Cardiac-vagal rhythm echoes on the heartbeat's mechanosensory imprint in the brain. [PDF]
Candia-Rivera D, Chavez M.
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Methodology for biomechanical investigation of implant malpositioning in total knee arthroplasty using a six degree of freedom joint simulator. [PDF]
Kleist E +5 more
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From Agent-Based Markov Dynamics to Hierarchical Closures on Networks: Emergent Complexity and Epidemic Applications. [PDF]
Klimenko AY, Rozycki A, Lu Y.
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A holistic stochastic model for precipitation events. [PDF]
Weyant A +4 more
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Breaking down per- and polyfluoroalkyl substances (PFAS): tackling multitudes of correlated electrons. [PDF]
Rask AE +18 more
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Deep learning-based encryption scheme for medical images using DCGAN and virtual planet domain. [PDF]
Kumar M, Chivukula AS, Barua G.
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On the Sixth Power Mean of the Two-term Exponential Sums
The article is devoted to the calculation problem of the sixth power mean of the two-term exponential sums. The main result is the following theorem. Let \(p>3\) be a prime and \(n\) be an integer. Then we have the identity \[ \sum_{m=1}^{p-1}\left|\sum_{a=0}^{p-1} e\left(\frac{m a^3+n a}{p}\right)\right|^6= \begin{cases}5 p^3 \cdot(p-1), & \text { if }
Zhang, Wen Peng, Meng, Yuan Yuan
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On the Character Sum of Polynomials and the Two-term Exponential Sums
Acta Mathematica Sinica, English Series, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lv, Xing Xing, Zhang, Wen Peng
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ON THE THIRD POWER MEAN OF TWO-TERM EXPONENTIAL SUMS
JP Journal of Algebra, Number Theory and ApplicationsUsing the properties of character sums and the classical Gauss sums, we study the computational problem of one kind of third power mean of the two-term exponential sums, and give an exact computational formula.
Cui, Dewang, Wang, Li
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On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums
Chinese Annals of Mathematics, Series B, 2020For any integer \(q \geq 3\), the high-dimensional Kloosterman sums \(K\left(c_{1}, c_{2}, \ldots, c_{k}, m ; q\right)\) are defined as follows: \[ K\left(c_{1}, c_{2}, \ldots, c_{k}, m ; q\right)=\mathop{\sum'}_{a_{1}=1}^{q} \cdots \mathop{\sum'}_{a_{k}=1}^{q} e\left(\frac{c_{1} a_{1}+\cdots+c_{k} a_{k}+m \bar{a}_{1} \cdots \bar{a}_{k}}{q}\right ...
Lv, Xingxing, Li, Xiaoxue
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