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Kyungpook mathematical journal
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Department of Mathematics, Kyungpook National University
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Volume 56, Issue 2 - Jun 2016
Volume 56, Issue 1 - Mar 2016
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An Error Embedded Runge-Kutta Method for Initial Value Problems
Bu, Sunyoung ; Jung, WonKyu ; Kim, Philsu ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 311~327
DOI : 10.5666/KMJ.2016.56.2.311
In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.
Korobov Polynomials of the Fifth Kind and of the Sixth Kind
Kim, Dae San ; Kim, Taekyun ; Kwon, Hyuck In ; Mansour, Toufik ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 329~342
DOI : 10.5666/KMJ.2016.56.2.329
Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.
Posner's First Theorem for *-ideals in Prime Rings with Involution
Ashraf, Mohammad ; Siddeeque, Mohammad Aslam ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 343~347
DOI : 10.5666/KMJ.2016.56.2.343
Posner's first theorem states that if R is a prime ring of characteristic different from two,
are derivations on R such that the iterate
is also a derivation of R, then at least one of
is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.
On the Numbers of Palindromes
Bang, Sejeong ; Feng, Yan-Quan ; Lee, Jaeun ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 349~355
DOI : 10.5666/KMJ.2016.56.2.349
For any integer
, each palindrome of n induces a circulant graph of order n. It is known that for each integer
, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. ). This bijection gives a one-to-one correspondence of the palindromes
to the connected circulant graphs. It was also shown that the number of palindromes
of n with
is the same number of aperiodic palindromes of n. Let
) be the number of aperiodic palindromes
of n with
) be the number of periodic palindromes
of n with
). In this paper, we calculate the numbers
in two ways. In Theorem 2.3, we
recurrence relations for
in terms of
. Afterwards, we nd formulae for
explicitly in Theorem 2.5.
On Deferred Statistical Convergence of Sequences
Kucukaslan, Mehme ; Yilmazturk, Mujde ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 357~366
DOI : 10.5666/KMJ.2016.56.2.357
In this paper, deferred statistical convergence is defined by using deferred
mean instead of
mean in the definition of statistical convergence. The obtained method is compared with strong deferred
mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.
Some Properties of (p, q) - Lucas Number
Suvarnamani, Alongkot ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 367~370
DOI : 10.5666/KMJ.2016.56.2.367
In this paper, we consider the generalized Lucas sequence which is the (p, q) - Lucas sequence. Then we used the Binet's formula to show some properties of the (p, q) - Lucas number. We get some generalized identities of the (p, q) - Lucas number.
Subalgebras and Ideals of BCK/BCI-Algebras in the Frame-work of the Hesitant Intersection
Jun, Young Bae ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 371~386
DOI : 10.5666/KMJ.2016.56.2.371
Using the hesitant intersection (
), the notions of
-hesitant fuzzy subalgebras,
-hesitant fuzzy ideals and
-hesitant fuzzy p-ideals are introduced,and their relations and related properties are investigated. Conditions for a
-hesitant fuzzy ideal to be a
-hesitant fuzzy p-ideal are provided. The extension property for
-hesitant fuzzy p-ideals is established.
Strongly Clean Matrices Over Power Series
Chen, Huanyin ; Kose, Handan ; Kurtulmaz, Yosum ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 387~396
DOI : 10.5666/KMJ.2016.56.2.387
matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let
. We prove, in this note, that
is strongly clean if and only if
is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.
Derivations with Power Values on Lie Ideals in Rings and Banach Algebras
Rehman, Nadeem ur ; Muthana, Najat Mohammed ; Raza, Mohd Arif ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 397~408
DOI : 10.5666/KMJ.2016.56.2.397
Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If
, where m, n, l are xed positive integers, then
. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.
Two Variants of the Reciprocal Super Catalan Matrix
Kilic, Emrah ; Omur, Nese ; Koparal, Sibel ; Ulutas, Yucel Turker ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 409~418
DOI : 10.5666/KMJ.2016.56.2.409
In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.
Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation
Yang, Wengui ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 419~430
DOI : 10.5666/KMJ.2016.56.2.419
In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.
