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95
Basis of Real Linear Space
, 1990
"... this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G ..."
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Cited by 250 (21 self)
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this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G
Many sorted algebras
 Journal of Formalized Mathematics
, 1994
"... Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between ..."
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Cited by 125 (14 self)
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Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras [8] and many sorted algebras with one sort only is described by introducing two functors mapping one into the other. The construction is done this way that the composition of both functors is the identity on universal algebras.
The sum and product of finite sequences of real numbers
 Journal of Formalized Mathematics
, 1990
"... Summary. Some operations on the set of ntuples of real numbers are introduced. Addition, difference of such ntuples, complement of a ntuple and multiplication of these by real numbers are defined. In these definitions more general properties of binary operations applied to finite sequences from [ ..."
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Cited by 118 (2 self)
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Summary. Some operations on the set of ntuples of real numbers are introduced. Addition, difference of such ntuples, complement of a ntuple and multiplication of these by real numbers are defined. In these definitions more general properties of binary operations applied to finite sequences from [9] are used. Then the fact that certain properties are satisfied by those operations is demonstrated directly from [9]. Moreover some properties can be recognized as being those of real vector space. Multiplication of ntuples of real numbers and square power of ntuple of real numbers using for notation of some properties of finite sums and products of real numbers are defined, followed by definitions of the finite sum and product of ntuples of real numbers using notions and properties introduced in [11]. A number of propositions and theorems on sum and product of finite sequences of real numbers are proved. As additional properties there are proved some properties of real numbers and set representations of binary operations on real numbers.
Combining of Circuits
, 2002
"... this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S ..."
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Cited by 90 (24 self)
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this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S
Homomorphisms of many sorted algebras
 Journal of Formalized Mathematics
, 1994
"... Summary. The aim of this article is to present the definition and some properties of homomorphisms of many sorted algebras. Some auxiliary properties of many sorted functions also have been shown. ..."
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Cited by 69 (1 self)
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Summary. The aim of this article is to present the definition and some properties of homomorphisms of many sorted algebras. Some auxiliary properties of many sorted functions also have been shown.
Some properties of restrictions of finite sequences
 Journal of Formalized Mathematics
, 1995
"... Summary. The aim of the paper is to define some basic notions of restrictions of finite sequences. ..."
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Cited by 41 (3 self)
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Summary. The aim of the paper is to define some basic notions of restrictions of finite sequences.
Binary operations on finite sequences
 Journal of Formalized Mathematics
, 1990
"... Summary. We generalize the semigroup operation on finite sequences introduced in [8] for binary operations that have a unity or for nonempty finite sequences. ..."
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Cited by 37 (2 self)
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Summary. We generalize the semigroup operation on finite sequences introduced in [8] for binary operations that have a unity or for nonempty finite sequences.