In this paper, some sufficient conditions are established for the oscillation of second-order neutral functional differential equation [ r(t)[x(t)+ p(t)x(τ(t))]′ ]′+q(t) f (x(σ(t))) = 0, t ≥ t0, where ∫ ∞ t0 dt/r(t) = ∞, or ∫ ∞ t0 dt/r(t) < ∞, 0 ≤ p(t) ≤ p0 < ∞. The results obtained here complement and improve some known results in the literature. 2010 Mathematics Subject Classification: 39A21,...

By using the general means, we establish some oscillation theorems for the even order delay differential equation (r(t)|x(n−1)(t)|α−1x(n−1)(t))′ + F (t, x[g(t)]) = 0, where α > 0 is a constant, r ∈ C([t0,∞),R+), F ∈ C([t0,∞) × R,R), and g ∈ C([t0,∞),R). The results obtained extend and improve some results known in the literature. 2000 Mathematics Subject Classification: 34K11, 34C10.

and Applied Analysis 3 capacity of the prey population x t is b/a, so it is meaningful that the economical threshold h is less than b/a. Thus, throughout this paper, we set up the following two assumptions: A1 D e < a b , A2 h ≤ b a . 2.1 From the biological point of view, it is reasonable that system 1.1 is considered to control the prey population in the biological meaning space { x, y : x ≥ ...

Vertebral samples of little skate (Leucoraja erinacea) and winter skate (Leucoraja ocellata) were collected from Cape Hatteras, USA, to Canadian waters to estimate age, growth, and length at weight relationships for both species throughout this range. Maximum observed age was 12.5 and 20.5 years for little skate and winter skate, respectively. Significant length at weight relationships were fou...

where f(t, x) is some given expression in t and x. Intuition dictates that there should be a unique function x satisfying this. The graph of x has to pass through the point (t0, x0), and the differential equation determines the slope of the graph at any given point. If one imagines a particle whose position at time t is (t, x(t)) then the differential equation is steering the particle, so to sp...

An eta-quotient of levelN is a modular form of the shape f(z) = ∏ δ|N η(δz) rδ . We study the problem of determining levels N for which the graded ring of holomorphic modular forms for Γ0(N) is generated by (holomorphic, respectively weakly holomorphic) eta-quotients of level N . In addition, we prove that if f(z) is a holomorphic modular form that is nonvanishing on the upper half plane and ha...

A remarkable feature of the Landau–Zener transition is insensitivity survival probability to decay rate, τ−1, excited state. Namely, for a particle which initially (at t→−∞) in ground state remain at t→∞ same insensitive τ−1 due e.g. coupling continuum (Akulin and Schleich, 1992). This was demonstrated case when density states energy-independent. We study opposite limit step-like function energ...

The aim of this study was to assess the effects of vigorous exercise on functional abilities by means of a Senior Fitness Test (SFT) in a group of elderly adults. Twenty healthy and inactive people performed vigorous exercise (VE: 12 men and 8 women, aged 69.6 ± 3.9 years). At the beginning of the study (T0) and after 3 months (T1), each subject's functional ability was tested for muscular stre...

In this paper, we present the numerical investigations of self-similar solutions for the nonlinear diffusion equation ht = −(hhxxx)x, which arises in the context of surface-tension-driven flow of a thin viscous liquid film. Here, h = h(x, t) is the liquid film height. A self-similar solution is h(x, t) = h(α(t)(x − x0) + x0, t0) = f (α(t)(x − x0)) and α(t) = [1 − 4A(t − t0)], where A and x0 are...

In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of T0 spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order.