where ∆pu= div(|∇u|p−2∇u) is the p-Laplacian, 1 < p <∞. ByW1,p(Ω) we denote the usual Sobolev space with dual space (W1,p(Ω))∗, andW 0 (Ω) denotes its subspace whose elements have generalized homogeneous boundary values and whose dual space is given by W−1,p(Ω). We assume the following growth and asymptotic behaviour of the nonlinear right-hand side f of (1.1): (H1) f :Ω×R → R is a Carathéodory...

in this paper the concept of homothetic dual exponential motions in d3 is discussed and theirvelocities obtained. due to the way in which the matter is presented, the paper gives some formula and factsabout dual exponential motions which are not generally known

in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

OBJECTIVE To evaluate how bone mineral density in the calcaneus measured by a dual energy X-ray laser (DXL) correlates with bone mineral density in the spine and hip in Turkish women over 40 years of age and to determine whether calcaneal dual energy X-ray laser variables are associated with clinical risk factors to the same extent as axial bone mineral density measurements obtained using dual ...

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...