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김대열 대한뇌신경재활학회 2014 뇌신경재활 Vol.7 No.2
The brain stem consists of medulla oblongta, pons and midbrain. It is sited in posterior cranial fossa. It contains numerous intrinsic neuron cell bodies and their processes, some of which are the brain stem homologues of spinal neuronal groups. These include the sites of termination and cells of origin of axons that enter or leave the brain stem through the cranial nerves. Cranial nerves provide sensory, motor and autonomic innervations of structures that are mostly in the head and neck. The reticular formation is an extensive network of neurons that extends throughout the length of brain stem and is continuous rostrally to diencephalon and caudally to its spinal counterpart. Clinically, damage to the brain stem is often devastating and life threatening. This is because it is a structurally and functionally compact region. Therefore, it is important to build basic knowledge about neuroanatomy of brain stem.
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APPLICATION OF CONVOLUTION SUM ΣN−1 k=1 σ1(k)1(2nN − 2nk)
김대열,김애란 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.1
Let S±(n;k) := {(a; b; x; y) ∈N4 : ax+by = n; x ≡ ±y (mod k)}.From the formula Σ(a;b;x;y)∈S±(n;k)ab = 4Σm∈Nm<n=kσ1(m)σ1(n - km)+1/6 σ3(n)- 1/6σ1(n)-σ3( n/k )+nσ1( n/k ), we find the Diophantine solutions formodulo 2m′and 3m′, where m′ ∈ N.
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ON THE CONVOLUTION SUMS OF CERTAIN RESTRICTED DIVISOR FUNCTIONS
김대열,김애란,Ayyadurai Sankaranarayanan 호남수학회 2013 호남수학학술지 Vol.35 No.2
We study convolution sums of certain restricted divisor functions in detail and present explicit evaluations in terms of usual divisor functions for some specific situations.
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Congruences of the Weierstrass p(x) and p"(x)(x=1/2,τ/2,τ+1/2)-functions on divisors
김대열,Aeran Kim,박화신 대한수학회 2013 대한수학회보 Vol.50 No.1
In this paper, we find the coefficients for the Weierstrass p(x) and p"(x)(x=1/2,τ/2,τ+1/2)-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan ([23]). Finally, we reprove congruences for the functions μ(n) and ν(n) in Hahn’s article [11, Theorems 6.1 and 6.2].
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CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS
김대열 호남수학회 2013 호남수학학술지 Vol.35 No.3
Let s(N) denote the sum of the s-th power of the positivedivisors of N and s;r(N;m) =PdjNdr mod mds with N; m; r; s; d2 Z, d; s > 0 and r 0. In a celebrated paper [33], RamanujanprovedPN 1k=1 1(k)1(N k) = 5123(N)+ 1121(N) 612N1(N) usingelementary arguments. The coecients' relation in this identity( 512 + 112 612 = 0) motivated us to write this article. In this article,we found the convolution sumsPk<N=m 1;i(dk; 2)1;j(N mk; 2)for odd and even divisor functions with i; j = 0; 1, m = 1; 2; 4,and djm. If N is an odd positive integer, i; j = 0; 1, m = 1; 2; 4,s = 0; 1; 2, and djmj2s P , then there exist u; a; b; c 2 Z satisfyingk<2sN=m 1;i(dk; 2)1;j(2sN mk; 2) = 1u [a3(N) + bN1(N) +c1(N)] with a + b + c = 0 and (u; a; b; c) = 1(Theorem 1.1). Wealso give an elementary problem (O) and solve special cases of themin (O) (Corollary 3.27).
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김대열,고은실,강보성,한태륜,이시욱 대한재활의학회 2008 Annals of Rehabilitation Medicine Vol.32 No.1
Objective: To investigate the benefit of electrical stimulation for dysphagia caused by stroke. Method: Ten consecutive stroke patients with dysphagia for 3 months or more were enrolled in this study and assigned to one of the two group (electrical stimulation group or sham group) according to randomization table. Five patients were allocated to electrical stimulation group and 5 patients to sham group. One patient in the sham group dropped out because of transfer to other hospital. Electrical stimulation with a maximal tolerable intensity was applied on both digastric muscles and both thyrohyoid muscles for 1 hour, 5 days a week for 4weeks in electrical stimulation group. Sham group received electrical stimulation in same condition except stimulation intensity of 1 mA. Clinical dysphagia scale, functional dysphagia scale and kinematic analysis of hyoid bone movement were assessed at baseline (before treatment), 2 weeks later (during treatment), 4 weeks later (after treatment). Results: The clinical dysphagia scale decreased in both group, of which the difference was not statistically significant. The functional dysphagia scale decreased significantly in the electrical stimulation group. The electrical stimulation group revealed greater improvement in clinical dysphagia scale and functional dysphagia scale compared to sham group. Conclusion: Electrical stimulation therapy with a maximally tolerable intensity to digastric and thyroid muscles might be effective in chronic stroke patients with dysphagia. Objective: To investigate the benefit of electrical stimulation for dysphagia caused by stroke. Method: Ten consecutive stroke patients with dysphagia for 3 months or more were enrolled in this study and assigned to one of the two group (electrical stimulation group or sham group) according to randomization table. Five patients were allocated to electrical stimulation group and 5 patients to sham group. One patient in the sham group dropped out because of transfer to other hospital. Electrical stimulation with a maximal tolerable intensity was applied on both digastric muscles and both thyrohyoid muscles for 1 hour, 5 days a week for 4weeks in electrical stimulation group. Sham group received electrical stimulation in same condition except stimulation intensity of 1 mA. Clinical dysphagia scale, functional dysphagia scale and kinematic analysis of hyoid bone movement were assessed at baseline (before treatment), 2 weeks later (during treatment), 4 weeks later (after treatment). Results: The clinical dysphagia scale decreased in both group, of which the difference was not statistically significant. The functional dysphagia scale decreased significantly in the electrical stimulation group. The electrical stimulation group revealed greater improvement in clinical dysphagia scale and functional dysphagia scale compared to sham group. Conclusion: Electrical stimulation therapy with a maximally tolerable intensity to digastric and thyroid muscles might be effective in chronic stroke patients with dysphagia.
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A REMARK OF P_(i,k) ON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING
김대열,김민수 호남수학회 2011 호남수학학술지 Vol.33 No.2
Greg(Greg) considered that [수식]where the P_(i,k)'s were polynomials with positive integer coefficients. In this paper, we will give the equations for ∑ P_(i,k) modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.
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CERTAIN COMBINATORIC CONVOLUTION SUMS AND THEIR RELATIONS TO BERNOULLI AND EULER POLYNOMIALS
김대열,Abdelmejid Bayad,Nazli Yildiz Ikikardes 대한수학회 2015 대한수학회지 Vol.52 No.3
In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as ap- plications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.
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