On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

On the Uniform Decay of the Local Energy

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Characterizations of Exponential Distribution via Conditional Expectations of Record Values

2000 Mathematics Subject Classification: 62G30, 62E10.

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

Characterizations of Exponential Distribution Based on Sample of Size Three

2010 Mathematics Subject Classification: 62G30, 62E10.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Exotic meson decay widths using lattice quantum chromodynamics

Most experiments in particle physics are scattering experiments, the analysis of which leads to masses, scattering phases, decay widths and other properties of one or multi-particle systems. Until the advent of Lattice Quantum Chromodynamics (LQCD) it was difficult to compare experimental results on low energy hadron-hadron scattering processes to the predictions of QCD, the current theory of strong interactions. The reason being, at low energies the QCD coupling constant becomes large and the perturbation expansion for scattering; amplitudes does not converge. To overcome this, one puts the theory onto a lattice, imposes a momentum cutoff, and computes the integral numerically. For particle masses, predictions of LQCD agree with experiment, but the area of decay widths is largely unexplored. ^ LQCD provides ab initio access to unusual hadrons like exotic mesons that are predicted to contain real gluonic structure. To study decays of these type resonances the energy spectra of a two-particle decay state in a finite volume of dimension L can be related to the associated scattering phase shift δ(k) at momentum k through exact formulae derived by Lüscher. Because the spectra can be computed using numerical Monte Carlo techniques, the scattering phases can thus be determined using Lüscher's formulae, and the corresponding decay widths can be found by fitting Breit-Wigner functions. ^ Results of such a decay width calculation for an exotic hybrid( h) meson (JPC = 1-+) are presented for the decay channel h → πa 1. This calculation employed Lüscher's formulae and an approximation of LQCD called the quenched approximation. Energy spectra for the h and πa1 systems were extracted using eigenvalues of a correlation matrix, and the corresponding scattering phase shifts were determined for a discrete set of πa1 momenta. Although the number of phase shift data points was sparse, fits to a Breit-Wigner model were made, resulting in a decay width of about 60 MeV. ^

Temporally dependent C, N, and P dynamics associated with the decay of Rhizophora mangle L. leaf litter in oligotrophic mangrove wetlands of the Southern Everglades

We performed two litter decomposition experiments using nearly-senesced red mangrove (Rhizophora mangle L.) leaves collected from an Everglades dwarf mangrove wetland to understand the short-term (3 weeks) and long-term (1 year) changes in mass, as well as C-, N-, and P-content of decomposing leaf litter. We expected that leaves decomposing in this oligotrophic environment would be short-term sources of C, N, and P, but potential long-term sinks for N and P. In May 1998, we conducted a 3-week leaching experiment, incubating fresh, individual leaves in seawater for up to 21 days. From May 1997 to May 1998, leaf litter in mesh bags decomposed on the forest floor at two dwarf mangrove sites. Leaching accounted for about 33% loss of dry mass from R. mangle leaves after 3 weeks. Leaching losses were rapid, peaking by day 2, and large, with leachate concentrations of total organic carbon (TOC) and total phosphorus (TP) increasing by more than an order of magnitude after 3 weeks. Mean leaf C:N increased from 105 to 115 and N:P increased from a mean of 74 to 95 after 21 days, reflecting the relatively large leaching losses of N and P. Loss of mass in the litterbags leveled off after 4 months, with roughly 60%dry mass remaining (DMR) after nearly 1 year of decomposition. The mass of carbon in each litterbag declined significantly after 361 days, but the mass of nitrogen and phosphorus doubled, indicating long-term accumulation of these constituents into the detritus. Subsequently, the leaf C:N ratio dropped significantly from 90 to 34 after 361 days. Following an initial 44-day increase, leaf N:P decreased from 222 to 144, reflecting high accumulation of P relative to N. A review of several estuarine macrophyte decomposition studies reveals a trend in nitrogen accumulation through time regardless of site, but suggests no clear pattern for C and P. We believe that the increase in litter P observed in this study was indicative of the P-limited status of the greater Everglades ecosystem and that decomposing mangrove litter may represent a substantial phosphorus pool in the system.

