Interpretation for Probability Wave and Quantum Measured Problem

By using Hamilton-Jacobi-Bellman equation with complex time, we investigate quantum theory in timelike curve. State vectors of a physical system in the two-dimensional timelike curve not only obey Schrödinger equation in the observed timespace but also involve random motion in the traversal timespace. The random motion with hidden variables is successfully to explain why the wave function is a probability wave. Quantum measurement are discussed in present work. The results are in agreement with the conventional interpretation of quantum theory.     

The NaDyBr4 complex; its molecular structure and thermodynamic properties

The molecular geometry, vibrational frequencies, relative stabilities, and some thermodynamic properties of different isomers of the NaDyBr₄ complex were determined by computation. We investigated, to our knowledge for the first time for such a complex, the possible effect of the partially filled 4f orbitals on the molecular properties of an MLnX₄ complex by using a “small core” effective core potential of the Stuttgart group. The tridentate complex, with three Na–Br bridges, was found to be the ground-state structure with the bidentate one only about 4–6 kJ/mol higher in energy. The relative abundance of these isomers changes with temperature and at the high-temperature conditions of a metal halide lamp the bidentate isomer is the more abundant isomer.     

Summability of formal solutions to the n-dimensional inhomogeneous heat equation

The Cauchy problem for n-dimensional inhomogeneous complex heat equation is considered. The Borel summability of formal solutions is characterised in terms of analytic continuation with an appropriate growth condition of some function connected with the inhomogeneity and the Cauchy data.     

Multistimuli responsive grafted poly(ether tert‐amine) (gPEA): Synthesis,characterization and controlled morphology in aqueous solution

Multistimuli responsive grafted poly(ether tert‐amine) (gPEAs), which were comprised of poly(propylene oxide) (PPO) in backbone and poly(ethylene oxide) (PEO) as grafted chain, were successfully synthesized through nucleophilic addition/ring‐opening reaction of commercial poly(propylene glycol) diglycidyl ether and Jeffamine L100. These gPEAs exhibit very sharp response to temperature, pH and ionic strength with tunable cloud point (CP). The CP of gPEA aqueous solution increases with increasing the PEO content or decreasing pH value, varying from 27 to 77 °C. Compared with linear PEA101, gPEA110 of completely grafted structure in aqueous solution exhibits sharper response to temperature with ΔT around 1 °C. The results obtained from TEM and dynamic light scattering reveal that gPEAs are dispersed as uniform sized nano‐micelles in aqueous at room temperature, which can further aggregate into mesoglobules of complex structure at high temperature (>CP). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6353–6361, 2009     

A complex semigroup approach to group algebras of infinite dimensional Lie groups

A host algebra of a topological group G is a C ^*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C ^*-algebra C ^*(S,α), and we describe a setting which permits us to conclude that this C ^*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative case is left for the future. To K.H. Hofmann on the occasion of his 75th birthday     

HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS

The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.     

Determination of trace vanadium in soil by cloud point extraction and graphite furnace atomic absorption spectroscopy

This work describes a new analytical procedure for trace vanadium by graphite furnace atomic absorption spectroscopy coupled to cloud point extraction (CPE) as the separation-preconcentration method. The CPE behavior of vanadium using methylene blue as complex agent and Triton X-100 as a surfactant was investigated systematically. Under the optimized conditions, the detection limit was 0.7 ng · mL⁻¹, and the relative standard deviation was 4.3% for vanadium (c = 50.0 ng · mL⁻¹, n = 5). The recovery of vanadium was in the range of 98.9–102.8%. The method was applied to the analysis of vanadium in certified reference materials and real samples. The results obtained were in good agreement with the certified values. Correspondence: Xiashi Zhu, Key Laboratory of Environmental Material and Environmental Engineering of Jiangsu province/College of Chemistry and Chemical Engineering, Yangzhou University, Yangzhou 225002, P.R. China     

Where do we stand on econophysics?

This issue contains papers selected from the contributions presented at the 5th International Conference on “Applications of Physics in Financial Analysis” (APFA5) held in Torino from June 29th to July 1st, 2006 (http://www.polito.it/apfa5). The issue collects recent applications of models and methods of statistical physics to economic problems. This interdisciplinary field of research, known as Econophysics, has seen intensive growth over the last decade. The challenge for econophysicists will be to go beyond the traditional views of economics and physics unifying the separate lines of development followed by the two disciplines over great part of the 20th century.“The conventional view serves to protect us from the painful job of thinking”, John Kenneth Galbraith (1908-2006).     

Geometrical and physical interpretation of evolution governed by general complex algebra

In this paper we explore a geometrical and physical matter of the evolution governed by the generator of General Complex Algebra, GC₂. The generator of this algebra obeys a quadratic polynomial equation. It is shown that the geometrical image of the GC₂-number is given by a straight line fixed by two given points on Euclidean plane. In this representation the straight line possesses the norm and the argument. The motion of the straight line conserving the norm of the line is described by evolution equation governed by the generator of the GC₂-algebra. This evolution is depicted on the Euclidean plane as rotational motion of the straight line around the semicircle to which this line is tangent. Physical interpretation is found within the framework of the relativistic dynamics where the quadratic polynomial is formed by mass-shell equation. In this way we come to a new representation for the momenta of the relativistic particle.