Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

Curvature in causal BD-type inflationary cosmology

We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe are obtained.     

Synthesis and Study of the Thermal and Chiro-Optical Properties of Polyacetylenes with Bulky Side Groups: Poly(1-ethynyl-4-biphenyl), Poly(1-ethynyl-4- phenoxybenzene) and Poly(1-ethynyl-4-pentylbenzene)

The monosubstituted acetylenes 1-ethynyl-4-biphenyl, 1-ethynyl-4-phenoxybenzene and 1-ethynyl-4-pentylbenzene were polymerized to the corresponding polyacetylenes with bulky side substituents: PEBIP, PEPHENO and PEPB, respectively, using a Rh(I) complex as polymerization catalyst. The FT-IR and UV-VIS spectra of PEBIP, PEPHENO and PEPB were studied using the corresponding spectra of polyphenylacetylene (PPA), polytolylacetylene (PETOL) and poly(1-ethynyl-naphthalene) PEN as reference. Based on the spectral analysis, high cis-trasoid structures were assigned to PEBIP, PEPHENO and PEPB. The specific optical rotation of PEBIP, PEPHENO and PEPB was measured in the chiral solvent α (-)pinene and, only for PEPB, also in α (+)pinene. It was found that even at low concentration PEBIP, PEPHENO and PEPB cause changes in the specific optical rotation of the chiral medium where they have been dissolved. This phenomenon has not been observed when toluene or atactic polystyrene are dissolved in the same chiral solvent in similar concentration. This suggests that the polyacetylenes with bulky side groups are able to rearrange in a helical configuration (prevalently right-handed or vice-versa, depending on the type of chiral medium used) once hosted in a chiral medium giving a contribution to the chirality of the solvent where they have been dissolved. The thermal stability of PEBIP, PEPHENO and PEPB was studied under N₂ flow by thermal analysis (TGA, DTG and DTA) in comparison to reference monosubstituted polyacetylenes PPA, PETOL and PEN. The results show that the thermal stability of monosubstituted polyacetylenes is greatly improved by the presence of bulky substitutents as theoretically expected, and similarly, also the char-forming tendency increases with the bulkiness of the side groups.     

Synthesis of HCN Polymer from Thermal Decomposition of Formamide

Prolonged heating of formamide (HCONH₂) at 185°C or 220°C produces a black insoluble product. The FT-IR spectroscopy and the X-ray photoelectron spectroscopy (XPS) suggest that the product has the chemical structure of a polymer of hydrocyanic acid: (HCN)_x. The pyrolysis of (HCN)_x prepared from formamide produces a large amount of gaseous HCN in a wide range of temperatures together with ammonia (NH₃) and isocyanic acid (H─N─C═O).

During the thermal decomposition of formamide to produce (HCN)_x, the volatile products evolved were monitored with gas phase infrared spectroscopy. At 185°C, the gaseous product released were CO₂, CO and NH₃ while at 220°C, also HCN was detected. In both cases, a white sublimate was collected in the upper part of the reaction vessel. It consists of ammonium carbamate and its hydrolysis products ammonium carbonate and hydrogen carbonate. It is therefore possible to synthesize the polymer of hydrocyanic acid (HCN)_x starting from formamide avoiding to handle the dangerous hydrocyanic acid.     

Customising excitation properties of polycyclic aromatic hydrocarbons by rational positional heteroatom doping: the peri-xanthenoxanthene (PXX) case

