16 research outputs found
Unified Modeling Language extensions for modeling user-oriented, multi-channel access CRM systems
In the advances of Internet technologies in recent years, Electronic Commerce CRM systems have gained much attention as a major theme for companies to maintain their competitiveness. The research shows that the effective customer relationship management is the major source for customer retention and gaining over new ones. On the other hand, modern technology allows to receive information through different channels (Internet, phone, WAP). Therefore analysts are forced to use faster, more reliable methods for system modeling. The author proposes a new method for modeling Customer Relationship Management systems. The UML new extensions are introduced. The customer-oriented and multichannel access patterns aim at improvement of system modeling with the high level of abstraction. This paper identifies and analyses the main advantages of language additions and compare them to object-oriented modeling with the pure UML patterns
The design patterns in PHP language for the web documents aggregation model
This paper considers the usage of design patterns in PHP language for the documents set model. The author discusses briefly to design patterns and one of the open web documents aggregation model. Some of new features on PHP and its consequences are also presented. The author states that usage of free, powerful development tools and standard problem solving in a new context gives the flexible and professional software building environment
Customer Relationship Management system models application in higher education
The paper present a short description of Customer Relationship Management models that can be applied in the university environment. It focuses on evolution of the models and their approximation to real-life situations
Analysis of functionality of distance learning platform moodle
The authors of this article, conducting the classes using the blended-learning method, focus their interest on the analysis of functionality of the Learning Content Management Systems software class. Architecture of open source distance learning platform Moodle was analyzed. The Author's experience with teaching students and student suggestions allow to present the influence of architectural design on functionality of the software. Facing with growing interests of usage of Moodle in the Polish universities, the authors present some advantages and disadvantages concerning the functional design and possibility of deployment in similar environments. They also suggest a few ways of improving the system architecture and give some clues that could be helpful for the deployers
Dual Lattice of â€-module Lattice
SummaryIn this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of â€-module is necessary for lattice problems, LLL(Lenstra, Lenstra and LovĂĄsz) base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].Futa Yuichi - Tokyo University of Technology, Tokyo, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377â382, 1990.Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543â547, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41â46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107â114, 1990.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529â536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1): 55â65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153â164, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47â53, 1990.Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013.Yuichi Futa and Yasunari Shidama. Lattice of â€-module. Formalized Mathematics, 24 (1):49â68, 2016. doi: 10.1515/forma-2016-0005.Yuichi Futa and Yasunari Shidama. Embedded lattice and properties of Gram matrix. Formalized Mathematics, 25(1):73â86, 2017. doi: 10.1515/forma-2017-0007.Yuichi Futa and Yasunari Shidama. Divisible â€-modules. Formalized Mathematics, 24 (1):37â47, 2016. doi: 10.1515/forma-2016-0004.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. â€-modules. Formalized Mathematics, 20(1):47â59, 2012. doi: 10.2478/v10037-012-0007-z.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of â€-module. Formalized Mathematics, 20(3):205â214, 2012. doi: 10.2478/v10037-012-0024-y.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Matrix of â€-module. Formalized Mathematics, 23(1):29â49, 2015. doi: 10.2478/forma-2015-0003.Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841â845, 1990.Eugeniusz Kusak, Wojciech LeoĆczuk, and MichaĆ Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335â342, 1990.A. K. Lenstra, H. W. Lenstra Jr., and L. LovĂĄsz. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4):515â534, 1982. doi: 10.1007/BF01457454.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: a cryptographic perspective. The International Series in Engineering and Computer Science, 2002.Andrzej Trybulec. Function domains and FrĂŠnkel operator. Formalized Mathematics, 1 (3):495â500, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569â573, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575â579, 1990.Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1 (5):877â882, 1990.Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883â885, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67â71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73â83, 1990.25215716
Lattice of â€-module
