Variation–iteration method in momentum space: Determination of Hartree–Fock atomic orbitals

A method using the Svartholm iterative procedure to solve atomic Hartree–Fock equations in momentum space is defined and applied to the ground states of Be and B⁺. The calculated atomic orbital properties follow a monotonic and stable convergence, but with rates of convergence depending on each property. The evolution of the orbitals during the iterations is explained by the combined actions of the variational principle, the Svartholm iterative procedure, and the momentum space representation. © 1993 John Wiley & Sons, Inc.     

Evaluation par analyse thermique differentielle des chaleurs de deshydratation de plusieurs aluns de chrome,aluminium et fer

Résumé L'emploi d'un analyseur thermique différentiel semi-micro a permis de déterminer semi-quantitativement les variations d'enthalpie accompagnant la déshydratation des aluns M^I M^III (SO₄)₂ 12 H₂O (M^III=Cr, Al; M^I=K, NH₄) et d'établir ainsi une distinction entre l'eau de cristallisation ( H < 13 kcal/mole) et l'eau de constitution ( H > 13 kcal/mole).

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The semi-quantitative determination of the heat of dehydration reactions has been realised by using a differential thermal analysis apparatus and differences in the heat of dehydration between water of crystallization ( H < 13 kcal/mole) and water of constitution ( H > 13 kcal/mole) have been established for some alums M^I M^III (SO₄)₂ 12 H₂O (M^III=Cr, Al; M^I=K, NH₄).

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Zusammenfassung Durch Anwendung eines differentialthermoanalytischen Halbmikrogeräts gelang es, die Enthalpieänderung der Dehydratation von Alaunen der Zusammensetzung M^IM^III(SO₄)₂ 12 H₂O (M^III=Cr, Al; M^I=K, NH₄) zu bestimmen und Kristallwasser ( H < 13 kcal/Mol) und Strukturwasser ( H > 13 kcal/Mol) zu unterscheiden.

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() ( < 13 /) ( > 13 /) M^I M^III (SO₄)₂ · 12 ₂ · (^III=Cr, l; ^I= K, NH₄).

     

Analysis of the metal-binding selectivity of the metallochaperone CopZ from Enterococcus hirae by electrospray ionization mass spectrometry

Metallochaperones are soluble proteins involved in metal transport and regulation in vivo. Copper metallochaperones belong to a structural family of metal binding domains displaying a ferredoxin-like fold (betaalphabetabetaalphabeta) and a consensus metal-binding motif MXCXXC. The metal-binding selectivities for this class of proteins are poorly documented so far. The present study focuses on the measurement of the selectivity of the copper metallochaperone CopZ from Enterococcus hirae for different metal ions using an experimental approach based on electrospray ionization mass spectrometry (ESI-MS). All the metal cations tested, i.e. Cu(I), Cu(II), Hg(II), Cd(II) and Co(II), form specific metal complexes with CopZ. The study of a chemically modified CopZ as well as variants of CopZ in the active site demonstrated that the complexes observed by ESI-MS, i.e. in the gas phase, corresponded to the complexes previously observed by other analytical methods in solution. Competition experiments allowed the classification of the metal ions by increasing affinities for CopZ as follows: Co < Cd < Hg < Cu. A dissociation constant in the range of 20 microM was determined for cobalt. The affinity of CopZ for the other metals tested was found to be higher, with dissociation constants smaller than micromolar.     

Association of cationic surfactants with maleic acid copolymers: dependence of binding on the nature of the neutral comonomer unit

Isotherms of binding of dodecylpyridinium chloride (DPC) and cetylpyridinium chloride (CPC) by copolymers of maleic acid (MA; degree of neutralization=1) with methyl methacrylate (MMA), styrene (St), and vinyl acetate (VA) were determined at various salt concentrations by using the potentiometric technique. The average composition of copolymers corresponds to designations MA(MMA)3, MASt, and MAVA. Very different binding behavior has been found. The cooperativity parameter, u, for binding to MA(MMA)3 is the lowest and displays no dependence on ionic strength, which is a consequence of significant hydrophobic polymer-surfactant interactions. Isotherms for the DPC/MASt system display a two-step binding mechanism, which could not be clearly identified in the CPC/MASt case, presumably due to interference of surfactant micellization with the second step. It is proposed that the first step of binding in DPC/MA(MMA)3 and in DPC/MASt solutions is of electrostatic origin, as is the second step in DPC/MASt. On the contrary, the second step in DPC/MA(MMA)3 is mostly due to hydrophobic interactions of surfactant hydrocarbon tails with the predominantly uncharged DPC/MA(MMA)3 complex. MAVA solutions display the highest critical aggregation concentration (cac) values, which show a slight decreasing trend with increasing ionic strength. The very compact form of the MAVA copolymer at high salt content was responsible for this.     

