Asymptotic behavior of functionals of cyclic long-range dependent random fields

Long-range dependent random fields with spectral densities, which are unbounded at some frequencies, are investigated. We demonstrate new examples of covariance functions, which do not exhibit a regular varying asymptotic behavior at infinity. However, the variances of averaged functionals of these fields are regularly varying. The limit theorems for weighted functionals of cyclic long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed.     

Local-in-time adjoint-based method for design optimization of unsteady flows

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.     

How Fear of Future Outcomes Affects Social Dynamics

Journal of Statistical Physics - Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a...     

(Hydroxyimino)Phosphonoacetic Acids: Synthesis,Stereochemistry and Reactivity

Abstract

Individual E/Z isomers of the C-methyl ester 1 of α-(hydroxyimino)phosphonoacetic acid (“troika acid”) were recently prepared as dicyclohexylammonium salts and found to be stable at neutral pH.¹ On alkaline demethylation followed by pH adjustment to 6–7, E?1 and Z?1 stereospecifically undergo P-C_αand C_α-C_β cleavage, respectively.¹ Herein we report synthesis of the corresponding P-methyl ester from trimethyl phos-phonoacetate 2. The product was isolated as its bis-DCHA⁺ salt E-3, with stereochemistry assigned by NMR.²     

Effects of Divalent Metal Ions on pH-Dependent Hydrolysis of p-Nitrophenyl (E)-(Hydroxyminio) Phosphonoacetate

Abstract

The (E-oxime of phosphonoglyoxylic acid, or (E-troika acid [(E)-l] undergoe: fragmentation leading to phosphorylation of the aqueous solvent at neutral pH and room temperature.[1] In contrast, the corresponding C-methyl ester (a-2 is stable under these mild conditions. Conversion of the unreactive (E)-2 to (E)-1 requires dewthylation a pH 13–14, generating the polyanion of (E-1, which becomes reactive on protonation.[1]     

A Novel and Simple Synthesis of 2-(Trifluoromethyl)-4H-thiochromen-4-ones

Abstract

Alkyl 2-mercaptophenyl ketones react with trifluoroacetic anhydride in the presence of triethylamine to give 2-(trifluoromethyl)-4H-thiochromen-4-ones, which are transformed into the corresponding pyrazoles by treatment with hydrazine hydrate and into 1,1-dioxides by oxidation with H₂O₂ in AcOH.