Investors of any time and of any investment area are faced with the conflicting objective of minimizing risks and simultaneously maximizing returns. Considering the tradeoffs between risk and return, Harry Markowitz, an American financial economist, proposed the so-called optimal portfolio theory in 1952. The aim of this paper is to provide a practical study of Markowitz model on the Bulgarian stock market from 2013 to 2016. The significance of this study arises from the fact that although Markowitz model has been widely used by investors worldwide, its application on Bulgarian stock market is still relatively limited. From the data inputs which are weekly closing prices of 50 stocks traded on Bulgarian Stock Exchange between January 2013 and December 2016, efficient frontiers in addition to optimal portfolios are determined on the basis of Markowitz theory. As a result, Bulgarian investors can select their own optimal portfolio that maximizes portfolio rate of return with respect to their risk preference. AMS Subject Classification: 62-07, 49M37, 90C30, 34K60, 91B30 Received: 2017-06-14 Revised: 2017-11-15 Published: December 23, 2017 c © 2017 Academic Publications, Ltd. url: www.acadpubl.eu 292 M. Ivanova, L. Dospatliev
The present paper is focused on the analysis of electricity market, after its recent liberalization.In particular we provide a detailed analysis of the latter exploiting descriptive analysis and the feature selection approach for a multivariate time series dataset.Moreover we will apply a pool of regression models on the features selection methodology focusing our study on the 2014-Global Energy Forecasting Competition dataset.
When fitting a mathematical model to a given data set using inverse problems, the correctness of both the mathematical model and the statistical error models are important since an incorrect statistical or observational model directly affects both the estimates and their corresponding standard errors.The effects of these models, among many other factors, are dependent on the sample size and the information content of the data set.In this article, we investigate how the choice of the statistical error model affects the mathematical model fit and accuracy of parameter estimates in small sample size tumor growth data sets.We specifically seek to determine the appropriate statistical error model for small sample size breast, lung and HPV tumor growth data sets obtained from studies on mice.
In this work is presented a study of two algorithms for patterns recognition and classification to solving a specific application task.Three criteria are studied and compared: performance (execution time), the number of errors in classification and the influence of the selection and structuring of data.
We developed an algorithm based on combination of regularization and wavelet collocation method to solve Fredholm integral equations of the first kind. As first kind Fredholm integral equations are often ill-posed problems, regularization method is implemented to convert it into an approximate well posed Fredholm integral equation of the second kind whose solution converges to the solution of the original problem. Then wavelet collocation method is applied to obtain the numerical solution of the resulting problem. We have applied proposed method using Legendre and Chebyshev wavelets to some examples and compared their efficiency.
Let G = (V, E) be a graph, where V (G) is a non-empty set of vertices and E(G) is a set of edges, e = uv ∈ E(G), du be degree of vertex u.The distance between two vertices of G is the length of a shortest path connecting these two vertices.The eccentricity ǫu of a vertex u in G is the largest distance between u and any other vertex of G.In this paper, we consider an infinite family of Nanostar Dendrimers and compute its First Eccentric Zagreb index.The First Eccentric Zagreb index was introduced by Ghorbani and Hosseinzadeh as Zg * 1 (G) = uv∈E(G) ǫu +ǫv , that ǫu is the eccentricity of a vertex u and ǫv is the eccentricity of a vertex v of G.
The methods of energy transfer and transformation in macroscopic systems are of importance in various areas of science and technology, such as power and heat engineering, chemistry, aerospace technologies, mechanical and biomedical engineering, etc.That is why the present work is topical.Its main target is application of the molecular-kinetic concepts at introducing the equation of the first law of thermodynamics.When presenting this law in textbooks, some troubles appear in differentiating between energy (energy change) and heat or work as well as between heat and work.Therefore the present paper contains a critical analysis of the methods of introducing miscellaneous equations of energy for a closed system and flux, as well as the concepts of heat, work and energy in the scientific literature.By using mathematical manipulations of the Newton's second law written for each single microparticle, a transition is made to the law of energy change (known as the first law of thermodynamics) of all microparticles of a system.Based on the molecular-kinetic concepts, rigorous definitions of such physical quantities as heat and work are formulated.
A total-coloring c of a directed graph G is called edge-distinguishing if for any two edges e1 = u1v1 and e2 = u2v2 of G the associated ordered triplets (c(u1), c(e1), c(v1)) and (c(u2), c(e2), c(v2)) are different.The problem is to determine the minimum number of colors used in such a coloring of G.In this paper we investigate this parameter for directed subdivided stars.
The object of this paper is to study 3-dimensional ψ-recurrent (LCS)n-manifold and prove that it is a manifold of constant curvature and finally we prove that a 3-dimensional (LCS)n-manifold is locally ψ-concircularly symmetric if and only if the scalar curvature r is constant.
Julia sets are certain fractal sets in the complex plane that arise from the dynamics of complex polynomials and it characterize by the structure (i.e., boundary) is the main aim to discuss the complex polynomial.
