We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upwardplanar L-drawings. We show that directed st-graphs admitting an upward(resp. upward-rightward-) planar L-drawing are exactly ...

We analyze the welfare impacts of price discrimination in a two-dimensional spatial differentiation model. Consumer information of varying qualities is available on one dimension which allows firms to price discriminate, and better information leads to more refined price discrimination. We find that as information quality improves, firms’ profits monotonically increase while consumer surplus an...

2014 We measured the strain and the stress of a perforated metal foil and of a diluted elastic network near the percolation threshold. We used two different techniques : in the first, the strain is increased continuously and monotonically until the system ruptures, whereas in the second, it is the stress which is increased monotonically. We determined the critical exponent of the fracture stres...

In this article we present an algorithm to extend continuous crisp functions to fuzzy numbers using the extension principle; the functions must be monotonically increasing in some of the arguments and monotonically decreasing in the others. Then, we present two different solutions to the problem of extending inverse functions that we have called possible extension and necessary extension. Final...

Benford’s Law can be seen as one of the many first significant digit (FSD) distributions in a family of monotonically decreasing distributions. We examine the interrelationship between Benford and other monotonically decreasing distributions such as those arising from Stigler, Zipf, and the power laws. We examine the theoretical basis of the Stigler distribution and extend his reasoning by inco...

Let a be a nonnegative real number and define a quasi-Fibonacci polynomial sequence by F a 1 (x) = −a, F a 2 (x) = x − a, and F a n (x) = F a n−1(x) + xF a n−2(x) for n ≥ 2. Let ra n denote the maximum real root of F a n . We prove for certain values of a that the sequence {ra 2n} converges monotonically to βa = a 2 + a from above and the sequence {ra 2n+1} converges monotonically to βa from be...

Replace certain edges of a directed graph by chains and consider the e ect on the spectrum of the graph. It is shown that the spectral radius decreases monotonically with the expansion and that, for a strongly connected graph that is not a single cycle, the spectral radius decreases strictly monotonically with the expansion. A limiting formula is given for the spectral radius of the expanded gr...

‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...

If aging is understood as some process of damage accumulation, it does not necessarily lead to increasing mortality rate. Within the framework of a suggested generalization of the Strehler-Mildwan (1960) [B.L. Strehler, A.S. Mildvan (1960). General theory of mortality and aging, Science, 132, 14] model, we show that even for models with monotonically increasing degradation, the mortality rate c...

Massive Open Online Courses (MOOCs) have become an emergent paradigm of large-scale knowledge distribution. One of the dilemma faced by MOOC teachers is the trade-off between introducing new material and reviewing taught material. We model the recap activities as units of monotonically decreasing lengths and study the their schedule. We validate our model with the data of a Digital Signal Proce...