Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 6/2019, Volume 60, Issue 2, pp. 391 - 398

In the synthetic study of the real projective plane, harmonic conjugates have an essential role, with applications to projectivities, involutions, and...

Geometry | Algebra | Constructive mathematics | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Harmonic conjugates | Projective geometry | Secondary 03F65 | Primary 51A05

Geometry | Algebra | Constructive mathematics | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Harmonic conjugates | Projective geometry | Secondary 03F65 | Primary 51A05

Journal Article

2015, SIAM spotlights, ISBN 161197383X, Volume SL01, ix, 104

Book

Advances in Mathematics, ISSN 0001-8708, 01/2020, Volume 359, p. 106849

We count the algebraic numbers of fixed degree by their w-weighted lp-norm which generalizes the naïve height, the length, the Euclidean and the Bombieri...

Correlations between algebraic numbers | Bombieri norm | Integral polynomials | Distribution of algebraic numbers | Random polynomials | Conjugate algebraic numbers | MATHEMATICS | REAL ZEROS | ROOTS | EXPECTED NUMBER

Correlations between algebraic numbers | Bombieri norm | Integral polynomials | Distribution of algebraic numbers | Random polynomials | Conjugate algebraic numbers | MATHEMATICS | REAL ZEROS | ROOTS | EXPECTED NUMBER

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2019, Volume 200, Issue 1, pp. 241 - 254

The conjugate locus of a point on a surface is the envelope of geodesics emanating radially from that point. In this paper we show that the conjugate loci of...

Evolute | Convex | Conjugate locus | Mathematics | Topology | Rotation index | Convex and Discrete Geometry | Geodesic | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Jacobi field | Differential Geometry

Evolute | Convex | Conjugate locus | Mathematics | Topology | Rotation index | Convex and Discrete Geometry | Geodesic | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Jacobi field | Differential Geometry

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2016, Volume 37, Issue 1, pp. 469 - 489

We consider the solution of a system of linear algebraic equations which is obtained from a Raviart-Thomas mixed finite element formulation of Darcy's...

Krylov subspace method | Bramble-Pasiack cg method | Darcýs law | Preconditioning technique | H(div) preconditioner | Saddle point problems | ALGEBRAIC MULTIGRID METHOD | MATHEMATICS, APPLIED | SADDLE-POINT PROBLEMS | STABILIZED STOKES SYSTEMS | preconditioning technique | saddle point problems | Bramble-Pasiack CG method | BLOCK-TRIANGULAR PRECONDITIONERS | ELLIPTIC PROBLEMS | EIGENVALUES | ELEMENT | MATRICES | FAST ITERATIVE SOLUTION | INDEFINITE SYSTEMS | Darcy's law

Krylov subspace method | Bramble-Pasiack cg method | Darcýs law | Preconditioning technique | H(div) preconditioner | Saddle point problems | ALGEBRAIC MULTIGRID METHOD | MATHEMATICS, APPLIED | SADDLE-POINT PROBLEMS | STABILIZED STOKES SYSTEMS | preconditioning technique | saddle point problems | Bramble-Pasiack CG method | BLOCK-TRIANGULAR PRECONDITIONERS | ELLIPTIC PROBLEMS | EIGENVALUES | ELEMENT | MATRICES | FAST ITERATIVE SOLUTION | INDEFINITE SYSTEMS | Darcy's law

Journal Article

RSC Advances, ISSN 2046-2069, 2015, Volume 5, Issue 63, pp. 50962 - 50967

New corrole–BODIPY conjugates have been synthesized in high yield under mild conditions. Upon excitation at the absorption maximum of the BODIPY antenna...

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2017, Volume 86, Issue 304, pp. 935 - 950

We show that the number \alpha =(1+\sqrt {3+2\sqrt {5}})/2 with minimal polynomial x^4-2x^3+x-1 is the only Pisot number whose four distinct conjugates \alpha...

