Algorithm for constructing

Petlyuk FB, Kievskii VY and Serafimov LA (1975) Thermodynamic and Topological Analysis of the Phase Diagrams of Polyazeotropic Mixtures II. Algorithm for Construction of Structural Graphs for Azeotropic Ternary Mixtures, Russ J Phys Chem, 49 1836. 

This lemma is nonconstructive. It only says that there is an infinite path, but gives no formula or algorithm for constructing the path. Whether the proof can be nade constructive in an individual case depends on the infinite tree T and tow T is specified. An infinite path in T can be described by an infinite sequence of nodes, n n, ..., n, ... such that (1) nQ is the initial node and... 

The developed methods are computationally cheap, for example, the algorithm for construction of dominant system has linear complexity ( number of reactions). From a practical point of view, it is attractive to use exact rational expressions for the dominant system modes (3), (34) and (36) instead of the zero-one approximation. Also, we can use exact formula (11) for irreversible cycle steady state instead of linear approximation (13). These improvements are computationally cheap and may enhance accuracy of computations. 

In contrast to the isomorphism problem for general graphs, the isomorphism problem for trees is relatively easy. Any tree with n vertices has exactly n-1 edges. We shall describe an algorithm for constructing, in 0(n) time, a code for any tree, such that two trees are isomorphic if and only if they have... 

The rest of this paper will deal exclusively with algorithms for construction of electronic wavefunctions because these are central to the overall problem. In order to appreciate the methods used, one must recall that we are interested in solving a partial differential equation eigenvalue problem for several wavefunctions at several different arrangements of the nuclei. This differential equation involves one- and two-body operators in the potential energy operator and partial derivatives with respect to 3N coordinates (where N is the number of electrons). 

The above illustration suggests an algorithm for construction of k-Clar structures that can be outfined as follows ... 

Cook, R.D. and Nachtsheim, C.J., A comparison of algorithms for constructing exact D-optimal designs, Technometrics, 22, 315-324, 1980. 

Such applications would be accelerated by the development of a universal set of numerical software and data analysis algorithms for constructing multiscale simulations that optimally utilize high-end computing to make predictions and facilitate new applications. To address really challenging multiscale problems, these methods would be designed to distribute data and computations among... 

Algorithm for construction of implicit derivatives of exchange-correlation matrices... 

The problem of finding an algorithm for constructing all the valence isomers of the annulenes (CH)2i (k = 1,2,...) is equivalent to constructing all possible connected cubic graphs [51]. This was an... 

S. Kimura and E. M. Clarke. A Parallel Algorithm for Constructing Binary Decision Diagrams. In Proc. IEEE ICCD 90, pages 220-223, November 1990. 

Another general problem, the development of an algorithm for the construction of kinetic models for the quasi-stationary state of the evolution of non-equilibrium chemical system, is solved by the method of linear routes as simple cycles of a graph assigned to sets of elementary reactions and intermediate substances (see Chapter 2). A general algorithm for construction of kinetic models for the linear catalytic and un-branched radical-chain processes, including a free radical polymerization, is proposed. 

For wide classes of singularly perturbed problems, we will present algorithms for constructing series in powers of e of the form... 

It turns out that under suitable conditions, the asymptotics for both the initial value problem and the boundary value problem in the critical case have the same form as in Sections II.B and III.A. In particular, the solution of the initial value problem approaches one of the solutions of the reduced equation in the limit as /x. 0. But the algorithm for constructing the asymptotic expansion undergoes some changes. 

The algorithm for constructing the asymptotics for the solution of system (7.31) is in many ways similar to the algorithm for the system of ordinary differential equations in the critical case described in Section IV. 

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