The Scalar Curvature of a Causal Set

A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well-approximated by 4 dimensional Minkowski spacetime, the operators are Lorentz invariant but nonlocal, are parametrised by the scale of the nonlocality and approximate the continuum scalar D'Alembertian, $\Box$, when acting on fields that vary slowly on the nonlocality scale. The same operators can be applied to scalar fields on causal sets which are well-approximated by curved spacetimes in which case they approximate $\Box - {{1/2}}R$ where $R$ is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.Comment: Typo in definition of equation (3) and definition of n(x,y) corrected. Note: published version still contains typ

The continuum limit of a 4-dimensional causal set scalar d'Alembertian

The continuum limit of a 4-dimensional, discrete d'Alembertian operator for scalar fields on causal sets is studied. The continuum limit of the mean of this operator in the Poisson point process in 4-dimensional Minkowski spacetime is shown to be the usual continuum scalar d'Alembertian $\Box$. It is shown that the mean is close to the limit when there exists a frame in which the scalar field is slowly varying on a scale set by the density of the Poisson process. The continuum limit of the mean of the causal set d'Alembertian in 4-dimensional curved spacetime is shown to equal $\Box - \frac{1}{2}R$, where $R$ is the Ricci scalar, under certain conditions on the spacetime and the scalar field.Comment: 31 pages, 2 figures. Slightly revised version, accepted for publication in Classical and Quantum Gravit

An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

Effect of spin orbit scattering on the magnetic and superconducting properties of nearly ferromagnetic metals: application to granular Pt

We calculate the effect of scattering on the static, exchange enhanced, spin susceptibility and show that in particular spin orbit scattering leads to a reduction of the giant moments and spin glass freezing temperature due to dilute magnetic impurities. The harmful spin fluctuation contribution to the intra-grain pairing interaction is strongly reduced opening the way for BCS superconductivity. We are thus able to explain the superconducting and magnetic properties recently observed in granular Pt as due to scattering effects in single small grains.Comment: 9 pages 3 figures, accepted for publication in Phys. Rev. Letter

Ultradiscretization of the solution of periodic Toda equation

A periodic box-ball system (pBBS) is obtained by ultradiscretizing the periodic discrete Toda equation (pd Toda eq.). We show the relation between a Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure

Gravitational Field of a Global Monopole in a Modified Gravity

In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=\frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.Comment: 9 pages, work presented in the 8th Alexander Friedmann International Seminar on Gravitation and Cosmology, in Rio de Janeiro, 30/05 to 03/06/201

Integrating TV/digital data spectrograph system

A 25-mm vidicon camera was previously modified to allow operation in an integration mode for low-light-level astronomical work. The camera was then mated to a low-dispersion spectrograph for obtaining spectral information in the 400 to 750 nm range. A high speed digital video image system was utilized to digitize the analog video signal, place the information directly into computer-type memory, and record data on digital magnetic tape for permanent storage and subsequent analysis

Effects of maternal subnutrition during early pregnancy on cow hematological profiles and offspring physiology and vitality in two beef breeds

This experiment evaluated the effects of subnutrition during early gestation on hematology in cows (Bos Taurus) and on hematological, metabolic, endocrine, and vitality parameters in their calves. Parda de Montaña and Pirenaica dams were inseminated and assigned to either a control (CONTROL, 100% requirements) or a nutrient‐restricted group (SUBNUT, 65%) during the first third of gestation. Dam blood samples were collected on days 20 and 253 of gestation, and calf samples were obtained during the first days of life. Pirenaica dams presented higher red series parameters than Parda de Montaña dams, both in the first and the last months of gestation. During early pregnancy, granulocyte numbers and mean corpuscular hemoglobin were lower in Pirenaica‐SUBNUT than in Pirenaica‐CONTROL cows. Calves from the SUBNUT cows did not show a physiological reduction in red series values in early life, suggesting later maturation of the hematopoietic system. Poor maternal nutrition affected calf endocrine parameters. Newborns from dystocic parturitions showed lower NEFA concentrations and weaker vitality responses. In conclusion, maternal nutrition had short‐term effects on cow hematology, Pirenaica cows showing a higher susceptibility to undernutrition; and a long‐term effect on their offspring endocrinology, SUBNUT newborns showing lower levels of IGF‐1 and higher levels of cortisol.This work was supported by the Spanish Ministry of Economy and Business and the European Union Regional Development Funds (INIA RTA 2013‐00059‐C02 and INIA RZP 2015‐001) and the Government of Aragon under the Grant Research Group Funds (A14_17R). A. Noya received a PhD grant from INIA‐Government of Aragon

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page