133 research outputs found
New contractivity condition in a population model with piecewise constant arguments
No full textAbstractIn this paper, we improve contractivity conditions of solutions for the positive equilibrium N∗=1a+∑i=0mbi of the following differential equation with piecewise constant arguments:{dN(t)dt=N(t)r(t){1−aN(t)−∑i=0mbiN(n−i)},n⩽t<n+1,n=0,1,2,…,N(0)=N0>0andN(−j)=N−j⩾0,j=1,2,…,m, where r(t) is a nonnegative continuous function on [0,+∞), r(t)≢0, ∑i=0mbi>0, bi⩾0, i=0,1,2,…,m, and a+b0>∑i=1mbi. In particular, for the case a=0 and m⩾1, we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75–83]). For the other case a≠0 and m⩾1, under the condition ∑j=1mbj−2b0<a⩽(∑j=1mbj)/(1+b0/∑j=0mbj), the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] and others
Global attractivity for discrete models of nonautonomous logistic equations
No full textAbstractConsider the following discrete model of a nonautonomous logistic equation: {N(n+1)=N(n)exp{c(n)−∑j=0mbj(n)N(n−j)},n≥0,N(0)=N0>0andN(−j)=N−j≥0,1≤j≤m, where c(n) and bj(n),0≤j≤m,n≥0 are bounded and c(n)>0,b0(n)>0,bj(n)≥0,1≤j≤m,n≥0. In this paper, using some kind of iterative method to the above equation, we establish sufficient conditions that ensure the global attractivity for solutions. The result is an extension of the former work [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2004) 560–580] to the nonautonomous case
Persistence and global stability in discrete models of Lotka–Volterra type
No full textAbstractIn this paper, we establish new sufficient conditions for global asymptotic stability of the positive equilibrium in the following discrete models of Lotka–Volterra type:{Ni(p+1)=Ni(p)exp{ci−aiNi(p)−∑j=1naijNj(p−kij)},p⩾0,1⩽i⩽n,Ni(p)=Nip⩾0,p⩽0,andNi0>0,1⩽i⩽n, where each Nip for p⩽0, each ci, ai and aij are finite and{ai>0,ai+aii>0,1⩽i⩽n,andkij⩾0,1⩽i,j⩽n. Applying the former results [Y. Muroya, Persistence and global stability for discrete models of nonautonomous Lotka–Volterra type, J. Math. Anal. Appl. 273 (2002) 492–511] on sufficient conditions for the persistence of nonautonomous discrete Lotka–Volterra systems, we first obtain conditions for the persistence of the above autonomous system, and extending a similar technique to use a nonnegative Lyapunov-like function offered by Y. Saito, T. Hara and W. Ma [Y. Saito, T. Hara, W. Ma, Necessary and sufficient conditions for permanence and global stability of a Lotka–Volterra system with two delays, J. Math. Anal. Appl. 236 (1999) 534–556] for n=2 to the above system for n⩾2, we establish new conditions for global asymptotic stability of the positive equilibrium. In some special cases that kij=kjj, 1⩽i,j⩽n, and ∑j=1najiajk=0, i≠k, these conditions become ai>∑j=1naji2, 1⩽i⩽n, and improve the well-known stability conditions ai>∑j=1n|aji|, 1⩽i⩽n, obtained by K. Gopalsamy [K. Gopalsamy, Global asymptotic stability in Volterra's population systems, J. Math. Biol. 19 (1984) 157–168]
Dynamics of ionized poly(4-hydroxystyrene)-type resist polymers with tert-butoxycarbonyl-protecting group
No full textOkamoto K., Muroya Y., Kozawa T.. Dynamics of ionized poly(4-hydroxystyrene)-type resist polymers with tert-butoxycarbonyl-protecting group. Scientific Reports 14, 16729 (2024); https://doi.org/10.1038/s41598-024-67794-0.The imaging reactions of resist materials used for nano-patterning have become radiation-chemical reactions, with the shortening of wavelengths of the exposure light sources in lithography systems. The most widely used patterning materials in industrial lithography are chemically amplified resists (CAR). Understanding the deprotonation mechanism of ionized polymers (radical cations) is important for acid generation in CARs. In this study, the dynamics of radical cations in poly(4-hydroxystyrene) (PHS)–type resist polymers, partially and totally protected by tert-butoxycarbonyl (t-BOC) groups, are investigated using a combination of electron pulse radiolysis experiments, acid yield measurements, and quantum chemical calculations. The t-BOC(oxy) group exhibits π-electron-donating behavior in the monomer cation but changes to electron-accepting behavior in the polymer cation, owing to the interaction between substituents. The destabilization of radical cations due to decreased intramolecular charge resonance may contribute to the high deprotonation efficiency of t-BOC-capped PHS polymers
