Rapid intramolecular interactions between organic isocyanates and hexafluorobut-2-yne on a dirhodium centre; X-ray crystal structure of (η-C5H5)2Rh2 {μ2(η3-C(CF3)C(CF3)C(O)N(Ph)}

Complexes of formula (η-C₅H₅₂Rh₂{CF₃C₂CF₃ · RNCO} have been prepared by three methods, from reactions between organic isocyanates and (η-C₅H₅)₂Rh₂(CO)(CF₃C₂CF₃) or (η-C₅H₅)₂Rh₂(CO)₂(CF₃C₂CF₃); by treatment of (η-C₅H₅)₂Rh₂(CO)(CF₃C₂CF₃) with organic azides; and by oxidation with Me₃NO of the organic isocyanide in (η-C₅H₅)₂Rh₂(CO)(CNR)(CF₃C₂CF₃). The crystal and molecular structure of the complex (η-C₅H₅)₂Rh₂{CF₃C₂CF₃ · RNCO} with R = Ph has been determined from single crystal X-ray diffraction data. This reveals that the isocyanate has condensed with the hexafluorobut-2-yne to form an amide ligand of the form C(CF₃)C(CF₃)C(=O)N(R); this bridges the two rhodium atoms in a μ₂η³-manner.     

Scheduling jobs on heterogeneous processors

We consider the problem of schedulingn jobs nonpreemptively onm processors to minimize various weighted cost functions of job completion times. The time it takes processorj to process a job is distributed exponentially with rate parameter _j , independent of the other processors. Associated with jobi is a weightw _i . There are no precedence constraints and any job may be processed on any processor. Assume that _{1 2}...µ _m andw ₁w ₂...w _n . Then for certain weighted cost functions, the optimal policy is such that the processors can be partitioned into setsS ₁, ...,S _n+1 such that if the fastest available processor is in setS _i ,i=1, ...,n, then jobi should be assigned to it, and if it isS _n+1, it will never be used. After each assignment the jobs are renumbered (so that jobi+1 becomes jobi if jobi is assigned to a processor). The partitioning is independent of the job weights and the states (busy or idle) of the processors. The optimal policy can be determined in at most max {m, n} steps. If all the weights are identical, the optimal policy reduces to a simple threshold rule such that a job should be assigned to the fastest available processor, sayj, if there are more thanK _j jobs waiting.K _j will depend on ₁, ..., _j but not on _j+1, ...,µ _m . The optimal policy is also individually optimal in the sense that it minimizes the cost for each jobi subject to the constraint that processors will first be offered to the jobs in the order 1, 2, ...,n.We explicitly characterize the optimal policy for several specific examples of cost functions, such as weighted flow time, weighted discounted flowtime, and weighted number of tardy jobs.     

Nanocrystalline iron oxide aerogels as mesoporous magnetic architectures

We have developed crystalline nanoarchitectures of iron oxide that exhibit superparamagnetic behavior while still retaining the desirable bicontinuous pore-solid networks and monolithic nature of an aerogel. Iron oxide aerogels are initially produced in an X-ray-amorphous, high-surface-area form, by adapting recently established sol-gel methods using Fe(III) salts and epoxide-based proton scavengers. Controlled temperature/atmosphere treatments convert the as-prepared iron oxide aerogels into nanocrystalline forms with the inverse spinel structure. As a function of the bathing gas, treatment temperature, and treatment history, these nanocrystalline forms can be reversibly tuned to predominantly exhibit either Fe(3)O(4) (magnetite) or gamma-Fe(2)O(3) (maghemite) phases, as verified by electron microscopy, X-ray and electron diffraction, microprobe Raman spectroscopy, and magnetic analysis. Peak deconvolution of the Raman-active Fe-O bands yields valuable information on the local structure and vacancy content of the various aerogel forms, and facilitates the differentiation of Fe(3)O(4) and gamma-Fe(2)O(3) components, which are difficult to assign using only diffraction methods. These nanocrystalline, magnetic forms retain the inherent characteristics of aerogels, including high surface area (>140 m(2) g(-1)), through-connected porosity concentrated in the mesopore size range (2-50 nm), and nanoscale particle sizes (7-18 nm). On the basis of this synthetic and processing protocol, we produce multifunctional nanostructured materials with effective control of the pore-solid architecture, the nanocrystalline phase, and subsequent magnetic properties.     