Existence and Stability Results on Nonlinear Delay Integro-Differential Equations with Random Impulses
Vinodkumar, Arumugam ; Gowrisankar, Muthusamy ; Mohankumar, Prathiban ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 431~450
DOI : 10.5666/KMJ.2016.56.2.431
In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.
A Further Result Related to a Conjecture of R. Brück
Li, Nan ; Yang, Lianzhong ; Liu, Kai ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 451~464
DOI : 10.5666/KMJ.2016.56.2.451
In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R.
Some Finite Integrals Involving Srivastava's Polynomials and the Aleph Function
Bhargava, Alok ; Srivastava, Amber ; Mukherjee, Rohit ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 465~471
DOI : 10.5666/KMJ.2016.56.2.465
In this paper, we establish certain integrals involving Srivastava's Polynomials  and Aleph Function (, ). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.
Recursion Formulas for Exton's triple Hypergeometric Functions
Sahai, Vivek ; Verma, Ashish ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 473~506
DOI : 10.5666/KMJ.2016.56.2.473
This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in , the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and k-variable Lauricella functions. Further, in , we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions.
Behavior of Solutions of a Fourth Order Difference Equation
Abo-Zeid, Raafat ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 507~516
DOI : 10.5666/KMJ.2016.56.2.507
In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation
where a, b, c are positive real numbers and the initial conditions
are real numbers.
Existence and Exponential Stability for a Thermoviscoelastic Equation with Boundary Output Feedback Control
Kang, Yong Han ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 517~527
DOI : 10.5666/KMJ.2016.56.2.517
In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.
Controllability and Observability of Sylvester Matrix Dynamical Systems on Time Scales
Appa Rao, Bhogapurapu Venkata ; Prasad, Krosuri Anjaneya Siva Naga Vara ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 529~539
DOI : 10.5666/KMJ.2016.56.2.529
In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.
Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonflat Complex Space Form
Ki, U-Hang ; Kim, Soo Jin ; Kurihara, Hiroyuki ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 541~575
DOI : 10.5666/KMJ.2016.56.2.541
Let M be a real hypersurface of a complex space form with almost contact metric structure (
, g). In this paper, we prove that if the structure Jacobi operator
commute with the structure tensor
, then M is a homogeneous real hypersurface of Type A provided that
Equivalence of ℤ
-actions on Handlebodies of Genus g
Prince-Lubawy, Jesse ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 577~582
DOI : 10.5666/KMJ.2016.56.2.577
In this paper we consider all orientation-preserving
-actions on 3-dimensional handlebodies
of genus g > 0. We study the graph of groups (
, G(v)), which determines a handlebody orbifold
. This algebraic characterization is used to enumerate the total number of
group actions on such handlebodies, up to equivalence.
Areas associated with a Strictly Locally Convex Curve
Kim, Dong-Soo ; Kim, Dong Seo ; Kim, Young Ho ; Bae, Hyun Seon ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 583~595
DOI : 10.5666/KMJ.2016.56.2.583
Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle
. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane
, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property
for parabolas we study strictly locally convex curves in the plane
are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.
Some Inclusion Properties of New Subclass of Starlike and Convex Functions associated with Hohlov Operator
Sokol, Janusz ; Murugusundaramoorthy, Gangadharan ; Kothandabani, Thilagavathi ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 597~610
DOI : 10.5666/KMJ.2016.56.2.597
For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions,
. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.
Translating Integer Factoring into Graph Coloring
Jensen, Tommy Rene ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 611~624
DOI : 10.5666/KMJ.2016.56.2.611
This paper gives for every positive integer n an explicit construction of a graph G with fewer than
vertices, such that there exists a nontrivial factoring of n if and only if G is 3-colorable.
Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds
Shukla, Shiv Sharma ; Yadav, Akhilesh ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 625~638
DOI : 10.5666/KMJ.2016.56.2.625
In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions
and RadTM on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.
Erratum to 'Some Limits of the Colored Jones Polynomials of the Figure-eight Knot'
Murakami, Hitoshi ;
Kyungpook mathematical journal, volume 56, issue 2, 2016, Pages 639~645
DOI : 10.5666/KMJ.2016.56.2.639
In  the main theorem was erroneously stated. We needed to assume that the irrationality measure of 1/r is finite to prove the theorem.