Dynamics of ionized poly(4-hydroxystyrene)-type resist polymers with tert-butoxycarbonyl-protecting group
No full textOkamoto K., Muroya Y., Kozawa T.. Dynamics of ionized poly(4-hydroxystyrene)-type resist polymers with tert-butoxycarbonyl-protecting group. Scientific Reports 14, 16729 (2024); https://doi.org/10.1038/s41598-024-67794-0.The imaging reactions of resist materials used for nano-patterning have become radiation-chemical reactions, with the shortening of wavelengths of the exposure light sources in lithography systems. The most widely used patterning materials in industrial lithography are chemically amplified resists (CAR). Understanding the deprotonation mechanism of ionized polymers (radical cations) is important for acid generation in CARs. In this study, the dynamics of radical cations in poly(4-hydroxystyrene) (PHS)–type resist polymers, partially and totally protected by tert-butoxycarbonyl (t-BOC) groups, are investigated using a combination of electron pulse radiolysis experiments, acid yield measurements, and quantum chemical calculations. The t-BOC(oxy) group exhibits π-electron-donating behavior in the monomer cation but changes to electron-accepting behavior in the polymer cation, owing to the interaction between substituents. The destabilization of radical cations due to decreased intramolecular charge resonance may contribute to the high deprotonation efficiency of t-BOC-capped PHS polymers
Mental retardation in a boy with an interstitial deletion at Xp22.3 involving STS, KAL1, and OA1: implication for the MRX locus
No full textPersistence, contractivity and global stability in logistic equations with piecewise constant delays
No full textAbstractWe establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N∗=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: dN(t)dt=N(t)r(t)1−aN(t)−∑i=0mbiN(n−i),n⩽t<n+1,n=0,1,2,…,N(0)=N0>0andN(−j)=N−j⩾0,j=1,2,…,m, where r(t) is a nonnegative continuous function on [0,+∞), r(t)≢0, ∑i=0mbi>0, bi⩾0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: dx(t)dt=x(t)r(t){1−ax(t)−g(x([t]),x([t−1]),…,x([t−m]))},t⩾0,x(−k)=φ(−k)⩾0,0⩽k⩽m,andφ(0)>0, where r(t) is a nonnegative continuous function on [0,+∞), r(t)≢0, 1−ax−g(x,x,…,x)=0 has a unique solution x∗>0 and g(x0,x1,…,xm)∈C1[(0,+∞)×(0,+∞)×⋯×(0,+∞)]
Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments
No full textIn this paper, a logistic equation with multiple piecewise constant arguments is investigated in detail. We generalize the approach in two papers, [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2) (2004) 560580] and [Y. Muroya, E. Ishiwata, N. Guglielmi, Global stability for nonlinear difference equations with variable coefficients, J. Math. Anal. Appl. 334 (1) (2007) 232247], and establish a new condition for the global stability of the equation. Their results are given as one of the special cases. Moreover, we improve the 3/2 type stability condition under several dominance assumptions on the coefficients of the equation. Some examples and numerical simulations are also presented. All of these examples show that there are several conditions for the global stability of the equation, depending on the coefficients on the delay terms of the equation, beyond the 3/2 type stability condition. © 2010 Elsevier Ltd. All rights reserved
Mental retardation in a boy with an interstitial deletion at Xp22.3 involving STS, KAL1, and OA1: Implication for MRX locus.
No full textOperational semantics with hierarchical abstract syntax graphs
No full textThis is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical language automatically incorporates desirable features, such as α-equivalence and how it can describe pure computation, imperative store, and control features in a uniform framework. The graph semantics combines some of the best features of structural operational semantics and abstract machines, while offering powerful new methods for reasoning about contextual equivalence. All technical details are available in an extended technical report by Muroya and the author [11] and in Muroya’s doctoral dissertation [21].</p
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