On automorphisms of finite simple Chevalley groups

The paper deals with the splitting properties of the automorphism groups of finite Chevalley groups. Using the action of symmetries of a Dynkin diagram on the corresponding Weyl group, a sufficient condition is developed for the existence of a complement for the inner automorphism group in the automor ph-ism group of a finite Chevalley group. The condition is verified for Chevalley groups of the classical types (viz., the group of type A_l, B_l, C_l,and D_l) as well as the exceptional groups of type E₆ and E₇, under suitable restrictions on the base fields.     

Raman spectral signatures of mouse mammary tissue and associated lymph nodes: normal,tumor and mastitis

Raman spectroscopy involves the interaction of light with the molecular vibrations and therefore can provide information about molecular structure, tissue composition and changes in its environment. We explored whether Raman spectroscopy can reliably distinguish mammary tumors from normal mammary tissues and other pathological states in mice. We analyzed a large number of Raman spectra from the tumor and normal mammary glands of mice injected with 4T1 tumor cells, which were collected using a high‐resolution (less than 4 cm⁻¹) Raman spectrometer at a fixed (785 nm) laser excitation wavelength and with 60 mW of laser power. The spectra of normal and tumor mammary glands showed consistent differences in the intensity of certain Raman bands and loss of some bands in the tumor spectra. Multivariate statistical methods—principal component analysis (PCA) and discriminant functional analysis (DFA)—were used to separate the data into different groups of mammary tumors, mastitis, lymph nodes contralateral and tumor‐cell‐injected sides, and normal contralateral and tumor‐cell‐injected sides. We demonstrate that this spectroscopic technique has the feasibility of discriminating tumor and mastitis from normal tissues and other pathological states in a short period of time and may detect tumor transformation earlier than the standard histological examination stage. Copyright © 2006 John Wiley & Sons, Ltd.     

A robust method for automated background subtraction of tissue fluorescence

This paper introduces a new robust method for the removal of background tissue fluorescence from Raman spectra. Raman spectra consist of noise, fluorescence and Raman scattering. In order to extract the Raman scattering, both noise and background fluorescence must be removed, ideally without human intervention and preserving the original data. We describe the rationale behind our robust background subtraction method, determine the parameters of the method and validate it using a Raman phantom against other methods currently used. We also statistically compare the methods using the residual mean square (RMS) with a fluorescence‐to‐signal (F/S) ratio ranging from 0.1 to 1000. The method, ‘adaptive minmax’, chooses the subtraction method based on the F/S ratio. It uses multiple fits of different orders to maximize each polynomial fit. The results show that the adaptive minmax method was significantly better than any single polynomial fit across all F/S ratios. This method can be implemented as part of a modular automated real‐time diagnostic in vivo Raman system. Copyright © 2007 John Wiley & Sons, Ltd.     

Generation of sub wavelength multiple focal hole segments using azimuthally polarized annular multi-Gaussian beam

We propose a new approach for generating multiple focal hole segment of sub wavelength size, by tight focusing of phase modulated annular multi-Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observed that focal segment with multiple focal rings structure separated with different axial distance can be generated by properly tuning the phase of the incident azimuthally polarized annular multi-Gaussian beam. Potential applications of this focal shaping technique are also discussed.     

Spin and the Thermal Equilibrium Distribution of Wave Functions

Consider a quantum system S weakly interacting with a very large but finite system B called the heat bath, and suppose that the composite S∪B is in a pure state Ψ with participating energies between E and E+δ with small δ. Then, it is known that for most Ψ the reduced density matrix of S is (approximately) equal to the canonical density matrix. That is, the reduced density matrix is universal in the sense that it depends only on S’s Hamiltonian and the temperature but not on B’s Hamiltonian, on the interaction Hamiltonian, or on the details of Ψ. It has also been pointed out that S can also be attributed a random wave function ψ whose probability distribution is universal in the same sense. This distribution is known as the “Scrooge measure” or “Gaussian adjusted projected (GAP) measure”; we regard it as the thermal equilibrium distribution of wave functions. The relevant concept of the wave function of a subsystem is known as the “conditional wave function.” In this paper, we develop analogous considerations for particles with spin. One can either use some kind of conditional wave function or, more naturally, the “conditional density matrix,” which is in general different from the reduced density matrix. We ask what the thermal equilibrium distribution of the conditional density matrix is, and find the answer that for most Ψ the conditional density matrix is (approximately) deterministic, in fact (approximately) equal to the canonical density matrix.     

The influence of linking group in exterior point on mesogenic properties of the basket moulded molecules: calix[4]arene

Novel basket-shaped molecules having calix[4]arene as central rigid core possessing azomaterial in outer space unit in the lengthening arm were synthesised and characterised by elemental analysis and different spectroscopic methods such as Fourier Transform Infrared (FT-IR), electron spin ionization (ESI)-MASS, ¹H nuclear magnetic resonance (NMR) and ¹³C NMR. Mesomorphism behaviour of novel materials was studied using optical polarising microscopy, differential scanning calorimetry and higher-temperature powder X-ray diffraction method to confirm smectic C phase. In most of the compounds, we found rod-like mosaic texture and focal conic textures of smectic C phases. Nematic phases were also quite often found in materials during cooling and heating stage from isotropic phases. The dielectric measurements have been carried out for the determination of real and imaginary parts of the permittivity of the newly designed scaffolds. These studies will give adequate prospects in the field of supramolecular system, especially in calixarene organisation to explore new epoch of calixarene-based liquid crystals with different linking groups.