Security investment and information sharing in the market of complementary firms: impact of complementarity degree and industry size

We study a differential game of information security investment and information sharing in a market consisting of n complementary firms. Two game approaches, the non-cooperative game and the totally cooperative game, are employed to investigate the steady state strategy of each firm. Under certain conditions, a unique steady state can be obtained for both games. We find that the steady state security investment and information sharing level are not always less in the non-cooperative game than that in the totally cooperative game. In addition, some theoretical analyses are made on the impacts of the complementarity degree and industry size on firms’ steady state strategies for both games. Finally, some numerical experiments are conducted to give some insights related to the instantaneous profit in the steady state. It can be found that a firm will obtain more instantaneous profit in the steady state of the totally cooperative game than that of the non-cooperative game, which emphasizes the importance of coordinating strategies. The effects of the complementarity degree and industry size on the instantaneous profits in the steady state are also obtained through the numerical experiment results.     

A preconditioned general modulus-based matrix splitting iteration method for linear complementarity problems of <Emphasis Type="Italic">H</Emphasis>-matrices

In this paper, we propose a preconditioned general modulus-based matrix splitting iteration method for solving modulus equations arising from linear complementarity problems. Its convergence theory is proved when the system matrix is an H₊-matrix, from which some new convergence conditions can be derived for the (general) modulus-based matrix splitting iteration methods. Numerical results further show that the proposed methods are superior to the existing methods.     

套代数上的可加双导子和中心化映射

令$\mathcal N$是Banach空间$X$上的套, Alg$\mathcal N$是相应的套代数. 本文证明了, 如果套$\mathcal N$中存在非平凡元$N$在$X$中可补, 且$\dim N\not=1$, 则Alg$\mathcal N$上的每个可加双导子是内导子. 作为此定理的应用, 分别给出了套代数上中心化(交换)映射, 斜中心化导子以及斜交换的广义导子的具体刻画.     

一类解析函数类的Hankel行列式的上界估计

本文对在单位圆盘U={z∈C：l│z│〈1}内解析且满足（1-λ）f（z）/z＋λf^1（z）〈1＋Az/1＋Bz（-1≤B＜A≤1;z∈U的函数f所对应的Hankel行列式│a2a4-a^23│,利用Toeplitz行列式的性质得到了其上界估计。     

Stochastic resonance in multi-scale bistable array

This Letter explores a new mechanism of stochastic resonance (SR) that is induced by the multi-scale noise decomposed from the input signal, which is promising in signal detection and processing under heavy background noise. The input signal is firstly decomposed to multi-scale signals by orthogonal wavelet transform. Then, the approximate signal, which contains the driving signal, is processed by an uncoupled parallel bistable array with the detailed signal of each scale as the internal noise. At last, a SR mechanism combining the effects of colored noise and array SR is proposed. The simulation results show that a high quality output signal can be obtained by the new mechanism. The proposed model is more adaptive to input signal with high noise intensity than single bistable SR system, which can be seen from the signal-to-noise ratio curves and average noise intensity curves.     

Optimality of a Class of Entanglement Witnesses for 3⊗3 Systems

Let $\varPhi_{t,\pi}: M_{3}({\mathbb{C}}) \rightarrow M_{3}({\mathbb{C}})$ be a linear map defined by $\varPhi_{t,\pi}(A)=(3-t)\*\sum_{i=1}^{3}E_{ii}AE_{ii}+t\sum_{i=1}^{3}E_{i,\pi (i)}AE_{i,\pi(i)}^{\dag}-A$ , where 0≤t≤3 and π is a permutation of (1,2,3). We show that the Hermitian matrix $W_{\varPhi_{t,\pi}}$ induced by Φ _t,π is an optimal entanglement witness if and only if t=1 and π is cyclic.     

L p Error Estimates for Scattered Data Interpolation On Spheres

In this article, working with the sphere 𝕊 ^d embedded in the (d + 1)-dimensional Euclidean space ? ^d+1 as the underlying manifold, we obtain an error estimate for interpolating functions f ∈ H _μ from shifts of a smooth positive definite function defined on 𝕊 ^d , where H _μ is a Sobolev space. We also get an L ^p error estimate for f by using a method of Duchon framework.     

浙江大学求是化学班人才培养的多层次科研实践体系

浙江大学化学系在求是化学班的培养过程中,以基础学科拔尖创新人才为培养目标,注重提升本科生科研能力,依托学科优势,从科研基础知识体系构建、科研思维模式拓展和科研创新实践能力强化等方面构筑分阶段、分层次、多平台、多模式的科研实践培养体系。该体系总体上以科研训练为主线,从广度科研认知到深度科研实践,融通校内第一、二课堂和校外第三、四课堂,贯穿整个拔尖人才培养过程。经过多年的探索与实践,该科研实践体系在培养学生的科研能力、创新思维和国际视野等方面已经初见成效。     

The temperature dependence of the magnetoelastic characteristics of cores for force sensors utilizing Fe<Subscript>70</Subscript>Ni<Subscript>8</Subscript>Si<Subscript>10</Subscript>B<Subscript>12</Subscript> amorphous alloy

This paper presents the results of investigation on the influence of temperature on magnetoelastic characteristics of the two ring-shaped cores, made of Fe₇₀Ni₈Si₁₀B₁₂ amorphous alloy. The cores were annealed for 1 h at 350 and 400°C, respectively. The compressive force F was applied perpendicular to the direction of the magnetizing field H in the sample. Special cylindrical backing enables application of the uniform compressive stress σ to the wound ring sample. A resistive furnace heated the experimental set-up. Results presented in the paper indicate a significant influence of the temperature on the magnetoelastic characteristics of Fe₇₀Ni₈Si₁₀B₁₂ amorphous alloy. Information about the magnetoelastic characteristics of this material may be useful in the magnetoelastic sensor development. Also this will create new possibilities in the development of physical model of magnetoelastic effect.