International Journal of Mathematics and Mathematical Sciences https://www.hindawi.com The latest articles from Hindawi © 2018 , Hindawi Limited . All rights reserved. Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity Wed, 17 Jan 2018 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2018/1467235/ A new SEIRS epidemic model with nonlinear incidence rate and nonpermanent immunity is presented in the present paper. The fact that the incidence rate per infective individual is given by a nonlinear function and product of rational powers of two state variables, as well as the introduction of an epidemic-induced death rate, leads to a more realistic modeling of the physical problem itself. A stability analysis is performed and the features of Hopf bifurcation are investigated. Both the corresponding critical regions in the parameter space and their stability characteristics are presented. Furthermore, by using algorithms based on a new symbolic form as regards the restriction of an -dimensional nonlinear parametric system to the center manifold and the normal forms of the corresponding Hopf bifurcation, as well, the associated bifurcation diagram is derived, and finally various emerging limit cycles are numerically obtained by appropriate implemented methods. M. P. Markakis and P. S. Douris Copyright © 2018 M. P. Markakis and P. S. Douris. All rights reserved. Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator” Mon, 01 Jan 2018 10:29:41 +0000 http://www.hindawi.com/journals/ijmms/2018/2135740/ The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space established in “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator,” Int. J. Math. Math. Sci. 2004 (2004), no. 60, 3219–3235, are observed to remain true due to more recent findings. Marat V. Markin Copyright © 2018 Marat V. Markin. All rights reserved. Solving Volterra Integrodifferential Equations via Diagonally Implicit Multistep Block Method Mon, 01 Jan 2018 06:38:26 +0000 http://www.hindawi.com/journals/ijmms/2018/7392452/ The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (PECE) mode. The strategy to obtain the numerical solution of an integral part is discussed and the stability analysis of the diagonally implicit multistep block method was investigated. Numerical results showed the competence of diagonally implicit multistep block method when solving Volterra integrodifferential equations compared to the existing methods. Nur Auni Baharum, Zanariah Abdul Majid, and Norazak Senu Copyright © 2018 Nur Auni Baharum et al. All rights reserved. Banana Xanthomonas Wilt Infection: The Role of Debudding and Roguing as Control Options within a Mixed Cultivar Plantation Wed, 13 Dec 2017 08:25:40 +0000 http://www.hindawi.com/journals/ijmms/2017/4865015/ An optimal control framework is designed in which the use of clean planting materials, debudding, disinfection of tools, and roguing are considered as control measures of Banana Xanthomonas Wilt (BXW) within a plantation of multiple cultivars. A model for a special case of two cultivars (AAA- and ABB-genome cultivars) was analyzed. By Pontryagin’s Maximum Principle, we characterized and discussed possible control strategies that substantially reduce the infection levels of BXW within a plantation of ABB- and AAA-genome cultivars. A combination of both prevention and containment controls yielded the greatest decline in the infection levels in both cultivars. Additionally, for effective BXW management, it is important to assess the endemic level of the plantation before application of controls, and once implemented, this should be maintained even when the disease is undetectable to eliminate possible resurgence. Juliet Nakakawa, Joseph Y. T. Mugisha, Michael W. Shaw, William Tinzaara, and Eldad Karamura Copyright © 2017 Juliet Nakakawa et al. All rights reserved. A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants Tue, 12 Dec 2017 09:55:47 +0000 http://www.hindawi.com/journals/ijmms/2017/4349153/ For the tuple set of commuting invertible matrices with coefficients in a given field, the joint determinants are defined as generalizations of the determinant map for the square matrices. We introduce a natural topology on Milnor’s -groups of a topological field as the quotient topology induced by the joint determinant map and investigate the existence of a nontrivial continuous joint determinant by utilizing this topology, generalizing the author’s previous results on the continuous joint determinants for the commuting invertible matrices over and . Sung Myung Copyright © 2017 Sung Myung. All rights