-
On the Solution of a Optimal Control Problem for a Hyperbolic System
Issue:
Volume 7, Issue 3, June 2018
Pages:
75-82
Received:
24 April 2018
Accepted:
10 May 2018
Published:
25 May 2018
Abstract: In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We also find the approximate solutions of the test problems in numerical examples by a MAPLE® program. Finally, the numerical results are presented in the form of tables.
Abstract: In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We ...
Show More
-
Urban Smart Growth Mathematical Model and Application
Geng Liu,
Xiao Han,
Zhen Li
Issue:
Volume 7, Issue 3, June 2018
Pages:
83-88
Received:
25 June 2018
Published:
26 June 2018
Abstract: In view of urban sprawl brought about by urbanization development, this paper establishes a weighted comprehensive evaluation model to measure the city’s smart growth status. Bordeaux is selected as the research object, and relevant data are collected and processed. The data is then substituted into the established model to solve the problem. The results show that some indicators in the city are still at a poor level. Combining the indicators with higher weights and lower scores in the evaluation results, a better urban smart growth plan was proposed. Finally, the ARIMA forecasting model is used to predict the indicators in the future more than ten years. The results verify the effectiveness of the urban smart growth plan and the potential of the plans.
Abstract: In view of urban sprawl brought about by urbanization development, this paper establishes a weighted comprehensive evaluation model to measure the city’s smart growth status. Bordeaux is selected as the research object, and relevant data are collected and processed. The data is then substituted into the established model to solve the problem. The r...
Show More
-
Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions
Issue:
Volume 7, Issue 3, June 2018
Pages:
89-93
Received:
9 November 2017
Accepted:
8 February 2018
Published:
5 July 2018
Abstract: Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.
Abstract: Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean p...
Show More
-
Geometrical, Algebraic, Functional and Correlation Inequalities Applied in Support of James-Stein Estimator for Multidimensional Projections
Issue:
Volume 7, Issue 3, June 2018
Pages:
94-100
Received:
9 November 2017
Accepted:
5 December 2017
Published:
5 July 2018
Abstract: Isoperimetric, Milman reverse, Hilbert, Widder, Fan-Taussky-Todd, Landau, and Fortuin–Kasteleyn–Ginibre (FKG) inequalities in n dimensions in investigations of multidimensional estimators support the use of James-Stein estimator against classical least squares as applied to Cumulant Analysis, Associate Random Variables, and Time Series Analysis.
-
The Impacts of Climate Change on Regional Instability
Geng Liu,
Hao Sun,
YuLan Zhang
Issue:
Volume 7, Issue 3, June 2018
Pages:
101-111
Received:
18 July 2018
Published:
19 July 2018
Abstract: The effects of Climate Change may have the potential to cause the weakening and breakdown of social and governmental structures. In this paper, we construct a fragile index evaluation model to determine the fragility of different countries and measure the impacts of Climate Change. In the first part, by selecting 10 indicators on economic, political, social and national cohesion, we establish a fragile index evaluation model. Applying the calculation method of each indicator value and the Grey slope correlation model, we determine the weight of each indicator and obtain the fragile indicator value. Then we set up the five-level standards of fragility and determine the destructive levels of equally destructive climate disasters in different countries of fragility. In the second part, we study the fragility of Somalia. Based on the fragile index evaluation model, we obtain that Somalia is at a severe fragility level. Then, by analyzing the impact of the drought on the fragile index of Somalia, we obtain that the meteorological drought would cause ecological drought, hydrological arid and agricultural drought, moreover it would lead to food scarcity, environmental degradation and increased conflict, thus contributing to the increasing of the fragile index on Somalia. In the third part, we study the fragility of Cuba. According to the fragile index evaluation model, we conclude that Cuba is at a relatively stable level. By analyzing the historical data of the North Atlantic hurricane, we obtain that with the rising frequency of hurricanes and floods in the Caribbean would push up fragile index of Cuba. We also estimate that fragile degree of Cuba is likely to shift from a relatively stable level to a relatively fragile level within 30 years. In the fourth part, simulation with Global Mapper shows that the sea level rise of 1.5 meters would inundate most of Maldives territory, threatening the stability of the country seriously. While constructing the artificial island is a feasibility intervention to mitigate the threat. According to the economic situation of the country, we propose the phased construction plan with an estimated cost of 3-4 billion dollars. Finally, we test the sensitivity of model. The result shows this model is sensitive to the indicator values but insensitive to indicator weights. In order to adapt to the assessment of large area and small area, we propose the expansion of evaluation index and the optimization plan of weight distribution.
