scholarly journals Minimal rational threefolds II

1988 ◽  
Vol 110 ◽  
pp. 15-80 ◽  
Author(s):  
Hiroshi Umemura
Keyword(s):  
Algebraic Operation ◽  
View Point ◽  
Algebraic Subgroup ◽  
Birational Morphism ◽  
Cremona Group ◽  
Algebraic Operations

The Enriques-Fano classification ([E.F], [F]) of the maximal connected algebraic subgroups of the three variable Cremona group, despite of its group theoretic feature, seems to be the most significant result on the rational threefolds so far known. In this paper as in [MU] we interpret the Enriques-Fano classification from a geometric view point, namely the geometry of minimal rational threefolds. We explained in [MU] the link between the two objects; the maximal algebraic subgroups and the minimal rational threefolds. Let (G, X) be a maximal algebraic subgroup of three variable Cremona group. We denote by ℓ(G, X) the set of all the algebraic operations (G, Y) such that Y is non-singular and projective and such that (G, Y) is isomorphic to (G, X) as law chunks of algebraic operation: namely (G, Y) is birationally equivalent to (G, X). Then we define an order in ℓ(G, X): for (G, Z), (G, W) ∊ ℓ(G, X), (G, Z)>(G, W) if there exists an G-equivariant birational morphism of Z onto W.

Algebraic subgroups of the plane Cremona group over a perfect field

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Julia Schneider ◽  
Susanna Zimmermann
Keyword(s):  
Rational Points ◽  
Perfect Field ◽  
Algebraic Subgroup ◽  
Cremona Group ◽  
Birational Map

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map.

scholarly journals Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yonghong Shen ◽  
Wei Chen
Keyword(s):  
Fuzzy Sets ◽  
General Framework ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Sets ◽  
Extension Principle ◽  
Algebraic Operation ◽  
Multivariate Extension ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations

This paper mainly focuses on multivariate extension of the extension principle of IFSs. Based on the Cartesian product over IFSs, the multivariate extension principle of IFSs is established. Furthermore, three kinds of representation of this principle are provided. Finally, a general framework of the algebraic operation between IFSs is given by using the multivariate extension principle.

scholarly journals DESKRIPSI KOMUNIKASI MATEMATIS SISWA SMP NEGERI 9 SALATIGA PADA MATERI OPERASI ALJABAR

2018 ◽  
Vol 1 (1) ◽  
pp. 77
Author(s):  
Sabrina Nur Annisa ◽  
Novisita Ratu
Keyword(s):  
Data Collection ◽  
Mathematical Thinking ◽  
Descriptive Study ◽  
Algebraic Operation ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Qualitative Descriptive ◽  
Class Viii ◽  
Algebraic Operations ◽  
Data Collection Technique

Abstrak: Penelitian ini merupakan penelitian deskriptif kualitatif yang bertujuan mendeskripsikan komunikasi matematis siswa SMP Negeri 9 Salatiga pada materi operasi aljabar. Subjek penelitian terdiri dari 3 siswa kelas VIII SMP Negeri 9 Salatiga. Teknik pengumpulan data menggunakan teknik tes, wawancara, dan dokumentasi. Hasil penelitian menunjukkan bahwa semua subjek mampu mengekspresikan dan mengorganisasikan ide-ide matematika serta berpikir matematis menggunakan bentuk lisan, visual, dan tulisan. Semua subjek mampu menggunakan simbol, kata-kata, istilah-istilah dalam bentuk lisan, visual, dan tulisan. Namun hanya subjek berkemampuan rendah yang belum mampu mengkomunikasikan kepada pendengar yang berbeda dan bertujuan untuk menyelesaikan soal operasi aljabar.Abstract: This research is qualitative descriptive study aimed to describe the mathematical communication students of SMP Negeri 9 Salatiga on algebraic operation material. Subject in this study consist of 3 students of class VIII SMP Negeri 9 Salatiga. The data collection technique using the technique of tests, interviews, and documentation. The results showed that all subjects were able to express and organize mathematical ideas and mathematical thinking using oral, visual, and written forms. All subjects were able to use symbols, words, terms in the form of oral, visual, and written. However, only low ability subjects that have not been able to communicate to different audiences and aims to solving algebraic operations.

scholarly journals Algebraic Operations on Delta-Sigma Bit-Streams

2018 ◽  
Vol 23 (3) ◽  
pp. 49
Author(s):  
Axel Klein ◽  
Walter Schumacher
Keyword(s):  
Digital Signal ◽  
Small Scale ◽  
Algebraic Operation ◽  
Output Stage ◽  
Delta Sigma ◽  
Algebraic Operations ◽  
Scale Integration ◽  
Nonlinear Operation ◽  
Bit Stream ◽  
Made In

