The paper focuses on development of a multifunctional material which allows conducting of electrical current and simultaneously holds mechanical properties of a polymeric composite. Such material could be applied for exterior fuselage elements of an aircraft in order to minimize damage occurring during lightning strikes. The concept introduced in this paper is presented from the points of view of various scientific disciplines including materials science, chemistry, structural physics and mechanical engineering with a discussion on results achieved to-date and further plans of research.

For a number q bigger than 1, we consider a q-difference version of a second-order singular differential operator which depends on a real parameter. We give three exact parameter intervals in which the operator is semibounded from above, not semibounded, and semibounded from below, respectively. We also provide two exact parameter sets in which the operator is symmetric and self-adjoint, respectively. Our model exhibits a more complex behavior than in the classical continuous case but reduces to it when q approaches 1.

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This methodological note introduces the concept of and calculates percolation transition characteristics for a Sierpinski carpet with hybrid (énite-inénite) ramifying. Recurrence formulas for calculating the force éelds of Sierpinski prefractals of arbitrary generation are obtained. The possibility of using the obtained results in the model of oscillatory interacting different-scale inner boundaries of a heterogeneous material is discussed. . 182, å 5] ¬°£ §² ³¦²±ª¯³¬°¤°³ ¤ª¢²ª¥¯°« ²¡©£¦´£ §¯¯°³´¾À

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