212,076 research outputs found
Some Basic Properties of Some Special Matrices. Part III
This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.Liang Xiquan - Qingdao University of Science and Technology, ChinaWang Tao - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Karol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007, doi:10.2478/v10037-007-0024-5.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 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.Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993
New Constructions of Zero-Correlation Zone Sequences
In this paper, we propose three classes of systematic approaches for
constructing zero correlation zone (ZCZ) sequence families. In most cases,
these approaches are capable of generating sequence families that achieve the
upper bounds on the family size () and the ZCZ width () for a given
sequence period ().
Our approaches can produce various binary and polyphase ZCZ families with
desired parameters and alphabet size. They also provide additional
tradeoffs amongst the above four system parameters and are less constrained by
the alphabet size. Furthermore, the constructed families have nested-like
property that can be either decomposed or combined to constitute smaller or
larger ZCZ sequence sets. We make detailed comparisons with related works and
present some extended properties. For each approach, we provide examples to
numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor
Designing structured tight frames via an alternating projection method
Tight frames, also known as general Welch-bound- equality sequences, generalize orthonormal systems. Numerous applications - including communications, coding, and sparse approximation- require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm
On moving averages
We show that the moving arithmetic average is closely connected to a
Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and
which was observed to converge only numerically. Our analysis establishes a
rigorous proof of convergence of their algorithm in a special case; moreover,
limit is explicitly identified. Moving averages in Banach spaces and Kolmogorov
means are also studied. Furthermore, we consider moving proximal averages and
epi-averages of convex functions
Self-consistent renormalization as an efficient realization of main ideas of the Bogoliubov-Parasiuk R-operation
By self-consistent renormalization (SCR) it is meant that all formal
relations between UV-divergent Feynman amplitudes are automatically retained as
well as between their regular values obtained in the framework of the SCR. The
SCR is efficiently applicable on equal grounds both to renormalizable and
nonrenormalizable theories. SCR furnishes new means for the constructive
treatment of new subjects: i) UV-divergence problems associated with
symmetries, Ward identities, and quantum anomalies; ii) new relations between
finite bare and finite physical parameters of quantum field theories. The aim
of this paper is to describe main ideas and properties of the SCR and clearly
to describe three mutually complementary algorithms of the SCR that are
presented in the form maximally suited for practical applications.Comment: 17 pages, ujp.st
Submatrices of character tables and basic sets
In this investigation of character tables of finite groups we study basic
sets and associated representation theoretic data for complementary sets of
conjugacy classes. For the symmetric groups we find unexpected properties of
characters on restricted sets of conjugacy classes, like beautiful
combinatorial determinant formulae for submatrices of the character table and
Cartan matrices with respect to basic sets; we observe that similar phenomena
occur for the transition matrices between power sum symmetric functions to
bounded partitions and the -Schur functions introduced by Lapointe and
Morse. Arithmetic properties of the numbers occurring in this context are
studied via generating functions.Comment: 18 pages; examples added, typos removed, some further minor changes,
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