reserved. Convolutions of Harmonic Functions with Certain Dilatations Wed, 29 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/4015268/ The convolution of harmonic functions, unlike the analytic case, proved to be very challenging. In this paper, we introduce dilatation conditions that guarantee the convolution of two harmonic functions to be locally one-to-one, sense-preserving, and close-to-convex harmonic in the unit disk. Om P. Ahuja and Jay M. Jahangiri Copyright © 2017 Om P. Ahuja and Jay M. Jahangiri. All rights reserved. Improving Volatility Risk Forecasting Accuracy in Industry Sector Tue, 07 Nov 2017 09:21:19 +0000 http://www.hindawi.com/journals/ijmms/2017/1749106/ Recently, the volatility of financial markets has contributed a necessary part to risk management. Volatility risk is characterized as the standard deviation of the constantly compound return per day. This paper presents forecasting of volatility for the Jordanian industry sector after the crisis in 2009. ARIMA and ARIMA-Wavelet Transform (WT) have been conducted in order to select the best forecasting model in the content of industry stock market data collected from Amman Stock Exchange (ASE). As a result, the researcher found that ARIMA-WT has more accuracy than ARIMA directly. The results have been introduced using MATLAB 2010a and R programming. S. Al Wadi Copyright © 2017 S. Al Wadi. All rights reserved. Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers Tue, 07 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/5897049/ Let be a graph and be a -total coloring. Let denote the sum of color on a vertex and colors assigned to edges incident to . If whenever , then is called a neighbor sum distinguishing total coloring. The smallest integer such that has a neighbor sum distinguishing -total coloring is denoted by . In 2014, Dong and Wang obtained the results about depending on the value of maximum average degree. A -assignment of is a list assignment of integers to vertices and edges with for each vertex and for each edge . A total--coloring is a total coloring of such that whenever and whenever . We state that has a neighbor sum distinguishing total--coloring if has a total--coloring such that for all . The smallest integer such that has a neighbor sum distinguishing total--coloring for every -assignment is denoted by . In this paper, we strengthen results by Dong and Wang by giving analogous results for . Patcharapan Jumnongnit and Kittikorn Nakprasit Copyright © 2017 Patcharapan Jumnongnit and Kittikorn Nakprasit. All rights reserved. A Joint Representation of Rényi’s and Tsalli’s Entropy with Application in Coding Theory Sun, 15 Oct 2017 07:01:18 +0000 http://www.hindawi.com/journals/ijmms/2017/2683293/ We introduce a quantity which is called Rényi’s-Tsalli’s entropy of order and discussed some of its major properties with Shannon and other entropies in the literature. Further, we give its application in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel is proved. The theorem states that the proposed entropy is the lower bound of mean code word length. Litegebe Wondie and Satish Kumar Copyright © 2017 Litegebe Wondie and Satish Kumar. All rights reserved. -Primary Hyperideals on Commutative Hyperrings Wed, 11 Oct 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/5428160/ The purpose of this paper is to define the hyperideal expansion. Hyperideal expansion is associated with prime hyperideals and primary hyperideals. Then, we define some of their properties. Prime and primary hyperideals’ numerous results can be extended into expansions. Elif Ozel Ay, Gürsel Yesilot, and Deniz Sonmez Copyright © 2017 Elif Ozel Ay et al. All rights reserved. Quantitative Analysis of the Relationship between Three Psychological Parameters Based on Swallowtail Catastrophe Model Tue, 26 Sep 2017 08:51:30 +0000 http://www.hindawi.com/journals/ijmms/2017/7418132/ A sudden jump in the value of the state variable in a certain dynamical system can be studied through a catastrophe model. This paper presents an application of catastrophe model to solve psychological problems. Since we will have three psychological aspects or parameters, intelligence (I), emotion (E), and adversity (A), a Swallowtail catastrophe model is considered to be an appropriate one. Our methodology consists of three steps: solving the Swallowtail potential function, finding the critical points up to and including threefold degenerates, and fitting the model into our measured data. Using a polynomial curve fitting derived from the potential function of Swallowtail