A stochastic particle method for the McKean-Vlasov and the Burgers equation

In this paper we introduce and analyze a stochastic particle method for the McKean-Vlasov and the Burgers equation; the construction and error analysis are based upon the theory of the propagation of chaos for interacting particle systems. Our objective is three-fold. First, we consider a McKean-Vlasov equation in with sufficiently smooth kernels, and the PDEs giving the distribution function and the density of the measure , the solution to the McKean-Vlasov equation. The simulation of the stochastic system with particles provides a discrete measure which approximates for each time (where is a discretization step of the time interval ). An integration (resp. smoothing) of this discrete measure provides approximations of the distribution function (resp. density) of . We show that the convergence rate is for the approximation in of the cumulative distribution function at time , and of order for the approximation in of the density at time ( is the underlying probability space, is a smoothing parameter). Our second objective is to show that our particle method can be modified to solve the Burgers equation with a nonmonotonic initial condition, without modifying the convergence rate . This part extends earlier work of ours, where we have limited ourselves to monotonic initial conditions. Finally, we present numerical experiments which confirm our theoretical estimates and illustrate the numerical efficiency of the method when the viscosity coefficient is very small.

     

Lecture Hall Partitions

We prove a finite version of the well-known theorem that says that the number of partitions of an integer N into distinct parts is equal to the number of partitions of N into odd parts. Our version says that the number of lecture hall partitions of length n of N equals the number of partitions of N into small odd parts: 1,3,5, ldots, 2n-1 . We give two proofs: one via Bott's formula for the Poincaré series of the affine Coxeter group , and one direct proof.     

Experimental determination of optical constants in the vacuum ultra violet wavelength region between 80 and 140 nm: A reflectance versus thickness method and its application to ZnSe

The 80-120 nm spectral range is a key domain for solar physics. Below 105 nm solids do not transmit light and the reflectance of available mirrors is particularly low which makes optical measurements specifically difficult. Optical constants of the materials may consequently be unavailable or unreliable.We present here a two media reflectance method at normal incidence suited to this VUV range, in which the variable is not the incidence angle but the thickness of the top layer made of the material to be analyzed. The real (n) and imaginary (k) parts of the complex index are directly and graphically determined in the (n, k) plane as the common intersection point of isoreflectance curves corresponding to samples different only in the thickness of the top layer.The method is tested and illustrated with ZnSe films evaporated on Al covered float glass substrates. In the literature, the reflectance magnitudes measured on ZnSe crystals differ strongly from an author to the other, leading to discrepant data for ZnSe in the VUV domain.We obtain precise and reliable values of (n, k), which fit the experimental values determined on freshly cleaved ZnSe crystals by J.L. Freeouf and the theoretical values calculated from the electronic band structure of ZnSe by John P. Walter and Marvin L. Cohen, but strongly differ from the optical constants selected by E.D. Palik in his tables.     

Shape Minimization of Dendritic Attenuation

What is the optimal shape of a dendrite? Of course, optimality refers to some particular criterion. In this paper, we look at the case of a dendrite sealed at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the dendrite which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal.     

An investigation of the structural aspects of the tomato fruit by means of quantitative nuclear magnetic resonance imaging

In this study, magnetic resonance imaging (MRI) was applied to study the structural aspects of the tomato fruit. The main study was performed on tomatoes (cv. Tradiro) using a 0.2-T electromagnet scanner. Spin-echo images were acquired to visualize the tomato macrostructure. The air bubble content in tissues was evaluated by exploiting susceptibility effects using multiple gradient echo images. The microstructure was further studied by measuring spin–spin (T₂) and spin–lattice (T₁) relaxation time distributions. Nuclear magnetic resonance relaxometry, macro vision imaging and chemical analysis were used as complementary and independent experimental methods in order to emphasize the MRI results. MRI images showed that the air bubble content varied between tissues. The presence of gas was attested by macro vision images. Quantitative imaging showed that T₂ and T₁ maps obtained by MRI reflected the structural differences between tomato tissues and made it possible to distinguish between them. The results indicated that cell size and chemical composition contribute to the relaxation mechanism.     

Synthesis and photophysical properties of new conjugated fluorophores designed for two-photon-excited fluorescence

[structure: see text] Novel elongated push-push fluorophores (e.g., 9) were synthesized by 2-fold Sonogashira or Wittigminus signHorner reactions. Modulation of the length and topology of the conjugated connectors allows tuning of their photophysical properties. In addition, their photoluminescence can be adjusted by playing on polarity. Derivatives combining enhanced two-photon absorption cross section (sigma2) in the visible red and high fluorescence quantum yield (Phi) have been obtained. Such fluorophores hold promise for nonlinear imaging of biological systems.