having selected quhistan as one of the important centers of the nazaris’ activity in iran, the local muhtashams of this province focused their efforts on increasingly expanding their spheres of influence in the region. one of the important centers that the nazaris had in mind to expand was nīmrūz province (sistan). by occupying the fortresses in the passageways at the entrance of sistan, they w...

The Roman imperial monarchy is generally studied from the vantage point of ancient Roman history: the “Roman emperor” is viewed and analyzed as an element of the Roman world. This conventional approach fails to place this institution in a broader comparative context, that of monarchical rulers across world history. Systematic comparison opens up new perspectives and is indispensable in identify...

Systematic backtracking is used in many constraint solvers and combinatorial optimisation algorithms. It is complete and can be combined with powerful search pruning techniques such as branchand-bound, constraint propagation and dynamic variable ordering. However, it often scales poorly to large problems. Local search is incomplete, and has the additional drawback that it cannot exploit pruning...

GOLOMB RULERS Stephen W. Soliday soliday@gar eld.ncat.edu Abdollah Homaifar homaifar@gar eld.ncat.edu Department of Electrical Engineering North Carolina A&T State University Greensboro, North Carolina 27411 Gary L. Lebby lebby@gar eld.ncat.edu Abstract The success of genetic algorithm in nding relatively good solutions to NP-complete problems such as the traveling salesman problem and job-shop...

AGolombRuler is a rulerwith integermarkswhere the distances between every twomarks are distinct. Golomb Rulers find diverse applications in computer science and electrical engineering. According to our knowledge the computational complexity of problems related to the construction of Golomb Rulers is unknown. We provide natural definitions for problems related to the construction of such rulers....

A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for optimal Golomb rulers (those of minimal length given a fixed number of mark...

Individual pairs of polymer-tethered silver nanoparticles, so-called silver plasmon rulers, enable distance and orientation measurements on the nanoscale. The reduced linear dichroism and the spectrum of the light scattered from individual plasmon rulers encode information about their orientation and average interparticle separation, respectively. We took advantage of the gain in information si...

We consider Golomb rulers and their construction. Common rulers feature marks at every unit measure, distances can often be measured with numerous pairs of marks. On Golomb rulers, for every distance there are at most two marks measuring it. The construction of optimal—with respect to shortest length for given number of marks or maximum number of marks for given length—is nontrivial, various pr...