Holographic multi-band superconductor

We propose a gravity dual for the holographic superconductor with multi-band carriers. Moreover, the currents of these carriers are unified under a global flavored SO(3) symmetry, which is dual to the bulk SO(3) gauge symmetry. We study the phase diagram of our model, and find it qualitatively agrees with the one for the realistic 2-band superconductor, such as MgB₂. We also identify the bulk field dual to the electromagnetic UEM(1) current, which should be invariant under the global flavored SO(3) rotation. We then evaluate the corresponding holographic conductivity and find the expected mean field like behaviors.     

Unruh effect and holography

We study the Unruh effect on the dynamics of quarks and mesons in the context of AdS₅/CFT₄ correspondence. We adopt an AdS₅ metric with the boundary Rindler horizon extending into a bulk Rindler-like horizon, which yields the thermodynamics with Unruh temperature verified by computing the boundary stress tensor. We then embed in it a probe fundamental string and a D7 brane in such a way that they become the dual of an accelerated quark and a meson in Minkowski space, respectively. Using the standard procedure of holographic renormalization, we calculate the chiral condensate, and also the spectral functions for both the accelerated quark and meson. Especially, we extract the corresponding strength of random force of the Langevin dynamics and observe that it can characterize the phase transition of meson melting. This result raises an issue toward a formulation of complementarity principle for the Rindler horizon. We find most of the dynamical features are qualitatively similar to the ones in the thermal bath dual to the AdS black hole background, though they could be quite different quantitatively.     

Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.     

Interior Continuity of Two-Dimensional Weakly Stationary-Harmonic Multiple-Valued Functions

In his big regularity paper, Almgren has proven the regularity theorem for mass-minimizing integral currents. One key step in his paper is to derive the regularity of Dirichlet-minimizing Q _Q (? ⁿ )-valued functions in the Sobolev space \(\mathcal{Y}_{2}(\varOmega, \mathbf{Q}_{Q} (\mathbb{R}^{n}))\) , where the domain Ω is open in ? ^m . In this article, we introduce the class of weakly stationary-harmonic Q _Q (? ⁿ )-valued functions. These functions are the critical points of Dirichlet’s integral under smooth domain-variations and range-variations. We prove that if Ω is a two-dimensional domain in ?² and \(f\in\mathcal{Y}_{2} (\varOmega,\mathbf{Q}_{Q}(\mathbb{R}^{n}) )\) is weakly stationary-harmonic, then f is continuous in the interior of the domain Ω.     

Impulsive synchronization for a chaotic system with channel time-delay

This paper discusses the synchronization of the chaotic system. Some new and less conservative sufficient conditions are established by impulsive control method with channel time-delay and different time-varying parameter uncertainties. An example and its simulations are finally included to visualize the effectiveness and feasibility of the method.     

A simple and facile route for the synthesis of 2H-1,4-benzoxazin-3-(4H)-ones via reductive cyclization of 2-(2-nitrophenoxy)acetonitrile adducts in the presence of Fe/acetic acid

A simple route for the synthesis of 1,4-benzoxazin-3-(4H)-ones is described herein. This method involves the reductive cyclization of 2-(2-nitrophenoxy)acetonitrile adducts in the presence of Fe/acetic acid in good to excellent yields. This system was compatible with various other functional groups.     

Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education

The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.     

Fuzzy-valued integrals based on a constructive methodology

The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals.     

Synthesis and characterization of LiFePO4 prepared by sol–gel technique

LiFePO₄ powder was synthesized by means of a new route, using a two step process. In the first step, an intermediate compound was synthesized by the sol–gel method. This precursor compound to LiFePO₄ was characterized by thermal analysis (TG/DTG and DSC), Mössbauer spectroscopy, Transmission Electronic Microscopy (TEM) and Small Angle Scattering (SAXS). In the second step, the precursor was sintered and analyzed by X-ray diffraction (XRD), showing the formation of the proposed single phase material.