Noncomputability,unpredictability, undecidability,and unsolvability in economic and finance theories

We outline, briefly, the role that issues of the nexus between noncomputability and unpredictability, on the one hand, and between undecidability and unsolvability, on the other hand, have played in Computable Economics (CE). The mathematical underpinnings of CE are provided by (classical) recursion theory, varieties of computable and constructive analysis and aspects of combinatorial optimization. The inspiration for this outline was provided by Professor Graça's thought‐provoking recent article. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Spin-resolved NEXAFS from resonant X-ray scattering (RXS): Application to MnO

Resonantly excited metal K core line spectra of NiO, MnO, CuO and other compounds have been investigated at the beamlines X21 (NSLS/BNL), BW1 and W1.1 (HASYLAB/DESY). A novel technique for quantitative resolution of NEXAFS spectra into spin-up and spin-down components has been developed. Since the method employs spin conservation and local spin references, it needs no circularly polarized radiation and no sample magnetization for taking both the RXS and NEXAFS spectra. Hence antiferromagnetic and paramagnetic materials can be investigated as well.By utilizing linear dichroism with angular-dependent measurements on single-crystal samples, additional resolution of NEXAFS spectra is possible with respect to the orbital symmetry. Application of the method to paramagnetic MnO, for the first time, provides new and unambiguous experimental results confirming modern (LSDA+U) calculations. Received: 29 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

NSLS Marks Silver Anniversary

November 22, 2007, marked the 25^th anniversary of the National Synchrotron Light Source's (NSLS) dedication. During the last quarter-century, Brookhaven National Laboratory's NSLS has made significant contributions to the field of synchrotron radiation, ranging from the Chasman-Green Lattice, novel insertion devices, and free electron laser research, to the development of numerous synchrotron experimental techniques and instrumentation.     

Two-photon excited photoluminescence of photonic quantum ring laser structures

We report on the two-photon excited photoluminescence of photonic quantum ring laser structures using Ti:Sapphire femtosecond pulsed laser. Using two-photon excited photoluminescence microscopy, we were able to image the laser structures when optically excited and compare the results with previously obtained images on electrically pumped photonic quantum ring lasers. We also propose a method to evaluate the Rayleigh band on the circumference of these structures.     

Modified Lagrangian vortex method with improved boundary conditions for water waves past a thin bottom‐standing barrier

Herein, the modified Lagrangian vortex method (LVM), a hybrid analytical‐numerical algorithm per se, is devised to simulate the process of vortex formation and shedding from the sharp edge of a zero‐thickness vertical plate under linear water‐wave attack. Application of the Helmholtz decomposition facilitates a convenient switch between the inviscid‐ and viscous‐flow models, thereby enabling easy incorporation of vorticity effects into the potential‐flow calculations for the viscous‐dominated region. In evaluating the potential‐flow component, making good use of the quickly convergent technique with singular basis functions, correctly capturing the singular behavior in velocity fields near the tip of the plate, leads to a considerable reduction of computational burdens and to 12‐decimal‐place accuracy. The viscous correction is carried out via the meshless LVM with improved boundary conditions. Comparisons with previously published results show good agreement. Simulations of vortex generation and evolution illuminate the ability of the present method, and provide a supplement to pertinent experimental works. The hybrid scheme proposed herein allows flexibility for the former LVM and convenience in the code development. Such a compromise fits particularly well for the high‐resolution modeling of sharp‐edged vortex shedding without heavy numerical developments. Copyright © 2014 John Wiley & Sons, Ltd.     

A Uniform Approach to the Analysis of Trie Structures That Store Prefixing-Keys

Triesare data structures for storing sets where each element is represented by a key that can be viewed as a string of characters over a finite alphabet. These structures have been extensively studied and analyzed under several probability models. All of these models, however, preclude the occurrence of sets in which the key of one element is a prefix of that of another—such a key is called aprefixing-key. This paper presents an average case analysis of several trie varieties, which we generically calledprefixing-tries, for representing sets with “unrestricted” keys, that is, sets in which the key of one element may be a prefix of that of another. The underlying probability model, which we call theprefix model, _{h, n, m}assumes as equally likely alln-element sets whose keys are composed of at mosthcharacters from a fixed alphabet of sizem. For each of the trie varieties analyzed, we derive exact formulas for the expected space required to store such a set, and the average time required to retrieve an element given its key, as functions ofh,n, andm. Our approach to the analysis is of interest in its own right. It provides a unifying framework for computing the expectations of a wide class of random variables with respect to the prefix model. This class includes the cost functions of the trie varieties analyzed here.     

Lesions involving the fourth ventricle evaluated by CT and MR: A comparative study

A retrospective review of 21 patients with lesions involving the fourth ventricle was performed to determine the relative capability of computed tomography (CT) and MR for detection, characterization, localization, and diagnosis. Lesions involving the fourth ventricle included ependymoma (three), subependymoma (one), glioma (five), cysticercosis cyst (three), medulloblastoma (three), bleeding into the fourth ventricle (two), epidermoid cyst (two), “trapped” fourth ventricle (one), and lymphomatoid granuloma (one). Posterior fossa lesions that displaced but did not invade the fourth ventricle were excluded. Lesion detectability on CT was judged excellent in ten, good in 8, and fair or poor in 3. Detectability of lesions by MR was judged excellent in 16 and good in 5. There was complete agreement on lesion extension between CT and MR in 6 lesions, mild disagreement in 4, and moderate to significant disagreement in 11. Preoperatively, MR alone correctly diagnosed seven lesions, and CT alone correctly diagnosed three lesions. A review of the combined scans (after the correct diagnosis was given) showed both CT and MR were equal in the diagnosis of 14 lesions, MR better than CT in six, and CT better in one. There was complete agreement on both CT and MR with the surgical/pathologic findings in three lesions. Both studies proved disappointing in their ability to make the correct histologic diagnosis, probably because CT and MR characteristics may not always offer a definitive diagnosis and because of the wide spectrum of pathologic processes that may involve the fourth ventricle.     

The MT-MSXα(R) method: Applications to Li2, F2, and N2 molecules

The multiple scattering Xα(R) method with the scaling parameter α expressed as a function of the internuclear distance is applied to the Li₂, N₂, and F₂ molecules. Compared with the results obtained by the Xα method, the calculated Xα(R) equilibrium distances are smaller, the total energies are lower, and the dissociation energies are larger.     

Electrochemical Study on Decomposition of Hydrogen Peroxide with Fe(II)

Decomposition of H₂O₂ with Fe²⁺ was studied with SnO₂ electrodes. By chronoamperometric and voltammetric techniques, the diffusion coefficients of Fe^3* and H ₂O₂ were estimated to be 5 × 10-₆ and 2 × 10^?5 cm²/s, respectively; the rate of decomposition of H₂O₂ with Fe²⁺ was proportional to [H₂O₂]^1/2·[Fe²⁺]² at a smaller concentration of Fe²⁺, but to [H₂O₂]^1/2·[Fe²⁺] when [Fe²⁺] was increased, indicating the formation of ferryl ion and the electron exchange between it and Fe²⁺ playing important roles. This catalytic decomposition. was dependent on pH; the maximum rate was observed to occur about pH = 1.5.