Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

A New Recurrence Relation and Related Determinantal form for Binomial Type Polynomial Sequences

For polynomial sequence of binomial type we propose a new recurrence formula equivalent to a determinantal form of the sequence, from which known and unknown properties are deducted. Relationships whit \({\delta}\)–functionals, \({\delta}\)–operators and generating function are pointed out. Finally, some classical examples are studied, highlighting interesting determinantal identities.     

Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.     

On a stochastic disease model with vaccination

We propose a stochastic disease model where vaccination is included and such that the immunity isn’t permanent. The existence, uniqueness and positivity of the solution and the stability of disease free equilibrium is studied. The numerical simulation is done.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Preparation of luminescent Si nanoparticles by tailoring the size,crystallinity and surface composition

The preparation of sizeable quantities of luminescent Si nanoparticles (Si-np) with controlled morphology is a challenging task. Here, we describe two strategies aiming at size reduction of the Si-np produced in a laser-assisted silane pyrolysis reactor without detrimental effects on the process yield and on the nanoparticle structural and compositional properties. The first method is based on the addition of a sensitizer gas to dilute silane and consequently reduce the nucleation centres density without decreasing the reaction temperature. The second consists in the introduction of a collector at a variable distance from the irradiated region to freeze the particle growth and decrease the inter-particle sintering probability. We report on the characterization of the produced Si-np, and we show that by combining the two methods, we are able to prepare 4 nm crystalline core size nanoparticles with a productivity of 1 g per hour. We also describe the enhancement effect of the wet-chemical oxidation processes on the luminescence emission intensity of the Si-np.     

C2C12 myoblast sensitivity to different apoptotic chemical triggers

Apoptosis is a form of cell death crucial for normal development and tissue homeostasis. Its typical features include chromatin changes, nuclear breakdown, plasma membrane blebbing and splitting of cellular content into apoptotic bodies, that progressively undergo phagocytosis.Apoptosis is considered essential for skeletal muscle development, where defective cells are deleted during differentiation. In addition, it plays a relevant role in several muscle myopathies, as well as in denervation and disuse.The aim of this study was to evaluate muscle cell sensitivity to different apoptotic triggers, acting through different mechanisms of action. Chemical agents, active against distinct intracellular targets, such as mitochondrial respiratory chain and DNA, have been chosen to better highlight cell death mechanisms. To induce apoptosis, C2C12 myoblasts have been exposed to H₂O₂, staurosporine, cisplatin and etoposide, at different doses and incubation times, and they have been analysed by flow cytometry, scanning and transmission electron microscopy.Flow cytometry analysis revealed a certain subdiploid peak after all treatments. The best apoptotic effect was observable, as confirmed at reverted microscope, at minimum doses and after the major exposure time.At ultrastructural level programmed cell death has been observed. Characteristic chromatin condensation and margination, as well as apoptotic bodies, frequently appeared, even if in the presence of secondary necrosis; surface blebs were also observed during scanning microscopic observation.In particular, exposure to H₂O₂ or staurosporine showed the largest number of myoblasts in late apoptotic stages and in secondary necrosis. Cisplatin treatments revealed few early apoptotic cells. The analysis of etoposide-induced apoptosis was in agreement with data obtained from flow cytometry, indicating a significant increase of apoptotic cell number.These results suggest that all conditions are able to induce apoptosis in C2C12 myoblasts, which occurs, considering trigger mechanisms of action, mostly following the mitochondrial pathway, if not excluding that due to DNA damage. Therefore, mitochondria permeability alteration is an important step in skeletal muscle programmed cell death. This last conclusion seems to have a significant relevance in understanding the mechanisms involved in muscle disorders, denervation and chronic muscle disuse, conditions frequently characterized by a decline in mitochondrial content and by an increase of mitochondrial apoptosis susceptibility.     

Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log law, estimated experimentally by Virk as V+(y+) approximately 11.7logy+ - 17. Here V+(y+) and y+ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input.     

Crystal structure of the complex between 7,7,8,8-tetracyanoquinodimethane and 1-oxide-2-phenyl-quinoline

A series of complexes between 1-oxide quinolines and 7,7,8,8-tetracyanoquinodimethane has been synthesized and one of them has been analyzed by x-ray diffraction methods. Crystals of the title compound are monoclinic (C₁₅H₁₁NO·C₁₂H₄N₄), space groupP2₁/n,a=44.525(4),b=7.326(2),c=6.531(2) Å,=90.23(3)°. The structure was solved by direct methods and refined by block-matrix least-squares to giveR=0.047 for 1865 reflections above 2(I). Molecular dimensions, interplanar distances, empirical method and IR spectra suggest a -^* interaction with very low charge-transfer in the complex.     

Link of groups and homogeneous Hörmander operators

We study a notion of link of Lie groups suggested by the structure of the partial differential operators of Kolmogorov type. As an application of our link procedure we construct explicit examples of stratified Lie groups, with dimension and step arbitrarily large. We also give a set of examples of hypoelliptic second-order operators which are left translation invariant and homogeneous of degree two on the previous groups.