Search results for "Operation"

Upper and lower generalized factoraggregations based on fuzzy equivalence relation

2014

We develop the concept of a general factoraggre-gation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. By using a left-continuous t-norm and its residuum we define and investigate two modifications of such generalized construction: upper and lower generalized factoraggregations. These generalized factoraggregations can be used for construction of extensional fuzzy sets.

Lambda substitution algebras

1993

In the paper an algebraic metatheory of type-free λ-calculus is developed. Our version is based on lambda substitution algebras (λSAs), which are just SAs introduced by Feldman (for algebraizing equational logic) enriched with a countable family of unary operations of λ-abstraction and a binary operation of application. Two representation theorems, syntactical and semantic, are proved, what directly provides completeness theorems.

The Dynamical Problem for a Non Self-adjoint Hamiltonian

2012

After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrodinger and Heisenberg representations.

Fibred Categories and the Six Functors Formalism

2019

In Section 1, we introduce the basic language used in this book, the so-called premotivic categories and their functoriality. This is an extension of the classical notion of fibered categories. They appear with different categorical structures. In Section2, the language of premotivic categories is specialized to that of triangulated categories and to algebraic geometry. We introduce several axioms of such categories which ultimately will lead to the full six functors formalism. An emphasis is given on the study of the main axioms, with a special care about the so-called localization axiom. Then in Section 3, the general theory of descent is formulated in the language of premotivic model cat…

On Conditioning Operators

1999

The construction of conditional events (so-called measure-free conditioning) has a long history and is one of the fundamental problems in non-deterministic system theory (cf. [6]). In particular, the iteration of measure-free conditioning is still an open problem. The present paper tries to make a contribution to this question. In particular, we give an axiomatic introduction of conditioning operators which act as binary operations on the universe of events. The corresponding axiom system of this type of operators focus special attention on the intuitive understanding that the event ‘α given β’ is somewhere in “between” ‘α and β’ and ‘β implies α’. A detailed motivation of these axioms can …

1988

Deviations in the determination of the unperturbed dimensions of polymers arising in ternary polymer systems (solvent (1)/solvent (2)/polymer) can be explained by the inaccurate use of an interaction parameter independent of polymer molecular weight. On this basis, a new formalism for the calculation of the second virial coefficient from intrinsic viscosity is proposed. This formalism was tested (and compared with well established formalisms) for all ternary polymer systems with simultaneous intrinsic viscosity and second virial coefficient data in the literature.

1987

The intrinsic viscosities, [η], for the ternary systems alkane (1)/2-butanone (2)/poly(dimethylsiloxane) (PDMS)(3), with the alkanes decane, dodecane and hexadecane, are determined at 20,0°C. The constants a of the Mark-Houwink equation and the constant of the unperturbed dimensions, KΘ, of the polymer are evaluated over the whole composition range of the binary solvent mixture. [η] shows a pronounced maximum at intermediate compositions as found in cosolvent mixtures. In these cosolvent mixtures, the numerical values of KΘ are higher than in the single-component solvents, because the cosolvent mixtures correspond to a mixed solvent with an excess free energy, GE ≥ 0, the increase in KΘ bei…

Public Administration and the Study of Political Order: Towards a Framework for Analysis

2020

The contribution of this study is two-fold: First, it outlines a conceptual framework on political order; and secondly, it offers empirical illustrations on the case of Nordic cooperation. Taken together, the article makes a plea for public administration scholarship in the study of political order. Political order consists of a relatively stable arrangement of institutions that are fairly formalized and institutionalized. A common political order, moreover, entails that relevant institutions: (i) are fairly independent of pre-existing institutions; (ii) are relatively integrated and internally cohesive; and (iii) are reasonably able to influence governance processes within other institutio…

GRASP with exterior path-relinking and restricted local search for the multidimensional two-way number partitioning problem

2017

In this work, we tackle multidimensional two-way number partitioning (MDTWNP) problem by combining GRASP with Exterior Path Relinking. In the last few years, the combination of GRASP with path relinking (PR) has emerged as a highly effective tool for finding high-quality solutions for several difficult problems in reasonable computational time. However, in most of the cases, this hybridisation is limited to the variant known as interior PR. Here, we couple GRASP with the "exterior form" of path relinking and perform extensive experimentation to evaluate this variant. In addition, we enhance our GRASP with PR method with a novel local search method specially designed for the MDTWNP problem. …

Principal component analysis for the selection of variables in the application of the H-point and generalised H-point standard addition method

2000

The present paper deals with the selection of variables for the H-point and generalised H-point standard additions methods (HPSAM and GHPSAM, respectively). Both methods are applied for the resolution of spectroscopic interfered signals in the UV-vis range. The HPSAM is a suitable method for the resolution of binary and ternary mixtures when the interferent is known. The GHPSAM is applied for the resolution of samples that contain unknown interferents. In this paper, a method based on the study of a principal components analysis (PCA) for the selection of variables for the HPSAM and GHPSAM is proposed. The PCA results show the isolation of the analyte signal from the sample signal, achieved…