Let X be a compact connected subset of Rd, let Sj , j = 1, ...,N , be contractive self-conformal maps on a neighborhood of X, and let {pj(x)}j=1 be a family of positive continuous functions on X. We consider the probability measure μ that satisfies the eigen-equation

We establish several Hermite-Hadamard’s inequalities on time scales. One of these results says as follows: Suppose that (1) f a b R : [ , ]® is convex; (2) p q p q , (0,1), = 1 ∈ + ; g C a b R rd ∈ + ([ , ], ) is symmetric with respect to x pa qb = + = : x on [ , ] a b , i.e., g qt g pt t b a ( ) = ( ), [0, ], x x − + ∀ ∈ − then:

We present results for pseudodifferential operators on Rd whose symbol a(·,ξ) is almost periodic (a.p.) for each ξ ∈ Rd and belongs to a Hörmander class Sm ρ,δ. We study a linear transformation a 7→ U(a) from a symbol a(x,ξ) to a frequency-dependent matrix U(a)(ξ)λ,λ′ , indexed by (λ,λ′) ∈ Λ×Λ where Λ is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential ope...

CASE REPORT A male with cylindrical anisometropia secondary to retinal detachment (RD) surgery in the right eye (OD) was referred for contact lens (CL) fitting. His refraction was OD -1.25 -2.75 x 60 degrees VA 1.0 and OS +0.25 VA 1.2. He was complaining of diplopia with spectacles. Seven years prior to the RD surgery, he had undergone LASIK without complications. The diplopia was eliminated af...

conclusions with regard to improving the understanding of the differences in the biodiversity of the fecal microbiota between rd infants and h infants, the findings of this study can provide a possible basis to reveal the relationship between rd and intestinal microbiota. objectives this study aimed to reveal the changes in the biodiversity of the fecal microbiota of infants with rd. patients a...

Let G(d,n) be the Grassmannian manifold of n-dimensional subspaces Rd, and let πV:Rd→V orthogonal projection. We prove that if μ is a compactly supported Radon measure on Rd satisfying s-dimensional Frostman condition μ(B(x,r))⩽Crs for all x∈Rd r>0, then∫G(d,n)‖πVμ‖Lp(V)pdγd,n(V)<∞,1⩽p<2d−n−sd−s. The upper bound p sharp, at least, d−1⩽s⩽d, every 0<n<d. Our motivation this question comes from fi...

— We give a proof, based on the Poincaré inequality, of the symmetric property (τ) for the Gaussian measure. If f :Rd → R is continuous, bounded from below and even, we define Hf(x) = infy f(x+y)+ 1 2 |y|2 and we have ∫ e−f dγd ∫ e dγd 1. This property is equivalent to a certain functional form of the BlaschkeSantaló inequality, as explained in a paper by Artstein, Klartag and Milman. RÉSUMÉ. —...

Gardiner [5] and Bannai and Bannai [1] classified symmetric association schemes (X, {Ro, ... , Rd}) such that for (at least) two different choices of i, the graph (X, Ri ) is distance-regular with diameter d. It turns out that except in the case of a polygon there are never more than two choices for i. Let one of the choices be i = 1, and let the ordering of the relations be such that R j is th...

We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator D = Dc(1I + RDc) −1 with R = r1I. For Dc in the free fermion limit is free of species doubling and behaves like iγμpμ as p → 0, the axial anomaly tr[γ5(RD)(x, x)] for U(1) lattice gauge theory with single fermion flavor is equal to e 2 32π2 ǫμνλσFμν(x)Fλσ(x) plus terms which are higher orders in Aμ and/or derivatives...