Consider the first order neutral delay differential equation with positive and negative coefficients:[x(t)-c(t)x(t-γ)]+p(t)x(t-τ)-Q(t)x(t-δ)=0,t≥t 0,(1)where c,p,Q∈C((t 0,∞),R +),R +=(0,∞),γ】0,t】δ≥0. W...Consider the first order neutral delay differential equation with positive and negative coefficients:[x(t)-c(t)x(t-γ)]+p(t)x(t-τ)-Q(t)x(t-δ)=0,t≥t 0,(1)where c,p,Q∈C((t 0,∞),R +),R +=(0,∞),γ】0,t】δ≥0. We obtain the sufficient condition for the existence of positive solutions of Eq.(1). As a corollary, we improve the correspondent result in by removing the condition∫ ∞ c 0 (t) d t=∞,where (t)=p(t)-Q(t-τ+δ)≥0.展开更多
A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of ...A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of nonlinearity.展开更多
Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian...Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .展开更多
文摘Consider the first order neutral delay differential equation with positive and negative coefficients:[x(t)-c(t)x(t-γ)]+p(t)x(t-τ)-Q(t)x(t-δ)=0,t≥t 0,(1)where c,p,Q∈C((t 0,∞),R +),R +=(0,∞),γ】0,t】δ≥0. We obtain the sufficient condition for the existence of positive solutions of Eq.(1). As a corollary, we improve the correspondent result in by removing the condition∫ ∞ c 0 (t) d t=∞,where (t)=p(t)-Q(t-τ+δ)≥0.
文摘A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of nonlinearity.
文摘Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .
