• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.377-389
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• 2019

We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

• Journal of Broadcast Engineering
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• 제27권7호
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• pp.1011-1020
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• 2022

Recent high-performance panoptic segmentation models are based on transformer architectures. However, transformer-based panoptic segmentation methods are basically slower than convolution-based methods, since the attention mechanism in the transformer requires quadratic complexity w.r.t. image resolution. Also, sine and cosine computation for positional embedding in the transformer also yields a bottleneck for computation time. To address these problems, we adopt three modules to speed up the inference runtime of the transformer-based panoptic segmentation. First, we perform channel-level reduction using depth-wise separable convolution for inputs of the transformer decoder. Second, we replace sine and cosine-based positional encoding with convolution operations, called conv-embedding. We also apply a separable self-attention to the transformer encoder to lower quadratic complexity to linear one for numbers of image pixels. As result, the proposed model achieves 44% faster frame per second than baseline on ADE20K panoptic validation dataset, when we use all three modules.

• The Journal of the Korea Contents Association
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• 제8권4호
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• pp.17-29
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• 2008

In Computer Graphics, fluid dynamics is used for animating and expressing the various special effects of water. As the hardware performance is getting higher, the several algorithms for fluid dynamics become to be executed in real time. However, it still requires a lot of computational time to get the realistic and detailed results. Therefore, there are many researches on the techniques of balancing between performance and quality. It must give priority to the executive performance preserving the visual reality even though sacrificing the physical reality, specially in applications with the game context which need to express the interaction between 3D objects and the surface of the water such as the sea or a lake. In this paper, we propose a method for the realtime animation of interactions between 3D objects and the surface of the water using the linear convolution of height fields and the bounding spheres of object.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.631-646
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• 2009

In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.

• Journal of Broadcast Engineering
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• 제14권5호
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• pp.543-550
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• 2009

The most widely used block convolution method is the overlap save algorithm (OSA), where a block of M data to be convolved with a filter is concatenated with the previous block and 2M-point FFT and multiplications are performed for this overlapped block. By discarding half of the results, we obtain linear convolution results from the circular convolution. This paper proposes a new transform which reduces the block size to only M for the block convolution. The proposed transform can be implemented as the M multiplications followed by M-point FFT Hence, existing efficient FFT libraries and hardware can be exploited for the implementation of proposed method. Since the required transform size is half that of the conventional method, the overall computational complexity is reduced. Also the reduced transform size results in the reduction of data access time and cash miss-hit ratio, and thus the overall CPU time is reduced. Experiments show that the proposed method requires less computation time than the conventional OSA.

• The Journal of the Acoustical Society of Korea
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• 제39권5호
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• pp.414-423
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• 2020

In this paper, we propose a Dilated Convolution Gate Linear Unit (DCGLU) to mitigate the lack of sparsity and small receptive field problems caused by the segmentation map extraction process in sound event detection with weak labels. In the advent of deep learning framework, segmentation map extraction approaches have shown improved performance in noisy environments. However, these methods are forced to maintain the size of the feature map to extract the segmentation map as the model would be constructed without a pooling operation. As a result, the performance of these methods is deteriorated with a lack of sparsity and a small receptive field. To mitigate these problems, we utilize GLU to control the flow of information and Dilated Convolutional Neural Networks (DCNNs) to increase the receptive field without additional learning parameters. For the performance evaluation, we employ a URBAN-SED and self-organized bird sound dataset. The relevant experiments show that our proposed DCGLU model outperforms over other baselines. In particular, our method is shown to exhibit robustness against nature sound noises with three Signal to Noise Ratio (SNR) levels (20 dB, 10 dB and 0 dB).

• Journal of the Korean Mathematical Society
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• 제53권1호
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• pp.147-159
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• 2016

In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.47-55
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• 2009

In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, S$\u{a}$l$\u{a}$gean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.217-232
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• 2011

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.