scholarly journals A Note on Colored Tornheim's Double Series

Integers ◽  
2010 ◽  
Vol 10 (6) ◽  
Author(s):  
Jianqiang Zhao
Keyword(s):  
Explicit Formula ◽  
Short Note ◽  
Double Series ◽  
Numerical Data ◽  
Roots Of Unity ◽  
Double Zeta ◽  
Zeta Values ◽  
Almost All

AbstractIn this short note, we provide an explicit formula to compute every colored double Tornheim's series by using double polylogarithm values at roots of unity. When the colors are given by ±1 our formula is different from that of Tsumura [Proc. AMS 131: 3633–3641, 2003] even though numerical data confirm both are correct in almost all the cases. This agreement can also be checked rigorously by using regularized double shuffle relations of the alternating double zeta values in weights less than eight.

scholarly journals ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA
Keyword(s):  
Explicit Formula ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values ◽  
Sum Formula

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

scholarly journals On multiple zeta values and finite multiple zeta values of maximal height

2018 ◽  
Vol 14 (04) ◽  
pp. 975-987
Author(s):  
Hideki Murahara ◽  
Mika Sakata
Keyword(s):  
Explicit Formula ◽  
Alternative Proof ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values

An explicit formula for the height-one multiple zeta values (MZVs) was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values (FMZVs).

scholarly journals On algebraic closure in pseudofinite fields

2012 ◽  
Vol 77 (4) ◽  
pp. 1057-1066 ◽  
Author(s):  
Özlem Beyarslan ◽  
Ehud Hrushovski
Keyword(s):  
Automorphism Group ◽  
Finite Field ◽  
Algebraic Closure ◽  
Roots Of Unity ◽  
Prime Field ◽  
Almost All ◽  
Pseudofinite Fields

AbstractWe study the automorphism group of the algebraic closure of a substructureAof a pseudo-finite fieldF. We show that the behavior of this group, even whenAis large, depends essentially on the roots of unity inF. For almost all completions of the theory of pseudofinite fields, we show that overA, algebraic closure agrees with definable closure, as soon asAcontains the relative algebraic closure of the prime field.

scholarly journals Eagle View: An Abstract Evaluation of Machine Learning Algorithms based on Data Properties

2021 ◽  
Author(s):  
Dhairya Vyas
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Time Series Data ◽  
Learning Algorithms ◽  
Numerical Data ◽  
Machine Learning Algorithms ◽  
Series Data ◽  
Learning Methods ◽  
Machine Learning Methods ◽  
Almost All

In terms of Machine Learning, the majority of the data can be grouped into four categories: numerical data, category data, time-series data, and text. We use different classifiers for different data properties, such as the Supervised; Unsupervised; and Reinforcement. Each Categorises has classifier we have tested almost all machine learning methods and make analysis among them.

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