Masatake Hirao

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All published works

Action	Title	Year	Authors
+ PDF Chat	More on the corner-vector construction for spherical designs	2025	Kenji Tanino T. Tamaru Masatake Hirao Masanori Sawa
+	Spherical designs and modular forms of the $$D_4$$ lattice	2023	Masatake Hirao Hiroshi Nozaki Koji Tasaka
+ PDF Chat	On <i>p</i>-frame potentials of the Beltrán and Etayo point processes on the sphere	2023	Masatake Hirao
+	Spherical designs and modular forms of the $D_4$ lattice	2023	Masatake Hirao Hiroshi Nozaki Koji Tasaka
+ PDF Chat	Finite frames, frame potentials and determinantal point processes on the sphere	2021	Masatake Hirao
+	Geometric Designs and Rotatable Designs I	2021	Masanori Sawa Masatake Hirao Kanami Ito
+ PDF Chat	On $p$-frame potentials of determinantal point processes on the sphere	2021	Masatake Hirao
+	On almost tight Euclidean designs for rotationally symmetric integrals	2019	Masatake Hirao Masanori Sawa
+	Constructions of Optimal Euclidean Design	2019	Masanori Sawa Masatake Hirao Sanpei Kageyama
+	Kernel Functions	2019	Masanori Sawa Masatake Hirao Sanpei Kageyama
+	Cubature Formula	2019	Masanori Sawa Masatake Hirao Sanpei Kageyama
+	Euclidean Design Theory	2019	Masanori Sawa Masatake Hirao Sanpei Kageyama
+ PDF Chat	A construction of the fourth order rotatable designs invariant under the hyperoctahedral group	2018	Hirotaka Yamamoto Masatake Hirao Masanori Sawa
+	QMC Designs and Determinantal Point Processes	2018	Masatake Hirao
+	Some remarks on cubature formulas with linear operators	2016	Masatake Hirao Takayuki Okuda Masanori Sawa
+	Constructions of Φ p -Optimal Rotatable Designs on the Ball	2014	Masatake Hirao Masanori Sawa Masakazu Jimbo
+	On minimal cubature formulae of odd degrees for circularly symmetric integrals	2012	Masatake Hirao Masanori Sawa
+ PDF Chat	A New Approach for the Existence Problem of Minimal Cubature Formulas Based on the Larman--Rogers--Seidel Theorem	2012	Masatake Hirao Hiroshi Nozaki Masanori Sawa Vesselin Vatchev
+	Large deviations for the radial processes of the Brownian motions on hyperbolic spaces	2011	Masatake Hirao
+ PDF Chat	On the existence of minimum cubature formulas for Gaussian measure on ℝ2 of degree t supported by $[\frac{t}{4}]+1$ circles	2011	Eiichi Bannaĭ Etsuko Bannai Masatake Hirao Masanori Sawa
+	A new approach for the existence problem of minimal cubature formulas based on the Larman-Rogers-Seidel theorem	2011	Masatake Hirao Hiroshi Nozaki Masanori Sawa Vesselin Vatchev
+	Some remarks on Euclidean tight designs	2010	Masatake Hirao Masanori Sawa Yuanyuan Zhou
+	Cubature formulas in numerical analysis and Euclidean tight designs	2009	Eiichi Bannaĭ Etsuko Bannai Masatake Hirao Masanori Sawa
+	On Minimal Cubature Formulae of Small Degree for Spherically Symmetric Integrals	2009	Masatake Hirao Masanori Sawa

