let $g$ be a connected graph with vertex set $v(g)$‎. ‎the‎ ‎degree resistance distance of $g$ is defined as $d_r(g) = sum_{{u‎,‎v} subseteq v(g)} [d(u)+d(v)] r(u,v)$‎, ‎where $d(u)$ is the degree‎ ‎of vertex $u$‎, ‎and $r(u,v)$ denotes the resistance distance between‎ ‎$u$ and $v$‎. ‎in this paper‎, ‎we characterize $n$-vertex unicyclic‎ ‎graphs having minimum and second minimum degree resista...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

Order picking is one of the most significant components warehouse management. More than 50% cost incurred in warehouses due to order process. Although this process has mostly been considered within framework economic objectives, recent years ergonomic perspective become increasingly visible. studies regarding objectives have focused on low-level systems, but human factor ignored high-level pick...

We describe the main features of the Dynamic Dictionary of Mathematical Functions (version 1.5). It is a website consisting of interactive tables of mathematical formulas on elementary and special functions. The formulas are automatically generated by computer algebra routines. The user can ask for more terms of the expansions, more digits of the numerical values, or proofs of some of the formu...

Perhaps I should start at the beginning and relate how I first found out about Ramanujan’s existence. In March, 1931 I found a simple proof of the following old and well-known theorem of Tchebychev: “Given any integer n, there is always a prime p such that n ≤ p < 2n.” My paper was not very well written. Kalmar rewrote my paper and said in the introduction that Ramanujan found a somewhat simila...

We give a proof, following an argument of H.W. Lenstra, of the conjecture of L. Carlitz (1966) as generalized by D. Wan (1993). This says, there are no exceptional polynomials of degree n over Fq if (n, q− 1) > 1. Fried, Guralnick and Saxl proved a much stronger result, showing that primitive exceptional polynomials have monodromy groups with degrees either a power of the characteristic (and th...

a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.