| Published Papers |
| No. | Title URL, Journal, Vol( Number), From Page- To Page, Publication date, DOI
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| 1 | Exploring of the relationship between a circle and a hyperbola" , Far East Journal of Mathematical Education, 25( 2), 47- 55, Nov. 2023,
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| 2 | Geometric structure of sum of the powers of a natural number , Far East Journal of Mathematical Education, 24( 1), 37- 44, Jun. 2023,
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| 3 | Proof without words: The sum of the product of two consecutive integers , Far East Journal of Mathematical Educatio, 24( 1), 17- 20, Mar. 2023,
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| 4 | Proof without words: Relationship among the sum of cubic integer numbers, sum of consecutive odd numbers, and sum of natural numbers , Far East Journal of Mathematical Education, 24( 1), 1- 3, Jan. 2023,
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| 5 | Using the sum of triangular numbers as the most fundamental number of combinations found using heuristic methods , European Journal of Pure and Applied Mathematics, 15( 3), 1237- 1253, Jul. 2022,
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| 6 | A pedagogical study of geometric relations between the sums of cubic integer numbers and the sums of square integer numbers with the sums of odd numbers , European Journal of Pure and Applied Mathematics, 15( 3), 864- 877, Jul. 2022,
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| 7 | Proof without words: a = c ⇒ a = c = a ± c / b ± d in the range of natural numbers , Far East Journal of Mathematical Education, 22( 1), 29- 32, Jun. 2022,
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| 8 | Proof without words: Relationship between the sum of natural numbers and the sum of the product of two consecutive integer , Far East Journal of Mathematical Education, 22( 1), 1- 3, Feb. 2022,
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| 9 | Incident position of refracted light beam for reaching a target point , Far East Journal of Mathematical Education, 21( 2), 143- 154, Dec. 2021,
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| 10 | Proof without Words: Relationship between the sum of triangular numbers, sum of natural numbers, and sum of square numbers , Far East Journal of Mathematical Education, 21( 1), 83- 91, Jun. 2021,
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| 11 |
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| 12 | Proof without words: Relationship between combination ({n}_C_{2))^{2} and sum of cubic numbers , Far East Journal of Mathematical Education, 20( 3), 79- 82, Nov. 2020,
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| 13 | Proof without words: The relation among $\cos (60^{\circ} \pm \theta)$, $\sin (60^{\circ} \pm \theta)$, $\cos (30^{\circ} \pm \theta)$, and $\sin (30^{\circ} \pm \theta)$ , Far East Journal of Mathematical Education, 20( 1), 37- 38, Jun. 2020,
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| 14 | An illustrated guide to effect of phase to wave phenomena , Journal of Physics Education (IAPT), 35( 4), Article Number 6 (11 pages)- , Jan. 2020,
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| 15 | Proof without words: Relationship between combination $_{n}C_{2}$ and arithmetic numbers from a pedagogical viewpoint , Far East Journal of Mathematical Education, 19( 1), 57- 58, 2019,
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| 16 | Proof without words: Sum of consecutive odd numbers $(2 n + 1) + (2 n - 1) = 4n$ , Far East Journal of Mathematical Education, 19( 1), 59- 60, 2019,
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| 17 | Recurrence relation between infinite series and generalised harmonic numbers from a pedagogical viewpoint , Far East Journal of Mathematical Education, 18, 101- 112, 2018,
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| 18 | Work done by internal forces on a multi body system with constraints , Journal of Physics Education (IAPT), 34( 1), Article Number: 5 (9 pages)- , 2018,
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| 19 |
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| 20 | Proof without words: Product of sum and difference , , 17( 3), 163- , 2017,
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| 21 |
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| 22 | Alternative method for introducing torque and angular momentum , Journal of Physics Education (IAPT), 32( 1), Article Number: 3 (10 pages)- , 2016,
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| 23 |
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| 24 | Elementary remarks on the ambiguous explanation of pressure in chemical thermodynamics , Journal of Physics Education (IAPT), 31( 1), Article Number: 5 (7 pages)- , 2015,
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| 25 |
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| 26 |
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| 27 | Simple and intuitive mathematics for learning elementary physics , JPS Conference Proceedings, 1, 17036- , 2014,
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| 28 | Commutative law for the multiplication of matrices as viewed in terms of Hankel's principle , , 7, 405- 411, 2014,
