Influence of storage humidity on the in vitro inhalation properties of salbutamol sulfate dry powder with surface covered lactose carrier

The influence of storage humidity on the in vitro inhalation properties of salbutamol sulfate dry powder with surface covered lactose carrier was investigated. In the present study, drug/carrier powder mixtures were prepared consisting of micronized salbutamol sulfate and lactose carriers with different particle surface conditions prepared by surface covering. Lactose carrier surfaces were covered with vegetable magnesium stearate (Mg-St-V) by a high-speed elliptical-rotor-type powder mixer (Theta-Composer). These powder mixtures were aerosolized by a Jethaler), and the in vitro inhalation properties of salbutamol sulfate were evaluated by a twin impinger. Compared with the powder mixed with uncovered lactose carrier, the in vitro inhalation properties of the powder mixture prepared using the surface covered lactose carrier were little decreased with increased in relative humidity (RH), showing that the in vitro inhalation properties of salbutamol sulfate were improved at high RH. Using this surface covering technique would thus be valuable for storage humidity of dry powder inhalation (DPI) with lactose carrier particles.     

A combined penalty function and gradient projection method for nonlinear programming

A new programming algorithm for nonlinear constrained optimization problems is proposed. The method is based on the penalty function approach and thereby circumyents the necessity to maintain feasibility at each iteration, but it also behaves much like the gradient projection method. Although only first-order information is used, the algorithm converges asymptotically at a rate which is independent of the magnitude of the penalty term; hence, unlike the simple gradient method, the asymptotic rate of the proposed method is not affected by the ill-conditioning associated with the introduction of the penalty term. It is shown that the asymptotic rate of convergence of the proposed method is identical with that of the gradient projection method.Dedicated to Professor M. R. HestenesThis research was supported by the National Science Foundation, Grant No. GK-16125.     

Effect of surface layering time of lactose carrier particles on dry powder inhalation properties of salbutamol sulfate

The effect of the surface layering time of lactose carrier particles on the dry powder inhalation properties of salbutamol sulfate was investigated. Lactose carrier particles were layered with vegetable magnesium stearate by physical mixing. In the present study, drug/carrier powder mixtures were designed consisting of micronized salbutamol sulfate and lactose carriers with various particle surface conditions prepared by surface layering. These powder mixtures were aerosolized by a Jethaler, and the in vitro deposition properties of salbutamol sulfate were evaluated by a twin impinger. Compared with the powder mixed with unlayered lactose carrier, the in vitro inhalation properties of the powder mixture prepared using the surface layering lactose carrier were significantly different, showing that the in vitro inhalation properties of the drug/carrier powder mixtures were improved. In vitro deposition properties (RP) increased with surface layering time. Using this surface layering system would thus be valuable for increasing the inhalation properties of dry powder inhalation.     

Effects of surface processing of lactose carrier particles on dry powder inhalation properties of salbutamol sulfate

The effects of the surface processing of lactose carrier particles on the dry powder inhalation properties of salbutamol sulfate were investigated. Lactose carrier particles were processed using a high-speed elliptical-rotor-type powder mixer (Theta-Composer). In the present study, drug/carrier powder mixtures were prepared, consisting of micronized salbutamol sulfate and coarse lactose carriers with various particle surface conditions prepared by surface processing. These powder mixtures were aerosolized by a Jethaler, and the in vitro inhalation properties of salbutamol sulfate were evaluated with a twin impinger. Compared with those of the powder mixed with unprocessed lactose carriers, the in vitro inhalation properties of the powder mixture prepared using the surface processed lactose carriers were significantly different, showing that the in vitro inhalation properties of salbutamol sulfate were improved. The in vitro inhalation properties increased with the rotor rotation rate. Using this surface processing system would thus be valuable for increasing the inhalation properties of dry powder inhalation with lactose carrier particles.     

An approach to nonlinear programming

A nonlinear programming problem with inequality constraints and with unknown vectorx is converted to an unconstrained minimization problem in unknownsx and , where is a vector of Lagrange multipliers. It is shown that, if the original problem possesses standard convexity properties, then local minima of the associated unconstrained problem are in fact global minima of that problem and, consequently, Kuhn-Tucker points for the original problem. A computational procedure based on the conjugate residual scheme is applied in thex-space to solve the associated unconstrained problem. The resulting algorithm requires only first-order derivative information on the functions involved and will solve a quadratic programming problem in a finite number of steps.This research was supported by the National Science Foundation under Grant No. GK-16125. The author is indebted to the referee for several valuable comments and suggestions for improvement.     

Projection Pricing

A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases.     

Neighborhood effects and maintenance of the urban housing stock*

This paper presents and analyzes a theoretical model of the impact of neighborhood effects upon the maintenance of urban housing stock. The rental value of a dwelling unit is related not only to its own physical characteristics but also to those of other dwelling units in its neighborhood. The physical characteristics of dwelling units depend upon how much their owners spend on maintenance. Since these expenditures are undertaken only in so far as they enhance the rental value of properties, the maintenance policies of a neighborhood's owners are interdependent. The model focuses explicitly on the aspects of this process that involve multiperson decisions. Concepts concerning equilibrium are introduced; short run equilibria are shown to exist, and conditions for their uniqueness are derived. Comparative static results are established, and stability properties of the static equilibria analyzed.     

Complete stability of noncooperative games

This paper is concerned with a class of noncooperative games ofn players that are defined byn reward functions which depend continuously on the action variables of the players. This framework provides a realistic model of many interactive situations, including many common models in economics, sociology, engineering, and political science. The concept of Nash equilibrium is a suitable companion to such models.A variety of different sufficient conditions for existence, uniqueness, and stability of a Nash equilibrium point have been previously proposed. By sharpening the noncooperative aspect of the framework (which is really only implicit in the original framework), this paper attempts to isolate one set of natural conditions that are sufficient for existence, uniqueness, and stability. It is argued thatl quasicontraction is such a natural condition. The concept of complete stability is introduced to reflect the full character of noncooperation. It is then shown that, in the linear case, the condition ofl quasicontraction is both necessary and sufficient for complete stability.This research was supported by the Air Force Office of Scientific Research under Grant No. AFOSR 77-3141 and by the National Science Foundation under Grant No. GK18748.