Wyniki wyszukiwania - BazTech

1

Toehold purchase problem: a comparative analysis of two strategies

Banakh I., Banakh T., Vovk M., Trisch P.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

|

2015

|

Vol. 4, No 1

3--10

EN

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold strategies and compare the expected profits of the investor and the probabilities of takeover the firm in both strategies. It turns out that the expected profits of the investor in both strategies coincide. On the other hand, the probability of takeover the firm using the toehold strategy is considerably higher comparing to the no-toehold strategy. In the analysis of the models we apply the apparatus of incomplete Beta functions and some refined bounds for central binomial coefficients.

2

A further generalization of Hardy-Hilbert's integral inequality with parameter and applications

He L., Dragomir S. S., Yang Q.

Journal of Applied Analysis

|

2006

|

Vol. 12, nr 1

59-70

EN

In this paper, by introducing some parameters and by employing a sharpening of Hölder's inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder's theorem is given.

3

Beta neuro-fuzzy systems

Alimi A. M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

|

2003

|

Vol. 7, No 1

23-41

EN

In this paper we present the Beta function and its main properties. A key feature of the Beta function, which is given by the central-limit theorem, is also given. We then introduce a new category of neural networks based on a new kernel: the Beta function. Next, we investigate the use of Beta fuzzy basis functions for the design of fuzzy logic systems. The functional equivalence between Beta-based function neural networks and Beta fuzzy logic systems is then shown with the introduction of Beta neuro-fuzzy systems. By using the SW theorem and expanding the output of the Beta neuro-fuzzy system into a series of Beta fuzzy-based functions, we prove that one can uniformly approximate any real continuous function on a compact set to any arbitrary accuracy. Finally, a learning algorithm of the Beta neuro-fuzzy system is described and illustrated with numerical examples.

4

Beta Fuzzy Logic Systems: Approximation Properties in the mimo Case

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

|

2003

|

Vol. 13, no 2

225-238

EN

Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.

5

Beta Fuzzy Logic Systems: Approximation Properties in the Siso Case

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

|

2000

|

Vol. 10, no 4

857-875

EN

In this paper, a Single-Input Single-Output (SISO) Sugeno fuzzy model of the zeroth order with Beta membership functions for input variables is adopted. After the introduction of Beta Fuzzy Logic Systems (BFLS) a constructive theory is developed to establish the fact that they are universal approximators. Based on this theory, an algorithm, which can actually construct a BFLS approximating a given continuous function with an arbitrary degree of accuracy, is described. We then show that BFLSs satisfy more critical properties which are the best approximation property and the interpolation property. We complete the paper with a series of numerical comparisons between the approximation performances of BFLSs and other classes of widely used fuzzy logic systems. These comparisons confirm that BFLSs perform best in all the cases studied.