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We study the following third-order p-Laplacian m-point boundary value problems on time scales: φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T, βu 0 − γuΔ 0 0, u T ∑m−2 i 1 aiu ξi , φp u Δ∇ 0 ∑m−2 i 1 biφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive(More)
An effective approach to dynamic obstacle avoidance for mobile robots is described in this paper. The main concepts in this approach include local Polar Object Chart (POC) for defining possible ways out, obstacle definition, detour mode, anchor for preventing getting lost, steering delimiting and velocity delimiting. The presented concepts and methods were(More)
We study the following third-order p-Laplacian m-point boundary value problems on time scales φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T , u 0 ∑m−2 i 1 biu ξi , u Δ T 0, φp uΔ∇ 0 ∑m−2 i 1 ciφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive solutions(More)
In this paper, we study the nonlinear second-order m-point boundary value problem u′′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, βu(0)− γu′(0) = 0, u(1) = m−2 X i=1 αiu(ξi), where the nonlinear term f is allowed to change sign. We impose growth conditions on f which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones.(More)
In this paper, three important preparation tasks of a planetary exploration system are described, namely calibration, terrain reconstruction and path planning. The calibration is retrieved from the images of the planetary terrain (the same images from which the 3D measurements of the terrain are obtained). Once the system has been calibrated, the same(More)
Mouse resources such as Collaborative Cross (CC), Outbred Stocks (OS), Hybrid Mouse Diversity Panel (HMDP), and Chromosome Substitution Strains (CSSs) have been instrumental to many progresses in the studies of complex traits genetics. We have established a population of chromosome 1 (Chr 1) substitution lines (C1SLs) in which donor chromosomes were derived(More)
We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In(More)