Results 111 to 120 of about 1,790 (152)

Overseas reception of English translations of Journey to the West: Temporal dynamics, cross-platform sentiment patterns, and topic modeling. [PDF]

PLoS One
Jia N, Xin J, Wang Y.
europepmc   +1 more source

Decoding Digital Discourse Through Multimodal Text and Image Machine Learning Models to Classify Sentiment and Detect Hate Speech in Race- and Lesbian, Gay, Bisexual, Transgender, Queer, Intersex, and Asexual Community-Related Posts on Social Media: Quantitative Study. [PDF]

J Med Internet Res
Nguyen TT, Yue X, Mane H, Seelman K, Mullaputi PSP, Dennard E, Alibilli AS, Merchant JS, Criss S, Hswen Y, Nguyen QC.   +10 more
europepmc   +1 more source

Initiation of decohesion between a flat punch and a thin bonded incompressible layer. [PDF]

Math Mech Solids
Argatov II, Mishuris GS, Popov VL.
europepmc   +1 more source

On Gauss sums with Dirichlet characters

On Gauss sums with Dirichlet characters
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ON DIRICHLET CHARACTERS OF POLYNOMIAL

Bulletin of the London Mathematical Society, 2002
The classical result, due to Pólya and Vinogradov, is that the estimates \[ \sum_{n=N+1}^{N+H}\chi(n)\ll q^{1/2}\log q \] holds for all nonprincipal Dirichlet characters \(\chi\) modulo \(q\). The main result of the note under review is to show that for certain primitive characters \(\chi\) modulo \(q\) and some special polynomials \(f(x)\) with ...
Zhang, Wenpeng, Yi, Yuan
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On primitivity of Dirichlet characters

International Journal of Number Theory, 2015
Recall that a Dirichlet character is called imprimitive if it is induced from a character of smaller level, and otherwise it is called primitive. In this paper, we introduce a modification of "inducing to higher level" which causes imprimitive characters to behave primitively, in the sense that the properties of the associated Gauss sum and the ...
Daileda, R., Jones, N.
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On Dirichlet Characters of Polynomials

Proceedings of the London Mathematical Society, 1963
Let \(q\) be a fixed positive integer and \(f(x)\) a nonlinear product of rational linear polynomials which is not a perfect \(q\)-th power. Let \(A\ll B\) mean \(A < k\vert B\vert\) for some positive constant \(k\). Theorem 1. For \(\varepsilon > 0\) if \(p\equiv 1\pmod q\) is a sufficiently large prime and \(\chi\) is a \(q\)-th order character ...
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Sums with convolutions of Dirichlet characters

manuscripta mathematica, 2010
Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1 ...
Banks, William D., Shparlinski, Igor E.
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Dirichlet character sums

Acta Arithmetica, 1999
Let \(\chi\) be a Dirichlet character of conductor \(p^n\) with \(p \in {\mathbb{P}}\), \(n \in {\mathbb{N}}\), and let \(f(x) = a_0 + a_1 x + \cdots + a_k x^k\) be an integral polynomial such that \(k>3\) and \((p^n,a_1,\ldots,a_k)= p^m\). Using a special iteration the author proves some general character sum estimates of type \[ p^{-(n-m)(1-1/k ...
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