Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

More elementary operators that are spectrally bounded

We discuss some necessary and some sufficient conditions for an elementary operator x↦∑ⁿ_i=1a_ixb_i on a Banach algebra A to be spectrally bounded. In the case of length three, we obtain a complete characterisation when A acts irreducibly on a Banach space of dimension greater than three.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

A quasi stationary approach to drying kinetics of cylindrical food particulates in a heat pump asisted fluid bed dryer

Experiments were undertaken to study drying kinetics of moist cylindrical shaped food particulates during fluidised bed drying. Cylindrical particles were prepared from Green beans with three different length:diameter ratios, 3:1, 2:1 and 1:1. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

Prediction of fluidization behaviour and a quasi-stationary approach to drying kinetics of irregular particulate food materials

Changes in fluidization behaviour behaviour was characterised for parallelepiped particles with three aspect ratios, 1:1, 2:1 and 3:1 and spherical particles. All drying experiments were conducted at 500C and 15 % RH using a heat pump dehumidifier system. Fluidization experiments were undertaken for the bed heights of 100, 80, 60 and 40 mm and at 10 moisture content levels. Due to irregularities in shape minimum fluidisation velocity of parallelepiped particulates (potato) could not fitted to any empirical model. Also a generalized equation was used to predict minimum fluidization velocity. The modified quasi-stationary method (MQSM) has been proposed to describe drying kinetics of parallelepiped particulates at 30o C, 40o C and 50o C that dry mostly in the falling rate period in a batch type fluid bed dryer.

A quasi-stationary approach to drying kinetics of different shaped food particulates in a heat pump assisted by fluid bed dryer

Experiments were undertaken to study drying kinetics of different shaped moist food particulates during heat pump assisted fluidised bed drying. Three particular geometrical shapes of parallelepiped, cylindrical and spheres were selected from potatoes (aspect ratio = 1:1, 2:1, 3:1), cut beans (length: diameter = 1:1, 2:1, 3:1) and peas respectively. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Due to complex hydrodynamics of the fluidised beds, drying kinetics are dryer or material specific. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

A quasi four dimensional radiation detector

Techniques for the accurate measurement of ionising radiation have been evolving since Roentgen first discovered x-rays in 1895; until now experimental measurements of radiation fields in the three spatial dimensions plus time have not been successfully demonstrated. In this work, we embed an organic plastic scintillator in a polymer gel dosimeter to obtain the first quasi-4D experimental measurement of a radiation field.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

A comprehensive literature review of the pelvis and the lower extremity digital human models under quasi-static conditions

Finite Element Modeling (FEM) has become a vital tool in the automotive design and development processes. FEM of the human body is a technique capable of estimating parameters that are difficult to measure in experimental studies with the human body segments being modeled as complex and dynamic entities. Several studies have been dedicated to attain close-to-real FEMs of the human body (Pankoke and Siefert 2007; Amann, Huschenbeth et al. 2009; ESI 2010). The aim of this paper is to identify and appraise the state of-the art models of the human body which incorporate detailed pelvis and/or lower extremity models. Six databases and search engines were used to obtain literature, and the search was limited to studies published in English since 2000. The initial search results identified 636 pelvis-related papers, 834 buttocks-related papers, 505 thigh-related papers, 927 femur-related papers, 2039 knee-related papers, 655 shank-related papers, 292 tibia-related papers, 110 fibula-related papers, 644 ankle related papers, and 5660 foot-related papers. A refined search returned 100 pelvis-related papers, 45 buttocks related papers, 65 thigh-related papers, 162 femur-related papers, 195 kneerelated papers, 37 shank-related papers, 80 tibia-related papers, 30 fibula-related papers and 102 ankle-related papers and 246 foot-related papers. The refined literature list was further restricted by appraisal against a modified LOW appraisal criteria. Studies with unclear methodologies, with a focus on populations with pathology or with sport related dynamic motion modeling were excluded. The final literature list included fifteen models and each was assessed against the percentile the model represents, the gender the model was based on, the human body segment/segments included in the model, the sample size used to develop the model, the source of geometric/anthropometric values used to develop the model, the posture the model represents and the finite element solver used for the model. The results of this literature review provide indication of bias in the available models towards 50th percentile male modeling with a notable concentration on the pelvis, femur and buttocks segments.