Exponential Decay

Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\hat q

Patterns of fungal colonization, mass loss and biochemical changes during the decomposition of predried and fresh (naturally fallen) leaves of Rhizophora mucronata were studied in a southwest mangrove of India. Dried and fresh leaves in litter bags were introduced at the mid-tide zone and retrieved after 1, 2, 4, 8, 10, 12 and 14 weeks. On incubation in the laboratory, a total of 5 ascomycetes and 18 anamorphic fungi were recorded. The majority of anamorphic taxa were natural inhabitants of the phyllosphere of senescent leaves. Following two weeks of exposure, they were largely replaced by marine fungi (ascomycetes and anamorphic fungi). More taxa were recovered from dried than from fresh leaves, and predrying accelerated the initial rate of mass loss. Ergosterol levels were much lower than those reported from vascular plant detritus exposed in other aquatic habitats. Both ergosterol and nitrogen levels peaked after between 4 weeks and 8 weeks of exposure; ergosterol levels subsequently declined, while nitrogen remained stable in predried leaves and fell in fresh leaves. The dynamics of remaining mass for the first 8 weeks of exposure were best described by a double-exponential decay model. The decay rate then appeared to accelerate, and the second phase was best described by a single exponential decay model. The apparent breakpoint coincided with an increase in the salinity of the mangrove swamp.

We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.

Quantum mechanics has revolutionized the way we view the physical world. This theory has required a dramatic revision in the structure of the laws of mechanics governing the behavior of the particles and lead to the discovery of macroscopic quantum e¤ects ranging from lasers and superconductivity to neutron stars and radiation from black holes. Though its validity is well con…rmed by the experimental evidence available, quantum mechanics remains somewhat of a mystery. The purpose of this study is to identify students’conceptual and mathematical di¢ culties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these di¢ culties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. ...

A nonlinear statistical method for the inversion of ocean color spectra is used to determine three inherent optical properties (IOPs), the absorption coefficients for phytoplankton and dissolved and detrital materials, and the backscattering coefficient due to particulates. The inherent optical property inversion model assumes that (1) the relationship between remotesensing reflectance and backscattering and absorption is well known, (2) the optical coefficients for pure water are known, and (3) the spectral shapes of the specific absorption coefficients for phytoplankton and dissolved and detrital materials and the specific backscattering coefficient for particulates are known. This leaves the magnitudes for the three unknown coefficients to be determined. A sensitivity analysis is conducted to determine the best IOP model configuration for the Sargasso Sea using existing bio-optical models. The optical and biogeochemical measurements used were collected as part of the Bermuda Bio-Optics Project and the U.S. Joint Global Ocean Flux Study Bermuda Atlantic Time Series (BATS). The results demonstrate that the lOP ......... ' mouc• is most sensitive to-' ....... useu to mourn changes in me exponential decay constant .............. absorption by dissolved and detrital materials. The retrieved chlorophyll a estimates show excellent correspondence to chlorophyll a determinations (r 2 = 81%), similar to estimates from standard band ratio pigment algorithms, while providing two additional retrievals simultaneously. The temporal signal of retrieved estimates of absorption by colored dissolved and detrital materials is mirrored in ratios of Kd(410) to Kd(488), a qualitative indicator for nonalgal light attenuation coefficients. The backscatter coefficient for particles is nearly constant in time and shows no correspondence with the temporal signal observed for chlorophyll a concentrations. Last, the IOP model is evaluated using only those wavelengths which closely match the Sea Viewing Wide Field of View Sensor wave bands. This results in only a 1 to 6% decrease in hindcast skill with the BATS biogeochemical data set. This is encouraging for the long-range goal of applying the IOP model to data from upcoming ocean color satellite missions. the inversion of ocean color spectra to produce three relevant inherent optical properties (IOPs) for the analysis of biogeochemical variability: the absorption coefficient by phytoplankton, the absorption coefficient by dissolved and detrital materials, and the backscattering coefficient due to Copyright 1997 by the American Geophysical Union. Paper number 96JC03243. 0148-0227/97/96JC-03243509.00 particulates. Methods to invert ocean color observations, such as those employed here, have been extensively explored by Morel and Prieur [1977], Sugihara et al. [1985], Sathyendranath et al. [1989], Gordon et al. [1988], and Roeslet and Perry [1995]. The color of the sea will be related to those photons which are backscattered from within the water column and are not absorbed before entering the atmosphere. Hence changes in the total absorption coefficient, a(;L) (notation list is provided), and the backscattering coefficient, b b (;L), regulate the variations in ocean color spectra or remotely sensed reflectance [Rrs(•.)], where Rrs(•.) is defined as the ratio of upwelled radiance to downwelled irradiance (=Lu(•.)/Ed(•.)). Values of a(;L) an be effectively partitioned into absorption due to water, phytoplankton, and nonalgal materials [e.g.,

