Algebraic method

In the 2018 Mathematics General Curriculum, the content of mathematics is integrated into three branches of knowledge: numbers, algebra, and elements of analysis; geometry and measurement; and statistics and probability. This article introduces a method for developing students' mathematical communication competence through lessons on triangular and quadrilateral right prisms in grade 7.

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In this paper, we introduce a new method for image reconstruction in ultrasound tomography by using the algebraic method. The numerical results indicate that this method has a shorter computational time and achieves highresolution reconstructions and accurate solutions.

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This paper systematically presents a specific application of linear algebra in information security and cryptography, highlighting the crucial role of matrix operations and linear techniques in the design and analysis of encryption algorithms.

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Lecture "Fundamentals of control systems - Chapter 4: System stability analysis system stability analysis" presentation of content: Stability concept, algebraic stability criteria, root locus method, frequency response analysis.

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Proposing a model to classify by fuzzy decision trees and a method to select the feature training samples set for classification process. Recommending the linguistic value treatment method of inhomogeneous attributes based on hedge algebra. Proposing the algorithms by fuzzy decision tree in order to be effective in predicting and simple for users.

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In this article we study several homology theories of the algebra E ∞ (X) of Whitney functions over a subanalytic set X ⊂ Rn with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for E ∞ (X), when X is a regular subset of Rn having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of E ∞ (X) for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories. ...

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Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity).

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We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem. This method was recently introduced in [CZ] for the case of curves, leading to a new proof of Siegel’s celebrated theorem that any affine algebraic curve defined over a number field has only finitely many S-integral points, unless it has genus zero and not more than two points at infinity. Here, under certain conditions involving the intersection matrix of the divisors at infinity, we shall conclude that the integral points on a surface all lie on a curve. We shall...

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By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of nonuniruled polarized varieties. Contents Introduction Singular hermitian metrics Deformation theory of framed manifolds; V -structures Cyclic coverings Canonically polarized framed manifolds Singular Hermitian metrics for families of canonically polarized framed manifolds 7.

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SMOOTH AND DISCRETE SYSTEMS—ALGEBRAIC, ANALYTIC, AND GEOMETRICAL REPRESENTATIONS ˇ FRANTISEK NEUMAN Received 12 January 2004 What is a differential equation? Certain objects may have different, sometimes equivalent representations. By using algebraic and geometrical methods as well as discrete relations, different representations of objects mainly given as analytic relations, differential equations can be considered.

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