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Showing papers in "Journal of The Korean Mathematical Society in 2013"


Journal ArticleDOI
TL;DR: In this paper, the authors considered a class of periodic Ito-delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic so-lution of the delay equations are given.
Abstract: . In this paper, we consider a class of periodic Itoˆ stochasticdelay differential equations by using the properties of periodic Markovprocesses, and some sufficient conditions for the existence of periodic so-lution of the delay equations are given. These existence theorems improvethe results obtained by Itoˆ et al. [6], Bainov et al. [1] and Xu et al. [15].As applications, we study the existence of periodic solution of periodicstochastic logistic equation and periodic stochastic neural networks withinfinite delays, respectively. The theorem for the existence of periodic so-lution of periodic stochastic logistic equation improve the result obtainedby Jiang et al. [7]. 1. IntroductionSince Itoˆ introduced his stochastic calculus about 50 years ago, the theory ofstochastic differential equations has been developed very quickly [1–15,17]. Itis now being recognized to be not only richer than the corresponding theory ofdifferential equations without stochastic perturbation but also represent a morenatural framework for mathematical modeling of many real-world phenomena.Now there also exists a well-developed qualitative theory of stochastic differ-ential equations [6,10,12]. However, not so much has been developed in thedirection of the periodically stochastic differential equations. Till now only afew papers have been published on this topic [1,3,4,15,17]. In papers [3,6], theauthors got the conditions for the existence of periodic solution of differentialequations with random right sides. Hasminskii in [4] gave some basic resultson the existence of periodic solution of stochastic differential equations withoutdelays. But, the above results can not be used to check the existence of peri-odic solution of general stochastic delay differential equations. In [15], Xu et

35 citations


Journal ArticleDOI
TL;DR: The one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels are described and applications to computing the dimensions of Siegel modular forms are given.
Abstract: We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.

24 citations


Journal ArticleDOI
TL;DR: In this article, the optimistic limits of the colored Jones poly-nomials of the hyperbolic knots coincide with the optimistic limit of the Kashaev invariants modulo 4 2.
Abstract: We show that the optimistic limits of the colored Jones poly- nomials of the hyperbolic knots coincide with the optimistic limits of the Kashaev invariants modulo 4 2 .

16 citations


Journal ArticleDOI
TL;DR: National Natural Science Foundation of China [10601042]; Fundamental Research Funds the Central Universities [HIT.NSRIF.2010052]
Abstract: National Natural Science Foundation of China [10601042]; Fundamental Research Funds the Central Universities [HIT.NSRIF.2010052]

15 citations


Journal ArticleDOI
TL;DR: Using the three critical points theorem by B. Ricceri (23), this paper obtained a multiplicity result for a class of nonlocal problems in Orlicz- Sobolev spaces.
Abstract: Using the three critical points theorem by B. Ricceri (23), we obtain a multiplicity result for a class of nonlocal problems in Orlicz- Sobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.

15 citations


Journal ArticleDOI
TL;DR: In this paper, a commutative ring R is w-Noetherian if and only if the direct limit of GV-torsion-free injective R-modules is injective.
Abstract: . By utilizing known characterizations of w-Noetherian rings interms of injective modules, we give more characterizations of w-Noether-ian rings. More precisely, we show that a commutative ring R is w-Noetherian if and only if the direct limit of GV-torsion-free injective R-modules is injective; if and only if every R-module has a GV-torsion-freeinjective (pre)cover; if and only if the direct sum of injective envelopes ofw-simple R-modules is injective; if and only if the essential extension ofthe direct sum of GV-torsion-free injective R-modules is the direct sumof GV-torsion-free injective R-modules; if and only if every F w,f (R)-injective w-module is injective; if and only if every GV-torsion-free R-module admits an i-decomposition. 1. IntroductionFor the last few decades, characterizingNoetherian rings in terms ofinjectivemodules has drawn considerable attention from many algebraists. Matlis ([19]),Papp ([20]), Bass ([2]), Faith and Walker ([8]), Kurshan ([18]), Goursaud andValette ([11]), Beidar and Ke ([4]), and Beidar, Jain and Srivastava ([3]) havedone much meaningful work in this field. Since the birth of the theory of staroperations, heavy concentration has been put on ideal theory. Even so, we stillhope that the theory of star operations can play a role in researching the directsum representations of injective modules and related topics [14]. Inspired bythe study on injective modules over Noetherian rings, some researchers havepaid attention to the studies on injective modules over w-Noetherian rings.In [26], Yin et al. defined a w-Noetherian ring as a commutative ring whichsatisfies the ascending chain condition of w-ideals. As for the integral domain, aw-Noetherian ring actually is a strong Mori domain. In 2005, Fuchs provedthatthe integral domain R is a strong Mori domain if and only if E(Q/R) is a Σ-injective module [9]. According to the Cartan-Eilenberg-Bass-Papp Theorem,R is a Noetherian ring if and only if the direct sum of injective modules isinjective. In 2008, Kim et al. proved that the integral domain R is a strong

