Narrow Results

In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in R³ are Kossowski metrics, and the pull-back metrics of surfaces consisting only of cross cap singularities are Whitney metrics. Since the singular sets of Kossowski metrics are the union of regular curves on the domains of definitions, and Whitney metrics admit only isolated singularities, these two classes of metrics are disjoint. In this paper, we give several characterizations of intrinsic invariants of cuspidal edges and cross caps in these classes of metrics. Moreover, we prove Gauss–Bonnet type formulas for Kossowski metrics and for Whitney metrics on compact 2-manifolds.

A theoretical comparison has been made for some calcium isotopes (${}_{20}$Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some ${}_{20}$Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ($Q_{0\mathrm{\text{Th}}})$ and theoretical deformation parameters (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0\mathrm{\text{Th}}}$ and the (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0\mathrm{\text{Th}}}$ and theoretical deformation parameter (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$, using the fpbm, the fpd6 and the kb3 interactions were the best.

This study examines the effect of network externalities and flow on continual usage of e-banking services. A sample of 400 e-banking users was conveniently engaged using a structured questionnaire. The method of analysis used included Spearman’s correlation analysis, confirmatory factor analysis and structural equation modelling analysis. The findings indicate that referent network size does not significantly influence continuance intention of e-banking users. However, flow positively influences continuance intention of e-banking users. Stakeholders in the financial institutions will understand the driving factors behind continual usage of e-banking services. Some researchers have explored continual usage of e-banking but such studies are rare in the African context. This study will contribute to extant literature by adding a new dimension, intrinsic and extrinsic factors, of e-banking continual usage.

This paper concerns an outdoor and indoor autonomous navigation algorithm using stereo vision camera as the environment sensing device. The algorithm integrates binocular stereo vision system along with proposed probabilistic navigation approach to form a robust robotic system for navigation in unstructured environment. We use probabilistic clearance approach to avoid obstacles along with the introduction of speed control function for sharper turning and more time for the navigator to detect additional nearby obstacles. We show stereo vision as a remarkable alternative to active sensing devices such as sonar and laser range finder. Our approach considers 3D point data and thus it is able to avoid hanging obstacles with insufficient ground clearance and chair like obstacles also. We introduce the concept of low cost navigators which is very important for industrial and daily life applications.

The algorithm has been successfully tested on an autonomous robot Lakshya- an Unmanned Ground Vehicle platform at Delhi College of Engineering, India.

Our preceding paper “Implementing Maxwell’s aether.……” (Paper I) concluded:- (A) Maxwell’s aether, ignored in Relativity, is a massless, quasi-superfluid continuum of extremely high negative charge density; (B) Fundamental particles are not infinitesimal singularities within the aether but develop their mass by being ‘made out of it’ (hence the name Continuum Theory) as finite-sized vortical constructs of its motion. So reproduction (‘auto-creation’) of more of them requires only the addition of suitable dynamical energy, with Ampere’s law providing charge-coupling in shear to get rotations. (C) In the resulting gravitational process, generating the Newtonian force simultaneously also generates a radial electric field, the Gravity-Electric (G-E) field, whose action on astronomical plasmas could explain the flat tangential velocity profiles of spiral galaxies without resort to Cold Dark Matter (CDM) if outward disc flow is present. One of the objectives here is to provide that flow by axial infall and to examine its consequences. But first, if particles are ‘made out of aether’ the associated random aether-charge motion will generate radiation (the CMB) and impose four distance-cumulative, wavelength-independent transmission effects upon electromagnetic waves. One of these – a redshift – we see here as the cosmic redshift, plus intrinsic redshifts in stellar and galaxy ‘atmospheres’. Such a redshift appears to have been reliably observed with caesium clocks over long ground-level paths in 1968 but, lacking an appreciation of its mechanism, its wide significance was doubted. In fact, our extrapolation to intergalactic conditions dispenses with the BigBang. The other 3 transmission effects are:- spectral line broadening, scattering and attenuation, each of which has significant astronomical/cosmological expression. If the cosmic redshift is not a velocity, the reason for Dark Energy vanishes. In the resulting no-expansion cosmology the Universe was originally equipped with randomly moving aether, from whose motion and energy content the entire mass content of the Universe has grown over time by auto-creation, the local rate of which experiences positive feedback and acceleration as gravitational accumulations drive energy levels higher. Hence the clumpiness of galaxy distributions. The infall of cosmogonally young material from the auto-creation auras of clusters has 3 major implications. (1) It completely inverts the Big Bang perspective that lowmetallicity material, widespread in galaxy haloes, is very ancient. (2) Quasi-axial infall of such broadly neutral material (mostly H) onto a Spiral will spread out in the galactic plane, driven radially from the ionizing bulge by the G-E field, maintaining constant tangential velocity; all without CDM. This pattern means that the arms, although trailing, are actually being blown outward (unwrapping). See Paper I for detail. For such ongoing disruption of Spirals to prevail so widely means that originally each must have started life as an a.m.-conserving, tightly-wound spiral of mostly neutral, cosmogonically young material (mainly H), in which G-E field action was minimal until star formation and ionization had set in. (3) In cluster interiors, other cluster members may deflect the two infall streams as they converge onto a Spiral, introducing a dynamical rotational couple near the centre, with an axis roughly in the galactic plane, to produce a Barred Spiral. Cessation of infall then results in endwise collapse of that bar, yielding a fattened Elliptical. Those are indeed typically concentrated in the centres of clusters and show a dearth of active star formation, consistent with being deprived of young infall. We present images and diagrams in support and elaboration of (2) and (3). The CT model for quasars provides large intrinsic redshift by the CT analogue of Transverse Doppler Effect and offers light-element synthesis by the evolutionary precipitation of a runaway rotational shrinkage, with mass annihilation and emission of a GRB. Of special interest, relative to the arm’s-length nature of BigBang cosmology, is that continuous auto-creation (CAC) cosmology is in principle available near-by for direct study and the development of strong observational constraints. In the context of (1), the very low metallicity (Pop II) of globular (star) clusters abundantly present in the haloes of galaxies points to them being (infallen?) local concentrations of quite young auto-creation. In that case the ‘blue straggler’ stars more recently formed in their core regions may be our youngest examples of ongoing auto-creation. In summary, CT offers a much more directly observable Universe, with no Big Bang, CDM, or Dark Energy, and a CMB that records the true temperature of intergalactic space along the path taken by the radiation. Its closely cavity-radiation character arises from the random aether’s transmission-related opacity (Olbers’ Paradox) of the infinite CT Universe. Fundamentally, the aether’s random motion constitutes all-penetrating random electromagnetic excitation at the atomic scale that may offer the accommodation between classical physics and stochastic quantum electrodynamics so long obstructed by Relativity Theory.