Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

We investigate the Castelnuovo--Mumford regularity and the multiplicity of the toric ring associated to a three-dimensional Ferrers diagram. In particular, in the rectangular case, we are able to provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanied pair of Ferrers diagrams under some mild conditions, and bound the Castelnuovo--Mumford regularity for more general cases.Comment: 22 pages, 2 figures and comments are welcom

Use Quickest Path to Evaluate the Performance for An E-Commerce Network

In the E-Commerce network, it is an important issue to reduce the transmission time. The quickest path problem is to find the path in the network to send a given amount of data from the source to the sink with minimum transmission time. This problem traditionally assumed that the capacity of each arc in the network is deterministic. However, the capacity of each arc is stochastic due to failure, maintenance, etc. in many real-life networks. This paper proposes a simple algorithm to evaluate the probability that d units of data can be sent through the E-Commerce network within T units of time. Such a probability is a performance index for E-Commerce networks

Quality Management for an E-Commerce Network under Budget Constraint

In general, several types of information data are transmitted through an E-Commerce network simultaneously. Each type of information data is set to one type of commodity. Under the budget constraint, this paper studies the probability that a given amount of multicommodity can be transmitted through an E-Commerce network, where each node and each arc has several possible capacities. We may take this probability as a performance index for this network. Based on the properties of minimal paths, a simple algorithm is proposed to generate all lower boundary points for (d1 ,d2 ,…,dp ;C) where di is the demand of commodity i and C is the budget. The probability can then be calculated in terms of such points

Evaluation of Network Reliability for Computer Networks with Multiple Sources

Evaluating the reliability of a network with multiple sources to multiple sinks is a critical issue from the perspective of quality management. Due to the unrealistic definition of paths of network models in previous literature, existing models are not appropriate for real-world computer networks such as the Taiwan Advanced Research and Education Network (TWAREN). This paper proposes a modified stochastic-flow network model to evaluate the network reliability of a practical computer network with multiple sources where data is transmitted through several light paths (LPs). Network reliability is defined as being the probability of delivering a specified amount of data from the sources to the sink. It is taken as a performance index to measure the service level of TWAREN. This paper studies the network reliability of the international portion of TWAREN from two sources (Taipei and Hsinchu) to one sink (New York) that goes through a submarine and land surface cable between Taiwan and the United States

Minimally invasive strategy for gynecologic cancer with solitary periacetabular metastasis

SummaryTumor with bone metastases to the periacetabulum is rare, and its surgical management is challenging. Instead of wide excision with reconstruction of the hip joint, we used a relatively noninvasive method to manage periacetabular metastasis. Such a procedure for this condition has the benefits of short surgical time, less bleeding, and fewer complications during surgery. Our surgical management of the case reported here included curettage, phenol cauterization and filling of cisplatin-loaded cement in order to reduce local recurrence. After following-up for 2 years, there was no local recurrence and disease progression