15 citations


Journal ArticleDOI
TL;DR: In this paper, two different methods of proving Jensen's in-equality on time scales for superquadratic functions are demonstrated, and some refinements of classical inequalities on time-scale are obtained us- ing properties of super-quadratic functions and some known results for isotonic linear functionals.
Abstract: cari´ Abstract. In this paper, two different methods of proving Jensen's in- equality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained us- ing properties of superquadratic functions and some known results for isotonic linear functionals.

13 citations


Journal ArticleDOI
TL;DR: In this paper, a new family of simply connected minimal com- plex surfaces of general type with pg = 1, q = 0, and K 2 = 3, 4, 5, 6, 8 using a Q-Gorenstein smoothing theory was constructed.
Abstract: We construct a new family of simply connected minimal com- plex surfaces of general type with pg = 1, q = 0, and K 2 = 3; 4; 5; 6; 8 using a Q-Gorenstein smoothing theory.

13 citations


Journal ArticleDOI
TL;DR: The quasi-partial difference family (QPDF) as mentioned in this paper admits a group of automorphisms that fixes a vertex of the graph and acts semiregularly on the other vertices.
Abstract: We introduce a new class of graphs, called quasi -Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices. We determine when these graphs are strongly regular, and this leads us to define a new algebro-combinatorial structure, called quasi-partial difference family, or QPDF for short. We give several infinite families and sporadic examples of QPDFs. We also study several properties of QPDFs and determine, under several conditions, the form of the parameters of QPDFs when the group G is cyclic.

12 citations


Journal ArticleDOI
TL;DR: In this article, the structures of posets which have an associ-ation scheme structure whose relations are indexed by the poset distance between the points in the space were characterized.
Abstract: It is known that being hierarchical is a necessary and suffi- cient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an associ- ation scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

11 citations


Journal ArticleDOI
TL;DR: In this paper, the concepts of -torsion modules, -flat modules, and -von Neumann regular rings were introduced for commutative rings, and the concept of regular rings was extended to regular rings.
Abstract: Let R be a commutative ring with and let = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If , then R is called a -ring. In this paper, we introduce the concepts of -torsion modules, -flat modules, and -von Neumann regular rings.

Journal ArticleDOI
TL;DR: In this paper, the sum of the sth powers of the positive divisors of a positive integer N was shown to be a function of the number of positive integers in the positive integer n.
Abstract: Let s(N) denote the sum of the sth powers of the positive divisors of a positive integer N and let e s(N) = P djN ( 1) d 1 d s with d, N, and s positive integers. Hahn (12) proved that

Journal ArticleDOI
TL;DR: In this article, the problem of how to squeeze multiple ciphertexts without losing original message information is addressed, and the notion of decomposability for public-key encryption is formalized.
Abstract: In this work we deal with the problem of how to squeeze mul- tiple ciphertexts without losing original message information. To do so, we formalize the notion of decomposability for public-key encryption and investigate why adding decomposability is challenging. We construct an ElGamal encryption scheme over extension fields, and show that it sup- ports the efficient decomposition. We then analyze security of our scheme under the standard DDH assumption, and evaluate the performance of our construction.