Pisot numbers | Mahler's measure | Additive relations | ALGEBRAIC-NUMBERS | MATHEMATICS, APPLIED | LOWER BOUNDS | HEIGHTS | NEIGHBORHOOD | SALEM-NUMBERS | TENT MAP EXPANSIONS | LIMIT-POINT | additive relations | PERIODIC POINTS

Pisot numbers | Mahler's measure | Additive relations | ALGEBRAIC-NUMBERS | MATHEMATICS, APPLIED | LOWER BOUNDS | HEIGHTS | NEIGHBORHOOD | SALEM-NUMBERS | TENT MAP EXPANSIONS | LIMIT-POINT | additive relations | PERIODIC POINTS

Journal Article

Publications de l'Institut Mathematique, ISSN 0350-1302, 2016, Volume 99, Issue 113, pp. 281 - 285

Journal Article

ARS MATHEMATICA CONTEMPORANEA, ISSN 1855-3966, 2018, Volume 14, Issue 1, pp. 165 - 176

In this paper we show that the relative normalised size with respect to a number field K of an algebraic integer alpha not equal -1, 0, 1 is greater than 1...

Algebraic number field | TRACE | MATHEMATICS | MATHEMATICS, APPLIED | Schur-Siegel-Smyth trace problem | CODES | relative size | relative normalised size | Mahler measure | NUMBER-FIELDS

Algebraic number field | TRACE | MATHEMATICS | MATHEMATICS, APPLIED | Schur-Siegel-Smyth trace problem | CODES | relative size | relative normalised size | Mahler measure | NUMBER-FIELDS

Journal Article

RSC Advances, ISSN 2046-2069, 2015, Volume 5, Issue 63, pp. 50962 - 50967

New corrole-BODIPY conjugates have been synthesized in high yield under mild conditions. Upon excitation at the absorption maximum of the BODIPY antenna...

ROUTE | DESIGN | DYES | PI-ELECTRON SYSTEMS | B-TERMS | MAGNETIC CIRCULAR-DICHROISM | PORPHYRIN | CHEMISTRY, MULTIDISCIPLINARY | ALGEBRAIC-SOLUTION | MCD | PERIMETER | Conjugates | Parents | Fluorescence | Phosphorescence | Chromophores | Excitation | Energy transfer | Antennas

ROUTE | DESIGN | DYES | PI-ELECTRON SYSTEMS | B-TERMS | MAGNETIC CIRCULAR-DICHROISM | PORPHYRIN | CHEMISTRY, MULTIDISCIPLINARY | ALGEBRAIC-SOLUTION | MCD | PERIMETER | Conjugates | Parents | Fluorescence | Phosphorescence | Chromophores | Excitation | Energy transfer | Antennas

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 01/2013, Volume 33, Issue 1, pp. 57 - 79

The long-time integration of Hamiltonian differential equations requires special numerical methods. Symplectic integrators are an excellent choice, but there...

Lobatto IIIA methods | simplifying assumptions | B-series | energy-preserving integrators | backward error analysis | Hamiltonian differential equations | conjugate symplecticity | modified equations | Lobatto IIIB methods | rooted trees | MATHEMATICS, APPLIED | ALGEBRAIC STRUCTURES | Conjugates | Algebra | Numerical analysis | Differential equations | Integrators | Mathematical models | Runge-Kutta method | Criteria

Lobatto IIIA methods | simplifying assumptions | B-series | energy-preserving integrators | backward error analysis | Hamiltonian differential equations | conjugate symplecticity | modified equations | Lobatto IIIB methods | rooted trees | MATHEMATICS, APPLIED | ALGEBRAIC STRUCTURES | Conjugates | Algebra | Numerical analysis | Differential equations | Integrators | Mathematical models | Runge-Kutta method | Criteria

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2019, Volume 350, pp. 80 - 86

A fast iterative algorithm is proposed for numerically computing an interval matrix containing the Hermitian positive definite solution to the conjugate...

Hermitian positive definite solution | Verified numerical computation | Perron–Frobenius theory | Discrete-time algebraic Riccati equation | MATHEMATICS, APPLIED | Perron-Frobenius theory | Algorithms

Hermitian positive definite solution | Verified numerical computation | Perron–Frobenius theory | Discrete-time algebraic Riccati equation | MATHEMATICS, APPLIED | Perron-Frobenius theory | Algorithms

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 7, pp. 2295 - 2310

By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested to solve a class of complex matrix equations. With...

