Quaternary liquid-liquid equilibria: Experimental determination and correlation of equilibrium data. Part III. New methods of representation and correlation of liquid-liquid equilibria in quaternary systems

Part III of this work describes two new methods of representation and correlation of liquid-liquid equilibria in quaternary systems. These methods are appropiate for the interpolation of new nonexperimental equilibrium data. The methods suggested are applied to the quaternary systems presented in Parts I and II of this series (Ruiz and Prats, 1982a,b).     

Simplified expansion of Slater orbitals about displaced centers

A new and very simple one-range expansion of the 0s function is derived and employed as the starting point of three recurrence relations which allow the expansion of arbitrary Slater functions over displaced centers. Convergence of the expansions, both pointwise and in norm, are analyzed, and three-center nuclear attraction integrals are chosen for a further test of the formal developments and the numerical behavior of these expansions.     

Approximated solutions to the schrödinger equation

We are currently working on a couple of the well-known dificiencies of the variation method and we present here some of the results that we have obtained so far. The variation method does not give information a prior on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, we present a geometric interpretation of the variation method. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included.     

Synthese de composes aromatiques comportant les groupements ocf2br et scf2brI - Action du dibromodifluoronéthane sur les thiophénate et phénate de potassium

The synthesis of, C₆H₅OCF42Br and C₆H₅SCF₂Br from CF₂Br₂ is discribed.     

Formation of an unusual charge-transfer network from an ionic liquid

An intriguing and novel charge-transfer complex between dimethyldihydrophenazine and diethylviologen has been crystallized from an ionic liquid at room temperature, resulting in an interesting stacking motif of interrupted D***A***D type triads: efficient formation of the complex is seen within an ionic liquid and acetone, with the complex absorbing strongly across nearly the entire visible-NIR spectral region.     

Matching interdiction

We introduce two interdiction problems involving matchings, one dealing with edge removals and the other dealing with vertex removals. Given is an undirected graph G with positive weights on its edges. In the edge interdiction problem, every edge of G has a positive cost and the task is to remove a subset of the edges constrained to a given budget, such that the weight of a maximum matching in the resulting graph is minimized. The vertex interdiction problem is analogous to the edge interdiction problem, with the difference that vertices instead of edges are removed. Hardness results are presented for both problems under various restrictions on the weights, interdiction costs and graph classes. Furthermore, we study the approximability of the edge and vertex interdiction problem on different graph classes. Several approximation-hardness results are presented as well as two constant-factor approximations, one of them based on iterative rounding. A pseudo-polynomial algorithm for solving the edge interdiction problem on graphs with bounded treewidth is proposed which can easily be adapted to the vertex interdiction problem. The algorithm presents a general framework to apply dynamic programming for solving a large class of problems in graphs with bounded treewidth. Additionally, we present a method to transform pseudo-polynomial algorithms for the edge interdiction problem into fully polynomial approximation schemes, using a scaling and rounding technique.     

A De Giorgi–Nash type theorem for time fractional diffusion equations

We study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order $\alpha \in (0,1)$ . The coefficients are merely assumed to be bounded and measurable, and they satisfy a uniform parabolicity condition. Our main result is a De Giorgi–Nash type theorem, which gives an interior Hölder estimate for bounded weak solutions in terms of the data and the $L_\infty $ -bound of the solution. The proof relies on new a priori estimates for time fractional problems and uses De Giorgi’s technique and the method of non-local growth lemmas, which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional Laplacian.     

Towards a Living Radical Polymerization of Styrene by Using Dithiolactone as a New Type of Mediating Agent

In this communication, γ‐phenyl‐γ‐butyrodithiolactone (DTL1) is presented as the first example of a new type of control agent. The styrene polymerization carried out at 60 °C in the presence of DTL1 exhibits living characteristics, without consuming DTL1 during the process. This unprecedented behavior was explained by a mechanism based on the reversible formation of a persistent radical adduct between the DTL1 and the polystyrene macroradicals.

     

Approximate dynamic programming for stochastic linear control problems on compact state spaces

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal policies usually cannot be computed, not even for instances of moderate size.