Synthesis,Characterization and Thermal Behaviors of 4-Amino-5-nitro-1,2,3-triazole(ANTZ)and Its Derivatives

4‐Amino‐5‐nitro‐1,2,3‐triazole (ANTZ) and its derivatives, such as 2‐(4‐amino‐5‐nitro‐1,2,3‐trazole‐1‐yl)‐1,3,5‐trinitrobenzene (T‐ANTZ) and 4‐amino‐5‐nitro‐1,2,3‐triazole (M‐ANTZ), were synthesized and characterized, whose structures were confirmed by IR, NMR and elemental analysis. The thermal behaviors of ANTZ, T‐ANTZ and M‐ANTZ were studied by the methods of DSC and TG‐DTG, and the results showed that there is an obvious melting process of ANTZ with melting point of 278.38°C, while there is no melting process in the thermal behavior of T‐ANTZ and M‐ANTZ (the derivatives of ATNZ).     

Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

The fractional complex transform is suggested to convert a fractional differential equation with Jumarie?s modification of Riemann-Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically.     

Selective depiction of susceptibility transitions using Laplace-filtered phase maps

In this work, we aim to demonstrate the ability of Laplace-filtered three-dimensional (3D) phase maps to selectively depict the susceptibility transitions in an object. To realize this goal, it is first shown that both the Laplace derivative of the z component of the static magnetic field in an object and the Laplacian of the corresponding phase distribution may be expected to be zero in regions of constant or linearly varying susceptibility and to be nonzero when there is an abrupt change in susceptibility, for instance, at a single point, a ridge, an interface, an edge or a boundary. Next, a method is presented by which the Laplace derivative of a 3D phase map can be directly extracted from the complex data, without the need for phase unwrapping or subtraction of a reference image. The validity of this approach and of the theory behind it is subsequently demonstrated by simulations and phantom experiments with exactly known susceptibility distributions. Finally, the potential of the Laplace derivative analysis is illustrated by simulations with a Shepp-Logan digital brain phantom and experiments with a gel phantom containing positive and negative focal susceptibility deviations.     

Three‐photon absorption properties of a novel symmetrical Carbazole derivative having terminal 1,10‐phenanthroline rings via carbon–nitrogen (C = N) double bond

Three‐photon absorption (3PA) properties of symmetric‐type carbazole derivatives show great potential for application in light‐activated therapy and optical limiting. A novel symmetrical carbazole derivative (abbreviated as POCP) with end‐groups of 1,10‐phenanthroline rings as the donor moieties, chained via carbon–nitrogen (C = N) double bond, has been synthetized and its three photon absorption properties has been also determined by using a Q‐switched Nd: YAG laser pumped with 30 ps pulses at 1064 nm in dimethylformamide. The measurement of 3PA cross‐section of this compound is performed by open aperture Z‐scan and σ_3PA is 481 × 10^–78 cm⁶ ? s²/photon² for the transition S₀ → S₁. The influence of the molecular structure of this compound on three‐photon absorption cross‐sections is discussed micromechanically by Austin model 1 and Zerner's Intermediate Neglect of Differential Overlap/S method. Copyright © 2012 John Wiley & Sons, Ltd.     

Fractional differential equations of motion in terms of combined Riemann—Liouville derivatives

In this paper,we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system.A combined Riemann-Liouville fractional derivative operator is defined,and a fractional Hamilton principle under this definition is established.The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle.A number of special cases are given,showing the universality of our conclusions.At the end of the paper,an example is given to illustrate the application of the results.     

Hamilton formalism and Noether symmetry for mechanico—electrical systems with fractional derivatives

This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented.Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results.     

Arithmetic Asian Options under Stochastic Delay Models

Abstract

Motivated by the increasing interest in past-dependent asset pricing models, shown in recent years by market practitioners and prominent authors such as Hobson and Rogers (1998 Hobson, D. and Rogers, L. C. G. 1998. Complete models with stochastic volatility. Mathematical Finance, 8(1): 27–48.  [Google Scholar], Complete models with stochastic volatility, Mathematical Finance, 8(1), pp. 27–48), we explore option pricing techniques for arithmetic Asian options under a stochastic delay differential equation approach. We obtain explicit closed-form expressions for a number of lower and upper bounds and compare their accuracy numerically.     

Optimal Cross Hedging of Insurance Derivatives

Abstract

We consider insurance derivatives depending on an external physical risk process, for example, a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover, we check the optimal investment strategies for standard admissibility criteria. Finally, we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation.     

The Generator of the Transition Semigroup Corresponding to a Stochastic Variational Inequality

One proves that the generator of the transition semigroup of a stochastic differential equation with boundary reflection on a convex set K is the realization of a second order elliptic operator on K with zero oblique derivative boundary conditions. Several implications to parabolic problems with oblique derivative are also derived.