Real representation | Hierarchical identification principle | Sylvester-conjugate matrix equation | Convergence | MATHEMATICS, APPLIED | EIGENVALUE LOWER BOUNDS | LEAST-SQUARES SOLUTIONS | LINEAR MATRIX | ALGEBRAIC RICCATI | DISCRETE LYAPUNOV EQUATION | REFLEXIVE SOLUTIONS | NORM | SYSTEMS | Analysis | Algorithms | Numerical analysis

Real representation | Hierarchical identification principle | Sylvester-conjugate matrix equation | Convergence | MATHEMATICS, APPLIED | EIGENVALUE LOWER BOUNDS | LEAST-SQUARES SOLUTIONS | LINEAR MATRIX | ALGEBRAIC RICCATI | DISCRETE LYAPUNOV EQUATION | REFLEXIVE SOLUTIONS | NORM | SYSTEMS | Analysis | Algorithms | Numerical analysis

Journal Article

PLoS ONE, ISSN 1932-6203, 10/2017, Volume 12, Issue 10, p. e0186207

Certificateless-based signcryption overcomes inherent shortcomings in traditional Public Key Infrastructure (PKI) and Key Escrow problem. It imparts efficient...

SCHEME | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Algorithms | Telemedicine | Confidentiality | Computer Security | Humans | Wireless Technology | Internet | Usage | Safety and security measures | Mobile communication systems | Wireless communication systems | Data security | Research | Cryptography | Access control | Research & development--R&D | Network security | Public Key Infrastructure | Encryption | Communications networks | Security | Internet of Things | Distributing | Authenticity | Computer science | Design | Privacy | Wireless networks | Computer applications | Differential equations | Computational efficiency | Digital signatures | Communication | Research & development | R&D

SCHEME | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Algorithms | Telemedicine | Confidentiality | Computer Security | Humans | Wireless Technology | Internet | Usage | Safety and security measures | Mobile communication systems | Wireless communication systems | Data security | Research | Cryptography | Access control | Research & development--R&D | Network security | Public Key Infrastructure | Encryption | Communications networks | Security | Internet of Things | Distributing | Authenticity | Computer science | Design | Privacy | Wireless networks | Computer applications | Differential equations | Computational efficiency | Digital signatures | Communication | Research & development | R&D

Journal Article

American Journal of Mathematics, ISSN 0002-9327, 6/2010, Volume 132, Issue 3, pp. 731 - 750

We show that conjugation by an automorphism of C may change the topological fundamental group of a locally symmetric variety over C. As a consequence, we...

Homomorphisms | Algebra | Mathematical theorems | Quaternion algebra | Functors | Polynomials | Automorphisms | Algebraic conjugates | Arithmetic | Shimura varieties | MATHEMATICS | Research | Topological spaces | Theorems | Algorithms

Homomorphisms | Algebra | Mathematical theorems | Quaternion algebra | Functors | Polynomials | Automorphisms | Algebraic conjugates | Arithmetic | Shimura varieties | MATHEMATICS | Research | Topological spaces | Theorems | Algorithms

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2018, Volume 58, Issue 8, pp. 1247 - 1258

Matrix-free conjugate gradient algorithms are described as applied to large systems of algebraic equations arising in the implementation of implicit schemes...

Computational Mathematics and Numerical Analysis | robustness | continuum mechanics | Mathematics | matrix-free conjugate gradient method | implicit schemes | large systems of algebraic equations | MATHEMATICS, APPLIED | FORMULATIONS | FLOWS | PHYSICS, MATHEMATICAL | Algorithms | Computer-aided design | Research institutes | Memory (Computers) | Computer memory | Conjugates | Continuum mechanics | Debugging

Computational Mathematics and Numerical Analysis | robustness | continuum mechanics | Mathematics | matrix-free conjugate gradient method | implicit schemes | large systems of algebraic equations | MATHEMATICS, APPLIED | FORMULATIONS | FLOWS | PHYSICS, MATHEMATICAL | Algorithms | Computer-aided design | Research institutes | Memory (Computers) | Computer memory | Conjugates | Continuum mechanics | Debugging

Journal Article

Mechanical Systems and Signal Processing, ISSN 0888-3270, 01/2015, Volume 50-51, pp. 249 - 259

A preconditioned conjugate gradient method is proposed for computing eigenvector derivatives with distinct and repeated eigenvalues in the real symmetric...

