A MINI MULTI-GAS DETECTION SYSTEM BASED ON INFRARED PRINCIPLE

To counter the problems of gas accidents in coal mines, family safety resulted from using gas, a new infrared detection system with integration and miniaturization has been developed. The infrared detection optics principle used in developing this system is mainly analyzed. The idea that multi gas detection is introduced and guided through analyzing single gas detection is got across. Through researching the design of cell structure, the cell with integration and miniaturization has been devised. The way of data transmission on Controller Area Network (CAN) bus is explained. By taking Single-Chip Microcomputer (SCM) as intelligence handling, the functional block diagram of gas detection system is designed with its hardware and software system analyzed and devised. This system designed has reached the technology requirement of lower power consumption, mini-volume, big measure range, and able to realize multi-gas detection.     

Beyond Cartesian limits: Leibniz's passage from algebraic to “transcendental” mathematics

This article deals with Leibniz's reception of Descartes' “geometry.” Leibnizian mathematics was based on five fundamental notions: calculus, characteristic, art of invention, method, and freedom. On the basis of methodological considerations Leibniz criticized Descartes' restriction of geometry to objects that could be given in terms of algebraic (i.e., finite) equations: “Descartes's mind was the limit of science.” The failure of algebra to solve equations of higher degree led Leibniz to develop linear algebra, and the failure of algebra to deal with transcendental problems led him to conceive of a science of the infinite. Hence Leibniz reconstructed the mathematical corpus, created new (transcendental) notions, and redefined known notions (equality, exactness, construction), thus establishing “a veritable complement of algebra for the transcendentals”: infinite equations, i.e., infinite series, became inestimable tools of mathematical research.     

A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

Complete systems, elementary submodels and the tightness of upper hyperspaces

We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.     

Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see [Gir1], [Gir2], [Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in [Gir1], [Gir2], [Dan], [Ret] and [Tro].     

On the existence of nontrivial extremal metrics on complete noncompact surfaces

In this paper, we consider the 2-dimensional local Calabi flow on a complete noncompact surface . Then, based on the Harnack-type estimate, we show the long-time existence and asymptotic convergence of a subsequence of solutions of such a flow on with and bounded from above by a negative constant on a ball. For its applications, this will lead to the existence of extremal metrics on a complete noncompact surface of finite topological type. In particular, there exists an extremal metric of nonconstant Gaussian curvature on or Received: 21 June 2001 / 18 January 2002 / Published online: 27 June 2002 Research supported in part by NSC and NCTS.     

Random orderings of the integers and card shuffling

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.     

Induction and foundation in the theory of hereditarily finite sets

The paper contains an axiomatic treatment of the intuitionistic theory of hereditarily finite sets, based on an induction axiom-schema and a finite set of single axioms. The main feature of the principle of induction used (due to Givant and Tarski) is that it incorporates Foundation. On the analogy of what is done in Arithmetic, in the axiomatic system selected the transitive closure of the membership relation is taken as a primitive notion, so as to permit an immediate adaptation of the theory to cases of restricted induction (in particular primitive recursive induction). At the end of the paper several different forms of induction, which play an important role in the development of the theory, are compared. An alternative axiomatization of the theory, which is of intrinsic interest, is also discussed.