The stability of limit cycles in nonlinear systems

In this paper, a necessary condition is first presented for the existence of limit cycles in nonlinear systems, then four theorems are presented for the stability, instability, and semistabilities of limit cycles in second order nonlinear systems. Necessary and sufficient conditions are given in terms of the signs of first and second derivatives of a continuously differentiable positive function at the vicinity of the limit cycle. Two examples considering nonlinear systems with familiar limit cycles are presented to illustrate the theorems.     

Gaugeability for Feynman-Kac functionals with applications to symmetric -stable processes

For symmetric -stable processes, an analytic criterion for a measure being gaugeable was obtained by Z.-Q. Chen (2002), M. Takeda (2002) and M. Takeda and T. Uemura (2004). Applying it, we consider the ultracontractivity of Feynman-Kac semigroups and expectations of the number of branches hitting closed sets in branching symmetric -stable processes.

     

On the global wellposedness for the nonlinear Schrödinger equations with L p -large initial data

We consider the Cauchy problem for the nonlinear Schrödinger equations $ \begin{array}{l} iu_t + \triangle u \pm |u|^{p-1}u =0, \qquad x \in \mathbb{R}^d, \quad t \in \mathbb{R} \\ u(x,0)= u_0(x), \qquad x \in \mathbb{R}^d \end{array} $ for 1 < p < 1 + 4/d and prove that there is a ${\rho (p ,d) \in (1,2)}We consider the Cauchy problem for the nonlinear Schr?dinger equations

l iut + \triangle u ±|u|p-1u = 0,        x ? \mathbbRd,     t ? \mathbbR u(x,0) = u0(x),        x ? \mathbbRd \begin{array}{l} iu_t + \triangle u \pm |u|^{p-1}u =0, \qquad x \in \mathbb{R}^d, \quad t \in \mathbb{R} \\ u(x,0)= u_0(x), \qquad x \in \mathbb{R}^d \end{array}      26. Diastereoselective Synthesis of a Hydroazulene Derivative by Tandem Michael-Wittig Reactions      Tomoko Nagao  Masayoshi Isozaki  Tetsuya Fujimoto  Iwao Yamamoto 《Phosphorus, sulfur, and silicon and the related elements》2013,188(8-9):1975-1976 The reaction of a cyclic phosphonium ylide [ 1 ] with enoate 2 gives a hydroazulene derivative with stereoselectivity.      27. Yttrium‐Catalyzed Addition of Benzylic C?H Bonds of Alkyl Pyridines to Olefins      Dr. Bing‐Tao Guan  Dr. Baoli Wang  Dr. Masayoshi Nishiura  Prof. Dr. Zhaomin Hou 《Angewandte Chemie (International ed. in English)》2013,52(16):4418-4421       28. Thermoswitching property in TCNQ salts of ionenes containing poly(ethylene oxide) segments      Yoshio Takizawa  Hirotsugu Aiga  Masayoshi Watanabe  Isao Shinohara 《Journal of polymer science. Part A, Polymer chemistry》1983,21(11):3145-3153 Ionene polymers characterized by the alternating structure of ionene and crystalline poly(ethylene oxide) (PEO) segments were prepared as a function of PEO segment size. A microstructure of these ionenes and their 7,7,8,8-tetracyanoquinodimethane (TCNQ) salts were investigated with x-ray diffraction patterns, thermal scanning behavior, and polarizing micrographs. On the basis of this microstructure, the change in resistivity with temperature was studied. In Arrhenius' plots of the resistivity the simple salts in which the spherulites consisting of the PEO segments were observed showed a sharp decrease in resistivity with a rise in temperature [critical temperature resistor (CTR)] at about the melting point of the PEO segments, whereas the other simple salts in which the spherulites were not observed showed linear temperature dependence. The switching properties were confirmed similarly in repetitive heating/cooling cycles. This CTR characteristic was attributed to an increase in continuity in the conduction paths by melting spherulites. The apparent switching properties were not observed in the complex salts.      29. Reactive oligomers. I. Preparation and polymerization of ethylene glycol bis(methyl fumarate)      Akira Matsumoto  Guang-Jie Jiang  Masayoshi Oiwa 《Journal of polymer science. Part A, Polymer chemistry》1983,21(11):3191-3199 Ethylene glycol bis(methyl fumarate) (EGBMF) was prepared as a new type of divinyl compound and reactive oligomer: a needle crystal, m.p. 104.5°C. Homopolymerization of EGBMF was carried out in dioxane with 0.1 mol/L AIBN at [M] = 1 mol/L and 60°C; the rate of polymerization was estimated to be 4.44 × 10?6 mol/L s in a good agreement with diethyl fumarate (DEF). The cyclization constant Kc was obtained as 1.64 mol/L, being rather low compared with diallyl oxalate which is 1,9-diene having two ester groups analogous to EGBMF. Gelatin occurred at about 35% conversion. Finally, the copolymerization of EGBMF (M1) with diallyl phthalate (DAP) (M2) is tentatively explored with the intention of the improvement of allyl resins in mechanical properties; remarkable rate enhancement was observed for copolymerization. The monomer reactivity ratios were estimated to be r1 = 0.96 and r2 = 0.025, the r1 value being reduced compared with the DEF-DAP copolymerization system. These results are discussed from the standpoint of steric effect on the polymerization of fumarate as an internal olefin.      30. Reactive oligomers. II. Polymerization of glycol bis(allyl phthalate)s and glycol bis(allyl succinate)s      Akira Matsumoto  Yutaka Kukimoto  Kazuhiro Aoki  Masayoshi Oiwa 《Journal of polymer science. Part A, Polymer chemistry》1983,21(12):3493-3502 Seven glycol bis(allyl phthalate)s (GBAP) and four glycol bis(allyl succinate)s (GBASu) as reactive oligomers were prepared and their polymerization behaviors were investigated in detail in terms of cyclopolymerization and gelation as compared with diallyl dicarboxylates. Thus, the rates of polymerization of GBAPs were reduced compared to diallyl phthalate, being attributed to the steric effect on the intermolecular propagation of the uncyclized radical, whereas those of GBASus were enhanced as a consequence of intermolecular association by dipole–dipole interaction in polar GBASu monomers. Cyclization was enhanced in the following order: diallyl aliphatic dicarboxylates series < GBASu series < GBAP series. Gelation was discussed according to Gordon's theory; the actual gel-point conversions increased with an increase in the molecular weight of monomers, although the discrepancy between actual and theoretical gel-point conversion inversely tended to be decreased. The decreased delay in gelation with an increase of the molecular weight of monomers is ascribed to the reduction of excluded volume effects on crosslinking.      [首页] « 上一页 [1] [2] 3 [4] [5] [6] [7] [8] [9] [10] [11] 下一页 » 末  页»

