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Results 1 - 10
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5,584
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
ALGEBRAIC GEOMETRY
"... Algebraic geometry is the mathematical study of geometric objects by means of algebra. Its origins go back to the coordinate geometry introduced by Descartes. A classic example is the circle of radius 1 in the plane, which is ..."
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Cited by 513 (6 self)
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Algebraic geometry is the mathematical study of geometric objects by means of algebra. Its origins go back to the coordinate geometry introduced by Descartes. A classic example is the circle of radius 1 in the plane, which is
Sheaves as essentially algebraic objects
, 2012
"... We develop the notion of essentially algebraic theories from [1]. We associate with each Grothendieck site a corresponding essentially algebraic theory whose models are the sheaves on that site. This is used to classify locally finitely presented toposes, and to show that the category of modules ove ..."
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We develop the notion of essentially algebraic theories from [1]. We associate with each Grothendieck site a corresponding essentially algebraic theory whose models are the sheaves on that site. This is used to classify locally finitely presented toposes, and to show that the category of modules
The number of views of piecewise-smooth algebraic objects
, 1995
"... A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we study the complexity of aspect graphs of piecewise-smooth algebraic objects using the modern tools of algebraic geometry, i.e. inter ..."
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Cited by 2 (2 self)
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A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we study the complexity of aspect graphs of piecewise-smooth algebraic objects using the modern tools of algebraic geometry, i
Intelligent Tutoring Goes to School in the Big City
- International Journal of Artificial Intelligence in Education
, 1997
"... Abstract. This paper reports on a large-scale experiment introducing and evaluating intelligent tutoring in an urban High School setting. Critical to the success of this project has been a client-centered design approach that has matched our client's expertise in curricular objectives and class ..."
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Cited by 421 (118 self)
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Abstract. This paper reports on a large-scale experiment introducing and evaluating intelligent tutoring in an urban High School setting. Critical to the success of this project has been a client-centered design approach that has matched our client's expertise in curricular objectives
Quantum Teichmüller space as a noncommutative algebraic object
, 2008
"... We consider the quantum Teichmüller space of the punctured surface introduced by Chekhov-Fock-Kashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3-dimensional topology, we put more attention ..."
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Cited by 15 (4 self)
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We consider the quantum Teichmüller space of the punctured surface introduced by Chekhov-Fock-Kashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3-dimensional topology, we put more
CONSTRUCTING COLLECTIVE ALGEBRAIC OBJECTS IN A CLASSROOM NETWORK
"... This paper presents a novel learning environment designed to support Algebra teaching and learning using a classroom network. We analyze a class session first at the level of the whole class, and then through more detailed examination of simultaneous activity in three student pairs. Classroom activi ..."
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This paper presents a novel learning environment designed to support Algebra teaching and learning using a classroom network. We analyze a class session first at the level of the whole class, and then through more detailed examination of simultaneous activity in three student pairs. Classroom
On Quadratic Almost Perfect Nonlinear Functions and Their Related Algebraic Object
"... Abstract. It is well known that almost perfect nonlinear (APN) functions achieve the lowest possible differential uniformity for functions defined on fields with even character-istic, and hence, from this point of view, they are the most ideal choices for S-boxes in block and stream ciphers to avoid ..."
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Cited by 1 (0 self)
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to avoid differential attack. They are also interesting by the link to many other areas, for instance topics in coding theory and combinatorics. In this paper, we present a characterization of quadratic APN functions by a certain kind of algebraic object, which is called an APN algebra in this paper
Fast Computation of the C-Space of Convex 2D Algebraic Objects
- The International Journal of Robotics Research
, 1995
"... Collision-free paths for a robot are commonly obtained in con-figuration space. The major problem with this approach is the computation of the boundary of the configuration space ob-stacles. While many results have been reported for polygonal environments, the general case of arbitrary object shape ..."
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Cited by 11 (0 self)
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has received little attention in the literature so far. This article presents a new method for tackling this problem in the case of objects for which the boundaries consist of segments of pa-rameterized algebraic curves. A fast numerical algorithm that computes the boundaries of the C-space obstacles
Algebras and Modules in Monoidal Model Categories
- Proc. London Math. Soc
, 1998
"... In recent years the theory of structured ring spectra (formerly known as A # - and E # -ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect t ..."
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Cited by 231 (30 self)
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, algebras, and modules. This includes, but is not limited to, each of the new theories of ring spectra. One model for structured ring spectra is given by the S-algebras of [##]. This example has the special feature that every object is brant, which makes it easier to fo...
Results 1 - 10
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5,584
