FOCK SPACE STRUCTURE FOR THE SIMPLEST PARASUPERSYMMETRIC SYSTEM

Structure of the state-vector space for a system consisting of one mode para-Bose and one mode para-Fermi degree of freedom with the same parastatistics order p is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with m parabosons and n parafermions, where m ≠ 0, n ≠ 0 and n ≠ p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.

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An Eigenvalue Inclusion Principle for Simple, Rotationally Periodic Structures

14th Biennial Conference on Mechanical Vibration and Noise: Vibration of Rotating Systems ◽

10.1115/detc1993-0195 ◽

1993 ◽

Author(s):

I. Y. Shen

Keyword(s):

Linear Combination ◽

Periodic Structure ◽

State Vector ◽

Transfer Functions ◽

Periodic Structures ◽

The State ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Inclusion Property ◽

Single Degree

Abstract This paper describes an eigenvalue inclusion principle for a simple, rotationally periodic structure P whose i-th substructure Si is connected to a neighboring substructure Si+1 through a single-degree-of-freedom interface constraint Ii+1. The state vector vi+1 at the interface Ii+1, consisting of the displacement and the force at the interface, is represented in terms of the state vector vi at the interface Ii through transfer functions of the substructure Si. The periodicity of the structure P then requires that a linear combination of the transfer functions of Si be zero. As a consequence, a simple periodic structure P with period N will have exactly N eigenvalues lying between two consecutive eigenvalues of the substructure Si. Finally, this eigenvalue inclusion property is illustrated on a periodic structure with known exact eigensolutions.

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The state-vector space for two-mode parabosons and charged parabose coherent states

Journal of Physics A General Physics ◽

10.1088/0305-4470/32/22/313 ◽

1999 ◽

Vol 32 (22) ◽

pp. 4131-4138 ◽

Cited By ~ 2

Author(s):

Sicong Jing ◽

Charles A Nelson

Keyword(s):

Vector Space ◽

State Vector ◽

Coherent States ◽

The State

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Generalization of Geyer’s commutation relations with respect to the orthogonal group in even dimensions

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08605-4 ◽

2020 ◽

Vol 80 (12) ◽

Author(s):

Yu. A. Markov ◽

M. A. Markova

Keyword(s):

Vector Space ◽

State Vector ◽

Orthogonal Group ◽

Coherent States ◽

Fock Space ◽

Star Product ◽

Grassmann Algebra ◽

Moyal Product ◽

Commutation Relations ◽

The Matrix

AbstractA connection between the deformed Duffin–Kemmer–Petiau (DKP) algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators $$a^{\pm }_{k}$$ a k ± and for an additional operator $$a_{0}$$ a 0 obeying para-Fermi statistics of order 2 based on the Lie algebra $${\mathfrak {s}}{\mathfrak {o}}(2M+2)$$ s o ( 2 M + 2 ) is established. An appropriate system of the parafermion coherent states as functions of para-Grassmann numbers is introduced. The representation for the operator $$a_{0}$$ a 0 in terms of generators of the orthogonal group SO(2M) correctly reproducing action of this operator on the state vectors of Fock space is obtained. A connection of the Geyer operator $$a_{0}^{2}$$ a 0 2 with the operator of so-called G-parity and with the CPT- operator $${\hat{\eta }}_{5}$$ η ^ 5 of the DKP-theory is established. In a para-Grassmann algebra a noncommutative, associative star product $$*$$ ∗ (the Moyal product) as a direct generalization of the star product in the algebra of Grassmann numbers is introduced. Two independent approaches to the calculation of the Moyal product $$*$$ ∗ are considered. It is shown that in calculating the matrix elements in the basis of parafermion coherent states of various operator expressions it should be taken into account constantly that we work in the so-called Ohnuki and Kamefuchi’s generalized state-vector space $${\mathfrak {U}}_{\;G}$$ U G , whose state vectors include para-Grassmann numbers $$\xi _{k}$$ ξ k in their definition, instead of the standard state-vector space $${\mathfrak {U}}$$ U (the Fock space).

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Operators and meaning of wave function

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i8.216 ◽

2016 ◽

pp. 4039-4042

Author(s):

Viliam Malcher

Keyword(s):

Wave Function ◽

Quantum Theory ◽

State Vector ◽

The State ◽

Physical Significance ◽

Central Problem ◽

Quantum Mechanical ◽

Mechanical Description ◽

Quantum Mechanical Description ◽

Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |Ïˆ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |Ïˆ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

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The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

Informacionno-technologicheskij vestnik ◽

10.21499/2409-1650-2018-1-12-22 ◽

2018 ◽

Vol 15 (1) ◽

pp. 12-22

Author(s):

V. M. Artyushenko ◽

D. Y. Vinogradov

Keyword(s):

Remote Sensing ◽

Gravitational Field ◽

State Vector ◽

Semimajor Axis ◽

The State ◽

Zonal Harmonics ◽

The Earth ◽

Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

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FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE

Journal of the Australian Mathematical Society ◽

10.1017/s1446788716000033 ◽

2016 ◽

Vol 101 (2) ◽

pp. 277-287

Author(s):

AARON TIKUISIS

Keyword(s):

Vector Space ◽

Inductive Limit ◽

Space Structure ◽

Vector Spaces ◽

Ordered Vector Space ◽

Finite Dimensional ◽

Ordered Vector Spaces

It is shown that, for any field $\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of $\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages $(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where $n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with $\mathbb{F}$ replaced by the integers, $\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with $\mathbb{Q}$.

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Combined assimilation of streamflow and snow water equivalent for mid-term ensemble streamflow forecasts in snow-dominated regions

10.5194/hess-2016-166 ◽

2016 ◽

Author(s):

Jean M. Bergeron ◽

Mélanie Trudel ◽

Robert Leconte

Keyword(s):

Data Assimilation ◽

State Vector ◽

Snow Water Equivalent ◽

Synthetic Data ◽

Hydrologic Model ◽

Open Loop ◽

The State ◽

Wide Range ◽

Snow Water ◽

The Impact

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the Ensemble Kalman Filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British-Columbia, Canada. Synthetic data includes daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than its individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.

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ISAR Signal Tracking and High-Resolution Imaging by Kalman Filtering

Remote Sensing ◽

10.3390/rs13173389 ◽

2021 ◽

Vol 13 (17) ◽

pp. 3389

Author(s):

Pei Ye ◽

Meng-Dao Xing ◽

Xiang-Gen Xia ◽

Guang-Cai Sun ◽

Yachao Li ◽

...

Keyword(s):

High Resolution ◽

Kalman Filtering ◽

State Vector ◽

Observation Time ◽

The State ◽

Range Resolution ◽

Resolution Image ◽

High Resolution Image ◽

Reconstruction Performance ◽

Short Observation Time

In a short observation time, after the range alignment and phase adjustment, the motion of a target can be approximated as a uniform rotation. The radar observing process can be simply described as multiplying an observation matrix on the ISAR image, which can be thought of as a linear system. It is known that the longer observation time is, the higher cross-range resolution is. In order to deal with the conflict between short observation time and high cross-range resolution, we introduce Kalman filtering (KF) into the ISAR imaging and propose a novel method to reconstruct a high-resolution image with short time observed data. As KF has excellent reconstruction performance, it leads to a good application in ISAR image reconstruction. At each observation aperture, the reconstructed image denotes the state vector in KF at the aperture time. It is corrected by a two-step KF process: prediction and update. As iteration continues, the state vector is gradually corrected to a well-focused high-resolution image. Thus, the proposed method can obtain a high-resolution image in a short observation time. Both simulated and real data are applied to demonstrate the performance of the proposed method.

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