A study of higher-order nonlinear ordinary differential equations with four-point nonlocal integral boundary conditions

This paper investigates some new existence results for an nth-order nonlinear differential equation with four-point nonlocal integral boundary conditions (strip/slit like conditions). Our results are based on some standard fixed point theorems and Leray-Schauder degree theory.     

The bend angle of water in ice Ih and liquid water: The significance of implementing the nonlinear monomer dipole moment surface in classical interaction potentials

The implementation of the physically accurate nonlinear dipole moment surface of the water monomer in the context of the Thole-type, polarizable, flexible interaction potential results in the only classical potential, which, starting from the gas phase value for the bend angle (104.52 degrees), reproduces its experimentally observed increase in the ice Ih lattice and in liquid water. This is in contrast to all other classical potentials to date, which predict a decrease of the monomer bend angle in ice Ih and in liquid water with respect to the gas phase monomer value. Simulations under periodic boundary conditions of several supercells consisting of up to 288 molecules of water used to sample the proton disorder in the ice Ih lattice yield an average value of vartheta(HOH)(I(h))=108.4 degrees +/-0.2 degrees for the minimized structures (T=0 K) and 108.1 degrees +/-2.8 degrees at T=100 K. Analogous simulations for liquid water predict an average value of vartheta(HOH)(liquid)=106.3 degrees +/-4.9 degrees at T=300 K. The increase of the monomer bend angle of water in condensed environments is attributed to the use of geometry-dependent charges that are used to describe the nonlinear character of the monomer's dipole moment surface. Our results suggest a new paradigm in the development of classical interaction potential models of water that can be used to describe condensed aqueous environments.     

Existence Results for Semilinear Perturbed Functional Differential Equations of Neutral Type with Infinite Delay

In this paper, by using semigroup theory and a nonlinear alternative for the sum of a completely continuous and a contraction operator, we establish sufficient conditions for the existence of solutions for perturbed semilinear neutral functional differential equations with infinite delay.     

Electrical conductance study of theta-liquid bridges

This work investigates the behavior of small liquid bridges that are formed between two horizontal supporting surfaces, aligned at the vertical direction. The contact lines of the liquid bridges are not edge-pinned but free to move across the supporting surfaces with the contact angle as a parameter (theta-bridges). An a.c. electrical conductance technique coupled with high resolution optical images is used to characterize the geometrical details of constant volume liquid bridges when their length is increased gradually until rupture. A mathematical framework is developed for the identification of the geometrical characteristics of theta-liquid bridges explicitly from conductance data. Theoretical predictions show good agreement with measurements for most of the bridge lengths (separation distance between supports) except close to the rupture point where the bridge is highly stretched. It is further shown that for short and moderate separation distances the present model can be used with confidence to determine the bridge volume and neck radius from the electrical signal.     

Synthesis and structures of Se analogues of the antithyroid drug 6-n-propyl-2-thiouracil and its alkyl derivatives: formation of dimeric Se-Se compounds and deselenation reactions of charge-transfer adducts of diiodine

Four selenium analogues of the antithyroid drug 6-n-propyl-2-thiouracil (PTU), of formulae RSeU, (R = methyl (Me) (1), ethyl (Et) (2), n-propyl (nPr) (3), and isopropyl (iPr) 4), have been synthesized. Reaction of 1-4 with diiodine in a 1:1 molar ratio in dichloromethane results in the formation of [(RSeU)I(2)] (R = methyl (5), ethyl (6), n-propyl (7) and isopropyl (8)). All compounds have been characterized by elemental analysis, FT-Raman, FT-IR, UV/Vis, (1)H-, (13)C-, (77)Se-1D and -2D NMR spectroscopy, and ESI-MS spectrometric techniques. Recrystallization of 4 from dichloromethane afforded (4CH(2)Cl(2)). Crystals of [(nPrSeU)I(2)] (7), a charge-transfer complex, were obtained from chloroform solutions, while crystallization of 6 and 7 from acetone afforded the diselenides [N-(6-Et-4-pyrimidone)(6-EtSeU)(2)] (92 H(2)O) and [N-(6-nPr-4-pyrimidone)(6-nPrSeU)(2)] (10) as oxidation products. Recrystallization of 7 from methanol/acetonitrile solutions led to deselenation with the formation of 6-n-propyl-2-uracil (nPrU) (11). [(nPrSeU)I(2)] (7) was found to be a charge-transfer complex with a Se--I bond. These results are discussed in relation to the mechanism of action of antithyroid drugs.     

