Formation of Aromatic and Other Unsaturated End Groups in Carboxymethyl Cellulose During Hot Alkaline Treatment

Carboxymethyl cellulose (CMC, DS 0.58) was treated in solutions of sodium hydroxide (0.001–1 M) at 95 °C. The treated (1–12 h) CMC samples were purified by dialysis and analyzed by UV spectroscopy and by UV resonance Raman spectroscopy (UVRRS) with excitation at 244 nm. A UV absorption maximum at 265 nm and a UVRR signal at 1650 cm⁻¹ were indicative of formation of -conjugated aldehyde end groups in CMC through -elimination. Another strong UVRR band at 1610 cm⁻¹ gave evidence on conversion of some of the -conjugated aldehyde end groups to alkali stable aromatic structures.     

Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

Modelling the crystalline deformation of native and regenerated cellulose

The molecular mechanics modelling of the deformation of a number of proposed structures for the crystalline regions of cellulose I- , I- and II are reported. The structures used are from coordinates that have recently been reported, which have made particular reference to the ability to locate the positions of hydrogen bonds. By comparison to previously reported structures of cellulose, where the emphasis on this has also been made, and in a diagnostic way, it is shown that it is possible to make some conclusions as to their validity. The effect of removing the intramolecular hydrogen bonding is also reported. All structures, with one exception, are shown to be sensitive to this operation. Two approaches to the molecular mechanics modelling are reported, wherein the structures are minimised under restraint, by altering the c-spacing, within the COMPASS^TM forcefield to obtain a simple chain stiffness value or alternatively by performing a full elastic constants determination for the unit cell.     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: II. time-dependent case

Time-dependent properties of a state that interacts with an infinite dimensional quantum system containing several one-parameter eigenvalue bands are considered. This is done by a new mathematical method that produces correct results, however strong the interaction between the state and the system . It is shown that in the case of the weak interaction one obtains standard results that are usually obtained within the formalism of the perturbation expansion method. In particular, if the eigenvalue E of the state is embedded inside the range of the unperturbed eigenvalues, time evolution of the state that is initially prepared in the state has typical exponential decay behavior. One also reproduces standard results concerning probabilities of the transition of the state at infinite time (t=∞) into various eigenvalue bands. However, if the interaction is strong, one finds much more complex and much more complicated behavior.     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: I. Time-independent case

A new method for the exact solution of the interaction of an isolated state with an infinite dimensional quantum system §_∞ ^b containing several one-parameter eigenvalue bands is developed. Unlike standard perturbation expansion approach, this method produces correct results however strong the interaction between the state and the system . It is shown that in the case of the weak interaction this method correctly reproduces standard results obtained within the formalism of the perturbation expansion method. In particular, due to the interaction with the system , eigenvalue E of the state shifts to a new position. In addition, if this eigenvalue is embedded inside the range of the unperturbed eigenvalues, this shifted eigenvalue broadens and spectral distribution of the state has the shape of the universal resonance curve. However, if the interaction is strong, one finds much more complex and much more complicated behavior     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Di storted s-type orbital s: the $${\rm H}^{+}_{2}$$ problem revi sited

On the example of the molecular ion, we show that spherically distorted s-type orbitals possessing angular dependent orbital exponents, even in a minimal basis may lead to total energies the accuracy of which is comparable with the ones obtained by fully numerical (‘complete basis’) calculations.     

Characterizations for Some Types of DNA Graphs

Vertex induced subgraphs of directed de Bruijn graphs with labels of fixed length k and over α letter alphabet are (α,k)-labelled. DNA graphs are (4,k)-labelled graphs. Pendavingh et al. proved that it is NP-hard to determine the smallest value α _k (D) for which a directed graph D can be (α _k (D),k)-labelled for any fixed . In this paper, we obtain the following formulas: and for cycle C _n and path P _n . Accordingly, we show that both cycles and paths are DNA graphs. Next we prove that rooted trees and self-adjoint digraphs admit a (Δ,k)-labelling for some positive integer k and they are DNA graphs if and only if Δ ≤ 4, where Δ is the maximum number in all out-degrees and in-degrees of such digraphs.     

