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.     

硒化蓖麻酸多相脂质体抗癌机理研究

本文用小角ｘ射线射法法对硒化蓖麻酸多相脂质体的抗癌作用从结构和功能上进行了研究。     

滚齿切削厚度的计算

本文提出了滚齿时基面内切削厚度的计算方法．该方法可作为深入研究滚齿切削过程的理论基础．     

一个不动点的存在唯一性定理的反例

本文对现行泛函分析教材中的一个不动点的存在唯一性定理举出了一个反例,指出其唯一性不成立。     

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.     

“926”植物生长调节剂的经济效益与生态环境

简要评估了“９２６”植物生长调节剂的经济效益和生态环境。分析了开发应用的前景。