On the field method in non-holonomic mechanics

This paper deals with the generalization of the field method to non-holonomic systems whose motion is subject to either non-linear constraints or those of a higher order, while their motion is modeled by the generalized Lagrange equations of the second kind. Two examples are given to illustrate the theory.The project supported by the Ministry of Science, Technologies and Development, Republic of Serbia (1874)     

Modeling the vapor–liquid equilibria of polymer–solvent mixtures: Systems with complex hydrogen bonding behavior

The vapor–liquid equilibria of binary polymer–solvent systems was modeled using the Non-Random Hydrogen Bonding (NRHB) model. Mixtures of poly(ethylene glycol), poly(propylene glycol), poly(vinyl alcohol) and poly(vinyl acetate) with various solvents were investigated, while emphasis was put on hydrogen bonding systems, in which functional groups of the polymer chain can self-associate or cross-associate with the solvent molecules. Effort has been made to explicitly account for all hydrogen bonding interactions. The results reveal that the NRHB model offers a flexible approach to account for various self- or cross-associating interactions. In most cases model's predictions (using no binary interaction parameter k_ij = 0) and model's correlations (using one temperature independent binary interaction parameter, k_ij ≠ 0) are in satisfactory agreement with the experimental data, despite the complexity of the examined systems.     

Solution of the isochoric–isoenergetic flash problem by direct entropy maximization

A new algorithm to find the phase equilibrium conditions in systems with specified values of internal energy, volume, and number of moles of each component present (isochoric–isoenergetic flash problem) is proposed. The core of the procedure consists of maximizing the system entropy by iterating on the values, in each phase, of internal energy, volume, and number of moles of each component. Analytical expressions for the physical properties and derivatives required by the calculations were generated by computer algebra. The algorithm tests for the possible need to add or remove phases during the course of iterations. The paper discusses possible numerical difficulties during application of the procedure and how to overcome them. The algorithm has shown to be robust and capable of solving multiphase equilibrium problems, avoiding trivial solutions.     

Prediction of critical transitions of ternary mixtures containing ammonia and n-alkanes

The analysis of the critical transitions that occur in ternary mixtures is important to describe their physical behavior. It also enables the phase behavior of multi-component mixtures at high temperatures to be inferred. The objective of this work was to identify the critical transitions that occur in ternary mixtures containing ammonia and n  -alkane. The mixture’s critical loci were obtained and tested for stability using thermodynamic criteria expressed in terms of the Helmholtz free energy. Two equations of state were used to represent the Helmholtz free energy: the Carnahan–Starling–Redlich–Kwong (CSRK) and the Simplified Perturbed Hard Chain Theory (SPHCT). In order to identify the existing critical transitions, profiles of the critical loci were calculated along constant compositional ratios χ=x₁/x₂$\chi =x_1/x_2$. Some of the curves depict higher order critical transitions between liquid–liquid and gas–liquid critical point regions, or two different liquid–liquid critical regions. One of the critical transitions found could be considered as a new sub-class within existing classifications for ternary mixtures proposed by Sadus [R.J. Sadus, J. Phys. Chem. 96 (1992) 5197–5202].     

Realtime control of robots with initial value perturbations via nonlinear programming methods

The mathematical model of an industrial robot with initial value perturbations is considered as a parametric nonlinear control problem subject to control and state constraints. Based on recent stability results for parametric control problems, a robust nonlinear programming method is proposed for computing the sensitivity derivatives of optimal solutions. Real-time control approximations of perturbed optimal solutions are obtained by evaluating a first order Taylor expansion of the perturbed solution. The efficiency of the real-time approximation is demonstrated for the robot model     

Optimal control of time delay parabolic systems

Various optimal control problems for linear parabolic systems with multiple constant time delays are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in the feedback formMaking use of the results of Schwartz's, the representation of the optimal feedback control is given. A simple example of application is also provided     

On optimal management of resources in distributed networks

In a network of processors, a distributed operating system must handle the management of shared resources. In this paper, it is shown how to solve this problem in using the model previously introduced in [1]. This model (interconnection of N Markov chains each representing locally a distributed process) allows us to prove the good functioning properties for some distributed problems such as the mutual exclusion problem and the deadlock problem, We also prove that fairness is a basic notion for setting the model’s parameters and obtain an optimal working of the network.     

Estimation of the Solubility of Sulfonamides in Aqueous Media from Partition Coefficients and Entropies of Fusion

Semi empirical equation developed by Yalkowsky and Valvani, and another equation extended by Jain and Yalkowsky were used to estimate the aqueous solubility S w , of some sulfonamides using experimental octanol-water partition coefficients P , entropies of fusion j S f , and melting points t m , determined by DSC measurements. The calculated solubilities were compared with those experimentally determined. When experimental j S f and t m were used, the S w calculated values were in good agreement in most cases.     

Asymmetric Schiff Base (N 2 O 3 ) Complexes as Ligands Towards Mn(II), Fe(III) and Co(II), Synthesis and Characterization

Heterobi- and tri-nuclear complexes [LMM'Cl] and [(LM) 2 M'](M=Ni or Cu and M'=Mn, Fe or Co) have been synthesised. The heteronuclear complexes were prepared by stepwise reactions using two mononuclear Ni(II) and Cu(II) complexes of the general formula [HLM]·1/2H 2 O, as ligands towards the metal ions, Mn(II), Fe(III) and Co(II). The asymmetrical pentadentate (N 2 O 3 ) Schiff-base ligands used were prepared by condensing acetoacetylphenol and ethylenediamine, molar ratio 1 1, to yield a half-unit compound which was further condensed with either salicylaldehyde or naphthaldehyde to yield the ligands H 3 L 1 and H 3 L 2 which possess two dissimilar coordination sites, an inner four-coordinate N 2 O 2 donor set and an outer three-coordinated O 2 O set. 1 H NMR and IR spectra indicate that the Ni(II) and Cu(II) ions are bonded to the inner N 2 O 2 sites of the ligands leaving their outer O 2 O sites vacant for further coordination. Different types of products were obtained according to the type of metal ion. These products differ in stoichiometry according to the type of ligand in the parent compound. Electronic spectra and magnetic moments indicate that the structures of the parent Ni(II) and Cu(II) complexes are square-planar while the geometry around Fe(III), Mn(II) and Co(II) in their products are octahedral as elucidated from IR, UV-visible, ESR, 1 H NMR, mass spectrometry and magnetic moments.