An integrated principle solution synthesis method in multi-disciplinary mechatronic product conceptual design

Synthesizing suitable principle solutions together to form the design solution is a universal method in conceptual design. For the modern mechatronic product, the conceptual design is often multi-disciplinary, which would be extremely time consuming and labour-intensive for designers to synthesize multi-disciplinary principle solutions together. Taking advantage of functional knowledge and structural knowledge of principle solution, this article proposes an integrated principle solution synthesis method which not only achieves the automated synthesis of multi-disciplinary principle solutions but also solves the undesired physical conflicts among principle solutions to be synthesized. In integrated principle solution synthesis, a synthesis agent is developed to chain the functional flows of principle solutions to form the combinatorial principle solution set, and synthesis agent selects the combinatorial principle solution with highest availability value as the recommended combinatorial principle solution. Then extensic theory is employed to deal with the partial design conflicts hidden in recommended combinatorial principle solution by extending and transforming the conflict functional structures. A case study on the emergency cutting off device design is given to prove the industrial applicability of integrated principle solution synthesis, which indicates that compared with traditional synthesis method, integrated principle solution synthesis can not only get multi-disciplinary design result of emergency cutting off device but also further resolve the design conflict (i.e. vibration impact) to optimize the functional structure of emergency cutting off device.

Combinatorial Principle in the Use of Drum (Kendhang) Formulae in Gamelan Music of Yogyakarta. From Prescriptive Models to the Interpretation of a Composition: the Case of Kendhang Pinatut.

In this paper, I address the question to the use of drums (kendhang) in the traditional Gamelan music of Yogyakarta, by presenting some prescriptive models (or formulas). I illustrate how, the use of different prescriptive models in a composition follow what I labeled as “Combinatorial Principle”. In order to describe the essential elements of this principle, I will analyze the modalities of interaction between a very flexible drum formula (known as pinatut) and three other prescriptive models for drum within some exemplary pieces of traditional Gamelan music. The concept of combinatorial principle illustrated in these pages, on the one hand explains the way of interaction between the drum’s rhythmic formulas and their capacity to influence the choices made by the entire orchestra during a performance; on the other hand, through this principle we are able to trace a path that attempts to understand the “deep structures” that are the basics of making music in Gamelan tout court. Through the perspective of the combinatorial principle it is possible to analyze the prescriptive models and techniques of many other instruments of the Gamelan of central Java.

THE DEFINABILITY STRENGTH OF COMBINATORIAL PRINCIPLES

We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We prove that some consequences of Ramsey’s Theorem for colorings of pairs could help in simplifying the definitions of some ${\rm{\Delta }}_2^0$ sets, while some others could not. We also investigate some consequences of Ramsey’s Theorem for colorings of longer tuples. These results of definability strength have some interesting consequences in reverse mathematics, including strengthening of known theorems in a more uniform way and also new theorems.

ℵn-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL

A module M over a commutative ring R has an almost trivial dual if there is no homomorphism from M onto a free R-module of countable infinite rank. Using a new combinatorial principle (the ℵn-Black Box), which is provable in ordinary set theory, we show that for every natural number n, there exist arbitrarily large ℵn-free R-modules with almost trivial duals, when R is a complete discrete valuation domain. A corresponding result for torsion modules is also obtained.

□ on the singular cardinals

We give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen. Square on singular cardinals.

More on regular reduced products

The authors show, by means of a finitary version of the combinatorial principle of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ. if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ΠiMi/D and ΠiNi/D. If in addition 2λ = λ+ and i < λ implies |Mi| + |Ni| ≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].