Fourth SM Family Manifestations at CLIC

The latest electroweak precision data allow the existence of additional chiral generations in the standard model. We study prospects of search for the fourth standard model family fermions and quarkonia at $e^{+}e^{-}$ and $\gamma \gamma$ options of CLIC. It is shown that CLIC will be powerfull machine for discovery and investigation of both fourth family leptons and quarkonia. Moreover, the formation of the fourth family quarkonia will give a new opportunity to investigate Higgs boson properties.Comment: 7 pages, 6 Table

The Fourth SM Family Neutrino at Future Linear Colliders

It is known that Flavor Democracy favors the existence of the fourth standard model (SM) family. In order to give nonzero masses for the first three family fermions Flavor Democracy has to be slightly broken. A parametrization for democracy breaking, which gives the correct values for fundamental fermion masses and, at the same time, predicts quark and lepton CKM matrices in a good agreement with the experimental data, is proposed. The pair productions of the fourth SM family Dirac $(\nu_{4})$ and Majorana $(N_{1})$ neutrinos at future linear colliders with $\sqrt{s}=500$ GeV, 1 TeV and 3 TeV are considered. The cross section for the process $e^{+}e^{-}\to\nu_{4}\bar {\nu_{4}}(N_{1}N_{1})$ and the branching ratios for possible decay modes of the both neutrinos are determined. The decays of the fourth family neutrinos into muon channels $(\nu_{4}(N_{1})\to\mu^{\pm}W^{\mp})$ provide cleanest signature at $e^{+}e^{-}$ colliders. Meanwhile, in our parametrization this channel is dominant. $W$ bosons produced in decays of the fourth family neutrinos will be seen in detector as either di-jets or isolated leptons. As an example we consider the production of 200 GeV mass fourth family neutrinos at $\sqrt{s}=500$ GeV linear colliders by taking into account di-muon plus four-jet events as signatures.Comment: 16 pages, 3 figures, 10 table

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Kaluza-Klein Mesons in Universal Extra Dimensions

In models with universal extra dimensions, the isosinglet Kaluza-Klein (KK) quarks, q^1, have very narrow widths, of O(5-10) MeV, and will thus hadronize. Studies of KK-quarkonia, \bar{q}^1 q^1, show very sharp resonances and dramatic signatures at the Linear Collider. In this Brief Report, we consider the possibility of detecting KK-mesons, \bar{q}^1 q, and show that detection at a Linear Collider is unlikely.Comment: One paragraph regarding KK-meson annihilation added. Version to appear in Physical Review

Role of Alpha Oscillations During Short Time Memory Task Investigated by Graph Based Partitioning

In this study, we investigate the clustering pattern of alpha band (8 Hz - 12 Hz) electroencephalogram (EEG) oscillations obtained from healthy individuals during a short time memory task with 3 different memory loads. The retention period during which subjects were asked to memorize a pattern in a square matrix is analyzed with a graph theoretical approach. The functional coupling among EEG electrodes are quantified via mutual information in the time-frequency plane. A spectral clustering algorithm followed by bootstrapping is used to parcellate memory related circuits and for identifying significant clusters in the brain. The main outcome of the study is that the size of the significant clusters formed by alpha oscillations decreases as the memory load increases. This finding corroborates the active inhibition hypothesis about alpha oscillations

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex