the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

the performance of a decision making unit (dmu) can be evaluated in either across-sectional or a time-series manner, and data envelopment analysis (dea) is a useful method for both types of evaluation. the malmquist productivity index (mpi) evaluates the change in efficiency of a dmu between two time periods. it is defined as the product of the catch-up and frontier-shift terms. in this paper, ...

The Apnea-Hypopnea Index (AHI) is one of the most-used parameters from sleep study that allows assessing both severity obstructive apnea and reliability new devices methods. However, in many cases, it compared with a reference only via correlation coefficient, or this value at least most emphasized. In paper, we discuss limitations such an approach list several alternative quantitative qualitat...

OBJECTIVES: The purpose of this study was to compare the Type 2 diabetes mellitus patients and non-diabetics in terms Papillary bleeding index (PBI) periodontal disease. METHODOLOGY: This comparative cross-sectional conducted during period November 2020 February 2021 three (3) tertiary care hospitals Peshawar. sampling technique purposive sampling. sample comprised 105 individuals, 56 participa...

In my article I have taken up different expressions for the terms of trade in foreign trade, and especially I have been interested in a breakdown of total gain into two parts, namely the part due to the terms-of-trade effects and the part due to the price level effects. I have also taken up the intersectoral gain from terms of trade and the relation to the terms of trade in foreign trade. Besid...

It is known that with a very small number of exceptions, for a term of a Lehmer sequence {Un( √ R,Q)} to be prime its index must be prime. For example, F4 = U4(1,−1) = 3 is prime. Also, Un(1, 2) is prime for n = 6, 8, 9, 10, 15, 25, 25, 65, while Vn(1, 2) is prime for n = 9, 12, and 20. This criterion extends to the companion Lehmer sequences {Vn( √ R,Q)}, with the exception that primality may ...