We study β-deformed matrix models with Penner type potentials, which correspond to N = 2 SU (2) supersymmetric gauge theories with N F = 2, 3, and 4 flavors. We compute explicitly the genus one corrections to the free energy of the matrix model and show that they match the corresponding results obtained from the Nekrasov partition function.

A railway signalling system is the control equipment performing vital functions, and the validation on functional safety of its software is a very important issue. Recently, various software testing tools have been applied to verify signalling system software. However, these tools are unable to support black-box testing to verify the functional safety of embedded signalling system software, and few black-box testing tools are currently commercialized. Since most of these commercialized black-box testing tools depend on a testing method through direct accessing to the target memory under test, there are a lot of difficulties when applying them to the test. In the case of using the existing tool, it is possible to test them only if the internal memory addresses values that are occupied by the executing embedded software. Therefore they are rarely utilized to verify the embedded software in the actual operating environment. To overcome these problems, this study developed a black-box testing tool using communication interfaces which are utilized when actually operating. The real interface channel is used as an input and monitoring channel for black-box testing. This approach carries out the test in a manner where the test data are input and the results are fed back to these interface channels by utilizing interface channels with other signalling equipment already operating. Boundary value analysis and equivalence class analysis modules were used to generate test cases within the developed new testing tool. The pilot of the proposed testing tool has been completed, and the feasibility study is now in progress with railway signalling system software in Korea as its test target.

Many railway signalling functions have increasingly depended on computer software with recent development in computing technology, leading to evolution into more flexible and intelligent railway signalling system. Meanwhile, software programs are likely to have many errors and the cost incurred by such errors has increased.Especially, if fatal software error occurs during railway operation, it may result in loss of lives. So the software verification and validation have become more important. It is needed for software functional safety tool to support these, but most commercial tools depend on direct access to the system's memory, resulting in many difficulties in application. Owing to such difficulties and complexity, they are rarely used in railway signalling system software validation. In this study, a new testing tool for software functional testing through an external interface that can be easily used in functional testing of software was developed. Such testing tool allows development and analysis of test cases for black-box testing through analysis of actually used interface protocols, leading to increased user convenience.

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Chiral rings of two-dimensional (2,2) theories coupled to 4d N = 2 theories with matter hypermultiplets are studied. Specifically, the vacua of the twisted superpotential of the 2d theories with vanishing sum of matter charges are computed by considering the resolvent of the bulk theory. The solutions to the chiral ring equations are also obtained from the instanton partition function via Higgsing for simple surface operators and via the orbifold description for full surface operators. These 2d/4d coupled theories are lifted to 3d/5d theories and vacua are found similarly in two different methods: by solving the 3d chiral ring equations taking into account the effect of 5d resolvent and by computing the 5d instanton partition function in the presence of a surface operator. We also check the Seiberg-like duality for both 2d/4d and 3d/5d coupled systems with a specific Chern-Simons coefficient for the latter.