Approximate Solutions of Polynomial Equations

AbstractIn this paper, we introduce “approximate solutions" to solve the following problem: given a polynomial F(x, y) over Q, where x represents an n -tuple of variables, can we find all the polynomials G(x) such that F(x, G(x)) is identically equal to a constant c in Q ? We have the following: let F(x, y) be a polynomial over Q and the degree of y in F(x, y) be n. Either there is a unique polynomial g(x) ∈Q [ x ], with its constant term equal to 0, such that F(x, y) =∑j=0ncj(y−g(x))jfor some rational numbers cj, hence, F(x, g(x) +a) ∈Q for all a∈Q, or there are at most t distinct polynomials g1(x),⋯ , gt(x), t≤n, such that F(x, gi(x)) ∈Q for 1 ≤i≤t. Suppose that F(x, y) is a polynomial of two variables. The polynomial g(x) for the first case, or g1(x),⋯ , gt(x) for the second case, are approximate solutions of F(x, y), respectively. There is also a polynomial time algorithm to find all of these approximate solutions. We then use Kronecker’s substitution to solve the case of F(x, y)

Bending of isosceles right triangular plates

In this thesis the series expansion method is used to obtain the moments and deflections of an isosceles right triangular plate bent by arbitrary transverse loads. The method is based on using an antisymmetric load on a square plate. Two boundary conditions are solved and the numerical results obtained for these cases are tabulated --Abstract, page ii

Standardized maximim D-optimal designs for enzyme kineticinhibition models

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters.An alternative is the maximin approach that allows the user to specify a range of values for each parameter ofinterest. However, the maximin approach is difficult because we first have to determine the locally optimal designfor each set of nominal values before maximin types of optimal designs can be found via a nested optimizationprocess. We show that particle swarm optimization (PSO) techniques can solve such complex optimizationproblems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae forstandardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact andnonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibitionmodels are not necessarily supported at a minimum number of points. To facilitate use of such designs, wecreate a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs

Using Machine Learning for Handover Optimization in Vehicular Fog Computing

Smart mobility management would be an important prerequisite for future fog computing systems. In this research, we propose a learning-based handover optimization for the Internet of Vehicles that would assist the smooth transition of device connections and offloaded tasks between fog nodes. To accomplish this, we make use of machine learning algorithms to learn from vehicle interactions with fog nodes. Our approach uses a three-layer feed-forward neural network to predict the correct fog node at a given location and time with 99.2 % accuracy on a test set. We also implement a dual stacked recurrent neural network (RNN) with long short-term memory (LSTM) cells capable of learning the latency, or cost, associated with these service requests. We create a simulation in JAMScript using a dataset of real-world vehicle movements to create a dataset to train these networks. We further propose the use of this predictive system in a smarter request routing mechanism to minimize the service interruption during handovers between fog nodes and to anticipate areas of low coverage through a series of experiments and test the models' performance on a test set

Toward a Framework of E-Business Strategy: A Case Study Approach

E-business is erasing the typical boundaries of space, time, organization and community with shared interest and cooperation. The two most critical features of e-business practices are: (1) the unique capacity for customization, and (2) the trust-based sharing of information along supply chains. E-business strategy should be particularly effective for globalization. The case of Haier from China suggests that legacy firms need to develop e-business strategy to compete in the Internet Age. However, e-business must be built on a solid basis of sound business practices. The case of Haier also suggests that companies need to be creative when formulating e-business strategies for operations in the developing countries where infrastructure is underdeveloped. Further, strategic alliances between local and multinational firms are imperative for e-business in the developing countries such as China

On polynomials taking small values at integral arguments II

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A Network Stability Monitoring Mechanism of Cluster-Oriented Wireless Sensor Network

In wireless sensor network (WSN), every sensor node could active dynamically. Therefore, those sensor nodes will affect the stability of network topology because of clustering and de-clustering, and continuously make reconfiguration for the clusters of wireless sensor network, all that will influence the overall function of network. It is an important issue that how to elect a cluster manager (CM) to keep the stability of network topology. In addition, large amount of events maybe flood suddenly in a local area. Such the case might raise the overload of CM, even lead CM to fail or crash and the WSN topology maybe self-organized. However, a mechanism needs to be considered that allows coping with the additional loads and can balance the workload of CM. In this study, a preventable and supportable monitor mechanism to avoid CM overload cause network unstable and to reduce load imbalance problem is proposed. Hence, it can prolong lifetime of network and raise performance of network efficiently