A Modified Fractional Derivative and its Application to Fractional Vibration Equation

In this paper, a new modified definition of the fractional derivative is presented. The Laplace transform of the modified fractional derivative involves the initial values of the integer-order derivatives, but does not involve the initial values of the fractional derivatives as the Caputo fractional derivative. Using this new definition, Nutting’s law of viscoelastic materials can be derived from the Scott-Blair stress-strain law as the Riemann-Liouville fractional derivative. Moreover, as the order a approaches n− and (n−1)+, the new modified fractional derivative †Da t f (t) approaches the corresponding integer-order derivatives f (n)(t) and f (n−1)(t), respectively. Therefore, the proposed modified fractional derivative preserves the merits of the Riemann-Liouville fractional derivative and the Caputo fractional derivative, while avoiding their demerits. By solving a fractional vibration equation, we confirm the advantages of the proposed fractional derivative

Development of a more effective behavioral approach to controlling Rhagoletis pomonella flies.

The apple maggot fly, Rhagoletis pomonella (Walsh), is a key pest attacking apple fruit in eastern and midwestern North America. Sticky-coated 8-cm spheres baited with fruit odor (butyl hexanoate) have been the mainstay of a behavioral approach to direct maggot fly control. Improvements upon the red sphere trapping system are needed, however, if it is to be feasible and cost-effective for widespread commercial use. Several aspects of visual and odor stimuli influencing apple maggot fly captures on sticky red spheres were investigated. Results indicated that the efficacy of spheres in capturing adults was not improved by increasing sphere size to a diameter greater than that of 8-cm or by using more synthetic fruit odor (butyl hexanoate). Significant improvement was attained by using synthetic food odor (ammonium carbonate) together with butyl hexanoate. Distance (15-60 cm) of a butyl hexanoate source from a red sphere had no significant effect on fly captures. Semi-natural (field cage) conditions were used to examine response patterns of females to red spheres in relation to fly age and prior ovipositional experience. As fly age increased from a reproductively immature stage to a mature stage, the probability of a fly finding a sphere hung in a host tree increased. Simultaneously, the likelihood that a fly would deposit eggs in host fruit before encountering a sphere increased. Prior experience with different species or cultivars of host fruit did not have significant effect on the ability of flies to find red spheres but reduced the likelihood of oviposition in unfamiliar fruit. Prior experience with the same species or cultivar of host fruit had no apparent effect on fly ability to find a red sphere trap or to oviposit in familiar fruit. Various feeding stimulants, pesticides, and residue-extending agents were evaluated in laboratory and field cage experiments for suitability in developing a nonsticky lethal sphere. Spheres treated with a mixture containing 1.05% (a.i.) dimethoate (insecticide), 58.95% corn syrup (feeding stimulant) and 40% latex paint (residue extending agent) and not exposed to weather killed a great majority of alighting flies. However, these spheres became ineffective after exposure to weather (rainfall). Retreating weather-exposed spheres with feeding stimulant restored effectiveness. Studies conducted in commercial orchards showed that pesticide-treated spheres, like the sticky spheres, had much potential for eliminating insecticide sprays against the flies. Current necessity of retreating pesticide-treated spheres with feeding stimulant after each rainfall compromises present utility for commercial use. Development of a polymer to protect residual effectiveness of feeding stimulant is key to further widespread commercial use of this simpler behavioral approach to controlling apple maggot flies

Effects of Finite Deformed Length in Carbon Nanotubes

The effect of finite deformed length is demonstrated by squashing an armchair (10,10) single-walled carbon nanotube with two finite tips. Only when the deformed length is long enough, an effectual metal-semiconductor-metal heterojunction can be formed in the metallic tube. The effect of finite deformed length is explained by the quantum tunnelling effect. Furthermore, some conceptual designs of nanoscale devices are proposed from the metal-semiconductor-metal heterojunction.Comment: 4 pages, 4 figure