Diophantine geometry over groups IV: An iterative procedure for validation of a sentence

This paper is the fourth in a series on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the fourth paper we present an iterative procedure that validates the correctness of anAE sentence defined over a free group. The terminating procedure presented in this paper is the basis for our analysis of elementary sets defined over a free group presented in the next papers in the series. Partially supported by an Israel Academy of Sciences Fellowship.     

Ring Size Determines the Conformation,Global Aromaticity and Photophysical Properties of Macrocyclic Oligofurans

In π-conjugated macrocycles, there is a trade-off between the global and local expression of effects such as aromaticity, with the outcome of the trade-off determined by the geometry and aromaticity of the constituent units. Compared with other aromatic rings, the aromatic character of furan is relatively small, and therefore global effects in macrocyclic furans are expected to be more pronounced. Following our introduction of macrocyclic oligofuran, we present the first synthesis of a series of π-conjugated bifuran macrocycles of various ring sizes, from trimer to hexamer, and characterize them using both computational and experimental methods. The properties of macrocyclic oligofurans change considerably with size: The smaller trimer is rigid, weakly emissive and planar as revealed by its single crystal structure, and displays global antiaromaticity. In contrast, the larger pentamer and hexamer are flexible, emissive, have non-planar structures, and exhibit local aromaticity. The results are supported by NICS and ACID calculations that indicate the global antiaromaticity of planar furan macrocycles, and by transient absorption measurements showing sharp absorption band for the trimer and only the internal conversion decay pathway.     

Replacing the carbonyl's oxygen with the difluoromethyl group

Aldehydes or ketones were reacted with 2-(trimethylsilyl)-1,3-dithiane (1) and the products reduced to the corresponding dithianes using tetrafluoroboric acid and sodium borohydride. These sulfur containing compounds were reacted with bromine trifluoride under mild conditions (1-2 min, 0 °C) with a net result of replacing the carbonyls' oxygen with the desired difluoromethyl moiety.     

Diverging rabi oscillations in subwavelength photonic lattices

We show that Rabi oscillations between Bloch modes of an optical waveguide array with subwavelength periodicity diverge, both in frequency and in field amplitude, when the optical wavelength approaches a mathematical exceptional point at which the Bloch mode becomes self-orthogonal.     

Investigation of Painlevé’s paradox and dynamic jamming during mechanism sliding motion

The paradox of Painlevé occurs when the dynamics of a sliding rigid body has solution inconsistency. When approaching a configuration of inconsistency, the contact forces and accelerations may grow unbounded in finite time, a scenario which is called dynamic jamming. Painlevé’s paradox was originally formulated for a sliding rod with uniform mass distribution, for which inconsistency occurs only under unrealistically high contact friction conditions. This paper shows that when the sliding rod is replaced by a sliding mechanism, the dynamic jamming predicted by Painlevé’s paradox can occur under relatively low friction. The paper proposes a particular mechanism, called IPOS, which consists of an inverted pendulum hinged to a plate that slides on an inclined plane (IPOS = Inverted Pendulum On a Slider). The IPOS mechanism can reach solution inconsistency under practical friction conditions, and can thus be used to experimentally validate the theoretical predictions. The conditions under which dynamic jamming occurs in the IPOS mechanism dynamics are explicitly derived, and numerical simulations illustrate the feasibility of dynamic jamming experiments.     

Photoinduced electron transfer and surface plasmon resonance in materials consisting of pyrene fluorophore and Au nanorods immobilized on MCM-48 surface

Mesoporous silica of the MCM-48 type as a support for fluorophore molecules was functionalized with 3-aminopropyl and 3-thiolopropyl groups. Then, molecules consisting of a fluorophore pyrene group and receptor fragments with donor N and O atoms were covalently attached by grafting of carboxyl groups to amino groups on a mesoporous silica surface. Additionally, Au nanorods were attached to thiol groups on the same surface. The vicinity of Au nanorods in a material with pyrene derivatives covalently grafted on the functionalized MCM-48 silica enhanced fluorescence of the composite material due to the surface plasmon resonance effect. The fluorescence emission of the prepared recognition material is quenched specifically owing to the photoinduced electron transfer effect after coordination reactions with Cu(II) ions. Moreover, the material exhibits selectivity for Cu(II) cations in aqueous solutions in presence of such metal ions as: alkali, alkaline earth, transition and heavy metals. During UV irradiation the studied material undergoes slowly photochemical degradation as a potential recognition element.     

ODMR Spectroscopy of NV<Superscript>−</Superscript> Centers in Diamond Under High MW Power

We have studied negatively charged nitrogen vacancy centers (NV\(^-\) centers) in diamond using the technique of optically detected magnetic resonance (ODMR). Due to the use of the MW power amplifier we have easily observed in the ODMR spectrum all the lines known to date, including the lines of the excited state of the NV\(^-\) centers. The g values and the hyperfine interaction constants of the ground and the excited triplet states of the NV\(^-\) center are given. Hamiltonian parameters of the ground and the excited triplet states of the NV\(^-\) center at ambient temperature have been confirmed and refined. In addition, an evidence of a slight g value asymmetry of the excited state of the NV\(^-\) center has been obtained.     

Model of the Internet mortgage market optimization

The Internet mortgages are currently a fast growing market, allowing selling mortgages cheaper and faster than in the traditional methods such as in bank departments. Given the specificity of selling mortgages in the Internet, banks try to sell more mortgages by spending more money on advertising and paying higher commission to the brokers selling their products. It is important to optimise the amounts of money in both sectors (the balance of money for advertising and for brokers) and to compare these amounts with the level of mortgages can be sold within this period (which is related to the economic indicators such as the current level of interest rate, unemployment rate etc.)It is suggested to create a knowledge base rule model defining the Internet mortgage market which will include the variables important for the problem (preliminary choice of such indicators the level of commission that is paid to the brokers, the current interest rate in the country), restrictions concentrating optimising the amounts of money that will be spend with the correlation to the current possibilities of selling mortgages (defined by the current situation of the economy). The model will be supported with the data from two banks and two brokers representing the market. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.