Results 81 to 90 of about 64,415 (198)

On the Foundational Arguments of Sufficient Dimension Reduction

WIREs Computational Statistics, Volume 18, Issue 2, June 2026.
Contemporary Sufficient Dimension Reduction, a versatile method for extracting material information from data, can serve as a preprocessor for classical modeling and inference, or as a standalone theory that leads directly to statistical inference. ABSTRACT Sufficient dimension reduction (SDR) refers to supervised methods of dimension reduction that ...
R. Dennis Cook
wiley   +1 more source

Grassmann algebras as Hilbert space

Journal of Algebra, 1968
Let \(A= (A_{ij})\) \((1\le i, j \le m)\) be an \((mn)\)-square positive definite Hermitian matrix, where each \(A_{ij}\) is an \(n\)-square matrix. Let \(A_{(k)} = (A_{ij})_{1\le i, j \le k}\) be the upper left \((nk)\)-square submatrix of \(A\), and let \(\tilde A_{(k)} = (\det A_{ij})_{1\le i, j \le k}\) denote the \(k\)-square matrix obtained by ...
openaire   +2 more sources

On Involutive Weak Exchange Algebras

Bulletin of the Section of Logic
In this paper, involutive weak exchange algebras (for short, involutive WE algebras) are introduced and studied. Their properties and characterizations are investigated. Some important results and examples are given.
Andrzej Walendziak
doaj   +1 more source

An extended definition of Anosov representation for relatively hyperbolic groups

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
wiley   +1 more source

On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5)

Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
The generalized and ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants of autonomous polynomial differential systems are of particular importance for some problems of qualitative theory of differential systems.
Lidia Mușinschi, Victor Pricop
doaj   +1 more source

Quiver theories and formulae for nilpotent orbits of Exceptional algebras

Journal of High Energy Physics, 2017
We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their representation content.
Amihay Hanany, Rudolph Kalveks
doaj   +1 more source

Shannon and Rényi Entropies of Molecular Densities Under Atomic Partitioning: Insights Into Extensity and an Incomplete Description of Electron Correlation

International Journal of Quantum Chemistry, Volume 126, Issue 10, May 15, 2026.
At infinite separation, a diatomic molecule reduces to two noninteracting subsystems. The electron density decomposes into atomic densities, while the Rényi entropy functional reveals both additive atomic contributions and nonadditive terms. None of these terms contains any trace of the presence of static correlation effects, particularly important in ...
Diogo J. L. Rodrigues, Evelio Francisco, Ángel Martín Pendás   +2 more
wiley   +1 more source

Countable Basis for Free Electromagnetic Fields

Annalen der Physik, Volume 538, Issue 5, May 2026.
ABSTRACT Polychromatic electromagnetic fields are expanded as integrals over monochromatic fields, such as plane waves, multipolar fields, or Bessel beams. However, monochromatic fields do not belong to the Hilbert space of free Maxwell fields, since their norms diverge.
Ivan Fernandez‐Corbaton
wiley   +1 more source

Perfect Hilbert algebras

Reports on Mathematical Logic
In [S. Celani and L. Cabrer. Duality for finite Hilbert algebras. Discrete Math., 305(1-3):74{99, 2005.] the authors proved that every finite Hilbert algebra A is isomorphic to the Hilbert algebra HK(X) = {w ⇒ i v : w ∈ K and v ⊆ w}, where X is a finite poset, K is a distinguished collection of subsets of X, and the implication ⇒i is defined by: w ⇒i ...
openaire   +1 more source

Trees, parking functions, syzygies, and deformations of monomial ideals

, 2003
For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ...
Postnikov, Alexander, Shapiro, Boris
core   +5 more sources