Search Results

81 - 90 of 116 items :

  • Cartesian product x
  • Numerical and Computational Mathematics x
Clear All
Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms

. On the isomorphism between finite chains. Formalized Mathematics , 9( 2 ):429-430, 2001. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1( 1 ):73-83, 1990

Open access
Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages

-334, 1990. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. Edmund Woronowicz. Many-argument relations. Formalized Mathematics , 1( 4 ):733-737, 1990. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1( 1 ):73-83, 1990. Edmund Woronowicz. Relations defined on sets

Open access
Continuity of Bounded Linear Operators on Normed Linear Spaces

Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics , 12( 3 ):269–275, 2004. [10] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics , 19( 1 ):51–59, 2011. doi:10.2478/v10037-011-0009-2. [11] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics , 12( 1 ):39–48, 2004. [12] Yasunari Shidama. The series on Banach algebra. Formalized Mathematics , 12( 2 ):131–138, 2004. [13] Kosaku Yoshida

Open access
Quotient Module of Z-module

Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002. [15] Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics , 8( 1 ):29-34, 1999. [16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [17] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics , 11( 4 ):341-347, 2003. [18] Michał

Open access
Towards the Construction of a Model of Mizar Concepts

Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [34] Andrzej Trybulec. Enumerated sets. Formalized Mathematics , 1(1):25-34, 1990. [35] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1(1):97-105, 1990. [36] Andrzej Trybulec. Many-sorted sets. Formalized Mathematics , 4(1):15-22, 1993. [37] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics , 5(1):37-42, 1996. [38] Andrzej

Open access
The Real Vector Spaces of Finite Sequences are Finite Dimensional

(2):329-334, 1990. [25] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [26] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics , 1(5):847-850, 1990. [27] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics , 1(5):979-981, 1990. [28] Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics , 1(3):581-588, 1990

Open access
Solutions of Linear Equations

field. Formalized Mathematics , 15(4):199-211, 2007. [18] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics , 15(3):143-150, 2007. [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [20] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics , 1(5):883-885, 1990. [21] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1(5):821-827, 1990. [22

Open access
Brouwer Fixed Point Theorem for Simplexes

Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics , 2( 4 ):535-545, 1991. Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics , 1( 2 ):291-296, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990

Open access
Jordan Matrix Decomposition

. [26] Karol Pąk. Eigenvalues of a linear transformation. Formalized Mathematics , 16(4):289-295, 2008. [27] Karol Pąk. Linear map of matrices. Formalized Mathematics , 16(3):269-275, 2008. [28] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1(2):329-334, 1990. [29] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [30] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1

Open access
Groups – Additive Notation

] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics , 1(1):223-230, 1990. [31] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics , 5(2):233-236, 1996. [32] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics , 2(4): 535-545, 1991. [33] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1): 115-122, 1990. [34] Andrzej Trybulec. Enumerated sets. Formalized

Open access