In this article, we formalize the definition of lattice of â€-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers â. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of â€-module is necessary for lattice problems, LLL (Lenstra, Lenstra and LovĂĄsz) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, JapanShidama Yasunari - Shinshu University Nagano, JapanGrzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3): 537-541, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. â€-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of â€-module. Formalized Mathematics, 20(3):205-214, 2012. doi:10.2478/v10037-012-0024-y.Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, and Yasunari Shidama. Torsion â€-module and torsion-free â€-module. Formalized Mathematics, 22(4):277-289, 2014. doi:10.2478/forma-2014-0028.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Matrix of â€-module. Formalized Mathematics, 23(1):29-49, 2015. doi:10.2478/forma-2015-0003.A. K. Lenstra, H. W. Lenstra Jr., and L. LovĂĄsz. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4), 1982.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective. The International Series in Engineering and Computer Science, 2002.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990
Divisible â€-modules
In this article, we formalize the definition of divisible â€-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible â€-modules are not finitely-generated.We introduce a divisible â€-module, equivalent to a vector space of a torsion-free â€-module with a coefficient ring â. â€-modules are important for lattice problems, LLL (Lenstra, Lenstra and LovĂĄsz) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, JapanShidama Yasunari - Shinshu University Nagano, JapanGrzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.CzesĆaw ByliĆski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. â€-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of â€-module. Formalized Mathematics, 20(3):205-214, 2012. doi:10.2478/v10037-012-0024-y.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Free â€-module. Formalized Mathematics, 20(4):275-280, 2012. doi:10.2478/v10037-012-0033-x.Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, and Yasunari Shidama. Torsion â€-module and torsion-free Z-module. Formalized Mathematics, 22(4):277-289, 2014. doi:10.2478/forma-2014-0028.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Torsion part of â€-module. Formalized Mathematics, 23(4):297-307, 2015. doi:10.1515/forma-2015-0024.Eugeniusz Kusak, Wojciech LeoĆczuk, and MichaĆ Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.A. K. Lenstra, H. W. Lenstra Jr., and L. LovĂĄsz. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4), 1982.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective. The International Series in Engineering and Computer Science, 2002.Jan PopioĆek. Some properties of functions modul and signum. Formalized Mathematics, 1(2):263-264, 1990.MichaĆ 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.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990
Isomorphism Theorem on Vector Spaces over a Ring
SummaryIn this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. â€-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and LovĂĄsz) [5] base reduction algorithm and cryptographic systems [6, 2].Futa Yuichi - Tokyo University of Technology, Tokyo, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Submodule of free â€-module. Formalized Mathematics, 21(4):273â282, 2013. doi:10.2478/forma-2013-0029.Adam Grabowski, Artur KorniĆowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191â198, 2015. doi:10.1007/s10817-015-9345-1.A. K. Lenstra, H. W. Lenstra Jr., and L. LovĂĄsz. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4):515â534, 1982. doi:10.1007/BF01457454.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: a cryptographic perspective. The International Series in Engineering and Computer Science, 2002.Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31â40, 2012. doi:10.2478/v10037-012-0005-1.25317117
Formalization of Integral Linear Space
In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-LovĂĄsz) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice [8].Futa Yuichi - Shinshu University, Nagano, JapanOkazaki Hiroyuki - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.CzesĆaw ByliĆski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.JarosĆaw Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.MichaĆ J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 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.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992
Set of Points on Elliptic Curve in Projective Coordinates
In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.Futa Yuichi - Shinshu University, Nagano, JapanOkazaki Hiroyuki - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.JĂłzef BiaĆas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata DarmochwaĆ. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.G. Seroussi I. Blake and N. Smart. Elliptic Curves in Cryptography. Number 265 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1999.Eugeniusz Kusak, Wojciech LeoĆczuk, and MichaĆ Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.RafaĆ Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Konrad Raczkowski and PaweĆ Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.Christoph Schwarzweller. The ring of integers, euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.MichaĆ J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 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.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990