New Wavelet Bases and Isometric Between Symbolic Operators Spaces $$ {\text{OP}}S^{m}_{{1,\delta }} $$ and Kernel Distributions Spaces

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces     

Factorization Index for Completely Positive Graphs

In this paper, we prove that the set of all factorization indices of a completely positive graph has no gaps. In other words, we give an affirmative answer to a question raised by N. Kogan and A. Berman [8] in the case of completely positive graphs. Received December 9, 1997, Accepted May 16, 2002     

Similarity-Invariant Subspaces and Similarity-Preserving Linear Maps

In this paper, the similarity-invariant subspaces of B(H), which is the Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given. Received November 3, 1999, Revised September 20, 2000, Accepted February 5, 2001     

Transcendence of Certain Trigonometric Series

In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The proof of the theorem is based on a criterion for linear independence over a number field. Received November 9, 1999, Accepted February 5, 2001     

Gerbes and Duality

We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes; these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1-form potentials coincides with the quantization of the magnetic flux. We apply our global approach to refine the proof of the duality equivalence between the d=11 supermembrane and d=10 IIA Dirichlet supermembrane.     

Resonance Rayleigh scattering spectral characteristics of interaction of nucleic acids with some cationic surfactants and their analytical applications

In near neutral medium, the resonance Rayleigh scattering (RRS) intensities of an alone cationic surfactant and nucleic acid are very weak. However, when they combine with each other to form a complex, the RRS intensity of the solution is enhanced greatly. In this paper the reactions of five cationic surfactants with nucleic acids have been studied. The results show that the reaction conditions and RRS spectral characteristics of these reactions are similar, but their sensitivities are obviously different. Among them, the sensitivity of cetyldimethyl benzylammonium chloride (CDBAC) with an aryl and large molecular weight is the highest, while that of cetyl-trimethylammonium bromide (CTAB) without aryl and with small molecular weight is the lowest. The detection limits for ctDNA and yRNA of the former are 6.6 and 29.4 ng · mL-1, while that of the latter are 13.3 and 53.6 ng · mL-1. The method has better selectivity and can be applied to the determination of trace amounts of nucleic acids. Furthermore, i     

Retrosynthetic analysis of fullerene C(60): structure, stereochemistry, and calculated stability of C(30) fragments.

The total number of possible retrosynthetic bisections of C(60) leads to nine different isometric C(30) fragments. These molecules include five chiral units, four of which derive from partitions corresponding to four distinct "Coupes du Roi". The energies, curvatures, and homodesmotic stabilization energies of the C(30) fragments are evaluated at the ab initio 6-31G level.     

Selective cleavage of the linear ether bond in benzyl glycidyl ether and triphenylmethyl glycidyl ether by potassium alkalide as two-electron-transfer reagent

The linear ether bond was exclusively cleaved in benzyl glycidyl ether and triphenylmethyl glycidyl ether under the influence of K⁻, K⁺(15-crown-5)₂ (1), whereas the strongly strained three-membered oxacyclic ring remained undisturbed. Potassium glycidoxide and benzylpotassium were found as the primary reaction products of benzyl glycidyl ether with 1. Subsequently, benzylpotassium reacted with benzyl glycidyl ether giving the next potassium glycidoxide molecule and bibenzyl. Benzyl phenyl ether was used as a model compound to explain the mechanism of bibenzyl formation. The reaction of triphenylmethyl glycidyl ether with 1 resulted in potassium glycidoxide and stable triphenylmethylpotassium. After treating with a quenching agent a new glycidyl ether or glycidyl ester was obtained from potassium glycidoxide. These results were found when the reaction occurred at the excess of glycidyl ether. In another case, i.e. at the excess of 1 further reactions took place with the participation of potassium anions and various new compounds were observed in the reaction mixture after benzylation or methylation. Thus, the method of substrates delivery influences the course of studied processes in a decisive way.     

Subcellular mass determination by <Superscript>4</Superscript>He<Superscript>+</Superscript> energy-loss micro-spectrometry

The scanning transmission ion microscope (STIM) has been used to determine the intracellular mass of human cultured cells. A 4He+ microbeam of 2.0 MeV energy was chosen to obtain enhanced ion-energy-loss sensitivity through the micron-thick freeze-dried cells. Local sample mass calculation, based on energy-loss conversion by use of appropriate matrix stopping powers, was performed by use of dedicated software. The method was validated with epoxy resin sections and polymer foil as analogues of biological samples in the range of (intra)cellular thickness, 150 to 3000 nm. STIM analysis resulted in less than 5% error in mass determination. 4He+ energy-loss micro-spectrometry was performed on freeze-dried human ovarian cancer cells, the mean areal mass obtained was 120 microg cm(-2) (200 microg cm(-2) in the nucleus and 250 microg cm(-2) in nucleoli). This method is particularly useful for mass normalization of X-ray fluorescence yields resulting from particle-induced X-ray emission microanalysis (micro-PIXE). When performed successively these two ion-beam micro-analytical methods enable the mapping of true element concentrations within single cells.