Results 151 to 160 of about 17,341,617 (212)

A hyperelliptic saga on a generating function of the squares of Legendre polynomials

Journal of Experimental Mathematics, 2023
We decompose the generating function ∑ (2n choose n) Pn(y)2 zn of the squares of Legendre polynomials as a product of periods of hyperelliptic curves. These periods satisfy a family of second order differential equations.
Mark van Hoeij, Duco van Straten, W. Zudilin   +2 more
semanticscholar   +1 more source

Jensen-information generating function and its connections to some well-known information measures

, 2021
In this work, we consider the information generating function measure and develop some new results associated with it. We specifically propose two new divergence measures and show that some of the well-known information divergences such as Jensen–Shannon,
O. Kharazmi, N. Balakrishnan
semanticscholar   +1 more source

Discrete Generating Functions

Mathematical Notes, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akhtamova, S. S., Alekseev, V. S., Lyapin, A. P.   +2 more
openaire   +2 more sources

On the (2, F) Generalizations of the Fibonacci Sequence

The Fibonacci quarterly, 1992
A generalization of the Fibonacci sequence to vectors was defined in Atanassov, Atanassova, & Sasselov [1]. In a later article, Atanassov [2] defined the four distinct (2, F) generalizations of the Fibonacci sequence and determined a solution for one of ...
W. R. Spickerman, R. N. J O Y N E R, R. L. Creech, Generating Function, X-X   +4 more
semanticscholar   +1 more source

Generating Diverse and Natural 3D Human Motions from Text

Computer Vision and Pattern Recognition, 2022
Automated generation of 3D human motions from text is a challenging problem. The generated motions are expected to be sufficiently diverse to explore the text-grounded motion space, and more importantly, accurately depicting the content in prescribed ...
Chuan Guo, Shihao Zou, X. Zuo, Sen Wang, Wei Ji, Xingyu Li, Li Cheng   +6 more
semanticscholar   +1 more source

Generalized Production Functions

The Review of Economic Studies, 1969
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zellner, A., Revankar, N. S.
openaire   +2 more sources

A Multi-State Model for Reliability Assessment of Integrated Gas and Power Systems Utilizing Universal Generating Function Techniques

IEEE Transactions on Smart Grid, 2019
Large-scale adoption of gas-fired power plants (GPPs) significantly accelerates the integration of power systems and natural gas systems (NGSs). Because the operation of NGS has a significant impact on the reliability of power system, it is important to ...
Minglei Bao, Yi Ding, C. Singh, Changzheng Shao   +3 more
semanticscholar   +1 more source

Generalized Poisson Functionals

Probability Theory and Related Fields, 1988
With the aim of treating nonlinear systems with inputs being discrete and outputs being generalized functions, generalized Poisson functionals are defined and analysed, where the U-transforms and the renormalizations play essential roles. For Poisson functionals, the differential operators with respect to a Poisson white noise Ṗ(t), their adjoint ...
openaire   +1 more source

APIGen: Automated Pipeline for Generating Verifiable and Diverse Function-Calling Datasets

Neural Information Processing Systems
The advancement of function-calling agent models requires diverse, reliable, and high-quality datasets. This paper presents APIGen, an automated data generation pipeline designed to synthesize verifiable high-quality datasets for function-calling ...
Zuxin Liu, Thai Hoang, Jianguo Zhang, Ming Zhu, Tian Lan, Shirley Kokane, Juntao Tan, Weiran Yao, Zhiwei Liu, Yihao Feng, Rithesh Murthy, Liangwei Yang, Silvio Savarese, Juan Carlos Niebles, Huan Wang, Shelby Heinecke, Caiming Xiong   +16 more
semanticscholar   +1 more source

Generalized Conjugate Functions

Mathematische Operationsforschung und Statistik. Series Optimization, 1977
Conjugate functions introduced in nonlinear programming by Fenchel are closely connected with polarity with respect to a special hypersurface of the order two. In the paper a wider class of conjugate functions is considered, basing on the polarity with respect to a nondegenerate hypersurface φ of order two. Important properties of so-called φ-conjugate
Deumlich, R., Elster, K.-H.
openaire   +1 more source