Operations in the Delta-Sigma ( Δ Σ ) domain are a broad field of research. In this article the main, focus is on applications in control systems, nevertheless the results are generally applicable for dssp in other fields. As the bit-stream does not have an instantaneous value, algebraic operations cannot be executed directly. The first approaches were made in the 1980s based on small-scale integration logic chips by Kouvaras and by Lagoyannis. Further algebraic operations and other implementations were introduced by Zrilic, by Ng, by Bradshaw and by Homann. Other publications utilize complex networks and operations to achieve the desired algebraic operations. These presented operations can be divided into different operation classes by the based implementation idea. In this paper, the known algebraic operation classes are further developed and new operation classes are presented. All implementations are compared and evaluated. For linear operations in control applications, the introduced Bipolar Interpretation is best rated. It compensates for the signal offset of bipolar bit-streams and results in the best signal quality by mapping the logic values true and false of bit-stream to plus and minus one before the algebraic operation. The output of the algebraic operation is a multibit value, to achieve a bit-stream as output value a third step is taken. The result is modulated by a digital dsm. For nonlinear operations the most universal implementation is also based on three steps. In the first stage, the bit-streams are processed with short sinc 3 filters, resulting in multibit values. This signal is processed by digital signal processing (DSP). The output stage is a dsm. For some nonlinear algebraic operations there can be better solutions than DSP, like shown for limiting. In short, this paper gives a detailed overview about different dssp classes for linear and nonlinear operations. Newly presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on dsp, the modified multiplication based on Delta Adder and benchmarks of all presented operations.

Introduction to Eigenanalysis

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Data Analysis ◽  
Numerical Analysis ◽  
Dynamical Systems ◽  
Applied Mathematics ◽  
Algebraic Operation ◽  
Systems Modeling ◽  
Dynamical Systems Modeling ◽  
Algebraic Operations ◽  
Eigen Decomposition ◽  
Data Matrices

Eigenanalysis and its numerous offsprings form the suite of algebraic operations most important and relevant to data analysis, as well as to dynamical systems, modeling, numerical analysis, and related key branches of applied mathematics. This chapter introduces and places in a broader context the algebraic operation of eigen-decomposition. To have eigen-decomposition, a matrix must be square. Yet data matrices are very rarely square. The direct relevance of eigen-decomposition to data analysis is therefore limited. Indirectly, however, generalized eigenanalysis is enormously important to studying data matrices. Because of the centrality of generalized eigenanalysis to data matrices, and because those generalizations build, algebraically and logically, on eigenanalysis itself, it makes sense to discuss eigenanalysis at some length.

CHARACTERIZATION OF TERNARY ALGEBRAIC OPERATIONS OF IDEMPOTENT ALGEBRAS

2010 ◽  
Vol 20 (08) ◽  
pp. 991-999 ◽  
Author(s):  
J. PASHAZADEH ◽  
YU. MOVSISYAN
Keyword(s):  
Algebraic Operation ◽  
Fixed Element ◽  
Algebraic Operations

In this paper, we characterize the set of all ternary algebraic (or polynomial) operations of idempotent algebras that have at least one binary and one ternary algebraic operation depending on every variable, and there exists an integer r > 2 such that there is not any r-ary algebraic operation depending on every variable. We prove that this set forms a finite DeMorgan algebra with a fixed element and then we characterize this DeMorgan algebra.

scholarly journals STUDENTS’ CRITICAL THINKING IN DETERMINING COEFFICIENTS OF ALGEBRAIC FORMS

2020 ◽  
Vol 5 (1) ◽  
pp. 61-68
Author(s):  
Aci Maria Jehaut Putri ◽  
Yus Mochamad Cholily ◽  
Putri Ayu Kusgiarohmah
Keyword(s):  
Critical Thinking ◽  
Junior High School ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Algebraic Operation ◽  
Main Attention ◽  
Algebraic Form ◽  
Algebraic Operations ◽  
Algebraic Forms ◽  
Algebraic Solutions

This paper reports the study of the critical thinking skills of 7th-grade students in junior high school on determining the coefficients of algebraic operation. Data were collected using worksheet and interviews. 34 students were involved during the study. The study reveals that there were 35% students who performed algebraic operations correctly. Students’ difficulty is mainly on determining the coefficients associated with the algebraic forms. In general, errors occur in the process of finding algebraic solutions, explaining the reasons for the stages of strategies taken and drawing conclusions. This is due to the fact that the main attention was given to the final result of the process of working on algebraic form problems, and less focus was paid on giving reasons for the process of working on problems that stimulate the students to think critically.

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