• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.523-537
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• 2019

We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.1
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• pp.14-24
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• 2002

In this paper, a design of the pulsewidth-modulation(PWM) neural network with both retrieving and learning function is proposed. In the designed PWM neural system, the input and output signals of the neural network are represented by PWM signals. In neural network, the multiplication is one of the most commonly used operations. The multiplication and summation functions are realized by using the PWM technique and simple mixed-mode circuits. Thus, the designed neural network only occupies the small chip area. By applying some circuit design techniques to reduce the nonideal effects, the designed circuits have good linearity and large dynamic range. Moreover, the delta learning rule can easily be realized. To demonstrate the learning capability of the realized PWM neural network, the delta learning nile is realized. The circuit with one neuron, three synapses, and the associated learning circuits has been designed. The HSPICE simulation results on the two learning examples on AND function and OR function have successfully verified the function correctness and performance of the designed neural network.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1013-1024
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• 2018

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

• International Journal of CAD/CAM
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• v.1 no.1
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• pp.23-32
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• 2002

In this paper, a new technique of space deformation for parametric surfaces with so-called extension function (EF) is presented. Firstly, a special extension function is introduced. Then an operator matrix is constructed on the basis of EF. Finally the deformation of a surface is achieved through multiplying the equation of the surface by an operator matrix or adding the multiplication of some vector and the operator matrix to the equation. Interactively modifying control parameters, ideal deformation effect can be got. The implementation shows that the method is simple, intuitive and easy to control. It can be used in such fields as geometric modeling and computer animation.

• The Journal of Information Technology
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• v.8 no.3
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• pp.1-10
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• 2005

Cosine and Sine function is widely used for the arithmetic, translation, object drawing, Simulation and etc. of Computer Graphics in Natural Science and Engineering. In general, Cordic Algorithm is effective method since it has relatively small size and simple architecture on trigonometric function generation. However profitably it has those merits, the problem of operation speed is occurred. In graphic display system, the operation result of object drawing is quantized and has the condition that is satisfied with rms error less than 1. So in this paper, the proposed generator is composed of partition operation at each ${\pi}/4$ and basic Cosine, Sine function generator in the range of $0{\sim}{\pi}/4$ using the lower order of Tayler's series in an acceptable error range, that enlarge the range of $0{\sim}2{\pi}$ according to a definition of the trigonometric function for the purpose of having a high speed Cosine, Sine function generation. And, division operator using code partition for divisor three is proposed, the proposed function generator has high speed operation, but it has the problems in the other application parts with accurate results, is need to increase the speed of the multiplication.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1189-1208
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• 2017

In this paper, we study vanishing properties for $L^2$ harmonic 1-forms on a gradient shrinking Ricci soliton. We prove that if (M, g, f) is a complete oriented noncompact gradient shrinking Ricci soliton with potential function f, then there are no non-trivial $L^2$ harmonic 1-forms which are orthogonal to df. Second, we show that if the scalar curvature of the metric g is greater than or equal to (n - 2)/2, then there are no non-trivial $L^2$ harmonic 1-forms on (M, g). We also show that any multiplication of the total differential df by a function cannot be an $L^2$ harmonic 1-form unless it is trivial. Finally, we derive various integral properties involving the potential function f and $L^2$ harmonic 1-forms, and handle their applications.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.515-525
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• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

• Proceedings of the ESK Conference
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• 1997.04a
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• pp.107-113
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• 1997

In this paper, an interfacing method to control rehabilitation assitance system with bio-signal is proposed. Controlling with EMG signals method has certain advantage on signal-collecting, but has some drawbacks in the function resolution of EMG signals because data-processing process is not efficient. To improve function-resolution and to increase the efficiency of EMG signal interfacing with rehabilitation assistance system, Multi-layer Perception which is highly effective with static signal and hidden-Markov model for dynamic signal resolving are fused together. In proposed method. The direction and average speed of the rehabilitation assitance system are controlled by the trajectory control and estimation of the moving direction result from the fused model. From the experiment, proposed GMM and 2-level MLP hybrid-classifier yielded 8.6% perception-error rate, improving function resolution. New acceleration control method constructed with 3 nested linear filter produced continuous acceleration paths without the information of destination point. Thus, the mass output caused by non- continuous acceleration-deceleration was eliminated. In the simulation, the necessary calculation, in the case of multiplication, was reduced by 11.54%.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.5
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• pp.18-22
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• 1989

We calculate the distribution of the induced current on the strip by the TE waves on the infinite conducting strip. The boundary equations represented as the spatial domain function becomevery complicated equations including convolution integral. As we transform it to the spectral domain, we have a very simple equation expressed by some algebraic multiplication of the current density function and Green's function. It is shown that the computation result of the induced current distribution gives the optimum value, when the stop condition of iteration presented in this paper are satisfied.