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.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Reduced-parameter model of head-related transfer functions for synthesized spatial audio

Digital systems can generate left and right audio channels that create the effect of virtual sound source placement (spatialization) by processing an audio signal through pairs of Head-Related Transfer Functions (HRTFs) or, equivalently, Head-Related Impulse Responses (HRIRs). The spatialization effect is better when individually-measured HRTFs or HRIRs are used than when generic ones (e.g., from a mannequin) are used. However, the measurement process is not available to the majority of users. There is ongoing interest to find mechanisms to customize HRTFs or HRIRs to a specific user, in order to achieve an improved spatialization effect for that subject. Unfortunately, the current models used for HRTFs and HRIRs contain over a hundred parameters and none of those parameters can be easily related to the characteristics of the subject. This dissertation proposes an alternative model for the representation of HRTFs, which contains at most 30 parameters, all of which have a defined functional significance. It also presents methods to obtain the value of parameters in the model to make it approximately equivalent to an individually-measured HRTF. This conversion is achieved by the systematic deconstruction of HRIR sequences through an augmented version of the Hankel Total Least Squares (HTLS) decomposition approach. An average 95% match (fit) was observed between the original HRIRs and those re-constructed from the Damped and Delayed Sinusoids (DDSs) found by the decomposition process, for ipsilateral source locations. The dissertation also introduces and evaluates an HRIR customization procedure, based on a multilinear model implemented through a 3-mode tensor, for mapping of anatomical data from the subjects to the HRIR sequences at different sound source locations. This model uses the Higher-Order Singular Value Decomposition (HOSVD) method to represent the HRIRs and is capable of generating customized HRIRs from easily attainable anatomical measurements of a new intended user of the system. Listening tests were performed to compare the spatialization performance of customized, generic and individually-measured HRIRs when they are used for synthesized spatial audio. Statistical analysis of the results confirms that the type of HRIRs used for spatialization is a significant factor in the spatialization success, with the customized HRIRs yielding better results than generic HRIRs.

Winter sea surface temperature reconstruction from planktic foraminiferal transfer functions in the northeastern Arabian Sea over the last two millennia

The Indian monsoon system is an important climate feature of the northern Indian Ocean. Small variations of the wind and precipitation patterns have fundamental influence on the societal, agricultural, and economic development of India and its neighboring countries. To understand current trends, sensitivity to forcing, or natural variation, records beyond the instrumental period are needed. However, high-resolution archives of past winter monsoon variability are scarce. One potential archive of such records are marine sediments deposited on the continental slope in the NE Arabian Sea, an area where present-day conditions are dominated by the winter monsoon. In this region, winter monsoon conditions lead to distinctive changes in surface water properties, affecting marine plankton communities that are deposited in the sediment. Using planktic foraminifera as a sensitive and well-preserved plankton group, we first characterize the response of their species distribution on environmental gradients from a dataset of surface sediment samples in the tropical and sub-tropical Indian Ocean. Transfer functions for quantitative paleoenvironmental reconstructions were applied to a decadal-scale record of assemblage counts from the Pakistan Margin spanning the last 2000?years. The reconstructed temperature record reveals an intensification of winter monsoon intensity near the year 100 CE. Prior to this transition, winter temperatures were >1.5°C warmer than today. Conditions similar to the present seem to have established after 450 CE, interrupted by a singular event near 950 CE with warmer temperatures and accordingly weak winter monsoon. Frequency analysis revealed significant 75-, 40-, and 37-year cycles, which are known from decadal- to centennial-scale resolution records of Indian summer monsoon variability and interpreted as solar irradiance forcing. Our first independent record of Indian winter monsoon activity confirms that winter and summer monsoons were modulated on the same frequency bands and thus indicates that both monsoon systems are likely controlled by the same driving force.

Mechanisms Predisposing Penile Fracture And Long-term Outcomes On Erectile And Voiding Functions.

