JOURNAL OF MATHEMATICS AND TECHNOLOGY |

**JOURNAL OF MATHEMATICS AND TECHNOLOGY (JMT)**

ISSN: 2078-0257 | Next issue: **March 30, 2014**

**DOI:** 10.7813/jmt.2014

The Journal of Mathematics and Technology is published two times per year in **March and November**. Journal publishes original papers in mathematics and technology in general, but giving a preference to those in the areas of mathematics and technology represented by the editorial board. All submitted papers are considered subject to the undersanding that they have not been published and are not being considered for publication elsewhere. To be publishable, papers must treat new research, be well written, and be of interest to a significant segment of the science community.
There is no publication fee. But, subscribe to receive 1 print copy __(see example)__ of the journal is compulsory for authors. Please, see __Print Subscription Price List__ for 2014.

March, 2013 | Vol. 4. No. 1. | DOI: 10.7813/jmt.2013/4-1 |

**JMT13V4N1**| Purchase a single issue

**1. Manuel Alberto M. Ferreira, Marina Andrade **

The Hahn-Banach theorem and the separation of a vector space convex parts

**Abstract:** The main objective of this article is to present the separation theorems, important consequences of the Hahn-Theorem theorem. These results are the fundamentals of the convex optimization mathematical approach. Along this work begin to consider vector spaces, in general, then normed spaces and posteriorly Hilbert spaces. It ends with the presentation of applications of these results in convex programming and in minimax theorem, two important tools in operations research, management and economics, for instance.

**Keywords: ** Hahn-Banach theorem, separation theorems, convex programming, minimax theorem

** Pages**: 5-15

**Cite this article**:

M.A.M. Ferreira, M. Andrade. The Hahn-Banach theorem and the separation of a vector space convex parts. Journal of Mathematics and Technology 2013; 4(1), 5-15.

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**2. I.A. Adeleke, E.E.E. Akarawak, R.O. Okafor **

Investigating the distribution of the ratio of beta and Weibull random variables

**Abstract:** The beta and Weibull distributions are well known and widely used continuous probability distributions. While the beta distribution has been applied to studies on proportions or prevalence, the Weibull is widely used in studies on survival and reliability analysis. Various generalizations and extensions of both distributions have been studied. Yet, there is need for continuous generalization and extension of these distributions to more complex situations in which its use can be deployed. In this work, we investigated the distribution of the ratio of independent beta and Weibull random variables. We obtained expressions for the pdf, cdf, generalized rth moment and rth cumulant of the ratio. Some properties of the resulting ratio distributions were also studied via simulations. It is our expectations that this ratio generalization may provide an efficient techinique of addressing problems on ratio of two independent random variables that arise in real life encounters.

**Keywords: ** Incomplete beta function, Beta distribution, Weibull distribution, Ratio, binomial series

** Pages**: 16-22

**Cite this article**:

I.A. Adeleke, E.E.E. Akarawak, R.O. Okafor. Investigating the distribution of the ratio of beta and Weibull random variables. Journal of Mathematics and Technology 2013; 4(1), 16-22.

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**3. Ivana Malá **

The impact of the choice of model distribution on conditional distributions of incomes

**Abstract:** In the text equivalised net annual income of the Czech households is modeled with the use of lognormal and Dagum distribution and mixtures of two these distributions defined by the gender of the head of the household. Conditional distributions are studied given information that an income is less, greater than a given amount or it is included in a finite interval. Conditional distribution functions are derived and characteristics of location and variability are evaluated with the use of the known formulas and numerical methods. The impact of the choice of the model for the whole populations of households and given amounts are shown in figures and discussed. From the results a gap between households headed by a man and a woman is quantified with the use of estimated characteristics of the location and variability.

**Keywords: ** lognormal distribution, Dagum distribution, finite mixture of distributions, conditional distributions

** Pages**: 23-31

**Cite this article**:

I. Malá. The impact of the choice of model distribution on conditional distributions of incomes. Journal of Mathematics and Technology 2013; 4(1), 23-31.

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**4. Seifedine Kadry **

When Kolmogorov philosophy meets the imaginary numbers

**Abstract:** The Kolmogorov’s probability philosophy is based on set of axioms that can be extended to encompass the imaginary set of numbers and this by adding to the original five axioms of Kolmogorov an additional three axioms. Hence, any experiment can thus be executed in what is now the complex set C which is the sum of the real set R with its corresponding real probability, and the imaginary set M with its corresponding imaginary probability. Whatever the probability distribution of the random variable in R is, the corresponding probability in the whole set C is always one, so the outcome of the random experiment in C can be predicted totally. Hence chance and luck in R is replaced by total determinism in C. This is the consequence of the fact that the probability in C is got by subtracting the chaotic factor from the degree of our knowledge of the system.

**Keywords: ** Kolmogorov’s axioms, random variable, probability, real set, imaginary set, complex set, complex number, probability norm, degree of knowledge of the system, chaotic factor, Bernoulli experiment, Binomial distribution, Gaussian or normal distribution, density function, Young’s modulus

** Pages**: 32-35

**Cite this article**:

S. Kadry. When Kolmogorov philosophy meets the imaginary numbers. Journal of Mathematics and Technology 2013; 4(1), 32-35.

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**5. M.H. Masud, F. Anwar, S.M. S. Bari **

Enhanced handoff latency reduction mechanism in layer 2 and layer 3 of mobile IPv6 (MIPv6) network

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**6. D. Singh, T.O. William **

A note on application of compatibility relation in network decentralization

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**7. Manouchehr Behboudi Asl, Hamid Baghban **

Stability quartic double centralizers and quartic multipliers on non-Archimedean Banach algebras

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**8. Saif Ur Rehman, Sohail Asghar **

Performance evaluation of frequent subgraph discovery techniques

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