Showing papers in "Journal of The Korean Mathematical Society in 2015"

Third order hankel determinant for certain univalent functions

Abstract: . The estimate of third Hankel determinantH 3,1 (f) =a 1 a 2 a 3 a 2 a 3 a 4 a 3 a 4 a 5 of the analytic function f(z) = z+ a 2 z 2 + a 3 z 3 + ··· , for which ℜ(1 +zf ′′ (z)/f ′ (z)) >−1/2 are investigated. The corrected version of a knownresults [2, Theorem 3.1 and Theorem 3.3] are also obtained. 1. IntroductionLet H(D) denote the class of analytic functions in the open unit disk D={z ∈ C: |z| 0, z ∈ D. Functions in R are known to be close-to-convex (andhence univalent) in D. Further, a function f ∈ A is called starlike (with respectto the origin 0), if tw ∈ f(D) whenever w ∈ f(D) and t ∈ [0,1]. We denote byS ∗ the subclass of A whose members are starlike in D. It is well known thatf ∈ S

Sufficient conditions for starlikeness

Abstract: We obtain the conditions onso that 1+�zp ' (z) ≺ 1+4z/3+ 2z 2 /3 implies p(z) ≺ (2+z)/(2−z), 1+(1−�)z, (1+(1−2�)z)/(1−z), (0 ≤ � < 1), exp(z) or √ 1 + z. Similar results are obtained by considering the expressions 1+�zp ' (z)/p(z), 1+�zp ' (z)/p 2 (z) and p(z)+�zp ' (z)/p(z). These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition |log(zf ' (z)/f(z))| < 1 or |(zf ' (z)/f(z)) 2 −1| < 1 or zf ' (z)/f(z) lying in the region bounded by the cardioid (9x 2 + 9y 2 − 18x + 5) 2 − 16(9x 2 + 9y 2 − 6x + 1) = 0.

Gegenbauer wavelets operational matrix method for fractional differential equations

Abstract: In this article we introduce a numerical method, named Ge- genbauer wavelets method, which is derived from conventional Gegen- bauer polynomials, for solving fractional initial and boundary value prob- lems. The operational matrices are derived and utilized to reduce the lin- ear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Translation and homothetical surfaces in euclidean space with constant curvature

Abstract: . We study surfaces in Euclidean space which are obtained asthe sum of two curves or that are graphs of the product of two functions.We consider the problem of finding all these surfaces with constant Gausscurvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space. 1. IntroductionIn this paper we study two types of surfaces in Euclidean space R 3 . Thefirst kind of surfaces are translation surfaces which were initially introducedby S. Lie. A translation surface S is a surface that can be expressed as thesum of two curves α : I ⊂ R→ R 3 , β : J ⊂ R→ R 3 . In a parametric form,the surface S writes as X(s,t) = α(s) + β(t), s ∈ I, t ∈ J. See [2, p. 138].A translation surface S has the property that the translations of a parametriccurve s = constant by β(t) remain in S (similarly for the parametric curvest = constant). It is an open problem to classify all translation surfaces withconstant mean curvature (CMC) or constant Gauss curvature (CGC). A firstexample of a CMC translation surface is the Scherk surfacez(x,y) =1alog cos(ay)cos(ax) , a > 0.This surface is minimal (H = 0) and belongs to a more general family of Scherksurfaces ([7, pp. 67–73]). In this case, the curves α and β lie in two orthogonalplanes and after a change of coordinates, the surface is locally described as thegraph of z = f(x)+g(y). Other examples of CMC or CGC translation surfacesgiven as a graph z = f(x) + g(y) are: planes (H = K = 0), circular cylinders

ON v-MAROT MORI RINGS AND C-RINGS

Abstract: C-domains are defined via class semigroups, and every C- domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ordinary Marot rings and investigate their theory of regular divisorial ideals. Based on this we establish a generalization of a result well-known for integral domains. Let R be a v-Marot Mori ring, b R its complete integral closure, and suppose that the conductor f = (R : b R) is regular. If the residue class ring R/f and the class group C( b R) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.