Triplet state sublevel spectroscopy using optical detection of magnetic resonance (ODMR) in zero magnetic field can be successfully employed to study (i) the environment of tryptophan (Trp) residues in a protein by observing the position and structure of phosphorescence spectra, zero field ODMR transitions and triplet state sublevel kinetics, (ii) the energy transfer among Trp residues, and (iii) whether any

A model of type III solar radio bursts is developed that incorporates large-angle scattering and reabsorption of fundamental emission amid ambient density fluctuations in the corona and solar wind. Comparison with observations shows that this model accounts semiquantitatively for anomalous harmonic ratios, the exponential decay constant of bursts, burst rise times, and the directivity of fundamental emission. It is concluded that the long emission tail on interplanetary type III bursts is mostly fundamental emission, while much of the anomalous time delay of fundamental relative to harmonic emission from a given location must be ascribed to other causes.

A tagging study was undertaken on Blood Reef off Durban, South Africa, to investigate movement patterns of Panulirus homarus rubellus as well as inshore/offshore population differences. Lobsters were collected by SCUBA divers and baited traps. Traps caught larger lobsters than divers and trap catches were somewhat male-dominated (40% female:60% male). Lobsters were predominately resident with only 3% of recaptured lobsters moving over 500 m. Long shore movements were probably related to foraging behaviour and sanding and scouring of reefs. Larger lobsters were caught on offshore reefs (!10 m depth) than on inshore reefs (B10 m depth). The absence of large lobsters (!100 mm carapace length, CL) on inshore reefs may be related to fishing mortality. Low juvenile numbers (B50 mm CL) on offshore reefs suggest that post-larval lobsters settle on inshore reefs. An exponential decay model indicated that a small percentage of the population (males: 1.3%; females: 2.5%) move offshore with females mainly moving at 3 years of age and males between 1 and 3 years of age.

We propose a physical model of gamma-ray burst spectral evolution in which impulsively accelerated nonthermal leptons cool by saturated Compton upscattering of soft photons. This model naturally explains the recently discovered exponential decay of the spectral break energy with photon fluence, the hard-to-soft spectral evolution patterns, and other spectral and temporal properties of gamma-ray bursts. Subject headings: gamma rays: bursts L36 LIANG ET AL. Vol. 479

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Intertidal flats are frequently colonised by microphytobenthos (MPB) assemblages that form transient biofilms at the sediment surface which are responsible for large fractions of estuarine primary production. The large spatio-temporal variability in MPB biomass distribution in concert with the fact that tidal flats can cover many km 2 makes the use of remote sensing particularly useful in assessing MPB distribution. Water content, sediment type and MPB vertical migration are variables that affect the relationship between ground truth measurements and remote sensing of benthic chlorophyll. The effect of chlorophyll depth distribution (top 2 mm) on the relationship between benthic chlorophyll and several remote sensing indices (NDVI, PI, R562/R647, derivative indices and PAM fluorescence) was investigated over a 2 year sampling period at 6 sites (Tagus estuary, Portugal). Additionally, the effect of the dark adaptation time required to measure the minimum fluorescence parameter (F 0) was also tested. Sediment type strongly affected MPB depth distribution with muddy sites showing a strong negative exponential decay in chlorophyll with distance from the surface while sandy sites had a homogenous distribution over the same scale (2 mm). Chlorophyll content (mass per unit mass, Ag g À 1) in the top 2 mm was better correlated with remote sensing indices than concentration (mass per unit volume, mg m À 3), both for NDVI (0.72 vs. 0.45) and for PAM fluorescence (0.70 vs. 0.55). Separating the data by transect increased the correlation values in all situations. A fitted model of chlorophyll depth distribution showed that the effect of asymmetrical chlorophyll depth distribution was stronger on the correlations between chlorophyll concentration and NDVI than on chlorophyll content and NDVI (0.46-2 mm vs. 0.74-125 Am, muddy site) the same was valid for fluorescence (0.66-2 mm vs. 0.92-125 Am, muddy site). Dark adapting the samples for more than 5 min did not result in any significant difference in the relationship between F 0 and chlorophyll a. The residuals from the regression of chlorophyll content on NDVI were positively correlated (0.7) with the mass per unit of mass of sediment b 63 Am and negatively (À0.6) with chlorophyll concentration, this indicates that if no correction is performed to account for chlorophyll depth distribution both units will be strongly affected by the mass of b 63 Am particles. The results demonstrate that although expressing chlorophyll a as concentration is generally a better option for ground truth measurements care should be taken to account for chlorophyll depth distribution since strong asymmetries within the sampling depth can introduce large errors.

