Qualitative interpretation of physico-chemical and isotopic parameters in the Krka River (Croatia) assessed by multivariate statistical analysis

Multivariate statistical analyses were applied on the measured physico-chemical (Cd, Pb, Cu, Zn, Mg, Ca, O₂, alkalinity, temperature, pH, SAS, DOC and DIC) and isotopic parameters (δ¹³C and δ¹⁸O) to estimate and distinguish anthropogenic from natural influences to the water system of the Krka River. Analyses were conducted on the data collected during six years from twelve sampling sites. On the basis of orientation, positioning and grouping of parameters arranged by biplots, four main hypotheses were defined and finally statistically confirmed. Thereof, two main and distinct processes occurring in the Krka River could be highlighted: (i) upstream pollution, caused by the inflow of untreated waste-waters of city of Knin and (ii) downstream self-purification, caused by the sedimentation and/or co-precipitation of pollutants coupled by the inflow of clean subterranean water (groundwater recharge). Grouping of (i) hydrological and carbon cycle connected parameters, and (ii) anthropogenically influenced correlated parameters were proposed as a result of statistical analysis. Regarding the pH, it is shown that a stream section influenced by the subterranean inflow of Zrmanja River is statistically significantly different for all sampling campaigns during six years, being lower for about 0.5 pH unit.     

Anderson acceleration of the alternating projections method for computing the nearest correlation matrix

In a wide range of applications it is required to compute the nearest correlation matrix in the Frobenius norm to a given symmetric but indefinite matrix. Of the available methods with guaranteed convergence to the unique solution of this problem the easiest to implement, and perhaps the most widely used, is the alternating projections method. However, the rate of convergence of this method is at best linear, and it can require a large number of iterations to converge to within a given tolerance. We show that Anderson acceleration, a technique for accelerating the convergence of fixed-point iterations, can be applied to the alternating projections method and that in practice it brings a significant reduction in both the number of iterations and the computation time. We also show that Anderson acceleration remains effective, and indeed can provide even greater improvements, when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. Alternating projections is a general method for finding a point in the intersection of several sets and ours appears to be the first demonstration that this class of methods can benefit from Anderson acceleration.     

CaII Binding Regulates and Dominates the Reactivity of a Transition‐Metal‐Ion‐Dependent Diesterase from Mycobacterium tuberculosis

The diesterase Rv0805 from Mycobacterium tuberculosis is a dinuclear metallohydrolase that plays an important role in signal transduction by controlling the intracellular levels of cyclic nucleotides. As Rv0805 is essential for mycobacterial growth it is a promising new target for the development of chemotherapeutics to treat tuberculosis. The in vivo metal‐ion composition of Rv0805 is subject to debate. Here, we demonstrate that the active site accommodates two divalent transition metal ions with binding affinities ranging from approximately 50 nm for Mn^II to about 600 nm for Zn^II. In contrast, the enzyme GpdQ from Enterobacter aerogenes, despite having a coordination sphere identical to that of Rv0805, binds only one metal ion in the absence of substrate, thus demonstrating the significance of the outer sphere to modulate metal‐ion binding and enzymatic reactivity. Ca^II also binds tightly to Rv0805 (K_d≈40 nm ), but kinetic, calorimetric, and spectroscopic data indicate that two Ca^II ions bind at a site different from the dinuclear transition‐metal‐ion binding site. Ca^II acts as an activator of the enzymatic activity but is able to promote the hydrolysis of substrates even in the absence of transition‐metal ions, thus providing an effective strategy for the regulation of the enzymatic activity.     

Volumetric properties of aqueous solutions of quinic acid and its sodium salt

Abstract  

The apparent molar volume of quinic acid and its sodium salt were determined from the density data of aqueous solutions up to molality of 0.4 mol kg⁻¹ and in the temperature range from 293.15 to 328.15 K. The apparent molar volume of sodium quinate comprises the ionic and the associated ion-pair contributions. From the apparent molar volumes of quinic acid and the quinate ion, the molecular contributions to that of quinic acid are derived. At 298.15 K, the limiting apparent molar volume of quinic acid is 119.8 ± 0.5 cm³ mol⁻¹, and that of the quinic ion is 111.6 ± 0.3 cm³ mol⁻¹. Similarly, at 298.15 K, the limiting apparent molar expansibility of sodium quinate is 0.198 ± 0.003 cm³ mol⁻¹ K⁻¹, and that of quinic acid is 0.142 ± 0.003 cm³ mol⁻¹ K⁻¹. From these limiting ionic and molecular apparent molar volumes, the limiting volume change caused by ionization of quinic acid was calculated as −8.2 cm³ mol⁻¹ at 298.15 K. The coefficients of thermal expansion of these solutions were calculated from the density data, and from these the apparent molar expansibilities of quinic acid and its sodium salt were derived.     

Dipole moment and self-association of cyclohexylsulfamic acid in 1,4-dioxane solution at 298.15?K

Abstract  

The density, refractive index, and electrical permittivity of cyclohexylsulfamic acid in 1,4-dioxane solutions were measured at 298.15 K. The limiting apparent specific volume, refraction, and polarization were calculated from the experimental data. The electrical dipole moment of cyclohexylsulfamic acid was estimated using the Debye, Onsager, and Kirkwood equations. The dipole association of cyclohexylsulfamic acid was treated with the assumption that the dipole moment of dimeric species is zero. The dimerization constant and dipole moment of monomeric species were evaluated.     

Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation

We prove that linear instability implies non-linear instability in the energy norm for the critically dissipative quasi-geostrophic equation.     

Thermodynamics of Transfer of Some Alkyl Acetates from Water to Water–Ethanol Mixtures

 The solubility of methyl acetate (MeOAc), ethyl acetate (EtOAc), 1-propyl acetate(1-PrOAc), 1-butyl acetate (1-BuOAc), 2-methyl-1-propyl acetate (iso-BuOAc), 2-butyl acetate (sec-BuOAc), 2-methyl-2-propyl acetate (tert-BuOAc), 1-pentyl acetate (1-PeOAc), and 1-hexyl acetate(1-HeOAc) in 2.5, 5.0, 7.5, and 10.0 weight per cent of ethanol in water were determined at 298.2 K. The solubility of the same compounds, except for tert-BuOAc, 1-PeOAc, and 1-HeOAc, was determined as a function of temperature at 10.0 weight per cent of ethanol in water. From the solubility measurements the standard Gibbs energy (), enthalpy (), and entropy () of transfer were determined. The calculated thermodynamic functions show that the predominant factors in the transfer of alkyl acetate molecules are the transfer of the cavity and the hydrophobic interaction of the non-polar alkyl chain. Scaled particle theory calculations were used to determine the thermodynamics of cavity transfer, which were combined with the experimental total transfer quantities to obtain the corresponding interaction transfer quantities. It was found that the Gibbs energy of interaction for the transfer is negative, whereas the enthalpy and entropy of interaction for the transfer are positive; almost complete compensation of enthalpy and entropy components occurs.     

On the scattering problem for infinitely many fermions in dimensions d ≥ 3 at positive temperature

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\ge 3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper [11], and extends the important recent result of M. Lewin and J. Sabin in [19] of a similar type for dimension $d=2$. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\ge 3$.     

Penalty variable sample size method for solving optimization problems with equality constraints in a form of mathematical expectation

Numerical Algorithms - Equality-constrained optimization problems with deterministic objective function and constraints in the form of mathematical expectation are considered. The constraints are...