Pricing European options with a log Student’s t-distribution: A Gosset formula

The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.     

Evidence for energy regularity in the Mendeleev periodic table

We show that the dependence of the total energy of the atoms on their atomic number can follow a q-exponential (as proposed by C. Tsallis), for practically all elements of the periodic table. The result is qualitatively explained in terms of the way the atomic configurations are arranged to minimize energy.     

Variability of scaling parameters in non-conservative systems: Geophysical aspect

Newly obtained data on the critical dynamics of the drifting/fracturing sea ice in the Arctic Ocean were analyzed and compared with published data on the dynamic processes in the Earth’s crust. Substantial similarities were found in the scaling behavior of both geophysical systems; the most important of them is the b-value space/time variability including a pre-failure drop of this parameter. The b-value pattern of the ensemble of drifting ice floes is an analogue of the b-value distribution over areas and depths in tectonic structures. A common feature of the pre-failure state in the cryosphere and in the Earth’s crust is the increased degree of the energy conservation that manifests itself both in the sea ice consolidation prior to basin-wide ice pack fragmentations, and in involving harder geological formations in the fracture process before earthquakes, respectively. From the viewpoint of the conservative SOC concept, this relation between the system’s conservativity and the occurrence of large-scale fracture events means that the expected scale level of failure is determined by the system’s closeness to “true” SOC behavior.     

Dots in rods as polarized single photon sources

We report the evidence of a polarized single photon flux from a colloidal nanoparticle. We analyze, by time and polarization resolved spectroscopy measurements, the polarization behavior of a single CdSe/CdS core/shell dot in rod, achieving a polarization ratio at room temperature of ∼75% and a lifetime of the excited state of ∼11 ns.     

Application of kinoform lens for X‐ray reflectivity analysis

In this paper the first practical application of kinoform lenses for the X‐ray reflectivity characterization of thin layered materials is demonstrated. The focused X‐ray beam generated from a kinoform lens, a line of nominal size ～50 µm × 2 µm, provides a unique possibility to measure the X‐ray reflectivities of thin layered materials in sample scanning mode. Moreover, the small footprint of the X‐ray beam, generated on the sample surface at grazing incidence angles, enables one to measure the absolute X‐ray reflectivities. This approach has been tested by analyzing a few thin multilayer structures. The advantages achieved over the conventional X‐ray reflectivity technique are discussed and demonstrated by measurements.     

What is “Twang”?

A single female professional vocal artist and pedagogue sang examples of “twang” and neutral voice quality, which a panel of experts classified, in almost complete agreement with the singer's intentions. Subglottal pressure was measured as the oral pressure during the occlusion during the syllable /pae/. This pressure tended to be higher in “twang,” whereas the sound pressure level (SPL) was invariably higher. Voice source properties and formant frequencies were analyzed by inverse filtering. In “twang,” as compared with neutral, the closed quotient was greater, the pulse amplitude and the fundamental were weaker, and the normalized amplitude tended to be lower, whereas formants 1 and 2 were higher and 3 and 5 were lower. The formant differences, which appeared to be the main cause of the SPL differences, were more important than the source differences for the perception of “twanginess.” As resonatory effects occur independently of the voice source, the formant frequencies in “twang” may reflect a vocal strategy that is advantageous from the point of view of vocal hygiene.     

Research on adaptive temperature control in sound field induced by self-focused concave spherical transducer

Temperature control of hyperthermia treatments is generally implemented with multipoint feedback system comprised of phased-array transducer, which is complicated and high cost. Our simulations to the acoustic field induced by a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture width, 8.0 cm focal length) show that the distribution of temperature can keep the same “cigar shape” in the focal region during ultrasound insonation. Based on the characteristic of the temperature change, a two-dimensional model of a “cigar shape” tumor is designed and tested through numerical simulation. One single-point on the border of the “cigar shape” tumor is selected as the control target and is controlled at the temperature of 43 °C by using a self-tuning regulator (STR). Considering the nonlinear effects of biological medium, an accurate state-space model obtained via the finite Fourier integral transformation to the bioheat equation is presented and used for calculating temperature. Computer simulations were performed with the perfusion rates of 2.0 kg/(m³ s) and 4.5 kg/(m³ s) to the different targets, it was found that the temperatures on the border of the “cigar shape” tumor can achieve the desired temperature of 43 °C by control of one single-point. A larger perfusion rate requires a higher power output to obtain the same temperature elevation under the same insonation time and needs a higher cost for compensating the energy loss carried away by blood flow after steady state. The power output increases with the controlled region while achieving the same temperature at the same time. Especially, there is no overshoot during temperature elevation and no oscillation after steady state. The simulation results demonstrate that the proposed approach may offers a way for obtaining a single-point, low-cost hyperthermia system.     

40 MCi tritium source for experiments with low energy neutrino

The artificial tritium source of 40 MCi activity was developed for the source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009001136-si2.gif"> scattering experiment to measure the electron antineutrino magnetic moment. We present R&D results which specify source design and physical parameters, its experimental effectiveness and guarantee safety during its life-cycle. Relevant technological issues are featured.     

Prospects of reactor neutrino experiments

Since the energy of a reactor neutrino is a few MeV, all source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si6.gif">, source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si7.gif"> and source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si8.gif"> oscillations are accessible by reactor neutrino experiments. KamLAND observed the source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si9.gif"> oscillation and currently Double Chooz, RENO and Dayabay experiments are under construction aiming to detect source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si10.gif"> oscillation. There are still good prospects for future reactor neutrino experiments after them. For example, there is room to further improve sin²2θ₁₃ accuracy at a baseline of ∼1.5 km, a very precise sin²2θ₁₂ measurement and the determination of mass hierarchy may be possible at a baseline ∼50 km, and if KamLAND is enlarged to the SuperKamiokande size, better measurement of source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0146641009000805-si13.gif"> and sin²2θ₁₂ will be anticipated. It is important to take into account such possibilities when planning future neutrino program after θ₁₃ is measured by current experiments.