Comparison of Analytic and HEFF Analysis of Displacements and Stresses Through a Heated Thick Cylinder. . 63 ii Comparison of Analytic and HEFF Analysis of Displacements and Stresses in a Semi-Infinite Region With Heated Thick , 64 Layer ....... 12 Geometrical Data for Analysis of a Vertical , ,. 65 Emplacement Drift ]3 Thermal and Thermal-Mechanical Data for Analysis 66 of a Vertical Emplacement Drift 14 Comparison of Results of Bounda1:y-Element and Finite-Element Analyses of a Vertical Emp].acement Drift. , 67

In this paper, we present new experimental results which speak of the topic of temporal properties of processes underlying the selection of spatial location. We used the double motion induction paradigm to assess the strength of the selective effects. Prior exposure of an area to flicker, decreased the effectiveness of a cueing spot presented later at that location. This effect lasted for at least 1.5 s. In further experiments, it was found that both static and flickering cues, with time, lose their effectiveness to facilitate processing. While the static cueing decays quickly to very low effectiveness, flicker cueing decays to a level of effectiveness which can be maintained for a long time. Thus with time two flickering cues presented with a temporal offset become equivalent to each other, but remain more effective than a static cue. We conclude that mechanisms coding temporal change determine cue effectiveness for capturing attention. Simple exponential decay functions with different temporal constants and different lower asymptotes can describe these effects.

Abstract: The luminosity and the spectral distribution of the afterglow of GRB 031203 have been presented within our theoretical framework, which envisages the GRB structure as composed by a proper-GRB, emitted at the transparency of an electron-positron plasma with suitable baryon loading, and an afterglow comprising the" prompt emission" as due to external shocks. In addition to the GRB emission, there appears to be a prolonged soft X-Ray emission lasting for 10^ 6-10^ 7 seconds followed by an exponential decay. This ...

Dispersal of the southwestern corn borer, Diatraea grandiosella Dyar, was examined by release and recapture of dye-marked adults and by capture of feral adults in and around 50-ha center pivot irrigated Þelds of Bacillus thuringiensis (Bt) maize. Pheromone and blacklight traps were used to capture the adults.

DOSY NMR can be used as a non-invasive separation method for complex mixtures. It is more and more attractive for industrial laboratories, for the main advantage DOSY NMR over routine separation methods such as LC-NMR is easy and economical implementation. With NMR instruments, DOSY NMR data can be obtained routinely but data analysis is still the main challenge to put DOSY NMR in real-world applications. A DOSY data set is obtained by measuring a series of spin echo spectra with different gradient strengths. The signals of each component attenuate with a different exponential decay rate (depending on the diffusion coefficient) as the gradient strength increases. Consequently, each channel (frequency) of the spectra is a sum of the exponential signals of the components. Traditionally, the diffusion coefficients of the components in each channel can be calculated by single channel methods, which are based on exponential fitting. In fact, the routine methods that have been implemented...

This paper reports on the influencing factors and their effects on the intensity of flash evaporation that occurs in the superheated water jets. A variety of experiments were conducted and four variables were investigated namely velocity of flow, initial temperature, superheat degree and injection nozzle diameter. An exponentially decaying curve model that predicts temperature variation at the centerline of the upward flowing jet was proposed and employed in the demonstration of the nature of influence of each experimented variable. Evaporation end height was estimated and correlated by an empirical equation; this equation is thought to be useful in designing the flash evaporation chamber.

In this paper we investigate the asymptotic behavior of the semigroup associated to the solutions of the initial boundary value problem for a one-dimensional nonsimple thermoelastic solids. We show that the semigroup is exponentially stable but is not analytic. Moreover we show the impossibility of time localization of the solutions.