Lowest-energy structures of water clusters (H2O)11 and (H2O)13

We employed a four-step searching/screening approach to determine best candidates for the global minima of (H2O)11 and (H2O)13. This approach can be useful when there exist a large number of low-lying and near-isoenergetic isomers, many of which have the same oxygen-skeleton structure. On the two new candidates for the global minimum of (H2O)11, one isomer can be viewed as placing the 11th molecule onto the side of the global minimum of (H2O)10 and the other can be viewed as removing the 12th molecule from the middle layer of the global minimum of (H2O)12. The three leading lowest-energy clusters of (H2O)13 can all be built starting from the global minimum of (H2O)12, with the difference being in the location of the 13th water molecule.     

Structural dependence of the efficiency of functionalization of silica-coated FeOx magnetic nanoparticles studied by ATR-IR

The efficiency of propylamino functionalization of magnetic silica-coated FeO_x nanoparticles prepared by different methods, including coprecipitation and flame aerosol synthesis, has been evaluated by attenuated total reflection infrared spectroscopy (ATR-IR) combined with a specific surface reaction, thus revealing the availability of the grafted functional groups. Large differences in the population of reactive groups were observed for the investigated materials, underlining the tight relation between the structure of nanoparticles and their suitability for organic functionalization. The materials possessed different core structure, surface area, and porosity, as evidenced by transmission electron microscopy and nitrogen adsorption-desorption isotherms. Grafting of aminopropyl groups using a standard procedure based on reaction with (3-aminopropyl)trimethoxysilane as source of the propylamino groups was performed, followed by classical dry analysis methods to determine the specific concentration of the organic functional groups (in mmol g⁻¹ of material). ATR-IR spectroscopy in a specially constructed reactor cell was applied as wet methodology to determine the chemically available amount of such functional groups, showing that the materials possess largely different loading capacity, with a variability of up to 70% in the chemical availability of the organic functional group. The amount of (3-aminopropyl)trimethoxysilane used for functionalization was optimized, thus reaching a saturation limit characteristic of the material.     

A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.     

On the importance of zero-point effects in molecular level classical simulations of water

We discuss the fundamental difficulties involved in comparing energetic results obtained via classical simulations of bulk water with the observed values. Emphasis is placed on the difference between quantum and classical dynamics, and correction techniques, which can be used to emulate quantum effects in a classical system, are investigated. We present molecular dynamics simulation results for liquid water using the ‘Thole-type’ all atom polarizable water model, which has previously been shown to give reasonable results for both ice Ih and small water clusters. We employ expressions for the density of states power spectrum in the liquid in either atomic or rigid-body coordinates that are appropriate for rigid molecule simulations. It is demonstrated that the atomic power spectra can be written as a linear combination of the center of mass and rotational power spectra via the use of the ‘coupling matrix’ of linear coefficients. This approach allows us to introduce the concept of ‘fractional degrees of freedom’ (DOF) for nuclei in rigid molecule simulation. Within this framework, it is illustrated that in a rigid water molecule the oxygen and hydrogen atoms have 2.82 and 1.59 DOF, respectively (for the TIP4P geometry). Within our suggested approach, we finally demonstrate that Debye–Waller factors can be obtained from the coupling matrix and show that quantum corrections to the structure can be accounted for by raising the temperature of the system in a classical simulation by approximately 50°, a result consistent with previous suggestions.