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| 29 | Recursion formulae of 1 ℓ + 2 ℓ + ··· + n ℓ and their combinatoric meaning in terms of the tree diagrams , International Journal of Mathematical Education in Science and Technology, 44( 1), 132- 142, Jan. 2013, https://doi.org/10.1080/0020739X.2012.662298 |
| 30 | Proof without words: Tangent double angle identity , College Mathematics Journal, 44, 47- , 2013,
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| 31 | Proof without words: Triangular sums , College Mathematics Journal, 44, 189- , 2013,
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| 32 | Visual thinking of mathematical concepts , Far East Journal of Mathematical Education, 10, 157- 174, 2013,
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| 33 | Pedagogical framework of elementary mechanics comparable to elementary electromagnetism: Introductory approach without reliance on equation of motion , Journal of Physics Education (IAPT), 28( 2), Aarticle Number: 6 (10 pages)- , 2012,
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| 34 | Common characteristics of elementary second-order ordinary differential equations with constant coefficients from a unified viewpoint , Far East Journal of Mathematical Education, 9, 185- 193, 2012,
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| 35 | Geometrical meaning of arithmetic series ∑ n<inf>k=1</inf> k, ∑ n<inf>k=1</inf> k 2 and ∑ n<inf>k=1</inf> k 3 in terms of the elementary combinatorics , International Journal of Mathematical Education in Science and Technology, 42( 5), 657- 664, Jul. 2011, https://doi.org/10.1080/0020739X.2010.550943 |
| 36 | Integral representation of the pictorial proof of ∑<inf>k=1</inf> n k 2 = 1/6 n(n+1)(2n+1) , International Journal of Mathematical Education in Science and Technology, 42( 2), 235- 239, Mar. 2011, https://doi.org/10.1080/0020739X.2010.510223 |
| 37 |
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| 38 |
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| 39 | A new approach to elementary mechanics , Journal of the Physics Education Society of Japan Supplement, , 276- 277, 2009,
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| 40 | Reports on “The Sixth Workshop for Refreshing Science in the Classroom” in Kanto-Area , Japanese Journal of Applied Physics Education, 33, 39- 44, 2009,
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| 41 | Intuitive understanding of solutions of partially differential equations , International Journal of Mathematical Education in Science and Technology, 39( 3), 365- 371, Apr. 2008, https://doi.org/10.1080/00207390600913343 |
| 42 | Understanding physics without using visual images , Japanese Journal of Applied Physics Education, 32, 51- 56, 2008,
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| 43 | Remarks on viewing situation in a rotating frame , European Journal of Physics, 29, 599- 606, 2008,
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| 44 |
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| 45 | Triangles As Viewed from Above , An International Journal Mathematics and Informatics Quarterly, 17, 116- 120, 2007,
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| 46 |
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| 47 | Relations among Powers of 2, Combinations, and Symbolic Algerba , Mathematics Teacher, 99( 8), 577- 578, 2006,
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| 48 | Instantaneous center of rotation in plane motion of sliding rod , IPS Physics Update Journal, 9, 35- 37, 2005,
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| 49 | Computer simulation of billiards problem , International Physics Education Newsletter, , 179- 181, 2005,
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| 50 |
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| 51 | A geometrical meaning of the triple angle formulas , An International Journal Mathematics and Informatics Quarterly, 15( 3), 93- 95, 2005,
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| 52 | Mathematical modeling of metal leaves , Mathematics Magazine, 76, 295- 298, 2003,
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| 53 | A simple derivation of the Doppler effect formulae , IPS Physics Update Journal, 8, 22- 24, 2003,
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| 54 | A geometrical key to solution of differential equation : d2x(t)/dt2 = -w2x(t) , Mathematical Gaaette, 87, 163- 166, 2003,
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| 55 | Center of Rotation of Rigid Bodies in a Plane , BUTSURI}, 57, 767- 768, 2002,
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| 56 | Significance of the Measurement of Physical Quantities: A Connection between Science Education and Mathematics Education  , Journal of the Physics Education Society of Japan, 50( 4), 243- 247, 2002, https://doi.org/10.20653/pesj.50.4_243 |
| 57 |
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| 58 | Combining trigonometrical functions through vector multiplication , The Mathematical Gazette, 85, 124- 125, 2001,
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| 59 | Derivative of trigonometrical functions via matrices , The Mathematical Gazette, 85, 116- 117, 2001,
