1. Minimal Completion of the Lie Algebra arising from Fractional Calculus

    ASADA Akira

    Sinsyu University, 3-6-21, Nogami, Takarazuka, 665-0022 Japan.

    Abstract: We showed the group $G_\mathbb{R}$ and Lie algebra $\mathfrak{g}_\mathbb{R}$ generated by $\{\frac{d^a}{dx^a}|a\in\mathbb{R}\}$ and $\{x^a|a\in\mathbb{R}\}$ and their generating operators $\log(\frac{d}{dx})$ and $\log x$ have unique maximal normal subgroup $\mathsf{A}_\mathbb{R}$ and maximal ideal $\mathfrak{a}$. It was shown taking suitable completion $\bar{\mathfrak{a}}$, $\vartheta$; $\vartheta g=g^{-1}\frac{dg}{dx}$ gives a monomorphism from $\mathsf{A}_\mathbb{R}$ into $\bar{\mathfrak{a}}$([6].). But to search “good” completion is remained as a problem.
    In this paper, we propose the good completion (in some sense, minimal) is $\mathfrak{a}_{\exp}$; \[\mathfrak{a}_{\exp}=\{\sum_n c_n\Psi^{(n)}(1+s)|\sum_n c_nx^n\in\mathrm{Exp}(\mathbb{C})\}. \]
    Here $\mathrm{Exp}(\mathbb{C})$ is the space of finite exponential type functions. Corresponding extension of $\mathsf{A}_\mathbb{R}$ is also proposed.

    Pages: 47 – 68 | Full PDF Paper
  2. Comprehensive Meta Analysis Meta Analysis and A Special Technics

    İrem Yanık, Prof.Dr.Hüseyin Tatlıdil

    Department of Statistics, Hacettepe University, Beytepe, 06800, Ankara, Turkey.


    Comprehensive Meta Analysis (CMA) is a package program developed to perform meta analysis. Meta analysis provides is a general judgment on the subject by combining work done independtly on the same subject.A general judgment on these studies is reached by analyzing independent studies on similar topics statistically.It is easier and more reliable to make a new study by taking advantage of the previous studies because the number of analyses performed on the same subject increases every day and every analysis is forced by the researcher in terms of material and time. In addition, the researcher may not have sufficient sample for the subject to be studied; since we combine independent studies in meta analysis, the sample of the subject to be studied has also been expanded, so the study will have more consistent results. Because multiple studies are combined in metadata analysis, the measure that is needed to combine these studies is the size of the impact. The concept of impact size is very important for meta analysis. To do meta analysis, the researcher must first select the work that he / she will include in the analysis. Then, each study should calculate the impact sizes and perform statistical analysis for impact sizes and interpret the results.

    In this study, the package program developed to perform meta analysis was introduced and the use of the program was explained. An original application was resolved with the help of Comprehensive Meta Analysis V3.

    Keywords: Comprehensive meta analysis, meta analysis, effect size.

    Pages: 69 – 80 | Full PDF Paper
  3. Diagnosis of Heart Diseases with Machine Learning

    Bogdanov M.R.1,2, Dumchikov A.A.3, Akhmerova A.Z3,  Nasyrov D.I1

    1. Ufa State Aviation Technical University, Ufa City, Russia.
    2. M.Akmullah named after Bashkir State Pedagogical University, Ufa City, Russia.
    3. B.N.Elcin Ural Federal University, Ekaterinburg, Russia.

    Abstract: Under the research, the effectiveness of 14 machine learning algorithms for the diagnosis of cardiovascular diseases was evaluated. A PTB database of digitized electrocardiograms was used. It was found that the most preferred are a Label Propagation classifier (accuracy of recognition is 0.94), An extremely randomized tree classifier (accuracy is 0.92) and a Classifier implementing the k-nearest neighbors vote (accuracy is 0.90).

    Keywords: Heart diseases, Diagnosis, Machine Learning, Electrocardiogram.

    Pages: 81 – 84 | Full PDF Paper