abstract

Long-time ECG time series for healthy subjects and diseased patients are analysed. In the first case, the power spectrum has the \(1/f\) shape in a broad frequency range. However, its behaviour for very low and very high frequency is different and the entire spectrum is integrable. For patients with post-ictal heart rate oscillation in partial epilepsy the \(1/f\) noise is not present. We determine the power spectrum by evaluating the Fourier transform of the signal in both cases and calculate the signal autocorrelation function. It falls with time faster for diseased patients then for healthy people. The presented method can serve as a diagnostic tool of some heart diseases.

abstract

We consider Poisson bialgebras on symplectic leaves of a Poisson manifold. New classes of completely integrable Hamiltonian systems with arbitrary many degrees of freedom are presented. Their Hamiltonians are defined as the \(k^{\rm th}\) coproduct of arbitrary smooth functions on symplectic foliations. We also consider modifications of the Poisson bialgebras by introducing the deformed coproduct and the deformed Poisson tensor.

abstract

The influence of a hypothetical CP violating \(|\Delta S|=2\) interaction on the masses and lifetimes of neutral mesons \(K^{0}\) and \(\overline {K^{0}}\) is investigated. It is shown, that the assumption of the existence of this superweak interaction does not significantly affect these parameters if phenomenological constraints based on recent experiments are imposed. To establish this result we use a computer simulation of a parameter corresponding to the difference between the diagonal elements of the effective Hamiltonian governing the time evolution in the \(K^{0} - \overline {K^{0}}\) system. Instead of the widely used Lee, Oehme and Yang approximation which is insensitive to the \(|\Delta S|=2\) interaction we use a formalism based on the Królikowski– Rzewuski equation.

abstract

A deformation of the Fock space based on the finite difference replacement for the derivative is introduced. The deformation parameter is related to the dimension of the finite analogue of the Fock space.

abstract

A numerical procedure is described for the maximization of the energy diffusion due to the backscattering of the gravitational radiation. The obtained maxima are solutions dominated by low frequency waves. They give rise to robust gravitational ringing, with amplitudes of the order of the original signal.

abstract

Renyi entropies for particle distributions following from the general cascade models are discussed. The \(p\)-model and the \(\beta \) distribution introduced in earlier studies of cascades are discussed in some detail. Some phenomenological consequences are pointed out.

abstract

Econophysics is an approach to quantitative economy using ideas, models, conceptual and computational methods of statistical physics. In recent years many of physical theories like theory of turbulence, scaling, random matrix theory or renormalization group were successfully applied to economy giving a boost to modern computational techniques of data analysis, risk management, artificial markets, macro-economy, etc. Econophysics became a regular discipline covering a large spectrum of problems of modern economy. It is impossible to review the whole field in a short paper. Here we shall instead attempt to give a flavor of how econophysics approaches economical problems by discussing one particular issue as an example: the emergence and consequences of large scale regularities, which in particular occur in the presence of fat tails in probability distributions in macro-economy and quantitative finance.

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The system of CCFM equations for unintegrated parton distributions in a photon is considered in the single loop approximation. We include quarks and non-singular parts of the splitting functions in the corresponding evolution equations. We solve the system of CCFM equations utilising the transverse coordinate representation which diagonalises these equations in the single loop approximation. The results for the unintegrated gluon distributions in a photon are presented and confronted with the approximate form expressing those distributions in terms of the integrated gluon and quark distributions and a suitably defined Sudakov-like form factor.

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The weight method of implementing the BE effect into Monte Carlo generators is discussed and presented in some detail. We show how the choice of free parameters and the definition of “direct” pions influence the results for the hadronic \(Z^0\) decays.

abstract

In the simple model of neutrino texture presented in this paper, the Majorana lefthanded mass matrix is zero, the Majorana righthanded mass matrix — diagonal and degenerate, and the Dirac mass matrix has a hierarchical structure, deformed unitarily by nearly bimaximal mixing. In the case, when the Majorana righthanded term dominates over the Dirac term, the familiar seesaw mechanism leads effectively to the nearly bimaximal oscillations of active neutrinos, consistent with solar and atmospheric neutrino experiments. If the Dirac term, before its unitary deformation, is similar in shape to the known charged-lepton mass matrix, then parameters for solar \(\nu _e\)’s and atmospheric \(\nu _\mu \)’s become related to each other, predicting from the SuperKamiokande value of \({\mit \Delta } m_{32}^2\) a tiny \({\mit \Delta } m_{21}^2\) typical for MSW LOW solar solution rather than for MSW Large Mixing Angle solution. The predicted mass spectrum is then hierarchical. In Appendix a suggestive form of nearly bimaximal effective mass matrix is derived.

abstract

Measuring the \({\mit \Gamma }(h\rightarrow \gamma \gamma )\ {\rm {BR}} (h\rightarrow b\overline {b})\) decay at the photon collider at TESLA is studied for a Standard Model Higgs boson of mass \(m_{\rm h}=120\) GeV. The main background due to the process \(\gamma \gamma \rightarrow Q\overline {Q}(g)\), where \(Q=b,\, c \), is estimated using the NLO QCD program (G. Jikia); the results obtained are compared with the corresponding LO estimate. Using a realistic luminosity spectrum and performing a detector simulation with the SIMDET program, we find that the \({\mit \Gamma }(h\rightarrow \gamma \gamma ){\rm BR}(h\rightarrow b\overline {b})\) decay can be measured with an accuracy better than 2% after one year of photon collider running.

abstract

We used the generalized form of the Thomas–Fermi type for the density profile inside spherical nuclei to obtain a leptodermous expansion for the matter density. This expansion was used to calculate the energy coefficients of the liquid drop model formula. We obtained analytical expressions for the volume, surface, curvature and higher order energy coefficients. These analytical expressions were used to derive a liquid drop model expansion for compressibility of spherical nuclei. We studied the energy and compressibility expansion coefficients and also their convergence. Particular interest was focused on the study of surface and curvature properties.

abstract

A definition of colour as ratios of cones’ stimulation functions is proposed. Gauss functions are chosen as model for these functions. The definition explains features of human colour vision without any additional assumptions. The opponent pairs of colours: red-green and yellow-blue are the result, not the principle of colour vision.

abstract

We extend our modeling of cooling of superfluid Neutron Stars (NSs) by including the production of muons in the core, in addition to neutrons, protons, and electrons. The results are confronted with observations of middle-aged isolated NSs. Muons have little effect on the hydrostatic structure of NSs, on the slow cooling of low-mass NSs (RX J0822–43 and PSR 1055–52 in our model) and on the rapid cooling of massive NSs. They affect, however, the moderately fast cooling of medium-mass NSs (1E 1207–52, RX J0002+62, PSR 0656+14, Vela, and Geminga) and shift appreciably the mass range of these NSs to lower masses, which is important for correct interpretation of the observations. Moreover, the effects of muons can accurately be reproduced by a simple renormalization of NS models with no muons in the NS cores.