Ordinal proportional cost sharing

We consider cost sharing problems with variable demands of heterogeneous goods. We study the compatibility of two axioms imposed on cost sharing methods: ordinality and average cost pricing for homogeneous (ACPH) goods. We generalize the ordinal proportional method (OPM) for the two-agent case, Sprumont [Journal of Economic Theory 81 (1998) 126162] to arbitrary number of agents

An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$

Complete Solutions for a Combinatorial Puzzle in Linear Time

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n + m$. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of $n$ black checkers and $m$ white checkers, and finally, we present an explicit solution for the general game

Novel waveguide filters in communication systems

This thesis presents the design and fabrication of several waveguide bandpass filters operating at X band (8-12 GHz), V band (50-75 GHz) and WR-1.5 band (500-750 GHz). A WR-1.5 band (500-750 GHz) 3$^{rd}$ order waveguide bandpass filter has been designed and manufactured using high-precision computer numerically controlled (CNC) metal machining. This filter is used as a prototype to find the tolerance of commercial CNC milling machine. The sensitivity analysis and yield analysis are presented to help estimate the real production and improve the fabrication tolerance. However, the long waveguide section in that filter leads to additional losses. To reduce the loss of waveguide, the filter can be shortened by applying folded structure, which can make the whole structure more compact. Therefore, the filters with folded structure was developed. The folded structure allows a very compact filter with axial connection to waveguide ports. However, the compact structure leads to small bandwidth and increases the difficulty of fabrication. In order to increase the bandwidth, a new coupling structure has been introduced. The bandwidth is increased successfully. The designs of three-dimensional (3D) printed filters are also presented in this thesis. 3D printing presents attractive benefits such as flexibility in structural and material selection. In contrast to filters fabricated by conventional milling technologies, these two 3D printed filters can be manufactured in a single piece without assembly. To take advantage of the flexibility in structural selection, bent, twisted and triangular resonators are analyzed and applied on the filter. Bend and twist structure can change port orientation and polarization, respectively. In traditional, to realize port orientation and polarization, two components are needed. However, the twist waveguide filter in this thesis can be considered as integration of filtering and polarization change. 3D printing shows great potential for the devices working at 60 GHz or higher frequency. However, the fabrication still requires external support structures to avoid overhang structure. These additional support structures will be no longer needed if the resonators are triangular with appropriate angle range. Therefore, the waveguide filter with triangular resonators are designed. The results show that the triangular resonator can realize self-supporting structure and no more additional internal supporting structure are needed. Because the structure of filter is raised to make sure the filter port is on the middle of the flange, external support structure is still needed under the filter. But it is a relatively easy support structure and requires less support materials

A Calibration Method for Misalignment Angle of Vehicle-mounted IMU

AbstractIn order to get accurate navigation data via Strapdown Inertial Navigation System (SINS), calibration of misalignment angle between Inertial Measurement Unit (IMU) and vehicle is necessary. The misalignment angle model is simplified, assuming that vehicle travels on a horizontal plane. Due to the velocity of vehicle is small, equation of specific force is simplified. And then equation of misalignment angle is deduced on condition that vehicle travels on a horizontal plane, making straight motion ideally. Angular rate is used to discriminate that vehicle making straight motion. Steps for calibrate misalignment angle are established. In calibration experiment, data are collected and misalignment angle of vehicle-mounted IMU is calibrated using simple techniques of data processing. Analysis shows that, compensation of misalignment angle helps improving the accuracy of SINS. Position error of SINS solution is decreased and the acceleration of vehicle is more accurate

Analytical model of spread of epidemics in open finite regions

Epidemic dynamics, a kind of biological mechanisms describing microorganism propagation within populations, can inspire a wide range of novel designs of engineering technologies, such as advanced wireless communication and networking, global immunization on complex systems, and so on. There have been many studies on epidemic spread, but most of them focus on closed regions where the population size is fixed. In this paper, we proposed a susceptible-exposed-infected-recovered model with a variable contact rate to depict the dynamic spread processes of epidemics among heterogeneous individuals in open finite regions. We took the varied number of individuals and the dynamic migration rate into account in the model. We validated the effectiveness of our proposed model by simulating epidemics spread in different scenarios. We found that the average infected possibility of individuals, the population size of infectious individuals in the regions, and the infection ability of epidemics have great impact on the outbreak sizes of epidemics. The results demonstrate that the proposed model can well describe epidemics spread in open finite regions