Real symmetric eigensystems | PCG method | Singularity | Distinct and repeated eigenvalues | Particular solutions | Eigenvector derivatives | STRUCTURAL REANALYSIS | NELSONS METHOD | ENGINEERING, MECHANICAL | COMPLEX EIGENVECTORS | MODAL SENSITIVITIES | ASYMMETRIC DAMPED SYSTEMS | EFFICIENT ALGEBRAIC-METHOD | CALCULATING DERIVATIVES | COMPUTATION | EIGENSOLUTION SENSITIVITY | CORRESPONDING EIGENVECTORS | Derivatives (Financial instruments) | Analysis | Methods | Computation | Mathematical analysis | Eigenvalues | Eigenvectors | Mathematical models | Derivatives | Iterative methods | Coefficients

Real symmetric eigensystems | PCG method | Singularity | Distinct and repeated eigenvalues | Particular solutions | Eigenvector derivatives | STRUCTURAL REANALYSIS | NELSONS METHOD | ENGINEERING, MECHANICAL | COMPLEX EIGENVECTORS | MODAL SENSITIVITIES | ASYMMETRIC DAMPED SYSTEMS | EFFICIENT ALGEBRAIC-METHOD | CALCULATING DERIVATIVES | COMPUTATION | EIGENSOLUTION SENSITIVITY | CORRESPONDING EIGENVECTORS | Derivatives (Financial instruments) | Analysis | Methods | Computation | Mathematical analysis | Eigenvalues | Eigenvectors | Mathematical models | Derivatives | Iterative methods | Coefficients

Journal Article

Comptes Rendus Mathematique, ISSN 1631-073X, 11/2015, Volume 353, Issue 11, pp. 1001 - 1005

Let X= G/ Γ be the quotient of a connected reductive algebraic C-group G by a finite subgroup Γ. We describe the topological fundamental group of the...

Homogeneous space | Linear algebraic group | Conjugate variety | Fundamental group

Homogeneous space | Linear algebraic group | Conjugate variety | Fundamental group

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2002, Volume 39, Issue 1, pp. 300 - 329

We give a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the conjugate gradient...

Approximation | Spectral theory | Eigenvalues | Potential theory | Poisson equation | Boundary conditions | Polynomials | Mathematics | Algebraic conjugates | Greens function | Toeplitz systems | Conjugate gradients | Superlinear convergence | Logarithmic potential theory | Krylov subspace methods | MATHEMATICS, APPLIED | EXTREMAL POLYNOMIALS | conjugate gradients | APPROXIMATION | superlinear convergence | ORTHOGONAL POLYNOMIALS | logarithmic potential theory | LANCZOS

Approximation | Spectral theory | Eigenvalues | Potential theory | Poisson equation | Boundary conditions | Polynomials | Mathematics | Algebraic conjugates | Greens function | Toeplitz systems | Conjugate gradients | Superlinear convergence | Logarithmic potential theory | Krylov subspace methods | MATHEMATICS, APPLIED | EXTREMAL POLYNOMIALS | conjugate gradients | APPROXIMATION | superlinear convergence | ORTHOGONAL POLYNOMIALS | logarithmic potential theory | LANCZOS

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 11/2015, Volume 353, Issue 11, pp. 1001 - 1005

Let X=G/Γ be the quotient of a connected reductive algebraic C-group G by a finite subgroup Γ. We describe the topological fundamental group of the homogeneous...

Homogeneous space | Linear algebraic group | Fundamental group | Conjugate variety | MATHEMATICS | ABSOLUTE GALOIS GROUP | VARIETIES

Homogeneous space | Linear algebraic group | Fundamental group | Conjugate variety | MATHEMATICS | ABSOLUTE GALOIS GROUP | VARIETIES

Journal Article

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