On minimal energies of trees of a prescribed diameter

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let denote the set of trees on n vertices and diameter d, . Yan and Ye [Appl. Math. Lett. 18 (2005) 1046–1052] have recently determined the unique tree in with minimal energy. In this article, the trees in with second-minimal energy are characterizedAMS Subject Classification: 05C50, 05C35     

A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

An exact expression for the wiener index of a TUC<Subscript>4</Subscript>C<Subscript>8</Subscript>(R) nanotorus

The Wiener index of a graph G is defined as , where V(G) is the set of all vertices of G and for denotes the length of a minimal path between x and y. A C ₄ C ₈ net is a trivalent decoration made by alternating squares C ₄ and octagons C ₈. It can cover either a cylinder or a torus. In this paper, an algorithm for computing the distance matrix of a C ₄ C ₈(R) nanotorus T = T[p,q] is given. Using this matrix, the Wiener index of T is computed.     

Evaluation of recurrence relationships and numerical solutions for finite rotation matrix elements by using auxiliary functions

In this article, we derived several new recurrence relations of the rotation matrix elements by using Gauss’ recurrence formulas for hypergeometric functions and auxiliary functions , and . The aim of this contribution is to obtain general algorithm to compute the rotation matrix elements, paying attention to the use recurrence relationships of the auxiliary functions that allow the treatment of the functions with high angular momentum quantum numbers.     

Synthesis and thermal evolution of TiO2-RuO2 xerogels

Gels of the Ti Ru O system, where , 0.001, 0.01, 0.02, 0.05, 0.1, 0.15, 0.2, 0.3 and 0.5 (mol), have been synthesized by a polymeric sol-gel route from Ti (IV)-iso-propoxide and Ru (III) acetyl-acetonate (acac). The mechanisms of the hydrolysis and polycondensation reactions were studied by using Fourier Transform Infrared Spectroscopy (FTIR). The evolution of the xerogels as a function of temperature was also determined. At temperatures, as low as 200°C, mixtures of antase Ti Ru O (Ass) solid solution and rutile Ti Ru O solid solution (Rss) were attained for compositions with 0.3. For , only the anatase phase is present (A) and for , mixtures of anatase Ti Ru O (Ass) solid solution, rutile Ti Ru O solid solution (Rss) and Ru Ti O (RuO ss) solid solution were attained. RuO catalyzes the anatase to rutile transformation, even at RuO contents as low as 0.001 mol. Although, from 300 to 400°C the solid solubility of RuO into rutile-TiO phase is located at , from 500°C that value is located in the 0.05 range. This fact could be due to the metastability of the rutile solid solutions containing ruthenium oxide above 400°C. According to semiquantitative transmission electron microscopy-energy dispersive X-ray spectroscopy (TEM-EDX) analyses, at 700°C, there are compositional variations in both solid solutions, Rss and RuO ss. Thus, the system is chemically heterogeneous. The amount of Ti ions hosted into the RuO lattice in the solid solution is lower than that of Ru ions into the rutile-TiO lattice. At this temperature, the contents of these solid solutions are mol% RuO into the TiO lattice (the maximum value found) and around 8.0 mol% TiO (the maximum value found) into RuO . The RuO volatilization can promote the segregation of the ruthenium oxide giving rise to the heterogeneity and the metastability observed in this system.     

Synthesis of β‐Chlorinated Macrocyclic [Au(C14H20N4Cl2)]X (X = AuCl2, ClO4, AuCl4) Gold(III) Complexes. Crystal and Molecular Structures of [Au(C14H20N4Cl2)]ClO4

A squareplanar [AuL₂]⁺ gold(III) complex [L₂ = 6.13dichloro5,7,12,14tetramethyl1,4,8,11tetraaza4,6,11,13tetraenato(2-)] containing two chlorine atoms in the position of the ligand hexacyclic ring was first synthesized by the reaction of the [AuL₁]⁺ tetraiminate complex [L₁ = 5,7,12,14tetramethyl1,4,8,11tetraaza4,6,11,13tetraenato(2-)] with HAuCl₄ in an acetone – DMFA solution. The complex was isolated in the form of dichloroaurite (I), perchlorate (II), and tetrachloroaurate (III). Compounds I–III were studied by elemental and Xray diffraction analyses and IR and NMR spectroscopies. Single crystals of [AuL₂]ClO₄ were obtained, and the crystal structure of this compound was determined from Xray diffraction patterns. The crystals are monoclinic: a = 10.147(2), b = 7.260(1), c = 12.519(2), = 96.70(1)°, V = 915.9(3)³, Z = 2, space group P2/c, d_calc = 2.218, d_meas = 2.209 g/cm³ The crystal structure is built of nearly planar [Au(C₁₄H₂₀N₄Cl₂)]⁺ cations and [ClO₄]^- anions. Introduction of chlorine atoms into the positions of the hexacyclic rings of the tetraazamacrocycle hardly changes the lengths of the delocalized C N and C C bonds.     

