Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point $x=0$ and a smooth behaviour in the vicinity of the point $x=1.$Comment: 25 page

Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Part 1

In this paper we proceed to study properties of Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions. In our previous papers [Nuclear Physics B 870 (2013) 243], [Nuclear Physics B 876 (2013) 322] we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms and that the higher-order UD functions were obtained in terms of a differential operator by applying it to a slightly modified first UD function. The result is valid in $d=4$ dimensions and its analog in $d=4-2\varepsilon$ dimensions exits too [Theoretical and Mathematical Physics 177 (2013) 1515]. In [Nuclear Physics B 870 (2013) 243] the chain of recurrent relations for analytically regularized UD functions was obtained implicitly by comparing the left hand side and the right hand side of the diagrammatic relations between the diagrams with different loop orders. In turn, these diagrammatic relations were obtained due to the method of loop reduction for the triangle ladder diagrams proposed in 1983 by Belokurov and Usyukina. Here we reproduce these recurrent relations by calculating explicitly via Barnes lemmas the contour integrals produced by the left hand sides of the diagrammatic relations. In such a way we explicitly calculate a family of multi-fold contour integrals of certain ratios of Euler gamma functions. We make a conjecture that similar results for the contour integrals are valid for a wider family of smooth functions which includes the MB transforms of UD functions.Comment: 7 pages, 1 figure, minor changes in the text; accepted for publication in Nuclear Physics

Aproximació crítica a l'estudi dels espais prehistòrics

Actualment hi ha una preocupació notable pels temes ecològics aplicats i/o transvasats al camp de les ciències socials. Això obeeix tant a raons internes, d'ordre científic, com estranyes al cos mateix de discussió científica, relacionades amb el moment cultural i la seva infrastructura històrica

Chilean Unsustainable Inequality Explored Through a Simple Economic Magnitude During First Decades of 21th Century

La insostenible desigualdad chilena parece estar relacionada con el estallido social observado en este país desde octubre de 2019 y el reciente cambio de escenario político. Más aún, este fenómeno social derivó recientemente en un acuerdo sociopolítico para cambiar la Constitución chilena, dictada por el general Pinochet en 1978. ¿Cómo explicar un hecho tan tectónico cuando la economía chilena parecía ser un ejemplo de éxito en América Latina, es decir, una especie de "oasis regional" como pocas semanas antes del estallido de octubre el Presidente Piñera citó con orgullo durante una conferencia de prensa internacional? En este trabajo, proponemos una nueva magnitud que nos permite cuantificar, y luego comparar, la dinámica económica chilena en su contexto regional y con algunas de las economías del "primer mundo económico", como las utilizadas por Piketty. A partir de este autor, tomamos variables clave y las combinamos en un modelo simple, que produjo profundas percepciones sobre la dinámica económica insostenible en Chile, pero también en otras democracias occidentales.Chilean unsustainable inequality seems related to the social outburst observed in this country since October 2019 and the recent change in political scenario. Moreover, this social phenomenon recently derived into a socio-political agreement to change the Chilean Constitution, dictated by General Pinochet in 1978. How to explain such a tectonic fact when the Chilean economy seemed to be a successful example in Latin America, namely a kind of “regional oasis” such as few weeks before the October outburst President Piñera proudly quoted during an international press conference? In this paper, we propose a new rationale allowing us to quantify, and, then to compare the Chilean economic dynamics in its regional context and with some of the “first economic world” economies, such as those used by Piketty. From this author, we took key variables and combined them into a simple model, which produced deep insights into unsustainable economic dynamics in Chile but also in other western democracies

Autoconciencia y reconocimiento del otro en la <i>Fenomenología del Espíritu</i> de Hegel

En este trabajo procuramos dar cuenta del problema de la autoconciencia y el reconocimiento del otro en la Fenomenología del Espíritu de Hegel. Con esta finalidad en mente, presentaremos en primer lugar el contexto histórico en el que se origina el idealismo alemán, del que Hegel es uno de los representantes más importantes. En un momento posterior haremos una presentación somera de la dialéctica hegeliana, de modo tal de poder dar cuenta de la estructura argumentativa de la dialéctica del amo y el esclavo. En un momento final, apuntaremos a desarrollar el problema de la autoconciencia y el reconocimiento del otro en la dialéctica del amo y el esclavo, mostrando el devenir y la superación de esta figura de la conciencia.Facultad de Trabajo Socia

Physical fitness, screen time and sleep habits according to obesity levels in schoolchildren: findings from the health survey of the extreme south of Chile

Obesity is a worry because it is associated with a greater burden of disease, and it has been shown to be related to the health habits and physical condition of children and adolescents. Objective: To associate physical fitness, screen time, and sleep habits with the different categories of obesity in schoolchildren from the extreme south of Chile. Methods: 583 schoolchildren were included in this cross-sectional analysis. The screen time and sleep habits were measured with the Sleep Self-Report questionnaire, while the physical fitness was assessed with the Alpha Fitness test battery. The Body Mass Index/age (BMI/age) and the Waist-to-Height ratio (WtHr) were used to define adiposity using the following categories: healthy weight/low-risk waist-to-height ratio (H/LR), healthy weight/high-risk waist-to-height ratio (H/HR), overweight/low-risk waist to height ratio (O/LR), and overweight/high-risk waist to height ratio (O/HR). Results: A considerable number of schoolchildren (23.2%) presented sleep problems, while the mean screen time was 9.3 (95% CI: 8.4; 10.1) hours/day. Schoolchildren classified as H/HR showed better physical fitness than the O/HR group but worse physical fitness than the H/LR group. Conclusions: Significant differences were evidenced in the physical fitness between the adiposity categories, which could open future lines of research concerning the characterization of the healthy weight-obese adiposity categories in children

Association between walking pace and diabetes: findings from the Chilean National Health Survey 2016-2017

Background: Walking pace is a well-known indicator of physical capability, but it is also a strong predictor of type 2 diabetes (T2D). However, there is a lack of evidence on the association between walking pace and T2D, specifically, within developing countries such as Chile. Aim: To investigate the association between self-reported walking pace and T2D in the Chilean adult population. Methods: 5520 Chilean participants (aged 15 to 90 years, 52.1% women) from the Chilean National Health Survey 2016–2017 were included in this cross-sectional study. Both walking pace (slow, average, and brisk) and diabetes data were collected through self-reported methods. Fasting blood glucose (reported in mg/dl) and glycosylated haemoglobin A (HbA1c) scores were determined via blood exams. Results: In the unadjusted model, and compared to people who reported a slow walking pace, those with average and brisk walking pace had lower blood glucose levels (β = −7.74 mg/dL (95% CI: −11.08 to −4.40) and β = −11.05 mg/dL (95% CI: −14.36 to −7.75), respectively) and lower HbA1c (β = −0.34% (95% CI: −0.57 to −0.11) and β= −0.72% (95% CI: −0.94 to −0.49)), respectively. After adjusting for sociodemographic, Body Mass Index and lifestyle factors, the association between glycaemia and HbA1c remained only for brisk walkers. Both the average and brisk walker categories had lower odds of T2D (OR: 0.59 (95% CI: 0.41 to 0.84) and (OR 0.48 (95% CI: 0.30 to 0.79), respectively). Conclusion: Brisk walkers were associated with lower blood glucose and HbA1c levels. Moreover, average to brisk walking pace also showed a lower risk for T2D