Abstract: The effects of Climate Change may have the potential to cause the weakening and breakdown of social and governmental structures. In this paper, we construct a fragile index evaluation model to determine the fragility of different countries and measure the impacts of Climate Change. In the first part, by selecting 10 indicators on economic, politica...
Show More
-
Oscillations of Solutions of Neutral Nonlinear Differential Equations
Jinyu Wang,
Min Xi,
Ailing Xiao
Issue:
Volume 7, Issue 3, June 2018
Pages:
112-120
Received:
18 July 2018
Published:
19 July 2018
Abstract: This paper aims to establish a new class of differential equations and study the oscillatory behavior of a kind of first-order neutral nonlinear differential equation with time delay arguments. The oscillatory properties of the solutions of the type of first order neutral functional differential equations applied in chemomedical problems are studied. Sufficient conditions for the oscillations of solutions of the above equations are obtained. Also, some results which demonstrate in literature [1-4] will be extended, and the paper focuses on expanding the main finding of literature [2, 3]. Moreover, a new kind of method to be used to discuss the properties of oscillation of the first-order neutral nonlinear differential equations and some theorems are obtained in the paper.
Abstract: This paper aims to establish a new class of differential equations and study the oscillatory behavior of a kind of first-order neutral nonlinear differential equation with time delay arguments. The oscillatory properties of the solutions of the type of first order neutral functional differential equations applied in chemomedical problems are studie...
Show More
-
A Forecast Model for Language Under the Influence of Immigration
Geng Liu,
Keai Yang,
Zhuojun Yao
Issue:
Volume 7, Issue 3, June 2018
Pages:
121-129
Received:
18 July 2018
Published:
19 July 2018
Abstract: Under the influence of globalization, population distribution of different languages has become a matter of universal concern. In this paper, the mater is considered from three aspects. First of all, Gray Model is used to predict the number of second language speakers. Then, the influencing factors are taken into account to predict the number of net immigrants through the BP neural network. Finally, while considering the impact of immigration, Logistic growth model are used to predict the population of native speakers. In order to analyze the demographic changes in different regions, firstly, logistic growth model is used to predict the population in different regions. Secondly, influencing factors are combined with the BP neural network to predict the number of net immigrants in the next 50 years. Based on the forecast, French will surpass the Punjabi, which ranks number nine to become the tenth language with the greatest number of native speakers. As for the total number of speakers using a particular language, native speakers plus second language speakers are considered. The Gray Model is used to predict the number of second language speakers in different regions over the next 50 years. Based on the forecast, no language in the current top-ten lists will be replaced by another language. Net immigration is used to reflect the changing global language distribution over the next 50 years. GDP per capita, education funds, medical expenses and tourism revenue are identified as four factors. BP neural network are used to find out the relationship between influencing factors and net immigrants, and then the number of net immigration of different regions in the next 50 years are predicted. Numerical results demonstrated that model in this paper is efficient and promising.
Abstract: Under the influence of globalization, population distribution of different languages has become a matter of universal concern. In this paper, the mater is considered from three aspects. First of all, Gray Model is used to predict the number of second language speakers. Then, the influencing factors are taken into account to predict the number of ne...
Show More
-
Airport Simulation Technology in Airport Planning, Design and Operating Management
Issue:
Volume 7, Issue 3, June 2018
Pages:
130-138
Received:
18 July 2018
Published:
19 July 2018
Abstract: The promotion and application of airport simulation technology can help improve the soft power of China's civil aviation, and achieve the scientific assessment and refined decision-making for airport planning, construction and operating programs. This paper first sorted out the concepts and types of airport simulation, namely airport airside ground operating simulation, terminal area and airway airspace simulation, terminal building internal process simulation and airport landside curbside traffic simulation, highlighting its relevant applications in airport planning, design and operating management. Taking airport airside ground operating simulation as an example, the application of simulation technology to airport operating capacity of parallel runways was introduced. Finally, the problems and developments of airport simulation technology were discussed in depth.
