Let phi : R(n) -> R boolean OR {+infinity} be a convex function and L phi be its Legendre tranform. It is proved that if phi is invariant by changes of signs, then integral e(-phi) integral e(-L phi) >= 4(n). Th...
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Let phi : R(n) -> R boolean OR {+infinity} be a convex function and L phi be its Legendre tranform. It is proved that if phi is invariant by changes of signs, then integral e(-phi) integral e(-L phi) >= 4(n). This is a functional version of the inverse Santalo inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on R(n) x R(n) together with a functional form of Lozanovskii's lemma. In the last section, we prove that for some c > 0, one has always integral e-(phi) integral e(-L phi) >= c(n). This generalizes a result of B. Klartag and V. Milman.
If d and e are increasing functions in a partial order, then the fixed points on their functional composition ( d ∘ e ) are just the points that are fixed for both d and e . The same is true of a form of parallel com...
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If d and e are increasing functions in a partial order, then the fixed points on their functional composition ( d ∘ e ) are just the points that are fixed for both d and e . The same is true of a form of parallel composition ( fx V gx ), using the least upper bound V in the partial order. This fact may be useful in cases when fixed points are computed by iteration, with arbitrary mixture of sequential and parallel composition.
We study local Lipschitz continuity and interpolation properties of some classes of increasing functions defined on the cone R-++(n) of n-vectors with positive coordinates. We also study the so-called self-conjugate i...
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We study local Lipschitz continuity and interpolation properties of some classes of increasing functions defined on the cone R-++(n) of n-vectors with positive coordinates. We also study the so-called self-conjugate increasing positively homogeneous functions.
Abstract: In this article a local characterization theorem is given for closed sets in a linear topological space that have recession cones with nonempty interior. This theorem is then used to characterize the...
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Abstract: In this article a local characterization theorem is given for closed sets in a linear topological space that have recession cones with nonempty interior. This theorem is then used to characterize the class of upper semicontinuous increasing functions defined on closed $E_ + ^d$-recessional subsets of ${E^d}$.
Let OMEGA:=aleph1. For any alpha OMEGA: zeta = omega(zeta)} let E(OMEGA)(alpha) be the finite set of epsilon-numbers below OMEGA which are needed for the unique representation of alpha in Cantor-normal form using 0, ...
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Let OMEGA:=aleph1. For any alpha < epsilon(OMEGA+1):=min{zeta > OMEGA: zeta = omega(zeta)} let E(OMEGA)(alpha) be the finite set of epsilon-numbers below OMEGA which are needed for the unique representation of alpha in Cantor-normal form using 0, OMEGA, +, and omega. Let alpha*:=max(E(OMEGA)(alpha) or increasing). A function f:epsilon(OMEGA+1) --> OMEGA is called essentially increasing, if for any alpha < epsilon(OMEGA +1);f(alpha) greater-than-or-equal-to alpha*: f is called essentially monotonic, if for any alpha, beta < epsilon(OMEGA+1);alpha less-than-or-equal-to beta AND alpha* less-than-or-equal-to beta* double-line arrow pointing right f(alpha) less-than-or-equal-to f(beta). Let Cl(f)(0) be the least set of ordinals which contains 0 as an element and which satisfies the following two conditions: (a) alpha,beta is-an-element-of Cl(f)(0) double-line arrow pointing right omega(alpha) + beta is-an-element-of Cl(f)(0), (b) E(OMEGA)alpha subset-or-equal-to Cl(f)(0) double-line arrow pointing right f(alpha) is-an-element-of Cl(f)(0). Let thetaepsilon(OMEGA+1) be the Howard-Bachmann ordinal, which is, for example, defined in [3]. The following theorem is shown: If f:epsilon(OMEGA+1) --> OMEGA is essentially monotonic and essentially increasing, then the order type of Cl(f)(0) is less than or equal to thetaepsilon(OMEGA+1).
Author studies the problem of stretching a tube into an annulus. The procedure used is a semi-inverse method in the sense that one specifies the inner radius of the annulus in equilibrium and looks for the stress requ...
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Author studies the problem of stretching a tube into an annulus. The procedure used is a semi-inverse method in the sense that one specifies the inner radius of the annulus in equilibrium and looks for the stress required on the outer boundary. The inner boundary of the annulus is assumed to be free of stresses. Exact solutions are obtained for both M. Mooney material and neo-Hookean material.
A cycle time-throughput curve quantifies the relationship of average cycle time to throughput rates in a manufacturing system. Moreover, it indicates the asymptotic capacity of a system. Such a curve is used to charac...
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A cycle time-throughput curve quantifies the relationship of average cycle time to throughput rates in a manufacturing system. Moreover, it indicates the asymptotic capacity of a system. Such a curve is used to characterize system performance over a range of start rates. Simulation is a fundamental method for generating such curves since simulation can handle the complexity of real systems with acceptable precision and accuracy. A simulation-based cycle time-throughput curve requires a large amount of simulation output data;the precision and accuracy of a simulated curve may be poor if there is insufficient simulation data. To overcome these problems, sequential simulation experiments based on a nonlinear D-optimal design are suggested. Using the nonlinear shape of the curve, such a design pinpoints p starting design points, and then sequentially ranks the remaining n-p candidate design points, where n is the total number of possible design points being considered. A model of a semiconductor wafer fabrication facility is used to validate the approach. The sequences of experimental runs generated can be used as references for simulation experimenters.
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