Solanum sisymbriifolium is a trap crop for potato cyst nematodes (PCN). In this study, we quantified the effect of different periods of growth of S. sisymbriifolium and root length density on hatching of Globodera pallida, using potato and fallow treatments as references. One-year-old and 2-year-old G. pallida cysts were used in greenhouse experiments carried out in containers over 2 years. Two methods were used in study hatching. In the first method, 7.5-cm-diameter soil cores were removed and backfilled with infested soil. In the second method, cysts were buried in nylon bags. The soil cores infested with cysts used in the first method had very poor root colonisation as compared to surrounding bulk soil. Therefore, the effect of S. sisymbriifolium was strongly underestimated by the soil core method. Hatching of PCN juveniles from cysts, measured with the nylon bag method, increased with the duration of growth of S. sisymbriifolium from 47% after 6 weeks of crop growth up to 75% after 21 weeks of crop growth. Reductions per depth layer were also correlated with root length density and varied between 42.6% at 0.26 cm cm 23 and 85.3% at 5.8 cm cm 23. Based on a single exponential decay function, a general method is presented to estimate for any PCN management measure the average reduction in the number of years needed to ensure that the PCN population falls below a given density. Calculated reductions in the number of years ranged from 2.3 years for 59% hatching (equivalent to 90 days of S. sisymbriifolium) to 4.4 years for 75% of hatching (equivalent to 150 days of S. sisymbriifolium). These reductions were independent of initial and final population density. Our results corroborate the hatchinducing effect of S. sisymbriifolium, underline the importance of growth duration and root length density as determinants of the reduction in PCN population that can be achieved and draw attention to the pitfall in methodology that can arise in the study of hatch stimulation.

The phosphoinositide signal transduction system, and particularly, phospholipase C␤ isozymes, are relevant in the etiopathogeny of human neuropsychiatric pathologies such as depression. Stimulation of phospholipase C␤ activity by muscarinic receptors and G proteins was determined in crude and synaptosomal membrane preparations from nine postmortem human frontal cortices (postmortem delay range 8 to 50 h). Thus, the phospholipase C␤ activity was determined by measuring the hydrolysis of exogenous [ 3 H]-phosphatidylinositol 4,5-bisphosphate. There was a postmortem delay-mediated decrease in the PIP 2 hydrolysis irrespective of the membrane preparation used (P Ͻ 0.05). Moreover, there were statistically significant differences for exponential decay curve parameters (K factor and Span) of PLC␤ activity induced by agonist-mediated activation between crude and synaptosomal membrane preparations. These results show that the postsynaptic component of the PLC␤ activity is more sensible to the postmortem delay effect.

Curcumin, the main yellow bioactive component of turmeric, has recently acquired attention by chemists due its wide range of potential biological applications as an antioxidant, an anti-inflammatory, and an anti-carcinogenic agent. This molecule fluoresces weakly and poorly soluble in water. In this detailed study of curcumin in thirteen different solvents, both the absorption and fluorescence spectra of curcumin was found to be broad, however, a narrower and simple synchronous fluorescence spectrum of curcumin was obtained at = 10-20 nm. Lippert-Mataga plot of curcumin in different solvents illustrated two sets of linearity which is consistent with the plot of Stokes' shift vs. the E T 30. When Stokes's shift in wavenumber scale was replaced by synchronous fluorescence maximum in nanometer scale, the solvent polarity dependency measured by max SFS vs. Lippert-Mataga plot or E T 30 values offered similar trends as measured via Stokes' shift for protic and aprotic solvents for curcumin. Better linear correlation of max SFS vs. * scale of solvent polarity was found compared to max abs or max em or Stokes' shift measurements. In Stokes' shift measurement both absorption/excitation as well as emission (fluorescence) spectra are required to compute the Stokes' shift in wavenumber scale, but measurement could be done in a very fast and simple way by taking a single scan of SFS avoiding calculation and obtain information about polarity of the solvent. Curcumin decay properties in all the solvents could be fitted well to a double-exponential decay function.

We study the two-dimensional S =-, antiferromagnet with next-nearest-neighbor antiferromagnetic coupling using a sublattice-symmetric spin-wave theory and exact diagonalization. For sufticiently large frustration the theory predicts a transition to a disordered state with an energy gap and exponentially decaying correlations, rather than to a gapless spin-liquid state. Comparisonwith exact results on finite lattices up to 26 sites indicates that the theory overestimates the disordering effect of the next-nearest-neighbor coupling, implying that the long-range antiferromagnetic order is surprisingly robust.

One of potential applications of quantum processors should be a simulation of dynamics of quantum systems. In this paper we analyse whether it is possible to simulate a paradigmatic model of an exponential decay of a two-level system using a programmable quantum gate array. That is, we would like to simulate the decay of a two-level system in such a way that the parameters of the decay itself are encoded in the state of the ancilla that serves as a program for the programmable gate array. We show that it is impossible to simulate the exponential decay precisely with the finite-dimensional programmable gate array. On the other hand, we present a very simple model of a Markovian decay process that can be efficiently simulated on a simple programmable gate array. We compare this Markovian process with the exponential decay.

