We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

New extension of nanoparticles used in the last two decades and hence, entrance of them to industrialand non-industrial sewage necessitate study of probable effects of these materials in aquatic ecosystems.This research was performed in order to determine the toxicity effect of silica dioxide (SiO2</spa...

BACKGROUND Although the depth of the counting chamber is an important factor influencing sperm counting, no research has yet been reported on the measurement and comparison of the depth of the chamber. We measured the exact depths of six kinds of sperm counting chambers and evaluated their accuracy. MATERIALS AND METHODS In this prospective study, the depths of six kinds of sperm counting cha...

Parameterized complexity has so far been largely con ned to consideration of computational problems as decision or search prob lems However it is becoming evident that the parameterized point of view can lead to new insight into counting problems The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems

Background: Chest compression with adequate depth and number is one of the main indicators of high-quality cardiopulmonary resuscitation (CPR). Nevertheless, no proper counting technique is suggested to provide sufficient number of massages. Aim: To compare the effects of three techniques of chest compression counting on the quality of CPR and rescuer fatigue. Method: Inthis clinical trial, 30 ...

The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The vertex PI polynomial is defined as PIv (G)  euv nu (e)  nv (e). Then Omega polynomial (G,x) for counting qoc strips in G is defined as (G,x) = cm(G,c)xc with m(G,c) being the number of strips of length c. In this paper, a new infinite class of fullerenes is constructed. ...

We study the fixed parameter tractability of the counting version of a parameterization of the restrictive list H-coloring problem. The parameterization is defined by fixing the number of preimages of a subset C of the vertices in H through a weight assignment K on C. We show the fixed parameter tractability of counting the number of list (H,C,K)-colorings, for the case in which (H,C,K) is simp...

Recent developments in the understanding of N = 2 supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting SU(2) instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a “dual” equati...

A new method of optical frequency beat counting based on fast Fourier transform (FFT) analysis is described. Signals with a worse signal-to-noise ratio can be counted correctly comparing to the conventional counting method of detecting each period separately. The systematic error of FFT counting below 10 Hz is demonstrated and can be decreased. Additionally the modulation width of a frequency-s...

Specific counting systems are characterized by a combination of two features: They are based on larger counting units (multiplication function) and apply to certain objects only (object specificity). This paper analyzes the constitutive role that numeral classifiers may play for specific counting systems, with instances from Polynesian and Micronesian languages. Despite a considerable divergenc...