Reduced rank static error covariance for high‐dimensional applications

A method for creating static (e.g., stationary) error covariance of reduced rank for potential use in hybrid variational‐ensemble data assimilation is presented. The choice of reduced rank versus full rank static error covariance is made in order to allow the use of an improved Hessian preconditioning in high‐dimensional applications. In particular, this method relies on using block circulant matrices to create a high‐dimensional global covariance matrix from a low‐dimensional local sub‐matrix. Although any covariance used in variational data assimilation would be an acceptable choice for the pre‐defined full‐rank static error covariance, for convenience and simplicity, we use a symmetric Topelitz matrix as a prototype of static error covariance. The methodology creates a square root covariance, which has a practical advantage for Hessian preconditioning in reduced rank, ensemble‐based data assimilation. The experiments conducted examine multivariate covariance that includes the impact of cross‐variable correlations, in order to have a more realistic assessment of the value of the constructed static error covariance approximation. The results show that it may be possible to reduce the rank of matrix to O(10) and still obtain an acceptable approximation of the full‐rank static covariance matrix. Copyright © 2016 John Wiley & Sons, Ltd.     

The method of dynamic mode decomposition in shallow water and a swirling flow problem

In this paper, a new vector‐filtering criterion for dynamic modes selection is proposed that is able to extract dynamically relevant flow features from dynamic mode decomposition of time‐resolved experimental or numerical data. We employ a novel modes selection criterion in parallel with the classic selection based on modes amplitudes, in order to analyze which of these procedures better highlight the coherent structures of the flow dynamics. Numerical tests are performed on two distinct problems. The efficiency of the proposed criterion is proved in retaining the most influential modes and reducing the size of the dynamic mode decomposition model. By applying the proposed filtering mode technique, the flow reconstruction error is shown to be significantly reduced. Copyright © 2016 John Wiley & Sons, Ltd.     

Continuity of the null space basis and constrained optimization

Many constrained optimization algorithms use a basis for the null space of the matrix of constraint gradients. Recently, methods have been proposed that enable this null space basis to vary continuously as a function of the iterates in a neighborhood of the solution. This paper reports results from topology showing that, in general, there is no continuous function that generates the null space basis of all full rank rectangular matrices of a fixed size. Thus constrained optimization algorithms cannot assume an everywhere continuous null space basis. We also give some indication of where these discontinuities must occur. We then propose an alternative implementation of a class of constrained optimization algorithms that uses approximations to the reduced Hessian of the Lagrangian but is independent of the choice of null space basis. This approach obviates the need for a continuously varying null space basis.Research supported by NSF grant MCS 81-15475 and DCR-8403483Research supported by ARO contracts DAAG 29-81-K-0108 and DAAG 29-84-K-0140     

Theorems on unions ofU-sets

The properties of families of subsets of topological spaces that make it possible to separate out the common core of the proofs of theorems on unions of sets of uniqueness for series in various systems of functions are considered. As a consequence of the results obtained, it is proved, in particular, that the countable union of closed sets of uniqueness for the trigonometric series is a set of uniqueness for the Abel-Poisson summation method. Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 778–787, May, 2000.     

Diagnostic of Plasma Produced by a Spark Plug at Atmospheric Pressure: Reduced Electric Field and Vibrational Temperature

The electric discharge generated between the electrodes of a classic spark plug could not assure a fast and total combustion of the air – hydrocarbon mixture. To be able to improve the quality of the combustion process through the ignition system improvement it is necessary to have a complete diagnostic of the discharge produced by a spark plug, from physical and chemical point of view. This work presents a comparative study of the reduced electric field and the vibrational temperature for a classic spark produced in air at atmospheric pressure, as functions of pulses widths applied by the power supply. The reduced electric field was calculated by using the rotational temperature values established by a previous study, considering them as temperature plasma gas temperatures. The vibrational temperature was determined by using the N2second positive molecular emission spectra. The spark plug was supplied with trains of pulses containing one or two pulses having variable widths provided by a special power supply. The results obtained for the vibrational temperature of nitrogen molecules are close to these obtained for the rotational temperature calculated by using a spectroscopic diagnostic method based on the OH UV molecular band spectra (between 2000 and 3500 K). The electron temperature values, imposed by the reduced electric field (up to 2000 Td), are superior to 10000 K. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stable orders of stunted lens spaces mod

Let be the stunted lens space mod and its stable order. If , then was determined by H. Toda (1963). In this paper, we determine the number for .

     

Reduced products which are not saturated

Summary IfT is a complete theory of Boolean algebra, then we writeA ⊲_T B to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2 _F ^I of all subsets ofI reduced byF is a model ofT, the reduced powerA _F ^I isK ⁺-saturated wheneverB _F ^I isK ⁺-saturated. The relation ⊲_T generalizes the relation ◃ introduced by Keisler. As in the case of Keisler's ◃ it happens that ⊲_T’s are relations between complete theories, i.e. ifA≡B thenA ⊲_T B andB ⊲_T A. In this paper some examples of theories which are maximal (minimal) with respect to ⊲_T’s are provided and the relations ⊲_T are compared with each other. Presented by J. Mycielski     

Reduced systems in Markov chains and their applications in queueing theory

A reduced system is a smaller system derived in the process of analyzing a larger system. While solving for steady-state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability matrix. In this paper, we catagorize reduced systems as standard and nonstandard and explore the existence of reduced systems and their properties relative to the original system. We also discuss first passage probabilities and means for the standard reduced system relative to the original system. These properties are illustrated while determining the steady-state probabilities and first passage time characteristics of a queueing system.     

Determination of energy minima and saddle points using multireference configuration interaction methods in combination with reduced gradient following: the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene

The implementation of the reduced gradient following (RGF) method into the COLUMBUS quantum-chemical program system is reported using the newly developed analytic MR-CISD/AQCC gradient feature. By this combination a very useful tool has been developed for general searches of stationary points on ground- and excited-state energy surfaces. This procedure is applied to the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene. For H(2)CO we investigated three minima (formaldehyde, s-trans, and s-cis hydroxycarbene) and five saddle points. For the T(1) and T(2) states of acetylene the cis- and trans-minima and the planar and nonplanar saddle points were computed.     

Synthesis, Characterization, and Luminescence Spectroscopic Accessibility Studies of tris(2,2′-Bipyridine)Ruthenium(II)-Labeled Inorganic-Organic Hybrid Polymers

The modified tris(2,2-bipyridine)ruthenium(II) complex 2 was anchored via a sol-gel process to different polysiloxane matrices to give a series of novel inorganic–organic hybrid polymers. One of the bipyridine ligands of 2 was provided with a long-chain spacer carrying a triethoxysilyl function (T group) at the end, which enables almost free mobility of the transition metal center. The polymers were swollen in several organic solvents of different polarity to investigate the luminescence behavior in the presence of quencher molecules. The luminescence of 2 was quenched using anthracene and atmospheric oxygen in appropriate concentrations of 5 · 10^–4 to 5 · 10^–3 and 3 · 10^–3 M, respectively. The luminescence behavior of 2 was determined by steady-state and time-resolved luminescence experiments. Translational mobilities of molecular species dissolved in the liquid phase were investigated by the kinetics of luminescence quenching after laser excitation. Both the translational mobility of anthracene and atmospheric oxygen, specified with the rate constant k₂ and the percentage of accessible luminescent centers were determined. Translational mobilities and the accessibility for anthracene and atmospheric oxygen in hybrid materials are significantly higher than in conventional Q type polysiloxanes.