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Full-Text Articles in Physical Sciences and Mathematics
Revisiting The Newsboy Problem-Optimization With A Little Help From The Airline Industry, Tamas Lengyel
Revisiting The Newsboy Problem-Optimization With A Little Help From The Airline Industry, Tamas Lengyel
Tamas Lengyel
In a typical inventory planning problem with a life cycle of only one planning period, we incur the cost of production per unit produced, profit per unit sold, loss per unit not sold, and lost revenue per unit ordered but not matched due to the lack of availability. The goal is to find the inventory level that maximizes the expected net profit. Textbooks often use the newsboy problem to illustrate the inventory management paradigm. The derivation of the formulas for the optimal level is usually done on an ad hoc basis, by dull and rote mathematical manipulations, for each modification …
On Divisibility Properties Of Some Differences Of Motzkin Numbers, Tamas Lengyel
On Divisibility Properties Of Some Differences Of Motzkin Numbers, Tamas Lengyel
Tamas Lengyel
We discuss divisibility properties of some differences of Motzkin numbers Mn. The main tool is the application of various congruences of high prime power moduli for binomial coefficients and Catalan numbers combined with some recurrence relevant to these combinatorial quantities and the use of infinite disjoint covering systems. We find proofs of the fact that, for different settings of a and b, more and more p-ary digits of Mapn+1+b and Mapn+b agree as n grows.
Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel
Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel
Tamas Lengyel
Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1,X2,...,Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased estimators and present the best estimators.
On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel
On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel
Tamas Lengyel
We analyze some 2 adic properties of the sequence defined by the recurrence Z(1) =1; Z(n) = n−1 k=1 S(n, k) Z(k), n ≥ 2, which counts the number of ultra-dissimilarity relations, i.e., ultra-metrics on an n-set. We prove the 2 adic growth property v2 (Z(n) ≥ log 2 n - 1) and present conjectures on the exact values.