scholarly journals Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors

2019 ◽  
Vol 15 (2) ◽  
pp. 775-789 ◽  
Author(s):  
Yining Gu ◽  
◽  
Wei Wu
Keyword(s):  
Rectangular Tensors ◽  
Partially Symmetric

On copositiveness identification of partially symmetric rectangular tensors

2020 ◽  
Vol 372 ◽  
pp. 112678 ◽  
Author(s):  
Chunyan Wang ◽  
Haibin Chen ◽  
Yiju Wang ◽  
Guanglu Zhou
Keyword(s):  
Rectangular Tensors ◽  
Partially Symmetric

l k,s -Singular values and spectral radius of partially symmetric rectangular tensors

2015 ◽  
Vol 11 (3) ◽  
pp. 605-622 ◽  
Author(s):  
Hongmei Yao ◽  
Bingsong Long ◽  
Changjiang Bu ◽  
Jiang Zhou
Keyword(s):  
Spectral Radius ◽  
Singular Values ◽  
Rectangular Tensors ◽  
Partially Symmetric

scholarly journals An SDP Method for Copositivity of Partially Symmetric Tensors

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chunyan Wang ◽  
Haibin Chen ◽  
Haitao Che
Keyword(s):  
Numerical Results ◽  
Semidefinite Relaxation ◽  
Symmetric Tensors ◽  
Relaxation Algorithm ◽  
Rectangular Tensors ◽  
Partially Symmetric

In this paper, we consider the problem of detecting the copositivity of partially symmetric rectangular tensors. We first propose a semidefinite relaxation algorithm for detecting the copositivity of partially symmetric rectangular tensors. Then, the convergence of the proposed algorithm is given, and it shows that we can always catch the copositivity of given partially symmetric tensors. Several preliminary numerical results confirm our theoretical findings.

scholarly journals A Flower-Shape Geometry and Nonlinear Problems on Strip-Like Domains

2020 ◽  
Author(s):  
Giuseppe Devillanova ◽  
Giovanni Molica Bisci ◽  
Raffaella Servadei
Keyword(s):  
Symmetric Functions ◽  
Geometrical Structure ◽  
Nonlinear Problems ◽  
Entire Space ◽  
Lebesgue Spaces ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Partially Symmetric

AbstractIn the present paper, we show how to define suitable subgroups of the orthogonal group $${O}(d-m)$$ O ( d - m ) related to the unbounded part of a strip-like domain $$\omega \times {\mathbb {R}}^{d-m}$$ ω × R d - m with $$d\ge m+2$$ d ≥ m + 2 , in order to get “mutually disjoint” nontrivial subspaces of partially symmetric functions of $$H^1_0(\omega \times {\mathbb {R}}^{d-m})$$ H 0 1 ( ω × R d - m ) which are compactly embedded in the associated Lebesgue spaces. As an application of the introduced geometrical structure, we prove (existence and) multiplicity results for semilinear elliptic problems set in a strip-like domain, in the presence of a nonlinearity which either satisfies the classical Ambrosetti–Rabinowitz condition or has a sublinear growth at infinity. The main theorems of this paper may be seen as an extension of existence and multiplicity results, already appeared in the literature, for nonlinear problems set in the entire space $${\mathbb {R}}^d$$ R d , as for instance, the ones due to Bartsch and Willem. The techniques used here are new.

Partially Symmetric Values

2000 ◽  
Vol 25 (4) ◽  
pp. 573-590 ◽  
Author(s):  
Ori Haimanko
Keyword(s):  
Partially Symmetric

Non-hyperbolic P-Invariant Closed Characteristics on Partially Symmetric Compact Convex Hypersurfaces

2018 ◽  
Vol 18 (4) ◽  
pp. 763-774
Author(s):  
Hui Liu ◽  
Gaosheng Zhu
Keyword(s):  
Compact Convex ◽  
Convex Hypersurface ◽  
Closed Characteristics ◽  
Compact Convex Hypersurfaces ◽  
Partially Symmetric ◽  
Convex Hypersurfaces

AbstractLet {n\geq 2} be an integer, {P=\mathrm{diag}(-I_{n-\kappa},I_{\kappa},-I_{n-\kappa},I_{\kappa})} for some integer {\kappa\in[0,n]}, and let {\Sigma\subset{\mathbb{R}}^{2n}} be a partially symmetric compact convex hypersurface, i.e., {x\in\Sigma} implies {Px\in\Sigma}, and {(r,R)}-pinched. In this paper, we prove that when {{R/r}<\sqrt{5/3}} and {0\leq\kappa\leq[\frac{n-1}{2}]}, there exist at least {E(\frac{n-2\kappa-1}{2})+E(\frac{n-2\kappa-1}{3})} non-hyperbolic P-invariant closed characteristics on Σ. In addition, when {{R/r}<\sqrt{3/2}}, {[\frac{n+1}{2}]\leq\kappa\leq n} and Σ carries exactly nP-invariant closed characteristics, then there exist at least {2E(\frac{2\kappa-n-1}{4})+E(\frac{n-\kappa-1}{3})} non-hyperbolic P-invariant closed characteristics on Σ, where the function {E(a)} is defined as {E(a)=\min{\{k\in{\mathbb{Z}}\mid k\geq a\}}} for any {a\in\mathbb{R}}.

Singular value inclusion sets of rectangular tensors

2019 ◽  
Vol 576 ◽  
pp. 181-199 ◽  
Author(s):  
Hongmei Yao ◽  
Can Zhang ◽  
Lei Liu ◽  
Jiang Zhou ◽  
Changjiang Bu
Keyword(s):  
Singular Value ◽  
Rectangular Tensors

THE RATE OF CONVERGENCE AND WEAKER CONVERGENT CONDITION FOR THE METHOD FOR FINDING THE LARGEST SINGULAR VALUE OF RECTANGULAR TENSORS

2016 ◽  
Vol 78 (6-5) ◽  
Author(s):  
Nur Fadhilah Ibrahim ◽  
Nurul Akmal Mohamed
Keyword(s):  
Quantum Physics ◽  
Solid Mechanics ◽  
Linear Convergence ◽  
Singular Value ◽  
Strong Ellipticity ◽  
Ellipticity Condition ◽  
Condition Problem ◽  
Strong Ellipticity Condition ◽  
Weak Irreducibility ◽  
Rectangular Tensors

The applications of real rectangular tensors, among others, including the strong ellipticity condition problem within solid mechanics, and the entanglement problem within quantum physics. A method was suggested by Zhou, Caccetta and Qi in 2013, as a means of calculating the largest singular value of a nonnegative rectangular tensor. In this paper, we show that the method converges under weak irreducibility condition, and that it has a Q-linear convergence.   

scholarly journals Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank

2019 ◽  
Vol 40 (4) ◽  
pp. 1453-1477
Author(s):  
Fulvio Gesmundo ◽  
Alessandro Oneto ◽  
Emanuele Ventura
Keyword(s):  
Partially Symmetric
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