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Addition Formulas of Leaf Functions and Hyperbolic Leaf Functions

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Computer Modeling in Engineering & Sciences 2020年第5期123卷 441-473页

作者： kazunori Shinohara Department of Mechanical Systems Engineering Daido UniversityNagoya457-8530Japan

Addition formulas exist in trigonometric ***-angle and half-angle formulas can be derived from these ***,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary *** inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher *** such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary *** this study,we refer to this function as the hyperbolic leaf *** making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf *** the addition formulas,we can also derive the double-angle and half-angle *** then verify the consistency of these formulas by constructing graphs and numerical data.

关键词： Leaf functions hyperbolic leaf functions lemniscate functions Jacobi elliptic functions ordinary differential equations nonlinear equations

Lemniscate of Leaf Function

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Computer Modeling in Engineering & Sciences 2021年第1期126卷 275-292页

作者： kazunori Shinohara Department of Mechanical Systems Engineering Daido University10-3 Takiharu-choMinami-kuNagoya457-8530Japan

A lemniscate is a curve defined by two foci,F_(1) and F_(2).If the distance between the focal points of F_(1)−F_(2) is 2a(a:constant),then any point P on the lemniscate curve satisfy the equation PF_(1)·PF_(2)=a^(2).Jacob Bernoulli first described the lemniscate in *** Fagnano discovered the double angle formula of the lemniscate(1718).The Euler extended the Fagnano’s formula to a more general addition theorem(1751).The lemniscate function was subsequently proposed by Gauss around the year *** insights were summarized by Jacobi as the theory of elliptic functions.A leaf function is an extended lemniscate *** formulas of leaf functions have been presented in previous papers;these included the addition theorem of this function and its application to nonlinear *** this paper,the geometrical properties of leaf functions at n=2 and the geometric relation between the angle θ and lemniscate arc length l are presented using the lemniscate *** relationship between the leaf functions sleaf_(2)(l)and cleaf_(2)(l)is derived using the geometrical properties of the lemniscate,similarity of triangles,and the Pythagorean *** the literature,the relation equation for sleaf_(2)(l)and cleaf_(2)(l)(or the lemniscate functions,sl(l)and cl(l))has been derived analytically;however,it is not derived geometrically.

关键词： Geometry lemniscate of Bernoulli leaf functions lemniscate functions Pythagorean theorem triangle similarity

Exact Solutions of the Cubic Duffing Equation by Leaf Functions under Free Vibration

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Computer Modeling in Engineering & Sciences 2018年第5期115卷 149-215页

作者： kazunori Shinohara Daido University 10-3 Takiharu-choMinami-kuNagoya 457-8530Japan

Exact solutions of the cubic Duffing equation with the initial conditions are *** exact solutions are expressed in terms of leaf functions and trigonometric *** leaf function r=sleafn(t)or r=cleafn(t)satisfies the ordinary differential equation dx2/dt2=-*** second-order differential of the leaf function is equal to-n times the function raised to the(2n-1)power of the leaf *** using the leaf functions,the exact solutions of the cubic Duffing equation can be derived under several *** solutions are constructed using the integral functions of leaf functions sleaf2(t)and cleaf2(t)for the phase of a trigonometric *** the leaf function and the trigonometric function are used in combination,a highly accurate solution of the Duffing equation can be easily obtained based on the data of leaf *** this study,seven types of the exact solutions are derived from leaf functions;the derivation of the seven exact solutions is detailed in the ***,waves obtained by the exact solutions are graphically visualized with the numerical results.

关键词： Duffing equation nonlinear equations ordinary differential equation leaf functions

Damped and Divergence Exact Solutions for the Duffing Equation Using Leaf Functions and Hyperbolic Leaf Functions

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Computer Modeling in Engineering & Sciences 2019年第3期118卷 599-647页

作者： kazunori Shinohara Daido University 10-3 Takiharu-choMinami-kuNagoya 457-8530Japan

According to the wave power rule,the second derivative of a functionχ(t)with respect to the variable t is equal to negative n times the functionχ(t)raised to the power of 2n?*** the ordinary differential equations numerically results in waves appearing in the *** ordinary differential equation is very simple;however,waves,including the regular amplitude and period,are drawn in the *** this study,the function for obtaining the wave is called the leaf *** on the leaf function,the exact solutions for the undamped and unforced Duffing equations are *** the ordinary differential equation,in the positive region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes ***,in the case that the curves vary with the time under the conditionχ(t)>0,the gradient dχ(t)/d constantly decreases as time *** is,the tangential vector on the curve of the graph(with the abscissa and the ordinate χ(t)changes from the upper right direction to the lower right direction as time *** the other hand,in the negative region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes *** gradient d χ(t)/d constantly increases as time *** is,the tangent vector on the curve changes from the lower right direction to the upper right direction as time *** the behavior occurring in the positive region of the variable χ(t)and the behavior occurring in the negative region of the variableχ(t)alternately occur in regular intervals,waves appear by these *** this paper,I present seven types of damped and divergence exact solutions by combining trigonometric functions,hyperbolic functions,hyperbolic leaf functions,leaf functions,and exponential *** each type,I show the derivation method and numerical examples,as well as describe the features of the waveform.