Purpose. To determine the mechanisms predisposing penile fracture as well as the rate of long-term penile deformity and erectile and voiding functions. Methods. All fractures were repaired on an emergency basis via subcoronal incision and absorbable suture with simultaneous repair of eventual urethral lesion. Patients' status before fracture and voiding and erectile functions at long term were assessed by periodic follow-up and phone call. Detailed history included cause, symptoms, and single-question self-report of erectile and voiding functions. Results. Among the 44 suspicious cases, 42 (95.4%) were confirmed, mean age was 34.5 years (range: 18-60), mean follow-up 59.3 months (range 9-155). Half presented the classical triad of audible crack, detumescence, and pain. Heterosexual intercourse was the most common cause (28 patients, 66.7%), followed by penile manipulation (6 patients, 14.3%), and homosexual intercourse (4 patients, 9.5%). Woman on top was the most common heterosexual position (n = 14, 50%), followed by doggy style (n = 8, 28.6%). Four patients (9.5%) maintained the cause unclear. Six (14.3%) patients had urethral injury and two (4.8%) had erectile dysfunction, treated by penile prosthesis and PDE-5i. No patient showed urethral fistula, voiding deterioration, penile nodule/curve or pain. Conclusions. Woman on top was the potentially riskiest sexual position (50%). Immediate surgical treatment warrants long-term very low morbidity.

Two-component System Vicrk Regulates Functions Associated With Establishment Of Streptococcus Sanguinis In Biofilms.

Streptococcus sanguinis is a commensal pioneer colonizer of teeth and an opportunistic pathogen of infectious endocarditis. The establishment of S. sanguinis in host sites likely requires dynamic fitting of the cell wall in response to local stimuli. In this study, we investigated the two-component system (TCS) VicRK in S. sanguinis (VicRKSs), which regulates genes of cell wall biogenesis, biofilm formation, and virulence in opportunistic pathogens. A vicK knockout mutant obtained from strain SK36 (SKvic) showed slight reductions in aerobic growth and resistance to oxidative stress but an impaired ability to form biofilms, a phenotype restored in the complemented mutant. The biofilm-defective phenotype was associated with reduced amounts of extracellular DNA during aerobic growth, with reduced production of H2O2, a metabolic product associated with DNA release, and with inhibitory capacity of S. sanguinis competitor species. No changes in autolysis or cell surface hydrophobicity were detected in SKvic. Reverse transcription-quantitative PCR (RT-qPCR), electrophoretic mobility shift assays (EMSA), and promoter sequence analyses revealed that VicR directly regulates genes encoding murein hydrolases (SSA_0094, cwdP, and gbpB) and spxB, which encodes pyruvate oxidase for H2O2 production. Genes previously associated with spxB expression (spxR, ccpA, ackA, and tpK) were not transcriptionally affected in SKvic. RT-qPCR analyses of S. sanguinis biofilm cells further showed upregulation of VicRK targets (spxB, gbpB, and SSA_0094) and other genes for biofilm formation (gtfP and comE) compared to expression in planktonic cells. This study provides evidence that VicRKSs regulates functions crucial for S. sanguinis establishment in biofilms and identifies novel VicRK targets potentially involved in hydrolytic activities of the cell wall required for these functions.

Monte Carlo Simulation Of The Response Functions Of Cdte Detectors To Be Applied In X-ray Spectroscopy.

In this work, the energy response functions of a CdTe detector were obtained by Monte Carlo (MC) simulation in the energy range from 5 to 160keV, using the PENELOPE code. In the response calculations the carrier transport features and the detector resolution were included. The computed energy response function was validated through comparison with experimental results obtained with (241)Am and (152)Eu sources. In order to investigate the influence of the correction by the detector response at diagnostic energy range, x-ray spectra were measured using a CdTe detector (model XR-100T, Amptek), and then corrected by the energy response of the detector using the stripping procedure. Results showed that the CdTe exhibits good energy response at low energies (below 40keV), showing only small distortions on the measured spectra. For energies below about 80keV, the contribution of the escape of Cd- and Te-K x-rays produce significant distortions on the measured x-ray spectra. For higher energies, the most important correction is the detector efficiency and the carrier trapping effects. The results showed that, after correction by the energy response, the measured spectra are in good agreement with those provided by a theoretical model of the literature. Finally, our results showed that the detailed knowledge of the response function and a proper correction procedure are fundamental for achieving more accurate spectra from which quality parameters (i.e., half-value layer and homogeneity coefficient) can be determined.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Charm and longitudinal structure functions within the Kharzeev-Levin-Nardi model

