On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

On the Ne—Ne potential-energy curve and related properties

The construction of interatomic pair potentials according to the HFD (Hartree—Fock—dispersion) and the XC (exchange—Coulomb) models is reviewed briefly. A new XC potential is constructed for Ne; as in a successful application to Ar, the adjustable parameters in the model are fixed by fitting only second virial coefficient data. The new XC potential, two slight modifications of it, and five literature potentials, are compared with respect to their ability to predict the second virial coefficients and transport properties of dilute Ne gas, the Ne—Ne differential and total scattering cross sections, and the spectroscopic constants of the dimer. A reassessment of the experimental data leads to the conclusion that a literature HFD-C potential is less reliable than previously thought. The new potentials constructed in this paper appear preferable to the other potentials considered; they reproduce essentially all the experimental data used for test purposes to within experimental error.     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.     

Atom transport in random two sublattice structures: analogue of the random alloy sum rule

A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.     

A reliable single parameter interatomic potential for argon

A simple semiempirical approximation previously proposed for the isotropic intermolecular forces between two closed shell systems is tested in detail for the argon-argon interaction. The potential is based on the knowledge of the first-order coulomb interaction energy, a suitably damped three term long range asymptotic expansion of the second order coulomb energy, and a semiempirical representation of the exchange interaction energy which contains one adjustable parameter. The single adjustable parameter can be reliably determined by fitting the second virial coefficient for argon in the 130–773 K temperature range with the long range interaction coefficients being constrained within the theoretical bounds specified by Tang, Norbeck and Certain. The reliability of the potential is compared with that of several literature potentials by comparing the theoretical predictions obtained from the potentials with experimental results for the second virial coefficient, viscosity, thermal conductivity and thermal diffusion ratios for dilute argon gas, and with spectroscopic data for the dimer, and with SCF calculations of the Ar-Ar potential at small interatomic separations. Our best potential predicts these properties with a precision as good as or better than other recent potentials which generally contain more adjustable parameters and/or involve more input data. The results confirm earlier work that suggested that the scheme tested is capable of yielding reliable isotropic potentials for the interaction of closed shell systems for 0·3 ? R/R_m ? ∞ where R_m is the intermolecular distance at the van der Waals minimum. The scheme appears to offer a method for obtaining reliable potentials while avoiding problems associated with optimizing many parameters with respect to fitting experimental constraints.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

A high accuracy diffusion kinetics formalism for random multicomponent alloys: application to high entropy alloys

In this paper, a new, lighter, version of the highly accurate Moleko, Allnatt and Allnatt formalism for describing both tracer (self) and collective diffusion kinetics in multicomponent random alloys is presented. Verification of the resulting expressions is performed by means of kinetic Monte Carlo simulation. The accuracy of the new formalism is much higher than that of the combined Manning and Holdsworth and Elliott formalism discussed recently. Using this formalism the possible range of the tracer diffusion ratio of the highest to the lowest atomic component is examined for equiatomic (or near equiatomic) binary, ternary, quaternary and quinary alloys. It is shown that in the random alloy model, the correlation effect is the highest with a reduction of the fastest tracer diffusion by 40–55%, when moving from two pure metals to their equiatomic binary alloy. By adding the third component (with an intermediate mobility) this effect can be further increased with a possible total reduction of the fastest tracer diffusion by up to 70% (depending on the combinations of mobilities), while adding the fourth component brings this reduction up to 80% and with a possible maximum of up to 85% reduction for the 5-component alloy (again depending on the combinations of mobilities). But the slowest diffusing components are not affected by this. This suggests that kinetics arguments alone are not enough for explaining the sluggish diffusion observed of all atomic components in (equiatomic) high-entropy alloys.     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.     

Semileptonic (Λ b → Λcev) decay in a field theoretic quark model

The semileptonic decay width of heavy baryons such as (Λ _b → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.