Results 81 to 90 of about 1,690,008 (302)
A weighted interpretation for the super Catalan numbers [PDF]
, 2014 The super Catalan numbers $T(m,n)=(2m)!(2n)!/2m!n!(m+n)!$ are integers which generalize the Catalan numbers. With the exception of a few values of $m$, no combinatorial interpretation in known for $T(m,n)$.
Allen, Emily, Gheorghiciuc, Irina
core
On generalised catalan numbers
Discrete Mathematics, 1978 AbstractThe Catalan number Cn is defined to be 2nn(n+1). One of its occurrences is as the number of ways of bracketing a product of n+1 terms taken from a set with binary operation. In this note the corresponding result for a set with a k-ary operation is considered.
openaire +2 more sources
Tracing the Dynamic Chemical Transformations of Spiro‐OMeTAD in Operating Perovskite Solar Cells
Advanced Science, EarlyView.Mapping of Spiro‐OMeTAD layer's chemistry and electronic properties in PSC: Advanced cluster ion‐beam sputtering depth profile XPS reveals that environmental stressors (light, potential, and moisture) trigger the decomposition of LiTFSI dopants in Spiro‐OMeTAD.
Chittaranjan Das +6 more
wiley +1 more source
On ideal convergence of sequences via Catalan matrix operator
Miskolc Mathematical NotesCatalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc.
Vakeel Ahmad Khan, Mikail Et, Umme Tuba
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Success Run Waiting Times and Fuss-Catalan Numbers
Journal of Probability and Statistics, 2015 We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of k consecutive successes in a sequence of independent Bernoulli trials, that is, the ...
S. J. Dilworth, S. R. Mane
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Advanced Science, EarlyView.The action spectrum of a tailored azobenzene is shifted toward bio‐optical window through the chemical modification of its singlet and triplet energy levels. Consequently, the bidirectional photo‐switching of azobenzene in physiological conditions is achieved when excited by red and far‐red light, which offers greater tissue penetration.
Mila Miroshnichenko +11 more
wiley +1 more source
Some explicit expressions for twisted q-analogues of Catalan numbers and polynomials [PDF]
Discrete Mathematics Letters, 2022 Dongkyu Lim
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Simplifying coefficients in differential equations for generating function of Catalan numbers
Journal of Taibah University for Science, 2019 In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating ...
Feng Qi (祁锋), Yong-hong Yao
semanticscholar +1 more source
Parametric Catalan numbers and Catalan triangles
Linear Algebra and its Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SPICE‐Compatible Compact Modeling of Cuprate‐Based Memristors Across a Wide Temperature Range
Advanced Electronic Materials, EarlyView.A physics‐guided compact model for YBCO memristors is introduced, incorporating carrier trapping, field‐induced detrapping, and a differential balance equation to describe their switching dynamics. The model is compared with experiments and implemented in LTspice, allowing realistic circuit‐level simulations.
Thomas Günkel +6 more
wiley +1 more source