Results 71 to 80 of about 142,847 (376)
An integral representation, complete monotonicity, and inequalities of the Catalan numbers
, 2018 In the paper, by virtue of the Cauchy integral formula in the theory of complex functions, the authors establish an integral representation for the generating function of the Catalan numbers in combinatorics.
Feng Qi (祁锋) +2 more
semanticscholar +1 more source
Enumerative Combinatorics and Applications, 2023 We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other
Richard Ehrenborg +2 more
openaire +3 more sources
Supramolecular Design of Polymeric Random Lasers
Advanced Optical Materials, EarlyView.This research investigates the application of PolyHIPE scaffolds as scattering media inRLs. By modifying the scaffold's morphology, pore size, and surface chemistry, the dye distribution within the material is precisely controlled, achieving a tunable laser threshold.
Junyang Chen +6 more
wiley +1 more source
Shifted Hankel determinants of Catalan numbers and related results II: Backward shifts [PDF]
arXiv, 2023 By prepending zeros to a given sequence Hankel determinants of backward shifts of this sequence become meaningful. We obtain some results for the sequences of Catalan numbers and of some numbers and polynomials which are related to Catalan numbers and propose conjectures for sequences of convolution powers of Catalan numbers.
arxiv
Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj +1 more source
Advanced Science, EarlyView.An embedded bioprinting enabled‐arrayed patient‐derived organoids (Eba‐PDO) platform that replicates intrinsic and extrinsic tumor characteristics is introduced. Eba‐PDOs more accurately mimic tissue than standard PDOs (Std‐PDOs) due to maturation in the tumor microenvironment.
Jonghyeuk Han +15 more
wiley +1 more source
Cahiers d’Études Romanes, 2001 Tout comme le suggère le titre du troisième tome des mémoires de Terenci Moix, Extraño en el paraiso (Etranger au paradis), Paris est la ville de tous les espoirs pour le jeune Catalan qui arrive dans la capitale de la France alors que l’Espagne vit sous
Philippe Merlo
doaj +1 more source
Discrete Mathematics, 2008 AbstractRaney’s lemma is often used in a counting argument to prove the formula for (generalized) Catalan numbers. It ensures the existence of “good” cyclic shifts of certain sequences, i.e. cyclic shifts for which all partial sums are positive.We introduce a simple algorithm that finds these cyclic shifts and also those with a slightly weaker property.
openaire +2 more sources
Advanced Science, EarlyView.Upgrading lignocellulosic wastes into value‐added compounds represents an excellent option to reduce the current overreliance on fossil fuels. γ‐Valerolactone is especially attractive for its multiple applications such as biofuel or green solvent.
Roger Bujaldón +8 more
wiley +1 more source