On weakly 2-absorbing primary ideals of commutative rings

Abstract: Let R be a commutative ring with 1 6 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a,b,c ∈ R and 0 6 abc ∈ I, then ab ∈ I or ac ∈ √ I or bc ∈ √ I. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

A parallel hybrid method for equilibrium problems, variational inequalities and nonexpansive mappings in hilbert space

Abstract: In this paper, a novel parallel hybrid iterative method is pro- posed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong con- vergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

On the growth of algebraic polynomials in the whole complex plane

Abstract: In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

Parameter change test for nonlinear time series models with garch type errors

Abstract: Abstract. In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

Some fixed point theorems in generalized darbo fixed point theorem and the existence of solutions for system of integral equations

Abstract: . In this paper we introduce the notion of the generalizedDarbo fixed point theorem and prove some fixed and coupled fixed pointtheorems in Banach space via the measure of non-compactness, whichgeneralize the result of Aghajani et al. [6]. Our results generalize, extend,and unify several well-known comparable results in the literature. One ofthe applications of our main result is to prove the existence of solutionsfor the system of integral equations. 1. IntroductionThe integral equation creates a very important and significant part of themathematical analysis and has various applications into real world problems.On the other hand, Measures of noncompactness are very useful tools in thewide area of functional analysis such as the metric fixed point theory andthe theory of operator equations in Banach spaces. They are also used in thestudies of functional equations, ordinary and partial differential equations, frac-tional partial differential equations, integral and integro-differential equations,optimal control theory, etc., see [1, 2, 3, 4, 7, 13, 14, 15, 16, 17]. In our inves-tigations, we apply the method associated with the technique of measures ofnoncompactness in order to generalize the Darbo fixed point theorem [10] andto extend some recent results of Aghajani et al. [6], and also we are going tostudy the existence of solutions for the following system of integral equations(1.1)x(t,s) =a(t,s)+f(t,s,x(t,s),y(t,s))+g(t,s,x(t,s),y(t,s))R

Finite groups whose intersection graphs are planar

Abstract: . The intersection graph of a group G is an undirected graphwithout loops and multiple edges defined as follows: the vertex set is theset of all proper non-trivial subgroups of G, and there is an edge betweentwo distinct vertices Hand Kif and only if H∩K6= 1 where 1 denotes thetrivial subgroup of G.In this paper we characterize all finite groups whoseintersection graphs are planar. Our methods are elementary. Among thegraphs similar to the intersection graphs, we may count the subgrouplattice and the subgroup graph of a group, each of whose planarity wasalready considered before in [2, 10, 11, 12]. 1. Introduction and preliminariesA graph is called planar if it can be drawn on the plane in such a way thatits edges intersect only at their endpoints. There are interesting graphs con-structed from algebraic objects such as the subgroup lattice and the subgroupgraph of a group. Planarity of the subgroup lattice and the subgroup graph ofa group were studied by Bohanon and Reid in [2] and by Schmidt in [10, 11]and by Starr and Turner III in [12], and planarity of the intersection graph ofa module over any ring was studied in [13].Here we study planarity of the intersection graph of a finite group. Let G bea group. By the intersection graph of G we mean an undirected graph withoutloops and multiple edges defined as follows: the vertex set is the set of allproper non-trivial subgroups of G, and there is an edge between two distinctvertices H and K if and only if H∩K 6= 1 where 1 denotes the trivial subgroupof G.We call a group planar if its intersection graph is planar. For any naturalnumbers m and n, we use C

SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD

Abstract: . In this paper, we investigate p-biharmonic maps u : (M,g) →(N,h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that ifR M |τ(u)| a+p dv g < ∞ andR M |d(u)| 2 dv g < ∞, then u is harmonic, where a ≥ 0 is a nonnegativeconstant and p ≥ 2. We also obtain that any weakly convex p-biharmonichypersurfaces in space formN(c) with c ≤ 0 is minimal. These results giveaffirmative partial answer to Conjecture 2 (generalized Chen’s conjecturefor p-biharmonic submanifolds). 1. IntroductionHarmonic maps play a central roll in geometry. They are critical pointsof the energy E(u) =R M|du| 2 2 dv g for smooth maps between manifolds u :(M,g) → (N,h) and the Euler-Lagrange equation is that tension field τ(u)vanishes. Extensions to the notions of p-harmonic maps, F-harmonic mapsand f-harmonic maps were introduced and many results have been carried out(for instance, see [1, 2, 3, 8, 23]). In 1983, J. Eells and L. Lemaire [10] proposedthe problem to consider the biharmonic maps: they are critical maps of thefunctionalE