关键词： Leaf functions hyperbolic leaf functions lemniscate functions jacobi elliptic functions ordinary differential equations duffing equation nonlinear equations

Weakly Closed Graphs and F-Purity of Binomial Edge Ideals

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Algebra Colloquium 2018年第4期25卷 567-578页

作者： kazunori Matsuda Kitami Institute of Technology Kitami

Herzog,Hibi,Hreinddttir et *** the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is *** this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly *** fact is a generalization of Ohtani's theorem.

关键词： binomial edge ideal closed graph weakly closed graph F-pure

Efficacy of glucagon-like peptide-1 mimetics for neural regeneration

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Neural Regeneration Research 2015年第11期10卷 1723-1724页

作者： kazunori Sango kazunori Utsunomiya Diabetic Neuropathy Project (Former ALS/Neuropathy project) Department of Sensory and Motor Systems Tokyo Metropolitan Institute of Medical Science Division of Diabetes Metabolism & Endocrinology Department of Internal Medicine Jikei University School of Medicine

Glucagon-like peptide 1（GLP-1）is secreted from enteroendocrine L cells in response to nutrient ingestion and exhibits insulinotropic properties by stimulating specific G protein-linked receptors（GLP-1Rs）on pancreaticβ*** GLP-1 mimetics,such as exenatide（exendin-4（Ex-4））,liraglutide,and lixisenatide,have been developed and approved as treatments for patients with type 2 *** peptides show bioactiv-ities almost identical to those of GLP- 1 and have a substantially longer plasma half-life than GLP-1 because of their resistance to dipeptidyl peptidase-4, a GLP-1 degrading enzyme.

关键词： GLP DRG Efficacy of glucagon-like peptide-1 mimetics for neural regeneration

Novel neuron-Schwann cell co-culture models to study peripheral nerve degeneration and regeneration

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Neural Regeneration Research 2023年第8期18卷 1732-1733页

作者： kazunori Sango Diabetic Neuropathy Project Department of Diseases and InfectionTokyo Metropolitan Institute of Medical ScienceTokyoJapan

Schwann cells are glial cells in the peripheral nervous system that provide trophic support for the growth and maintenance of sensory,motor,and autonomic neurons and ensheath their axons in either a myelinating or an unmyelinating *** Schwann cells wrap around largedia meter axons to form m ultilayered myelin structures essential for the rapid action potential propagation from one node of Ranvier to the next node(saltatory conduction).

关键词： degeneration culture conduction

Magic sheets:Visual cryptography with common shares

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Computational Visual Media 2018年第2期4卷 185-195页

作者： Naoki Kita kazunori Miyata Japan Advanced Institute of Science and Technology Nomi923-1292Japan.

Visual cryptography(VC) is an encryption technique for hiding a secret image in distributed and shared images(referred to as shares). VC schemes are employed to encrypt multiple images as meaningless,noisy patterns or meaningful images. However,decrypting multiple secret images using a unique share is difficult with traditional VC. We propose an approach to hide multiple images in meaningful shares. We can decrypt multiple images simultaneously using a common share, which we refer to as a magic sheet. The magic sheet decrypts multiple secret images depending on a given share. The shares are printed on transparencies, and decryption is performed by physically superimposing the transparencies. We evaluate the proposed method using binary, grayscale,and color images.

关键词： visual cryptography (VC) information hiding secret sharing

Potential utility of aldose reductase-deficient Schwann cells IKARS1 for the study of axonal degeneration and regeneration

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Neural Regeneration Research 2018年第6期13卷 979-980页

作者： Naoko Niimi kazunori Sango Diabetic Neuropathy Project Department of Sensory and Motor Systems Tokyo Metropolitan Institute of Medical Science

Diabetic peripheral neuropathy（DPN）is one of the most common and intractable complications of diabetes *** irritating symptoms,such as paresthesia,hyperalgesia and allodynia,can be causes of insomnia and depression;whereas its progression to more advanced stages can result in serious consequences,such as lower limb amputations and lethal arrhythmias.

关键词： DPN Potential utility of aldose reductase-deficient Schwann cells IKARS1 for the study of axonal degeneration and regeneration NGF NCV AR PNS