A system dynamics sustainable business model for Petroleos Mexicanos (Pemex): case based on the Global Reporting Initiative

We propose a System Dynamics model to explain the implementation and development of business sustainable policies at Petroleos Mexicanos (Pemex). The model is built using information reported by this company on the Global Reporting Initiative website. The simulation model incorporates the participation and expectations of internal and external stakeholders in defining sustainability (as perceived by the organization) and implementing its initiatives. Three variables (leadership, stakeholder motivation and external factors), identified as leverage points in the model, are used as means to improve the organization's journey towards achieving sustainability. The results of the simulation model seem to indicate that by increasing leadership activity and levels of stakeholder motivation, the journey towards sustainability can be greatly improved, and that external economic factors do not have a significant impact on sustainability achievement. These findings are pertinent for organizations currently in the process of implementing sustainable policies and strategies.     

Existence of Words over Tree-Letter Alphabet not Containing Squares with Replacement Errors

The paper concerns some issues related to the existence of periodic structures in words from formal languages. Squares, i.e., fragments of the form xx, where x is some word, and ?-squares, i.e., fragments of the form xy, where the word x is different from the word y by not more than ? letters, are considered as periodic structures. We show the existence of arbitrarily long words over three-letter alphabet not Containing ?-Squares with the period exceeding ?. In particular, such words are constructed for all possible values ?.     

Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential

For the abstract parabolic equation \(\dot x = Bx + bv\left( t \right)\) with an unbounded self-adjoint operator B, where b is a vector and v(t) is a scalar function, we suggest a solution method based on the evaluation of some rational function of the operator B. We obtain a priori estimates of the approximation error for the output function y(t) = <x(t), l>, where l is a given vector. The results of a numerical experiment for the inhomogeneous heat equation are presented.     

Systemic problem structuring applied to community involvement in water conservation

Many advocates of problem structuring approaches mix methods to enhance the flexibility and responsiveness of OR practice. A number of ‘multi-methodology’ approaches have been developed to support practitioners in doing this, and one of these is systemic intervention. A distinguishing feature of systemic intervention is boundary critique: a theory and set of methodological ideas for exploring the inclusion, exclusion and marginalization of both people and issues. This paper argues that boundary critique can enhance the choice and process of application of problem structuring methods. An application of boundary critique is presented to illustrate the argument, focusing on community participation in the management of ongoing water shortages in a small seaside town in New Zealand. The theory of boundary critique helped to reframe people's understanding of a 30-year conflict between the District Council and community. This led to the design of a participative problem structuring workshop, and a way forward was identified that both the District Council and community could accept. Feedback from the workshop participants suggested that the intervention generated valuable results for all the parties involved. The paper concludes with some brief reflections on how the research agenda on boundary critique and problem structuring methods can be progressed into the future.     

Filter factors of truncated tls regularization with multiple observations

The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems Ax ≈ b were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of A applied to b. This paper focuses on the situation when multiple observations b ₁,..., b _d are available, i.e., the T-TLS method is applied to the problem AX ≈ B, where B = [b ₁,..., b _d ] is a matrix. It is proved that the filtering representation of the T-TLS solution can be generalized to this case. The corresponding filter factors are explicitly derived.     

On the Wick theorem for mixtures of centered Gaussian distributions

We consider centered conditionally Gaussian d-dimensional vectors X with random covariance matrix Ξ having an arbitrary probability distribution law on the set of nonnegative definite symmetric d × d matrices M _d ⁺. The paper deals with the evaluation problem of mean values \( E\left[ {\prod\nolimits_{i = 1}^{2n} {\left( {{c_i},X} \right)} } \right] \) for c _i ∈ ? ^d , i = 1, …, 2n, extending the Wick theorem for a wide class of non-Gaussian distributions. We discuss in more detail the cases where the probability law ?(Ξ) is infinitely divisible, the Wishart distribution, or the inverse Wishart distribution. An example with Ξ \( = \sum\nolimits_{j = 1}^m {{Z_j}{\sum_j}} \), where random variables Z _j , j = 1, …, m, are nonnegative, and Σ _j ∈ M _d ⁺, j = 1, …, m, are fixed, includes recent results from Vignat and Bhatnagar, 2008.     

