Evolution of bank efficiency in Brazil: A DEA approach

This paper investigates cost, technical and allocative efficiencies for Brazilian banks in the recent period (2000–2007). We use Data Envelopment Analysis (DEA) to compute efficiency scores. Brazilian banks were found to have low levels of economic (cost) efficiency compared to banks in Europe and in the US. For the period with high macroeconomic volatility (2000–2002) the economic inefficiency in Brazilian banks can be attributed mainly to technical inefficiency rather than allocative inefficiency. State-owned banks are significantly more cost efficient than foreign, private domestic and private with foreign participation. There is no evidence of differences in economic efficiency due to type of activity and bank size. These results may provide some useful guidance for financial regulators and bank managers.     

Weak barrelledness for C(X) spaces

Buchwalter and Schmets reconciled C_c(X) and C_p(X) spaces with most of the weak barrelledness conditions of 1973, but could not determine if -barrelled ⇔ ?^∞-barrelled for C_c(X). The areas grew apart. Full reconciliation with the fourteen conditions adopted by Saxon and Sánchez Ruiz needs their 1997 characterization of Ruess' property (L), which allows us to reduce the C_c(X) problem to its 1973 status and solve it by carefully translating the topology of Kunen (1980) and van Mill (1982) to find the example that eluded Buchwalter and Schmets. The more tractable C_p(X) readily partitions the conditions into just two equivalence classes, the same as for metrizable locally convex spaces, instead of the five required for C_c(X) spaces. Our paper elicits others, soon to appear, that analytically characterize when the Tychonov space X is pseudocompact, or Warner bounded, or when C_c(X) is a df-space (Jarchow's 1981 question).     

Improvement sets and vector optimization

In this paper we focus on minimal points in linear spaces and minimal solutions of vector optimization problems, where the preference relation is defined via an improvement set E. To be precise, we extend the notion of E-optimal point due to Chicco et al. in [4] to a general (non-necessarily Pareto) quasi ordered linear space and we study its properties. In particular, we relate the notion of improvement set with other similar concepts of the literature and we characterize it by means of sublevel sets of scalar functions. Moreover, we obtain necessary and sufficient conditions for E-optimal solutions of vector optimization problems through scalarization processes by assuming convexity assumptions and also in the general (nonconvex) case. By applying the obtained results to certain improvement sets we generalize well-known results of the literature referred to efficient, weak efficient and approximate efficient solutions of vector optimization problems.     

Mathematical programming approaches for generating p-efficient points

Probabilistically constrained problems, in which the random variables are finitely distributed, are non-convex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we consider a random vector characterized by a finite set of scenarios and generate pLEPs by solving a mixed-integer programming (MIP) problem. We solve this computationally challenging MIP problem with a new mathematical programming framework. It involves solving a series of increasingly tighter outer approximations and employs, as algorithmic techniques, a bundle preprocessing method, strengthening valid inequalities, and a fixing strategy. The method is exact (resp., heuristic) and ensures the generation of pLEPs (resp., quasi pLEPs) if the fixing strategy is not (resp., is) employed, and it can be used to generate multiple pLEPs. To the best of our knowledge, generating a set of pLEPs using an optimization-based approach and developing effective methods for the application of the p-efficiency concept to the random variables described by a finite set of scenarios are novel. We present extensive numerical results that highlight the computational efficiency and effectiveness of the overall framework and of each of the specific algorithmic techniques.     

Property (X) for Second-Order Nonlinear Differential Equations of Generalized Euler Type

In this paper the generalized nonlinear Euler differential equation t²k(tu′)u″ + t(f(u)+ k(tu′))u′ + g(u) = 0 is considered. Here the functions f(u), g(u) and k(u) satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are assumed. We present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property (X⁺), which is very important for the existence of periodic solutions and oscillation theory.     