Abstract: The promotion and application of airport simulation technology can help improve the soft power of China's civil aviation, and achieve the scientific assessment and refined decision-making for airport planning, construction and operating programs. This paper first sorted out the concepts and types of airport simulation, namely airport airside ground...
Show More
-
Application of Classifiers in Predicting Problems of Hydropower Engineering
Liming Huang,
Yi Chen,
Chunyong She,
Yangfeng Wu,
Shuai Zhang
Issue:
Volume 7, Issue 3, June 2018
Pages:
139-145
Received:
18 July 2018
Published:
19 July 2018
Abstract: It’s of vital importance to supervise hydropower engineering in order to make better use of water resources. To supervise it efficiently and effectively, it’s advisable to predict potential problems of hydropower engineering beforehand, after which the people concerned can inspect problems accordingly. Due to the complexity and large quantity of data, data mining techniques are indispensable and useful when making predictions. This study compares performance of Random Forest, C4.5 and Naïve Bayes on the basis of accuracy, precision, recall and F-measure. It comes out that Random Forest is more suitable for this problem. For purpose of more precise results, numbers of trees and features are determined in advance before constructing the forest. Furthermore, which feature influences the prediction result most is also investigated.
Abstract: It’s of vital importance to supervise hydropower engineering in order to make better use of water resources. To supervise it efficiently and effectively, it’s advisable to predict potential problems of hydropower engineering beforehand, after which the people concerned can inspect problems accordingly. Due to the complexity and large quantity of da...
Show More
-
Breast Cancer Diagnosis Using Imbalanced Learning and Ensemble Method
Tongan Cai,
Hongliang He,
Wenyu Zhang
Issue:
Volume 7, Issue 3, June 2018
Pages:
146-154
Received:
2 August 2018
Published:
3 August 2018
Abstract: Worldwide, breast cancer is one of the most threatening killers to mid-aged women. The diagnosis of breast cancer aims to classify spotted breast tumor to be Benign or Malignant. With recent developments in data mining technique, new model structures and algorithms are helping medical workers greatly in improving classification accuracy. In this study, a model is proposed combining ensemble method and imbalanced learning technique for the classification of breast cancer data. First, Synthetic Minority Over-Sampling Technique (SMOTE), an imbalanced learning algorithm is applied to selected datasets and second, multiple baseline classifiers are tuned by Bayesian Optimization. Finally, a stacking ensemble method combines the optimized classifiers for final decision. Comparative analysis shows the proposed model can achieve better performance and adaptivity than conventional methods, in terms of classification accuracy, specificity and AuROC on two mostly-used breast cancer datasets, validating the clinical value of this model.
Abstract: Worldwide, breast cancer is one of the most threatening killers to mid-aged women. The diagnosis of breast cancer aims to classify spotted breast tumor to be Benign or Malignant. With recent developments in data mining technique, new model structures and algorithms are helping medical workers greatly in improving classification accuracy. In this st...
Show More
-
An Explicit Algorithm for the Construction of 3-Band Wavelet Frames Based on FMRA
Zhaofeng Li,
Yuanyuan Zhang
Issue:
Volume 7, Issue 3, June 2018
Pages:
155-160
Received:
9 August 2018
Published:
13 August 2018
Abstract: In 1974, an French engineer, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing and in 1986, the famous mathematician, Y. Meyer, created a real small wave base. From then on, Wavelet transform is a rapidly developing new subfield in mathematics and is used in more and more fields, such as signal analysis, image processing, quantum mechanics and theoretical physics etc. Multiresolution analysis is a systematic method for constructing orthonormal wavelet bases and most of the current dilation is M=2 With the development of wavelet transform, M>2 -band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing. However, there are relatively less results for the case of M>2. Based on this fact and inspired by other similar papers, this paper studies the 3-band wavelets and wavelet frames associated with a given refinable function based on frame multiresolution analysis. In this paper, firstly, a sufficient and necessary condition which the refinable function should satisfy for the existence of wavelet frames is showed. Further, an explicit algorithm to construct this frames is worked out and finally, several designed examples are constructed to illustrate this algorithm.
