External stress-corrosion cracking of a 1.22-m-diameter type 316 stainless steel air valve

An investigation was conducted to determine the cause of the failure of a massive AISI Type 316 stainless steel valve which controlled combustion air to a jet engine test facility. Several through-the-wall cracks were present near welded joints in the valve skirt. The valve had been in outdoor service for 18 years. Samples were taken in the cracked regions for metallographic and chemical analyses. Insulating material and sources of water mist in the vicinity of the failed valve were analyzed for chlorides. A scanning electron microscope was used to determine whether foreign elements were present in a crack. On the basis of the information generated, the failure was characterized as external stress-corrosion cracking. The cracking resulted from a combination of residual tensile stress from welding and the presence of aqueous chlorides. Recommended countermeasures are included

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Ketidakoptimalan Penanganan Perkara Pidana Rehabilitasi Penyalahguna Narkotika di Wilayah Hukum Kejaksaan Negeri Mejayan Kabupaten Madiun

ABSTRAK Rahmat Hidayat S331302008, 2015, Ketidakoptimalan Penanganan Perkara Pidana Rehabilitasi Penyalahguna Narkotika di Wilayah Hukum Kejaksaan Negeri Mejayan Kabupaten Madiun. Tujuan dari penulisan tesis ini yaitu pelaksanaan rehabilitasi bagi penyalahguna narkotika yang belum dilaksanakan dan upaya yang dilakukan agar rehabilitasi secara optimal dilaksanakan di wilayah hukum Kejaksaan Negeri Mejayan Kabupaten Madiun. Adapun rumusan masalah yang diangkat dalam penulisan tesis ini adalah Mengapa rehabilitasi bagi penyalahguna narkotika di wilayah Hukum Kejaksaan Negeri Mejayan Kabupaten Madiun belum dilaksanakan secara optimal dan Upaya apa yang suharusnya dilakukan agar rehabilitasi penyalahguna narkotika di wilayah Hukum Kejaksaan Negeri Mejayan Kabupaten Madiun dilaksanakan secara optimal. Penelitian dalam tesis ini adalah penelitian hukum yuridis normatif dan yuridis empiris, jenis pendekatan yang dipergunakan dalam penulisan tesis ini adalah kualitatif adalah suatu cara analisis hasil penelitian yang menghasilkan data deskriptif analitis, yaitu data yang dinyatakan oleh responden sacara tertulis atau lisan serta juga tingkah laku yang nyata, yang diteliti dan dipelajari sebagai sesuatu yang utuh. Pelaksanaan rehabilitasi belum dilaksanakan secara optimal oleh penegak hukum di wilayah hukum Kejaksaan Negeri Mejayan Kabupaten Madiun terhadap pelaku penyalahguna narkotika. Upaya-upaya terhadap pelaksanaan rehabilitasi penyalahguna narkotika, aparat penegak hukum di wilayah hukum Kejaksaan Negeri Mejayan Kabupaten Madiun dibantu oleh Pemerintah Kabupaten Madiun dalam proses awal penegakan hukum terhadap penyalahguna narkotika sedini mungkin dilakukannya Assesmen Terpadu. Kata kunci : Rehabilitasi Narkotika, Penanganan Perkara Pidana

Hard constraint satisfaction problems have hard gaps at location 1

An instance of the maximum constraint satisfaction problem (Max CSP) is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Maxk-SAT and Max Cut) and is consequently NP-hard. Thus, it is natural to study how restrictions on the allowed constraint types (or constraint language) affect the complexity and approximability of Max CSP. The PCP theorem is equivalent to the existence of a constraint language for which Max CSP has a hard gap at location 1; i.e. it is NP-hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable. All constraint languages, for which the CSP problem (i.e., the problem of deciding whether all constraints can be satisfied) is currently known to be NP-hard, have a certain algebraic property. We prove that any constraint language with this algebraic property makes Max CSP have a hard gap at location 1 which, in particular, implies that such problems cannot have a PTAS unless P=NP. We then apply this result to Max CSP restricted to a single constraint type; this class of problems contains, for instance, Max Cut and Max DiCut. Assuming P≠NP, we show that such problems do not admit PTAS except in some trivial cases. Our results hold even if the number of occurrences of each variable is bounded by a constant. Finally, we give some applications of our results

Approximability of integer programming with generalised constraints

Given a set of variables and a set of linear inequalities over those variables, the objective in the Integer Linear Programming problem is to find an integer assignment to the variables such that the inequalities are satisfied and a linear goal function is maximised. We study a family of problems, called Maximum Solution, which are related to Integer Linear Programming. In a Maximum Solution problem, the constraints are drawn from a set of allowed relations, hence arbitrary constraints are studied instead of just linear inequalities. When the domain is Boolean (i.e. restricted to {0, 1}), the maximum solution problem is identical to the well-studied Max Ones problem, and the approximability is completely understood for all restrictions on the underlying constraints [Khanna et al., SIAM J. Comput., 30 (2000), pp. 1863-1920]. We continue this line of research by considering domains containing more than two elements. Our main results are two new large tractable fragments for the maximum solution problem and a complete classification for the approximability of all maximal constraint languages. Moreover, we give a complete classification of the approximability of the problem when the set of allowed constraints contains all permutation constraints. Our results are proved by using algebraic results from clone theory and the results indicates that this approach is very useful for classifying the approximability of certain optimisation problems