Dirac-Hestenes spinor fields in Riemann-Cartan spacetime

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all the three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K\"ahler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle (CB)) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.Comment: 45 pages, special macros kapproc.sty and makro822.te

Distance Functions and Normalization Under Stream Scenarios

Data normalization is an essential task when modeling a classification system. When dealing with data streams, data normalization becomes especially challenging since we may not know in advance the properties of the features, such as their minimum/maximum values, and these properties may change over time. We compare the accuracies generated by eight well-known distance functions in data streams without normalization, normalized considering the statistics of the first batch of data received, and considering the previous batch received. We argue that experimental protocols for streams that consider the full stream as normalized are unrealistic and can lead to biased and poor results. Our results indicate that using the original data stream without applying normalization, and the Canberra distance, can be a good combination when no information about the data stream is known beforehand.Comment: Paper accepted to the 2023 International Joint Conference on Neural Network

Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators

A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.Comment: 7 pages, 1 figure include

Pernambuco Semiarid Native Rhizobial Populations Nitrogen Fixation Potential with Native \u3cem\u3eMacroptilium\u3c/em\u3e

Nitrogen (N) is one of nature´s most abundant elements, accounting for about 78% of the atmospheric gases, but mostly as the inert N2 form. As such it is not directly available to plants, and is relatively scarce in most agroecosystems. Biological nitrogen fixation (BNF) through diazotrophic bacteria represents ca. 63% of the yearly N input in terrestrial ecosystems (Taiz and Zeiger 2004). Legumes which form effective symbiosis with the diazotrophic group of bacteria commonly known as rhizobia, are a very important source of available N. Tropical forage legumes are usually able to nodulate with a diverse population of rhizobia, and may have a relevant contribution to nitrogen availability in pastures (Santos et al. 2003). This diversity may be exploited to find more symbiotically efficient bacterial strains, thereby increasing legume effects on pastures. One way to evaluate this diversity is to isolate strains from different regions, vegetation covers or cultivation systems, and environmental conditions. This practice would potentially lead to a large number of isolates, which would increase the chance of finding some more efficient than those currently available (Chagas Junior et al, 2010). Native legumes, including several species of Macroptilium are an important forage resource in the Brazilian Northeast semiarid, contributing to the quality of ruminant diet, but they are still not well known in regards to their BNF ability. This work evaluated nodulation efficiency of Macroptilium lathyroides when inoculated with Litolic Neossol from eight municipalities of Pernambuco State semiarid

Supply Chain Coordination for False Failure Returns (ed.2)

False failure returns are products that are returned by consumers to retailers with no functional cosmetic defect. The cost of a false failure return includes the processing actions of testing, refurbishing if necessary, repackaging, the loss in value during the time the product spends in reverse supply chain (a time that can exceed several months for many firms), and the loss in revenue because the product is sold at a discounted price. This cost is significant, and is incurred primarily by the manufacturer. Reducing false failure returns, however, requires effort primarily by the retailer, for example informing consumers about the exact product that best fits their needs. We address the problem of reducing false failure returns via supply chain coordination methods. Specifically, we propose a target rebate contract that pays the retailer a specific dollar amount per each unit of false failure returns below a target. This target rebate provides an incentive to the retailer to increase her effort, thus decreasing the number of false failures and (potentially) increasing net sales. We show that this contract is Pareto–improving in the majority of cases. Our results also indicate that the profit improvement to both parties, and the supply chain, is substantial