Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.04.044
Abstract: Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several… read more here.
Keywords: harmonic functions; weakly conformal; generalized harmonic; horizontally weakly ... See more keywords
Sloshing in tanks with an internal horizontal perforated plate based on an immersed-boundary generalized harmonic polynomial cell method
Sign Up to like & getrecommendations! Published in 2025 at "Physics of Fluids"
DOI: 10.1063/5.0252935
Abstract: This study explores the challenges of sloshing in rectangular tanks, focusing on the use of an internal perforated plate to mitigate its adverse effects. A novel numerical flow model is developed to examine sloshing dynamics… read more here.
Keywords: harmonic polynomial; immersed boundary; perforated plate; plate ... See more keywords
Hypergeometric series and generalized harmonic numbers
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2024.2388746
Abstract: By computing the higher-order derivatives of some well-known hypergeometric summation theorems, we evaluate many different infinite series containing generalized harmonic functions and central binomial coefficients. read more here.
Keywords: hypergeometric series; harmonic numbers; generalized harmonic; series ... See more keywords
A congruence for some generalized harmonic type sums
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Number Theory"
DOI: 10.1142/s1793042118500628
Abstract: In 1862, Wolstenholme proved that the numerator of the (p − 1)th harmonic number is divisible by p2 for any prime p ≥ 5. A variation of this theorem was shown by Alkan and Leudesdorf.… read more here.
Keywords: generalized harmonic; type sums; harmonic type; congruence generalized ... See more keywords
Generalized harmonic number sums and quasisymmetric functions
Sign Up to like & getrecommendations! Published in 2020 at "Rocky Mountain Journal of Mathematics"
DOI: 10.1216/rmj.2020.50.1253
Abstract: We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))} {(n+z)^{s_1}(n+1+z)^{s_2}\cdots (n+k-1+z)^{s_k}}, $$ where $F(x_1,\ldots,x_\ell)\in\mathbb Q[x_1,\ldots,x_\ell]$, $H_n^{(m)}(z)=\sum^n_{j=1}1/(j+z)^m$, $z\in (-1,0]$, and $s_1,\ldots,s_k$ are nonnegative integers with $s_1+\cdots+s_k\geq 2$, as a linear combination of… read more here.
Keywords: sums quasisymmetric; number sums; ldots ell; quasisymmetric functions ... See more keywords
Some identities on generalized harmonic numbers and generalized harmonic functions
Sign Up to like & getrecommendations! Published in 2022 at "Demonstratio Mathematica"
DOI: 10.1515/dema-2022-0229
Abstract: Abstract The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this… read more here.
Keywords: harmonic numbers; harmonic functions; generalized harmonic; identities generalized ... See more keywords
Study on the stability of analytical periodic solutions of nonlinear gear systems
Sign Up to like & getrecommendations! Published in 2025 at "Mechanical Sciences"
DOI: 10.5194/ms-16-417-2025
Abstract: Abstract. The gear system with backlash is a strong nonlinear system. The generalized harmonic balance method is capable of dealing with most strong nonlinear problems. The analytical solutions of unstable periodic motion and quasi-periodic motion… read more here.
Keywords: system; generalized harmonic; periodic solutions; nonlinear gear ... See more keywords