Results 1  10
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49
Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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Cited by 219 (4 self)
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
Duality for modules over finite rings and applications to coding theory
 AMER. J. MATH
, 1999
"... This paper sets a foundation for the study of linear codes over finite rings. The finite Frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of MacWilliams, the extension theorem and the MacWilliams identities, generalize from finite ..."
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Cited by 40 (4 self)
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This paper sets a foundation for the study of linear codes over finite rings. The finite Frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of MacWilliams, the extension theorem and the MacWilliams identities, generalize from finite fields to finite Frobenius rings. It is over Frobenius rings that certain key identifications can be made between the ring and its complex characters.
AF embeddability of crossed products of AF algebras by the integers
 J. Funct. Anal
, 1998
"... This paper is concerned with the question of when the crossed product of an AF algebra by an action of Z is itself AF embeddable. It is well known that quasidiagonality and stable finiteness are hereditary properties. That is, if A and B are C ∗algebras with A ⊂ B and B has either of these properti ..."
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Cited by 19 (2 self)
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This paper is concerned with the question of when the crossed product of an AF algebra by an action of Z is itself AF embeddable. It is well known that quasidiagonality and stable finiteness are hereditary properties. That is, if A and B are C ∗algebras with A ⊂ B and B has either of these properties, then so does A. Since AF algebras enjoy both of these properties we have that quasidiagonality and stable finiteness are geometric obstructions to AF embeddability. For crossed products of AF algebras by Z, these turn out to be the only obstructions. If A is an AF algebra, then we may easily describe an algebraic obstruction to the AF embeddability of A ×α Z. Definition 0.1 If A is an AF algebra and α ∈ Aut(A) then we denote by Hα the subgroup of K0(A) given by all elements of the form α∗(x) − x for x ∈ K0(A). It follows from the PimsnerVoiculescu six term exact sequence ([PV]) that if A is unital and AF then K0(A ×α Z) = K0(A)/Hα. Now, if B is unital and stably finite (in particular, if B is AF) and p ∈ Mn(B) is a projection then [p] must be a nonzero element of K0(B). Thus, if A ×α Z embeds into B (or if A ×α Z is
Every smooth padic Lie group admits a compatible analytic structure
, 2003
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Moufang symmetry I. Generalized Lie and MaurerCartan equations
, 2008
"... The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the MaurerCartan equations. ..."
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Cited by 8 (8 self)
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The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the MaurerCartan equations.
group action and stability analysis of stationary solutions for a free boundary problem modeling tumor growth
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On approximations of groups, group actions and Hopf algebras
, 1999
"... We give new examples and criteria in the theory of approximation of groups by finite groups. ..."
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Cited by 7 (2 self)
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We give new examples and criteria in the theory of approximation of groups by finite groups.
The dynamics of group codes: Dual abelian group codes and systems
 IEEE Trans. Inf. Theory
, 2004
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Control Theory for a Class of 2D ContinuousDiscrete Linear Systems
"... This paper considers a general class of 2D continuousdiscrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and ..."
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Cited by 3 (0 self)
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This paper considers a general class of 2D continuousdiscrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and operator setting. In particular, important new results are developed on stability, controllability, stabilization, and optimal control. 1