Journal ArticleDOI
TL;DR: In this paper, it was shown that a G-Dedekind domain is a war-domain if and only if for any prime ideal P of R which contains (R : K T), P is Gorensteinprojective.
Abstract: . In this paper, we mainly discuss Gorenstein Dedekind do-mains (G-Dedekind domains for short) and their overrings. Let R be aone-dimensional Noetherian domain with quotient field K and integralclosure T. Then it is proved that R is a G-Dedekind domain if and onlyif for any prime ideal P of R which contains (R : K T), P is Gorensteinprojective. We also give not only an example to show that G-Dedekinddomains are not necessarily Noetherian Warfield domains, but also a defi-nition for a special kind of domain: a 2-DVR. As an application, we provethat a Noetherian domain R is a Warfield domain if and only if for anymaximal ideal M of R, R M is a 2-DVR. IntroductionThroughout this paper, all rings are commutative with identity element andall modules are unitary. Let Rbe a domain with quotient field K and J afractional ideal of R. The definition of J −1 can be found in [14] as follows:J −1 = {x| x∈ K, xJ⊂ R}.The definition of divisorial ideals can be found in [10]: A fractional ideal JofRis said to be divisorial if J

Journal ArticleDOI
TL;DR: In this paper, the Fourier-type functionals on Wiener space are considered and the analytic Feynman integrals involv-ing the ⋄-convolutions are established.
Abstract: . In this paper, we consider the Fourier-type functionals onWiener space. We then establish the analytic Feynman integrals involv-ing the ⋄-convolutions. Further, we give an approach to solution of theSchro¨dinger equation via Fourier-type functionals. Finally, we use this ap-proach to obtain solutions of the Schro¨dinger equations for harmonic oscil-lator and double-well potential. The Schro¨dinger equations for harmonicoscillator and double-well potential are meaningful subjects in quantummechanics. 1. IntroductionLet C 0 [0,T] denote the one-parameter Wiener space, that is, the space ofcontinuous real-valued functions xon [0,T] with x(0) = 0. In 1948, Feynmanassumed the existence of an integral over a space of paths and used this integralin a formal way in his approach to quantum mechanics [9]. A number ofmathematicians have attempted to give rigorously meaningful definitions ofthe Feynman integral with appropriate existence theorems and have expressedsolutions of the Schr¨odinger equation in terms of their integrals. One of theseapproaches is based on the similarity between the Wiener and the Feynmanintegrals, where procedures are developed to obtain the Feynman integralsfrom the Wiener integrals by an analytic extension from the real axis to theimaginary axis.Consider a differential equation(1.1)∂∂tψ(u,t) =12λ∆ψ(u,t) −V(u)ψ(u,t)with the initial condition ψ(u,0) = ϕ(u), where ∆ is the Laplacian and V is anappropriate potential function. For λ>0, this is the diffusion equation with

Journal ArticleDOI
TL;DR: This work shows the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces.
Abstract: . We show the existence of smooth isolated curves of differentdegrees and genera in Calabi-Yau threefolds that are complete intersec-tions in homogeneous spaces. Along the way, we classify all degrees andgenera of smooth curves on BN general K3 surfaces of genus µ, where5 ≤µ ≤10. By results of Mukai, these are the K3 surfaces that can berealised as complete intersections in certain homogeneous spaces. 1. IntroductionIn this note we extend the study of embeddings of complex projective curvesinto Calabi-Yau complete intersection threefolds from [9] to Calabi-Yau three-folds that are complete intersections in homogeneous spaces. For the back-ground and some history of the study of curves in Calabi-Yau threefolds werefer to the introduction of [9].We will pay special attention to families of Calabi-Yau threefolds in P m , for7 ≤ m ≤ 12, that are complete intersections in certain homogeneous spaces.We now briefly fix some notation and refer to Mukai’s papers [12, 13] for fur-ther details. We use the following notation: For a vector space V

