• Korean Journal of Mathematics
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• v.32 no.3
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• pp.439-451
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• 2024

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space SC₁(∆, q) which coincides with C¹₁(X, ∆, φ, λ, q) (one of the above defined Cesàro summable difference sequence spaces) under the restriction of bounded modulus function.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.193-206
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• 2010

In this paper we define and study the difference Orlicz space of entire sequence of fuzzy numbers. We study their different properties and statistical convergence in these spaces.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.591-595
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• 2006

In this paper, we define ${\Delta}^m$-Lacunary strongly convergent sequences defined by sequence of moduli and give various properties and inclusion relations on these sequence spaces.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.851-853
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• 2005

It is well known that the general term of a sequence can be represented by a linear combination of binomial coefficients. In this paper we give a simple proof for this fact.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• PNF and Movement
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• v.12 no.2
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• pp.97-106
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• 2014

Purpose: The purpose of this study was to investigate changes in EEG through attention. Concentration training and performing tasks are important factors in the improvement of motor learning ability. Methods: In the experiment, 22 healthy people were divided into two groups: the trail making test (TMT) group and the computerized neurocognitive function test (CNT) group. A one-way Neuro Harmony M test to see whether there was a significant difference among the groups. Results: The TMT group showed a significant increase in ${\alpha}$ wave, ${\alpha}$ wave sequence, and ${\beta}$ wave sequence; however, there were no significant differences in SMR wave, SMR wave sequence, and ${\beta}$ wave. The CNT group showed increases in ${\alpha}$ wave, ${\alpha}$ wave sequence, SMR wave, SMR wave sequence, and ${\beta}$ wave sequence; however, there was no significant difference in ${\beta}$ wave. In EEGs before and after two performance tasks were changed, there were significant differences in ${\beta}$ wave, SMR wave, SMR wave sequence; however, there were no significant differences in ${\alpha}$ wave sequence, ${\beta}$ wave, and ${\beta}$ wave sequence. Conclusion: Attention training and concentration training offer feedback and repetition for constant stimulus and response. Moreover, attention training and concentration training can contribute to new studies and motivation by developing fast sensory and motor skills through acceptable visual and auditory stimulation.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.219-228
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• 2024

In this paper, we compute the generalized 𝛼-Köthe Toeplitz duals of the X-valued (Banach space) difference sequence spaces E(X, ∆), E(X, ∆_𝜐) and obtain a generalization of the existing results for 𝛼-duals of the classical difference sequence spaces E(∆) and E(∆_𝜐) of scalars, E ∈ {ℓ_∞, c, c₀}. Apart from this, we compute the generalized 𝛼-Köthe Toeplitz duals for E(X, ∆^r) r ≥ 0 integer and observe that the results agree with corresponding results for scalar cases.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.2
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• pp.1-10
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• 1975

This paper presents an adaptive data compression algorithm for video data. The coling complexity due to the high correlation in the given data sequence is alleviated by coding the difference data, sequence rather than the data sequence itself. The adaptation to the nonstationary statistics of the data is confined within a code set, which consists of two constant length cades and six modified Shannon.Fano codes. lt is assumed that the probability distributions of tile difference data sequence and of the data entropy are Laplacian and Gaussion, respectively. The adaptive coding performance is compared for two code selection criteria: entropy and $P_r$[difference value=0]=$P_0$. It is shown that data compression ratio 2 : 1 is achievable with the adaptive coding. The gain by the adaptive coding over the fixed coding is shown to be about 10% in compression ratio and 15% in code efficiency. In addition, $P_0$ is found to he not only a convenient criterion for code selection, but also such efficient a parameter as to perform almost like entropy.