Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

DPSM technique for ultrasonic field modelling near fluid-solid interface

Distributed point source method (DPSM) is gradually gaining popularity in the field of non-destructive evaluation (NDE). DPSM is a semi-analytical technique that can be used to calculate the ultrasonic fields produced by transducers of finite dimension placed in homogeneous or non-homogeneous media. This technique has been already used to model ultrasonic fields in homogeneous and multi-layered fluid structures. In this paper the method is extended to model the ultrasonic fields generated in both fluid and solid media near a fluid-solid interface when the transducer is placed in the fluid half-space near the interface. Most results in this paper are generated by the newly developed DPSM technique that requires matrix inversion. This technique is identified as the matrix inversion based DPSM technique. Some of these results are compared with the results produced by the Rayleigh-Sommerfield integral based DPSM technique. Theory behind both matrix inversion based and Rayleigh-Sommerfield integral based DPSM techniques is presented in this paper. The matrix inversion based DPSM technique is found to be very efficient for computing the ultrasonic field in non-homogeneous materials. One objective of this study is to model ultrasonic fields in both solids and fluids generated by the leaky Rayleigh wave when finite size transducers are inclined at Rayleigh critical angles. This phenomenon has been correctly modelled by the technique. It should be mentioned here that techniques based on paraxial assumptions fail to model the critical reflection phenomenon. Other advantages of the DPSM technique compared to the currently available techniques for transducer radiation modelling are discussed in the paper under Introduction.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

Metastable states at low temperature in spin crossover compounds in the framework of the atom-phonon coupling model

In the current study we report on the unusual results obtained in the framework of the atom-phonon coupling model: two metastables states at low temperatures. These results can explain the experimental results reported by Ould Moussa et al. [9] and Matsumoto et al. [10]. This type of SCO behavior is due to the competition between the Light-Induced Excited Spin State Trapping (LIESST) effect, the elastic interaction between the molecules and the thermal activation. In order to determine the stability of the states founded at low temperature, the free energy F is presented for the case of the two step spin transition of a SCO compound.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

Software utilities for the interpretation of mass spectrometric data of glycoconjugates: application to glycosphingolipids of human serum

Glycosphingolipids (GSLs) are major components of the outer leaflet of the cell membrane. These lipids are involved in many cell surface events and show disease‐related expression changes. GSLs could thus serve as useful targets for biomarker discovery. The GSL structure is characterized by two entities: a hydrophilic glycan and a hydrophobic ceramide moiety. Both components exhibit numerous structural variations, the combination of which results in a large diversity of GSL structures that can potentially exist. Mass spectrometry (MS) is a powerful tool for high‐throughput analysis of GSL expression analysis and structural elucidation. Yet, the assignment of GSL structures using MS data is tedious and demands highly specialized expertise. SysBioWare, a software platform developed for MS data evaluation in glycomics, was here applied for the MS analysis of human serum GSLs. The program was tuned to provide automated compositional assignment, supporting a variety of glycan and ceramide structures. Upon in silico fragmentation, the masses of predicted ions arising from cleavages in the glycan as well as the ceramide moiety were calculated, thus enabling structural characterization of both entities. Validation of proposed structures was achieved by matching in silico calculated fragment ions with those of experimental MS/MS data. These results indicate that SysBioWare can facilitate data interpretation and, furthermore, help the user to deal with large sets of data by supporting management of MS and non‐MS data. SysBioWare has the potential to be a powerful tool for high‐throughput glycosphingolipidomics in clinical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Perturbation theory in a framework of iteration methods

In a previous paper [J. Phys. A 36 (2003) 11807], we introduced the ‘asymptotic iteration method’ for solving second-order homogeneous linear differential equations. In this Letter, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem.     

An Optimal Diversification Network Model with Fixed-Solution Universe Subsets

This paper develops a generalized dynamic network model for portfolio investment diversification. The model considers the situation of the fixed solution subset corresponding to a fixed single-resource economic investment such as that found in many oil-producing nations. Quadratic side constraints on the variance of the resultant flow distribution are added to the model to accommodate uncertainty. The model has been tested using a prototype example. The results indicate that the risk associated with a single-resource investment can be reduced by determining optimal investment weights.