منابع مشابه
Multiplicative Binding, Representation Operators & Analogy
Analogical inference depends on systematic substitution of the components of compositional structures. Simple systematic substitution has been achieved in a number of connectionist systems that support binding (the ability to create connectionist representations of the combination of component representations). These systems have used various implementations of two generic composition operators...
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This paper shows significant benefits from small extensions to typical compiler intermediate representations (IRs). We have added to such an IR two features that operate on sequences and thus hide simple loops. For example, we represent matrix multiplication with an expression dag of about 20 nodes and no explicit control flow. This design simplifies many optimizations. Examples include a 200-l...
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A~tract, In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for each n i> 0 a bilinear operation which assigns to two modular forms f and g of weight k and l a modular form If, g], of weight k + l + 2n. In the present paper we study these "Rankin-Cohen brackets" from t w o points of view. On the one hand we give ...
متن کاملMultiplicative Properties of Integral Binary Quadratic Forms
In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a klinear ...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2014
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-014-1398-z