a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem. in this note, we find all clt and supersolvable numbers up to $1000$. we also formulate some questions about the distribution of these numbers.

the zarankiewicz number z(b; s) is the maximum size of a subgraph of kb,b which does not contain ks,s as a subgraph. the two-color bipartite ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of kb,b with two colors contains a ks,s in the rst color or a kt,t in the second color.in this work, we design and exploit a computational method for bounding and computin...

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...

In previous work, authors have proposed two new aggregation operators for a class of LR fuzzy numbers known as triangular fuzzy numbers (TFNs) in which the Land Rapex angles of the piecewise continuous linear membership function of the composite or resultant or aggregate TFN are the arithmetic means [1] and the geometric means [2] of the Land Rapex angles of the individual TFNs. In another pape...

We show that the mutant Huntington's disease (HD) protein (mhtt) specifically inhibits endocytosis in primary striatal neurons. Unexpectedly, mhtt does not inhibit clathrin-dependent endocytosis as was anticipated based on known interacting partners. Instead, inhibition occurs through a non-clathrin, caveolar-related pathway. Expression of mhtt inhibited internalization of BODIPY-lactosylcerami...

Given two graphs Gi = (Vi, Ei) and G2 = (V2, £2), |Vi| = \V2\ = n, to determine whether they have a size-A; common subgraph is one of the earliest examples of an NP-complete problem (by a trivial reduction from the Maximum Clique problem). We show that this problem for equally sized G\ and G2, i.e. when |23i| = |2?2| = m, remains NP-complete. Moreover, the restriction to the case k = m—tfn, c> ...

Thin film nanocomposite (TFN) membranes containing MCM-41 silica nanoparticles (NPs) were synthesized by the interfacial polymerization (IP) process. An m-phenylenediamine (MPD) aqueous solution and an organic phase with trimesoyl chloride (TMC) dissolved in isooctane were used in the IP reaction, occurring on a nanoporous polysulfone (PSU) support layer. Isooctane was introduced as the organic...

OBJECTIVES Evaluation of the surgical management, outcome and complications in patients with pertrochanteric fractures treated with PFNA nail. MATERIAL AND METHOD A retrospective study was conducted on 200 patients treated consecutively between April 2010 and February 2012. Radiological assessments were performed before and after the surgery, and during the follow-up (fracture reduction, blad...