Results 11 to 20 of about 50,068 (195)
Integer partitions detect the primes. [PDF]
Proc Natl Acad Sci U S ACraig W, van Ittersum JW, Ono K.
europepmc +2 more sources
The part-frequency matrices of a partition [PDF]
, 2016 A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection.
Keith, William J.
core +4 more sources
Elementary proofs in the theory of partitions
Mathematische Zeitschrift, 1963 Let \(k>1\) be an integer, and let \(a_1, a_2, \ldots, a_s\) be \(s\) distinct positive integers not exceeding \(k\). The set of nonnegative integers \(\nu\) such that \(\nu\equiv a_i \pmod k\) for some \(i\), \(1\leq i\leq s\) is called a congruence set modulo \(k\), and is denoted by \(a\). Let \(F(x; a)= \prod_{\nu\in a} (1-x^\nu)^{-1} = \sum p_n(a)
openaire +2 more sources
A Lost Theorem: Definite Integrals in Asymptotic Setting [PDF]
, 2008 We present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums ...
Cavalcante, Ray, Todorov, Todor D.
core +3 more sources
Notes on Schubert, Grothendieck and Key Polynomials [PDF]
, 2016 We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco-Zinn-Justin polynomials.
Kirillov, Anatol N.
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Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
wiley +1 more source
Revisiting random tensor models at large N via the Schwinger-Dyson equations
, 2012 The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models.
B Eynard +25 more
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FEBS Open Bio, EarlyView.Bioscience students were asked for their opinions on the value and teaching of skills. 204 responded that teamwork, time management and study skills are necessary to reach University, that scientific writing, research, laboratory and presentation skills are taught effectively during their studies, while other skills are gained inherently through study ...
Janella Borrell, Susan Crennell
wiley +1 more source
Metric characterization of cluster dynamics on the Sierpinski gasket
, 2010 We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure.
Agliari E +19 more
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Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Accurate localization of epileptogenic tubers (ETs) in patients with tuberous sclerosis complex (TSC) is essential but challenging, as these tubers lack distinct pathological or genetic markers to differentiate them from other cortical tubers.
Tinghong Liu +11 more
wiley +1 more source