On subfields of gk and generalized gk function fields

Abstract: . In this article, we show that many of the genera that Giuliettiand Fanali obtained from subfields of the GK curve can be obtained byusing similar techniques used by Garcia, Stichtenoth and Xing. In themeantime, we obtain some new genera from the subfields of GK andgeneralized GK function fields. 1. IntroductionLet F/K be an algebraic function field of genus g with constant field Kwhere K is a finite field and N(F) be the number of rational places of F. ByHasse-Weil Theorem [13, Theorem 5.2.3], the number of rational places of F/Kis bounded by(1) | N(F)−(|K| +1) |≤ 2p|K|g.A function field is called maximal if its number of rational places attains theupper bound in the above inequality. Obviously, maximal function fields whichare not rational can only exist over finite fields of square cardinality. The mostwell-known example of a maximal function field is the Hermitian function fieldH = F q 2 (x,y), where F q 2 is the finite field with q 2 elements. H is defined bythe equation(2) x q +x = y q+1

Grossberg-karshon twisted cubes and basepoint-free divisors

Abstract: Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of an integral weight and a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of and .

Classification of smooth schubert varieties in the symplectic grassmannians

Abstract: . A Schubert variety in a rational homogeneous variety G/P isdefined by the closure of an orbit of a Borel subgroup Bof G. In general,Schubert varieties are singular, and it is an old problem to determinewhich Schubert varieties are smooth. In this paper, we classify all smoothSchubert varieties in the symplectic Grassmannians. 1. IntroductionA rational homogeneous manifold S= G/Pis a projective manifold, wherea connected complex semisimple group Gacts transitively. Under the actionof a Borel subgroup Bof G, Shas finitely many orbits. The closure of a B-orbit in Sis called a Schubert variety of S. In general, Schubert varieties aresingular, and it is an old problem to determine which Schubert varieties aresmooth. Lakshmibai-Weyman and Brion-Polo have studied the singular lociof Schubert varieties of S, when Sis a compact Hermitian symmetric space([9] and [2]). In particular, they showed that in this case any smooth Schubertvariety in Sis a homogeneous submanifold of Sassociated to a subdiagramof the marked Dynkin diagram of S. For example, a Schubert variety of theGrassmannian Gr(k,V) of k-subspaces in a vector space V is smooth if andonly if it is a linearly embedded sub-Grassmannian.More generally, when Sis associated to a long simple root, we have:Theorem 1.1 (Proposition 3.7 of Hong-Mok [4]). Let S= G/P be a rationalhomogeneous manifold associated to a long simple root. Then any smooth Schu-bert variety in Sis a homogeneous submanifold of Sassociated to a subdiagramof the marked Dynkin diagram of S.On the other hand, when Sis associated to a short simple root, there is asmooth Schubert variety that is not homogeneous. Let V be a vector spacewith a symplectic form ω, i.e., a nondegenerate skew-symmetric bilinear form.

The riesz decomposition theorem for skew symmetric operators

Abstract: An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

ON THE (n, d) th f-IDEALS

Abstract: For a field K, a square-free monomial ideal I of K[, . . ., ] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an f-ideal. In this paper, we prove the existence of f-ideal for and , and we also give some algorithms to construct f-ideals.

Comparison theorems in finsler geometry with weighted curvature bounds and related results

Abstract: We first extend the notions of weighted curvatures, includ- ing the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curva- ture bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curva- ture and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.

On “very palindromic” sequences

Abstract: We consider the problem of characterizing the palindromic sequences 〈cd−1, cd−2, . . . , c0〉, cd−1 6= 0, having the property that for any K ∈ N there exists a number that is a palindrome simultaneously in K different bases, with 〈cd−1, cd−2, . . . , c0〉 being its digit sequence in one of those bases. Since each number is trivially a palindrome in all bases greater than itself, we impose the restriction that only palindromes with at least two digits are taken into account. We further consider a related problem, where we count only palindromes with a fixed number of digits (that is, d). The first problem turns out not to be very hard; we show that all the palindromic sequences have the required property, even with the additional point that we can actually restrict the counted palindromes to have at least d digits. The second one is quite tougher; we show that all the palindromic sequences of length d = 3 have the required property (and the same holds for d = 2, based on some earlier results), while for larger values of d we present some arguments showing that this tendency is quite likely to change. Mathematics Subject Classification (2010): 11A63

On some classes of r-complex hermitian finsler spaces

Abstract: In this paper, we investigate the R-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the R-complex Hermitian Finsler spaces are defined, (e.g. weakly Kahler, Kahler, strongly Kahler). Here the notions of Kahler and strongly Kahler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an R-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an R-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.

