668 research outputs found

    Irreducibility criterion for algebroid curves

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    The purpose of this paper is to give an algorithm for deciding the irreducibility of reduced algebroid curves over an algebraically closed field of arbitrary characteristic. To do this, we introduce a new notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and then give irreducibility criterion for algebroid curves in terms local tropical varieties. We also give an algorithm for computing the value-semigroups of irreducible algebroid curves. Combining the irreducibility criterion and the algorithm for computing the value-semigroups, we obtain an algorithm for deciding the irreducibility of algebroid curves.Comment: 20 pages, v3: major revisio

    One-dimensional rings of finite F-representation type

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    We prove that a complete local or graded one-dimensional domain of prime characteristic has finite F-representation type if its residue field is algebraically closed or finite, and present examples of a complete local or graded one-dimensional domain which does not have finite F-representation type with a perfect residue field. We also present some examples of higher dimensional rings of finite F-representation type.Comment: 8 pages, title changed and typos correcte

    Toric ideals for high Veronese subrings of toric algebras

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    We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gr\"obner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gr\"obner basis. We give a lower bound on dd such that the defining ideal of dd-th Veronese subring admits a quadratic Gr\"obner basis. Eisenbud--Reeves--Totaro stated the same theorem without a proof with some lower bound on dd. In many cases, our lower bound is less than Eisenbud--Reeves--Totaro's lower bound.Comment: 9 pages, v2: Observation 3.16 added and typos corrected, v3: typos correcte

    Algorithms for computing multiplier ideals

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    We give algorithms for computing multiplier ideals using Gr\"obner bases in Weyl algebras. The algorithms are based on a newly introduced notion which is a variant of Budur--Musta\c{t}\v{a}--Saito's (generalized) Bernstein--Sato polynomial. We present several examples computed by our algorithms.Comment: 23 pages, title changed, Theorem 4.5 added, typos corrected, and some minor revisions (some notation changed, and Definition 2.1, Proposition 2.11, Observation 3.1, and Observation 4.2 added

    Sensitivity Analysis and its Application to the Control of Inner Furnace Temperature Distribution

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    Nowadays, various kind of reactor furnaces are widely used for the production in industry. The raw materials charged into the furnace generate reaction heat produced by blowing gas. Generally speaking, the reaction heat generated in the furnace is remarkably high. Therefore the occurrence of an inappropriate temperature distribution in the furnace may make damege or serious accident of the furnace. This is the motivation of furnace control. The author is considering the application of studied results to the furnace control of Blast Furnace in steel industry. To the propose, the approximated and simplified Macro Model of the Blast Furnace is constructed which has the function of representation of qualitative characteristics of the furnace in dynamical sense. The furnace temperature, distribution greatly effects both on the producting and the product quality of the furnace. Needless to say, stable furnace operation is indispensable for the economical prosperity of the industry. In this paper, macro simulation of the furnace is developed to support the analysis and design of the furnace control. Using the simulator, the stability and the control characteristics for inner furnace temperature distribtion are analised quantitatively
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