CONSTRUCTIVE KISSING NUMBERS IN HIGH-DIMENSIONAL SPACES

In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of the Gilbert-Varshamov bound in coding theory, we construct a spherical code sequence in exponential time which meets the best-known asymptotic bound by Shamsiev and Wyner.     

Philosophy of chemistry and the image of science

The philosophical analysis of chemistry has advanced at such a pace during the last dozen years that the existence of philosophy of chemistry as an autonomous discipline cannot be doubted any more. The present paper will attempt to analyse the experience of philosophy of chemistry at the, so to say, meta-level. Philosophers of chemistry have especially stressed that all sciences need not be similar to physics. They have tried to argue for chemistry as its own type of science and for a pluralistic understanding of science in general. However, when stressing the specific character of chemistry, philosophers do not always analyse the question ‘What is science?’ theoretically. It is obvious that a ‘monistic’ understanding of science should not be based simply on physics as the epitome of science, regarding it as a historical accident that physics has obtained this status. The author’s point is that the philosophical and methodological image of science should not be chosen arbitrarily; instead, it should be theoretically elaborated as an idealization (theoretical model) substantiated on the historical practice of science. It is argued that although physics has, in a sense, justifiably obtained the status of a paradigm of science, chemistry, which is not simply a physical science, but a discipline with a dual character, is also relevant for elaborating a theoretical model of science. The theoretical model of science is a good tool for examining various issues in philosophy of chemistry as well as in philosophy of science or science studies generally.     

Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling

It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.     

A non-commutative time-frequency tomography

The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).     

Conflict Pattern Analysis: Preparing the Ground for Participation in Policy Implementation

The participation of non-state actors in implementation processes is often understood as a means to increase compliance efficiency. But the implementation of spatial policies frequently focuses on pre-established goals, processes and instruments and thus renders difficult open discourse and shared decision-making. This paper introduces conflict pattern analysis (CPA) as a tool that supports the analysis of the actual actor constellation in order to define efficient approaches that avoid common problems of participatory processes. CPA is a semi-formalised method that helps to identify key-actors, their relations and interaction amongst each other as well as their core beliefs, interests and resources. It aggregates this information to interaction patterns that can be compared, classified and linked to different participatory methods on a theoretically informed basis. Particularly on the local and regional level, this could be the first step for successful (participatory) implementation strategies.     

ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.     

A theoretical model for mid-and low-latitude ionospheric electric fields in realistic geomagnetic fields

The geomagnetic fields, which play important roles in the ionospheric dynamo, can greatly affect the global distribution of ionospheric electric fields, currents and other ionospheric electrodynamics phenomena. In the study of ionospheric electrodynamics phenomena, such as the longitudinal variations of ionospheric electric fields, the non-dipolar component of the geomagnetic fields must be taken into account. In this paper, we deduce a theoretical electric field model for ionospheric dynamo at mid- and low-latitude which adopt a modified magnetic apex coordinates system. In the new electric field model, the geomagnetic fields can be calculated from either the IGRF model or the dipole field model, and the neutral winds and conductivities are calculated based on empirical models. Then the dynamo equation for the electric potential is finally solved in terms of the line-by-line iteration method, and the ionospheric electric fields and currents are derived from the calculated potential. Our model can reproduce the main features of the ionospheric electrodynamics processes, so it will be a useful tool for the investigation of the upper atmosphere and ionosphere.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Regulation of cellulose synthesis in Acetobacter xylinum by cyclic diguanylic acid

Cellulose is the most abundant renewable carbon resource on earth and is an indispensable raw material for the wood, paper, and textile industries. A model system to study the mechanism of cellulose biogenesis is the bacterium Acetobacter xylinum which produces pure cellulose as an extracellular product. It was from this organism that in vitro preparations which possessed high levels of cellulose synthase activity were first obtained in both membranous and soluble forms. We recently demonstrated that this activity is subject to a complex multi-component regulatory system, in which the synthase is directly affected by an unusual cyclic nucleotide activator enzymatically formed from GTP, and indirectly by a Ca (2+) -sensitive phosphodiesterase which degrades the activator. The cellulose synthase activator (CSA) has now been identified as bis-(3' 5')-cyclic diguanylic acid (5'G3'p5'G3'p) on the basis of mass spectroscopic data, nuclear magnetic resonance analysis and comparison with chemically synthesized material. We also report here on intermediary steps in the synthesis and degradation of this novel circular dinucleotide, which have been integrated into a model for the regulation of cellulose synthesis.