Influence of the chain length of long molecules on the equation of state in binary gas-liquid mixtures

The simple Flory-Huggins model can be combined with the lattice gas as was done by Tompa and others. Here the same method is used to obtain the van der Waals equation of state for a binary gas-liquid system containing a solute consisting of segmented molecules. The simplified equation of state developed here is useful for the study of the critical properties of such systems, in particular, the dependence of the various parameters on the chain length of the molecules.     

Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation

An original method to detect images in defocused scenes by means of a binary joint transform correlation is presented. Defocused images are described in frequency domain as the product between the Fourier transform of the in-focus scene by the optical transfer function of the imaging lens. This function, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm. Information provided by the algorithm allows to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.     

Associative monotonic operations in fuzzy set theory

The properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets, on fuzzy numbers and on fuzzy probabilistic sets.     

{0, 1/2}-Chvátal-Gomory cuts

Given the integer polyhedronP _t := conv{x ∈ℤ ⁿ :Ax⩽b}, whereA ∈ℤ ^{m × n} andb ∈ℤ ^m , aChvátal-Gomory (CG)cut is a valid inequality forP ₁ of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ ₊ ^m such that λτA∈ℤ ⁿ . In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2} ^m . We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of strong inequalities forP ₁. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering polytopes are briefly discussed.     

An analytical technique for 3-dimensional interpolation

Given the values of a 3-dimensional function at unevenly spaced grid points on the grid structure of a channel, we describe a new analytical algorithm to determine the function value at an arbitrary point inside the channel. This algorithm has been implemented on a Univac 1100/81 computer in PL/I.     

Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums

Let s=(s₁,…,s_m) and t=(t₁,…,t_n) be vectors of non-negative integer-valued functions with equal sum . Let N(s,t) be the number of m×n matrices with entries from {0,1} such that the ith row has row sum s_i and the jth column has column sum t_j. Equivalently, N(s,t) is the number of labelled bipartite graphs with degrees of the vertices in one side of the bipartition given by s and the degrees of the vertices in the other side given by t. We give an asymptotic formula for N(s,t) which holds when S→∞ with 1?st=o(S^2/3), where and . This extends a result of McKay and Wang [Linear Algebra Appl. 373 (2003) 273-288] for the semiregular case (when s_i=s for 1?i?m and t_j=t for 1?j?n). The previously strongest result for the non-semiregular case required 1?max{s,t}=o(S^1/4), due to McKay [Enumeration and Design, Academic Press, Canada, 1984, pp. 225-238].     

Complexity results on restricted instances of a paint shop problem for words

We study the following problem: an instance is a word with every letter occurring twice. A solution is a 2-coloring of its letters such that the two occurrences of every letter are colored with different colors. The goal is to minimize the number of color changes between adjacent letters.This is a special case of the paint shop problem for words, which was previously shown to be NP-complete. We show that this special case is also NP-complete and even APX-hard. Furthermore, derive lower bounds for this problem and discuss a transformation into matroid theory enabling us to solve some specific instances within polynomial time.     

Degenerations of binary Lie and nilpotent Malcev algebras

We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ?. In particular, we describe all irreducible components of these varieties.     

Copula‐based robust optimal block designs

Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.     

Fibonacci, Van der Corput and Riesz-Nágy

What do the three names in the title have in common? The purpose of this paper is to relate them in a new and, hopefully, interesting way. Starting with the Fibonacci numeration system — also known as Zeckendorff's system — we will pose ourselves the problem of extending it in a natural way to represent all real numbers in (0,1). We will see that this natural extension leads to what is known as the ?-system restricted to the unit interval. The resulting complete system of numeration replicates the uniqueness of the binary system which, in our opinion, is responsible for the possibility of defining the Van der Corput sequence in (0,1), a very special sequence which besides being uniformly distributed has one of the lowest discrepancy, a measure of the goodness of the uniformity.Lastly, combining the Fibonacci system and the binary in a very special way we will obtain a singular function, more specifically, the inverse of one of the family of Riesz-Nágy.