We consider a family of manifolds with a class of degenerating warped product metrics gǫ = ρ(ǫ, t) dt + ρ(ǫ, t)2bds2M , with M compact, ρ homogeneous degree one, a ≤ −1 and b > 0. We study the Laplace operator acting on L differential p-forms and give sharp accumulation rates for eigenvalues near the bottom of the essential spectrum of the limit manifold with metric g0.

Introduction Vit D level is low in human milk (20-60 IU/Lit) thus dialy supplement of 400 Vit D is advised since birth for all infants. On the other hand upper limit dose for long term Vit D intake is 1000 IU/day for children less than one year of age. Excessive Vit D more than upper limit by physicians or parents can cause hypervitaminoseD. We report a rare case of hypervitaminose D in two mon...

The notion of run (also called maximal repetition) allows a compact representation of the set of all tandem periodicities, even fractional, in a string. Since the work of Kolpakov and Kucherov in [8, 9], it is known that ρ(n), the maximum number of runs in a string, is linear in the length n of the string. Lower bounds haven been provided by Franek et al. and Matsubara et al. (0.9445...) [5, 6,...

We present a new locality sensitive hashing (LSH) algorithm for c-approximate nearest neighbor search in `p with 1 < p < 2. For a database of n points in `p, we achieve O(dn) query time and O(dn + n1+ρ) space, where ρ ≤ O((ln c)2/cp). This improves upon the previous best upper bound ρ ≤ 1/c by Datar et al. (SOCG 2004), and is close to the lower bound ρ ≥ 1/c by O’Donnell, Wu and Zhou (ITCS 2011...

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

Background. Poststroke impairment may lead to fall and unsafe functional performance. The underlying mechanism for the balance dysfunction is unclear. Objective. To analyze the relation between the motor level of the affected limbs and balance in poststroke subjects. Method. A prospective, cross-sectional, and nonexperimental design was conducted in a rehabilitation institute. A convenience sam...

The advent of all-sky facilities, such as the Neil Gehrels Swift observatory, All Sky Automated Search for Supernovae (ASAS-SN), eROSITA and Gaia has led to a new appreciation importance transient sources in solving outstanding astrophysical questions. Identification catalogue cross-matching transients been eased over last two decades by Virtual Observatory but we still lack client capable prov...