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In this paper, we obtain some properties of the symbol algebras, starting from their connections with the quaternion and cyclic algebras over a field K_p, where K is an algebraic number field, p is a prime in K and K_p is the completion of K with respect to p- adic valuation, in the case when K = Q(eps), eps^3 = 1, " eps different of 1.
Read moreIn this paper, we obtain some properties of the symbol algebras, starting from their connections with the quaternion and cyclic algebras over a field K_p;where K is an algebraic number field, p is a prime in K and K_p is the completion of K with respect to p- adic valuation, in the case when K = Q(eps), eps^3 = 1, " eps different of 1.
Read moreWe give a characterization of the prime natural numbers p of the form x^q + ry^q, where q and r are distinct odd primes. Keywords: Diophantine equations; Kummer fields; cyclotomic fields; Hilbert class field. Mathematics Subject Classification 2000: 11D41, 11S15
Read moreA method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic
Read moreThe Maxwell–Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the
Read moreA method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of instability of harmonic boundary driving inside a band gap) in multicomponent nonintegrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefringent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for this model showing the broad applicability
Read moreAuthenticity has probably always been a major concern of many consumers and it is still gaining more and more importance. In our study we used two analytical methods to characterize antioxidant activity and to evaluate the authenticity of juices; isotope ratio mass spectrometer(IRMS) and Electron Paramagnetic resonance (EPR). Isotope ratio mass spectrometry is a promising tool for origin assignation of food, thus 13C, 18O and 2H measurements are
Read moreDuring polymerization of dimethacrylate monomers employed in dental materials, the gel effect leads to entrapment of radicals and unreacted monomers in the crosslinked network, affecting physico-mechanical properties and the biocompatibility. Reported here is a study of the effect of the resin composition, irradiation time and storage time of some new light-cured dental composites upon the free propagating radical concentration, using Electron Spin
Read moreAntioxidant status of foods, plant, or fruit products is generally characterized by means of spectroscopic methods. Methods like HPLC, UV-VIS, or MS spectroscopy are used to understand the chemical and physical properties of different samples, and also EPR spectroscopy seems to be a valuable tool to characterize antioxidant activity of juice beverages. In this technique, certain antioxidants present in fruit juices interact with free radicals interrupting
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