Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

A new principle for tight junction modulation based on occludin peptides

The aim of this study was to investigate whether peptides from the extracellular loops of the tight junction protein occludin could be used as a new principle for tight junction modulation. Peptides of 4 to 47 amino acids in length and covering the two extracellular loops of the tight junction protein occludin were synthesized, and their effect on the tight junction permeability in Caco-2 cells was investigated using [C-14] mannitol as a paracellular marker. Lipopeptide derivatives of one of the active occludin peptides (OPs), synthesized by adding a lipoamino acid containing 14 carbon atoms (C-14-) to the N terminus of the peptide, were also investigated. Peptides corresponding to the N terminus of the first extracellular loop of occludin increased the permeability of the tight junctions without causing short-term toxicity. However, the peptides had an effect only when added to the basolateral side of the cells, which could be partly explained by degradation by apical peptidases and aggregate formation. By contrast, the lipopeptide C-14-OP90-103, which protects the peptide from degradation and aggregation, displayed a rapid apical effect. The L- and D-diastereomers of C-14-OP90-103 had distinctly different effects. The D-isomer, which releases intact OP90-103 from the lipoamino acid, displayed a rapid and transient increase in tight junction permeability. The L- isomer, which releases OP90-103 more rapidly, gave a more sustained increase in tight junction permeability. In conclusion, C-14-OP90-103 represents a prototype of a new class of tight junction modulators that act on the extracellular domains of tight junction proteins.

First-principle density-functional calculation of the Raman spectra of BEDT-TTF

We present a first-principles density-functional calculation for the Raman spectra of a neutral BEDT-TTF molecule. Our results are in excellent agreement with experimental results. We show that a planar Structure is not a stable state of a neutral BEDT-TTF molecule. We consider three possible conformations and discuss their relation to disorder in these systems.

Testing the energetic equivalence rule with helminth endoparasites of vertebrates

As a general test of the energetic equivalence rule, we examined macroecological relationships among abundance, density and host body mass in a comparative analysis of the assemblages of trophically transmitted endoparasitic helminths of 131 species of vertebrate hosts. Both the numbers and total volume of parasites per gram of host decreased allometrically with host body mass, with slopes roughly consistent with those expected from the allometric relationship between host basal metabolic rate and body mass. From an evolutionary perspective, large body size may therefore allow hosts to escape from the deleterious effects of parasitism.

Equivalence between two-mode spin squeezed states and pure entangled states with equal spin

We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and provide a counterexample to the generalization of this result to two subsystems of unequal spin.

Comments on edge-to-edge matching and the equivalence of the invariant line, Delta g and Moire fringe approaches to the crystallographic features of precipitates

Three apparently distinct and different approaches have been proposed to account for the crystallographic features of diffusion-controlled precipitation. These three models are based on (a) an invariant line in the habit plane, (b) the parallelism of a pair of Deltags that are perpendicular to the habit plane and (c) the parallelism of a pair of Moire fringes that are in turn parallel to the habit plane. The purpose of the present paper is to show that these approaches are in fact absolutely equivalent and that when certain conditions are satisfied they are essentially the same as the recent edge-to-edge matching model put forward by the authors. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

On the equivalence of weighted Country-Product-Dummy (CPD) Method and the Rao-System for multilateral price comparisons

The country-product-dummy (CPD) method, originally proposed in Summers (1973), has recently been revisited in its weighted formulation to handle a variety of data related situations (Rao and Timmer, 2000, 2003; Heravi et al., 2001; Rao, 2001; Aten and Menezes, 2002; Heston and Aten, 2002; Deaton et al., 2004). The CPD method is also increasingly being used in the context of hedonic modelling instead of its original purpose of filling holes in Summers (1973). However, the CPD method is seen, among practitioners, as a black box due to its regression formulation. The main objective of the paper is to establish equivalence of purchasing power parities and international prices derived from the application of the weighted-CPD method with those arising out of the Rao-system for multilateral comparisons. A major implication of this result is that the weighted-CPD method would then be a natural method of aggregation at all levels of aggregation within the context of international comparisons.

The metaphysical equivalence of three and four dimensionalism

I argue that two competing accounts of persistence, three and four dimensionalism, are in fact metaphysically equivalent. I begin by clearly defining three and four dimensionalism, and then I show that the two theories are inter-translatable and equally simple. Through consideration of a number of different cases where intuitions about persistence are contradictory, I then go on to show that both theories describe these cases in the same manner. Further consideration of some empirical issues arising from the theory of special relativity lead me to conclude that the two theories are equally explanatory, and thus finally that they are metaphysically equivalent.

Equivalence of the Peleg, Pilosof and Singh-Kulshrestha models for water absorption in food

The similarity between the Peleg, Pilosof –Boquet–Batholomai and Singh–Kulshrestha models was investigated using the hydration behaviours of whey protein concentrate, wheat starch and whey protein isolate at 30 °C in 100% relative humidity. The three models were shown to be mathematically the same within experimental variations, and they yielded parameters that are related. The models, in their linear and original forms, were suitable (r2 > 0.98) in describing the sorption behaviours of the samples, and are sensitive to the length of the sorption segment used in the computation. The whey proteins absorbed more moisture than the wheat starch, and the isolate exhibited a higher sorptive ability than the concentrate.

Coadaptation: A unifying principle in evolutionary thermal biology

Over the last 50 yr, thermal biology has shifted from a largely physiological science to a more integrated science of behavior, physiology, ecology, and evolution. Today, the mechanisms that underlie responses to environmental temperature are being scrutinized at levels ranging from genes to organisms. From these investigations, a theory of thermal adaptation has emerged that describes the evolution of thermoregulation, thermal sensitivity, and thermal acclimation. We review and integrate current models to form a conceptual model of coadaptation. We argue that major advances will require a quantitative theory of coadaptation that predicts which strategies should evolve in specific thermal environments. Simply combining current models, however, is insufficient to understand the responses of organisms to thermal heterogeneity; a theory of coadaptation must also consider the biotic interactions that influence the net benefits of behavioral and physiological strategies. Such a theory will be challenging to develop because each organism's perception of and response to thermal heterogeneity depends on its size, mobility, and life span. Despite the challenges facing thermal biologists, we have never been more pressed to explain the diversity of strategies that organisms use to cope with thermal heterogeneity and to predict the consequences of thermal change for the diversity of communities.

First-principle study of adsorption of hydrogen on Ti-doped Mg(0001) surface

Ab initio density functional theory (DFT) calculations are performed to study the adsorption of H-2 molecules on a Ti-doped Mg(0001) surface. We find that two hydrogen molecules are able to dissociate on top of the Ti atom with very small activation barriers (0.103 and 0.145 eV for the first and second H-2 molecules, respectively). Additionally, a molecular adsorption state of H-2 above the Ti atom is observed for the first time and is attributed to the polarization of the H-2 molecule by the Ti cation. Our results parallel recent findings for H-2 adsorption on Ti-doped carbon nanotubes or fullerenes. They provide new insight into the preliminary stages of hydrogen adsorption onto Ti-incorporated Mg surfaces.