Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

Numerical analysis for the mixed Navier–Stokes and Darcy Problem with the Beavers–Joseph interface condition

In this article, we consider the coupled Navier–Stokes and Darcy problem with the Beavers–Joseph interface condition. With suitable restrictions of physical parameters α and ν, we prove the existence and local uniqueness of a weak solution. Then we propose a coupled finite element scheme and a decoupled and linearized scheme based on two‐grid finite element. Under suitable further restrictions, their optimal error estimates are obtained. Finally numerical experiments indicate the validity of the theoretical results as well as the efficiency and effectiveness of the decoupled and linearized two‐grid algorithm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1009–1030, 2015     

On independent sets in random graphs

The independence number of a sparse random graph G(n,m) of average degree d = 2m/n is well‐known to be with high probability, with in the limit of large d. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size , i.e., about half the maximum size. Yet in spite of 30 years of extensive research no efficient algorithm has emerged to produce an independent set with size for any fixed (independent of both d and n). In this paper we prove that the combinatorial structure of the independent set problem in random graphs undergoes a phase transition as the size k of the independent sets passes the point . Roughly speaking, we prove that independent sets of size form an intricately rugged landscape, in which local search algorithms seem to get stuck. We illustrate this phenomenon by providing an exponential lower bound for the Metropolis process, a Markov chain for sampling independent sets. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 436–486, 2015     

Random k‐SAT and the power of two choices

We study an Achlioptas‐process version of the random k‐SAT process: a bounded number of k‐clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well‐studied area of probabilistic combinatorics (Achlioptas processes) to random CSP's. In particular, while a rule to delay the 2‐SAT threshold was known previously, this is the first proof of a rule to shift the threshold of k‐SAT for . We then propose a gap decision problem based upon this semi‐random model. The aim of the problem is to investigate the hardness of the random k‐SAT decision problem, as opposed to the problem of finding an assignment or certificate of unsatisfiability. Finally, we discuss connections to the study of Achlioptas random graph processes. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 163–173, 2015     

A scheme for a topological insulator field effect transistor

We propose a scheme for a topological insulator field effect transistor. The idea is based on the gate voltage control of the Dirac fermions in a ferromagnetic topological insulator channel with perpendicular magnetization connecting to two metallic topological insulator leads. Our theoretical analysis shows that the proposed device displays a switching effect with high on/off current ratio and a negative differential conductance with a good peak to valley ratio.     

Observation of room temperature negative differential resistance in solution synthesized ZnO nanorod

We report the observation of negative differential resistance (NDR) in solution synthesized ZnO nanorod. The ZnO nanorod was fabricated as a two terminal planar device using lithographically patterned Au electrodes. The measured current–voltage response of the device has shown a negative differential resistance behavior. The peak-to-valley current ratio of the NDR is found to be greater than 4. The mechanism of this observed NDR effect has been explained based on charge trapping and de-trapping at the nanoscale contacts. It is the first observation of negative differential resistance effect in solution synthesized ZnO nanorod.     

Relaxation dynamics and fragility during liquid–glass transitions of poly(propylene glycol)s

The acoustic and thermal properties of the liquid–glass transitions of propylene glycol and its oligomers, poly (propylene glycol)s, were studied by temperature modulated DSC and Brillouin scattering. The fragility indices were determined from Angell plots using the observed modulation frequency dependence of the complex heat capacity. The variation in the glass transition temperatures is discussed on the basis of the free volume theory. The relaxation time of the structural relaxation obeys the Vogel–Fulcher law, and its high frequency end is in good agreement with the result of the dielectric measurement in the literature. The correlation between the observed thermal expansion coefficients and the glass transition temperature is discussed based on the free volume theory. The sound velocity and attenuation were accurately determined as a function of the temperature by Brillouin scattering by combination with the refractive index measurement. The relaxation dynamics were discussed by considering the relaxation from segmental motions. All of these physical properties were discussed based on the third-order anharmonicity and the Grüneisen parameter.     

S=1/2 One‐Dimensional Random‐Exchange Ferromagnetic Zigzag Ladder,Which Exhibits Competing Interactions in a Critical Regime

The synthesis, crystal structure, and magnetic properties (from a combined experimental and First‐Principles Bottom‐Up theoretical study) of the new compound catena‐dichloro(2‐Cl‐3Mpy)copper(II), 1 , [2‐Cl‐3Mpy=2‐chloro‐3‐methylpyridine] are described and rationalized. Crystals of 1 present well isolated magnetic 1D chains (no 3D order was experimentally observed down to 1.8 K) and magnetic frustration stemming from competing ferromagnetic nearest‐neighbor (J_NN) interactions and antiferromagnetic next‐nearest neighbor (J_NNN) interactions, in which α=J_NNN/J_NN <?0.25. These magnetic interactions give rise to a unique magnetic topology: a two‐leg zigzag ladder composed of edge‐sharing up‐down triangles with antiferromagnetic interactions along the rails and ferromagnetic interactions along the zigzag chain that connects the rails. Crystals of 1 also present a random distribution of the 2‐Cl‐3Mpy groups, which are arranged in two different orientations, each with a 50 % occupancy. This translates into a random static structural disorder within each chain by virtue of which the value of the J_NN magnetic interactions can randomly take one of the following three values: 53, 36, and 16 cm^?1. The structural disorder does not affect the J_NNN value, which in all cases is approximately ?9 cm^?1. A proper statistical treatment of this disorder provides a computed magnetic susceptibility curve that reproduces the main features of the experimental data.     

新型环状聚(ε-己内酯-co-γ-三乙基硅氧基-ε-己内酯)的合成

设计合成了具有精确分子结构的聚合物对深入了解其结构与性能之间的关系起着至关重要的作用。研究了一种合成带有三乙基硅氧侧基的环状无规共聚酯的新方法。功能性单体γ-三乙基硅氧基-ε-己内酯(γ-Et3SiOεCL)和ε-己内酯(ε-CL)在环状引发剂2,2-二丁基-2-锡-1,3-二氧环庚烷(DSDOP)的作用下,进行活性开环聚合反应以制备活性环状无规共聚酯(LCP(εCLcoγEt3SiOεCL))前体,当单体完全转化后,以该活性环状前体作为大分子引发剂,引发反应性单体α-(1-丙烯酰氧乙基)-ε-己内酯(αAEεCL)进行嵌段聚合反应,合成了在活性中心附近带有不饱和双键的功能性环状嵌段共聚酯,即活性环状聚(ε-己内酯-co-γ-三乙基硅氧基-ε-己内酯)-b-(α-(1-丙烯酰氧乙基)-ε-己内酯)。最后该活性环状嵌段共聚酯在紫外光照射下,反应性单体结构单元中的双键发生分子内交联反应,从而制得稳定的不含有机锡的新型环状无规共聚酯cP(εCLcoγEt3SiOεCL)(Mn,NMR=28500)。采用SEC、1H NMR以及DSC等技术手段对聚合物的结构和性能进行表征。该方法的突出特点是能够高效地合成带有功能性侧基的高相对分子质量的环状无规共聚酯。     

How Many Molecules are Required to Obtain a Steady Faradaic Current from Mediated Electron Transfer at a Single Nanoparticle on a Supporting Surface?

We investigate the chronoamperometric noise characteristics of electron‐transfer reactions occurring on single nanoparticles (NPs) and assemblies of well‐separated NPs on a supporting surface. To this end, we combine a formerly described expression for the steady‐state current of a single particle with the shot‐noise model and derive an expression for the signal‐to‐noise ratio as a function of bulk concentration and particle radius. Our findings are supported by random‐walk simulations, which closely match the analytical results.