A5016481249- graph theory and CDMA systems
- Limits and Structures in Graph Theory
- Mathematical Analysis and Transform Methods
- Coding theory and cryptography
- Matrix Theory and Algorithms
- Mathematical Dynamics and Fractals
- Point processes and geometric inequalities
- Cellular Automata and Applications
- Spectral Theory in Mathematical Physics
- Mathematical Approximation and Integration
- Mathematics and Applications
- Holomorphic and Operator Theory
- Finite Group Theory Research
- Advanced Topics in Algebra
- Analytic Number Theory Research
- semigroups and automata theory
- Computational Geometry and Mesh Generation
- Analytic and geometric function theory
- Advanced Mathematical Modeling in Engineering
- Advanced Combinatorial Mathematics
- Advanced Topology and Set Theory
- Advanced Photonic Communication Systems
- Quasicrystal Structures and Properties
- Relativity and Gravitational Theory
- Optical Network Technologies
Alfréd Rényi Institute of Mathematics
2014-2023
Budapest University of Technology and Economics
2016-2023
Hungarian Academy of Sciences
2012-2022
University of Szeged
2022
Hudson Institute
2018
John Wiley & Sons (United States)
2018
Eötvös Loránd University
2003-2006
A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. conjecture due Fuglede (1974) stated that $\Omega$ a and only it can tile by translations. While this was disproved for general sets, long been known convex body "tiling implies spectral" part in fact true. To contrary, "spectral tiling" direction bodies proved $\mathbb{R}^2$, also $\mathbb{R}^3$ under priori assumption polytope. In higher dimensions,...
We exhibit a subset of finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have common spectrum (orthogonal basis for their L2 space consisting characters). This disproves Universal Spectrum Conjecture Lagarias Wang [Lagarias J. C. Y.: Spectral sets factorizations groups.J. Func. Anal. 145 (1997), 73–98]. Further, we construct set in some but has no spectrum. extend this last example to groups ℤd ℝd (for d ≥5 ) thus disproving one direction...
In this note we modify a recent example of Tao and give an set <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega subset-of double-struck R Superscript 4"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:annotation...
We exhibit an infinite family of {\it triplets} mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier Hadamard matrices, $F(a,b)$. However, main result paper we also prove that for any values parameters $(a,b)$, standard basis and $F(a,b)$ cannot be extended to a MUB-quartet}. The novelty lies method} proof which may successfully applied future maximal number MUBs 6 is three.
This note concerns a particular case of the minimality problem in positive system theory. A standard result linear theory states that any nth-order rational transfer function discrete time-invariant single-input-single-output (SISO) admits realization order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e., system), and it known this restriction may force N be strictly larger than general solution determining smallest possible value N) not...
Complex Hadamard matrices have received considerable attention in the past few years due to their application quantum information theory. While a complete characterization currently available [5] is only up order 5, several new constructions of higher appeared recently [4, 12, 2, 7, 11]. In particular, classification self-adjoint complex 6 was completed by Beuachamp and Nicoara [2], providing previously unknown non-affine one-parameter orbit. this paper we classify all dephased, symmetric...
Applications in quantum information theory and tomography have raised current interest complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups constructions First, recover a recent, very general construction matrices due to Dita [2] via natural construction. Then find some necessary conditions for any given matrix be equivalent Dita-type matrix. Finally, using another construction, Szabó [8], arrive at new parametric families order 8, 12 16, use...
A basic phenomenon in positive system theory is that the dimension N of an arbitrary realization a given transfer function H(z) may be strictly larger than n its minimal realizations. The aim this brief to provide nontrivial lowerbound on value under assumption there exists time instant k/sub 0/ at which (always nonnegative) impulse response 0 but becomes for all k>k/sub 0/. Transfer functions with property regarded as extremal cases theory.
Abstract In this paper, we study algorithms for tiling problems. We show that the conditions (T1) and (T2) of Coven Meyerowitz [E. A. Meyerowitz, Tiling integers with translates one finite set, J. Algebra 212(1) (1999), pp. 161–174], conjectured to be necessary sufficient a set A tile integers, can checked in time polynomial diam (A). also give heuristic find all non-periodic tilings cyclic group ℤ N . particular, carry out full classification ℤ144. Keywords: translational tilesalgorithms...
It is a standard result in linear-system theory that an nth-order rational transfer function of single-input single-output system always admits realization order n. In some applications, however, one restricted to realizations with nonnegative entries (i.e. positive system), and it known this restriction may force the N be strictly larger than brief we present class functions where n do exist. With help our give improvements on earlier results positive-system theory.
It is possible to have a packing by translates of cube that maximal (i.e.\ no other can be added without overlapping) but does not form tiling. In the long running analogy and tiling orthogonality completeness exponentials on domain, we pursue question whether one orthogonal sets for them being complete. We prove this in dimensions 1 2, 3 higher. provide several examples such incomplete exponentials, differing size, raise relevant questions. also show even dimension $1$ there are which...
We give a new approach to the problem of mutually unbiased bases (MUBs), based on Fourier analytic technique borrowed from additive combinatorics. The method provides short and elegant generalization fact that there are at most d + 1 MUBs in ℂ . It may also yield proof no complete system exists some composite dimensions — long standing open problem.