A c l a s s o f c o u n t a n d t h r e s h o l d m e c h a n i s m s , c o l l e c t i v e l y d u b b e d α c o u n t , a b l e t o d i s c r i m i n a t e b e t w e e n t r a n s i e n t f a u l t s a n d i n t e r m i t t e n t f a u l t s i n c o m p u t i n g s y s t e m s i s p r e s e n t e d . T r a n s i e n t f a u l t s d i s c r i m i n a t i o n h a s l o n g b e e n p u r s u e d...

and Applied Analysis 3 A2 f t, u > 0 for t, u ∈ 0, σ T T × 0,∞ . A3 There exists a function c ∈ C 0, σ T T , 0,∞ such that f t, u ≥ c t u, t, u ∈ 0, σ T T × 0,∞ . 1.8 Obviously, A1 means that f is not necessarily linearizable at 0 and ∞. We consider the existence of positive solutions of problem 1.1 in this paper by using bifurcation techniques. The difference from 6 is that the branches of pos...

The g o a l o f t h e NLG p r o j e c t i s t o enhance p e r s o n c o m p u t e r i n t e r a c t i o n b y u s i n g more t h a n one mode o f c o m m u n i c a t i o n . The p r o j e c t uses a c o m b i n a t i o n o f n a t u r a l l anguage and g r a p h i c s f o r b o t h i n p u t and o u t p u t . T h i s a l l o w s deve lopmen t o f p r a c t i c a l , h a b i t a b l e sys tems s...

1 . a . F a l s e . T y p e 1 d i a b e t e s i s c a u s e d b y a u t o i m m u n e d e s t r u c t i o n o f t h e i n s u l i n s e c r e t i n g c e l l s i n t h e p a n c r e a s a n d c a n n o t b e p r e v e n t e d . b . t r u e . c . t r u e . d . F a l s e . T h e r e i s n o e v i d e n c e t h a t a n y d r u g i s s u p e r i o r t o a n y ...

In this work we consider equations of the form ∂tu + P(D)u u^{l}∂xu = 0, where P(D) is a two-dimensional differential operator, and l ∈ N. We prove that if u sufficiently smooth solution equation, such suppu(0), suppu(T) ⊂ [−B, B] × for some B > then there exists R0>0 suppu(t) [-R_0,R_0]×[-R_0,R_0] every t [0, T].

§1 – Introduction. In this paper, we compute the limits (1) γ p = lim t → ∞ t 1 2 (1 − 1 p) u(·, t) p , 1 ≤ p ≤ ∞ for solutions u(·, t) of the equation (2) u t + a u x + b u u x = c u xx satisfying the Cauchy condition (3) u(x, 0) = u 0 (x), u 0 ∈ L 1 (R), that is, u(·, t) − u 0 1 → 0 as t → 0, t > 0. Here, u(·, t) p denotes the L p norm of u(·, t) as a function of x for fixed t, i.e., (4) u(·,...

In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated Dirichlet conditions. \begin{equation*} \begin{cases} -\big{(}\nabla^{\nu}_{\rho(a)}u\big{)}(t) + \lambda u(t) = f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a 2}, \\ u(a) u(b) 0, \end{cases} \end{equation*} where $1 < \nu 2$, $a,b \mathbb{R}$ $b-a\in\mathbb{N}_{3}$...

() : ∆→ () σ : ∆→ Γ ∆ ` u : Aσ (σ, x = u) : ∆→ Γ, x : A σ : ∆→ Γ ∆ ` φ : I (σ, i = φ) : ∆→ Γ, i : I σ : ∆→ Γ Γ ` A ∆ ` Aσ σ : ∆→ Γ Γ ` t : A ∆ ` tσ : Aσ We can define 1Γ : Γ→ Γ by induction on Γ and then if Γ ` u : A we write (x = u) : Γ→ Γ, x : A for 1Γ, x = u. If we have further Γ, x : A ` t : B we may write t(u) and B(u) respectively instead of t(x = u) and B(x = u). Similarly if Γ ` φ : I w...

t o b e s h i p p e d a c r o s s b o r d e r s u s i n g i n t e r m o d a l t r a n s p o r t a t i o n . T r u c k s a r e s t i l l t h e m o s t p r e v a l e n t m o d e f o r s u r f a c e s h i p m e n t s a n d t i m e s e n s i t i v e t r a n s p o r t p e r i s h a b l e p r o d u c t s s u c h a s f r e s h p r o d u c e . T h i s s t u d y f o c u s e d o n m e a s u r i n g t h e...