A Note on Graphs of Linear Rank-Width 1

We prove that a connected graph has linear rank-width 1 if and only if it is a distance-hereditary graph and its split decomposition tree is a path. An immediate consequence is that one can decide in linear time whether a graph has linear rank-width at most 1, and give an obstruction if not. Other immediate consequences are several characterisations of graphs of linear rank-width 1. In particular a connected graph has linear rank-width 1 if and only if it is locally equivalent to a caterpillar if and only if it is a vertex-minor of a path [O-joung Kwon and Sang-il Oum, Graphs of small rank-width are pivot-minors of graphs of small tree-width, arxiv:1203.3606] if and only if it does not contain the co-K_2 graph, the Net graph and the 5-cycle graph as vertex-minors [Isolde Adler, Arthur M. Farley and Andrzej Proskurowski, Obstructions for linear rank-width at most 1, arxiv:1106.2533].Comment: 9 pages, 2 figures. Not to be publishe

Algorithmic Aspects of a General Modular Decomposition Theory

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, the terminology ``module'' not only captures the classical graph modules but also allows to handle 2-connected components, star-cutsets, and other vertex subsets. The main result is that most of the nice algorithmic tools developed for modular decomposition of graphs still apply efficiently on our generalisation of modules. Besides, when an essential axiom is satisfied, almost all the important properties can be retrieved. For this case, an algorithm given by Ehrenfeucht, Gabow, McConnell and Sullivan 1994 is generalised and yields a very efficient solution to the associated decomposition problem

Convolution for the transform induced by Fourier integral transform and its inverse

Joint Research on Environmental Science and Technology for the Eart

US-China rivalry in Southeast Asia region: a study on the South China Sea case

Southeast Asia is one of the places where fierce rivalry is taking place between the two leading powers in the world today - the US and China. The US-China rivalry in this region takes place in key fields, from politics - diplomacy, economy, security - defense to "soft power", the most prominent of which is the South China Sea issue. This article analyzes the strategic importance of the South China Sea in the policy of the US and China, the competition between the US and China in Southeast Asia in general, and the South China Sea in particular. To achieve this goal, the authors use research methods in international relations to analyze the main issues of the study. In addition to reviewing previous scholarly research and reviews, the authors use a comparative approach to assess the interactions between theory and data. The authors believe the data is important for accurately assessing the strategic competition between the US and China in Southeast Asia and the South China Sea. The rise of China in the early years of the XXI century strongly influenced the adjustment of the US policy in Southeast Asia and the powerful US-China rivalry in this region and the South China Sea. This rivalry is becoming increasingly complicated, and geopolitical conflicts between major powers are possible in the following years

Refinement of an inverse analysis procedure for estimating tensile constitutive law of UHPC

As regard to cementitious composite materials added a certain dosage of fiber, estimation of tensile constitutive law through inverse analysis methods is no longer extraordinary. However, development or improvement to achieve an effective method for estimating such a tensile behavior of fiber reinforced concrete (FRC) or Ultra high-performance concrete (UHPC) is still an interesting topic to researchers. In this respect, the paper presents a development of inverse analysis method developed by Lopez to obtain the stress-strain behavior of UHPC from the four-point bending test. By applying optimization algorithm into the iterative procedure of method, an improvement could be obtained for the inverse analysis with a high degree of automation in calculation. A post-process treatment for inverse analysis results is also proposed to bring a finer agreement between the tensile behavior curve obtained by the inverse analysis and result curve of uniaxial tensile test (UTT). The effectivity of process is shown through a comparison between the result obtained by the proposed method and the result in Lopez’s public paper