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Finite Sequences and Tuples of Elements of a Nonempty Sets
, 1990
"... this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D ..."
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Cited by 332 (7 self)
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this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
Infinitesimals Via the Cofinite Filter
, 2002
"... We observe that the field of complex and padic numbers, the ring of n matrices, the Euclidean spaces R (n > 1), and topological manifolds are models of the notion of infinitesimal. These models do not satisfy the axioms of total order and/or contain zero divisors. As a first consequence t ..."
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the notion of infinitesimal is logically independent of the notions of zero divisor and total order. As second consequence the notion of ultrafilter is not required for the definition of infinitesimal. We define the notion of infinitesimal using the cofinite filter as in C. Schmieden and D. Laugwitz [7]. We
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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of this section gives a practical description of the Cartesian case. The following parts are dedicated to general theory, SNR and error considerations, and sensitivity assessment. Sensitivity Encoding With Cartesian Sampling of kSpace In twodimensional (2D) Fourier imaging with common Cartesian sampling of k
A REPRESENTATION FORMULA FOR CURVES IN C3 WITH PRESET INFINITESIMAL ARC LENGTH
"... We consider an algebraic representation formula for meromorphic curves in C3 with preset innitesimal arc length, i. e., a dierential operator M assigning to triples (f; h; d) of meromorphic functions meromorphic curves = ('1; '2; '3)> such that d is the innitesimal arclength of , ..."
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We consider an algebraic representation formula for meromorphic curves in C3 with preset innitesimal arc length, i. e., a dierential operator M assigning to triples (f; h; d) of meromorphic functions meromorphic curves = ('1; '2; '3)> such that d is the innitesimal arclength
RESTRICTED SIMPLE LIE ALGEBRAS AND THEIR INFINITESIMAL DEFORMATIONS
, 2007
"... Abstract. In the first two sections, we review the BlockWilsonPremetStrade classification of restricted simple Lie algebras. In the third section, we compute their infinitesimal deformations. In the last section, we indicate some possible generalizations by formulating some open problems. 1. Rest ..."
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Cited by 4 (2 self)
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Abstract. In the first two sections, we review the BlockWilsonPremetStrade classification of restricted simple Lie algebras. In the third section, we compute their infinitesimal deformations. In the last section, we indicate some possible generalizations by formulating some open problems. 1
Whom You Know Matters: Venture Capital Networks and Investment Performance,
 Journal of Finance
, 2007
"... Abstract Many financial markets are characterized by strong relationships and networks, rather than arm'slength, spotmarket transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company inv ..."
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Cited by 138 (8 self)
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Abstract Many financial markets are characterized by strong relationships and networks, rather than arm'slength, spotmarket transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company
Remarks to Maurice Fréchet’s article “Sur la définition axiomatique d’une classe d’espaces distanciés vectoriellement applicable sur l’espace de Hilbert”. Annals of Mathematics 36(3
, 1935
"... 1. Frechet's developments in the last section of his article suggest an elegant solution of the follo\ving problem. Let (i ¢ k; i, k = 0, 1,. ·.,n) be!n(n + 1) given positive quantities. What are the necessary and sufficient conditions that they be the lengths of.the edges of ansimplex AoAl... ..."
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Cited by 100 (0 self)
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1. Frechet's developments in the last section of his article suggest an elegant solution of the follo\ving problem. Let (i ¢ k; i, k = 0, 1,. ·.,n) be!n(n + 1) given positive quantities. What are the necessary and sufficient conditions that they be the lengths of.the edges of ansimplex Ao
Modern Infinitesimal Analysis Applied to the Physical Metric dS and a Theoretical Verification of a Timedilation Conjecture.
, 2008
"... Abstract In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the timedependent Schrödinger equation, gravitational timedilation expressions are obtained ..."
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Abstract In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the timedependent Schrödinger equation, gravitational timedilation expressions
On the length of commutators in Chevalley groups
 Israel J. Math. (2010
"... In the present paper we carry over results of Theorem. Let G = G(Φ, R) be a Chevalley group of rank l 2 and let R be a ring such that dim Max(R) = d < ∞. Then there exists a natural number N depending only on Φ and d such that each commutator [x, y] of elements x ∈ G(Φ, R) and y ∈ E(Φ, R) is a ..."
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Cited by 8 (8 self)
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In the present paper we carry over results of Theorem. Let G = G(Φ, R) be a Chevalley group of rank l 2 and let R be a ring such that dim Max(R) = d < ∞. Then there exists a natural number N depending only on Φ and d such that each commutator [x, y] of elements x ∈ G(Φ, R) and y ∈ E(Φ, R) is a
Results 1  10
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1,563