Narrow Results

Researchers traditionally compute isolated points for an efficient frontier and assume a line which passes through a risk-free asset $r_f$ and is tangent to the frontier. The tangency plays pivotal roles for the capital asset pricing model (CAPM). However, the assumption may not hold in the presence of kinks (as non-differentiable points) on efficient frontiers. Kinks are detected by parametric-quadratic programming only and not by ordinary portfolio optimization. Up until now, there has been no research to theoretically scrutinize kink properties (especially implications to CAPM) and systematically quantify the nonexistence of the tangency. In such an area, this paper contributes to the literature. In theorems and corollaries, we prove the nonexistence of the tangency and substantiate that expected-return axis is composed of piecewisely connected intervals for which the tangency does not exist and intervals for which the tangency exists. Computationally, we reveal universal existence of kinks (e.g., 0.2 to 8.0 kinks for 5-stock to 1800-stock portfolio selections) and the tangency-nonexistence ratios as about 0.066.

The large-N limit of fermionic vectors models is studied using bilocal variables in the framework of a collective field theory approach. The large-N configuration is determined completely using only classical solutions of the model. Further, the Bethe–Salpeter equations of the model are cast as a Green's function problem. One of the main results of this work is to show that this Green's function is in fact the large-N bilocal itself.

We consider solitonic solutions of coupled scalar systems, whose Lagrangian has a potential term (quasisupersymmetric potential) consisting of the square of derivative of a superpotential. The most important feature of such a theory is that among soliton masses there holds a Ritz-like combination rule (e.g. M₁₂+M₂₃=M₁₃), instead of the inequality (M₁₂+M₂₃<M₁₃) which is a stability relation generally seen in N=2 supersymmetric theory. The promotion from N=1 to N=2 theory is considered.

Soliton solutions in a scalar field theory defined on an AdS₁₊₁ background space-time are investigated. An analytic soliton solution is obtained in a polynomial model, and the classical soliton mass is calculated. The fluctuation spectrum around the soliton solution is determined, and the one-loop quantum correction to the soliton mass is computed in the semi-classical approximation.

We investigate the propagation of a wave-packet in the ϕ⁴ model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink soliton solution. We extract the scattering matrix from the wave-packet in the kink background at very late times and compare it with the result from static potential scattering in the small amplitude approximation. We vary the size of the initial wave-packet to identify nonlinear effects as, for example, the replacement of the center of the kink.

In this work, we study kink–antikink and antikink–kink collisions in hyperbolic models of fourth and sixth orders. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial ${\varphi }^4$ and ${\varphi }^6$ models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with the fourth order differ sensibly from those governed by the polynomial ${\varphi }^4$ model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial models give intricate structures of scattering that differ only slightly. The dependence on the order of interaction is related to some characteristics of the models such as the potential of perturbations and the number of vibrational modes.

The basic cytoskeletal transport in cells is achieved by two oppositely directed processive motor proteins, kinesin and dynein, walking along microtubules. Here, we offer a new view of the mechanism of the transport direction regulation by the intrinsic cell's electric fields that interact with kinks elicited in microtubules.

We elucidate the model introduced by Tuszynski et al.¹ in order to obtain more biophysically tractable results regarding the role of actin filaments in ionic transport throughout living cells.

Dynamics of a pinned dislocation kink controlled by the acting DC and AC forces is studied analytically. The motion of the kink, described by sine-Gordon (sG) equation, is explored within the framework of McLaughlin–Scott perturbation theory. Assuming weakness of the acting AC force, the equation of motion of the dislocation kink in the pinning potential is linearized. Based on the equations derived, we study stochastic behavior of the kink, and determine the probability of its depinning. The dependencies of the depinning probability on DC and AC forces are analyzed in detail.

The threshold source-drain voltage for the kink occurring in 130 nm GaAs devices is found to be linear dependent on the temperature in experiments. And the source-drain current after kink is also observed to be linearly dependent on the reciprocal of the source-drain voltage. A physical model of source-drain current including multi-valley transport for arbitrary doping and uniform doping GaAs has been proposed to explain such experimental phenomenon. Multi-valley electron transport origins from electrons getting the energy higher than the energy difference between the valleys from the channel electric field due to channel length shorter than the free-length for nano-GaAs devices. High energy electrons due to ballistic transport leads to a redistribution channel electron in different valleys and high energy electrons have a larger probability to occupy the states in upper valley because the density of states of the upper valley is about 70 times larger than that of the lower valley, leads to the carrier density in L valley being comparable with that in Γ valley in the channel, lastly kinks occurs.

Relationship between the kink and radiation effects of SOI MOSFET is investigated. The experiment results show that radiation exposure can play an important role on the behavior of the kink. The mechanisms of both the kink and radiation effects are clearly illustrated and the way the radiation affects the behavior of the kink are described in detail.

Soliton solutions in a scalar field theory defined on an AdS₁₊₁ background space-time are investigated. An analytic soliton solution is obtained in a polynomial model, and the classical soliton mass is calculated. The fluctuation spectrum around the soliton solution is determined, and the one-loop quantum correction to the soliton mass is computed in the semi-classical approximation.