The theory of increasing positively homogeneous functions defined on the positive orthant is applied to the class of decreasing functions. A multiplicative version of the inf-convolution operation is studied for decre...
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The theory of increasing positively homogeneous functions defined on the positive orthant is applied to the class of decreasing functions. A multiplicative version of the inf-convolution operation is studied for decreasing functions. Modified penalty functions for some constrained optimization problems are introduced that are in general nonlinear with respect to the objective function of the original problem. As the perturbation function of a constrained optimization problem is decreasing, the theory of decreasing functions is subsequently applied to the study of modified penalty functions, the zero duality gap property, and the exact penalization.
Abstract: Let $\Gamma$ be a group. We associate to any length-function $L$ on $\Gamma$ the space $H_L^\infty (\Gamma )$ of rapidly decreasing functions on $\Gamma$ (with respect to $L$), which coincides with t...
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Abstract: Let $\Gamma$ be a group. We associate to any length-function $L$ on $\Gamma$ the space $H_L^\infty (\Gamma )$ of rapidly decreasing functions on $\Gamma$ (with respect to $L$), which coincides with the space of smooth functions on the $k$-dimensional torus when $\Gamma = {{\bf {Z}}^k}$. We say that $\Gamma$ has property (RD) if there exists a length-function $L$ on $\Gamma$ such that $H_L^\infty (\Gamma )$ is contained in the reduced ${C^*}$-algebra $C_r^*(\Gamma )$ of $\Gamma$. We study the stability of property (RD) with respect to some constructions of groups such as subgroups, over-groups of finite index, semidirect and amalgamated products. Finally, we show that the following groups have property (RD): (1) Finitely generated groups of polynomial growth; (2) Discrete cocompact subgroups of the group of all isometries of any hyperbolic space.
We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S*, on the full range 1 <= p <= infinity, for the cases of decreasing, positive or general functions (i...
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We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S*, on the full range 1 <= p <= infinity, for the cases of decreasing, positive or general functions (in fact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1 < p <= 2, we prove that all these estimates are the same, but for 2 < p < infinity, they exhibit a completely different behavior. (C) 2018 Elsevier Inc. All rights reserved.
In contrast to equations in exterior domains where local decay takes place because signals radiate to infinity, in the bounded case there must be some direct dissipative mechanism. The paper discusses two types. In on...
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In contrast to equations in exterior domains where local decay takes place because signals radiate to infinity, in the bounded case there must be some direct dissipative mechanism. The paper discusses two types. In one kind the energy of a wave will decrease when it passes through some fixed subregion of the domain. The second sort of decay occurs at the boundary;energy is lost when a wave is reflected from a fixed subset of the boundary are investigated. 7 refs.
The exit distribution problem for energy dependent radiative transfer in an inhomogeneous slab with isotropic scattering is solved in terms of operator-valued generalizations of Chandrasekhar's H-function.
The exit distribution problem for energy dependent radiative transfer in an inhomogeneous slab with isotropic scattering is solved in terms of operator-valued generalizations of Chandrasekhar's H-function.
Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life ...
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Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life with residual variance. To study this quantity, we develop a general result concerning the preservation of bathtub distributions. Using this result, we give a condition so that the residual coefficient of variation is bathtub-shaped. Furthermore, we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value, but not necessarily before the change point of the failure rate function.
Abstract: Water flowing down a dry channel and infiltrating into the channel bed constitutes a free boundary problem. The free boundary is the time history of the water edge or front. In this paper we discuss ...
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Abstract: Water flowing down a dry channel and infiltrating into the channel bed constitutes a free boundary problem. The free boundary is the time history of the water edge or front. In this paper we discuss a kinematic wave model of the problem. The problem is formulated in Sec. 1 and the results summarized in Sec. 2. In Secs. 3 and 4 the mathematical details are carried out, and in Sec. 5 a model using the continuity and momentum equations of hydraulics is discussed.
A maintenance system consists of o finite number of machines and a single-server repair facility that may be operated at several rates. Machines are subject to failure and machines that fail are sent to the repair fac...
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A maintenance system consists of o finite number of machines and a single-server repair facility that may be operated at several rates. Machines are subject to failure and machines that fail are sent to the repair facility. Under the assumption that costs depend on the repair rate and lost production, we derive conditions that ensure that, for a discrete time maintenance system, the optimal repair rate is a non-increasing function of the number of machines in good condition. By considering a continuous time maintenance system as a limit of a sequence of discrete time maintenance systems, we derive analogous conditions that ensure that the optimal repair rate for the continuous time maintenance system is a non-increasing function of the number of machines in good condition.
We consider the problem of maximizing the long-run average expected reward per unit time in a queuing-reward system, which we formulate as a semi-Markov decision process. Control of the system is effected by increasin...
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We consider the problem of maximizing the long-run average expected reward per unit time in a queuing-reward system, which we formulate as a semi-Markov decision process. Control of the system is effected by increasing or decreasing the price charged for the facility's service in order to discourage or encourage the arrival of customers. We assume that the arrival process is Poisson with arrival rate a strictly decreasing function of the currently advertized price, and that the service times are independent exponentially distributed random variables. The reward structure consists of customer payments and holding costs (possibly nonlinear). At each transition (customer arrival or service completion), the manager of the facility must choose one of a finite number of prices to advertize until the next transition. We show that there exist optimal stationary policies and that each possesses the monotonicity property: the optimal price to advertize is a nondecreasing function of the number of customers in the system. An efficient computational algorithm is developed that, in a finite number of steps, produces a stationary policy that is optimal.
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