which have warming amounts towards the lower levels of those that society is discussing

Concurrent whole brain radiotherapy and bortezomib for brain metastasis

Abstract Background Survival of patients with brain metastasis particularly from historically more radio-resistant malignancies remains dismal. A phase I study of concurrent bortezomib and whole brain radiotherapy was conducted to determine the tolerance and safety of this approach in patients with previously untreated brain metastasis. Methods A phase I dose escalation study evaluated the safety of bortezomib (0.9, 1.1, 1.3, 1.5, and 1.7 mg/m2) given on days 1, 4, 8 and 11 of whole brain radiotherapy. Patients with confirmed brain metastasis were recruited for participation. The primary endpoint was the dose-limiting toxicity, defined as any ≥ grade 3 non-hematologic toxicity or grade ≥ 4 hematologic toxicity from the start of treatment to one month post irradiation. Time-to-Event Continual Reassessment Method (TITE-CRM) was used to determine dose escalation. A companion study of brain diffusion tensor imaging MRI was conducted on a subset of patients to assess changes in the brain that might predict delayed cognitive effects. Results Twenty-four patients were recruited and completed the planned therapy. Patients with melanoma accounted for 83% of all participants. The bortezomib dose was escalated as planned to the highest dose of 1.7 mg/m2/dose. No grade 4/5 toxicities related to treatment were observed. Two patients had grade 3 dose-limiting toxicities (hyponatremia and encephalopathy). A partial or minor response was observed in 38% of patients. Bortezomib showed greater demyelination in hippocampus-associated white matter structures on MRI one month after radiotherapy compared to patients not treated with bortezomib (increase in radial diffusivity +16.8% versus 4.8%; p = 0.0023). Conclusions Concurrent bortezomib and whole brain irradiation for brain metastasis is well tolerated at one month follow-up, but MRI changes that have been shown to predict delayed cognitive function can be detected within one month of treatment.http://deepblue.lib.umich.edu/bitstream/2027.42/112849/1/13014_2013_Article_928.pd