• 제목/요약/키워드: Bounded variation

검색결과 90건 처리시간 0.037초

$\Phi$-유계 분산의 비단조 퍼지 측도에 관한연구 (On non-monotonic fuzzy measures of $\Phi$-bounded variation)

  • Jang, Lee-Chae;Kwon, Joong-Sung
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1995년도 추계학술대회 학술발표 논문집
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    • pp.314-321
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    • 1995
  • This paper discuss some properties of non-monotonic fuzzy measures of Ф -bounded variation. We show that there is an example of Ф such that $\beta$V(x, F) is a proper subspace of Ф$\beta$V(x, F) And also, we prove that Ф$\beta$V(x, F) is a real Banach space. Furthermore, we investigate some properties of non-monotonic fuzzy Ф -measures.

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INTEGRATION OF BICOMPLEX VALUED FUNCTION ALONG HYPERBOLIC CURVE

  • Chinmay Ghosh;Soumen Mondal
    • Korean Journal of Mathematics
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    • 제31권3호
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    • pp.323-337
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    • 2023
  • In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex valued functions on rectifiable hyperbolic path. Also we have established bicomplex analogue of the Fundamental Theorem of Calculus for hyperbolic line integral.

SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BV2α(I)

  • Aziz, Wadie;Guerrero, Jose Atilio;Merentes, Nelson
    • 대한수학회보
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    • 제52권2호
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    • pp.649-659
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    • 2015
  • The space $BV^2_{\alpha}(I)$ of all the real functions defined on interval $I=[a,b]{\subset}\mathbb{R}$, which are of bounded second ${\alpha}$-variation (in the sense De la Vall$\acute{e}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$, and prove, in particular, that if H maps $BV^2_{\alpha}(I)$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

GENERALIZED SOLUTION OF THE DEPENDENT IMPULSIVE CONTROL SYSTEM CORRESPONDING TO VECTOR-VALUED CONTROLS OF BOUNDED VARIATION

  • Shin, Chang-Eon;Ryu, Ji-Hyun
    • 대한수학회보
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    • 제37권2호
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    • pp.229-247
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    • 2000
  • This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

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INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF PRODUCT INTEGRATORS WITH APPLICATIONS

  • Dragomir, Silvestru Sever
    • 대한수학회지
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    • 제51권4호
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    • pp.791-815
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    • 2014
  • We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.

Option Pricing with Bounded Expected Loss under Variance-Gamma Processes

  • Song, Seong-Joo;Song, Jong-Woo
    • Communications for Statistical Applications and Methods
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    • 제17권4호
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    • pp.575-589
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    • 2010
  • Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.

On Stability of Discrete Time Nonlinear Systems with Slow-in-the-average Time Varying Inputs

  • Oh, Jun-Ho;Lim, Myo-Taeg
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2001년도 ICCAS
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    • pp.172.1-172
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    • 2001
  • In this paper we show the stability analysis of the discrete nonlinear system with average bounded variation of the input. This is the discrete counterpart of that continuous one. We use the Lyapunov stability to prove the boundedness of the steady-state error. Also the allowable maximum variation bounds and the region of attraction are given as the function of the system parameters. Moreover, we prove the uniform convergence for the constant input.

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