Determination of phosphorus in fertilizers by inductively coupled plasma atomic emission spectrometry

An inductively coupled plasma atomic emission spectrometry (ICP-AES) method was developed for the determination of phosphorus in fertilizers. Total phosphorus, direct extraction available phosphorus (EDTA), and water-soluble phosphorus, reported as phosphorus pentoxide (P205), in 15 Magruder check fertilizers were measured by ICP-AES, and the results were compared with those obtained by the AOAC official method. Five analytical wavelengths of phosphorus, 177.499, 178.287, 213.618, 214.914, and 253.565 nm, were tested for the determination of phosphorus in fertilizers, and their detection limits were obtained. Acid effects of perchloric acid and possible matrix effects of aluminum, calcium, magnesium, potassium, and sodium were negligible for phosphorus determination. Wavelength 213.618 nm was the best analytical wavelength for phosphorus determination by all 3 sample preparation methods for the selected Magruder fertilizers. The results demonstrated that the accuracy and precision of the ICP-AES method were comparable with those of the official methods.     

Staffing decisions for heterogeneous workers with turnover

In this paper we consider a firm that employs heterogeneous workers to meet demand for its product or service. Workers differ in their skills, speed, and/or quality, and they randomly leave, or turn over. Each period the firm must decide how many workers of each type to hire or fire in order to meet randomly changing demand forecasts at minimal expense. When the number of workers of each type can by continuously varied, the operational cost is jointly convex in the number of workers of each type, hiring and firing costs are linear, and a random fraction of workers of each type leave in each period, the optimal policy has a simple hire- up-to/fire-down-to structure. However, under the more realistic assumption that the number of workers of each type is discrete, the optimal policy is much more difficult to characterize, and depends on the particular notion of discrete convexity used for the cost function. We explore several different notions of discrete convexity and their impact on structural results for the optimal policy.     

Adaptation through minimization of the phase lag in coupled nonidentical systems

We show that the internal control of adaptation can be obtained from the properties of the phase lag that results from phase synchronization of two nonidentical chaotic oscillators. The direction and magnitude of the phase lag depend upon the relative internal properties of the coupled units, and they can be used as indicators during the adjustment of dynamics, i.e., adaptation of the target unit to match that of the control. The properties of the phase lag are obtained using a method based on the estimation of properties of the distributions of relative event times of both (target and control) units. The phase lag dependent mechanism to control the adaptation process was applied to a system of nonidentical R?ssler oscillators and a system of nonidentical Lorenz oscillators. We also elucidate its importance as a control mechanism of the changes of neuronal activity showing its application to neural adaptation.     

Structural Stability for Ill-Posed Problems in Banach Space

We prove Holder-continuous dependence results for the difference between solutions of certain ill-posed and approximate well-posed problems in both Hilbert and Banach spaces. We use operator-theoretic methods, including C-semigroups, to treat the abstract Cauchy problem $\frac{du}{dt} = Au, u(0) = \chi, 0 \leq t < T,$ where the operator $-A$ is the infinitesimal generator of a holomorphic semigroup.     

Unilateral recurrent laryngeal nerve paralysis:The importance of “preoperative” voice therapy

This preliminary retrospective study of 19 female patients and 22male patients with unilateral recurrent nerve lesions demonstrated the promise of objective measurements in predicting the need for surgery, the efficacy of voice therapy in ameliorating vocal symptoms, and the effects of therapy in conjunction with surgery. Sixty-eight percent (68%) of the female patients and 64% of the male patients did not elect to have surgery. Outcome satisfaction of nonsurgical and surgical patients appeared to be similar. The data from this study support the importance of preoperative therapy for patients with unilateral vocal fold paralysis.