Let f : X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g : X → I n with dim(f × g) = 0 is uniformly dense in C(X, I n ); (2) for every 0 ≤ k ≤ n− 1 there exists an Fσ-subset Ak of X such that dimAk ≤ k and the restriction f |(X\Ak) is (n−k−1)-dimensional. These are extensions of theorems by Pasynkov and Toru...

For positive integers a, k, let Ak(a) denote the sequence ak, ak + 1, ak + a, . . . , ak + ak−1. Let Γ ( Ak(a) ) denote the set of integers that are expressible as a linear combination of elements of Ak(a) with non-negative integer coefficients. We determine g ( Ak(a) ) and n ( Ak(a) ) which denote the largest (respectively, the number of) positive integer(s) not in Γ ( Ak(a) ) . We also determ...

Motivated by inhomogeneous scaling of left invariant Riemannian metrics on a Lie group G, we consider a family of stochastic differential equations (SDEs) on G with Markov operators L = 1 ∑ k(Ak) 2 + 1 A0 + Y0, where > 0, {Ak} generates a sub Lie-algebra h of the Lie algebra g, and Y0 ∈ g. Assuming that G/H is a reductive homogeneous space, in the sense of Nomizu, we take → 0 and study the asym...

Acanthamoeba keratitis (AK) is a sight-threating infection of the cornea that mostly affects contact lens wearers. Until now, AK treatment remains very difficult due to the existence of a highly resistant cyst stage in the life cycle of Acanthamoeba which is extremely resistant to most of the available anti-amoebic compounds. Moreover, current treatment of AK is usually based in the combination...

An elementary combinatorial method is presented which can be used for proving the closeness of the range of a probability on specific systems, like the set of all linear or affine subsets of a Euclidean space. The motivation for this note came from the second author’s research in statistics: high breakdown point estimation in linear regression. By a probability distribution P , defined on the B...

Velásquez and Felipe recently introduced quasi-Jordan algebras based on the product a / b = 1 2 (a a b + b ` a) in an associative dialgebra with operations a and `. We determine the polynomial identities of degree ≤ 4 satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity. Loday [1, 2] defined an (associa...

K.Balasubramanian , K. Chandrasekhara rao *2 Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur 613402, India 1 [email protected] * Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA University, Kumbakonam,India 2 [email protected] Abstract— This paper is devoted to the rate space of Hahn sequence space. It is denoted by . Some properti...

Actinic keratosis (AK) lesions are surrounded by field cancerization (areas of subclinical, non-visible sun damage). Existing AK grading tools rely on AK counts, which are not reproducible. An Actinic Keratosis Field Assessment Scale (AK-FAS) for grading the severity of AK/field was developed. Standardized photographs of patients representing the full range of AK severity were collected. Six in...

We derive numerous identities for multivariate q-Euler polynomials by using the umbral calculus. 1 1 Preliminaries Throughout this paper, we use the following notation, where C denotes the set of complex numbers, F denotes the set of all formal power series in the variable t over C with F = { f(t) = ∑∞ k=0 ak t k! | ak ∈ C } , P = C[x] and P denotes the vector space of all linear functional on ...