Results 61 to 70 of about 1,412,537 (346)
The Square-Zero Basis of Matrix Lie Algebras
Mathematics, 2020 A method is presented that allows one to compute the maximum number of functionally-independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a basis of square-zero matrices even on a field of positive
Raúl Durán Díaz +3 more
doaj +1 more source
Topology in Biological Piezoelectric Materials
Advanced Materials, EarlyView.This review summarizes the topological structures in biological piezoelectric materials, covering morphology evolution, spatial arrangement, and biomimetic strategies. These topologies modulate structure‐property relationships across multiple scales, enabling performance enhancement and multifunctional integration.
Chen Chen +7 more
wiley +1 more source
On the quantum security of high-dimensional RSA protocol
Journal of Mathematical CryptologyThe idea of extending the classical RSA protocol using algebraic number fields was introduced by Takagi and Naito (Construction of RSA cryptosystem over the algebraic field using ideal theory and investigation of its security.
Rahmani Nour-eddine +3 more
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Advancement in Colloidal Metasurfaces: Approaches for Scalable Photonic Devices
Advanced Materials Interfaces, EarlyView.This perspective explores colloidal metasurfaces composed of plasmonic and emitting nanoparticles assembled by laser interference lithography and template‐assisted self‐assembly methods. Precise design strategies achieve directional emission, low‐threshold lasing, and tunable photonic bandgaps.
Sezer Seçkin +2 more
wiley +1 more source
Lower Bounds for Heights in Relative Galois Extensions
, 2017 The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser.
CJ Smyth +18 more
core +1 more source
On the semigroup of ideal classes in an order of an algebraic number field
, 1961 There is a natural link between classes of ideals in orders of algebraic number fields and similarity classes of integral matrices defined by unimodular matrices.
E. Dade, O. Taussky, H. Zassenhaus
semanticscholar +1 more source
Advanced Optical Materials, EarlyView.Theoretical lessons are key for molecules presenting an inverted singlet‐triplet excited state (e.g. S1 and T1) energy difference. This perspective provides a snapshot of the role played by calculations in last years, not only to anticipate experimental findings but also for driving high‐throughput virtual screenings, as well as the main challenge to ...
Ángel José Pérez‐Jiménez +2 more
wiley +1 more source
The Genus Field and Genus Number in Algebraic Number Fields [PDF]
Nagoya Mathematical Journal, 1967 Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
openaire +3 more sources
Another formulation of the Wick’s theorem. Farewell, pairing?
Special Matrices, 2015 The algebraic formulation of Wick’s theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed.
Beloussov Igor V.
doaj +1 more source
, 1965 Here $A_{-1}$ , the residue of $\zeta_{K}(s)$ at $s=1$ , was determined by Dirichlet and Dedekind for any algebraic number field $K$. However, little is known about the constant term $A_{0}$ , in spite of its importance. As far as the author knows, $A_{0}
Shuji Konno
semanticscholar +1 more source