Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+ \Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition $[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of $\Theta$ simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

A Stochastic Latent Moment Model for Electricity Price Formation

The wide range of models needed to support the various short-term operations for electricity generation demonstrates the importance of accurate specifications for the uncertainty in market prices. This is becoming increasingly challenging, since electricity hourly price densities exhibit a variety of shapes, with their characteristic features changing substantially within the day and over time, and the influx of renewable power, wind and solar in particular, has amplified these effects. A general-purpose, analytically tractable representation of the stochastic price formation process would have considerable value for operations control and trading, but existing empirical approaches for the application of standard density functions are unsatisfactory. We develop a general four parameter stochastic model for hourly prices, in which the four moments of the density function are dynamically estimated as latent state variables and furthermore modelled as functions of several plausible exogenous drivers. This provides a transparent and credible model that is suffciently flexible to capture the shape-shifting effects, particularly with respect to the wind and solar output variations causing dynamic switches in the upside and downside risks. Extensive testing on German wholesale price data, benchmarked against quantile regression and other models in out-of-sample backtesting, validated the approach and its analytical appeal

Phytase-producing Bacillus sp. inoculation increases phosphorus availability in cattle manure

Organic wastes rich in phosphorus (P) are considered an alternative to decrease the dependence on chemical P fertilization in crops and pastures. Microbial inoculants are being studied as a tool to increase plant P availability in organic wastes. In this study, we explore the effect of inoculation with Bacillus sp. MQH-19 (a native phytase-producing bacterium) on the release of inorganic phosphorus (Pi) in cattle manure with low available P but a high total P content. Bacteria inoculation resulted in a higher release of Pi (8% in NaHCÜ3 and 13% in NaOH-EDTA extracts) compared with that of uninoculated manure (0.7% in NaHCÜ3 and 0.1% in NaOH-EDTA extracts). However, a greater amount of Pi was released in inoculated manure supplemented with phytate (47% in NaHCÜ3 and 117% in NaOH-EDTA extracts) compared with that of uninoculated manure supplemented with phytate (30% in NaHCÜ3 and 15% in NaOH-EDTA extracts). In addition, the use of denaturing gradient gel electrophoresis (DGGE) and quantitative PCR (qPCR) revealed that the bacterial community structure in manure was affected by inoculation and that the prevalence of Bacillus sp. MQH-19 decreased during incubation (6 days). This study demonstrates that Pi availability in cattle manure can be increased by phytase-producing bacteria inoculation. Phytase-producing bacteria inoculation might represent an attractive strategy to increase P availability in agricultural wastes, which are used as organic fertilizers in crops and pastures

A trading-based evaluation of density forecasts in a real-time electricity market

This paper applies a multi-factor, stochastic latent moment model to predicting the imbalance volumes in the Austrian zone of the German/Austrian electricity market. This provides a density forecast whose shape is determined by the flexible skew-t distribution, the first three moments of which are estimated as linear functions of lagged imbalance and forecast errors for load, wind and solar production. The evaluation of this density predictor is compared to an expected value obtained from OLS regression model, using the same regressors, through an out-of-sample backtest of a flexible generator seeking to optimize its imbalance positions on the intraday market. This research contributes to forecasting methodology and imbalance prediction, and most significantly it provides a case study in the evaluation of density forecasts through decision-making performance. The main finding is that the use of the density forecasts substantially increased trading profitability and reduced risk compared to the more conventional use of mean value regressions

Indigo degradation with purified laccases from Trametes hirsuta and Sclerotium rolfsii

The degradation of the textile dye indigo with purified laccases from the fungi Trametes hirsuta (THL1 and THL2) and Sclerotium rolfsii (SRL1) was studied. All laccases were able to oxidize indigo yielding isatin (indole-2,3-dione), which was further decomposed to anthranilic acid (2-aminobenzoic acid). Based on the oxygen consumption rate of the laccases during indigo degradation, a potential mechanism for the oxidation of indigo involving the step-wise abstraction of four electrons from indigo by the enzyme was suggested. Comparing the effect of the known redox-mediators acetosyringone, 1-hydroxybenzotriazole (HOBT) and 4-hydroxybenzenesulfonic acid (PHBS) on laccase-catalyzed degradation of indigo, we found a maximum of about 30% increase in the oxidation rate of indigo with SRL1 and acetosyringone. The particle size of indigo agglomerates after laccase treatment was influenced by the origin of the laccase preparation and by the incubation time. Diameter distributions were found to have one maximum and compared to the indigo particle size distribution of the control, for all laccases, the indigo agglomerates seemed to have shifted to smaller diameters. Bleaching of fabrics by the laccases (based on K/S values) correlated with the release of indigo degradation products. (C) 2001 Elsevier Science BY. All rights reserved

An acid-stable laccase from sclerotium rolfsii with potential for wool dye decolourization

The plant pathogen basidiomycete S. rolfsii secretes two laccases (SRL1 and SRL2) with molecular weights of 55 and 86 kDa, respectively. Laccase production was shown to be inducible by the addition of 2,5-xylidine to the cultural media. After treatment with a combination of chitinase and -1,3-glucanase, two different laccases were isolated from the sclerotia depending on the stage of sclerotia development. The more prominent laccase, SRL1, was purified and found to decolourize the industrially important wool azo dye Diamond Black PV 200 without the addition of redox mediators. The enzyme (pI 5.2) was active in the acidic pH range, showing an optimal activity at pH 2.4, with ABTS as substrate. The optimum temperature for activity was determined to be 62 ◦C. Enzyme stability studies revealed that SRL1 was notably stable at 18 ◦C and pH 4.5, retaining almost full activity after a week. Oxidation of tyrosine was not detectable under the reaction conditions but the enzyme did oxidize a variety of the usual laccase substrates. SRL1 was strongly inhibited by sodium azide and fluoride. Dye solutions decolourized with the immobilized laccase were successfully used for redyeing.(undefined

ANCA-associated vasculitis in childhood: Recent advances

Abstract Anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitides are rare systemic diseases that usually occur in adulthood. They comprise granulomatosis with polyangiitis (GPA, Wegener’s), microscopic polyangiitis (MPA) and eosinophilic granulomatosis with polyangiitis (EGPA, Churg-Strauss syndrome). Their clinical presentation is often heterogeneous, with frequent involvement of the respiratory tract, the kidney, the skin and the joints. ANCA-associated vasculitis is rare in childhood but North-American and European cohort studies performed during the last decade have clarified their phenotype, patterns of renal involvement and their prognostic implications, and outcome. Herein, we review the main clinical and therapeutic aspects of childhood-onset ANCA-associated vasculitis, and provide preliminary data on demographic characteristics and organ manifestations of an Italian multicentre cohort

Slowly progressive anti-neutrophil cytoplasmic antibody-associated renal vasculitis: clinico-pathological characterization and outcome.

BACKGROUND: Although rapidly progressive glomerulonephritis is the main renal phenotype of anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitis (AAV), slow renal disease progression is sometimes observed. These forms have been rarely discussed; we analysed their prevalence, clinico-pathological characteristics and outcome. METHODS: We screened patients with microscopic  polyangiitis (MPA) and granulomatosis with polyangiitis followed at seven referral centres and selected those with estimated glomerular filtration rate (eGFR) reduction 25% as compared with diagnosis, while 4/34 (12%) had started RRT. CONCLUSIONS: AAV may present with slow renal disease progression; this subset is hallmarked by advanced age at diagnosis, positive MPO-ANCA, subclinical interstitial lung lesions and chronic damage at kidney biopsy. Partial renal recovery may occur following immunosuppression