A model for operators with cyclic adjoint

It is proved that every bounded linear operator on a complex Banach space whose adjoint has aw ^*-cyclic vector, is similar to the differentiation operator on a Banach space of entire functions of finite exponential type. The relation of this model to the existence of non-trivial invariant subspaces is discussed.     

Primal and dual optimality criteria in convex programming

Summary This paper considers the problem of minimizing a convex differentiable function subject to convex differentiable constraints. Necessary and sufficient conditions (not requiring any constraints qualification) for a point to be an optimal solution are given in terms of a parametric linear program. Dual characterization theorems are then derived, which generalizes the classical results ofKuhn-Tucker andJohn.

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Zusammenfassung Es wird das Problem betrachtet, eine konvexe differenzierbare Funktion unter konvexen differenzierbaren Nebenbedingungen zu minimieren. Unter Verwendung eines parametrischen linearen Optimierungsproblems werden notwendige und hinreichende Bedingungen für Optimalität eines Punktes angegeben, die keine constraints qualifications benötigen. Sodann werden duale Charakterisierungstheoreme hergeleitet, welche die klassischen Resultate vonKuhn-Tucker undJohn verallgemeinern.

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This research was partly supported by Project No. NR 047-021, ONR Contract N00014-75-C-0569 with the Center for Cybernetic Studies, The University of Texas. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Sonochemical synthesis of cerium oxide nanoparticles-effect of additives and quantum size effect

Cerium oxide (CeO(2)) nanoparticles were prepared sonochemically, by using cerium nitrate and azodicarbonamide as starting materials, and ethylenediamine or tetraalkylammonium hydroxide as additives. The additives have a strong effect on the particle size and particle size distribution. CeO(2) nanoparticles with small particle size and narrow particle size distribution are obtained with the addition of additives; while highly agglomerated CeO(2) nanoparticles are obtained in the absence of additives. Monodispersed CeO(2) nanoparticles with a mean particle size of ca. 3.3 nm are obtained when tetramethylammonium hydroxide (TMAOH) is used as the additive and the molar ratio of cerium nitrate/azodicarbonamine/TMAOH is 1/1/1. Blue shifts of the absorption peak and the absorption edges of the products are observed in the UV-Vis absorption spectra as a result of the quantum size effect. The samples have been characterized using powder XRD, TEM, DLS, and absorption spectra.     

Wannier states of molecular impurity in a liquid rare gas

We have measured the vacuum ultraviolet absorption spectra of CH₃I in solid and in liquid krypton in the spectral region 2000–1450 Å. In both phases we have observed two Wannier series n(²E_{$\text{3}\text{2}$}) and n(²E_{$\text{1}\text{2}$}) up to n = 3. Information has been obtained concerning the features of the conduction band in a liquid rare gas.     

FTIR and computational studies of pure and water containing SO3 species in solid argon matrices

The FT infrared spectrum in the 4000–400 cm⁻¹ range of SO₃ vapors, matrix isolated in argon and in water doped argon solid layers, is reported. Vibrational bands are assigned to pure SO₃ monomeric and polymeric species and to SO₃H₂O complexes, on the basis of theoretical B3LYP and MP2 calculations employing the aug-cc-pVTZ basis sets. The spectroscopic evidence suggests that in addition to the monomer, both the dimeric and the cyclic trimeric (SO₃)_n complexes are the only other SO₃ forms present in the matrix. The spectra also indicate the presence of the 1:1 and the 1:2 SO₃·H₂O complexes as well as traces of H₂S₂O₇ and water complexed H₂SO₄, but no evidence for a stable 2:1 SO₃H₂O complex was found. The occurrence of the various species is discussed in the light of their calculated energies.     

On the average performance of the adjustable RO and its use as an offline tool for multi-period production planning under uncertainty

Robust optimization (RO) is a distribution-free worst-case solution methodology designed for uncertain maximization problems via a max-min approach considering a bounded uncertainty set. It yields a feasible solution over this set with a guaranteed worst-case value. As opposed to a previous conception that RO is conservative based on optimal value analysis, we argue that in practice the uncertain parameters rarely take simultaneously the values of the worst-case scenario, and thus introduce a new performance measure based on simulated average values. To this end, we apply the adjustable RO (AARC) to a single new product multi-period production planning problem under an uncertain and bounded demand so as to maximize the total profit. The demand for the product is assumed to follow a typical life-cycle pattern, whose length is typically hard to anticipate. We suggest a novel approach to predict the production plan’s profitable cycle length, already at the outset of the planning horizon. The AARC is an offline method that is employed online and adjusted to past realizations of the demand by a linear decision rule (LDR). We compare it to an alternative offline method, aiming at maximum expected profit, applying the same LDR. Although the AARC maximizes the profit against a worst-case demand scenario, our empirical results show that the average performance of both methods is very similar. Further, AARC consistently guarantees a worst profit over the entire uncertainty set, and its model’s size is considerably smaller and thus exhibit superior performance.     

Pulsed Electron-Nuclear Double Resonance in the Fourier Regime

Nuclear magnetic resonance (NMR) spectroscopy provides atomic-level molecular structural information. However, in molecules containing unpaired electron spins, NMR signals are difficult to measure directly. In such cases, data is obtained using the electron-nuclear double resonance (ENDOR) method, where nuclei are detected through their interaction with nearby unpaired electron spins. Unfortunately, electron spins spread the ENDOR signals, which challenges current acquisition techniques, often resulting in low spectral resolution that provides limited structural details. Here, we show that by using miniature microwave resonators to detect a small number of electron spins, integrated with miniature NMR coils, one can excite and detect a wide bandwidth of ENDOR data in a single pulse. This facilitates the measurement of ENDOR spectra with narrow lines spread over a large frequency range at much better spectral resolution than conventional approaches, which helps reveal details of the paramagnetic molecules’ chemical structure that were not accessible before.     

Core-shell nanorods of SnS-C and SnSe-C: synthesis and characterization

The straightforward, efficient, solventless, RAPET (reactions under autogenic pressure at elevated temperature) approach was explored for the fabrication of core-shell nanomaterials. Carbon-encapsulated SnS and SnSe nanorods were synthesized by a one-step thermal decomposition of tetramethyltin in the presence of either S or Se powder in a closed reactor at 700 degrees C for 40 min, under their autogenic pressure in an inert atmosphere. The powder X-ray diffraction measurements provided structural evidence for the formation of pure orthorhombic phases of SnS or SnSe particles. The Raman spectroscopy measurements ensured that the nature of the coated carbon was semigraphitic. The scanning electron micrographs verified the 1D morphology of the formed SnS and SnSe chalcogenides, and their stoichiometry was confirmed by EDAX measurements. The HR-TEM micrographs distinguished between core and shell morphologies. The nitrogen gas adsorption on the surface of core-shell nanostructures was determined by BET surface area analysis. The plausible mechanism for the creation of chalcogenide cores (SnS or SnSe) with a carbon shell was elucidated.