The influence of dislocations on electron transport properties of undoped InN thin films grown by molecular-beam epitaxy on AlN͑0001͒ pseudosubstrates is reported. The microstructure and the electron transport in InN͑0001͒ films of varying thickness were analyzed by transmission electron microscopy and variable temperature Hall-effect measurements. It was found that crystal defects have strong effects on the electron concentration and mobility of the carriers in the films. In particular, the combined analysis of microscopy and Hall data showed a direct dependence between free carrier and dislocation densities in InN. It was demonstrated that threading dislocations are active suppliers of the electrons and an exponential decay of their density with the thickness implies the corresponding decay in the carrier density. The analysis of the electron transport yields also a temperature-independent carrier concentration, which indicates degenerate donor levels in the narrow band-gap InN material. The relative insensitivity of the mobility with respect to the temperature suggests that a temperature-independent dislocation strain field scattering dominates over ionized impurity/defect and phonon scattering causing the increase of the mobility with rising layer thickness due to the reducing dislocation density. Room temperature mobilities in excess of 1500 cm 2 V −1 s −1 were obtained for ϳ800 nm thick InN layers with the dislocation densities of ϳ3 ϫ 10 9 cm −2 .

It has been shown in experiment that the heat capacity of glass formers has a frequency dependence, this is called the dynamic heat capacity. The dynamic heat capacity for a simple spin model known to be a glass former, the east Ising model, is measured by simulation. The result shows stretched exponential decay like relaxation, and the data is fit to the appropriate form. For low temperatures, the relaxation time grows proportionally to exponential inverse temperature squared, which is the theoretical low temperature limit. Another model is applied where the overall relaxation is made up of the relaxations of subdomains that each have their own characteristic times. Using Markov Chains, these times are computed numerically and symbolically, and the data is seen to fit the simulations very well in the low temperature limit. The dynamics of the east model are tracked very well by this procedure, and we compare this to the parameters of the stretched exponential fits showing that a di...

Population dynamics is analyzed by means of the power series expansion of a decay ratio F(P) with respect to the continuation probability, P, of survival. The truncation of the higher terms of the series yields the Verhulst equation as a first approximation. The approximation for higher age yields a simple exponential decay law of population, while the younger-age approximation recovers Gompertz's empirical law of human mortality. It is shown that there exists a finite survival probability in the limit of t=a. The validity of the present result is examined with real population dynamics of centenarians. In order to construct a commensurable definition of aging, an aging phenomenon in decay process is considered on the assumption of an ideal society, from which a simple relationship is derived between the extent of advancement of aging and the continuation probability.

A picosecond Kerr ellipsometry study of the transient anisotropy of the metal dithizonate Hg(HDz) 2 in solution with different organic solvents is presented. The Hg(HDz) 2 photochromic complex is one of the first organic dyes shown to exhibit photochromic proprieties. The complex exhibits reversible photochromism, changing from the normal form A (of orange-yellow colour) to the active form B (of blue colour) after excitation with 532 nm laser light. The Kerr ellipsometry signal is observed to decrease with a single exponential decay of about 100 ps, that is shown to be independent of the solvent. This indicates that the signal is dominated by the excited state lifetime of the molecule. The absence of any spectral signatures relevant to the excited states of the normal form indicates that formation of the photoisomer is a fast process with respect to the lifetime of the exited state.

We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ''vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light.

Ferromagnetic, in contrast to antiferromagnetic, Heisenberg chains can undergo a Spin-Peierls dimerization only at finite temperatures. They show reentrant behavior as a function of temperature, which might play a role for systems with small effective elastic constants as, for example, monatomic chains on surfaces. We investigate the physical properties of the dimerized ferromagnetic Heisenberg chain using a modified spin-wave theory. We calculate the exponentially decaying spin and dimer correlation functions, analyze the temperature dependence of the corresponding coherence lengths, the susceptibility, as well as the static and dynamic spin structure factor. By comparing with numerical data obtained by the density-matrix renormalization group applied to transfer matrices, we find that the modified spin wave theory yields excellent results for all these quantities for a wide range of dimerizations and temperatures.

In a bounded domain, we consider u tt − u + t 0 g(t −) u d = |u| u, where > 0, and g is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on g and , that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g.

