• Title/Summary/Keyword: nondegenerate

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A Novel Method of All-Optical Switching: Quantum Router

  • Ham, Byoung-Seung
    • ETRI Journal
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    • v.23 no.3
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    • pp.106-110
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    • 2001
  • Subpicosecond all-optical switching method based on the simultaneous two-photon coherence exchange is proposed and numerically demonstrated. The optical switching mechanism is based on the optical field induced dark resonance swapping via nondegenerate four-wave mixing processes. For potential applications of ultrafast all-optical switching in fiber-optic communications, 10-THz channel number independent quantum router is discussed.

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Optimization of Triple Response Systems by Using the Dual Response Approach and the Hooke-Jeeves Search Method

  • Fan, Shu-Kai S.;Huang, Chia-Fen;Chang, Ko-Wei;Chuang, Yu-Chiang
    • Industrial Engineering and Management Systems
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    • v.9 no.1
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    • pp.10-19
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    • 2010
  • This paper presents an extended computing procedure for the global optimization of the triple response system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the input factors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximated using a nonlinear mathematical program involving one primary (objective) function and two secondary (constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers of target (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrange multiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensure global optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. In the field of numerical optimization, as the family of TR approach always exhibits excellent mathematical properties during optimization steps, thus the proposed algorithm can guarantee the global optimal solution where the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustrated in terms of examples found in the quality literature where the comparison results with a gradient-based method are used to calibrate TRSALG.

CHARACTERIZATIONS OF GAMMA DISTRIBUTION

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.411-418
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    • 2007
  • Let $X_1$, ${\cdots}$, $X_n$ be nondegenerate and positive independent identically distributed(i.i.d.) random variables with common absolutely continuous distribution function F(x) and $E(X^2)$ < ${\infty}$. The random variables $X_1+{\cdots}+X_n$ and $\frac{X_1+{\cdots}+X_m}{X_1+{\cdots}+X_n}$are independent for 1 $1{\leq}$ m < n if and only if $X_1$, ${\cdots}$, $X_n$ have gamma distribution.

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REMARKS ON CURVES OF MAXIMAL REGULARITY IN ℙ3

  • Lee, Wanseok
    • East Asian mathematical journal
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    • v.36 no.3
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    • pp.349-357
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    • 2020
  • For a nondegenerate projective curve C ⊂ ℙr of degree d, it was shown that the Castelnuovo-Mumford regularity reg(C) of C is at most d - r + 2. And the curves of maximal regularity which attain the maximally possible value d - r + 2 are completely classified. In this short note, we first collect several known results about curves of maximal regularity. We provide a new proof and some partial results. Finally we suggest some interesting questions.

CONTINUATION THEOREMS OF THE EXTREMES UNDER POWER NORMALIZATION

  • Barakat, H.M.;Nigm, E.M.;El-Adll, M.E.
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.1-15
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    • 2002
  • In this paper an important stability property of the extremes under power normalizations is discussed. It is proved that the restricted convergence of the Power normalized extremes on an arbitrary nondegenerate interval implies the weak convergence. Moreover, this implication, in an important practical situation, is obtained when the sample size is considered as a random variable distributed geometrically with mean n.

A NOTE ON NULL DESIGNS OF DUAL POLAR SPACES

  • CHO, SOO-JIN
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.15-21
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    • 2005
  • Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.