It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual...It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.展开更多
While the threat of war has decreased, there have appeared intricate security issues that affect all aspects of human life, breaking through various defenses and threatening the well being of all actors in the contemp...While the threat of war has decreased, there have appeared intricate security issues that affect all aspects of human life, breaking through various defenses and threatening the well being of all actors in the contemporary world, including nations, groups and individuals. This risky situation calls for a new security concept, one that transcends traditional state centrism, national supremacy and coercion. The new security concept, which should assimilate the general theory of grand strategy,focuses on a vision that spans time and space, valuing humankind as it exists as one of the dynamic factors of nature and society. The essentials of the new security concept are to recognize balanced development as the substance of security and to govern national strength and the application of means and tactics. It aims at realizing comprehensive security across various social fields within states, to achieve mutual security among national, international and individual actors, as well as harmony between man and nature, continuous security leading to lasting and universal peace in the future.展开更多
文摘It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.
文摘While the threat of war has decreased, there have appeared intricate security issues that affect all aspects of human life, breaking through various defenses and threatening the well being of all actors in the contemporary world, including nations, groups and individuals. This risky situation calls for a new security concept, one that transcends traditional state centrism, national supremacy and coercion. The new security concept, which should assimilate the general theory of grand strategy,focuses on a vision that spans time and space, valuing humankind as it exists as one of the dynamic factors of nature and society. The essentials of the new security concept are to recognize balanced development as the substance of security and to govern national strength and the application of means and tactics. It aims at realizing comprehensive security across various social fields within states, to achieve mutual security among national, international and individual actors, as well as harmony between man and nature, continuous security leading to lasting and universal peace in the future.
