Rigorous Asymptotic Expansions for Critical Wave Speeds in a Family of Scalar Reaction-Diffusion Equations

We investigate traveling wave solutions in a family of reaction-diffusion equations which includes the Fisher–Kolmogorov–Petrowskii–Piscounov (FKPP) equation with quadratic nonlinearity and a bistable equation with degenerate cubic nonlinearity. It is known that, for each equation in this family, there is a critical wave speed which separates waves of exponential decay from those of algebraic decay at one of the end states. We derive rigorous asymptotic expansions for these critical speeds by perturbing off the classical FKPP and bistable cases. Our approach uses geometric singular perturbation theory and the blow-up technique, as well as a variant of the Melnikov method, and confirms the results previously obtained through asymptotic analysis in [J.H. Merkin and D.J. Needham, (1993). J. Appl. Math. Phys. (ZAMP) A, vol. 44, No. 4, 707–721] and [T.P. Witelski, K. Ono, and T.J. Kaper, (2001). Appl. Math. Lett., vol. 14, No. 1, 65–73].     

Isopiestic determination of the osmotic and activity coefficients of the {yKCl + (1 − y)K2HPO4}(aq) system at T = 298.15 K

The osmotic coefficients of aqueous mixtures of KCl and K₂HPO₄ have been measured at T = (298.15 ± 0.01) K by the isopiestic vapor pressure method over the range of ionic strengths from (2.3700 to 11.250) mol · kg⁻¹ using CaCl₂(aq) as the reference solution. Our new experimental results were modeled with an extended form of Pitzer’s ion-interaction model equations, both with the usual mixing terms and with Scatchard’s neutral–electrolyte mixing terms, and with the Clegg–Pitzer–Brimblecombe equations based on the mole-fraction-composition scale. There is a dearth of previously published isopiestic data for mixtures containing salts of and, consequently, no previous measurements are available for comparison with the present results. The present study yields mixing parameters for these three models that are needed for modeling the thermodynamic activities of solute components of natural waters and other complex aqueous electrolyte mixtures.     

Chiral Hexa‐ and Nonamethylene‐Bridged Bis(L‐Leu‐oxalamide) Gelators: The First Oxalamide Gels Containing Aggregates with a Chiral Morphology

Chiral amino acid‐ and amino alcohol‐oxalamides are well‐known as versatile and efficient gelators of various lipophilic and polar organic solvents and water. To further explore the capacity of the amino acid/oxalamide structural fragment as a gelation‐generating motif, the dioxalamide dimethyl esters 1₆Me and 1₉Me , and dicarboxylic acid 2₆OH / 2₉OH derivatives containing flexible methylene bridges with odd ( 9 ; n=7) and even ( 6 ; n=4) numbers of methylene groups were prepared. Their self‐assembly motifs and gelation properties were studied by using a number of methods (FTIR, ¹H NMR spectroscopy, CD, TEM, DSC, XRPD, molecular modeling, MMFF94, and DFT). In contrast to the previously studied chiral bis(amino acid or amino alcohol) oxalamide gelators, in which no chiral morphology was ever observed in the gels, the conformationally more flexible 1₆Me , 1₉Me , 2₆OH , and 2₉OH provide gelators that are capable of forming diverse aggregates of achiral and chiral morphologies, such as helical fibers, twisted tapes, nanotubules, straight fibers, and tapes, in some cases coexisting in the same gel sample. It is shown that the differential scanning calorimetry (DSC)‐determined gelation enthalpies could not be correlated with gelator and solvent clogP values. Spectroscopic results show that intermolecular hydrogen‐bonding between the oxalamide units provides the major and self‐assembly directing intermolecular interaction in the aggregates. Molecular modeling studies reveal that molecular flexibility of gelators due to the presence of the polymethylene bridges gives three conformations ( zz , p1 , and p2 ) close in energy, which could form oxalamide hydrogen‐bonded layers. The aggregates of the p1 and p2 conformations tend to twist due to steric repulsion between neighboring iBu groups at chiral centers. The X‐ray powder diffraction (XRPD) results of 1₆Me and 1₉Me xerogels prove the formation of p1 and p2 gel aggregates, respectively. The latter results explain the formation of gel aggregates with chiral morphology and also the simultaneous presence of aggregates of diverse morphology in the same gel system.     

