Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions

Opial inequality in q-calculus

Abstract In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281–300, 2004), we establish a new integral inequality of the q-Opial type

On the Summation of Series Involving Bessel or Struve Functions

AbstractThe subject called “summation of series” can be viewed in two different ways. From one point of view, it means numerical summation which involves acceleration of convergence, and from the other, it represents a variety of summation formulas which are considered important, but which are often not useful. The aim of this paper is to produce a compromise between the two opposite approaches when series of Bessel or Struve functions are considered. The proposed method leads to series of Riemann zeta and related functions which converge much faster than the originals. In the most significant cases, closed-form formulas were obtained

Comparative analysis of the first permanent molars caries prevalence in younger and older school children

Introduction. The data on the health-condition of the first permanent molars among children in our region is scarce. Therefore, the need for more thorough analysis of the state of health of these teeth in the children from our region imposes itself, along with the need to determine the most critical period in which a significant increase in caries prevalence of these teeth takes place. Aim. The aim of the research was to perform a comparative analysis of the prevalence, average rate and structure of decay, missed and filled first permanent molars in the children of the younger school age in relation to those of the older school age. Material and methods. The research included 1.119 examinees, aged from 7 to 14 years. Examinees were divided into two groups according to their age: examinees of the younger school age and older school age. Dental check-up of the students was performed by means of a dental probe and mirror and the health condition of the examined teeth was registered by means of Klein-Palmer's DMF system. Results. The research determined high values of the examined parameters of the first permanent molars caries prevalence which increases with the age of the examinees. In the examinees of the age of 8, 9, and 10, statistically more significant values of the examined teeth caries prevalence parameters were registered, in relation to the examinees of seven years of age. In the examinees of the older school age, statistically significantly higher values were registered only for TCI and ACI and only in the examinees aged 14 in relation to the examinees aged 11. With the age, the percent of decay is decreases, while the percent of filled and extracted first permanent molars increases. Conclusion. Results show that the period between 7 and 10 years of age is the most critical and the most important period for the implementation of preventive-prophylactic measures aimed to preserve the health of the first permanent molars