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近似代数とは、従来の代数演算に摂動項を加え、摂動項がある一定範囲内で変動することを許容しつつ、所与の演算を行うことである。1980年代の末に本研究代表者らが世界に先駆けて提案した概念で、数式処理の ...研究代表者: 佐々木建昭研究課題番号: 0930800

セケン ニ フリ マワサレズ キホン ニ タチ カエロウ トクシュウ ２０１０ネン ノ ツクバ ダイガク ノ キョウイク オ カンガエル

現在、学校(小･中･高)は我儘な児童･生徒に振り回され、大学は自立できない学生･院生に振り回され、教育全体が社会に振り回されている。学生を甘やかす施策は止めて、努力し勉強しようとする学生を伸ばす施策に切り替え、再度を簡素化しよう。学生には信賞必罰で対処して自立を促すべきだが、その為には世間に胸の張れる教育と研究を行う必要がある。 ..

An Attempt to Enhance Buchberger's Algorithm by Using Remainder Sequences and GCDs (II) (Computer Algebra - Theory and its Applications)

Let F = {F, , ..., Fm+1} ⊂ ℚ[x, u] be a given system, where m+l 2: 3, (x) = (x, , ..., xm) and (u) = (u, , ...，叫）， with ∀xi >-- ∀uj. Let GB(F) = {G₁, G₂, ・・・}, with G₁ --< G₂ --< ・・・, be the reduced Grabner basis of F w.r.t. the lexicographic order. In a previous paper [10], one of the authors proposed a method of enhancing Buchberger's algorithm for computing GB(F). His idea_is to compute a set g':= {G1 , G2, ... } ⊂ ℚ[x, u], such that each Gi is either O or as mall multiple of Gi, and apply Buchberger's algorithm to F ∨ g'. He proposed a scheme of computing G₁, G₂, ... by the PRSs (polynomial remainder sequences) and the GCDs in "G₁ ⇒ G₂ ⇒ ・・・" order, without computing Spolynomials. The scheme is supported by two new useful theorems and one proposition to remove the extraneous factor. In fact, for a simple but never toy example, his scheme has computed G₁ successfully (G₁ became G₁ by the proposition mentioned above). However, an unexpected difficulty occurred in computing G₂; it contained a pretty large extraneous factor which was not removed by the proposition. In this paper, we find a surprising phenomenon with which we can remove the above mentioned extraneous factor in G₂ and obtain G₂. As for G₃ and G₄, we obtain very good "body doubles" of them, by eliminating variables in leading coefficients of intermediate remainders of the PRSs computed for G₁. For systems of many sub-variables, n ≥ 3, our method introduces an extra factor in ℚ[u3, ..，un]， into the "LCto W" polynomial; see the text for the LCtoW polynomial. Furthermore, we present several techniques to enhance the computation

On Checking Products of Modular Factors in Berlekamp-Hensel Type Factorization *

Abstract This article tests empirically two &quot;dirty tricks&quot; for the trial-division step of BerlekampHensel type algorithm for the univariate polynomial factorization over Z. The tricks are 1) divisibility check of the constant term and 2) boundedness check of the second coefficient. So far, it has been said that 1) is quite effective but 2) is not so effective. However, defining the upper bound of the second coefficient suitably, we show by many examples that the trick 2) is also quite effective for polynomials of medium and large degrees, such as degree ≥ 15

Expression of ECM proteins fibulin-1 and -2 in acute and chronic liver disease and in cultured rat liver cells

Fibulin-2 has previously been considered as a marker to distinguish rat liver myofibroblasts from hepatic stellate cells. The function of other fibulins in acute or chronic liver damage has not yet been investigated. The aim of this study has been to evaluate the expression of fibulin-1 and -2 in models of rat liver injury and in human liver cirrhosis. Their cellular sources have also been investigated. In normal rat liver, fibulin-1 and -2 were both mainly present in the portal field. Fibulin-1-coding transcripts were detected in total RNA of normal rat liver, whereas fibulin-2 mRNA was only detected by sensitive, real-time quantitative polymerase chain reaction. In acute liver injury, the expression of fibulin-1 was significantly increased (17.23-fold after 48 h), whereas that of fibulin-2 was not modified. The expression of both fibulin-1 and -2 was increased in experimental rat liver cirrhosis (19.16- and 26.47-fold, respectively). At the cellular level, fibulin-1 was detectable in hepatocytes, “activated” hepatic stellate cells, and liver myofibroblasts (2.71-, 122.65-, and 469.48-fold over the expression in normal rat liver), whereas fibulin-2 was restricted to liver myofibroblasts and was regulated by transforming growth factor beta-1 (TGF-β1) in 2-day-old hepatocyte cultures and in liver myofibroblasts. Thus, fibulin-1 and -2 respond differentially to single and repeated damaging noxae, and their expression is differently present in liver cells. Expression of the fibulin-2 gene is regulated by TGF-β1 in liver myofibroblasts

A Computer Study of Electron-Electron Interaction in high Density Electron Beams

High density electron beams are simulated by a computer, and the trajectory displacement and energy broadening caused by electron-electron interaction are investigated computationally. The results are summarized into two empirical formulas which represent dependences of the average trajectory displacement and the average energy broadening on the beam parameters. The results show that the trajectory displacement caused by electron-electron interaction imposes a severe problem on system designers using high density beams, and that energy broadening on the order of 1eV may well be attributed to electron-electron interaction. The method of simulation is also described