• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.579-595
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• 1997

In this paper, we establish an $L_p$ analytic Fourier-Feynman transform theory for a class of cylinder functions on an abstract Wiener space. Also we define a convolution product for functions on an abstract Wiener space and then prove that the $L_p$ analytic Fourier-Feyman transform of the convolution product is a product of $L_p$ analytic Fourier-Feyman transforms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1783-1788
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• 1994

A comparison of the temperature distributions along the wall and center of the fin and the heat loss from the fin, computed assuming the fin tip is insulated and assuming it is not insulated in a triangular fin, is performed by the two-dimensional forced analytic method. When the fin tip is not insulated, a comparison between forced analytic method and analytic method is made in the heat loss and temperature along the fin wall. The value of Biot number varies from 0.01 to 1.0. The root temperature and surrounding convection coefficients of the fin are assumed as a constant. The results are (1) the analysis on the triangular fin assuming the fin tip is insulated does not produce a good value as compared to that of not-insulated case as the non-dimensional fin length decreases and as the value of Biot number increases and (2) the errors between forced analytic method and analytic method are very small, but the former method is better for computer running time and accuracy.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.99-117
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• 1998

Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.8
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• pp.1235-1240
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• 2013

We investigate an approximate analytic expression of signal distortion caused by the interaction between self-phase modulation (SPM) and dispersion in the dispersion-managed optical transmission where the dispersion is optimally compensated. From the analytic study, we obtain the analytic expression of the signal distortion in dispersion-managed optical transmission system. To confirm the validity of the analytic expression, we show that the eye-opening penalties calculated by the analytic expression correspond with the simulation results. Using the analytic result, we can easily estimate the signal distortion without complex nonlinear simulations.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.73-93
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• 2004

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.157-169
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• 2020

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Korean Journal of Logic
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• v.7 no.1
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• pp.1-22
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• 2004

The Kantian idea that some judgments are synthetic even in the area of a priori judgments cannot be accepted in its original version, but a modification of the notions 'analytic' and 'synthetic' discovers a rational core of that idea. The new definition of 'analytic' concerns concepts and makes it possible to distinguish between analytic concepts, which are effective ways of computing recursive functions, and synthetic concepts, which either define non-recursive functions, or define recursive functions in an ineffective way. To justify this claim we have to construe concepts as abstract procedures not reducible to set-theoretical entities.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1625-1647
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• 2014

By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.233-246
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• 2016

In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.211-220
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• 2014

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we prove several inclusion relations associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of analytic functions of complex order, which are introduced here by means of the Al-Oboudi derivative. Several special cases of the main results are mentioned.