The variance of a consensus

In proficiency tests the consensus of the participants' results is often used as the assigned value to calculate z-scores. Where the consensus is quantified as the robust mean of n results, the standard error of the assigned value is often taken to be , where is the robust standard deviation estimated from the same data ¹ . As some of the results are downweighted in robust estimation, is too large a denominator, so that tends to have a somewhat low bias. This bias is shown to be inconsequential for proficiency testing purposes. However, an unbiased estimate can be obtained by using the bootstrap.

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On the interaction between mercury(II) salts and 3-methylpyrazoline-5-one. The first crystal structure of a cyclic organomercuric compound with a dimercurated methylenic carbon atom

Synthesis and characterization of two types of novel organomercury derivatives of 3-methylpyrazoline-5-one (MepzH₂-one), (XHg)₂(MepzH-one) (X = Cl⁻, Br⁻) and Hg(MepzH-one)₂ are described. The ¹H and ¹³C NMR data revealed existence of dimercurated compounds in the dimethylsulfoxide-d ₆ solution. NMR spectra confirmed that the mercuration took place at the C-4 atom of the pyrazole ring. X-ray crystal structure analysis of 4,4-bis(chloromercurio)-3-methylpyrazoline-5-one revealed almost linear coordination of both mercury atoms [Hg–C 2.099(6) and 2.104(5) ; Hg–Cl 2.330(2) and 2.338(2) ; C–Hg–Cl 171.1(2) and 174.4(2)°]. The slight deviation from linearity is caused by contacts with nitrogen or oxygen atoms from the neighbouring molecule [HgN 2.768(5) and HgO 2.748(5) ]. The molecules are interconnected by hydrogen bonds N–HCl of 3.286(5) .     

On the largest eigenvalues of trees with perfect matchings

Let λ₁ (G) and Δ (G), respectively, denote the largest eigenvalue and the maximum degree of a graph G. Let be the set of trees with perfect matchings on 2m vertices, and . Among the trees in , we characterize the tree which alone minimizes the largest eigenvalue, as well as the tree which alone maximizes the largest eigenvalue when . Furthermore, it is proved that, for two trees T ₁ and T ₂ in (m≥ 4), if and Δ (T ₁) > Δ (T ₂), then λ₁ (T ₁) > λ₁ (T ₂).     

Unicyclic Graphs Possessing Kekulé Structures with Minimal Energy

Unicyclic graphs possessing Kekulé structures with minimal energy are considered. Let n and l be the numbers of vertices of graph and cycle C _l contained in the graph, respectively; r and j positive integers. It is mathematically verified that for and l = 2r + 1 or has the minimal energy in the graphs exclusive of , where is a graph obtained by attaching one pendant edge to each of any two adjacent vertices of C ₄ and then by attaching n/2 − 3 paths of length 2 to one of the two vertices; is a graph obtained by attaching one pendant edge and n/2 − 2 paths of length 2 to one vertex of C ₃. In addition, we claim that for has the minimal energy among all the graphs considered while for has the minimal energy.      

Unicycle graphs with extremal Merrifield–Simmons Index

The Merrifield–Simmons index f(G) of a (molecular) graph G is defined as the number of subsets of the vertex set, in which any two vertices are non-adjacent, i.e., the number of independent-vertex sets of G. By we denote the set of unicycle graphs in which the length of its unique cycle is k. In this paper, we investigate the Merrifield–Simmons index f(G) for an unicycle graph G in . Unicycle graphs with the largest or smallest Merrifield–Simmons index are uniquely determined.     

Estimation of partial linear error-in-variables models for ρ<Superscript>−</Superscript>-mixing dependence data

Consider the partly linear regression model Y = xβ + g(t) + e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is ρ⁻-mixing. Let be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of , which is ρ⁻-mixing data sets, an independent validation data containing n observations of is available. The exact observations on x may be obtained by some expensive or diffcult procedures for only a small subset of subjects enrolled in the study. In this paper, inspired by Berberan-Santos et al. [J. Math. Chem. 37 (2005)101], a semiparametric method with the primary data is employed to obtain the estimators of β and g(·) based on the least squares criterion with the help of validata. The proposed estimators are proved to be strongly consistent.