The tensor product of supersymmetric N = (1,1) spectral data

2018 ◽  
Vol 15 (12) ◽  
pp. 1850207 ◽  
Author(s):  
Satyajit Guin
Keyword(s):  
Quantum Theory ◽  
Tensor Product ◽  
Spectral Data ◽  
Noncommutative Geometry ◽  
Product Formula ◽  
Unitary Connection ◽  
The Individual

We define the notion of tensor product of supersymmetric [Formula: see text] spectral data in the context of supersymmetric quantum theory and noncommutative geometry. We explain in which sense our definition is canonical and also establish its compatibility with the tensor product of [Formula: see text] spectral data defined earlier by Connes. As an application, we show that the unitary connections on the individual [Formula: see text] spectral data give rise to a unitary connection on the product [Formula: see text] spectral data.

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

Environmental and geographical effects on fog occurrence

2021 ◽  
Author(s):  
Iva Hunova ◽  
Marek Brabec ◽  
Marek Malý ◽  
Alexandru Dumitrescu ◽  
Jan Geletič
Keyword(s):  
Air Pollution ◽  
Environmental Factors ◽  
Tensor Product ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Low Rank ◽  
Seasonal Component ◽  
Explanatory Variables ◽  
The Individual

<p>Fog is a very complex phenomenon (Gultepe et al., 2007). In some areas it can contribute substantially to hydrological and chemical inputs and is therefore of high environmental relevance (Blas et al., 2010). Fog formation is affected by numerous factors, such as meteorology, air pollution, terrain (geomorphology), and land-use.</p><p>In our earlier studies we addressed the role of meteorology and air pollution on fog occurrence (Hůnová et al., 2018) and long-term trends in fog occurrence in Central Europe (Hůnová et al., 2020). This study builds on earlier model identification of year-to-year and seasonal components in fog occurrence and brings an analysis of the deformation of the above components due to the individual explanatory variables. The aim of this study was to indicate the geographical and environmental factors affecting the fog occurrence.</p><p>       We have examined the data on fog occurrence from 56 meteorological stations of various types from Romania reflecting different environments and geographical areas. We used long-term records from the 1981–2017 period. </p><p>       We considered both the individual explanatory variables and their interactions. With respect to geographical factors, we accounted for the altitude and landform. With respect to environmental factors,   we accounted for proximity of large water bodies, and proximity of forests. Geographical data from Copernicus pan-European (e.g. CORINE land cover, high resolution layers) and local (e.g. Urban Atlas) projects were used. Elevation data from EU-DEM v1.1 were source for morphometric analysis (Copernicus, 2020).</p><p>        We applied a generalized additive model, GAM (Wood, 2017; Hastie & Tibshirani, 1990) to address nonlinear trend shapes in a formalized and unified way. In particular, we employed penalized spline approach with cross-validated penalty coefficient estimation. To explore possible deformations of annual and seasonal components with various covariates of interest, we used (penalized) tensor product splines to model (two-way) interactions parsimoniously, Wood (2006).</p><p>       The fog occurrence showed significant decrease over the period under review. In general the selected explanatory variables significantly affected the fog occurrence and their effect was non-linear. Our results indicated that, the geographical and environmental variables affected primarily the seasonal component of the model. Of the factors which were accounted for, it was mainly the altitude showing the clear effect on seasonal component deformation (Hůnová et al., in press).</p><p>      </p><p> </p><p>References:</p><p>Blas, M, Polkowska, Z., Sobik, M., et al. (2010). Atmos. Res. 95, 455–469.</p><p>Copernicus Land Monitoring Service (2020). Accessed online at: https://land.copernicus.eu/.</p><p>Gultepe, I., Tardif, R., Michaelidis, S.C., Cermak, J., Bott, A. et al. (2007). Pure Appl Geophys, 164, 1121-1159.</p><p>Hastie, T.J., Tibshirani, R.J. (1990). Generalized Additive Models. Boca Raton, Chapman & Hall/CRC.</p><p>Hůnová, I., Brabec, M., Malý, M., Dumitrescu, A., Geletič, J. (in press) Sci. Total Environ. 144359.</p><p>Hůnová, I., Brabec, M., Malý, M., Valeriánová, A. (2018) Sci. Total Environ. 636, 1490–1499.</p><p>Hůnová, I., Brabec, M., Malý, M., Valeriánová, A. (2020) Sci. Total Environ. 711, 135018.</p><p>Wood, S.N. (2006) Low rank scale invariant tensor product smooths for generalized additive mixed models. Biometrics 62(4):1025-1036</p><p>Wood, S.N. (2017). Generalized Additive Models: An Introduction with R (2nd ed). Boca Raton, Chapman & Hall/CRC.</p><p> </p>

The Tensor Product Formula for Reflexive Subspace Lattices

1995 ◽  
Vol 38 (3) ◽  
pp. 308-316 ◽  
Author(s):  
K. J. Harrison
Keyword(s):  
Tensor Product ◽  
Operator Algebra ◽  
Product Formula ◽  
Completely Distributive ◽  
Reflexive Subspace ◽  
Complemented Lattice ◽  
Csl Algebra ◽  
Subspace Lattices

AbstractWe give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.

scholarly journals An inverse spectral problem for a star graph of Krein strings

2016 ◽  
Vol 2016 (715) ◽  
Author(s):  
Jonathan Eckhardt
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Inverse Spectral Problem ◽  
Trace Class ◽  
Star Graph ◽  
Borel Measures ◽  
Inverse Spectral ◽  
The Individual

