Transreal calculus

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails.

Understanding consumer evaluations of personalised nutrition services in terms of the privacy calculus: a qualitative study

Background: Personalised nutrition (PN) may provide major health benefits to consumers. A potential barrier to the uptake of PN is consumers’ reluctance to disclose sensitive information upon which PN is based. This study adopts the privacy calculus to explore how PN service attributes contribute to consumers’ privacy risk and personalisation benefit perceptions. Methods: Sixteen focus groups (n = 124) were held in 8 EU countries and discussed 9 PN services that differed in terms of personal information, communication channel, service provider, advice justification, scope, frequency, and customer lock-in. Transcripts were content analysed. Results: The personal information that underpinned PN contributed to both privacy risk perception and personalisation benefit perception. Disclosing information face-to-face mitigated the perception of privacy risk and amplified the perception of personalisation benefit. PN provided by a qualified expert and justified by scientific evidence increased participants’ value perception. Enhancing convenience, offering regular face-to face support, and employing customer lock-in strategies were perceived as beneficial. Conclusion: This study suggests that to encourage consumer adoption, PN has to account for face-to-face communication, expert advice providers, support, a lifestyle-change focus, and customised offers. The results provide an initial insight into service attributes that influence consumer adoption of PN.

Near-infrared integral field spectroscopy of the Homunculus nebula around eta Carinae using Gemini/CIRPASS

This work presents the first integral field spectroscopy of the Homunculus nebula around eta Carinae in the near-infrared spectral region (J band). We confirmed the presence of a hole on the polar region of each lobe, as indicated by previous near-IR long-slit spectra and mid-IR images. The holes can be described as a cylinder of height (i.e. the thickness of the lobe) and diameter of 6.5 and 6.0 x 10(16) cm, respectively. We also mapped the blue-shifted component of He I lambda 10830 seen towards the NW lobe. Contrary to previous works, we suggested that this blue-shifted component is not related to the Paddle but it is indeed in the equatorial disc. We confirmed the claim of N. Smith and showed that the spatial extent of the Little Homunculus matches remarkably well the radio continuum emission at 3 cm, indicating that the Little Homunculus can be regarded as a small H II region. Therefore, we used the optically thin 1.3 mm radio flux to derive a lower limit for the number of Lyman-continuum photons of the central source in eta Car. In the context of a binary system, and assuming that the ionizing flux comes entirely from the hot companion star, the lower limit for its spectral type and luminosity class ranges from O5.5 III to O7 I. Moreover, we showed that the radio peak at 1.7 arcsec NW from the central star is in the same line-of-sight of the `Sr-filament` but they are obviously spatially separated, while the blue-shifted component of He I lambda 10830 may be related to the radio peak and can be explained by the ultraviolet radiation from the companion star.

Evaluating microfossil content of dental calculus from Brazilian sambaquis

To date, limited numbers of dental calculus samples have been analyzed by researchers in diverse parts of the world. The combined analyses of these have provided some general guidelines for the analysis of calculus that is non-destructive to archaeological teeth. There is still a need for a quantitative study of large numbers of calculus samples to establish protocols, assess the level of contamination, evaluate the quantity of microfossils in dental calculus, and to compare analysis results with the literature concerning the biology of calculus formation. We analyzed dental calculus from 53 teeth from four Brazilian sambaquis. Sambaquis are the shell-mounds that were established prehistorically along the Brazilian coast. The analysis of sambaqui dental calculi shows that there are relatively high concentrations of microfossils (phytoliths and starch), mineral fragments, and charcoal in dental calculus. Mineral fragments and charcoal are possibly contaminants. The largest dental calculi have the lowest concentrations of microfossils. Biologically, this is explained by individual variation in calculus formation between people. Importantly, starch is ubiquitous in dental calculus. The starch and phytoliths show that certainly Dioscorea (yam) and Araucaria angustifolia (Parana pine) were eaten by sambaqui people. Araceae (arum family), Ipomoea batatas (sweet potato) and Zea mays (maize) were probably in their diet. (C) 2009 Elsevier Ltd. All rights reserved.

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Measurement of thermal neutron cross section and resonance integral for the (165)Ho(n, gamma)(166g)Ho reaction

The ground state thermal neutron cross section and the resonance integral for the (165)Ho(n, gamma)(166)Ho reaction in thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been measured experimentally by activation technique. The reaction product, (166)Ho in the ground state, is gaining considerable importance as a therapeutic radionuclide and precisely measured data of the reaction are of significance from the fundamental point of view as well as for application. In this work, the spectrographically pure holmium oxide (Ho(2)O(3)) powder samples were irradiated with and without cadmium covers at the IEA-RI reactor (IPEN, Sao Paulo), Brazil. The deviation of the neutron spectrum shape from 1/E law was measured by co-irradiating Co, Zn, Zr and Au activation detectors with thermal and epithermal neutrons followed by regression and iterative procedures. The magnitudes of the discrepancies that can occur in measurements made with the ideal 1/E law considerations in the epithermal range were studied. The measured thermal neutron cross section at the Maxwellian averaged thermal energy of 0.0253 eV is 59.0 +/- 2.1 b and for the resonance integral 657 +/- 36b. The results are measured with good precision and indicated a consistency trend to resolve the discrepant status of the literature data. The results are compared with the values in main libraries such as ENDF/B-VII, JEF-2.2 and JENDL-3.2, and with other measurements in the literature.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.