A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Affine Near-Semirings Over Brandt Semigroups

In order to study the structure of A ⁺(B _n )—the affine near-semiring over a Brandt semigroup—this work completely characterizes the Green's classes of its semigroup reducts. In this connection, this work classifies the elements of A ⁺(B _n ) and reports the size of A ⁺(B _n ). Further, idempotents and regular elements of the semigroup reducts of A ⁺(B _n ) have also been characterized and studied some relevant semigroups in A ⁺(B _n ).     

Consciousness and the structuring property of typical data

The theoretical base for consciousness, in particular, an explanation of how consciousness is defined by the brain, has long been sought by science. We propose a partial theory of consciousness as relations defined by typical data. The theory is based on the idea that a brain state on its own is almost meaningless but in the context of the typical brain states, defined by the brain's structure, a particular brain state is highly structured by relations. The proposed theory can be applied and tested both theoretically and experimentally. Precisely how typical data determines relations is fully established using discrete mathematics. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

The apolar bilinear form in geometric modeling

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

     

Social welfare relations and irregular sets

Social welfare relations satisfying Pareto and equity principles on infinite utility streams have revealed a non-constructive nature, specifically by showing that in general they imply the existence of non-Ramsey sets and non-Lebesgue measurable sets. In [4, Problem 11.14], the authors ask whether such a connection holds with non-Baire sets as well. In this paper we answer such a question showing that several versions of Pareto principles acting on different utility domains imply the existence of non-Baire sets. Furthermore, we analyze in more details the needed fragments of AC and we start a systematic investigation of a social welfare diagram in a similar fashion done in the past decades concerning cardinal invariants and regularity properties of the reals. In doing that we use tools from forcing theory, such as specific tree-forcings (in particular variants of Silver and Mathias forcings) and Shelah's amalgamation.     

Geometric Design of Anode-Supported Micro-Tubular Solid Oxide Fuel Cells by Multiphysics Simulations

High volumetric power density (VPD) is the basis for the commercial success of micro-tubular solid oxide fuel cells (mtSOFCs). To find maximal VPD (MVPD) for anode-supported mtSOFC (as-mtSOFC), the effects of geometric parameters on VPD are analyzed and the anode thickness, t_an, and the cathode length, l_ca, are identified as the key design parameters. Thermo-fluid electrochemical models were built to examine the dependence of the electrical output on the cell parameters. The multiphysics model is validated by reproducing the experimental I-V curves with no adjustable parameters. The optimal l_ca and the corresponding MVPDs are then determined by the multiphysics model for 20 combinations of r_in, the inner tube radius, and t_an. And all these optimization are made at 1073.15 K. The results show that:(i) significant performance improvement may be achieved by geometry optimization, (ii) the seemingly high MVPD of 11 and 14 W/cm³ can be easily realized for as-mtSOFC with single-and double-terminal anode current collection, respectively. Moreover, the variation of the area specific power density with l_ca2(2 mm, 40 mm) is determined for three representative (r_in, t_an) combinations. Besides, it is demonstrated that the current output of mtSOFC with proper geometric parameters is comparable to that of planar SOFC.     

Preparation,Thermal Behaviour,and Crystal Structure of MgAl<Subscript>2</Subscript>F<Subscript>8</Subscript>(H<Subscript>2</Subscript>O)<Subscript>2</Subscript>

Summary.  Single crystals of MgAl₂F₈(H₂O)₂ have been obtained under hydrothermal conditions (250°C, 14 d) from a starting mixture of AlF₃ and MgAlF₅(H₂O)₂ in a 5% (w/w) HF solution. The crystal structure has been determined and refined from single crystal data (Fmmm (#69), Z = 4, a = 7.2691(7), b = 7.0954(16), c = 12.452(2) ?, 281 structure factors, 27 parameters, R(F ² > 2σ (F ²)) = 0.0282, wR(F ² all) = 0.0885). The obtained crystals were systematically twinned according to (010/100/001) as twinning matrix, reflecting the pseudo-tetragonal metric. The crystal structure is composed of perowskite-type layers built of corner sharing AlF₆ octahedra with an overall composition of AlF₄ ⁻ which are connected via common fluorine atoms of [MgF_4/2(H₂O)_2/1] octahedra. Group-subgroup relations of MgAl₂F₈(H₂O)₂ to WO₃(H₂O)_0.33 and to other M(II)M(III)₂ F₈(H₂O)₂ structures are briefly discussed. Above 570°C, MgAl₂F₈(H₂O)₂ decomposes under elimination of water into α-AlF₃, β-AlF₃, and MgF₂. Received October 29, 2001. Accepted (revised) December 6, 2001     

Parameter testing in bounded degree graphs of subexponential growth

Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well‐known that graph parameters such as the independence ratio or the edit‐distance from 3‐colorability are not testable in bounded degree graphs. We prove, however, that these and several other interesting graph parameters are testable in bounded degree graphs of subexponential growth. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Two linear transformations each tridiagonal with respect to an eigenbasis of the other

Let denote a field, and let V denote a vector space over with finite positive dimension. We consider a pair of linear transformations A:V→V and A^*:V→V satisfying both conditions below:

1. [(i)] There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A^* is irreducible tridiagonal.

2. [(ii)] There exists a basis for V with respect to which the matrix representing A^* is diagonal and the matrix representing A is irreducible tridiagonal.

We call such a pair a Leonard pair on V. Refining this notion a bit, we introduce the concept of a Leonard system. We give a complete classification of Leonard systems. Integral to our proof is the following result. We show that for any Leonard pair A,A^* on V, there exists a sequence of scalars β,γ,γ^*,,^* taken from such that both

where [r,s] means rs−sr. The sequence is uniquely determined by the Leonard pair if the dimension of V is at least 4. We conclude by showing how Leonard systems correspond to q-Racah and related polynomials from the Askey scheme.     

Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics

The generalized Gibbs free energy and enthalpy are derived in the framework of nonextensive thermodynamics by using the concept of the physical temperature and the physical pressure. Some relations of the thermodynamical potentials are changed due to the difference between the physical temperature and the inverse of Lagrange multiplier. We derive the thermodynamical relation between the heat capacities at a constant volume and at a constant pressure using the generalized thermodynamical potential. We find that it has a different form from the traditional one in Gibbs thermodynamics. But, the expressions of the heat capacities in this framework using the generalized thermodynamical potentials are still the same as the traditional one.