Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

二元液态金属Cu-Ni和Ag-Cu凝固过程的分子动力学模拟研究

用Quantum Sutton-Chen多体势对Ag6Cu4和CuNi液态金属凝固过程进行了分子动力学模拟研究.在冷却速率2×1012到2×1014K/s范围内,CuNi总是形成fcc晶体结构,而Ag6Cu4总是形成非晶态结构.考虑到CuNi及AgCu中原子半径之比分别为1.025和1.13,那么模拟结果证实了原子的尺寸差别是非晶态合金形成的一个主要影响因素.此外采用键对及原子多面体类型指数法对凝固过程中微观结构组态变化的分析,不但能说明二十面体结构在非晶态合金形成和稳定性中所起的关键作用,又有助于对液态金属的凝固过程、非晶态结构特征的深入理解.     

On Binary Computation Structures

Based on a modification of Moss' and Parikh's topological modal language [8], we study a generalization of a weakly expressive fragment of a certain propositional modal logic of time. We define a bimodal logic comprising operators for knowledge and nexttime. These operators are interpreted in binary computation structures. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove – as the main result of this paper – its completeness. Moreover, the question of decidability of T is treated.     

Towards the Exact Minimization of BDDs—An Elitism-Based Distributed Evolutionary Algorithm

Binary Decision Diagrams (BDDs) are the state-of-the-art data structure for representation and manipulation of Boolean functions. In general, exact BDD minimization is NP-complete. For BDD-based technology, a small improvement in the number of nodes often simplifies the follow-up problem tremendously. This paper proposes an elitism-based evolutionary algorithm (EBEA) for BDD minimization. It can efficiently find the optimal orderings of variables for all LGSynth91 benchmark circuits with a known minimum size. Moreover, we develop a distributed model of EBEA, DEBEA, which obtains the best-ever variable orders for almost all benchmarks in the LGSynth91. Experimental results show that DEBEA is able to achieve super-linear performance compared to EBEA for some hard benchmarks.     

Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n ⁷) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n ³), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s bound with the same computational complexity. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.     

10.1007/s10955-006-9040-z

We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species,which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, f_i (x, v, t), i = 1, 2. The solution of the VB equation is developed in a Hilbert expansion appropriate for this system. This yields incompressible Navier-Stokes equations for the velocity field u and a jump boundary condition for the pressure across the interface. The interface, in turn, moves with a velocity given by the normal component of u.     

Tracing of interference fringes using average gray value and simultaneous row and column scan

An algorithm for computer tracing of interference fringes is reported. The method uses the average gray-level value for thresholding, row and column scans for determining the type of the scan and simultaneous row and column scan for tracing. The proposed method yield good result even for low-contrast and high-noise images. The program for the interferogram tracing was written using MATLAB6.     

A New Family of Binary Layered Compounds of Platinum with Alkali Metals (A = K,Rb, Cs)

By reacting platinum with alkali metals (A = K, Rb, Cs) a new family of binary alkali metal platinides has been synthesized and characterized by chemical analysis, X‐ray powder diffraction, thermal analysis (DTA and DSC), and magnetic measurements. All three compounds exhibit similar XRD‐patterns with strong reflections that can be indexed on the basis of a rhombohedral crystal system (K_xPt: a = 2.6462(1), c = 17.123(1); Rb_xPt: a = 2.6415(1) Å, c = 17.871(1) Å; Cs_xPt: a = 2.6505(1) Å, c = 18.536(1) Å; x < ½. The a lattice constant is independent on the alkali metal used and of value close to the Pt–Pt distance in NaPt₂ (2.645Å). The c parameter increases monotonically with the growing atomic radius of the alkali metal. The average structure of the alloys consists of cubic close packed layers of platinum atoms with layers of disordered alkali metals in between. For all compounds besides the strong reflections small satellites are observed which cannot be indexed together with the rhombohedral peaks in any rational 3‐dimensional lattice. However, these satellites can be indexed as incommensurate modulations within the ab plane (found propagation vectors k = (0.1011, 0.2506, 0) for Cs_xPt, and k = (0.0168, 0.2785, 0) for Rb_xPt).     

Equilibrium Studies of Binary and Ternary Complexes Involving Tricine and Some Selected α-Amino Acids

Summary. The formation equilibria for the binary complexes of Co^II, Ni^II, Cu^II, Zn^II, Cd^II, Mn^II, Pb^II, Th^IV, UO₂^II, and Ce^III with tricine and for the ternary complexes involving some -amino acids (glycine, -alanine, proline, serine, asparagine, and aspartic acid) were investigated using pH-metric technique. The formation of binary and ternary complexes was inferred from the pH-metric titration curves. It was deduced that tricine acts as a primary ligand in the ternary complexes involving the monocarboxylic amino acids (glycine, -alanine, proline, serine, and asparagine), whereas it behaves as a secondary ligand in the ternary systems containing the dicarboxylic aspartic acid. The ternary complex formation was found to take place in a stepwise manner. The stability constants of the complexes formed in aqueous solutions were determined potentiometrically under the experimental conditions (t=25°C, I=0.1moldm^–3 NaNO₃). The order of stability of the ternary complexes in terms of the nature of the amino acids is investigated and discussed. The values of log K for the ternary complexes have been evaluated and discussed. Evaluation of the effects of ionic strength and temperature of the medium on the stability of the ternary system M^II-tricine--alanine (M^II=Co^II, Ni^II, and Cu^II) has been studied. The thermodynamic parameters were calculated and discussed.