Using the one-dimensional S-transform as a discrimination tool in classification of hyperspectral images

2007 ◽  
Vol 33 (6) ◽  
pp. 551-560 ◽  
Author(s):  
Bhaskar C Sahoo ◽  
Thomas Oommen ◽  
Debasmita Misra ◽  
Gregory Newby
Keyword(s):  
Hyperspectral Images ◽  
One Dimensional ◽  
S Transform ◽  
The One

scholarly journals Yang-Baxter and the Boost: splitting the difference

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Paul Ryan
Keyword(s):  
Hilbert Space ◽  
Sigma Model ◽  
Spin Chains ◽  
Baxter Equation ◽  
Regular Solutions ◽  
One Dimensional ◽  
Difference Form ◽  
The Difference ◽  
The One

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

scholarly journals OCTONIONIC REALIZATIONS OF ONE-DIMENSIONAL EXTENDED SUPERSYMMETRIES: A CLASSIFICATION

2003 ◽  
Vol 18 (11) ◽  
pp. 787-798 ◽  
Author(s):  
H. L. CARRION ◽  
M. ROJAS ◽  
F. TOPPAN
Keyword(s):  
Dynamical Systems ◽  
Dimensional Reduction ◽  
Spinning Particles ◽  
One Dimensional ◽  
The One ◽  
M Theory

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already classified associative representations for 1D extended supersymmetries. Examples of dynamical systems invariant under octonionic realizations of the extended supersymmetries are given. We cite among the others the octonionic spinning particles, the N = 8 KdV , etc. Possible applications to supersymmetric systems arising from dimensional reduction of the octonionic superstring and M-theory are mentioned.

scholarly journals Minimal-dimensional representations of reduced enveloping algebras for

2019 ◽  
Vol 155 (8) ◽  
pp. 1594-1617
Author(s):  
Simon M. Goodwin ◽  
Lewis Topley
Keyword(s):  
Coadjoint Orbit ◽  
Closed Field ◽  
One Dimensional ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Primitive Ideals ◽  
Levi Subalgebra ◽  
The One ◽  
Dimensional Module

Let $\mathfrak{g}=\mathfrak{g}\mathfrak{l}_{N}(\Bbbk )$ , where $\Bbbk$ is an algebraically closed field of characteristic $p>0$ , and $N\in \mathbb{Z}_{{\geqslant}1}$ . Let $\unicode[STIX]{x1D712}\in \mathfrak{g}^{\ast }$ and denote by $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ the corresponding reduced enveloping algebra. The Kac–Weisfeiler conjecture, which was proved by Premet, asserts that any finite-dimensional $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ -module has dimension divisible by $p^{d_{\unicode[STIX]{x1D712}}}$ , where $d_{\unicode[STIX]{x1D712}}$ is half the dimension of the coadjoint orbit of $\unicode[STIX]{x1D712}$ . Our main theorem gives a classification of $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ -modules of dimension $p^{d_{\unicode[STIX]{x1D712}}}$ . As a consequence, we deduce that they are all parabolically induced from a one-dimensional module for $U_{0}(\mathfrak{h})$ for a certain Levi subalgebra $\mathfrak{h}$ of $\mathfrak{g}$ ; we view this as a modular analogue of Mœglin’s theorem on completely primitive ideals in $U(\mathfrak{g}\mathfrak{l}_{N}(\mathbb{C}))$ . To obtain these results, we reduce to the case where $\unicode[STIX]{x1D712}$ is nilpotent, and then classify the one-dimensional modules for the corresponding restricted $W$ -algebra.

scholarly journals Differential modules on p-adic polyannuli

2009 ◽  
Vol 9 (1) ◽  
pp. 155-201 ◽  
Author(s):  
Kiran S. Kedlaya ◽  
Liang Xiao
Keyword(s):  
Complex Manifolds ◽  
Prior Work ◽  
One Dimensional ◽  
Formal Classification ◽  
Positive Residue ◽  
Numerical Invariants ◽  
Residue Characteristic ◽  
Differential Modules ◽  
The One

AbstractWe consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic 0. This extends prior work in the one-dimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevance to the study of Swan conductors for isocrystals, they are germane to the formal classification of flat meromorphic connections on complex manifolds.

scholarly journals Formal classification of unfoldings of parabolic diffeomorphisms

2008 ◽  
Vol 28 (4) ◽  
pp. 1323-1365 ◽  
Author(s):  
JAVIER RIBÓN
Keyword(s):  
Differential Equation ◽  
Complete System ◽  
Classification Problem ◽  
Higher Dimension ◽  
One Dimensional ◽  
Formal Classification ◽  
Linear Differential ◽  
The One ◽  
Tangent To The Identity

AbstractWe provide a complete system of invariants for the formal classification of unfoldings φ(x,x1,…,xn)=(f(x,x1,…,xn),x1,…,xn) of complex analytic germs of diffeomorphisms at $({\mathbb C},0)$ that are tangent to the identity. We reduce the formal classification problem to solving a linear differential equation. Then we describe the formal invariants; their nature depends on the position of the fixed points set Fix φ with respect to the regular vector field ∂/∂x. We get invariants specifically attached to higher dimension (n≥3), although generically they are analogous to the one-dimensional ones.

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