Results 321 to 330 of about 17,517,320 (360)

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

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

Testing for normality in any dimension based on a partial differential equation involving the moment generating function

Annals of the Institute of Statistical Mathematics, 2019
We use a system of first-order partial differential equations that characterize the moment generating function of the d-variate standard normal distribution to construct a class of affine invariant tests for normality in any dimension.
N. Henze, J. Visagie
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

The phase model and the norm-trace generating function of plane partitions

Journal of Statistical Mechanics: Theory and Experiment, 2018
A quantum phase model is considered and the temporal evolution of the exponential of the first moment of particles distribution is studied. The calculation of the temporal evolution is based on the properties of Schur functions.
N. Bogoliubov, C. Malyshev
semanticscholar   +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