• Title/Summary/Keyword: Bilinear functional

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Secure Inner Product Encryption Scheme with Attribute Hiding in Bilinear Groups (Bilinear Group에서 속성 은닉을 가지는 안전한 내적 암호화 방식)

  • Sadikin, Rifki;Park, YoungHo
    • Journal of the Institute of Electronics and Information Engineers
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    • v.51 no.1
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    • pp.57-70
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    • 2014
  • Inner product encryption (IPE) scheme is a cryptographic primitive that provides fine grained relations between secret keys and ciphertexts. This paper proposes a new IPE scheme which achieves fully attribute hiding security. Our IPE scheme is based on bilinear groups of a composite order. We prove the fully attribute hiding security of our IPE by using dual encryption system framework. In performance analysis, we compare the computation cost and memory requirement of our proposed IPE to other existing IPE schemes.

ORTHOGONAL POLYNOMIALS RELATIVE TO LINEAR PERTURBATIONS OF QUASI-DEFINITE MOMENT FUNCTIONALS

  • Kwon, K.H.;Lee, D.W.;Lee, J.H.
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.543-564
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    • 1999
  • Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

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A non-standard class of sobolev orthogonal polynomials

  • Han, S.S.;Jung, I.H.;Kwon, K.H.;Lee, J.K..
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.935-950
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    • 1997
  • When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

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Homogenization based continuum damage mechanics model for monotonic and cyclic damage evolution in 3D composites

  • Jain, Jayesh R.;Ghosh, Somnath
    • Interaction and multiscale mechanics
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    • v.1 no.2
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    • pp.279-301
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    • 2008
  • This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

STABILITY OF DELAY-DISTRIBUTED HIV INFECTION MODELS WITH MULTIPLE VIRAL PRODUCER CELLS

  • ELAIW, A.M.;ELNAHARY, E.KH.;SHEHATA, A.M.;ABUL-EZ, M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.1
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    • pp.29-62
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    • 2018
  • We investigate a class of HIV infection models with two kinds of target cells: $CD4^+$ T cells and macrophages. We incorporate three distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The viruses are produced from four types of infected cells: short-lived infected $CD4^+$T cells, long-lived chronically infected $CD4^+$T cells, short-lived infected macrophages and long-lived chronically infected macrophages. The drug efficacy is assumed to be different for the two types of target cells. The HIV-target incidence rate is given by bilinear and saturation functional response while, for the third model, both HIV-target incidence rate and neutralization rate of viruses are given by nonlinear general functions. We show that the solutions of the proposed models are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the positivity and stability of the three steady states of the models. Using Lyapunov functionals, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Development of a Quadrilateral Enhanced Assumed Strain Element for Efficient and Accurate Thermal Stress Analysis (효과적인 열응력 해석을 위한 사각형 추가 변형률 요소의 개발)

  • Ko, Jin-Hwan;Lee, Byung-Chai
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.7 s.166
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    • pp.1205-1214
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    • 1999
  • A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.