Results 31 to 40 of about 96,717 (274)
Factors of alternating convolution of the Gessel numbers [PDF]
Notes on Number Theory and Discrete MathematicsThe Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
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A rapidly convergent method for solving third-order polynomials
AIP Advances, 2022 We present a rapidly convergent method for solving cubic polynomial equations with real coefficients. The method is based on a power series expansion of a simplified form of Cardano’s formula using Newton’s generalized binomial theorem.
Ramón A. Fernández Molina +3 more
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Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws
Mathematics, 2022 The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal ...
Alexander Bulinski, Nikolay Slepov
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, 2010 The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients.
Warnaar, S. Ole, Zudilin, Wadim
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Restricted Tweedie stochastic block models
Canadian Journal of Statistics, EarlyView.Abstract The stochastic block model (SBM) is a widely used framework for community detection in networks, where the network structure is typically represented by an adjacency matrix. However, conventional SBMs are not directly applicable to an adjacency matrix that consists of nonnegative zero‐inflated continuous edge weights.
Jie Jian, Mu Zhu, Peijun Sang
wiley +1 more source
Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
, 2014 In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core
Markov branching processes with disasters: extinction, survival and duality to p-jump processes
, 2019 A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval.
Hermann, F., Pfaffelhuber, P.
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Earthquake Engineering &Structural Dynamics, EarlyView.ABSTRACT Recent tsunamigenic earthquakes in Japan have highlighted the emerging fire hazard triggered by tsunami inundation and its impact on tsunami vertical evacuation (TVE) structures. This new type of fire following earthquake, referred to as “tsunami fires,” may be a potential universal hazard that tsunami‐prone countries face; however, it has not
Tomoaki Nishino
wiley +1 more source
Stochastic Ordering of Exponential Family Distributions and Their Mixtures
, 2009 We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order.
Hardy +6 more
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Scaling‐Aware Rating of Poisson‐Limited Demand Forecasts
Journal of Forecasting, EarlyView.ABSTRACT Forecast quality should be assessed in the context of what is possible in theory and what is reasonable to expect in practice. Often, one can identify an approximate upper bound to a probabilistic forecast's sharpness, which sets a lower, not necessarily achievable, limit to error metrics.
Malte C. Tichy +4 more
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