Fire can be a catastrophic event which causes high mortality and injury in wildlife. While rehabilitation of injured animals is common, no studies have measured the success of rehabilitated wildlife following fire. This study compared the long-term survival and reproduction of a group of injured, rehabilitated and released koalas (n ¼ 16) with that of uninjured koalas (n ¼ 23) following fires in fragmented forest in Port Stephens, Australia, in 1994. Individual koalas were monitored for up to three years following release. Survival rates were calculated using the Kaplan-Meier estimate, modified for the staggered-entry of new animals. There was no significant difference in the survival of rehabilitated and uninjured koalas after fire. Annual survival, derived by fitting an exponential decay function to the data, was estimated to be 58% for rehabilitated koalas and 67% for the uninjured koalas. Predation by dogs was the major cause of mortality for both groups. Reproduction did not differ significantly between the two groups over two breeding seasons following fire. It was concluded that rehabilitation of injured koalas was successful from the perspective of the individuals. Furthermore, such efforts have the potential to contribute to the recovery of populations depleted after fire and thus contribute to the long-term survival of koala populations.

We present a transformation that reduces the (2+1)-dimensional nonlinear Schrödinger
equation to a second-order ordinary differential equation with cylindrical symmetry. The equation has a family of solutions, valid for both normal and anomalous dispersion, that is an oscillating and exponentially decaying function of the radial coordinate. The solution takes the appearance of a bright central spot surrounded by a dark ring whose radius increases with propagation distance. A simple algebraic relationship between the radius and the propagation distance is given.

The dynamic light scattering behavior of poly(butylmethacrylate) PBMA microgels and of kappa-casein micelles is compared with that from hard sphere latex particles. The latex particles and the kappa-casein micelles exhibited a single exponential decay of the time correlation function (TCF). For the microgels, progessively stronger deviations from a single exponential were observed as the scattering angle was made larger. These deviations are interpreted as being the result of internal modes of motion. From measurement of the first cumulant of the TCF, extrapolated towards zero angle, the translational diffusion coefficients D were determined, and the hydrodynamically effective radii were calculated via the Stokes-Einstein relationship. The ratio of the radius of gyration to the hydrodynamic radius was found to be.Q = 0.775+0.012 for the latex particles, in good agreement with theory. The microgels, however, exhibit much lower Oparameters of 0.49 to 0.58, while the kappa-casein micelles showed the opposite behavior with values between 1.1 and 2.5. The results are interpreted on the basis of the Debye-Bueche and Deutsch-Felderhof theory for porous spheres.

We prove in nite di erentiability of the magnetization and of all quenched correlation functions for disordered spin systems at high temperature or strong magnetic eld in the presence of Gri ths' singularities. We also show uniqueness of the Gibbs state and exponential decay of truncated correlation functions with probability one. Our results are obtained through new simple modi ed high temperature or low activity expansions whose convergence can be displayed by elementary probabilistic arguments. Our results require no assumptions on the probability distributions of the random parameters, except for the obvious one of no percolation of in nite couplings, and, in the strong eld situation, for the also obvious requirement that zero magnetic elds do not percolate.

The statistics of liquid-to-crystal nucleation are studied using an automated lag-time apparatus. A single 500 L sample of distilled water is repeatedly supercooled to a fixed temperature below its equilibrium freezing temperature, held until freezing occurred, and then thawed. Our raw data is then a set of approximately 300 lag-times for each of three set supercooling temperatures. In each case, a small insoluble AgI crystal was added to ensure heterogeneous nucleation and average nucleation temperatures around ⌬Tϭ8 K. The distribution of lag-times is analyzed, and shown to be well approximated by a single exponential decay, with average lag-times in the range of 1000-3000 seconds. This average lag-time decreases markedly at deeper levels of supercooling, and for the present data, this decrease is fit equally well by exponential, power law decay, and classical nucleation functional forms.

We propose a matrix approach to the computation of Battle-Lemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m. The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m. We approximate this bi-infinite matrix B2m by its finite section As , a square matrix of finite order. We use As to compute an approximation \s of x whose discrete Fourier transform is F(x). We show that xs converges pointwise to x exponentially fast. This gives a feasible method to compute the scaling function for any given tolerance. Similarly, this method can be used to compute the wavelets. Vita) = e-j0}/2Hico/2 + n)faco/2).

This study elaborates an inventory policy for perishable products where the products face exponential deterioration with time under the credit of trades. The demand rate is taken as a function of selling price and the delay in payment is permitted as per the order of quantity. Shortages are permitted and fully backlogged. The aim of the present study is to find the optimal ordering quantity of retailer and the optimal order cycle for optimizing the total profit. This study is also useful to find the optimal ordering scheme in the analysis of trade credit. A numerical example based on practical problems is presented which is helpful in the study of business decision making problems. A sensitivity analysis of the model is carried out for various parameters. The study concludes with a conclusion and an aspect at feasible future requirements.

