New size measurements in population ecology

In organizational ecology, we find the analysis of the impact exerted by competition between populations on vital ratios to be relatively under-developed. This paper intends to address this issue by developing new competition measurements whose common denominator is to give importance to organizational size. The application of these measurements in the case of competition between organizational forms in a population and their impact on mortality rates, demonstrates the usefulness of modelling competition on them. More specifically, results show how competition levels between firms in a population can be more adequately estimated when rival population mass is used (that is, the aggregate size of the organizations of which it is made up)

Is the risk-return paradox still alive?

To date, the validity of empirical Bowman's paradox papers that employ mean-variance approach for testing the risk/return relationship are inherently unverifiable and their results cannot be generalized. However, this problem can be overcome by developing an econometric model with two fundamental characteristics. The first one is the use of a time series model for each firm, avoiding the traditional cross-sectional analysis. The other one is to estimate a model with a single variable (the firm rate of return), but whose expectation and variance are mathematically related according to behavioral theories hypotheses, forming a heterocedastic model similar to "GARCH". Our results agree with behavioral theories and show that these theories can also be carry out with market measures

Survival as a success in the face of a scarcity of resources

From institutional, resource dependence and organizational ecology perspectives, there are two initial requirements for organizational survival: 1) there are sufficient resources in the niche, and 2) the organization can obtain these resources. A new concept, saturation, is created to measure the scarcity of resources by analyzing its influence on survival. However, organizational success also depends on organizational characteristics, which can hinder the securing of the resources necessary for survival. This article researches ownership structure as an organizational characteristic. These influences are tested utilizing data from a population of 1298 Spanish olive oil mills

Problems with extending conclusions between Bowman's paradox and Beta's death

This issue of Omega contains a commentary by P.L. Brockett, W.W. Cooper, K.H. Kwon, and T.W. Ruefli on the review of Bowman's paradox by Nickel and Rodríguez, published in the February 2002 issue of Omega. In their commentary, the authors describe an article, published in the 1992 issue of Decision Sciences but not covered by the review, and claim that they had previously overcome three of the outstanding problems noted in Nickel and Rodríguez's review. This reply to the commentary proves that the conclusions drawn in the review by Nickel and Rodríguez are relevant in spite of the Brockett et al. arguments against them. In this reply, we show that the paper by Brockett et al. neither explains Bowman's paradox nor resolves its underlying problems. First, the definitions of risk and return measures are mathematically linked, and second, a cross-sectional methodology is used. We also provide our opinion on what would be necessary to bear in mind in order to extend any conclusion from Bowman's paradox to beta's death and vice versa

A relationship between the ideals of Fq[x,y,x−1,y−1]\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right] and the Fibonacci numbers

Let $C_n(q)$ be the number of ideals of codimension $n$ of $\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right]$, where $\mathbb{F}_q$ is the finite field with $q$ elements. Kassel and Reutenauer [KasselReutenauer2015A] proved that $C_n(q)$ is a polynomial in $q$ for any fixed value of $n \geq 1$. For $q = \frac{3+\sqrt{5}}{2}$, this combinatorial interpretation of $C_n(q)$ is lost. Nevertheless, an unexpected connexion with Fibonacci numbers appears. Let $f_n$ be the $n$-th Fibonacci number (following the convention $f_0 = 0$, $f_1 = 1$). Define the series $$F(t) = \sum_{n \geq 1} f_{2n}\,t^n.$$ We will prove that for each $n \geq 1$, $$C_n\left( \frac{3+\sqrt{5}}{2}\right) = \lambda_n \, \left(f_{2n} \frac{3+\sqrt{5}}{2} - f_{2n-2} \right) ,$$ where the integers $\lambda_n \geq 0$ are given by the following generating function $$ \prod_{m \geq 1} \left(1+F\left( t^m\right)\right) = 1 + \sum_{n \geq 1} \lambda_n\,t^n. $

On prime numbers of the form 2n±k2^n \pm k

Consider the set $\mathcal{K}$ of integers $k$ for which there are infinitely many primes $p$ such that $p+k$ is a power of $2$. The aim of this paper is to show a relationship between $\mathcal{K}$ and the limits points of some set rational numbers related to a sequence of polynomials $C_n(q)$ introduced by Kassel and Reutenauer [KasselReutenauer]

Middle divisors and σ\sigma-palindromic Dyck words

Given a real number $\lambda > 1$, we say that $d|n$ is a $\lambda$-middle divisor of $n$ if $$\sqrt{\frac{n}{\lambda}} < d \leq \sqrt{\lambda n}.$$ We will prove that there are integers having an arbitrarily large number of $\lambda$-middle divisors. Consider the word $$\langle\! \langle n \rangle\! \rangle_{\lambda} := w_1 w_2 ... w_k \in \{a,b\}^{\ast},$$ given by $$w_i := \left\{ \begin{array}{c l} a & \textrm{if } u_i \in D_n \backslash \left(\lambda D_n\right), \\ b & \textrm{if } u_i \in \left(\lambda D_n\right)\backslash D_n, \end{array} \right.$$ where $D_n$ is the set of divisors of $n$, $\lambda D_n := \{\lambda d: \quad d \in D_n\}$ and $u_1, u_2, ..., u_k$ are the elements of the symmetric difference $D_n \triangle \lambda D_n$ written in increasing order. We will prove that the language $$\mathcal{L}_{\lambda} := \left\{\langle\! \langle n \rangle\! \rangle_{\lambda} : \quad n \in \mathbb{Z}_{\geq 1} \right\}$$ contains Dyck words having an arbitrarily large number of centered tunnels. We will show a connection between both results

On a function introduced by Erd\"{o}s and Nicolas

Erd\"os and Nicolas [erdos1976methodes] introduced an arithmetical function $F(n)$ related to divisors of $n$ in short intervals $\left] \frac{t}{2}, t\right]$. The aim of this note is to prove that $F(n)$ is the largest coefficient of polynomial $P_n(q)$ introduced by Kassel and Reutenauer [kassel2015counting]. We deduce that $P_n(q)$ has a coefficient larger than $1$ if and only if $2n$ is the perimeter of a Pythagorean triangle. We improve a result due to Vatne [vatne2017sequence] concerning the coefficients of $P_n(q)$