[vc_empty_space][vc_empty_space]
New spherical (2 s + 1) -designs from Kuperberg’s set: An experimental result
Samy Baladram M.a,b, Suprijanto D.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Japan
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2014 Elsevier Inc. All rights reserved.In 2005, Kuperberg proved that 2s points ±z1±z2±⋯±zs′ form a Chebyshev-type (2s+1)-quadrature formula on [-1,1] with constant weight if and only if the zi’s are the zeros of polynomialQ(x)=xs-xs-13+xs-245-⋯+(-1) s1·3·15⋯(4s-1).The Kuperberg’s construction on Chebyshev-type quadrature formula above may be regarded as giving an explicit construction of spherical (2s+1)-designs in the Euclidean space of dimension 3. Motivated by the Kuperberg’s result, in this paper, we observe an experimental construction of spherical (2s+1)-designs, for certain s, from the Kuperberg set of the form ± a1± a2±⋯± as in the Euclidean spaces of certain dimensions d≥4.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Kuperberg’s set,Quadrature formula,Spherical designs[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Chebyshev-type quadrature formula,Interval designs,Kuperberg’s set,Spherical designs[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.amc.2014.10.045[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]