Divergences without probability vectors and their applications

In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd.     

Balanced truncation for linear switched systems

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.     

A Heterogeneous Multiscale Dynamic Model for Simulation of Catalytic Reforming Reactors

The present work aims to establish a generic reforming reaction scheme to evaluate the performance of catalytic reforming systems with the aid of a one‐dimensional heterogeneous dynamic model. The novelty of the numerical model stems from the direct inclusion of interphase (fluid‐to‐particle surface), intraparticle (within particle), and intrareactor heat and mass transport resistances under transient conditions. The developed model accounts for the multicomponent gas mixture physicochemical properties and correlations for calculating mass and heat transfer coefficients. Effective macroscopic properties within the particle are calculated by incorporating diffusivities and conductivities of the porous network characteristics accounting for Knudsen and molecular transport as well as tortuosity and porosity of the overall porous path. The industrial case of a steam‐methane reforming multitubular reactor was studied as the most representative case of the generic reaction scheme, with all mass/energy resistances present under severe pressure and temperature conditions. It was shown that there are notable diffusional limitations within the particle, whereas there are also temperature and partial pressure gradients due to the heat and mass transport resistances in the particle film layer. It is further demonstrated that the proposed model can be utilized as a versatile design tool for catalytic reactor development and optimization.     

L-fuzzy ⋎ and ⋏ hyperoperations and the associated l-fuzzy hyperalgebras

In this paper we study two fuzzy hyperoperations, denoted by ⋎ (which can be seen as a generalization of ∨) and ⋏ (which can be seen as a generalization of ∧). ⋎ is obtained from a family of crisp ∨; _p hyperoperations and ⋏ is obtained from a family of crisp ∧ _p hyperoperations. The hyperstructure (X, ⋎, ∧) resembles ahyperlattice and the hyperstructure (X, ∨, ⋏) resembles adual hyperlattice     

Clays as a host matrix in the synthesis of organic macrocycles

A new approach for the synthesis of amide macrocycles, based on the use of organo-clay derivatives as controlling template, is proposed as an alternative to the rotaxane method. Dications of p-xylylene diamine inserted in the clay interlayer space act as molding pillars around which neutral diamine molecules are erected via hydrogen bonding and pi-pi interactions to form supramolecular arrays. Condensation of diamines in the supramolecular arrays with diacetyl dichlorides yields various tetramide macrocycles in good yields. Shape, aromaticity and dimensions of the reactants are factors affecting the condensation reaction.     

Proteolytic activity in various water-in-oil microemulsions as related to the polarity of the reaction medium

The catalytic behaviors of α-chymotrypsin and of trypsin were studied in anionic AOT-isooctane-water and cationic CTAB-ROH-isooctane-water microemulsion systems. The effects of various parameters, such as the pH and the water content expressed in terms of the molar ratio w_o = [H₂O]/[Surfactant], on the enzyme activity, were examined. The kinetic constants were calculated and it was found that in the case of trypsin the enzyme exhibited a remarkable “superactivityrd, when studied in the CTAB microemulsion systems. The effect of the alcohol cosurfactant used in these cationic systems was investigated in relation to the polarity of the reaction medium. By using the hydrophilic probe 1-methyl-8-oxyquinolinium betaine the micropolarity of the water core was determined and related to the kinetic results.     

A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm

The Vehicle Routing Problem (VRP) is one of the most well studied problems in operations research, both in real life problems and for scientific research purposes. During the last 50 years a number of different formulations have been proposed, together with an even greater number of algorithms for the solution of the problem. In this paper, the VRP is formulated as a problem of two decision levels. In the first level, the decision maker assigns customers to the vehicles checking the feasibility of the constructed routes (vehicle capacity constraints) and without taking into account the sequence by which the vehicles will visit the customers. In the second level, the decision maker finds the optimal routes of these assignments. The decision maker of the first level, once the cost of each routing has been calculated in the second level, estimates which assignment is the better one to choose. Based on this formulation, a bilevel genetic algorithm is proposed. In the first level of the proposed algorithm, a genetic algorithm is used for calculating the population of the most promising assignments of customers to vehicles. In the second level of the proposed algorithm, a Traveling Salesman Problem (TSP) is solved, independently for each member of the population and for each assignment to vehicles. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the average quality is less than 1%. More specifically in the set with the 14 classic instances proposed by Christofides, the quality is 0.479% and in the second set with the 20 large scale vehicle routing problems, the quality is 0.826%. The algorithm is ranked in the tenth place among the 36 most known and effective algorithms in the literature for the first set of instances and in the sixth place among the 16 algorithms for the second set of instances. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the Expanding Neighborhood Search Strategy is used.     

A global optimization approach for the linear two-level program

Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.The paper was completed while this author was visiting the Department of Mathematics of Linköping University.     

Polarity formation by a higher order interaction Markov-like chain

Vector property generation is discussed for chain growth by higher order interactions. Because of a deterministic property evolution a state space approach was used. Although not strictly Markovian, the system shows ergodic properties and convergence for a large number of attachment steps. For reasonable interaction energies attributed to increasing order, the main extra contribution to polarity formation results from interactions up to next nearest neighbours. Nonlinear equations up to third order were solved by an iterative procedure.     

Gas-chromatographische Multielementanalyse mit einfachen und fluorierten Di?thyldithiocarbamaten

Zusammenfassung Zur anorganischen Multielementanalyse ist die Gas-Chromatographie von Diäthyldithiocarbamaten geeignet. Mit einem FID können bereits Kationen im 0,6–0,06 ppm-Bereich nach Ausschütteln der wäßrigen Lösungen bestimmt werden. Di(trifluoräthyl)dithiocarbamate zeigen noch höhere Flüchtigkeiten. Eigenschaften und gas-chromatographisches Verhalten einiger dieser Chelate werden angegeben.Die Untersuchungen wurden in dankenswerter Weise durch Sachmittel der Deutschen Forschungsgemeinschaft und des Verbands der Chemischen Industrie unterstützt. Für die Gewährung eines Promotionsstipendiums sei der Friedrich-Ebert-Stiftung ebenfalls gedankt.