Linear Automorphisms that are Symplectomorphisms

Let K be the field of real or complex numbers. Let (X K²ⁿ,) be a symplectic vector space and take 0 < k < n,N =. Let L₁,...,L_N X be 2k-dimensionallinear subspaces which are in a sufficiently general position.It is shown that if F : X X is a linear automorphism whichpreserves the form ^k on all subspaces L₁,...,L_N, then F is an_k-symplectomorphism (that is, F^* = _k, where ). In particular, if K = R and k is odd then F mustbe a symplectomorphism. The unitary version of this theoremis proved as well. It is also observed that the set A_l,2r ofall l-dimensional linear subspaces on which the form has rank 2r is linear in the Grassmannian G(l,2n), that is, there isa linear subspace L such that A_l,2r = L G(l, 2n). In particular,the set A_l,2r can be computed effectively. Finally, the notionof symplectic volume is introduced and it is proved that itis another strong invariant.     

Separated sequences in nonreflexive Banach spaces

We prove that there is 1$"> such that the unit ball of any nonreflexive Banach space contains a -separated sequence. The supremum of these constants is estimated from below by and from above approximately by . Given any 1$">, we also construct a nonreflexive space so that if the convex hull of a sequence is sufficiently close to the unit sphere, then its separation constant does not exceed .

     

Effect of preparation and metal content on the introduction of Fe in BEA zeolite, studied by DR UV-vis, EPR and Mössbauer spectroscopy

Fe-containing SiBEA zeolites were prepared by a two-step postsynthesis method: creation of vacant T-sites by dealumination of tetraethylammonium BEA zeolite with nitric acid and then impregnation of the resulting SiBEA zeolite with an aqueous solution of Fe(NO₃)₃. X-ray diffraction shows that iron is incorporated in SiBEA at lattice sites. The presence of Fe in its oxidation state +3 and at isolated tetrahedral sites for low metal content, was demonstrated by diffuse reflectance UV-vis, EPR and Mössbauer spectroscopy. For high iron content, diffuse reflectance UV-vis and Mössbauer spectra revealed the additional presence of extra-lattice FeO_x oligomers and superparamagnetic Fe-oxyhydroxide. Mössbauer spectroscopy identified superparamagnetic Fe-oxyhydroxide as the main phase when basic conditions are used for the preparation.     

Formation of poly(ethylene phosphates) in polycondensation of H3PO4 with ethylene glycol. Kinetic and mechanistic study

Conditions of synthesis of poly(ethylene phosphates) in reaction of H₃PO₄ with HOCH₂CH₂OH (EG), the actual path of polycondensation, and structure of the obtained polymers (mostly oligomers) and kinetics of reaction are described. Preliminary kinetic information, based on the comparison of the MALDI‐TOF‐ms and ³¹P{¹H} NMR spectra as a function of conversion is given as well. Because of the dealkylation process fragments derived from di‐ and triethylene glycols are also present in the repeating units. Structures of the end groups (? CH₂CH₂OH or ? OP(O)(OH)₂) depend on the starting ratio of [EG]₀/[H₃PO₄]₀, although even at the excess of EG the acidic end groups prevail because of the dealkylation process. In MALDI‐TOF‐ms products with P_n equal up to 21 have been observed. The average polymerization degrees (P_n) are lower and have been calculated from the proportion of the end groups. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 830–843, 2008     

Recursive intermediate factorization and complete computational linearization of the coupled-cluster single,double, triple,and quadruple excitation equations

Summary The nonlinear CCSDTQ equations are written in a fully linearized form, via the introduction of computationally convenient intermediates. An efficient formulation of the coupled cluster method is proposed. Due to a recursive method for the calculation of intermediates, all computational steps involve the multiplication of an intermediate with aT vertex. This property makes it possible to express the CC equations exclusively in terms of matrix products which can be directly transformed into a highly vectorized program.This work has been supported by the U.S. Air Force Office of Scientific Research, Grant No. 90-0079     

Highly hydrophilic surfaces from polyglycidol grafts with dual antifouling and specific protein recognition properties

Homopolymer grafts from α-tert-butoxy-ω-vinylbenzyl-polyglycidol (PGL) were prepared on gold and stainless steel (SS) substrates modified by 4-benzoyl-phenyl (BP) moieties derived from the electroreduction of the parent salt 4-benzoyl benzene diazonium tetrafluoroborate. The grafted BP aryl groups efficiently served to surface-initiate photopolymerization (SIPP) of PGL. In similar conditions, SIPP of hydroxyethyl methacrylate (HEMA) permitted the production of PHEMA grafts as model surfaces. Water contact angles were found to be 66°, 15°, and 0° for SS-BP, SS-PHEMA, and SS-PPGL, respectively. The spontaneous spreading of water drops on SS-PPGL was invariably observed with 1.5 μL water drops. PPGL thus appears as a superhydrophilic polymer. Resistance to nonspecific adsorption of proteins of PPGL and PHEMA grafts on gold was evaluated by surface plasmon resonance (SPR) using antibovine serum albumin (anti-BSA). The results conclusively show that PPGL-grafts exhibit enhanced resistance to anti-BSA adsorption compared to the well-known hydrophilic PHEMA. PPGL grafts were further modified with BSA through the carbonyldiimidazole activation of the OH groups providing immunosensing surfaces. The so-prepared PPGL-grafted BSA hybrids specifically interacted with anti-BSA in PBS as compared to antimyoglobin. It is clear that the superhydrophilic character of PPGL grafts opens new avenues for biomedical applications where surfaces with dual functionality, namely, specific protein grafting together with resistance to biofouling, are required.     

Development and validation of a routine multiresidue method for determining 140 pesticides in fruits and vegetables by gas chromatography/tandem quadrupole mass spectrometry

A GC/tandem quadrupole MS/MS method was developed and validated for the determination of the residues of 140 pesticides in fruits and vegetables. Pesticides were extracted from samples by using a miniaturized acetonitrile-based extraction technique known as the quick, easy, cheap, effective, rugged, and safe (QuEChERS) method. Validation studies were carried out on carrots, tomatoes, and strawberries. In order to reduce systematic errors due to a matrix-induced effect, quantification was carried out using matrix-matched standard calibration curves. The recovery and precision results satisfied the European Union criteria (i.e., average recoveries were in the range 70-120% with RSDs < or = 20%) for 125 of the 140 pesticides at a spiking level of 0.01 mg/kg. At the higher spiking levels, there were just two instances of overall average recovery < 70% (chlorothalonil and captan). The measurement uncertainty was estimated following a "top down" approach as being 21 and 35%, on average, based on validation and ongoing recovery data, respectively (coverage factor k = 2, confidence level 95%). Practical application to 541 samples of apples, tomatoes, strawberries, cucumbers, currants, mushrooms, carrots, peppers, pears, onions, and gooseberries under strict QC conditions demonstrated the ruggedness of the total procedure.