scholarly journals Seeking for the Maximum Symmetric Rank

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 247 ◽  
Author(s):  
Alessandro De Paris
Keyword(s):  
State Of The Art ◽  
Symmetric Tensor ◽  
Upper Bounds ◽  
The State ◽  
Tensor Rank ◽  
Symmetric Tensors ◽  
Lower And Upper Bounds ◽  
Symmetric Tensor Rank ◽  
Set Up ◽  
Divided Powers

We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and the methods that have been set up in recent times to find new lower and upper bounds.

scholarly journals Symmetric Tensors and Symmetric Tensor Rank

2008 ◽  
Vol 30 (3) ◽  
pp. 1254-1279 ◽  
Author(s):  
Pierre Comon ◽  
Gene Golub ◽  
Lek-Heng Lim ◽  
Bernard Mourrain
Keyword(s):  
Symmetric Tensor ◽  
Tensor Rank ◽  
Symmetric Tensors ◽  
Symmetric Tensor Rank

scholarly journals An Upper Bound for the Symmetric Tensor Rank of a Low Degree Polynomial in a Large Number of Variables

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-2 ◽  
Author(s):  
E. Ballico
Keyword(s):  
Upper Bound ◽  
Homogeneous Polynomial ◽  
Symmetric Tensor ◽  
Tensor Rank ◽  
Degree Polynomial ◽  
Linear Forms ◽  
Symmetric Tensor Rank ◽  
Low Degree ◽  
Powers Of Linear Forms

Fix integers m≥5 and d≥3. Let f be a degree d homogeneous polynomial in m+1 variables. Here, we prove that f is the sum of at most d·⌈(m+dm)/(m+1)⌉d-powers of linear forms (of course, this inequality is nontrivial only if m≫d.)

Model Testing for Vortex Induced Motions of Spar Platforms

2004 ◽  
Author(s):  
Mehernosh Irani ◽  
Lyle Finn
Keyword(s):  
Gulf Of Mexico ◽  
Model Test ◽  
State Of The Art ◽  
Model Testing ◽  
Model Tests ◽  
The State ◽  
Test Results ◽  
Test Set ◽  
Vortex Induced Vibrations ◽  
Set Up

The state-of-the art in model testing for Vortex Induced Vibrations (VIV) of Spars is presented. Important issues related to Spar VIV model testing are highlighted. The parameters that need to be modeled including hull geometry, strake configuration, mass and mooring properties and, considerations of test set-up and instrumentation are discussed. Results are presented from model tests of an as-built Spar deployed in the Gulf of Mexico. It is shown that the model test results compare well with the VIV responses measured in the field.

scholarly journals Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 886
Author(s):  
Jun-Yi Wu
Keyword(s):  
Quantum State ◽  
Adaptive Method ◽  
Upper Bounds ◽  
The State ◽  
Entangled States ◽  
Lower And Upper Bounds ◽  
Bipartite Entanglement ◽  
Higher Dimensional ◽  
Computational Basis

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.

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