catastrophe model, relations among three parameters combinations are analyzed. Results show that there are catastrophe phenomena for each relation, meaning that a small change in one psychological aspect may cause a dramatic change in another aspect. Asti Meiza, Sutawanir Darwis, Agus Yodi Gunawan, and Efi Fitriana Copyright © 2017 Asti Meiza et al. All rights reserved. A Geometric Derivation of the Irwin-Hall Distribution Mon, 18 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/3571419/ The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution’s history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length. The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed. James E. Marengo, David L. Farnsworth, and Lucas Stefanic Copyright © 2017 James E. Marengo et al. All rights reserved. On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers Tue, 22 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/4515249/ A trapezoidal number, a sum of at least two consecutive positive integers, is a figurate number that can be represented by points rearranged in the plane as a trapezoid. Such numbers have been of interest and extensively studied. In this paper, a generalization of trapezoidal numbers has been introduced. For each positive integer , a positive integer is called an -trapezoidal number if can be written as an arithmetic series of at least terms with common difference . Properties of -trapezoidal numbers have been studied together with their trapezoidal representations. In the special case where , the characterization and enumeration of such numbers have been given as well as illustrative examples. Precisely, for a fixed -trapezoidal number , the ways and the number of ways to write as an arithmetic series with common difference have been determined. Some remarks on -trapezoidal numbers have been provided as well. Somphong Jitman and Chakrit Phongthai Copyright © 2017 Somphong Jitman and Chakrit Phongthai. All rights reserved. Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community Mon, 14 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/4804897/ Tungiasis is a permanent penetration of female sand flea “Tunga penetrans” into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits. Jairos Kahuru, Livingstone S. Luboobi, and Yaw Nkansah-Gyekye Copyright © 2017 Jairos Kahuru et al. All rights reserved. The Effect of Seasonal Weather Variation on the Dynamics of the Plague Disease Thu, 10 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/5058085/ Plague is a historic disease which is also known to be the most devastating disease that ever occurred in human history, caused by gram-negative bacteria known as Yersinia pestis. The disease is mostly affected by variations of weather conditions as it disturbs the normal behavior of main plague disease transmission agents, namely, human beings, rodents, fleas, and pathogens, in the environment. This in turn changes the way they interact with each other and ultimately leads to a periodic transmission of plague disease. In this paper, we formulate a periodic epidemic model system by incorporating seasonal transmission rate in order to study the effect of seasonal weather variation on the dynamics of plague disease. We compute the basic reproduction number of a proposed model. We then use numerical simulation to illustrate the effect of different weather dependent parameters on the basic reproduction number. We are able to deduce that infection rate, progression rates from primary forms of plague disease to more severe forms of plague disease, and the infectious flea abundance affect, to a large extent, the number of bubonic, septicemic, and pneumonic plague infective agents. We recommend that it is more reasonable to consider these factors that have been shown to have a significant effect on for effective control strategies. Rigobert C. Ngeleja, Livingstone S. Luboobi, and Yaw Nkansah-Gyekye Copyright © 2017 Rigobert C. Ngeleja et al. All rights reserved. New Results on the (Super) Edge-Magic Deficiency of Chain Graphs Wed, 12 Jul 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/5156974/ Let be a graph of order and size . An edge-magic labeling of is a bijection such that is a constant for every edge . An edge-magic labeling of with is called a super edge-magic labeling. Furthermore, the edge-magic deficiency of a graph , , is defined as the smallest nonnegative integer such that has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph , , is either the smallest nonnegative integer such that has a super edge-magic labeling or if there exists