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| 60 | Flow of ions in electrolyte solutions : Comparison of the fractal growth of metal leaves by electrodeposition and the simulation of DLA clusters , , , 57- 60, 2001,
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| 61 | Mathematics without Words , College Mathematics Journal, 32, 14- , 2001,
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| 62 |
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| 63 |
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| 64 | Are mixed numbers consistent with the rules of algebra? , Mathematics in School, 30, 28- , 2001,
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| 65 | Geometrical meaning of the quotient rule for differentiation , The Mathematical Gazette, 84, 303- 304, 2000,
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| 66 |
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| 67 | Physical foundation of protein architecture , International Journal of Modern Physics B, 13( 19), 2431- 2529, Jul. 1999,
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| 68 | Evaluation of Protein Secondary Structure Prediction , RIKEN Review, 25, 16- 17, 1999,
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| 69 |
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| 70 |
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| 71 | A geometric view of a vector identity , College Mathematics Journal, 29, 309- 310, 1998,
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| 72 | Trigonometric Identity : the difference of two sines or two cosines , College Mathematics Journal, 29, 133- , 1998,
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| 73 | Protein structure prediction by the island model , RIKEN Review, 19, 70- 72, 1998,
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| 74 | Trigonometric identity: The sum of two sines or two cosines , The College Mathematics Journal, 29, 157- 157, 1998,
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| 75 |
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| 76 |
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| 77 | Note on the evaluation method of the configurational partition function of a polypeptide molecule: Relationship between the matrix method and the generating function method , Journal of Chemical Physics, 104( 16), 6405- 6406, Apr. 1996, https://doi.org/10.1063/1.471767 |
| 78 | Development of statistical mechanical method for predicting protein secondary structures , High Performance Computing in RIKEN 1995, 1, 221- 223, 1996,
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| 79 | A model for neutron emission from condensed matter , Progress in New Hydrogen Energy, ( 1), 319- 323, 1996,
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| 80 | Cytochrome b562: Electroactive protein for bioelectronics , Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 255( 1), 271- 278, Oct. 1994, https://doi.org/10.1080/10587259408029798 |
| 81 | Protein secondary structure prediction using a statistical mechanical method , Protein Engineering, 7( 9), 1164- 1164, Sep. 1994,
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| 82 | Refolding of cytochrome b<inf>562</inf> and its structural stabilization by introducing a disulfide bond , Journal of Protein Chemistry, 12( 2), 121- 131, Apr. 1993, https://doi.org/10.1007/BF01026033 |
| 83 | Site-Directed mutagenesis of cytochrome b$_{562}$ for stabilization to form two-dimensional regular array , Electricity and Magnetism in Biology and Medicine, , 191- 194, 1993,
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| 84 | Refolding of BPTI and its intermediates , Computer Aided Innovation of New Materials II, PTS 1 AND 2, , 1275- 1278, 1993,
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| 85 | Statistical mechanical method for predicting secondary structures , Protein Engineering, 6, 1027- , 1993,
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| 86 |
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| 87 |
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| 88 | Tunnel disintegration and neutron emission probability , Frontiers of Cold Fusion (Universal Academy Press, Inc.), , 589- 592, 1992,
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| 89 | Third-order optical nonlinearities of soluble polythiophenes , Molecular Crystals and Liquid Crystals Science and Technology SectionB : Nonlinear Optics, 3, 169- 182, 1992,
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| 90 | Mechanism of protein folding and its application to structure prediction of proteins , Report on Progress of Polymer Physics in Japan, 35, 1- 22, 1992,
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| 91 | Folding mechanism of cytochrome $b_{562}$ , Proceedings of Frontier Research Forum on BIOELECTRONIC MATERIALS, , 9- 15, 1991,
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| 92 |
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| 93 |
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| 94 | Momentum dependence of the dynamic structure factor of core electrons in metallic lithium , Journal of the Physical Society of Japan, 56( 8), 2940- 2947, Aug. 1987, https://doi.org/10.1143/JPSJ.56.2940 |
| 95 | New representation of quantum chaos , Physics Letters A, 101( 3), 115- 119, 1984,
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