Definitions

1. Some notions are defined differently depending on context or author.
2. These notions are made precise in general through the use of pseudogroups.
3. These notions were borrowed by the Esoteric Buddhism and, combined with Buddhism doctrines, produced the theory of "the union of voidness and happiness".
4. Both notions are deemed desirable in designing algorithms, and are believed to lead to good generalization ability.
5. These notions are expressed by Klingon verbs immediately followed by a noun that is modified by the preceding verb.

Dangers

1. Most dangers in using Condorcet rules come from the notions held by voters and politicians accustomed to bad voting rules. (Web site)

Essential Properties

1. It is shown that these notions inherit most of the essential properties of the primal and weakly primal ideals of a commutative ring with non-zero identity.

Ultimate Reality

1. Tantrism * Tantrism and tantric ideas begin with notions in line with all forms of Buddhism, namely, the idea that Ultimate Reality is a singular Unity.
2. Ultimate reality in Buddhism has nothing to do with these fanciful notions.

Parallel Transport

1. The local theory concerns itself primarily with notions of parallel transport and holonomy.

Differentiable Manifolds

1. In dimensions at most 6 the notions of piecewise linear manifolds and differentiable manifolds coincide.

Differential Topology

1. Readers should be familiar with the basic notions of point-set topology and differential topology.

Abstract Algebra

1. In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms.

Five Common Notions

1. After the postulates, five common notions or axioms are listed.

Central Roles

1. Notions of race and racism, however, often have played central roles in such conflicts.

Notions Developed

1. The notions developed from their intensional ancestors because of internal pressures within mathematics, mathematical physics in particular.

Mystical Notions

1. He advocated a form of "pure realism" that rejected mystical notions of truth and accepted much quasi-empiricism in mathematics.

Existing Notions

1. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until.

Suitable Notions

1. Differentiable functions between two manifolds are needed in order to formulate suitable notions of submanifolds, and other related concepts.
2. In particular, such an approach induces suitable notions of equivalence and (behavioral) refinement for statecharts.

Corresponding Notions

1. Notions of continuity and differentiability of are introduced by means of the corresponding notions for its complex components.
2. The use of both terms in the modern context of multilinear algebra is a specific example of corresponding notions in category theory.
3. For contravariant functors the corresponding notions would be a functor that takes colimits to limits, or one that takes limits to colimits.

Forcing Notions

1. ABSTRACT: Laver proved that any supercompact cardinal can be made indestructible by a large class of forcing notions.

Infinite Linear Combinations

1. The common feature of the other notions is that they permit for taking infinite linear combinations of the basic vectors in order to generate the space.

Universal Algebra

1. Likewise, the notions of automorphism, endomorphism, epimorphism, homeomorphism, isomorphism, and monomorphism all find use in universal algebra.

Analogous Notions

1. They are also compared with the analogous notions in algebra of being finitely generated or presented (and with LFP categories).

Homological Algebra

1. The main goal of the course is to introduce students to the most important, basic notions and techniques of homological algebra.

Compactness

1. There are a lot of notions in topology strongly related to compactness [16].
2. Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces.
3. Basic notions of point set topology such as continuity, compactness, separation theorems, metrizability.

Key Notions

1. Other key notions in structural linguistics include paradigm, syntagm, and value (though these notions were not fully developed in Saussure's thought).

Similar Notions

1. Similar notions have found applications everywhere in differential geometry.

General Notions

1. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars.
2. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude.

Classical Notions

1. The notion of "algebras for a monad" generalizes classical notions from universal algebra, and in this sense, monads can be thought of as "theories".

Macro Structure

1. They dispelled many of the notions of Galen and Descartes, and resolved many facts about the macro structure of the brain.
2. They dispelled many of the wrong notions of Galen and Descartes and discovered many facts about the macro structure of the brain of animals and humans.

Conventional Notions

1. Thus conventional notions of the relation between theory and experiment have a tenuous foothold, at best.

Dual Notions

1. Dual notions to the above mentioned notions are coreflection, coreflection arrow, (mono)coreflective subcategory, coreflective hull.

Topological Notions

1. The theory of Whitehead's 1929 Process and Reality augmented the part-whole relation with topological notions such as contiguity and connection.

Several Notions

1. In probability theory, there are several notions of convergence for random variables.

Main Notions

1. This course unit introduces the main notions of modern differential geometry such as connection and curvature.

Important Notions

1. Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions.
2. The students will learn the most important notions of homological algebra, mainly the functors Ext and Tor.

Logical Notions

1. Boole then used algebraic expressions to define both algebraic and logical notions, e.g.

Central Notions

1. ABSTRACT: One of the central notions in model theory is that of dependence.
2. The central notions behind the Montague grammar were first proposed in the paper, " The Proper Treatment of Quantification in Ordinary English ".
3. This is an overview of the central notions and most important results in the theory of operator spaces.

Elementary Notions

1. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry.
2. The reader does get a taste of Morse theory here also, along with transversality, and thus a look at some elementary notions of differential topology.
3. An excellent introduction to some elementary notions from algebraic topology is done in chapter 3.

Traditional Notions

1. In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product.
2. The term served several purposes - first, it contrasted from traditional notions of theory, which were largely either positivist or scientific.

Fundamental Notions

1. Abstract: Locatedness is one of the fundamental notions in constructive mathematics.
2. The main objective is to demonstrate how much technology has changed the access to fundamental notions of curvature and closely related topics.

Common Notions

1. In the context of high performance computing there are two common notions of scalability.

Preconceived Notions

1. Descartes started his line of reasoning by doubting everything, so as to assess the world from a fresh perspective, clear of any preconceived notions.

Duality

1. The chief aim of all Sufis then is to let go of all notions of duality, therefore the individual self also, and realize the divine unity.

Homology

1. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae.

Needlework

1. Needlework and embroidery thread, accessories, notions, books and magazines, charts, kits, fabric, ribbons, cloth doll supplies and wool felt.

Confidentiality

1. The closely allied, perhaps even synonymous notions of confidentiality and privacy are often considered virtues.

Compatibility

1. This compatibility manifests itself in the following notions in various ways.
2. Compatibility with other topological notions Separation In general, quotient spaces are ill-behaved with respect to separation axioms.

Cultural Feminism

1. So notions that women are "inherently kinder and gentler" are one of the foundations of cultural feminism, and remain a major part of it.

Feminism

1. It suggests a fresh ideology, embracing the notions of "cyber" and "feminism" and all they signify.
2. In A Cyborg Manifesto Donna Haraway criticizes traditional notions of feminism, particularly its emphasis on identity, rather than affinity.
3. The play attempts to wrestle with and reconcile the rape of Leda, and contextualize for our contemporary notions of feminism, sexuality, and gender.

Vectors

1. Before finishing this section we need two more notions about vectors and functions, thought of as abstract vectors.
2. The tensor product—one of the central notions of multilinear algebra —can be seen as the extension of the hierarchy of scalars, vectors and matrices.

Categories

1. Notion
2. Information > Knowledge > Categorization > Category Theory
3. Information > Science > Mathematics > Algebra
4. Continuity
5. Condorcet

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