Breaking parameter degeneracy in interacting dark energy models from observations

We study the interacting dark energy model with time varying dark energy equation of state. We examine the stability in the perturbation formalism and the degeneracy among the coupling between dark sectors, the time-dependent dark energy equation of state and dark matter abundance in the cosmic microwave background radiation. Further we discuss the possible ways to break such degeneracy by doing global fitting using the latest observational data and we get a tight constraint on the interaction between dark sectors.     

Cold dark matter hypotheses in the MSSM

We perform a Bayesian model selection analysis in the R-parity conserving MSSM to compare two different assumptions: whether the lightest neutralinos make all or only part of the cold dark matter. This corresponds to either imposing full WMAP relic density limits or just its upper bound for constraining the MSSM parameters. We consider several realisations of the MSSM, namely, three GUT-scale SUSY breaking scenarios with a handful of parameters corresponding to the CMSSM, anomaly mediation and the large volume string scenarios as well as the weak-scale 25-parameter phenomenological MSSM (pMSSM). The results give a data-based quantitative evidence for a multicomponent cold dark matter. The pMSSM posterior samples indicate that the choice of imposing full WMAP limits or just its upper bound affects mostly the gaugino–higgsino content of the neutralino and, against naive expectations, essentially not any other sector.     

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

The author proves that if f : C→Cn is a transcendental vector valued meromorphic function of finite order and assume Σa∈Cn ∪{∞}δ(a) = 2, then,where .This result extends the related results for meromorphic function by Singh and Kulkarni.     

Utilization of characteristic polynomials in vibration analysis of non-uniform beams under a moving mass excitation

Vibration of non-uniform beams with different boundary conditions subjected to a moving mass is investigated. The beam is modeled using Euler–Bernoulli beam theory. Applying the method of eigenfunction expansion, equation of motion has been transformed into a number of coupled linear time-varying ordinary differential equations. In non-uniform beams, the exact vibration functions do not exist and in order to solve these equations using eigenfunction expansion method, an adequate set of functions must be selected as the assumed vibration modes. A set of polynomial functions called as beam characteristic polynomials, which is constructed by considering beam boundary conditions, have been used along with the vibration functions of the equivalent uniform beam with similar boundary conditions, as the assumed vibration functions. Orthogonal polynomials which are generated by utilizing a Gram–Schmidt process are also used, and results of their application show no advantage over the set of simple non-orthogonal polynomials. In the numerical examples, both natural frequencies and forced vibration of three different non-uniform beams with different shapes and boundary conditions are scrutinized.     

Spectral analysis of eigenparameter dependent boundary value transmission problems

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces.     

Dark solitonic excitations and collisions from a fourth-order dispersive nonlinear Schrödinger model for the alpha helical protein

Recent protein observations motivate the dark-soliton study to explain the energy transfer in the proteins. In this paper we will investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. Painlevé analysis is performed to prove the equation is integrable. Through the introduction of an auxiliary function, bilinear forms and dark N-soliton solutions are constructed with the Hirota method and symbolic computation. Asymptotic analysis on the two-soliton solutions indicates that the soliton collisions are elastic. Decrease of the coefficient of higher-order effects can increase the soliton velocities. Graphical analysis on the two-soliton solutions indicates that the head-on collision between the two solitons, overtaking collision between the two solitons and collision between a moving soliton and a stationary one are all elastic. Collisions among the three solitons are all pairwise elastic.     

Active only integrator and differentiator with tunable time constants

In this paper new active only current-mode integrator and differentiator with electronically tunable time constants are described. They are composed of one operational amplifier (OA) and two operational transconductance amplifiers (OTAs), and are suitable for monolithic implementation either with CMOS or bipolar technologies. No realizability conditions are imposed for the proposed circuits and all of the active sensitivities are low. The performances of the circuits are demonstrated on the PSPICE platform.