Phase Space Bounds for Quantum Mechanics on a Compact Lie Group

Let K be a compact, connected Lie group and its complexification. I consider the Hilbert space of holomorphic functions introduced in [H1], where the parameter t is to be interpreted as Planck's constant. In light of [L-S], the complex group may be identified canonically with the cotangent bundle of K. Using this identification I associate to each a “phase space probability density”. The main result of this paper is Theorem 1, which provides an upper bound on this density which holds uniformly over all F and all points in phase space. Specifically, the phase space probability density is at most , where and a _t is a constant which tends to one exponentially fast as t tends to zero. At least for small t, this bound cannot be significantly improved. With t regarded as Planck's constant, the quantity is precisely what is expected on physical grounds. Theorem 1 should be interpreted as a form of the Heisenberg uncertainty principle for K, that is, a limit on the concentration of states in phase space. The theorem supports the interpretation of the Hilbert space as the phase space representation of quantum mechanics for a particle with configuration space K. The phase space bound is deduced from very sharp pointwise bounds on functions in (Theorem 2). The proofs rely on precise calculations involving the heat kernel on K and the heat kernel on . Received: 9 July 1996/Accepted: 9 September 1996     

Feasibility Study on Quantitative Measurements of Singlet Oxygen Generation Using Singlet Oxygen Sensor Green

The purpose of this study is to investigate the feasibility for quantitative measurement of singlet oxygen (¹O₂) generation by using a newly developed ¹O₂-specific fluorescence probe Singlet Oxygen Sensor Green reagent (SOSG). ¹O₂ generation from photoirradiation of a model photosensitizer Rose Bengal (RB), in initially air-statured phosphate buffered saline (PBS) was indirectly monitored with SOSG. In the presence of ¹O₂, SOSG can react with ¹O₂ to produce SOSG endoperoxides (SOSG-EP) that emit strong green fluorescence with the maximum at 531 nm. The green fluorescence of SOSG-EP is mainly dependent on the initial concentrations of RB and SOSG, and the photoirradiation time for ¹O₂ generation. Furthermore, kinetic analysis of the RB-sensitized photooxidation of SOSG is performed that, for the first time, allows quantitative measurement of ¹O₂ generation directly from the determination of reaction rate. In addition, the obtained ¹O₂ quantum yield of porphyrin-based photosensitizer hematoporphyrin monomethyl ether (HMME) in PBS by using SOSG is in good agreement with the value that independently determined by using direct measurement of ¹O₂ luminescence. The results of this study clearly demonstrate that the quantitative measurement of ¹O₂ generation using SOSG can be achieved by determining the reaction rate with an appropriate measurement protocol.     

An infinite-time relaxation theorem for differential inclusions

The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.

     

Peptide mimotopes of phomopsins: Identification, characterization and application in an immunoassay

Peptide mimotopes of plant-associated toxins offer the potential for improving analytical and diagnostic methodologies as well as providing candidates for potential protective vaccines against plant poisoning diseases. Monoclonal antibody (mAb) C₃C₁₁, which recognizes the antimicrotubule phomopsin mycotoxins, was used to isolate peptide mimics of phomopsin A from a random 15-mer phage display peptide library. A total of 46 clones were isolated that showed specific reactivity with the mAb. Amino acid sequence analysis revealed four different types of mimotope sequences, all of which contained a common motif V-A-L/V-C. Of the 46 clones isolated, 44 contained the motif V-A-L-C while 2 contained the V-A-V-C motif. All four types of phage clones inhibited the reactivity of the mAb with phomopsin A in a competition ELISA. The clone with the mimotope sequence CT VALCNMYFGAKLD demonstrated the strongest binding. It was further shown that synthetic peptides containing these mimotope amino acid sequences were able to inhibit the mAb-phomopsin A interaction, indicating that the peptide mimotopes were responsible for the specific binding, independent of the phage framework. The results also suggest that the mimotope peptides bind to mAb C₃C₁₁ at the same site as phomopsin A. The application of recombinant phage particles carrying phomopsin mimotopes in immunoassay was evaluated and the results demonstrated approximately 100-fold increase in sensitivity in comparison with a conventional immunoassay using a chemically linked phomopsin-horseradish peroxidase conjugate.     

Small-angle Coulomb collision model for particle-in-cell simulations

We construct and investigate a set of stochastic differential equations that incorporate the physics of velocity-dependent small-angle Coulomb collisions among the plasma particles in a particle-in-cell simulation. Each particle is scattered stochastically from all the other particles in a simulation cell modeled as one or more Maxwellians. Total energy and momentum are conserved by linear transformation of the velocity increments. In two test simulations the proposed “particle-moment” collision algorithm performs well with time steps as large as 10% of the relaxation time – far larger than a particle-pairing collision algorithm, in which pairs of particles are scattered from one another, requires to achieve the same accuracy.     

On the time-dependent moments of Markovian queues with reneging

We give an explicit representation for the time-dependent moments of a Markovian queueing system with reneging. Our expressions are comparable in form to the moment expressions for the M/M/1 queue found in Abate and Whitt (Queueing Syst. 2:41–65, 1987; Adv. Appl. Probab. 20:145–178, 1988). We also illustrate how to use these expressions to derive analogous moment expressions for a reflected Ornstein–Uhlenbeck process, with reflection at zero.     

The middleman as a panacea for supply chain coordination problems

The prevalence of intermediaries (middlemen) in supply chains is often seen as a dying remnant of less efficient times. Despite predictions that supply chains will rapidly “cut out the middleman” as technological advances have eased logistics, middlemen have continued to thrive. In this paper, we demonstrate a transaction role of middlemen that may help clarify their staying power. In a model with self-interested decision-making by both a manufacturer and a retailer, wherein incentive misalignment creates investment and production inefficiencies, we show that the integrated (first-best) outcome can be achieved with simple cost-based contracts if and only if a middleman is present. We further show that the approach of utilizing a middleman to fully coordinate the supply chain is robust in that it can be applied to a variety of circumstances discussed in the literature, including multilateral investment/effort choices, multiple product providers, and logistical investments made by the middleman.     

Direct cryopreservation of winter buds of nine cultivars of blackcurrant (Ribes nigrum L)

Direct cryopreservation of overwintering, dormant buds has been applied to nine blackcurrant cultivars, using a 7 day dehydration period at c.-20° C before plunging directly into liquid nitrogen. The buds on shoots thawed from -20° C showed normal development simply by standing them in water and all the cultivars could be successfully recovered (> 58%) by grafting. None of the shoots thawed from liquid nitrogen showed any development after standing in water and all of the grafts failed. Shoots thawed from liquid nitrogen showed significant damage to xylem transport, and the cortical tissues necessary fro successful grafting showed significant loss of membrane semipermeability. However, buds excised from shoots immediately after thawing from liquid nitrogen were viable and could be recovered using in vitro culture. Survival ranged from 88 to 55%, depending upon cultivar.     

Global stability in the 2D Ricker equation

We improve a previous result for the 2D Ricker equation by reducing an infinite number of topological conditions to a finite number. We also give sufficient conditions in terms of the parameters where many of these topological conditions are satisfied. We also discuss the various pathologies that occur for other parameter choices.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.