Results 101 to 110 of about 610,031 (298)

Theta Function Identities of Level 16 and Their Applications to Colored Partitions

Mathematics
Theta function identities play an important role in the theory of modular forms and partitions, with Ramanujan’s q-series providing a fundamental analytical framework.
Fatemah Mofarreh, Arooj Fatima, Ahmer Ali   +2 more
doaj   +1 more source

The human gut microbiome across the life course

FEBS Letters, EarlyView.
Despite significant individual variation and continuous change throughout life, the human gut microbiome follows some life stage‐specific trends. This article provides a brief overview of how gut microbiome composition shifts across different phases of life. Created in BioRender. Özkurt, E. (2026) https://BioRender.com/8q4nrnc.
Alise J. Ponsero, Basak Bahcivanci, Antonietta Hayhoe, Animesh Acharjee, Ezgi Özkurt   +4 more
wiley   +1 more source

Combinatorial Identities and Inverse Binomial Coefficients [PDF]

, 2002
In this paper, we present a method for obtaining a wide class of combinatorial identities.
Mansour, Toufik
core   +1 more source

Microbiome−host proteostasis crosstalk—An emerging perspective on mechanisms and interventions toward healthy longevity

FEBS Letters, EarlyView.
Proteostasis and the gut microbiota play a key role in shaping host physiology. Microbiota‐derived metabolites, vitamins, and RNA modulate host proteostasis. Findings from model systems, including C. elegans, indicate microbes can either stabilize or disrupt host proteostasis.
Abhishek Anil Dubey, Maria Ermolaeva
wiley   +1 more source

A combinatorial proof of the Lebesgue identity

Discrete Mathematics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

From mice to humans—divergent strategies for intestinal homeostasis and regeneration

FEBS Letters, EarlyView.
Recent advances such as organoid genome editing, xenotransplantation, imaging, and whole‐genome sequencing have enabled direct studies of human intestinal stem cells (ISCs). These studies reveal species‐specific features, including slower ISC proliferation, distinct injury responses, slower somatic mutation accumulation in humans, and an inverse ...
Keiko Ishikawa, Shinya Sugimoto, Toshiro Sato   +2 more
wiley   +1 more source

A combinatorial approach to Berkovich type identities [PDF]

Motivated by Berkovich's nine $q$-binomial identities involving the Legendre symbol $(\frac{d}{3})$, we establish a unified form of $q$-binomial identities of this type through a combinatorial approach.
Liu, Ji-Cai
core   +1 more source

On three-dimensional q-Riordan arrays

Demonstratio Mathematica
In this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays.
Fang Gang, Koparal Sibel, Ömür Neşe, Duran Ömer, Khan Waseem Ahmad   +4 more
doaj   +1 more source

A new class of infinite products, and Euler's totient

International Journal of Mathematics and Mathematical Sciences, 1994
We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1.
Geoffrey B. Campbell
doaj   +1 more source

A combinatorial identity

, 2019
We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications.
Dorlas, T. C., Rebenko, Alexei L., Savoie, Baptiste   +2 more
openaire   +1 more source