Systemic Model for Diagnosis of the Micro,Small and Medium Enterprises from Two Cities from the Countryside of the State of <Emphasis Type="Italic">São Paulo</Emphasis> in Brazil

This article presents a proposal of a systemic model composed for the micro and small companies (MSE) of the region of Ribeirão Preto and the agents which influenced their environment. The proposed model was based on Stafford Beer’s (Diagnosing the system for organizations. Chichester, Wiley, 1985) systemic methodologies VSM (Viable System Model) and on Werner Ulrich’s (1983) CSH (Critical Systems Heuristics). The VSM is a model for the diagnosis of the structure of an organization and of its flows of information through the application of the cybernetics concepts (Narvarte, In El Modelo del Sistema Viable—MSV: experiencias de su aplicación en Chile. Proyecto Cerebro Colectivo del IAS, Santiago, 2001). On the other hand, CSH focus on the context of the social group applied to the systemic vision as a counterpoint to the organizational management view considered by the VSM. MSE of Ribeirão Preto and Sertãozinho had been analyzed as organizations inserted in systems that relate and integrate with other systems concerning the public administration, entities of representation and promotion agencies. The research questions: which are the bonds of interaction among the subsystems in this process and who are the agents involved? The systemic approach not only diagnosed a social group, formed by MSE of Ribeirão Preto and Sertãozinho, public authorities and support entities, but could also delineate answers that aimed the clarification of obscure questions generating financial assistance to the formularization of efficient actions for the development of this system.     

The Mind Could Accommodate Inconsistencies

The mathematical language of function is an important part of natural science since its inception. Its influence leaves visible traces in social science, in the theory of cognitive dissonance and prevailing systems approaches. They postulate that mental activities are analogous to mechanical principle, complying with the language of function. Yet, an inward introspection reveals that the mind is not thoroughly bounded by mathematical principles. An individual could experience an inconsistent mental status at a given time, which detaches itself from the prison of function. A preliminary survey demonstrates that the existence of inconsistent mental state at a given time is possible. The mechanists compel people to abide by mechanistic design. This approach is likely to make some innate characters, not amenable to mechanistic explanations, vanished. It also involves pointless applications of abstract mathematical operations on mental activities.     

Using Generic Structures in System Dynamics Model Building: Reflection from Modeling for Indian Shrimp Industry

The paper focused on how a system dynamics modeler could reduce model development and testing time by using “Generic Structures” as an interim benchmark between causal loop diagram and stock flow diagram. Using generic structures as a benchmark could prevent the modeler from including redundant structures to the model and getting affected by personal biases that in turn could reduce repetitive amendments to the model during model testing. Indian Shrimp Industry, during 1990–2010, sequentially showed an early growth, a hasty decline, a combative rejuvenation, and an inexorable re-decline behavior in terms of the annual shrimp production and production capacity. Average Yield continuously fluctuated throughout the Industry’s life cycle during 1990–2010. Breaking such progressive behavior into temporal units, we found that the unit behaviors resemble with the behaviors of generic structures like, exponential growth, goal-seeking, S-shaped growth, limits to success, and overshoot-and-collapse. We, using the related generic structures as the interim benchmarks, illustrated a step-by-step modeling exercise for studying the dynamic behavior of Indian Shrimp Industry during 1990–2010. The paper concluded that using generic structures as the benchmark during system dynamics modeling improved the efficiency and the effectiveness of model building due to reduction in model building and testing time.     

Weighted <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-estimates of solutions for damped wave equations with variable coefficients

The authors establish weighted L²-estimates of solutions for the damped wave equations with variable coefficients u _tt ? divA(x)?u+au _t = 0 in ? ⁿ under the assumption a(x) ≥ a₀[1+ρ(x)]^?l, where a₀ > 0, l < 1, ρ(x) is the distance function of the metric g = A^?1(x) on ? ⁿ . The authors show that these weighted L²-estimates are closely related to the geometrical properties of the metric g = A^?1(x).     

The determination on weight hierarchies of <Emphasis Type="Italic">q</Emphasis>-ary linear codes of dimension 5 in class IV

The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d ₁, d ₂, ···, d _k ) where d _r is the smallest support of any r-dimensional subcode of C. “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q-ary linear codes of dimension k”. In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.     

A class of constacyclic codes over ring <Emphasis Type="Italic">R</Emphasis> + <Emphasis Type="Italic">vR</Emphasis>

By constructing a Gray map, a class of constacyclic codes over ring R = R+vR is studied. Using cyclic codes and negacyclic codes of length p ^s over ring R, the structure of (1?2v)-constacyclic codes and dual codes of length p ^s over ring R are given, the Gray images of (1 ? 2v)-constacyclic codes in a particular case are also studied. It is shown that linear codes of length p ^s over ring R are (1?2v)-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p ^s over ring R.     

Partially function linear error-in-response models with validation data

This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.     

Construction of one-Lee weight and two-Lee weight codes over F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> + <Emphasis Type="Italic">v</Emphasis>F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over F _p + vF _p (v ² = v) with type \({p^{2{k_1}}}{p^{{k_2}}}{p^{{k_3}}}\) based on two different distance-preserving Gray maps from ((F _p + vF _p ) ⁿ , Lee weight) to (F _p ²ⁿ , Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p = 2.     

A unified approach to construct generalized B-splines for isogeometric applications

Generalized B-splines have been employed as geometric modeling and numerical simulation tools for isogeometric analysis(IGA for short). However, the previous models used in IGA,such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper,a unified approach to construct the generalized non-uniform B-splines over the space spanned by{α(t), β(t), ξ(t), η(t), 1, t, ···, t~(n-4)} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometric heat conduction problems are presented to show the effectiveness of the proposed methods.     

