Nucleon spin decomposition and differential geometry

In the last few years, the so-called Chen et al. approach of the nucleon spin decomposition has been widely discussed and elaborated on. In this letter we propose a genuine differential geometric understanding of this approach. We mainly highligth its relation to the "dressing field method" we advocated in [C. Fournel, J. Fran\c{c}ois, S. Lazzarini, T. Masson, Int. J. Geom. Methods Mod. Phys. 11, 1450016 (2014)]. We are led to the conclusion that the claimed gauge-invariance of the Chen et al. decomposition is actually unreal.Comment: 9 pages. v3: minor corrections in the text, addition of a new referenc

Faculty recital: Hung-Kuan Chen, March 18, 1990

This is the concert program of the Faculty Recital: Hung-Kuan Chen performance on Sunday, March 18, 1990 at 8:00 p.m., at the Tsai Performance Center, 685 Commonwealth Avenue, Boston, Massachusetts. Works performed were Nocturne, Op. 31 by Lowell Liebermann, Sonata in B-flat major, Op. 106 "Hammerklavier" by Ludwig van Beethoven, Nocturne in E-flat Major, Op. 55 No. 2 and Nocturne in C minor, Op. 48 No. 1 by Frédéric Chopin, and Variations on a Theme by Paganini, Op. 35 by Johannes Brahms. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Faculty recital: Hung-Kuan Chen, piano, October 29, 1986

This is the concert program of the Faculty Recital: Hung-Kuan Chen, piano performance on Wednesday, October 29, 1986 at 8:00 p.m., at the Concert Hall, 855 Commonwealth Avenue. Works performed were Sonata Op. 111 in C minor by Ludwig van Beethoven, "Gaspard de la Nuit" by Maurice Ravel, and Sonata in G minor by Franz Liszt. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Faculty recital: Hung-Kuan Chen, piano, February 4, 1987

This is the concert program of the Faculty Recital: Hung-Kuan Chen, piano performance on Wednesday, February 4, 1987 at 8:00 p.m., at the Concert Hall, 855 Commonwealth Avenue. Works performed were the following by Ludwig van Beethoven: Sonata Op. 10, No. 1 in C minor, Sonata Op. 27, No. 1 in E-flat major Quasi una Fantasia, Sonata Op. 54, in F major, and Sonata Op. 106 in B-flat major Hammerklaviersonata. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction

We consider the 3D quantum BBGKY hierarchy which corresponds to the $N$-particle Schr\"{o}dinger equation. We assume the pair interaction is $N^{3\beta -1}V(N^{\beta}\bullet).$ For interaction parameter $\beta \in(0,\frac23)$, we prove that, as $N\rightarrow \infty ,$ the limit points of the solutions to the BBGKY hierarchy satisfy the space-time bound conjectured by Klainerman-Machedon in 2008. This allows for the application of the Klainerman-Machedon uniqueness theorem, and hence implies that the limit is uniquely determined as a tensor product of solutions to the Gross-Pitaevski equation when the $N$-body initial data is factorized. The first result in this direction in 3D was obtained by T. Chen and N. Pavlovi\'{c} (2011) for $\beta \in (0,\frac14)$ and subsequently by X. Chen (2012) for $\beta\in (0,\frac27]$. We build upon the approach of X. Chen but apply frequency localized Klainerman-Machedon collapsing estimates and the endpoint Strichartz estimate in the estimate of the potential part to extend the range to $\beta\in (0,\frac23)$. Overall, this provides an alternative approach to the mean-field program by Erd\"os-Schlein-Yau (2007), whose uniqueness proof is based upon Feynman diagram combinatorics.Comment: v2, final version for Journal of the European Mathematical Society. v1 is a less technical versio

Peramalan Harga Ethereum Menggunakan Chen Fuzzy Time Series dengan Fuzzy C-Means Clustering (FCM)

Peramalan biasanya digunakan untuk meramalkan sesuatu yang akan terjadi di masa depan menggunakan data historis yang sudah ada. Penelitian ini bertujuan untuk meramalkan harga Ethereum menggunakan data historis pada bulan November 2021, terdapat tiga jenis data yang dipakai, yaitu open, high, dan low. Pada penelitian ini digunakan Chen fuzzy time series dengan fuzzy c-means clustering (FCM) untuk mencari intervalnya dan single exponential smoothing (SES) sebagai pembandingnya. Perhitungan menggunakan metode Chen fuzzy time series dengan fuzzy c-means clustering (FCM) dan single exponential smoothing (SES) didapatkan ramalan harga Ethereum pada tanggal 1 Desember 2021 untuk nilai open, high, dan low. Selanjutnya dihitung nilai average forecasting error rates (AFER) dari metode Chen fuzzy time series dengan fuzzy c-means clustering (FCM) dan metode single exponential smoothing (SES). Nilai AFER dari metode Chen fuzzy time series dengan fuzzy c-means clustering (FCM) untuk nilai open, high, dan low adalah {2,763%, 2,044%, 1,787%} sedangkan nilai AFER dari metode single exponential smoothing (SES) untuk nilai open, high, dan low adalah {3,063%, 2,336%, 2,870%}. Ini berarti bahwa peramalan dari Chen fuzzy time series dengan fuzzy c-means clustering lebih baik daripada single exponential smoothing dalam meramalkan harga Ethereum pada bulan November 2021