The contribution of leaching to the rapid release of nutrients and carbon in the early decay of wetland vegetation

Our goal was to quantify the coupled process of litter turnover and leaching as a source of nutrients and fixed carbon in oligotrophic, nutrient-limited wetlands. We conducted poisoned and non-poisoned incubations of leaf material from four different perennial wetland plants (Eleocharis spp., Cladium jamaicense, Rhizophora mangle and Spartina alterniflora) collected from different oligotrophic freshwater and estuarine wetland settings. Total phosphorus (TP) release from the P-limited Everglades plant species (Eleocharis spp., C. jamaicense and R. mangle) was much lower than TP release by the salt marsh plant S. alterniflora from N-limited North Inlet (SC). For most species and sampling times, total organic carbon (TOC) and TP leaching losses were much greater in poisoned than non-poisoned treatments, likely as a result of epiphytic microbial activity. Therefore, a substantial portion of the C and P leached from these wetland plant species was bio-available to microbial communities. Even the microbes associated with S. alterniflora from N-limited North Inlet showed indications of P-limitation early in the leaching process, as P was removed from the water column. Leaves of R. mangle released much more TOC per gram of litter than the other species, likely contributing to the greater waterborne [DOC] observed by others in the mangrove ecotone of Everglades National Park. Between the two freshwater Everglades plants, C. jamaicense leached nearly twice as much P than Eleocharis spp. In scaling this to the landscape level, our observed leaching losses combined with higher litter production of C. jamaicense compared to Eleocharis spp. resulted in a substantially greater P leaching from plant litter to the water column and epiphytic microbes. In conclusion, leaching of fresh plant litter can be an important autochthonous source of nutrients in freshwater and estuarine wetland ecosystems.

Changes in mass and nutrient content of wood during decomposition in a south Florida mangrove forest

1. Large pools of dead wood in mangrove forests following disturbances such as hurricanes may influence nutrient fluxes. We hypothesized that decomposition of wood of mangroves from Florida, USA (Avicennia germinans, Laguncularia racemosa and Rhizophora mangle), and the consequent nutrient dynamics, would depend on species, location in the forest relative to freshwater and marine influences and whether the wood was standing, lying on the sediment surface or buried. 2. Wood disks (8–10 cm diameter, 1 cm thick) from each species were set to decompose at sites along the Shark River, either buried in the sediment, on the soil surface or in the air (above both the soil surface and high tide elevation). 3. A simple exponential model described the decay of wood in the air, and neither species nor site had any effect on the decay coefficient during the first 13 months of decomposition. 4. Over 28 months of decomposition, buried and surface disks decomposed following a two-component model, with labile and refractory components. Avicennia germinans had the largest labile component (18 ± 2% of dry weight), while Laguncularia racemosa had the lowest (10 ± 2%). Labile components decayed at rates of 0.37–23.71% month−1, while refractory components decayed at rates of 0.001–0.033% month−1. Disks decomposing on the soil surface had higher decay rates than buried disks, but both were higher than disks in the air. All species had similar decay rates of the labile and refractory components, but A. germinans exhibited faster overall decay because of a higher proportion of labile components. 5. Nitrogen content generally increased in buried and surface disks, but there was little change in N content of disks in the air over the 2-year study. Between 17% and 68% of total phosphorus in wood leached out during the first 2 months of decomposition, with buried disks having the greater losses, P remaining constant or increasing slightly thereafter. 6. Newly deposited wood from living trees was a short-term source of N for the ecosystem but, by the end of 2 years, had become a net sink. Wood, however, remained a source of P for the ecosystem. 7. As in other forested ecosystems, coarse woody debris can have a significant impact on carbon and nutrient dynamics in mangrove forests. The prevalence of disturbances, such as hurricanes, that can deposit large amounts of wood on the forest floor accentuates the importance of downed wood in these forests.