We use the Kharzeev-Levin-Nardi (KLN) model of the low x gluon distributions to fit recent HERA data on F(L) and F(2)(c)(F(2)(b)). Having checked that this model gives a good description of the data, we use it to predict F(L) and F(2)(c) to be measured in a future electron-ion collider. The results are similar to those obtained with the de Florian-Sassot and Eskola-Paukkunen-Salgado nuclear gluon distributions. The conclusion of this exercise is that the KLN model, simple as it is, may still be used as an auxiliary tool to make estimates for both heavy-ion and electron-ion collisions.

Use of correlated potential harmonic basis functions for the description of the (4)He trimer and small clusters

A correlated many-body basis function is used to describe the (4)He trimer and small helium clusters ((4)HeN) with N = 4-9. A realistic helium dimer potential is adopted. The ground state results of the (4)He dimer and trimer are in close agreement with earlier findings. But no evidence is found for the existence of Efimov state in the trimer for the actual (4)He-(4)He interaction. However, decreasing the potential strength we calculate several excited states of the trimer which exhibit Efimov character. We also solve for excited state energies of these clusters which are in good agreement with Monte Carlo hyperspherical description. (C) 2011 American Institute of Physics. [doi:10.1063/1.3583365]

Balance functions from Au+Au, d+Au, and p+p collisions at root s(NN)=200 GeV

Balance functions have been measured for charged-particle pairs, identified charged-pion pairs, and identified charged-kaon pairs in Au + Au, d + Au, and p + p collisions at root s(NN) = 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These balance functions are presented in terms of relative pseudorapidity, Delta eta, relative rapidity, Delta y, relative azimuthal angle, Delta phi, and invariant relative momentum, q(inv). For charged-particle pairs, the width of the balance function in terms of Delta eta scales smoothly with the number of participating nucleons, while HIJING and UrQMD model calculations show no dependence on centrality or system size. For charged-particle and charged-pion pairs, the balance functions widths in terms of Delta eta and Delta y are narrower in central Au + Au collisions than in peripheral collisions. The width for central collisions is consistent with thermal blast-wave models where the balancing charges are highly correlated in coordinate space at breakup. This strong correlation might be explained by either delayed hadronization or limited diffusion during the reaction. Furthermore, the narrowing trend is consistent with the lower kinetic temperatures inherent to more central collisions. In contrast, the width of the balance function for charged-kaon pairs in terms of Delta y shows little centrality dependence, which may signal a different production mechanism for kaons. The widths of the balance functions for charged pions and kaons in terms of q(inv) narrow in central collisions compared to peripheral collisions, which may be driven by the change in the kinetic temperature.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Spin-polarized current and shot noise in the presence of spin flip in a quantum dot via nonequilibrium Green's functions

Using nonequilibrium Green's functions we calculate the spin-polarized current and shot noise in a ferromagnet-quantum-dot-ferromagnet system. Both parallel (P) and antiparallel (AP) magnetic configurations are considered. Coulomb interaction and coherent spin flip (similar to a transverse magnetic field) are taken into account within the dot. We find that the interplay between Coulomb interaction and spin accumulation in the dot can result in a bias-dependent current polarization p. In particular, p can be suppressed in the P alignment and enhanced in the AP case depending on the bias voltage. The coherent spin flip can also result in a switch of the current polarization from the emitter to the collector lead. Interestingly, for a particular set of parameters it is possible to have a polarized current in the collector and an unpolarized current in the emitter lead. We also found a suppression of the Fano factor to values well below 0.5.