Investment evaluation within project management: an information systems perspective

This paper is seeking to make a contribution through exploring project managementfrom the perspective of information systems (IS) investment evaluation.Organizational investments in IS are significant in financial terms and, as aresult, management would appear set to increasingly scrutinize such expenditurethrough tighter forms of decision-making and corporate governance. Inturn, this has increased the motivation of project managers toappropriately evaluate the impact of their IS before,during and after the investments are signed off. Thisperspective is not restricted to any one industry sector, with the authorseeking motivation for a better understanding of investment evaluation within aproject management context. This paper sets out to explain why andhow investment evaluation should be embedded in project managementin order to support an increase in the effectiveness of project management,thereby increasing the prospects of project success. While doing so,the reader will be provided with several touch-points that serve to outline thepurpose and challenges facing those seeking to evaluate their investments. Theauthor starts off with a contextualization of project management and its phasedactivities, such that a clear understanding of the contribution that investmentevaluation plays within robust project management can be demonstrated. Then, theperspective of investment versus consumption is presented, groundedwithin the strategic grid, which classifies information technology-basedprojects as either: strategic, turnaround, factory or support. The author thenpresents evaluation as a life-cycle process, where evaluation is classified intofour distinctive phases, namely ex-ante evaluation, metrics,command and control and ex-post evaluation, in doing so,emphasizing that evaluation needs to be seen as a process that runs through thelife cycle of a project rather than as a hurdle that needs to be cleared toensure financial approval.     

Hankel Determinants of the Generalized Factorials

Denote 〈x|d〉 _n = x(x + d)(x + 2d) · · · (x + (n - 1)d) for n = 1, 2, · · ·, and 〈x|d〉₀ = 1, where 〈x|d〉 _n is called the generalized factorial of x with increment d. In this paper, we present the evaluation of Hankel determinants of sequence of generalized factorials. The main tool used for the evaluation is the method based on exponential Riordan arrays. Furthermore, we provide Hankel determinant evaluations of the Eulerian polynomials and exponential polynomials.     

Token Graphs

For a graph G and integer k ≥ 1, we define the token graph F _k (G) to be the graph with vertex set all k-subsets of V(G), where two vertices are adjacent in F _k (G) whenever their symmetric difference is a pair of adjacent vertices in G. Thus vertices of F _k (G) correspond to configurations of k indistinguishable tokens placed at distinct vertices of G, where two configurations are adjacent whenever one configuration can be reached from the other by moving one token along an edge from its current position to an unoccupied vertex. This paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian products of token graphs.     

A realization theorem in the context of the Schur-Szegő composition

Every real polynomial of degree n in one variable with root ?1 can be represented as the Schur-Szeg? composition of n ? 1 polynomials of the form (x + 1) ^n?1(x + a _i ), where the numbers a _i are uniquely determined up to permutation. Some a _i are real, and the others form complex conjugate pairs. In this note, we show that for each pair (ρ, r), where 0 ? ρ, r ? [n/2], there exists a polynomial with exactly ρ pairs of complex conjugate roots and exactly r complex conjugate pairs in the corresponding set of numbers a _i .     

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

A large scale nonsymmetric algebraic Riccati equation XCX ? XE ? AX + B = 0 arising in transport theory is considered, where the n × n coefficient matrices B,C are symmetric and low-ranked and A, E are rank one updates of nonsingular diagonal matrices. By introducing a balancing strategy and setting appropriate initial matrices carefully, we can simplify the large-scale structure-preserving doubling algorithm (SDA_ls) for this special equation. We give modified large-scale structure-preserving doubling algorithm, which can reduce the flop count of original SDA_ls by half. Numerical experiments illustrate the effectiveness of our method.     

Discrete Universality in the Selberg Class

The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + iτ ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number.     

Tensor products of tilting modules

We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T ? T′: The main result is that T ? T′ turns out to be an (n + m)-tilting A ? B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.     