A characterization of class groups via sets of lengths

Abstract: Let $H$ be a Krull monoid with class group $G$ such that every class contains a prime divisor. Then every nonunit $a \in H$ can be written as a finite product of irreducible elements. If $a=u_1 \cdot \ldots \cdot u_k$, with irreducibles $u_1, \ldots u_k \in H$, then $k$ is called the length of the factorization and the set $\mathsf L (a)$ of all possible $k$ is called the set of lengths of $a$. It is well-known that the system $\mathcal L (H) = \{\mathsf L (a) \mid a \in H \}$ depends only on the class group $G$. In the present paper we study the inverse question asking whether or not the system $\mathcal L (H)$ is characteristic for the class group. Consider a further Krull monoid $H'$ with class group $G'$ such that every class contains a prime divisor and suppose that $\mathcal L (H) = \mathcal L (H')$. We show that, if one of the groups $G$ and $G'$ is finite and has rank at most two, then $G$ and $G'$ are isomorphic (apart from two well-known pairings).

The composition series of ideals of the partial-isometric crossed product by semigroup of endomorphisms

Abstract: Let + be the positive cone in a totally ordered abelian group , andan action of + by extendible endomorphisms of a C ∗ -algebra A. Suppose I is an extendible �-invariant ideal of A. We prove that the partial-isometric crossed product I := I × piso + embeds naturally as an ideal of A× piso + , such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal I together with the kernel of a natural homomorphism � : A× piso + ! A × iso + gives a composition series of ideals of A × piso + studied by Lindiarni and Raeburn.

Ω-result on coefficients of automorphic l-functions over sparse sequences

Abstract: . Let λ f (n) denote the n-th normalized Fourier coefficient ofa primitive holomorphic form f for the full modular group Γ = SL 2 (Z).In this paper, we are concerned with Ω-result on the summatorPy function n6x λ 2f (n 2 ), and establish the following resultX n6x λ 2f (n 2 ) = c 1 x + Ω(x 49 ),where c 1 is a suitable constant. 1. Introduction and main resultsAccording to the Langlands program, there are many hidden structures un-derlying the Fourier coefficients of an automorphic form. Thus it is very impor-tant and essential to investigateits summatoryfunction overa certain sequence.Let H ∗ k be the set of all normalized Hecke eigencuspforms of even integralweight kfor the full modular group Γ = SL 2 (Z). For f(z) ∈ H ∗ k , f(z) has thefollowing Fourier expansion at the cusp ∞f(z) =X ∞n=1 λ f (n)n k−12 e 2πinz ,where λ f (n) is real and satisfies the multiplicative property(1.1) λ f (m)λ f (n) =X d|(m,n) λ f mnd 2 for any integers m≥ 1 and n≥ 1.The size and oscillations of λ f (n) deserve deep research. In 1974, Deligne

Shape operator and gauss map of pointwise 1-type

Abstract: . We examine the relationship of the shape operator of a sur-face of Euclidean 3-space with its Gauss map of pointwise 1-type. Sur-faces with constant mean curvature and right circular cones with respectto some properties of the shape operator are characterized when theirGauss map is of pointwise 1-type. 1. IntroductionFor last thirty years or so, the notion of finite type immersions has beenwidely applied in classifying and characterizing the submanifolds in Euclideanspace since it was introduced in the late 1970’s: Let x : M → E m be anisometric immersion of a Riemannian manifold M into the Euclidean space ofdimension m. If we identify x with the position vector at each point p of M, itis a vector valued function. Let ∆ be the Laplacian operator defined on M. Ifx is decomposed as x = x 0 +x 1 +x 2 +··· + x k , it is said to be of finite type,where x 0 is a constant vector and x i non-constant maps satisfying ∆x i = λ i x i for some constant λ i . In particular, if λ i ’s are different, we say that it is ofk-type ([3, 4, 15]). It is well known that a submanifold of Euclidean space of1-type is either a minimal submanifold of E

Total identity-summand graph of a commutative semiring with respect to a co-ideal

Abstract: Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x,y 2 R, the vertices x and y are adjacent if and only if xy 2 S(I).

An iterative algorithm for the least squares solutions of matrix equations over symmetric arrowhead matrices

Abstract: This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares prob- lem over symmetric arrowhead matrices. As a matter of fact, we de- velop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.