Erdös raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words (sequences that may contain some h...

many shape and topology optimization methods have been inspired from the nature. in this paper, two different optimization algorithms based on the adaptive biological growth (abg) have been applied to some structural elements. the first algorithm is developed for the shape optimization and is applied to a plate with a central hole as well as a fillet plate. the second algorithm is the soft kill...

In the present work, we studied magnetization, vorticity, Cooper pairs density, and spatial distribution of local magnetic field in a three-dimensional superconductor with SQUID geometry (a square central hole connected to outside vacuum through very thin slit). Our investigation was carried out both Meissner-Ochsenfeld Abrikosov state solving two-band Ginzburg-Landau equations considering Jose...

BACKGROUD The Implantable Collamer Lens (ICL) has been used widely for refractive errors, We performed this prospective randomized comparative study to compare postoperative intraocular pressure (IOP) and vaults of the eyes implanted with conventional ICL and central hole ICL. METHODS This study evaluated 44 eyes of 22 patients who underwent central hole ICL implantation in one eye and conven...

We say that a partial word w over an alphabet A is square-free if every factor xx of w such that x and x are compatible is either of the form ⋄a or a⋄ where ⋄ is a hole and a ∈ A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes.

PURPOSE To evaluate the association between macular hole volume (MHV) and postoperative central macular thickness (CMT) using spectral-domain optical coherence tomography (SD-OCT). METHODS Thirty-three eyes of 30 patients with a large full-thickness idiopathic macular hole with or without vitreomacular traction who underwent surgical intervention were included in this cross-sectional study. C...

The supermassive black hole at the center of a distant galaxy can be weighed, in rare but realistic cases, when the galaxy acts as a strong gravitational lens. The central image that should be produced by the lens is either destroyed or accompanied by a second central image, depending upon the mass of the black hole. We demonstrate that when a central image pair is detected, the mass of the bla...

We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from other periodic expansions in the literature and can account for additional distortion to maps with piecewise constant expansion rate. Using asymptotic expan...

This paper describes a Lamb-wave scanning method for the detection of notches simulating cracks at rivet holes in thin plates. The approach requires the generation of an ultrasonic So-Mode Lamb wave using an incident transmitter excited with a tone burst centered at a near non-dispersive frequency. Area scans are performed on a plate with a hole with a notch to generate times series information...