Numerical computation of real or complex elliptic integrals

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included

Elliptic integrals: Symmetry and symbolic integration

Computation of elliptic integrals, whether numerical or symbolic, has been aided by the contributions of Italian mathematicians. Tricomi had a strong interest in iterative algorithms for computing elliptic integrals and other special functions, and his writings on elliptic functions and elliptic integrals have taught these subjects to many modern readers (including the author). The theory of elliptic integrals began with Fagnano`s duplication theorem, a generalization of which is now used iteratively for numerical computation in major software libraries. One of Lauricella`s multivariate hypergeometric functions has been found to contain all elliptic integrals as special cases and has led to the introduction of symmetric canonical forms. These forms provide major economies in new integral tables and offer a significant advantage also for symbolic integration of elliptic integrals. Although partly expository the present paper includes some new proofs and proposes a new procedure for symbolic integration

R-parity-violating SUSY and CP violation in B --> phi K_s

Recent measurements of CP asymmetry in B --> phi K_S appear to be inconsistent with Standard Model expectations. We explore the effect of R-parity-violating SUSY to understand the data.Comment: Equations corrected. Conclusions unchanged. Latex, 6 pages, one fi

Quantum Measurements and the kappa--Poincare Group

The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the kappa--Poincare group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the kappa--Poincare group contains some of the physical information of the quantum gravity vacuum, then this vacuum could entail decoherence. This last result will also allow us to consider the possibility of analyzing the continuous measurement problem of quantum theory from a group--theoretical point of view, but now taking into account the kappa--Poincare symmetries.Comment: Accepted in General Relativity and Gravitation. Dedicated to Alberto Garcia on the occasion of his 60th. birthda

New-Physics Effects on Triple-Product Correlations in Lambda_b Decays

We adopt an effective-lagrangian approach to compute the new-physics contributions to T-violating triple-product correlations in charmless Lambda_b decays. We use factorization and work to leading order in the heavy-quark expansion. We find that the standard-model (SM) predictions for such correlations can be significantly modified. For example, triple products which are expected to vanish in the SM can be enormous (~50%) in the presence of new physics. By measuring triple products in a variety of Lambda_b decays, one can diagnose which new-physics operators are or are not present. Our general results can be applied to any specific model of new physics by simply calculating which operators appear in that model.Comment: 20 pages, LaTeX, no figures. Added a paragraph (+ references) discussing nonfactorizable effects. Conclusions unchange

Analytical time-like geodesics

Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r=r(\lambda), t=t(\chi), and \tau=\tau(\chi), where \lambda\ is the true anomaly and \chi\ is a parameter along the orbit. A very simple relation between \lambda\ and \chi\ is also shown. These solutions are very useful for modeling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.Comment: 15 pages, 10 figures, accepted by General Relativity and Gravitatio

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of titl

Haematological and biochemical parameters in Churra-da-Terra-Quente ewes from the northeast of Portugal

Hematological and biochemical parameters, including plasma electrolytes and thyroid hormones, were determined in 73 clinically healthy Churra-da-Terra-Quente ewes, a typical breed from the northeast of Portugal. The hemogram values were: erythrocytes 9.8±1.51012/L; haemoglobin 118.1±19.1g/L; haematocrit 40.8±5.9%; leukocytes 5.7±1.8109/L; and platelets 544.3±177.2109/L. The thrombin time was 17.3±1.7 seconds. The values of biochemical parameters were: total protein 76.4±6.1g/L; glucose 2.87±0.60mmol/L; total cholesterol 1.65±0.33mmol/L; aspartate aminotransferase 155.9±49.2U/L; alanine aminotransferase 23.2±9.6U/L; γ-glutamyl transferase 48.0±18.7U/L; total alkaline phosphatase 121.6±76.1U/L; glutamate dehydrogenase 6.4±3.7U/L; urea 7.32±2.22mmol/L; creatinine 123.0±54.1μmol/L; total calcium 2.53±0.25mmol/L; phosphorus 2.10±0.46mmol/L; magnesium 1.01±0.09mmol/L; sodium 152.04±3.65mmol/L; potassium 4.7±0.4mmol/L; ionized calcium 1.32±0.07mmol/L; total thyroxine 111.75±42.29nmol/L; total triiodothyronine 1.01±0.28nmol/L; free T4 11.93±1.78pmol/L; free T3 4.22±1.33pmol/L; and thyroid-stimulating hormone 0.18±0.19μIU/mL. Although differences among the Churra-da-Terra-Quente breed and other breeds may occur, the hematological and biochemical parameters, plasma electrolytes, and thyroid hormones, for this indigenous breed, were generally situated within the reference intervals previously reported for sheep

Narrative Exposure Therapy for Posttraumatic Stress Disorder associated with repeated interpersonal trauma in patients with Severe Mental Illness: a mixed methods design

Background: In the Netherlands, most patients with severe mental illness (SMI) receive flexible assertive community treatment (FACT) provided by multidisciplinary community mental health teams. SMI patients with comorbid posttraumatic stress disorder (PTSD) are sometimes offered evidence-based trauma-focused treatment like eye movement desensitization reprocessing or prolonged exposure. There is a large amount of evidence for the effectiveness of narrative exposure therapy (NET) within various vulnerable patient groups with repeated interpersonal trauma. Some FACT-teams provide NET for patients with comorbid PTSD, which is promising, but has not been specifically studied in SMI patients. Objectives: The primary aim is to evaluate NET in SMI patients with comorbid PTSD associated with repeated interpersonal trauma to get insight into whether (1) PTSD and dissociative symptoms changes and (2) changes occur in the present SMI symptoms, care needs, quality of life, global functioning, and care consumption. The second aim is to gain insight into patients’ experiences with NET and to identify influencing factors on treatment results. Methods: This study will have a mixed methods convergent design consisting of quantitative repeated measures and qualitative semi-structured in-depth interviews based on Grounded Theory. The study population will include adult SMI outpatients (n=25) with comorbid PTSD and receiving NET. The quantitative study parameters will be existence and severity of PTSD, dissociative, and SMI symptoms; care needs; quality of life; global functioning; and care consumption. In a longitudinal analysis, outcomes will be analyzed using mixed models to estimate the difference in means between baseline and repeated measurements. The qualitative study parameters will be experiences with NET and perceived factors for success or failure. Integration of quantitative and qualitative results will be focused on interpreting how qualitative results enhance the understanding of quantitative outcomes. Discussion: The results of this study will provide more insight into influencing factors for clinical changes in this population