• Title/Summary/Keyword: real algebraic variety

Search Result 6, Processing Time 0.021 seconds

REAL ROOT ISOLATION OF ZERO-DIMENSIONAL PIECEWISE ALGEBRAIC VARIETY

  • Wu, Jin-Ming;Zhang, Xiao-Lei
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.1_2
    • /
    • pp.135-143
    • /
    • 2011
  • As a zero set of some multivariate splines, the piecewise algebraic variety is a kind of generalization of the classical algebraic variety. This paper presents an algorithm for isolating real roots of the zero-dimensional piecewise algebraic variety which is based on interval evaluation and the interval zeros of univariate interval polynomials in Bernstein form. An example is provided to show the proposed algorithm is effective.

EQUIVARIANT ALGEBRAIC APPROXIMATIONS OF G MAPS

  • Suh, Dong-Youp
    • Communications of the Korean Mathematical Society
    • /
    • v.10 no.4
    • /
    • pp.949-961
    • /
    • 1995
  • Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

  • PDF

Homotopical triviality of entire rational maps to even dimensional spheres

  • Suh, Dong-Youp
    • Communications of the Korean Mathematical Society
    • /
    • v.11 no.3
    • /
    • pp.807-814
    • /
    • 1996
  • Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

  • PDF

A Study on Formation of the Process-Object Perspective of Function Using Excel to Specialized High School Math Underachievers (특성화 고등학교 수학부진 학생들의 엑셀을 활용한 함수의 과정-대상 관점 형성에 대한 연구)

  • Choi, Jiyeon;Heo, Hye Ja
    • Journal of Educational Research in Mathematics
    • /
    • v.23 no.2
    • /
    • pp.213-235
    • /
    • 2013
  • The purpose of this study is to analyze how the teaching activities which used EXCEL influence the specialized high school underachieved students. They have difficulties in making use of various representations for better understanding of function. EXCEL is helpful for learning function because it enables the students to use real life materials in math learning as well as formulates Tabular, Algebraic and Graphical which represent function. Furthermore, the students in specialized high school also have the experience of using EXCEL while studying other subjects. For that reason they have no burdens and fears on using EXCEL in learning activities. Utilizing EXCEL in the classroom gives an expectation that it helps to have interests on studying function and prepare for the next learning in the end. Research classes were conducted in a group of five students who have different hopes of career and a variety of mathematical interests. Though the students couldn't transfer Algebraic to Graphical in the diagnostic evaluation, they could resolve the problem of connections between Graphical, Tabular and Algebraic in the process perspectives, and could also express graphical representation by linking object perspectives with process perspectives. Therefore, they solved the connection problem of Tabular, Algebraic and Graphical in the object perspectives. As a result, the students could make transitions between Algebraic and Graphical in object perspectives through the classes applying EXCEL. Consequently, teaching the students with underachievement utilizing EXCEL enables them to recover their interests on math and it helps them to complete their following curriculum.

  • PDF

A Study on the Optimization Problem Solving utilizing the Quadratic Curve using the Dynamic Geometry Software (동적기하프로그램을 활용한 이차곡선 최적화 문제해결에 관한 연구)

  • Kim, Jung Soo;Jeon, Bo Hyun;Chung, Young Woo;Kim, Boo Yoon;Lee, Yan
    • East Asian mathematical journal
    • /
    • v.30 no.2
    • /
    • pp.149-172
    • /
    • 2014
  • The problems of optimization addressed in the high school curriculum are usually posed in real-life contexts. However, because of the instructional purposes, problems are artificially constructed to suit computation, rather than to reflect real-life problems. Those problems have thus limited use for teaching 'practicalities', which is one of the goals of mathematics education. This study, by utilizing 'GeoGebra', suggests the optimization problem solving related to the quadratic curve, using the contour-line method which contemplates the quadratic curve changes successively. By considering more realistic situations to supplement the limit which deals only with numerical and algebraic approach, this attempt will help students to be aware of the usefulness of mathematics, and to develop interests in mathematics, as well as foster students' integrated thinking abilities across units. And this allows students to experience a variety of math.

Multi-Vector Document Embedding Using Semantic Decomposition of Complex Documents (복합 문서의 의미적 분해를 통한 다중 벡터 문서 임베딩 방법론)

  • Park, Jongin;Kim, Namgyu
    • Journal of Intelligence and Information Systems
    • /
    • v.25 no.3
    • /
    • pp.19-41
    • /
    • 2019
  • According to the rapidly increasing demand for text data analysis, research and investment in text mining are being actively conducted not only in academia but also in various industries. Text mining is generally conducted in two steps. In the first step, the text of the collected document is tokenized and structured to convert the original document into a computer-readable form. In the second step, tasks such as document classification, clustering, and topic modeling are conducted according to the purpose of analysis. Until recently, text mining-related studies have been focused on the application of the second steps, such as document classification, clustering, and topic modeling. However, with the discovery that the text structuring process substantially influences the quality of the analysis results, various embedding methods have actively been studied to improve the quality of analysis results by preserving the meaning of words and documents in the process of representing text data as vectors. Unlike structured data, which can be directly applied to a variety of operations and traditional analysis techniques, Unstructured text should be preceded by a structuring task that transforms the original document into a form that the computer can understand before analysis. It is called "Embedding" that arbitrary objects are mapped to a specific dimension space while maintaining algebraic properties for structuring the text data. Recently, attempts have been made to embed not only words but also sentences, paragraphs, and entire documents in various aspects. Particularly, with the demand for analysis of document embedding increases rapidly, many algorithms have been developed to support it. Among them, doc2Vec which extends word2Vec and embeds each document into one vector is most widely used. However, the traditional document embedding method represented by doc2Vec generates a vector for each document using the whole corpus included in the document. This causes a limit that the document vector is affected by not only core words but also miscellaneous words. Additionally, the traditional document embedding schemes usually map each document into a single corresponding vector. Therefore, it is difficult to represent a complex document with multiple subjects into a single vector accurately using the traditional approach. In this paper, we propose a new multi-vector document embedding method to overcome these limitations of the traditional document embedding methods. This study targets documents that explicitly separate body content and keywords. In the case of a document without keywords, this method can be applied after extract keywords through various analysis methods. However, since this is not the core subject of the proposed method, we introduce the process of applying the proposed method to documents that predefine keywords in the text. The proposed method consists of (1) Parsing, (2) Word Embedding, (3) Keyword Vector Extraction, (4) Keyword Clustering, and (5) Multiple-Vector Generation. The specific process is as follows. all text in a document is tokenized and each token is represented as a vector having N-dimensional real value through word embedding. After that, to overcome the limitations of the traditional document embedding method that is affected by not only the core word but also the miscellaneous words, vectors corresponding to the keywords of each document are extracted and make up sets of keyword vector for each document. Next, clustering is conducted on a set of keywords for each document to identify multiple subjects included in the document. Finally, a Multi-vector is generated from vectors of keywords constituting each cluster. The experiments for 3.147 academic papers revealed that the single vector-based traditional approach cannot properly map complex documents because of interference among subjects in each vector. With the proposed multi-vector based method, we ascertained that complex documents can be vectorized more accurately by eliminating the interference among subjects.