関: polynomial

WordNet

(genetics) the process of expressing a gene
the feelings expressed on a persons face; "a sad expression"; "a look of triumph"; "an angry face" (同)look, aspect, facial_expression, face
the act of forcing something out by squeezing or pressing; "the expression of milk from her breast"
expression without words; "tears are an expression of grief"; "the pulse is a reflection of the hearts condition" (同)manifestation, reflection, reflexion
the communication (in speech or writing) of your beliefs or opinions; "expressions of good will"; "he helped me find verbal expression for my ideas"; "the idea was immediate but the verbalism took hours" (同)verbal expression, verbalism
having the character of a polynomial; "a polynomial expression" (同)multinomial
a mathematical function that is the sum of a number of terms (同)multinomial

PrepTutorEJDIC

〈U〉〈C〉(思想・意見・考えなどを)『言葉で表すこと』,(…の)『表現』《+『of』+『名』》 / 〈C〉(考え・気持ちなどの)『現れ』,印《+『of』+『名』》 / 〈C〉(考え・気持ちなどを表す)『顔つき』,表情《+『of』+『名』》 / 〈U〉(考え・気持ちなどを表す)声の調子 / 〈C〉語句,言い回し,表現法 / 〈C〉(数量・運算などを示す)式
（数学）多項式（の）・（生物）多名（の）

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/01/16 05:31:03」(JST)

wiki en

In mathematics, and in particular in the field of algebra, a polynomial expression in one or more given entities E₁, E₂, ..., is any meaningful expression constructed from copies of those entities together with constants, using the operations of addition and multiplication. For each entity E, multiple copies can be used, and it is customary to write the product E×E×...×E of some number n of identical copies of E as Eⁿ; thus the operation of raising to a constant natural number power may also be used (as abbreviation) in a polynomial expression. Similarly, subtraction X – Y may be used to abbreviate X + (–1)×Y.

The entities used may be of various natures. They are usually not explicitly given values, since then the polynomial expression can just be evaluated to another such value. Often they are symbols such as "x", "λ" or "X", which according to the context may stand for an unknown quantity, a mathematical variable, a parameter, or an indeterminate, and in such cases the polynomial expression is just a polynomial. It is however also possible to form polynomial expressions in more complicated entities than just symbols. Here are examples of such uses of polynomial expressions.

The entities may be themselves expressions, not necessarily polynomial ones. For instance, it is possible to use the de Moivre's identity for any integer n to express cos(nx) as a polynomial expression in (the entity) cos(x), as in cos(3x) = 4 cos(x)³ − 3 cos(x). Here it would be incorrect to call the right hand side a polynomial.
The entities may be matrices; for instance the Cayley–Hamilton theorem applied to a matrix A equates a certain polynomial expression in A to the null matrix.
The entries may be "somewhat unknown" quantities without being completely free variables. For instance, for any monic polynomial of degree n that has n roots, Viète's formulas express its coefficients as (symmetric) polynomial expressions in those roots. This means that the relations expressed by those formulas exist independently of the choice of such a polynomial; therefore the n roots are not known values (as they would be if the polynomial were fixed), but they are not variables or indeterminates either.

References[edit]

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. 早産児のための搾乳 breast milk expression for the preterm infant
2. 遺伝学およびゲノミクスのためのツール：遺伝子発現 tools for genetics and genomics gene expression
3. 急性心臓同種移植拒絶反応：診断 acute cardiac allograft rejection diagnosis
4. 原発不明の低分化腫瘍 poorly differentiated neoplasms of unknown primary site
5. びまん性大細胞型B細胞性リンパ腫および原発性縦隔大細胞型B細胞リンパ腫の病理学 pathobiology of diffuse large b cell lymphoma and primary mediastinal large b cell lymphoma

English Journal

GlobalMIT: learning globally optimal dynamic bayesian network with the mutual information test criterion.

Vinh NX, Chetty M, Coppel R, Wangikar PP.SourceGippsland School of Information Technology, Faculty of IT, Monash University, Department of Microbiology, Faculty of Medicine, Nursing and Health Sciences, Monash University, Victoria, Australia and Department of Chemical Engineering, Indian Institute of Technology, Bombay, India.
Bioinformatics (Oxford, England).Bioinformatics.2011 Oct 1;27(19):2765-6. Epub 2011 Aug 3.
MOTIVATION: Dynamic Bayesian networks (DBN) are widely applied in modeling various biological networks including the gene regulatory network (GRN). Due to the NP-hard nature of learning static Bayesian network structure, most methods for learning DBN also employ either local search such as hill clim
PMID 21813478

Microarray gene expression: A study of between-platform association of Affymetrix and cDNA arrays.

Sarmah CK, Samarasinghe S.SourceCentre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand.
Computers in biology and medicine.Comput Biol Med.2011 Oct;41(10):980-6. Epub 2011 Sep 13.
Microarrays technology has been expanding remarkably since its launch about 15 years ago. With its advancement along with the increase of popularity, the technology affords the luxury that gene expressions can be measured in any of its multiple platforms. However, the generated results from the micr
PMID 21917247

Japanese Journal

数式処理システムを利用した表現様式の変換能力の育成 : 多項式を分類する活動を通して

廣野尚敏
数学教育学会誌 50(3), 91-98, 2010-09-25
NAID 10027455276

うねりのある面上におけるミリ波マルチパス受信強度の漸近近似計算法

井原俊夫,関健二
電子情報通信学会技術研究報告. A・P, アンテナ・伝播 110(196), 27-32, 2010-09-02
本稿では、うねりのある面上におけるミリ波帯マルチパス受信強度の漸近近似計算に関する初期的研究結果を報告する。まず、物理光学近似に基づき受信強度の積分表現を導く。さらに、その被積分関数に現れる位相関数が4次式で近似できる場合について、ピアシー積分を用いて0次の漸近表現を導く。導いた漸近法の特性について59.5GHzで数値的検討を行い、幾何光学法による計算結果が物理光学法とかなりの不一致を示すような場 …
NAID 110008107101