Solubility in K+-Na+-Mg 4 2− aqueous solution at T = 298.15 K

In the salt solubility predictions for K⁺-Na⁺-Mg ₄ ^2? aqueous solution the treatment of thermodynamic data of three-component systems at T = 298.15 K involved the application of the Extended Pitzer’s ion-interaction model for the pure and mixed electrolyte solutions and criteria of phase equilibrium. Osmotic coefficients data of three-component systems were revised according to recently published parameters of the solutions NaCl(aq) and KCl(aq) that served as reference standards in isopiestic measurements. Parameters of the extended ion-interaction model of K₂SO₄(aq) are determined by treatment of experimental and predicted values of osmotic coefficient in supersaturated region obtained by the Zdanovskii-Stokes-Robinson rule. Results of salt solubility prediction were compared to experimental solubility data from literature. The agreement between calculated and experimental solubility data in the systems K₂SO₄ + MgSO₄ + H₂O, Na₂SO₄ + MgSO₄ + H₂O, and Na₂SO₄ + K₂SO₄ + H₂O at T = 298.15 K, was excellent.     

Mössbauer spectroscopic and X-ray diffraction study of the thermal decomposition of Fe(CH3COO)2 and FeOH(CH3COO)2

Thermal decomposition of iron(II) acetate, Fe(CH₃COO)₂, and iron(III) acetate hydroxide, FeOH(CH₃COO)₂, has been studied using⁵⁷Fe Mössbauer spectroscopy and X-ray diffraction. Samples were thermally treated in air atmosphere between 150°C and 1000°C. The formation of maghemite '-Fe₂O₃, and hematite, -Fe₂O₃, is discussed. Hematite appears as the final decomposition product.     

Molecular vibration in Sn(Pb)GeS3 and GeS2

The vibrational properties of GeS₂, SnGeS₃ and PbGeS₃ are considered on the basis of the vibrational properties of GeS₄ tetrahedra connected in different ways. In this respect, Raman spectra of isolated GeS₄ and Ge₂S₆ molecules as well as Raman spectra of SnGeS₃, PbGeS₃ and GeS₂ crystals are presented and analysed.     

A Two-Parameter Distribution Obtained by Compounding the Generalized Exponential and Exponential Distributions

We introduce a new two-parameter lifetime distribution obtained by compounding the generalized exponential and exponential distributions. We assume that the shape parameter of the generalized exponential distribution is a random variable having the exponential distribution. The shapes of the density and hazard rate functions are derived. The model parameters are estimated by maximum likelihood, and an application of the proposed distribution is presented.

     

Synthesis and characterization of some novel cadmium(II) complexes with 3-hydroxypicolinic acid (3-OHpicH): Crystal and molecular structures of [CdI(3-OHpic)(3-OHpicH)(H2O)]2, [Cd(3-OHpic)2(H2O)2] and [Cd(3-OHpic)2]n

Cadmium(II) complexes of 3-hydroxypicolinic acid, namely [CdI(3-OHpic)(3-OHpicH)(H₂O)]₂ (1), [Cd(3-OHpic)₂(H₂O)₂] (2) and [Cd(3-OHpic)₂]_n (3) were prepared and characterized by spectroscopic methods (IR, NMR) and their molecular and crystal structures were determined by X-ray crystal structure analysis. Complexes 1 and 2 were prepared in similar reaction conditions using different cadmium(II) salts: cadmium(II) iodide and cadmium(II) acetate dihydrate, respectively, while 3 was prepared by recrystallization of 2 from N,N-dimethylformamide solution. Various coordination modes of 3-OHpicH in 1–3 were established in the solid state: bidentate N,O-chelated mode in 1 and 2, monodentate mode through the carboxylate O atom from zwitterionic ligand in 1 and bidentate N,O-chelated and bridging mode in 3. In the DMF solution of all prepared complexes, only monodentate mode of 3-OHpicH binding to cadmium(II) through the carboxylate O atom was established by ¹H, ¹³C, ¹⁵N and ¹¹³Cd NMR spectroscopy.