The Division Relation: Congruence Conditions and Axiomatisability

We examine a universal algebraic abstraction of the semigroup theoretic concept of “divides:” a divides b in an algebra A if for some n ∈ ω, there is a term t(x, y ₁,…, y _n ) involving all of the listed variables, and elements c ₁,…, c _n such that t ^A (a, c ₁,…, c _n ) = b. The first order definability of this relation is shown to be a very broad generalisation of some familiar congruence properties, such as definability of principal congruences. The algorithmic problem of deciding when a finitely generated variety has this relation definable is shown to be equivalent to an open problem concerning flat algebras. We also use the relation as a framework for establishing some results concerning the finite axiomatisability of finitely generated varieties.     

Mean‐Reverting Market Model: Speculative Opportunities and Non‐Arbitrage

The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean‐reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non‐trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean‐reverting model is arbitrage‐free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.     

Finitely generated relatively universal varieties of Heyting algebras

Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=_g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.     

三维RC网络仿真异质材料的通用介质响应

提出了一种三维RC网络模型,并采用MATLAB及C语言对该模型进行编码、建模和仿真,得到了该网络的归一化复介电常数.分别计算了元件数为54,144,300,540和882的三维RC网络,结果表明,元件数为300及其以上的网络,其通用介质响应(UDR)特性趋于稳定;获得了电容分别为100nF,10nF,1nF和100pF时,540个元件RC网络的归一化复介电常数与频率关系的仿真结果;仿真了540个元件的RC网络中,电阻比例分别为4％,7％,10％,16％和33％时,归一化复介电常数与角频率ω的 关键词： 三维RC网络 异质材料 介电常数 通用介质响应     

Quantification of multiple compounds containing heterogeneous elements in the mixture by one‐dimensional nuclear magnetic resonance spectroscopy of different nuclei using a single universal concentration reference

One‐dimensional (1D) quantitative NMR (qNMR) is a useful tool for concentration determination due to its experimental simplicity and the direct proportionality of the integrated signal area to the number of nuclei spin. For complex mixtures, however, signal overlapping often in one‐dimensional quantitative ¹H NMR (1D ¹H qNMR) spectrum limits the accurate quantification of individual compound. Here, we introduced employing joint 1D qNMR methods of different nuclei, such as ¹H and ³¹P (or/and ¹⁹F), to quantify multiple compounds in a complex mixture using a single universal concentration reference. When the concentration ratio of several compounds containing different elements in a complex mixture is of interest, the result calculated from measured intensities from 1D qNMR of different nuclei is independent of the gravimetric error from the reference. In this case, the common reference also serves as a ‘quantitative bridge’ among these 1D qNMR of different nuclei. Quantitative analysis of choline, phosphocholine, and glycerophosphocholine mixture is given as an example using trimethylphosphine oxide ((CH₃)₃P(O)) as concentration reference. Compounds containing multiple elements, such as tetramethylammonium hexafluorophosphate (N⁺(CH₃)₄PF₆^?), are proposed as the common concentration reference for ¹H, ¹³C, ¹⁵N, ³¹P, and ¹⁹F qNMR for the quantitative analysis of complex mixture containing these different elements. We anticipate that the proposed joint 1D qNMR approach using a universal concentration reference will be a valuable alternative for simultaneous quantification of multiple compounds in a complex mixture due to its accuracy and single and simple sample preparation. Copyright © 2014 John Wiley & Sons, Ltd.