In this paper we tackle the challenge of gaining control of the photophysical properties of PAHs through a site-specific N-doping within the structural aromatic framework. By developing a simple predictive tool that identifies C(sp²)-positions that if substituted with a heteroatom would tailor the changes in the absorption and emission spectral envelopes, we predict optimal substitutional patterns for the model peri-xanthenoxanthene (PXX) PAH. Specifically, TDDFT calculations of the electron density difference between the S₁ excited state and S₀ ground state of PXX allowed us to identify the subtleties in the role of sites i.e., electron donating or withdrawing character on excitation. The replacement of two C(sp²)-atoms with two N-atoms, in either electron donating or withdrawing positions, shifts the electronic transitions either to low or high energy, respectively. This consequently shifts the PXX absorption spectral envelop bathochromically or hypsochromically, as demonstrated by steady-state absorption spectroscopic measurements. Within the series of synthesised N-doped PXX, we tune the optical band gap within an interval of ∼0.4 eV, in full agreement with the theoretical predictions. Relatedly, measurements show the more blueshifted the absorption/emission energies, the greater the fluorescence quantum yield value (from ∼45% to ∼75%). On the other hand, electrochemical investigations suggested that the N-pattern has a limited influence on the redox properties. Lastly, depending on the N-pattern, different supramolecular organisations could be obtained at the solid-state, with the 1,7-pattern PXX molecule forming multi-layered, graphene-like, supramolecular sheets through a combination of weak H-bonding and π–π stacking interactions. Supramolecular striped patterned sheets could also be formed with the 3,9- and 4,10-congeners when co-crystallized with a halogen-bond donor molecule.

In this paper we tackle the challenge of gaining control of the photophysical properties of PAHs through a site-specific N-doping within the structural aromatic framework.     

Improved Detection Limit and Stability of Amperometric Carbon Nanotube-Based Immunosensors by Crosslinking Antibodies with Polylysine

Amperometric immunosensor configurations featuring covalently bound anti-biotin antibodies (Ab) embedded into a polylysine (PLL)-single walled carbon nanotube (SWCNT) composite layer were evaluated. Assemblies were made by first oxidizing pyrolytic graphite (PG) electrodes to form surface carboxylic acid groups, to which PLL, SWCNTs and anti-biotin were covalently linked. Incorporating SWCNT into PLL-antibody assemblies improved the amperometric detection limit for biotin (Ag) labeled with horseradish peroxidase to 10 fmol mL(-1). Anti-biotin embedded into the PLL matrix had improved thermal stability and retained its binding ability for biotin after exposure to temperatures of 42 degrees C for up to 3 hours, while the noncrosslinked antibody was inactivated at this temperature in several minutes.     

Radiolysis and ozonolysis of a landfill leachate

A landfill leachate sample was radiolyzed with ??-rays at 12.5, 25, 50, 100, 200 and 400?kGy. The radiolyzed solutions were studied by UV?CVIS?CNIR spectroscopy to measure the color change, by chemical oxygen demand (COD) analysis to check the degree of mineralization of the soluble organic matter present in the leachate and by FT?CIR spectroscopy of the humic substance of the leachate. The results have shown that the humic substance present in the landfill leachate is extremely refractory to radiolysis: even at 400?kGy it was detected and recovered only with minor changes. It is shown that the radiolysis followed by ozonolysis is able to cause important improvements of the leachate color and important reduction on the COD. However, the results in terms of bleaching and COD abatement after radiolysis and ozonolysis of the leachate can be achieved directly by a simple exhaustive ozonolysis of the leachate. The structural changes occurring in the humic substances and in the humic acids present in the leachate after radiolysis and ozonolysis were analyzed by FT?CIR spectroscopy.     

A remark on uniqueness for some ODE

Abstract We present a uniqueness result for the Cauchy problem associated to a particular type of ordinary differential equation (ODE), under the only assumption of continuity of the right hand side at the initial point. Keywords: Polar coordinates, Tangent vector, Inner product Mathematics Subject Classification (2000): 34A12     

LETTER: BTZ Black Hole from (3+1) Gravity

We propose an approach for constructing spatial slices of (3+1) spacetimes with cosmological constant but without a matter content, which yields (2+1) vacuum with solutions. The reduction mechanism from (3+1) to (2+1) gravity is supported on a criterion in which the Weyl tensor components are required to vanish together with a dimensional reduction via an appropriate foliation. By using an adequate reduction mechanism from the Plebaski–Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be obtained.