FROM THE HISTORY OF OSSETIC WRITING. G.V. BAEV’S MEMORANDUM OF 1925

Настоящая статья содержит ранее не публиковавшийся и неизвестный меморандум Г.В. Баева, который теперь хранится в его личном архиве (Берлин, Национальная библиотека). В этом коротком тексте (всего восемь страниц), написанном на русском языке в 1925 году и адресованном Исполнительному комитету Северо-Осетинской Автономной Области, автор выражает свое негативное мнение о введении латинского алфавита в Осетии, излагая культурные и практические причины предпочтения им кириллицы, которая впервые использовалась, в гражданском варианте, в осетинской грамматике, составленной академиком А.М. Шегреном в 1844 году. Издание меморандума основывается на двух практически идентичных машинописных черновиках и преследует две главные цели: сделать этот текст доступным для более широкой академической публики и, следовательно, стимулировать поиск оригинального текста в архивах Республики Северная Осетия-Алания. The present article features a hitherto unpublished and unknown memorandum by G.V. Baev, now kept in his personal archive (Berlin, National Library). In this short text (eight pages), written in Russian in 1925 and addressed to the executive committee of the North Ossetian autonomous region, G.V. Baev expresses his negative opinion about the introduction of a Latin-based alphabet in Ossetia and exposes the cultural and practical reasons of his preference of the Cyrillic script, firstly used, in the civil typeface, in the Ossetic grammar composed by the academician A.M. Sjögren in 1844. The edition of the memorandum is based on two almost identical machine-type drafts and has two major aims: to make this text available to a broader academic audience and, as a consequence, to stimulate the search of the original text in the archives of the Republic of North Ossetia-Alania.

A Polynomial Algorithm for Sequencing Jobs with Release and Delivery Times on Uniform Machines

The problem of sequencing $n$ equal-length non-simultaneously released jobs with delivery times on $m$ uniform machines to minimize the maximum job completion time is considered. To the best of our knowledge, the complexity status of this classical scheduling problem remained open up to the date. We establish its complexity status positively by showing that it can be solved in polynomial time. We adopt for the uniform machine environment the general algorithmic framework of the analysis of behavior alternatives developed earlier for the identical machine environment. The proposed algorithm has the time complexity $O(\gamma m^2 n\log n)$, where $\gamma$ can be any of the magnitudes $n$ or $q_{\max}$, the maximum job delivery time. In fact, $n$ can be replaced by a smaller magnitude $\kappa<n$, which is the number of special types of jobs (it becomes known only upon the termination of the algorithm).

PARALLEL MACHINE SCHEDULING WITH JOB DELIVERY COORDINATION

We analyse a parallel (identical) machine scheduling problem with job delivery to a single customer. For this problem, each job needs to be processed on $m$ parallel machines non-pre-emptively and then transported to a customer by one vehicle with a limited physical capacity. The optimization goal is to minimize the makespan, the time at which all the jobs are processed and delivered and the vehicle returns to the machine. We present an approximation algorithm with a tight worst-case performance ratio of $7/3-1/m$ for the general case, $m\geq 3$.

Shapley Value for Parallel Machine Sequencing Situation without Initial Order

We consider the parallel identical machine sequencing situation without initial schedule. For the situation with identical job processing time, we design a cost allocation rule which gives the Shapley value of the related sequencing game in polynomial time. For the game with identical job weight, we also present a polynomial time procedure to compute the Shapley value.