Abstract: In 1974, an French engineer, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing and in 1986, the famous mathematician, Y. Meyer, created a real small wave base. From then on, Wavelet transform is a rapidly developing new subfield in mathematics a...
Show More
-
The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA
Yuanyuan Zhang,
Zhaofeng Li
Issue:
Volume 7, Issue 3, June 2018
Pages:
161-166
Received:
9 August 2018
Published:
13 August 2018
Abstract: In 1974, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing. In 1986, Y. Meryer created a real small wave base, and the wavelet analysis began to flourish after a multi scale analysis of the same method of constructing the small wave base with S. Mallat. In order to analyze and deal with non-stationary signals, a series of new signal analysis theories are proposed.: Short Time Fourier Transform, time-frequency analysis, wavelet transform, and fractional Fourier transform and so on. In this paper, an explicit algorithm is given to construct the minimum-energy frames based on frame multiresolution analysis via characteristic vectors of the mask matrix. In section 2, we show the structure of minimum-energy wavelet frames in terms of their masks (Lemma 1) and discuss that we should eliminate the correlation of the rows of the mask matrix by the polyphase decomposition technique. Based on FMRA, an explicit algorithm is given to construct this frames. By this method, all the minimum-energy wavelet frames can be obtained. As an application, several examples are showed to explain this method in section 3. This method can also be applied in other fields of wavelet analysis.
Abstract: In 1974, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing. In 1986, Y. Meryer created a real small wave base, and the wavelet analysis began to flourish after a multi scale analysis of the same method of constructing the small wave base with S....
Show More
-
Axiomatization of Aristotelian Syllogistic Logic Based on Generalized Quantifier Theory
Issue:
Volume 7, Issue 3, June 2018
Pages:
167-172
Received:
9 August 2018
Published:
13 August 2018
Abstract: Syllogistic reasoning is important due to the prominence of syllogistic arguments in human reasoning, and also to the role they have played in theory of reasoning from Aristotle onwards. Aristotelian syllogistic logic is a formal study of the meaning of four Aristotelian quantifiers and of their properties. This paper focuses on logical system based on syllogistic reasoning. It firstly formalized the 24 valid Aristotle’s syllogisms, and then has proven that the other 22 valid Aristotle’s syllogisms can be derived from the syllogisms ‘Barbara’ AAA-1 and ‘Celarent’ EAE-1 by means of generalized quantifier theory and set theory, so the paper has completed the axiomatization of Aristotelian syllogistic Logic. This axiomatization needs to make full use of symmetry and transformable relations between/among the monotonicity of the four Aristotelian quantifiers from the perspective of generalized quantifier theory. In fact, these innovative achievements and the method in this paper provide a simple and reasonable mathematical model for studying other generalized syllogisms. It is hoped that the present study will make contributions to the development of generalized quantifier theory, and to bringing about consequences to natural language information processing as well as knowledge representation and reasoning in computer science.
Abstract: Syllogistic reasoning is important due to the prominence of syllogistic arguments in human reasoning, and also to the role they have played in theory of reasoning from Aristotle onwards. Aristotelian syllogistic logic is a formal study of the meaning of four Aristotelian quantifiers and of their properties. This paper focuses on logical system base...
Show More
-
General Distance Energies and General Distance Estrada Index of Random Graphs
Issue:
Volume 7, Issue 3, June 2018
Pages:
173-179
Received:
9 August 2018
Published:
13 August 2018
Abstract: In 2000s, Gutman and Güngör introduced the concept of distance energy and the distance Estrada index for a simple graph G respectively. Moreover, many researchers established a large number of upper and lower bounds for these two invariants. But there are only a few graphs attaining the equalities of those bounds. In this paper, however, the exact estimates to general distance energy are formulated for almost all graphs by probabilistic and algebraic approaches. The bounds to general distance Estrada index are also established for almost all graphs by probabilistic and algebraic approaches. The results of this paper generalize the results of the distance energy and distance Estrada of random graph.
Abstract: In 2000s, Gutman and Güngör introduced the concept of distance energy and the distance Estrada index for a simple graph G respectively. Moreover, many researchers established a large number of upper and lower bounds for these two invariants. But there are only a few graphs attaining the equalities of those bounds. In this paper, however, the exact ...
Show More