... We chose the Chilean lemon crab (Cancer porteri) because it is an abundant resource for artisanal fisheries in central-south Chile (Arancibia et al ... Miller (1975) estimated the effective fishing area for traps used in the fishery for snow crab (Chionoecetes opilio), as the quotient ...

We study exponential decay rates of eigenfunctions of self-adjoint higher order elliptic operators on R d. We are interested in decay rates as a function of direction. We show that the possible decay rates are to a large extent determined algebraically. Contents 1. Introduction and previous results 1 2. Directional decay rates, arbitrary φ 3 3. Calculating the decay rate, Hφ = λφ 6 4. An example, σ loc = σ s 12 5. The Agmon metric and a variational principle 15 5.1. The setĒ for the Green's function 17 6. The setĒ-smoothness 18 References 19

A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2 • N; 77.5 • E; mag: dip 3.5 • N) has been carried out to investigate the dynamical behaviour of the fluctuations of H. The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H , using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.

Under biotic/abiotic stresses, the red alga Kappaphycus alvarezii reportedly releases massive amounts of H 2 O 2 into the surrounding seawater. As an essential redox signal, the role of chloroplast-originated H 2 O 2 in the orchestration of overall antioxidant responses in algal species has thus been questioned. This work purported to study the kinetic decay profiles of the redox-sensitive plastoquinone pool correlated to H 2 O 2 release in seawater, parameters of oxidative lesions and antioxidant enzyme activities in the red alga Kappaphycus alvarezii under the single or combined effects of high light, low temperature, and sub-lethal doses of 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) and 2,5-dibromo-3-methyl-6isopropyl-p-benzoquinone (DBMIB), which are inhibitors of the thylakoid electron transport system. Within 24 h, high light and chilling stresses distinctly affected the availability of the PQ pool for photosynthesis, following Gaussian and exponential kinetic profiles, respectively, whereas combined stimuli were mostly reflected in exponential decays. No significant correlation was found in a comparison of the PQ pool levels after 24 h with either catalase (CAT) or ascorbate peroxidase (APX) activities, although the H 2 O 2 concentration in seawater (R = 0.673), total superoxide dismutase activity (R = 0.689), and particularly indexes of protein (R = 0.869) and lipid oxidation (R = 0.864), were moderately correlated. These data suggest that the release of H 2 O 2 from plastids into seawater possibly impaired efficient and immediate responses of pivotal H 2 O 2-scavenging activities of CAT and APX in the red alga K. alvarezii, culminating in short-term exacerbated levels of protein and lipid oxidation. These facts provided a molecular basis for the recognized limited resistance of the red alga K. alvarezii under unfavorable conditions, especially under chilling stress.

The nurse shark, Ginglymostoma cirratum, is an obligate suction feeder that preys on benthic invertebrates and fish. Its cranial morphology exhibits a suite of structural and functional modifications that facilitate this mode of prey capture. During suction-feeding, subambient pressure is generated by the ventral expansion of the hyoid apparatus and the floor of its buccopharyngeal cavity. As in suction-feeding bony fishes, the nurse shark exhibits expansive, compressive, and recovery kinematic phases that produce posterior-directed water flow through the buccopharyngeal cavity. However, there is generally neither a preparatory phase nor cranial elevation. Suction is generated by the rapid depression of the buccopharyngeal floor by the coracoarcualis, coracohyoideus, and coracobranchiales muscles. Because the hyoid arch of G. cirratum is loosely connected to the mandible, contraction of the rectus cervicis muscle group can greatly depress the floor of the buccopharyngeal cavity below the depressed mandible, resulting in large volumetric expansion. Suction pressures in the nurse shark vary greatly, but include the greatest subambient pressures reported for an aquatic-feeding vertebrate. Maximum suction pressure does not appear to be related to shark size, but is correlated with the rate of buccopharyngeal expansion. As in suction-feeding bony fishes, suction in the nurse shark is only effective within approximately 3 cm in front of the mouth. The foraging behavior of this shark is most likely constrained to ambushing or stalking due to the exponential decay of effective suction in front of the mouth. Prey capture may be facilitated by foraging within reef confines and close to the substrate, which can enhance the effective suction distance, or by foraging at night when it can more closely approach prey.

In this paper we study existence and properties of solutions of the problem ∆w = 0 on the half-space R N + with nonlinear boundary condition ∂w/∂η + w = |w| p−2 w where 2 < p < 2(N − 1)/(N − 2) and N ≥ 3. We obtain a ground state solution w = w(x1, ..., xN−1, t) which is radial and has exponential decay in the first N − 1 variables. Moreover, w has sharp polynomial decay in the variable t.

