Universal optimal configurations for the p-frame potentials
Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these po...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, X. [verfasserIn] Gonzalez, V. [verfasserIn] Goodman, E. [verfasserIn] Kang, S. [verfasserIn] Okoudjou, K. A. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Advances in computational mathematics - Bussum : Baltzer Science Publ., 1993, 46(2020), 1 vom: 29. Jan. |
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| Übergeordnetes Werk: |
volume:46 ; year:2020 ; number:1 ; day:29 ; month:01 |
| Links: |
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| DOI / URN: |
10.1007/s10444-020-09745-7 |
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| Katalog-ID: |
SPR010113142 |
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| 520 | |a Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. | ||
| 650 | 4 | |a Potential energy minimization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Frame potential |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sharp configuration |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Spherical designs |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Gonzalez, V. |e verfasserin |4 aut | |
| 700 | 1 | |a Goodman, E. |e verfasserin |4 aut | |
| 700 | 1 | |a Kang, S. |e verfasserin |4 aut | |
| 700 | 1 | |a Okoudjou, K. A. |e verfasserin |4 aut | |
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10.1007/s10444-020-09745-7 doi (DE-627)SPR010113142 (SPR)s10444-020-09745-7-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Chen, X. verfasserin aut Universal optimal configurations for the p-frame potentials 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 Gonzalez, V. verfasserin aut Goodman, E. verfasserin aut Kang, S. verfasserin aut Okoudjou, K. A. verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 29. Jan. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:29 month:01 https://dx.doi.org/10.1007/s10444-020-09745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 29 01 |
| spelling |
10.1007/s10444-020-09745-7 doi (DE-627)SPR010113142 (SPR)s10444-020-09745-7-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Chen, X. verfasserin aut Universal optimal configurations for the p-frame potentials 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 Gonzalez, V. verfasserin aut Goodman, E. verfasserin aut Kang, S. verfasserin aut Okoudjou, K. A. verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 29. Jan. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:29 month:01 https://dx.doi.org/10.1007/s10444-020-09745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 29 01 |
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10.1007/s10444-020-09745-7 doi (DE-627)SPR010113142 (SPR)s10444-020-09745-7-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Chen, X. verfasserin aut Universal optimal configurations for the p-frame potentials 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 Gonzalez, V. verfasserin aut Goodman, E. verfasserin aut Kang, S. verfasserin aut Okoudjou, K. A. verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 29. Jan. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:29 month:01 https://dx.doi.org/10.1007/s10444-020-09745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 29 01 |
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10.1007/s10444-020-09745-7 doi (DE-627)SPR010113142 (SPR)s10444-020-09745-7-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Chen, X. verfasserin aut Universal optimal configurations for the p-frame potentials 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 Gonzalez, V. verfasserin aut Goodman, E. verfasserin aut Kang, S. verfasserin aut Okoudjou, K. A. verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 29. Jan. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:29 month:01 https://dx.doi.org/10.1007/s10444-020-09745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 29 01 |
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10.1007/s10444-020-09745-7 doi (DE-627)SPR010113142 (SPR)s10444-020-09745-7-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Chen, X. verfasserin aut Universal optimal configurations for the p-frame potentials 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 Gonzalez, V. verfasserin aut Goodman, E. verfasserin aut Kang, S. verfasserin aut Okoudjou, K. A. verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 29. Jan. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:29 month:01 https://dx.doi.org/10.1007/s10444-020-09745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 29 01 |
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Chen, X. |
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Chen, X. ddc 510 bkl 31.76 misc Potential energy minimization misc Frame potential misc Sharp configuration misc Spherical designs Universal optimal configurations for the p-frame potentials |
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510 ASE 31.76 bkl Universal optimal configurations for the p-frame potentials Potential energy minimization (dpeaa)DE-He213 Frame potential (dpeaa)DE-He213 Sharp configuration (dpeaa)DE-He213 Spherical designs (dpeaa)DE-He213 |
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ddc 510 bkl 31.76 misc Potential energy minimization misc Frame potential misc Sharp configuration misc Spherical designs |
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ddc 510 bkl 31.76 misc Potential energy minimization misc Frame potential misc Sharp configuration misc Spherical designs |
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Universal optimal configurations for the p-frame potentials |
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Universal optimal configurations for the p-frame potentials |
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universal optimal configurations for the p-frame potentials |
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Universal optimal configurations for the p-frame potentials |
| abstract |
Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. |
| abstractGer |
Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. |
| abstract_unstemmed |
Abstract Given d, N ≥ 2, and $p\in (0, \infty ]$, we consider a family of functionals, the p-frame potentials $ FP_{p, N, d} $, defined on the set of all collections of N unit-norm vectors in $\mathbb R^{d}$. For the special cases p = 2 and $p=\infty $, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals $ FP_{p, N, d} $, by first establishing some general properties of their minima. Thereafter, we focus on the special case d = 2, for which, surprisingly, not much is known. One of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p-frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2). These experiments lead to some conjectures that we pose. |
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| title_short |
Universal optimal configurations for the p-frame potentials |
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https://dx.doi.org/10.1007/s10444-020-09745-7 |
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Gonzalez, V. Goodman, E. Kang, S. Okoudjou, K. A. |
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Gonzalez, V. Goodman, E. Kang, S. Okoudjou, K. A. |
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| doi_str |
10.1007/s10444-020-09745-7 |
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2024-07-03T14:01:05.012Z |
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| score |
7.398883 |