A periodic-review inventory system with a capacitated backup supplier for mitigating supply disruptions

We consider a periodic-review inventory system with two suppliers: an unreliable regular supplier that may be disrupted for a random duration, and a reliable backup supplier that can be used during a disruption. The backup supplier charges higher unit purchasing cost and fixed order cost when compared to the regular supplier. Because the backup supplier is used at unplanned moments, its capacity to replenish inventory is considered limited. Analytical results partially characterize the structure of the optimal order policy: a state-dependent (X(i), Y(i)) band structure (with corresponding bounds of X(i) and Y(i) to be given), where i represents the status of the regular supplier. Numerical studies illustrate the structure of the optimal policy and investigate the impacts of major parameters on optimal order decisions and system costs.     

Relative ageing of series and parallel systems: Effects of dependence and heterogeneity among components

The effect of system structure on relative ageing properties of coherent systems has been extensively studied in terms of the increasing [reversed] hazard ratio. In this paper, we investigate the effects of dependence and heterogeneity among components on the relative ageing of series and parallel systems. Numerical examples are provided as illustrations.     

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L^?-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.     

Fractional integrals on weighted Hardy spaces

In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to .     

Note on 2-rational fields

We give an alternative computation of the Galois group of the maximal 2-ramified and complexified pro-2-extension of any 2-rational number field (Theorem 2), a particular case of results of Movahhedi-Nguyen Quang Do. This short Note is motivated by the paper [J. Jossey, Galois 2-extensions unramified outside 2, J. Number Theory 124 (2007) 42-76] and, at this occasion, we bring into focus some classical technics of abelian ?-ramification which, unfortunately, are often ignored, especially those developed by J.-F. Jaulent with the ?-adic class field theory, and by G. Gras in his book on class field theory, and which considerably simplify the study of such subjects; for instance, our proof of Theorem 2 generalizes the purpose of Jossey's paper in such a way using a result of Herfort-Zalesskii. This Note is mainly an attempt of clarification about ?-rationality.     

Kernel systems on L-ordered sets

This paper presents fuzzy versions of kernel operators and kernel systems on L-ordered sets and establishes a one-to-one correspondence between them.     

Characterizations of α-Bloch spaces on the unit ball

We obtain a characterization of the α-Bloch space for any α>0 in the unit ball of Cn in terms of |f(z)−f(w)|/|z−w|. Moreover, a new characterization for the Bloch space is given.     

Polypotentials on a Riemannian manifold

Polyharmonic functions are considered on open sets in a Riemannian manifold R and their potential-theoretic properties are studied using the notion of complete m-potentials. Also one obtains here some characterizations of domains in R on which such complete m-potentials exist.     

The impact of production time variability on make-to-stock queue performance

In this paper, we exploit the distributional Little’s law to obtain the steady-state distribution of the number of customers in a GI/G/1 make-to-stock queueing system. Non-exponential service times in make-to-stock queue modeling are usually avoided or at best, considered in approximations due to difficulties in developing an exact method. By providing a numerical solution of the GI/G/1 make-to-stock queue, we observed the impact of production time variability on optimal inventory control policies. The numerical results prove the degree of errors in the results if an exponential service time distribution were assumed instead of the actual distribution.     

Polynomial sequential continuity on C(K,E) spaces

We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true when K is a scattered compact space. These conditions are related with some others appeared in the literature and they seem to be of independent interest.     

Duality of dams via mountain processes

We consider a G/M/1-type dam having finite capacity and a general release rule, and construct a ‘dual’ M/G/1-type dam with state-dependent jump sizes and without dry periods whose content process has the same stationary density (up to some transformation). For the dual dam the stationary distribution can be computed in closed form.     

Estimates of weighted Hardy-Littlewood averages on the p-adic vector space

In the p-adic vector space , we characterize those non-negative functions ψ defined on for which the weighted Hardy-Littlewood average is bounded on (1?r?∞), and on . Also, in each case, we find the corresponding operator norm ‖Uψ‖.     

Counting nowhere-zero flows on wheels

A wheel is a graph consisting from a vertex w and a circuit C such that each vertex of C is a neighbor of w. Two nowhere-zero group valued flows on a wheel are equivalent if their values differ only on the edges of C. We introduce recursive formulas for the numbers of classes of the same cardinality of this equivalence.     

Weighted integral inequalities for solutions of the A-harmonic equation

We prove the parametric versions of -weighted integral inequalities for differential forms satisfying the A-harmonic equation. These results can be considered as extensions of the classical inequalities for Sobolev functions.