The purpose of present research is to derive analytical expressions for the solution of steady MHD convective and slip flow due to a rotating disk. Viscous dissipation and Ohmic heating are taken into account. The nonlinear partial differential equations for MHD laminar flow of the homogeneous fluid are reduced to a system of five coupled ordinary differential equations by using similarity transformation. The derived solution is expressed in series of exponentially-decaying functions using homotopy analysis method (HAM). The convergence of the obtained series solutions is examined. Finally some figures are sketched to show the accuracy of the applied method and assessment of various slip parameter c, magnetic field parameter M, Eckert Ec, Schmidt Sc and Soret Sr numbers on the profiles of the dimensionless velocity, temperature and concentration distributions. Validity of the obtained results are verified by the numerical results.

This paper establishes a principle of Saint-Venant type associated with finite anti-plane shear of a cylinder whose cross-section is a semi-infinite strip. The long sides of the strip are traction-free, and the short side carries an arbitrarily distributed shear traction. At the infinity in the strip, the deformation is prescribed to be one of simple shear, and the associated shear stress is uniform. The analysis is based on the fully nonlinear theory of finite elastostatics and is carried out for a special class of homogeneous, isotropic incompressible materials. It is shown that, along the parallel sides of the strip, the nonvanishing component of shear stress differs from its average value (taken across the strip) by an exponentially decaying function of the distance from the end. A lower bound is given for the rate of decay.

In this paper we consider a thermoelastic system with boundary time-varying delay. Using the energy method, we show, under suitable assumptions, that the damping effect through heat conduction is still strong enough to uniformly stabilize the system even in the presence of boundary time-varying delay. Our result improves earlier results existing in the literature.

We investigate the transfer function of the discretized perfect lens in finite-difference time-domain (FDTD) and transfer matrix (TMM) simulations; the latter allow to eliminate the problems associated with the explicit time dependence in FDTD simulations. We argue that the peak observed in the FDTD transfer function near the maximum parallel momentum k ,max is due to finite time artifacts. We also find the finite discretization mesh acts like imaginary deviations from µ = ε = −1 and leads to a cross-over in the transfer function from constance to exponential decay around k ,max limiting the attainable super-resolution. We propose a simple qualitative model to describe the impact of the discretization. k ,max is found to depend logarithmically on the mesh constant in qualitative agreement with the TMM simulations.

In this paper we generalize and sharpen D. Sullivan's logarithm law for geodesics by specifying conditions on a sequence of subsets {A t | t ∈ N} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements f t of G under which #{t ∈ N | f t x ∈ A t } is infinite for a.e. x ∈ G/Γ. The main tool is exponential decay of correlation coefficients of smooth functions on G/Γ. Besides the general (higher rank) version of Sullivan's result, as a consequence we obtain a new proof of the classical Khinchin-Groshev theorem on simultaneous Diophantine approximation, and settle a conjecture recently made by M. Skriganov. §1. Introduction 1.1. This work has been motivated by the following two related results. The first one is the Khinchin-Groshev theorem, one of the cornerstones of metric theory of Diophantine approximation. We will denote by M m,n (R) the space of real matrices with m rows and n columns, and by · the norm on R k , k ∈ N, given by x = max 1≤i≤k |x i |.

Liquid phase epitaxy Garnets and perovskites Ce 3þ Pr 3þ La 3þ Sc 3þ Bi 3þ dopants a b s t r a c t This work reports the development of new types of UV-emitting phosphors based on single crystalline films (SCF) of aluminum garnet and perovskite compounds grown by the liquid phase epitaxy method. We consider peculiarities of the growth and the luminescent and scintillation properties of the following four types of UV SCF phosphors: i) Ce-doped SCF of Y-Lu-Al-perovskites with the Ce 3þ emission in the 300-450 nm range of the decay time of 16-17 ns; ii) Pr-doped SCF of Y-Lu-Al garnets and perovskites with the Pr 3þ emission in the 300-400 nm and 235-330 nm ranges with the decay time of 13-19 and 7-8 ns, respectively; iii) La 3þ or Sc 3þ doped SCF of Y-Lu-Al-garnets, emitting in the 280-400 nm range due to formation of the La Y,Lu , Sc Y,Lu and Sc Al centers with decay time of the order of several hundreds of nanoseconds; iv) Bi 3þ doped SCF of garnets with Bi 3þ emission in 275-350 nm with decay time of about 1.9 ms.