Some results on the annihilator graph of a commutative ring

Let R be a commutative ring. The annihilator graph of R, denoted by AG(R), is the undirected graph with all nonzero zero-divisors of R as vertex set, and two distinct vertices x and y are adjacent if and only if ann _R (xy) ≠ ann _R (x) ∪ ann _R (y), where for z ∈ R, ann _R (z) = {r ∈ R: rz = 0}. In this paper, we characterize all finite commutative rings R with planar or outerplanar or ring-graph annihilator graphs. We characterize all finite commutative rings R whose annihilator graphs have clique number 1, 2 or 3. Also, we investigate some properties of the annihilator graph under the extension of R to polynomial rings and rings of fractions. For instance, we show that the graphs AG(R) and AG(T(R)) are isomorphic, where T(R) is the total quotient ring of R. Moreover, we investigate some properties of the annihilator graph of the ring of integers modulo n, where n ? 1.     

Integral averaging technique for oscillation of damped half-linear oscillators

This paper is concerned with the oscillatory behavior of the damped half-linear oscillator (a(t)?_p(x′))′ + b(t)?_p(x′) + c(t)?_p(x) = 0, where ?p(x) = |x|^p?1 sgn x for x ∈ ? and p > 1. A sufficient condition is established for oscillation of all nontrivial solutions of the damped half-linear oscillator under the integral averaging conditions. The main result can be given by using a generalized Young’s inequality and the Riccati type technique. Some examples are included to illustrate the result. Especially, an example which asserts that all nontrivial solutions are oscillatory if and only if p ≠ 2 is presented.     

The space clcv(ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) with the Hausdorff-Bebutov metric and differential inclusions

The paper is devoted to studying the space of nonempty closed convex (but not necessarily compact) sets in ? ⁿ , a dynamical system of translations, and existence theorems for differential inclusions. We make this space complete by equipping it with the Hausdorff-Bebutov metric. The investigation of these issues is important for certain problems of optimal control of asymptotic characteristics of a control system. For example, the problem \(\dot x = A(t,u)x\), (u, x) ∈ ? ^m+n , λ _n (u(·))→ min, where λ _n (u(·)) is the largest Lyapunov exponent of the system {ie121-2} = A(t, u)x, leads to a differential inclusion with a noncompact right-hand side.     

An algorithm to compute <Emphasis Type="Italic">ω</Emphasis>-primality in a numerical monoid

Let M be a commutative, cancellative, atomic monoid and x a nonunit in M. We define ω(x)=n if n is the smallest positive integer with the property that whenever x∣a ₁???a _t , where each a _i is an atom, there is a T?{1,2,…,t} with |T|≤n such that x∣∏_k∈T a _k . The ω-function measures how far x is from being prime in M. In this paper, we give an algorithm for computing ω(x) in any numerical monoid. Simple formulas for ω(x) are given for numerical monoids of the form 〈n,n+1,…,2n?1〉, where n≥3, and 〈n,n+1,…,2n?2〉, where n≥4. The paper then focuses on the special case of 2-generator numerical monoids. We give a formula for computing ω(x) in this case and also necessary and sufficient conditions for determining when x is an atom. Finally, we analyze the asymptotic behavior of ω(x) by computing \(\lim_{x\rightarrow \infty}\frac{\omega(x)}{x}\).     

Solvability of the problem of taking the discrete logarithm

It is proved that consideration of the solvability problem for taking the discrete logarithm in a residue ring modulo composite M can be reduced to consideration of a similar problem in residue rings modulo pq, where p and q are prime divisors of M. For moduli of form pq, necessary and sufficient conditions for solvability checking are obtained in some cases. In addition, the problem of raising a solution of an exponential comparison in a residue ring modulo p ^α is solved.     

Calculating the Isotropic Subspace of a Symmetric Quasi-Definite Matrix

Solutions to the sesquilinear matrix equation X*DX + AX + X*B + C = 0, where all matrices are of size n × n, are put in correspondence with n-dimensional neutral (or isotropic) subspaces of the associated matrix M of order 2n. A way of constructing such subspaces is proposed for when M is a symmetric quasi-definite matrix of the (n, n) type.