Diastereoselective Synthesis of a Hydroazulene Derivative by Tandem Michael-Wittig Reactions

The reaction of a cyclic phosphonium ylide [ 1 ] with enoate 2 gives a hydroazulene derivative with stereoselectivity.     

Thermoswitching property in TCNQ salts of ionenes containing poly(ethylene oxide) segments

Ionene polymers characterized by the alternating structure of ionene and crystalline poly(ethylene oxide) (PEO) segments were prepared as a function of PEO segment size. A microstructure of these ionenes and their 7,7,8,8-tetracyanoquinodimethane (TCNQ) salts were investigated with x-ray diffraction patterns, thermal scanning behavior, and polarizing micrographs. On the basis of this microstructure, the change in resistivity with temperature was studied. In Arrhenius' plots of the resistivity the simple salts in which the spherulites consisting of the PEO segments were observed showed a sharp decrease in resistivity with a rise in temperature [critical temperature resistor (CTR)] at about the melting point of the PEO segments, whereas the other simple salts in which the spherulites were not observed showed linear temperature dependence. The switching properties were confirmed similarly in repetitive heating/cooling cycles. This CTR characteristic was attributed to an increase in continuity in the conduction paths by melting spherulites. The apparent switching properties were not observed in the complex salts.     

Reactive oligomers. I. Preparation and polymerization of ethylene glycol bis(methyl fumarate)

Ethylene glycol bis(methyl fumarate) (EGBMF) was prepared as a new type of divinyl compound and reactive oligomer: a needle crystal, m.p. 104.5°C. Homopolymerization of EGBMF was carried out in dioxane with 0.1 mol/L AIBN at [M] = 1 mol/L and 60°C; the rate of polymerization was estimated to be 4.44 × 10^?6 mol/L s in a good agreement with diethyl fumarate (DEF). The cyclization constant K_c was obtained as 1.64 mol/L, being rather low compared with diallyl oxalate which is 1,9-diene having two ester groups analogous to EGBMF. Gelatin occurred at about 35% conversion. Finally, the copolymerization of EGBMF (M₁) with diallyl phthalate (DAP) (M₂) is tentatively explored with the intention of the improvement of allyl resins in mechanical properties; remarkable rate enhancement was observed for copolymerization. The monomer reactivity ratios were estimated to be r₁ = 0.96 and r₂ = 0.025, the r₁ value being reduced compared with the DEF-DAP copolymerization system. These results are discussed from the standpoint of steric effect on the polymerization of fumarate as an internal olefin.     

Reactive oligomers. II. Polymerization of glycol bis(allyl phthalate)s and glycol bis(allyl succinate)s

Seven glycol bis(allyl phthalate)s (GBAP) and four glycol bis(allyl succinate)s (GBASu) as reactive oligomers were prepared and their polymerization behaviors were investigated in detail in terms of cyclopolymerization and gelation as compared with diallyl dicarboxylates. Thus, the rates of polymerization of GBAPs were reduced compared to diallyl phthalate, being attributed to the steric effect on the intermolecular propagation of the uncyclized radical, whereas those of GBASus were enhanced as a consequence of intermolecular association by dipole–dipole interaction in polar GBASu monomers. Cyclization was enhanced in the following order: diallyl aliphatic dicarboxylates series < GBASu series < GBAP series. Gelation was discussed according to Gordon's theory; the actual gel-point conversions increased with an increase in the molecular weight of monomers, although the discrepancy between actual and theoretical gel-point conversion inversely tended to be decreased. The decreased delay in gelation with an increase of the molecular weight of monomers is ascribed to the reduction of excluded volume effects on crosslinking.