AbstractWe solve an inverse spectral problem for a star graph of Krein strings, where the known spectral data comprises the spectrum associated with the whole graph, the spectra associated with the individual edges as well as so-called coupling matrices. In particular, we show that these spectral quantities uniquely determine the weight within the class of Borel measures on the graph, which give rise to trace class resolvents. Furthermore, we obtain a concise characterization of all possible spectral data for this class of weights.

scholarly journals A Quantum Approach to the Psychosomatic Phenomenon: Co-Emergence and Time Entanglement of Mind and Matter

KronoScope ◽  
2012 ◽  
Vol 12 (2) ◽  
pp. 219-244 ◽  
Author(s):  
Pierre Uzan
Keyword(s):  
Quantum Theory ◽  
Physical World ◽  
Neutral Monism ◽  
Quantum Approach ◽  
The Individual

AbstractThis paper explores the philosophy of neutral monism within the framework of a generalized version of quantum theory where all references to the physical world have been relaxed. Psychic and somatic features of the individual are conceived of as co-emergent, complementary properties of an underlying, psychophysical level of reality. It is shown that their entanglement can be interpreted in terms of non-causal correlations and parameterized by time, which thus plays the role of psychophysical interface.

A d-DEFORMATION OF FREE GAUSSIAN RANDOM VARIABLES

2005 ◽  
Vol 08 (04) ◽  
pp. 669-680 ◽  
Author(s):  
JANUSZ WYSOCZAŃSKI
Keyword(s):  
Tensor Product ◽  
Hypergeometric Series ◽  
Fock Space ◽  
Recurrence Formula ◽  
Random Variables ◽  
Product Formula ◽  
Continuous Part ◽  
Absolutely Continuous ◽  
Gaussian Random Variables ◽  
Special Case

We define a deformation of free creations (and annihilations), given by operators on the full Fock space, acting nontrivially only between the vacuum subspace ℂΩ and the twofold tensor product [Formula: see text]. Then we study the distribution of the deformed free gaussian operators, with the deformation containing also a real parameter d. The recurrence formula for moments is shown, and the Cauchy transform of the distribution measure is computed. This yields the description of the measure: absolutely continuous part and the atomic part. The existence of atoms depends on the parameter d. The special case d =1 is studied with all details, with the formula for moments is given as values of the hypergeometric series. Finally we show the formula for computing the mixed moments of the deformed operators.

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

scholarly journals On the Tensor Convolution and the Quantum Separability Problem

2010 ◽  
Vol 17 (04) ◽  
pp. 331-346
Author(s):  
Gabriel Pietrzkowski
Keyword(s):  
Abelian Group ◽  
Tensor Product ◽  
Hermitian Operator ◽  
Product Formula ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Equivalent Problem ◽  
Finite Dimensional ◽  
Separability Problem ◽  
Convolution Formula

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product [Formula: see text] is separable or entangled. We show that the tensor convolution [Formula: see text] defined for mappings [Formula: see text] on an almost arbitrary locally compact abelian group G , gives rise to formulation of an equivalent problem to the separability one.

A FEW HOMOLOGICAL CHARACTERIZATIONS OF COMPACT SEMISIMPLE RINGS

2005 ◽  
Vol 04 (05) ◽  
pp. 539-549
Author(s):  
ALINA ALB ◽  
MIHAIL URSUL
Keyword(s):  
Abelian Group ◽  
Tensor Product ◽  
Compact Abelian Group ◽  
Product Formula ◽  
Flat Module ◽  
Compact Ring ◽  
Module Theory ◽  
Flat Modules ◽  
Semisimple Module

Fix any compact ring R with identity. We associate to R the following categories of topological R-modules: (i) R𝔇 (𝔇R) the category of all discrete topological left (right) R-modules; (ii) Rℭ (ℭR) the category of all compact left (right) R-modules. We have introduced the following notions (analogous with classical notions of module theory): (i) the tensor product [Formula: see text] of A ∈ ℭR and B ∈Rℭ ([Formula: see text] has a structure of a compact Abelian group); (ii) a topologically semisimple module; (iii) a compact topologically flat module. We give a characterization of compact semisimple rings by using of flat modules.

Zur Existenz von [ReNCl4-nFn]- (n = 1-3) Nitridorhenat(VI)-Gemischt- ligandkomplexen -Eine EPR-Untersuchung / EPR Evidence of [ReNCl4-n FnJ– (n = 1-3) Nitridorhenate(VI) Mixed-Ligand Complexes

1998 ◽  
Vol 53 (10) ◽  
pp. 1183-1187 ◽  
Author(s):  
Andreas Voigt ◽  
Ulrich Abram ◽  
Reinhard Kirmse
Keyword(s):  
Spectral Data ◽  
Coordination Sphere ◽  
Linear Dependence ◽  
Mixed Ligand ◽  
Mixed Ligand Complexes ◽  
Additivity Rules ◽  
Hyperfine Splittings ◽  
Frozen Solutions ◽  
The Individual

AbstractThe formation of mixed-ligand complexes of the type [ReVlNCl4-nFn]- (n = 1 -3) during the reaction of [ReVINCl4]- with [n-(C4H9)4N]F, KF, and HF is reported. Evidence of the individual mixed-ligand compounds is given by their EPR spectral data. In frozen solutions a specific dependence of the EPR data on the composition of the coordination sphere could be detected. This is shown (i) by a nearly linear dependence of gII and AII Re on the Cl/F-content of the [ReVINCl4-nFn]- unit (additivity rules) and (ii) by well-resolved 19F hyperfine splittings.

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