Pricing Derivatives under a Markov Skeleton Process

In this paper, it is assumed that the underlying is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with fast Fourier transform (FFT) method, the pricing formula of derivatives under the Markov skeleton process is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives.     

广义加权极大Morrey空间中次线性算子的有界性质

该文给出定义在R~n上的一类广义加权极大Morrey空间.证明一类次线性算子,包括分数次积分算子,在该类空间中的有界性质.同时还研究该类次线性算子的交换子在广义加权极大Morrey空间中的有界性质.     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

Character and Dimension Formulae for Queer Lie Superalgebra

We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, \({{\rm L}_{+}}\) and \({{\rm L}_{-}}\), within their positive and negative sets respectively. A corresponding flux balance from one phase to another is also imposed. We establish existence and \({L^{\infty}}\) bounds of solutions. We also prove that variational solutions are non-degenerate and develop the regularity theory for solutions of such free boundary problems.     

An Investigation of the Effect of Semi-Acetal Formation on the Properties of Dialdehyde Starch and its Thermoplastic Blend with Glycerol

Dialdehyde sweet potato starch (DASS) with various aldehyde contents was prepared and the properties analyzed in terms of solubility, intrinsic viscosity, scanning electron microscopy (SEM), X-ray diffraction (XRD), and thermogravimetric analysis (TGA). The results demonstrated that when the aldehyede content of DASS was increased from 20% to 95%, the solubility, molecular weight, crystallizability, and thermal stability decreased. Thermoplastic DASS (TPDASS) was prepared by adding glycerol as a plasticizer; the thermal, rheological, hydrophobic, and tensile properties of TPDASS were investigated. The results indicated that, for the same glycerol content, with the increase of aldehyde content, the moisture adsorption decreased, while the shear viscosity, glass transition temperature, and tensile properties of TPDASS increased significantly. The effects were attributed to the introduction of aldehyde groups reducing the hydrogen bonds and decreasing the hydrophility of the starch. Moreover, the aldehyde and hydroxyl groups of DASS favored a semi-acetal formation with higher aldehyde content and cross-linking of DASS occurred with the increase of aldehyde content. In summary, compared to starch, the thermoplastic properties and hydrophobicity of DASS was improved. In the presence of water (10 wt%), the tensile strength of TPDASS with 95% aldehyde content (TPDASS95) moderately decreased, from 16.7 MPa to 14.0 MPa, when the glycerol content increased from 10% to 30%. The TPDASS with improved properties will find their applications in preparing biodegradable plastics.     

Rotationally resolved state-to-state photoelectron study of zirconium monoxide cation (ZrO+)

Using two-colour visible (Vis)–ultraviolet (UV) photoionisation and pulsed field ionisation–photoelectron (PFI–PE) methods, we have obtained cleanly rotationally resolved photoelectron spectra for ZrO⁺(X ²Δ_3/2,5/2; v⁺ = 0, 1, and 2). The rotation assignment of these state-to-state Vis–UV–PFI–PE spectra has allowed the unambiguous determination of the ground state term symmetry for ZrO⁺(X) to be ²Δ_3/2, and the adiabatic ionisation energy of ⁹⁰Zr¹⁶O, IE(⁹⁰Zr¹⁶O) = 54,948.3(8) cm^?1 [6.81272(10) eV]. The symmetry of the ionic ZrO⁺(X ²Δ_3/2) ground state determined here disagrees with that reported in previous experiments. The rotational and vibrational constants determined in this experiment for the ionic ⁹⁰Zr¹⁶O⁺(X ²Δ_3/2) ground state are: B_e⁺ = 0.4343(8) cm^?1 and α_e⁺ = 0.0019(5) cm^?1, and ω_e⁺ = 991.2(8) cm^?1 and ω_e⁺x_e⁺ = 3.5(8) cm^?1; and those for the ionic ⁹⁰Zr¹⁶O⁺(X ²Δ_5/2) excited spin-orbit state are: B_e⁺ = 0.4357(6) cm^?1 and α_e⁺ = 0.0022(4) cm^?1, and ω_e⁺ = 991.9(8) cm^?1 and ω_e⁺x_e⁺ = 3.6(8) cm^?1, respectively. Based on the latter B_e⁺ value, the equilibrium bond distances are determined to be r_e⁺ = 1.691(2) Å for ⁹⁰Zr¹⁶O⁺(X ²Δ_3/2) and r_e⁺ = 1.688(1) Å for ⁹⁰Zr¹⁶O⁺(X ²Δ_5/2). The IE(ZrO) along with the spectroscopic constants obtained here are valuable for benchmarking the ab initio quantum chemical calculations for energetic and structural predictions of ZrO/ZrO⁺.     

一类非光滑对称三次系统的全局分支

该文对一类对称三次Hamilton系统在非光滑对称摄动下产生的极限环数目进行研究.通过多参数摄动理论和定性分析方法,得到这类在非光滑摄动下的三次系统可以存在至少19个极限环.     

TMEDA-CATALYZED SYNTHESIS OF N-ARYL-N′-ETHOXYCARBONYL THIOUREA AND ARENE (OR POLYMETHYLENE)-BIS-ETHOXYCARBONYLTHIOUREA DERIVATIVES

A novel and efficient method for synthesis ethoxycarbonyl isothiocyanate and ethoxycarbonyl thioureas catalyzed by TMEDA is reported. A series of N-aryl-N′-ethoxycarbonyl thioureas and arene (or polymethylene)-bis-ethoxycarbonyl thiourea derivatives have been synthesized in good-to-excellent yields via this method at room temperature.     

A NEW SYSTEM EXHIBITING A HIGH BARRIER TO ROTATION ABOUT THE P—N BOND. SYNTHESES AND SPECTRAL STUDIES OF 1,3,2-DIAZAPHOSPHETIDIN-4-ONE DERIVATIVES

Abstract

1,3,2-Diazaphosphetidin-4-one derivatives were synthesized. Their ¹H NMR signals at ambient temperature displaed a broad doublet which eventually coalesced before becoming sharp upon warming, and the ¹³C NMR spectra also showed that the α-and β-carbons of the dialkylamino group were non-equivalent. The phenomena were ascribed to restricted rotation about the exocyclic P—N bond.