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

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}}.

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

Partially Symmetric Cubature Formulas for Even Degrees of Exactness

1986 ◽  
Vol 23 (3) ◽  
pp. 676-685 ◽  
Author(s):  
Johannes W. Wissmann ◽  
Thomas Becker
Keyword(s):  
Cubature Formulas ◽  
Partially Symmetric

scholarly journals Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuyan Yao ◽  
Gang Wang
Keyword(s):  
Fourth Order ◽  
Elastic Material ◽  
Quantum Physics ◽  
Upper Bounds ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Material Analysis ◽  
Nonlinear Elastic ◽  
Partially Symmetric

<p style='text-indent:20px;'><inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalues of partially symmetric nonnegative tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we establish two upper bounds for the maximum <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalue of partially symmetric nonnegative tensors, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.</p>

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