We give a uniform description of resolvents and complex powers elliptic semiclassical cone differential operators as the parameter h tends to 0. An example such an operator is shifted Laplacian 2 ? g + 1 $h^2\Delta _g+1$ on manifold ( X , ) $(X,g)$ dimension n ? 3 $n\ge 3$ with conic singularities. Our approach constructive based techniques from geometric microlocal analysis: we construct Schwa...

We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dμ) and 1 n Kn(x, x) dμ(x). By combining this with the asymptotic upper bounds of Máté–Nevai and Totik on nλn(x), we prove some general results on ∫ I 1 n Kn(x, x) dμs → 0 for the singular part of dμ and ∫ I |ρE(x) − w(x) n Kn(x, x)| dx → 0, where ρE is the...

G is any simple graph with m edges and n veriices where these vertices have vertex degrees d(l)zd(2)r...rd(n), respectively. General algorithms for the exact calculation of x(G), the chromatic number of G, are almost always of ‘branch and bound’ type; this type of algorithm requires an easily constructed lower bound for x(G). In this paper it is shown that, for a number of such bounds (many of ...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

We study the higher fractional differentiability properties of gradient solutions to variational obstacle problems form $\min \left\{ {\int_\Omega {F\left( {x,w,Dw} \right){\rm{d}}x\,:\,w\, \in \,{\kappa _\psi }\left( \Omega \right)} } \right\},$ with F double phase functional $F\left( {x,\,w,\,z} \right) = b\left( {x,w} \right)\left( {{{\left| z \right|}^p} + a\left( x \right){{\left| \right|}...

In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed spaces.

We study differential-difference equation of the form d dx t(n+ 1, x) = f(t(n, x), t(n + 1, x), d dx t(n, x)) with unknown t(n, x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, {t(n ± k, x)}k=−∞, { d dxk t(n, x) }∞ k=1 , such that DxF = 0 and DI = I, where Dx is ...

and Applied Analysis 3 ∂u ∂η x, t, a 0 on Σ ∂Ω × 0, T × 0, A , u x, 0, a u0 x, a in Ω × 0, A , u x, t, 0 ∫A 0 β x, t, a u x, t, a da in Ω × 0, T , Pw x, t ∫A 0 w x, α u x, t, α dα in Ω × 0, T , 1.3 whereΩ is a bounded domain inR with smooth boundary ∂Ω, v x, t, a is a harvesting rate, and w is a positive function in L∞ Ω × 0, A . We study an optimal control problem relating to the dynamic syste...

Let X denote a finite nonempty set, and let W denote a matrix whose rows and columns are indexed by X and whose entries belong to some field K. We study three planar algebras related to W . Briefly, a planar algebra is a graded vector space V = ∪n∈Z+∪{+,−}Vn which is closed under “planar” operators. The first planar algebra which we study, FW = ∪FW n , is defined by the group theoretic properti...