Condition 2. With probability one, Z(.) has bounded total variation in [0, τ ]. In addition, if there exists a vector γ and a deterministic function γ0(t) such that γ0(t) + γ T Z(t) = 0 with probability one, then γ = 0 and γ0(t) = 0. Condition 3. With probability one, there exists a positive constant δ such that pr(C ≥ τ |Z) > δ and pr(Y (τ) = 1|Z) > δ, where Y (τ) = 1 means that Y ∗(t) = 1 for...

A new condition called T condition is introduced for the first time and used to study a pair of isotopic loops. Under this condition, a loop in the pair is a WIPL if and only if the other loop is a WIPL. Furthermore, such WIPLs are isomorphic. The translation elements f and g of a CIPL with the T condition(such that its f, g-isotope is an automorphic inverse property loop) are found to be alter...

BACKGROUND AND OBJECTIVES Turner and colleagues introduced a new method that can detect tinnitus in animals. The stimulus is composed of a small background noise that is identical to the pitch of the tinnitus and a large pulse noise that can evoke a startle response. In normal rats, the gap decreases the startle reflex. However, in tinnitus rats, the gap does not decrease the startle reflex. Th...

Contrast thresholds of six semisupine, visually adapted subjects were obtained under short (10-14 sec.) periods of weightlessness and under 1 G control conditions. The target, viewed binocularly, subtended 1.5 ~ and the background 2.6*. Three background luminance levels were used: 0.03, 0.28 and 30.0 ft-L. The contrast required to detect the target was found to be slightly, but consistently, lo...

• The dual problem is always convex no matter if the primal problem is convex, i.e., g is always concave. • The primal and dual optimal values, f∗ and g∗, always satisfy weak duality: f∗ ≥ g∗. • Slater’s condition: for convex primal, if there is an x such that h1(x) < 0, · · · , hm(x) < 0 and l1(x) = 0, · · · , lr(x) = 0 (12.5) then strong duality holds: f∗ = g∗. Note that the condition can be ...

A graph G is called a fractional (g, f)-deleted graph if G - {e} admits a fractional (g, f)-factor for any e ∈ E(G). A graph G is called a fractional (g, f, n)-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g, f)-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received sign...

Let f : X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. If G is the special Euclidean group SE(2) we show that in the set of C2 G-extensions of f there exists an open and dense subset of stably transitive transformations. If G = K × Rn, where K is a compact connected Lie group, we show that an open and dense set of C2 G-extensions satisfying a certain separation c...

Assume G is a finite symplectic group Sp2n(q) over a finite field Fq of odd characteristic. We describe the action of the automorphism group Aut(G) on the set Irr(G) of ordinary irreducible characters of G. This description relies on the equivariance of Deligne–Lusztig induction with respect to automorphisms. We state a version of this equivariance which gives a precise way to compute the autom...

In the past decades, quantitative study of different disciplines such as system sciences, physics, ecological sciences, engineering, economics and biological sciences, have been driven by new modeling known as stochastic dynamical systems. This paper aims at studying these important dynamical systems in the framework of G-Brownian motion and G-expectation. It is demonstrated that, under the con...