Certain triple q-integral equations involving third Jackson qq-Bessel functions as kernel

In this paper, we employ the fractional $q$-calculus in solving a triple system of $q$-Integral equations, where the kernel is the third Jackson $q$-Bessel functions. The solution is reduced to two simultaneous Fredholm $q$-integral equation of the second kind. Examples are included. We also apply a result in~[Pacific J. Math. \textbf{275}(1) (2015)63--102] for solutions of dual $q^2$-integral equations to solve certain triple integral equations

Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

Adaptation Algorithm and Theory Based on Generalized Discrepancy

We present a new algorithm for domain adaptation improving upon a discrepancy minimization algorithm previously shown to outperform a number of algorithms for this task. Unlike many previous algorithms for domain adaptation, our algorithm does not consist of a fixed reweighting of the losses over the training sample. We show that our algorithm benefits from a solid theoretical foundation and more favorable learning bounds than discrepancy minimization. We present a detailed description of our algorithm and give several efficient solutions for solving its optimization problem. We also report the results of several experiments showing that it outperforms discrepancy minimization

The incidence of prostate cancer in Iran: Results of a population-based cancer registry

Background: Little is known about the epidemiology of prostate cancer in Iranian men. We carried out an active prostate cancer surveillance program in five provinces of Iran. Methods: Data used in this study were obtained from population-based cancer registries between 1996 and 2000. Results: The age-standardized incidence rate of prostate carcinoma in the five provinces was 5.1 per 100,000 person-years. No significant difference was seen in the age-standardized incidence rate of prostate cancer within the provinces studied. The mean±SD age of patients with prostate cancer was 67±13.5 years. Conclusion: The incidence of prostate cancer in Iran is very low as compared to the Western countries. This can partly be explained by lack of nationwide screening program, younger age structure and quality of cancer registration system in Iran

Assessing the performance of insulating fluids via point of statistical inference view

In this paper, the statistical inference is used in order to study the performance or aging of the insulating fluids. Transformer oil is used as an example of insulating fluids. The insulation property of insulating oil or transformer oil is lost by consumption. Breakdown tests are performed to check oil’s efficiency, but the cost of these tests is not inexpensive. Hence this statistical study aims to reduce the cost of these tests by applying statistical inference approaches to censored data. The Type-II Gumbel distribution fits well real-life data which contains failure times to breakdown of an insulating fluid between electrodes. The Type-II hybrid censored scheme is proposed to assess the study and also to reduce the cost of breakdown tests in practical tests.Publisher's Versio

Formulating an Efficient Statistical Test Using the Goodness of Fit Approach with Applications to Real-life Data

Statistical tests are very important for researchers to make decisions. In particular, when the tests are non- parametric, they are of greater importance because they can be applied to a wide range of data sets regardless of knowing the distribution of these data. Researchers are therefore racing to obtain efficient tests for making good decisions based on the results of these tests. In this study, NBU (2)L was used based on the goodness of fit approach to present an efficient statistical test. The efficiency of the proposed test was computed, and the results were compared to those of other tests. Critical values were computed and tabulated, and the power of this test was estimated. Finally, this test was applicable to both real, complete data and censored data