Common Coauthors

Coauthor	Papers Together
Masanori Sawa	17
Hiroshi Nozaki	4
Sanpei Kageyama	4
Koji Tasaka	2
Vesselin Vatchev	2
Etsuko Bannai	2
Eiichi Bannaĭ	2
Takayuki Okuda	1
Kanami Ito	1
Yuanyuan Zhou	1
Masakazu Jimbo	1
Hirotaka Yamamoto	1
T. Tamaru	1
Kenji Tanino	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Discrete measures for spherical designs, eutactic stars and lattices	1988	Arnold Neumaier J.J. Seidel	11
+	Spherical codes and designs	1977	P. Delsarte J.-M. Goethals J.J. Seidel	9
+ PDF Chat	On antipodal Euclidean tight (2e + 1)-designs	2006	Etsuko Bannai	9
+	Cubature formulas in numerical analysis and Euclidean tight designs	2009	Eiichi Bannaĭ Etsuko Bannai Masatake Hirao Masanori Sawa	9
+	Lower Bounds for the Number of Nodes in Cubature Formulae	1979	H. Michael Möller	9
+	Fisher type inequalities for Euclidean t-designs	1989	P. Delsarte J.J. Seidel	8
+	Asymmetric Cubature Formulae with Few Points in High Dimension for Symmetric Measures	2004	Nicolas Victoir	8
+	On cubature formulae of degree 4k+1 attaining M�ller's lower bound for integrals with circular symmetry	1992	Pierre Verlinden Ronald Cools	7
+	A survey on spherical designs and algebraic combinatorics on spheres	2009	Eiichi Bannaĭ Etsuko Bannai	7
+ PDF Chat	Orbits of the hyperoctahedral group as Euclidean designs	2006	Béla Bajnok	6
+	On positive cubature rules on the simplex and isometric embeddings	2013	Masanori Sawa Yuan Xu	6
+ PDF Chat	Tight Gaussian 4-Designs	2005	Eiichi Bannaĭ Etsuko Bannai	6
+	On Minimal Cubature Formulae of Small Degree for Spherically Symmetric Integrals	2009	Masatake Hirao Masanori Sawa	6
+	On the number of nodes in n-dimensional cubature formulae of degree 5 for integrals over the ball	2004	М. В. Носков Hans Schmid	5
+	None	1998	Yuan Xu	5
+	QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere	2014	J. Brauchart E. B. Saff Ian H. Sloan Robert S. Womersley	5
+	Approximate Calculation of Multiple Integrals	1973	W. G. A. H. Stroud	5
+	Lower bound for the number of nodes of cubature formulae on the unit ball	2003	Yuan Xu	5
+ PDF Chat	Note on Cubature Formulae and Designs Obtained from Group Orbits	2011	Hiroshi Nozaki Masanori Sawa	5
+	Averaging sets: A generalization of mean values and spherical designs	1984	Paul Seymour Thomas Zasĺavsky	5
+	Cubature on Wiener space	2004	Terry Lyons Nicolas Victoir	4
+	Zeros of Gaussian Analytic Functions and Determinantal Point Processes	2009	J. Hough Manjunath Krishnapur Yuval Peres Bálint Virág	4
+	On Euclidean designs	2006	Béla Bajnok	4
+	Algorithms for optimal design with application to multiple polynomial regression	1995	Norbert Gaffke Berthold Heiligers	4
+	Optimum Multivariate Designs	1985	R. H. Farrell J. Kiefer A. Walbran	4
+	Measures of strength $2e$ and optimal designs of degree $e$	1992	Arnold Neumaier J.J. Seidel	4
+	A new lower bound for the number of nodes in cubature formulae of degree 4 n + 1 for some circularly symmetric integrals	1993	Ronald Cools Hans Schmid	4
+	Constructions of Φ p -Optimal Rotatable Designs on the Ball	2014	Masatake Hirao Masanori Sawa Masakazu Jimbo	4
+ PDF Chat	Remarks on Hilbert identities, isometric embeddings, and invariant cubature	2014	Hiroshi Nozaki Masanori Sawa	4
+ PDF Chat	Numerical Cubature Using Error-Correcting Codes	2006	Greg Kuperberg	4
+ PDF Chat	Orthogonal Polynomials of Several Variables	2014	Charles F. Dunkl Yuan Xu	3
+ PDF Chat	Optimal asymptotic bounds for spherical designs	2013	Andriy Bondarenko Danylo Radchenko Maryna Viazovska	3
+	None	2003	John J. Benedetto Matthew Fickus	3
+	Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres	2016	Carlos Beltrán Jordi Marzo Joaquim Ortega‐Cerdà	3
+	Cubature Formulae, Polytopes, and Spherical Designs	1981	J.-M. Goethals J.J. Seidel	3
+	Constructing cubature formulae by the method of reproducing kernel	2000	Yuan Xu	3
+	On the approximate calculation of multiple integrals	2015	N. S. Bakhvalov	3
+	Gaussian Quadrature for Kernel Features	2017	Tri Dao Christopher De Christopher Ré	3
+	A generalization of the spherical ensemble to even-dimensional spheres	2019	Carlos Beltrán Ujué Etayo	3
+ PDF Chat	On Euclidean tight 4-designs	2006	Eiichi Bannaĭ Etsuko Bannai	3
+ PDF Chat	The Projective Ensemble and Distribution of Points in Odd-Dimensional Spheres	2018	Carlos Beltrán Ujué Etayo	3
+ PDF Chat	The spherical ensemble and uniform distribution of points on the sphere	2015	Kasra Alishahi Mohammadsadegh Zamani	3
+	Cubature formulae and orthogonal polynomials	2001	Ronald Cools I.P. Mysovskikh Hans Schmid	3
+ PDF Chat	Euclidean designs and coherent configurations	2010	Eiichi Bannaĭ Etsuko Bannai	3
+	On optimal tight 4-designs on 2 concentric spheres	2004	Eiichi Bannaĭ Etsuko Bannai	3
+	On minimal cubature formulae of odd degrees for circularly symmetric integrals	2012	Masatake Hirao Masanori Sawa	3
+	Zeros of Random Analytic Functions	2006	Manjunath Krishnapur	2
+	An encyclopaedia of cubature formulas	2003	Ronald Cools	2
+ PDF Chat	Experimental Study of Energy-Minimizing Point Configurations on Spheres	2009	Brandon Ballinger Grigoriy Blekherman Henry Cohn Noah Giansiracusa Elizabeth M. Kelly Achill Schürmann	2
+	Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝ^{𝕕}	1999	Yuan Xu	2