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u_1, u_2, ···, u_m over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of x~i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u_1, u_2, ···, u_m), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr?bner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.     

Linear Bayes estimators applied to the inverse Gaussian lifetime model

For the two-parameter inverse Gaussian distribution denoted by I G(μ,λ),the authors employ a linear Bayes procedure to estimate the parameters μ and λ.The superiority of the proposed linear Bayes estimator(LBE) over both the classical UMVUE and the maximum likelihood estimator(MLE) is established in terms of the mean squared error matrix(MSEM) criterion.Compared with the usual Bayes estimator,which is obtained by an MCMC method,the proposed LBE is simple and easy to use.Some numerical results are presented to verify that the LBE performs well.     

Adaptive Event-Based Consensus of Multi-Agent Systems with General Linear Dynamics

In this paper, adaptive event-based consensus of multi-agent systems with general linear dynamics is considered. A novel adaptive event-based controller and a state-dependent triggering function are proposed for each agent. The consensus can be achieved without the assumption that (A,B) is stabilizable. Furthermore, the Zeno-behavior of the concerned closed-loop system is also excluded under certain conditions. Finally, a numerical simulation example is presented to show the effectiveness of the theoretical results.     

An improved algorithm for solving all <Emphasis Type="Italic">d</Emphasis>-MPs in multi-state networks

Reliability is a desirable performance indicator of many real-world systems to measure the quality level. One general method for evaluating multi-state reliability is using d-minimal paths (d-MPs). However, being an NP-hard problem, searching for all d-MPs is a rather challenging task. This paper proposes an improved algorithm to solve the d-MP problem. To reduce the search space of d-MPs, a concept of lower capacity bound is introduced into the d-MP problem, and an effective technique is developed to find lower capacity bounds. Meanwhile, the fast enumeration method which is a recent improvement to the traditional enumeration method is employed to solve d-MPs. In addition, by introducing the operation of transforming undirected edges into directed edges, the proposed algorithm is applicable to solving both directed networks and undirected networks. Through numerical experiments, it is found that the proposed algorithm holds a distinct advantage over the existing methods in solving all d-MPs.     

On the axioms of revealed preference in fuzzy consumer theory

The revealed preference is a central subject in classical consumer theory.Authors likeSamuelson,Arrow,Richter,Sen,Uzawa and others have proposed an axiomatic setting of revealedpreference theory.Consequently revealed preference axioms WARP and SARP and congruence axioms WCA andSCA have been considered.An important theorem of Sen establishes the equivalence between these axioms provided thefamily of budgets includes all non-empty finite sets of bundles.Fuzzy consumer theory(＝fuzzy choice functions)is a topic that appears in a lot of papers.Particularly,Banerjee studies in fuzzy context axioms of revealed preference and congruenceextending some results of Arrow and Sen.In this paper we modify the Banerjee definition of a fuzzy choice function(＝fuzzy consumer)and we study some fuzzy versions of the axioms of revealed preference and congruence.Banerjeefuzzifies only the range of a consumer;we use a fuzzification of both the domain and the range of aconsumer.The axioms WAFRP,SAFRP,WFCA,SFCA generalize to fu     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in ) O(T ²) time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O(T) when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O(T ³logT) time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.     

Pricing and inventory control strategy for a periodic-review energy buy-back system

Along with the rapid development of economics and enhancement of industrialization, the power demand keeps rising and frequently creates mismatch between demand and supply in electricity. This provides miscellaneous energy buy-back programs with great opportunities. Such programs, when activated, offer certain amount of financial compensations to participants for reducing their energy consumption during peak time. They aim at encouraging participants to shift their electricity usage from peak to non-peak time, and thereby release the demand pressure during peak time. This paper considers a periodic-review joint pricing and inventory decision model under an energy buy-back program over finite planning horizons, in which the compensation levels, setup cost and additive random demand function are incorporated. The objective is to maximize a manufacturer’s expected total profit. By using Veinott’s conditions, it is shown that the manufacturer’s optimal decision is a state dependent (s, S, P) policy under a peak market condition, or partly an (s, S, A, P) policy under the normal market condition.     

An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Control Cost

Elliptic PDE-constrained optimal control problems with L¹-control cost (L¹-EOCP) are considered. To solve L¹-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers (ADMM), we consider extending the ADMM to L¹-EOCP. To discretize L¹-EOCP, the piecewise linear finite element (FE) is considered. However, different from the finite dimensional l1-norm, the discretized L¹-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L¹-norm and L²-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem, an inexact heterogeneous ADMM (ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates, but also show that the ihADMM and the two-phase strategy are highly efficient.     

Construction of one-gray weight codes and two-Gray weight codes over ℤ<Subscript>4</Subscript> + <Emphasis Type="Italic">u</Emphasis>ℤ<Subscript>4</Subscript>

This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over ?₄+u?₄(u ² = u) with type \({16^{{k_1}}}{8^{{k_2}}}{8^{{k_3}}}{4^{{k_4}}}{4^{{k_5}}}{4^{{k_6}}}{2^{{k_7}}}{2^{{k_8}}}\) based on a distance-preserving Gray map from (?₄ + u?₄) ⁿ to ? ₄ ²ⁿ . Secondly, the authors use the similar approach to do works on two-Gray (projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.     

The equivalent representation of the breadth-one <Emphasis Type="Italic">D</Emphasis>-invariant polynomial subspace and its discretization

This paper demonstrates the equivalence of two classes of D-invariant polynomial subspaces, i.e., these two classes of subspaces are different representations of the breadth-one D-invariant subspace. Moreover, the authors solve the discrete approximation problem in ideal interpolation for the breadth-one D-invariant subspace. Namely, the authors find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given D-invariant subspace, as the evaluation points all coalesce at one point.