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

Construction of cubature formulas with fourth and fifth degrees by the reproducing kernel and Radon methods

2020 ◽  
Vol 2020 (2) ◽  
pp. 76-84
Author(s):  
G.P. Ismatullaev ◽  
S.A. Bakhromov ◽  
R. Mirzakabilov
Keyword(s):  
Reproducing Kernel ◽  
Cubature Formulas

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.

scholarly journals Asymptotically optimal cubature formulas on manifolds for prefixed weights

2021 ◽  
pp. 105632
Author(s):  
Martin Ehler ◽  
Ujué Etayo ◽  
Bianca Gariboldi ◽  
Giacomo Gigante ◽  
Thomas Peter
Keyword(s):  
Asymptotically Optimal ◽  
Cubature Formulas

Partially Symmetric Values

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

scholarly journals The existence of Gaussian cubature formulas

2012 ◽  
Vol 164 (5) ◽  
pp. 572-585 ◽  
Author(s):  
Jean B. Lasserre
Keyword(s):  
Cubature Formulas

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}}.

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