Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schrödinger equation coupled with a 1D nonlinear Schrödinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.     

Spectrophotometric determination and computational evaluation of the rates of hydrolysis of 9-amino-substituted acridines

Aminoacridines have a long history in the drug and dye industries and display a wide range of biological and physical properties. Despite the historical relevance of 9-aminoacridines, there have been few studies investigating their stability. 9-Aminoacridines are known to hydrolyze at the C9-N15 bond, yielding acridones. In this study, the pH-dependent hydrolysis rates of a series of 9-substituted aminoacridines are investigated. In addition, ground-state physical properties of the compounds are determined using ab initio quantum mechanics calculations to gain insight into the forces that drive hydrolysis. An analysis of the bond orders, bond dissociation energies, and conformational energies show that the rate of hydrolysis depends on two main factors: delocalization across the C9-N15 bond and steric effects. The computational results are applied to explain the change in experimental rates of hydrolysis going from primary to secondary and to tertiary substituted 9-aminoacridines. In the case of tertiary substituted amines, the calculations indicate the C9-N15 bond is forced into a more gauche-like conformation, greatly diminishing delocalization (as shown by reductions in bond orders and bond energy), which leads to rapid hydrolysis. A model of intramolecular hydrogen bonding is also presented, which explains the increased rate of hydrolysis observed for highly substituted compounds under acidic conditions.     

Three-parameter complex Hadamard matrices of order 6

A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and two-parameter families as subfamilies.     

Photocrosslinking of ultra high strength polyethylene fibers

Ultra high strength polyethylene (HSPE) fibers have been successfully photocrosslinked using benzophenone as photoinitiator. The introduction of photoinitiator without disturbing the fiber structure is a difficult problem which was solved by vapor absorption at elevated temperature while keeping the fiber under constant strain. The crosslinked fiber showed no decrease in mechanical properties at room temperature as is the case when fibers are crosslinked by other reported methods such as radiation and chemical crosslinking. The crosslinked fiber showed enhanced high temperature resistance as well as much lower creep rate on prolonged stressing. Photocrosslinking of HSPE fiber is superior to other crosslinking methods reported in the literature.     

The determination of nitrate and chloride in sodium hydroxide solutions by means of cation exchangers,in the manufacturing control of alkaline batteries

The most important types of alkaline batteries are described. A method for the determination of chloride and nitrate ions in sodium hydroxide solutions has been developed The analysis is performed in the following manner: the solution is passed through a layer of a cation exchanger in the hydrogenform,wherebythe sodium hydroxide is neutralized. The liberated hydrochloric and nitric acids respectively are determined through titration. This method has been used for the manufacturing control of nickel-cadmium batteries.     

The magnetic circular dichroism of five-membered ring heterocycles

The MCD spectra of pyrrole, furan, thiophene, selenophene and teburophene and some of their derivatives are reported and the corresponding energies, oscillator strengths, transition moment directions, and MCD terms are calculated from semi-empirical quantum mechanical calculations hi the π-electron approximation. The MCD spectrum of thiophene is only slightly perturbed by substituents, and this is also expected to be true of the quite similar MCD spectra of selenophene and tellurophene. These molecules can then be classified as “hard” chromophores. On the other hand, pyrrole and furan have different and much weaker MCD spectra which change shape considerably when substituents are introduced. The implications of these observations are further discussed.     

Painlevé IV with both Parameters Zero: A Numerical Study

The six Painlevé equations were introduced over a century ago, motivated by rather theoretical considerations. Over the last several decades, these equations and their solutions, known as the Painlevé transcendents, have been found to play an increasingly central role in numerous areas of mathematical physics. Due to extensive dense pole fields in the complex plane, their numerical evaluation remained challenging until the recent introduction of a fast “pole field solver” [ 1 ]. The fourth Painlevé equation has two free parameters in its coefficients, as well as two free initial conditions. The present study applies this new computational tool to the special case when both of its parameters are zero. We confirm existing analytic and asymptotic knowledge about the equation, and also explore solution regimes which have not been described in the previous literature.     

Determination of reduced folates in tumor and adjacent mucosa of colorectal cancer patients using LC‐MS/MS

A liquid chromatography electrospray ionization tandem mass spectrometry (LC‐MS/MS) method has been developed for the determination of 5,10‐methylenetetrahydrofolate (methyleneTHF), tetrahydrofolate (THF) and 5‐methyltetrahydrofolate (methylTHF) in colorectal mucosa and tumor tissues. The folate extraction method includes homogenization, heat and folate conjugase treatment to hydrolyze polyglutamyl folate to monoglutamyl folate. Before analysis on LC‐MS/MS, simple and fast sample purification with ultrafiltration (molecular weight cut‐off membrane, 10 kDa) was performed. Folates were detected and quantified using positive electrospray. The method described in the present paper was successfully applied to determine the level of three folate monoglutamates in mucosa and tumor samples from 77 colorectal cancer patients, starting from a limited amount of tissue. The results showed that the LC‐MS/MS method has a great advantage over other previously used methods because of its high sensitivity and selectivity. Significantly higher levels of methyleneTHF and THF were found in tumor compared with matched mucosa tissues. Folate levels in adjacent mucosa were associated with tumor location, age and gender. The correlation between folate levels and tumor site further strengthens the fact that development of right‐ and left‐sided tumors follows different pathways. Copyright © 2012 John Wiley & Sons, Ltd.