A 3-dimensional Catalan word is a on three letters so that the subword any two Dyck path. For given path D, recently defined statistic counts number of words with property exactly D. In this paper, we enumerate paths equal to certain values, including all primes. The formulas obtained are in terms Motzkin numbers and ballot numbers.

Understanding the number of people and the flow of the persons is useful for efficient promotion of the institution managements and company’s sales improvements. This paper introduces an automated method for counting passerby using virtualvertical measurement lines. The process of recognizing a passerby is carried out using an image sequence obtained from the USB camera. Space-time image is rep...

Difficulties in obtaining reproducible and accurate enumeration of circulating basophils with existing techniques have hampered investigation of this infrequent cell population. A new basophil staining method is described that employs alcian blue dye for staining of heparin within basophils at low pH and in the presence of lanthanum ions. Basophil recognition is facilitated by reducing nonspeci...

Let f1, . . . , fp be entire functions that do not all vanish at any point, so that (f1, . . . , fp) is a holomorphic curve in CPp−1. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions f1, . . . , fp at any point where such a linear combination vanishes, and, if all the f1, . . . , fp are polynomials, also at infinity. This enab...

hyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related todiamond, and having a significant amount of sp3 carbon atoms. design of severalhypothetical crystal networks was performed by using our original software programscvnet and nano-studio. the topology of the networks is described in terms of the netparameters and several counting polynomials, calculated by ...

background: we investigated the efficacy of a mobile-based  bolus advisor app in comparison with the usual multiple daily  injections (mdis) in diabetic patients. materials and methods: in a nonrandomized, controlled clinical trial, 62 diabetic patients  were selected to receive a 12-week intensive glycemic control by either a mobile-based bolus advisor (app) or mdi in the usual manner.we compa...

A theoretical framework is presented that distinguishes among three knowledge sources thot form the basis for generative performance. The three knowledge sources, termed conceptual, procedural, and utilizational competence, were implemented as o computational model that derives plans for counting procedures. In a previous analysis, Greeno, Riley, and Gelman (1984) developed a characterization o...