Novel Optimization Approach to Mixing Process Intensification

An approach was presented to intensify the mixing process. Firstly, a novel concept, the dissipation of mass transfer ability(DMA) associated with convective mass transfer, was defined via an analogy to the heat-work conversion. Accordingly, the focus on mass transfer enhancement can be shifted to seek the extremum of the DMA of the system. To this end, an optimization principle was proposed. A mathematical model was then developed to formulate the optimization into a variational problem. Subsequently, the intensification of the mixing process for a gas mixture in a micro-tube was provided to demonstrate the proposed principle. In the demonstration example, an optimized velocity field was obtained in which the mixing ability was improved, i.e., the mixing process should be intensified by adjusting the velocity field in related equipment. Therefore, a specific procedure was provided to produce a mixer with geometric irregularities associated with an ideal velocity.

Successive Approximation of p-Class Towers

Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.

Deep Transfers of p-Class Tower Groups

Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.

Pattern classification using fuzzy relation and genetic algorithm

Purpose–This paper aims to consider a soft computing approach to pattern classification using the basic tools of fuzzy relational calculus(FRC)and genetic algorithm(GA).Design/methodology/approach–The paper introduces a new interpretation of multidimensional fuzzy implication(MFI)to represent the author’s knowledge about the training data set.It also considers the notion of a fuzzy pattern vector(FPV)to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space.The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication.For the estimation of Ri floating point representation of GA is used.Thus,a set of fuzzy relations is formed from the new interpretation of MFI.This set of fuzzy relations is termed as the core of the pattern classifier.Once the classifier is constructed the non-fuzzy features of a test pattern can be classified.Findings–The performance of the proposed scheme is tested on synthetic data.Subsequently,the paper uses the proposed scheme for the vowel classification problem of an Indian language.In all these case studies the recognition score of the proposed method is very good.Finally,a benchmark of performance is established by considering Multilayer Perceptron(MLP),Support Vector Machine(SVM)and the proposed method.The Abalone,Hosse colic and Pima Indians data sets,obtained from UCL database repository are used for the said benchmark study.The benchmark study also establishes the superiority of the proposed method.Originality/value–This new soft computing approach to pattern classification is based on a new interpretation of MFI and a novel notion of FPV.A set of fuzzy relations which is the core of the pattern classifier,is estimated using floating point GA and very effective classification of patterns under vague and imprecise environment is performed.This new approach to pattern classification avoids the curse of high dimensionality of feature vector.It can provide multiple classifications under overlapped classes.