Multifractality in Time Series

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000

Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus

For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker's double series. The latter can be expressed in terms of the elliptic theta-functions in all orders of the asymptotic expansion.Comment: REVTeX, 22 pages, this is expanded version which includes exact asymptotic expansions of the free energy, the internal energy and the specific hea

Electron transport and optical properties of shallow GaAs/InGaAs/GaAs quantum wells with a thin central AlAs barrier

Shallow GaAs/InGaAs/GaAs quantum well structures with and without a three monolayer thick AlAs central barrier have been investigated for different well widths and Si doping levels. The transport parameters are determined by resistivity measurements in the temperature range 4-300 K and magnetotransport in magnetic fields up to 12 T. The (subband) carrier concentrations and mobilities are extracted from the Hall data and Shubnikov-de Haas oscillations. We find that the transport parameters are strongly affected by the insertion of the AlAs central barrier. Photoluminescence spectra, measured at 77 K, show an increase of the transition energies upon insertion of the barrier. The transport and optical data are analyzed with help of self-consistent calculations of the subband structure and envelope wave functions. Insertion of the AlAs central barrier changes the spatial distribution of the electron wave functions and leads to the formation of hybrid states, i.e. states which extend over the InGaAs and the delta-doped layer quantum wells.Comment: 14 pages, pdf fil

Местный рецидив рака предстательной железы после радикальной простатэктомии. Трансректальная ультразвуковая диагностика

Research purpose. Investigate possibilities of the transrectal ultrasonography (TRUS) in early diagnostics of the local recurrence of the prostate cancer (PC) following radical prostatectomy (RPE). Materials and methods. 50 PC patients at the age of 52–73 years (mean age – 62,5 years) that have undergone RPE in different clinics were under our observation. Preoperational prostate-specific antigen (PSA) value mounted 1,7–30 ng/ml. The following stages were determined clinically: Т1N0M0 – 8 patients, Т2N0M0 – 42 patients (Т2а – 38, Т2b – 2, T2c – 2). Following RPE, a positive surgical edge was revealed in 7 patients, tumor invasion to the seminal vesicles – in 3. After performed RPE, PSA level was determined 1 time per 3 months and TRUS in B-mode using energetic mapping (EM) was performed in all the patients. For this, MEDISON company SonoAce 8800 device with convex intracavitary sensor with a frequency 7,5 MHz was used. Results. In 1,5 years after RPE, PSA level increase more then 0,2 ng/ml (0,58–28 ng/ml) was observed. Patients have been examined, including: digital rectal investigation (DRI), TRUS of the prostate bed, helical computed tomography (HCT) of the minor pelvis organs, skeleton scintigraphy. DRI revealed a hardening part in 1 patient, bone metastatic lesion in 2 patients. Via HCT of the minor pelvis organs, a pathologic structure in the prostate bed region with invasion of the posterior bladder wall was revealed. By B-mode TRUS using EM, the areas of solid structure in the region of vesico-urethral anastomosis or behind the posterior bladder wall were revealed in 9 patients, including hypoechogenic with deformed coiled vessels – in 6, isoechogenic with solitary signals by EM – in 2, mixed echogenicity with the posterior bladder wall invasion – in 1 patients. By histological examination of the biopsy materials from the doubtful regions, the PC recurrence is diagnosed in 8 patients, in 1 – histologically local PC recurrence has not been confirmed. Conclusions. TRUS with using EM – is a higly informative, economically and clinically significant method of early diagnostics of the local PC recurrence following RPE.

Local relapse of the prostate cancer following radical prostatectomy. Transrectal ultrasound diagnosis

Research purpose. Investigate possibilities of the transrectal ultrasonography (TRUS) in early diagnostics of the local recurrence of the prostate cancer (PC) following radical prostatectomy (RPE). Materials and methods. 50 PC patients at the age of 52–73 years (mean age – 62,5 years) that have undergone RPE in different clinics were under our observation. Preoperational prostate-specific antigen (PSA) value mounted 1,7–30 ng/ml. The following stages were determined clinically: Т1N0M0 – 8 patients, Т2N0M0 – 42 patients (Т2а – 38, Т2b – 2, T2c – 2). Following RPE, a positive surgical edge was revealed in 7 patients, tumor invasion to the seminal vesicles – in 3. After performed RPE, PSA level was determined 1 time per 3 months and TRUS in B-mode using energetic mapping (EM) was performed in all the patients. For this, MEDISON company SonoAce 8800 device with convex intracavitary sensor with a frequency 7,5 MHz was used. Results. In 1,5 years after RPE, PSA level increase more then 0,2 ng/ml (0,58–28 ng/ml) was observed. Patients have been examined, including: digital rectal investigation (DRI), TRUS of the prostate bed, helical computed tomography (HCT) of the minor pelvis organs, skeleton scintigraphy. DRI revealed a hardening part in 1 patient, bone metastatic lesion in 2 patients. Via HCT of the minor pelvis organs, a pathologic structure in the prostate bed region with invasion of the posterior bladder wall was revealed. By B-mode TRUS using EM, the areas of solid structure in the region of vesico-urethral anastomosis or behind the posterior bladder wall were revealed in 9 patients, including hypoechogenic with deformed coiled vessels – in 6, isoechogenic with solitary signals by EM – in 2, mixed echogenicity with the posterior bladder wall invasion – in 1 patients. By histological examination of the biopsy materials from the doubtful regions, the PC recurrence is diagnosed in 8 patients, in 1 – histologically local PC recurrence has not been confirmed. Conclusions. TRUS with using EM – is a higly informative, economically and clinically significant method of early diagnostics of the local PC recurrence following RPE