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.

Corrigendum for "Weierstrass Points with first Non-Gap four on a Double Covering of a Hyperelliptic Curve"

In the proof of Lemma 3.1 in [1] we need to show that we may take the two points p and q with p ≠ q such that p+q+(b-2)g21(C′)∼2(q1+… +qb-1) where q1,…,qb-1 are points of C′, but in the paper [1] we did not show that p ≠ q. Moreover, we hadn't been able to prove this using the method of our paper [1]. So we must add some more assumption to Lemma 3.1 and rewrite the statements of our paper after Lemma 3.1. The following is the correct version of Lemma 3.1 in [1] with its proof.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

Weighted Sum of Correlated Lognormals: Convolution Integral Solution

Probability density function (pdf) for sum of n correlated lognormal variables is deducted as a special convolution integral. Pdf for weighted sums (where weights can be any real numbers) is also presented. The result for four dimensions was checked by Monte Carlo simulation.

Tax morale and tax evasion: Social preferences and bounded rationality

We study a family of models of tax evasion, where a flat-rate tax finances only the provision of public goods, neglecting audits and wage differences. We focus on the comparison of two modeling approaches. The first is based on optimizing agents, who are endowed with social preferences, their utility being the sum of private consumption and moral utility. The second approach involves agents acting according to simple heuristics. We find that while we encounter the traditionally shaped Laffer-curve in the optimizing model, the heuristics models exhibit (linearly) increasing Laffercurves. This difference is related to a peculiar type of behavior emerging within the heuristics based approach: a number of agents lurk in a moral state of limbo, alternating between altruism and selfishness.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Noise in gallium nitride-based quantum well structures used for nanometer devices in the frequency range 1 Hz--3 Mhz and temperature range 77K--324K

Electronic noise has been investigated in AlxGa1−x N/GaN Modulation-Doped Field Effect Transistors (MODFETs) of submicron dimensions, grown for us by MBE (Molecular Beam Epitaxy) techniques at Virginia Commonwealth University by Dr. H. Morkoç and coworkers. Some 20 devices were grown on a GaN substrate, four of which have leads bonded to source (S), drain (D), and gate (G) pads, respectively. Conduction takes place in the quasi-2D layer of the junction (xy plane) which is perpendicular to the quantum well (z-direction) of average triangular width ∼3 nm. A non-doped intrinsic buffer layer of ∼5 nm separates the Si-doped donors in the AlxGa1−xN layer from the 2D-transistor plane, which affords a very high electron mobility, thus enabling high-speed devices. Since all contacts (S, D, and G) must reach through the AlxGa1−xN layer to connect internally to the 2D plane, parallel conduction through this layer is a feature of all modulation-doped devices. While the shunting effect may account for no more than a few percent of the current IDS, it is responsible for most excess noise, over and above thermal noise of the device. ^ The excess noise has been analyzed as a sum of Lorentzian spectra and 1/f noise. The Lorentzian noise has been ascribed to trapping of the carriers in the AlxGa1−xN layer. A detailed, multitrapping generation-recombination noise theory is presented, which shows that an exponential relationship exists for the time constants obtained from the spectral components as a function of 1/kT. The trap depths have been obtained from Arrhenius plots of log (τT2) vs. 1000/T. Comparison with previous noise results for GaAs devices shows that: (a) many more trapping levels are present in these nitride-based devices; (b) the traps are deeper (farther below the conduction band) than for GaAs. Furthermore, the magnitude of the noise is strongly dependent on the level of depletion of the AlxGa1−xN donor layer, which can be altered by a negative or positive gate bias VGS. ^ Altogether, these frontier nitride-based devices are promising for bluish light optoelectronic devices and lasers; however, the noise, though well understood, indicates that the purity of the constituent layers should be greatly improved for future technological applications. ^

Concentrations and d13C compositions of n-alkanes, n-alcohols, n-alkanoic acids in a 34-month time series of suspended sediments from the outflow of the Congo River

The concentrations, distributions, and stable carbon isotopes (d13C) of plant waxes carried by fluvial suspended sediments contain valuable information about terrestrial ecosystem characteristics. To properly interpret past changes recorded in sedimentary archives it is crucial to understand the sources and variability of exported plant waxes in modern systems on seasonal to inter-annual timescales. To determine such variability, we present concentrations and d13C compositions of three compound classes (n-alkanes, n-alcohols, n-alkanoic acids) in a 34-month time series of suspended sediments from the outflow of the Congo River. We show that exported plant-dominated n-alkanes (C25-C35) represent a mixture of C3 and C4 end members, each with distinct molecular distributions, as evidenced by an 8.1 ± 0.7 per mil (±1Sigma standard deviation) spread in d13C values across chain-lengths, and weak correlations between individual homologue concentrations (r = 0.52-0.94). In contrast, plant-dominated n-alcohols (C26-C36) and n-alkanoic acids (C26-C36) exhibit stronger positive correlations (r = 0.70-0.99) between homologue concentrations and depleted d13C values (individual homologues average <= -31.3 per mil and -30.8 per mil, respectively), with lower d13C variability across chain-lengths (2.6 ± 0.6 per mil and 2.0 ± 1.1 per mil, respectively). All individual plant-wax lipids show little temporal d13C variability throughout the time-series (1 Sigma <= 0.9 per mil), indicating that their stable carbon isotopes are not a sensitive tracer for temporal changes in plant-wax source in the Congo basin on seasonal to inter-annual timescales. Carbon-normalized concentrations and relative abundances of n-alcohols (19-58% of total plant-wax lipids) and n-alkanoic acids (26-76%) respond rapidly to seasonal changes in runoff, indicating that they are mostly derived from a recently entrained local source. In contrast, a lack of correlation with discharge and low, stable relative abundances (5-16%) indicate that n-alkanes better represent a catchment-integrated signal with minimal response to discharge seasonality. Comparison to published data on other large watersheds indicates that this phenomenon is not limited to the Congo River, and that analysis of multiple plant-wax lipid classes and chain lengths can be used to better resolve local vs. distal ecosystem structure in river catchments.