abstract

In this paper we investigate the dependence structure for Ornstein–Uhlenbeck process with tempered stable distribution that is natural extension of the classical Ornstein–Uhlenbeck process with Gaussian and \(\alpha \)-stable behavior. However, for the \(\alpha \)-stable models the correlation is not defined, therefore in order to compare the structure of dependence for Ornstein–Uhlenbeck process with tempered stable and \(\alpha \)-stable distribution, we need another measures of dependence defined for infinitely divisible processes such as Lévy correlation cascade or codifference. We show that for analyzed tempered stable process the rate of decay of the Lévy correlation cascade is different than in the stable case, while the codifference of the \(\alpha \)-stable Ornstein–Uhlenbeck process has the same asymptotic behavior as in tempered stable case. As motivation of our study we calibrate the Ornstein–Uhlenbeck process with tempered stable distribution to real financial data.

abstract

We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation derived in our earlier work are determined within the Krylov–Bogoliubov–Mitropolsky (KBM) approach used to compute the amplitude profiles \(A({\mit \Omega }) \). Dependence of the amplitude \(A\) of nonlinear resonances on the frequency \({\mit \Omega }\) is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function \(A({\mit \Omega })\) induced by changes of the control parameters near a singular point of this function. It follows that dynamics can be controlled in the neighbourhood of a singular point.

abstract

In this paper, we have analyzed the entanglement and nonclassicality of two-mode superposition coherent states based on two coherent states shifted in phase by \(\pi \)/\(2\). Here, the relative phase of the superposition will be taken equal to the phase shift between the two coherent states i.e. \(\phi =\pi \)/\(2\). Entanglement-sensitivity is investigated and it was found that out of four, only one state is maximally entangled. Moreover, it is also revealed that the considered states have stronger nonclassical features than those of even–odd entangled coherent states.

abstract

Sine-Gordon kinks are non-dispersive solutions in a much studied integrable system. Recent studies on sine-Gordon kinks with space-dependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with wells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.

abstract

It is known that for any 2-to-2 process in MSSM, only the helicity conserving (HC) amplitudes survive asymptotically. Studying many such processes, at the 1-loop Electroweak (EW) order, it is found that their high energy HC amplitudes are determined by just three forms: a log-squared function of the ratio of two of the \((s,t,u)\) variables, to which a \(\pi ^2\) is added; and two Sudakov-like \(\ln \)- and \(\ln ^2\)-terms accompanied by respective mass-dependent constants. Apart from a possible additional residual constant (which is also discussed), these HC amplitudes, may be expressed as linear combinations of the above three forms, with coefficients being rational functions of the \((s,t,u)\) variables. This 1-loop property, called supersimplicity, is of course claimed for the 2-to-2 processes considered; but no violating examples are known at present. For \(ug\to dW\), supersimplicity is found to be a very good approximation at LHC energies, provided the SUSY scale is not too high. SM processes are also discussed, and their differences are explored.

abstract

A higher than predicted rate of two leptons plus missing transverse energy events, reported at the summer HEP conferences, can originate from a decay of the Higgs boson into a \(WW^{~(*)}\) pair, a misjudgement of the rate of SM background processes or a statistical fluctuation. In this paper we discuss a way to resolve this three-fold ambiguity.

abstract

In this work, the three dimensional Woods–Saxon potential is studied within the context of Supersymmetry Quantum Mechanics. We have applied the SUSY method by using the Pekeris approximation to the centrifugal potential \(l\neq 0\) states. By application of this method, it is possible to solve the Schrödinger equation for this potential. We obtain exactly bound state spectrum and wave function of Woods–Saxon potential for nonzero angular momentum. Hamiltonian hierarchy method and the shape invariance property are used in the calculations.

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We consider few-min oscillations in a gravitationally-stratified solar corona. These oscillations are triggered by initial pulse in the vertical velocity component that is launched below the transition region. We develop the model in the frame of two-dimensional Euler equations which are solved numerically. Our numerical results reveal that few-min (1–7 min) oscillations are effectively excited by the velocity pulses, with their waveperiod depending on a shape and a vertical position of the initial pulse.