Homotopy analysis natural transform method (HANTM) is used to solve fractional physical models.This method is a combined form of the natural transform method and the homotopy analysis method.The fractional derivatives are described in the Caputo sense.The results reveal that the method is very effective, simple and can be applied to other fractional physical models.
Boundedness of the sum of two Hardy-type operators with not necessarily nonnegative coefficients has been discussed between amalgams ℓ q (Xu)ℓ b (L r , v) for the case 1 < r, q, b < ∞ where Xu is weighted Banach function space.
Statistical convergence has become an active area of research under the name of statistical convergence since 1990s of the last century.It has appeared in a wide variety of topics such as number theory, measure theory, trigonometric series, summability theory, in the study of strong integral summability and Banach spaces.In this paper statistical convergence is used to obtain some new results on amarts.Amarts generalize martingales considerably since every convergent sequence of random variables with integrable supremum is an amart.Our goal is the study of statistical convergence of asymptotic martingales of statistical Bochner integrable functions.We obtain some results for the statistical convergence of vector valued uniform amarts without assuming the Radon-Nikodym Property.
The enumeration formula of a non-contemporaneous genealogy with total sample size n = n1 + n2 requires a nested sum-product.The set of ancestral patterns in the noncontemporaneous genealogy yields a multiplicity factor that translates from the set of ancestral patterns in the isochronous genealogy.A computation formula of the multiplicity factor proves to be non-recursive.Evaluation of small sample sizes demonstrates the emergent complexity.Extension to the enumeration formula in the heterochronous genealogy with m samples of total size n = n1 + • • • + nm yields a non-recursive nested sum-product.These enumeration formulae measure sample spaces of Bayesian prior distributions of trees relevant to theoretical and computational phylogenetics.
Programming languages are one of the main knowledge areas in the Computer Science curriculum. Software development professionals often need to learn new languages, constructs and concepts to effectively combine them in solutions they develop. Universities must adequately prepare their students for the challenges they will face. Studying programming languages is a part of more general knowledge covering programming paradigms, concepts, technologies, patterns and algorithms. The first programming language plays and important role since freshmen have different backgrounds and different expectations. This paper presents a recent survey on programming languages used in Bulgarian academic courses and discusses results in the light of the recent index of programming languages popularity and industry trends. The survey of languages studied at universities is juxtaposed with industry demands for professionals with specific knowledge in particular programming languages. The study covers all Bulgarian universities with undergraduate courses in the professional field of informatics and computer science and the programming skills demanded in job offers during the last six months in Bulgaria. AMS Subject Classification: 68N15, 97P40
A mathematical model of adaptive immune response to a viral infection is formulated by five nonlinear ordinary differential equations.The model describes the interactions between a virus, uninfected cells, infected cells, and the adaptive immune response represented by the antibodies and cytotoxic T lymphocytes.Theorems of existence, uniqueness and non-negativity of solution are proven.Numerical simulations of the model are presented.
German import represents 5.6% of total global imports and this establishes Germany as the third largest importer in the world.This study examines the dependence of imports on consumption, investment and exports in Germany, using time series data for the period 1997-2013.We received an error correction model that involved short-term and long-term effects and seasonal components.Based on the estimated model, with 1% increase in investment or exports the short-term effect would result in an increase in imports by 0.39% and 0.58%, respectively.We determined the period for which there would be a balance of imports in case of shock on independent variables.There is also a slight constant change in imports during different seasons and a general reduction of import growth by 5.59% on average.
In this paper the author defines and discuses the concept of approximate sequences.First, in a separate section, he discusses proximate and approximate sequences.After that he presents some properties of approximate sequences that are anoloqous to similar results for fundamental sequences, established in previous paper [1] titled equivalence of intrinsic shape, based on V-continuous functions and shape (N.Shekutkovski, Z. Misajleski, G. Markoski, M. Shoptrajanov, Bulletin mathematique, 2013, No. 1, 39-48).The author gives an optional definition of the function rV , with the help of intersections, which in [1] is defined using notion of depth.Also he shows that in a compact metric space there exists a cofinal sequence of finite regular coverings.In addition he shows that it is possible to choose the images of functions of approximate as subsets of the union of elements of such a sequence of coverings.Furthermore, analogue theorems of [1], which refers to approximate instead for fundamental sequences, he present and prove.Finally, the author shows that shape category constructed with the classes of approximate sequences, is equivalent with the intrinsic shape category constructed with the classes of proximate sequences.
A mathematical model of adaptive immune response to viral infection is formulated as a system of six ordinary differential equations (ODE).The model describes the interactions between virus, uninfected cells, infected cells, and the adaptive immune response represented by antibodies and two subpopulations of cytotoxic T lymphocytes (CTL): CTLprecursors and CTL-effectors.Theorems of existence, uniqueness and non-negativity of solutions are proven.Primary and secondary immune responses against viral infection are investigated by numerical simulations using Matlab.