no such integer . In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems. Ngurah Anak Agung Gede and Adiwijaya Copyright © 2017 Ngurah Anak Agung Gede and Adiwijaya. All rights reserved. New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems Mon, 10 Jul 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/5742965/ We apply new modified recursion schemes obtained by the Adomian decomposition method (ADM) to analytically solve specific types of two-point boundary value problems for nonlinear fractional order ordinary and partial differential equations. The new modified recursion schemes, which sometimes utilize the technique of Duan’s convergence parameter, are derived using the Duan-Rach modified ADM. The Duan-Rach modified ADM employs all of the given boundary conditions to compute the remaining unknown constants of integration, which are then embedded in the integral solution form before constructing recursion schemes for the solution components. New modified recursion schemes obtained by the method are generated in order to analytically solve nonlinear fractional order boundary value problems with a variety of two-point boundary conditions such as Robin and separated boundary conditions. Some numerical examples of such problems are demonstrated graphically. In addition, the maximal errors or the error remainder functions of each problem are calculated. Sekson Sirisubtawee and Supaporn Kaewta Copyright © 2017 Sekson Sirisubtawee and Supaporn Kaewta. All rights reserved. Star-Supermagic Decompositions of the Complete Bipartite Graph Minus a One-Factor Wed, 21 Jun 2017 10:08:42 +0000 http://www.hindawi.com/journals/ijmms/2017/5104701/ Let be a graph and let be a subgraph of . Assume that has an -decomposition such that for all . An -supermagic decomposition of is a bijection such that is a constant for each in the decomposition and . If admits an -supermagic decomposition, then is called -supermagic decomposable. In this paper, we give necessary and sufficient conditions for the existence of -supermagic decomposition of the complete bipartite graph minus a one-factor. Tanawat Wichianpaisarn and Uthoomporn Mato Copyright © 2017 Tanawat Wichianpaisarn and Uthoomporn Mato. All rights reserved. Mass Renormalization in the Nelson Model Tue, 06 Jun 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/4760105/ The asymptotic behavior of the effective mass of the so-called Nelson model in quantum field theory is considered, where is an ultraviolet cutoff parameter of the model. Let be the bare mass of the model. It is shown that for sufficiently small coupling constant of the model, can be expanded as . A physical folklore is that as . It is rigorously shown that ,   with some constants , , and . Fumio Hiroshima and Susumu Osawa Copyright © 2017 Fumio Hiroshima and Susumu Osawa. All rights reserved. Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect Sun, 28 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/8273430/ We analyze the dynamics of a fractional order modified Leslie-Gower model with Beddington-DeAngelis functional response and additive Allee effect by means of local stability. In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Grünwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Grünwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties. Agus Suryanto, Isnani Darti, and Syaiful Anam Copyright © 2017 Agus Suryanto et al. All rights reserved. Calculation of Precise Constants in a Probability Model of Zipf’s Law Generation and Asymptotics of Sums of Multinomial Coefficients Sun, 07 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2017/9143747/ Let be a full set of outcomes (symbols) and let positive , , be their probabilities . Let us treat as a stop symbol; it can occur in sequences of symbols (we call them words) only once, at the very end. The probability of a word is defined as the product of probabilities of its symbols. We consider the list of all possible words sorted in the nonincreasing order of their probabilities. Let be the probability of the th word in this list. We prove that if at least one of the ratios , , is irrational, then the limit exists and differs from zero; here is the root of the equation . The limit constant can be expressed (rather easily) in terms of the entropy of the distribution . Vladimir Bochkarev and Eduard Lerner Copyright © 2017 Vladimir Bochkarev and Eduard Lerner. All rights reserved. A Note on the Performance of Biased Estimators with Autocorrelated Errors Mon, 30 Jan 2017 06:34:57 +0000 http://www.hindawi.com/journals/ijmms/2017/2045653/ It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators. Gargi Tyagi and Shalini Chandra Copyright © 2017 Gargi Tyagi and Shalini Chandra. All rights reserved. On Killing Forms and Invariant Forms of Lie-Yamaguti Superalgebras Thu, 12 Jan 2017 09:34:48 +0000 http://www.hindawi.com/journals/ijmms/2017/7842482/ The notions of the Killing form and invariant form in Lie algebras are extended to the ones in Lie-Yamaguti superalgebras and some of their properties are investigated. These notions are also -graded generalizations of the ones in Lie-Yamaguti algebras. Patricia L. Zoungrana and A. Nourou Issa Copyright © 2017 Patricia L. Zoungrana and A. Nourou Issa. All rights reserved. Modal Logic Axioms Valid in Quotient Spaces of Finite CW-Complexes and Other Families of Topological Spaces Mon, 26 Dec 2016 06:01:11 +0000 http://www.hindawi.com/journals/ijmms/2016/9163014/ In this paper we consider the topological interpretations of , the classical logic extended by a “box” operator interpreted as interior. We present extensions of S4 that are sound over some families of topological spaces, including particular point topological spaces, excluded point topological spaces, and quotient spaces of finite CW-complexes. Maria Nogin and Bing Xu Copyright © 2016 Maria Nogin and Bing Xu. All rights reserved. Vector Spaces of New Special Magic Squares: Reflective Magic Squares, Corner Magic Squares, and Skew-Regular Magic Squares Wed, 30 Nov 2016 11:17:13 +0000 http://www.hindawi.com/journals/ijmms/2016/9721725/ The definition of a regular magic square motivates us to introduce the new special magic squares, which are reflective magic squares, corner magic squares, and skew-regular magic squares. Combining the concepts of magic squares and linear algebra, we consider a magic square as a matrix and find the dimensions of the vector spaces of these magic squares under the standard addition and scalar multiplication of matrices by using the rank-nullity theorem. Thitarie Rungratgasame, Pattharapham Amornpornthum, Phuwanat Boonmee, Busrun Cheko, and Nattaphon Fuangfung Copyright © 2016 Thitarie Rungratgasame et al. All rights reserved. Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly Cosymplectic Manifolds Mon, 14 Nov 2016 11:09:29 +0000 http://www.hindawi.com/journals/ijmms/2016/9613182/ Attention is drawn to some distributions on ascreen Quasi-Generalized Cauchy-Riemannian (QGCR) null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finally discuss the geometric effects of geodesity conditions on such submanifolds. Fortuné Massamba and Samuel Ssekajja Copyright © 2016 Fortuné Massamba and Samuel Ssekajja. All rights reserved. Symmetric Integer Matrices Having Integer Eigenvalues Mon, 07 Nov 2016 09:33:15 +0000 http://www.hindawi.com/journals/ijmms/2016/3471438/ We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem. Lei Cao and Selcuk Koyuncu Copyright © 2016 Lei Cao and Selcuk Koyuncu. All rights reserved. Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations Wed, 26 Oct 2016 14:31:29 +0000 http://www.hindawi.com/journals/ijmms/2016/1414595/ Double Laplace transform method is applied to find exact solutions of linear/nonlinear space-time fractional telegraph equations in terms of Mittag-Leffler functions subject to initial and boundary conditions. Furthermore, we give illustrative examples to demonstrate the efficiency of the method. Ranjit R. Dhunde and G. L. Waghmare Copyright © 2016 Ranjit R. Dhunde and G. L. Waghmare. All rights reserved. Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation Tue, 25 Oct 2016 08:10:52 +0000 http://www.hindawi.com/journals/ijmms/2016/9121249/ A sufficient literature is available for the wavelet error of approximation of certain functions in the -norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function belonging to class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function belonging to class using the projection of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis. Shyam Lal and Susheel Kumar Copyright © 2016 Shyam Lal and Susheel Kumar. All rights reserved. On Degrees of Modular Common Divisors and the Big Prime Algorithm Wed, 05 Oct 2016 13:47:51 +0000 http://www.hindawi.com/journals/ijmms/2016/3262450/ We consider a few modifications of the Big prime modular algorithm for polynomials in . Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms for calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular on polynomials from Knuth’s example of intermediate expression swell. Vahagn Mikaelian Copyright © 2016 Vahagn Mikaelian. All rights reserved.