Journal ArticleDOI
TL;DR: In this article, the authors considered a continuous time risk model in volving two types of dependent claims, namely main claims and by-claims, and derived the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system.
Abstract: In this paper, we consider a continuous time risk model in- volving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by- claim may be delayed depending on associated main claim amount. Using Rouche's theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival proba- bility. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

Journal ArticleDOI
TL;DR: In this paper, the concept of "orbifold embedding" is introduced, which is more general than sub-orbifolds and is shown to be equivalent to strong equivariant immersion.
Abstract: The concept of "orbifold embedding" is introduced. This is more general than sub-orbifolds. Some properties of orbifold embeddings are studied, and in the case of translation groupoids, orbifold embedding is shown to be equivalent to a strong equivariant immersion.

Journal ArticleDOI
TL;DR: In this paper, three classes of abelian p-groups are defined and studied: the m,n-simply presented groups, the m,n-balanced projective groups and the m n-totally projec- tive groups.
Abstract: If m and n are non-negative integers, then three new classes of abelian p-groups are defined and studied: the m,n-simply presented groups, the m,n-balanced projective groups and the m,n-totally projec- tive groups. These notions combine and generalize both the theories of simply presented groups and p !+n -projective groups. If m,n = 0, these all agree with the class of totally projective groups, but when m+n � 1, they also include the p !+m+n -projective groups. These classes are related to the (strongly) n-simply presented and (strongly) n-balanced projective groups considered in (15) and the n-summable groups considered in (2). The groups in these classes whose lengths are less than ! 2 are character- ized, and if in addition we have n = 0, they are determined by isometries of their p m -socles.

Journal ArticleDOI
TL;DR: A generalization of the right NC-McCoy ring, called a right nilpotent coefficient McCoy ring, was introduced in this paper, and the structure and several kinds of extensions of such rings are investigated.
Abstract: Rege-Chhawchharia, and Nielsen introduced the concept of right McCoy ring, based on the McCoy's theorem in 1942 for the anni- hilators in polynomial rings over commutative rings. In the present note we concentrate on a natural generalization of a right McCoy ring that is called a right nilpotent coefficient McCoyring (simply, a right NC-McCoy ring). The structure and several kinds of extensions of right NC-McCoy rings are investigated, and the structure of minimal right NC-McCoy rings is also examined. Throughout this paper R denotes an associative ring with identity unless otherwise stated. Let N(R) be the set of all nilpotent elements in R. We use R(x) to denote the polynomial ring with an indeterminate x over R. Let Cf(x) denote the set of all coefficients off(x) ∈ R(x). Denote the n by n full matrix ring over R by Matn(R) and the n by n upper triangular matrix ring over R by Un(R). Use Eij for the matrix with (i,j)-entry 1 and elsewhere 0. By Zn we mean the ring of integers modulo n. McCoy (27) showed that if two polynomials annihilate each other over a commutative ring, then each polynomial has a nonzero annihilator in the base ring. Weiner (16) showed this fact fails in non-commutative rings. Based on this result, Nielsen (29) and Rege-Chhawchharia (30) each called a non-commutative ring R right McCoy (resp., left McCoy) if whenever any nonzero polynomials f(x),g(x) ∈ R(x) satisfy f(x)g(x) = 0, then f(x)c = 0 (resp., cg(x) = 0) for some nonzero c ∈ R, and a ring R is called McCoy if it is both left and right McCoy. Rege-Chhawchharia also called R an Armendariz ring (30, Definition 1.1) if whenever any polynomials f(x),g(x) ∈ R(x) satisfy f(x)g(x) = 0, then ab = 0 for each a ∈ Cf(x) and b ∈ Cg(x). Any reduced ring (i.e., it has no nonzero nilpotent elements) is Armendariz by (4, Lemma 1). Armendariz rings are clearly McCoy but the converse does not hold by (30, Remark 4.3). A ring is called Abelian if every idempotent is central. Armendariz rings are Abelian by the proof of (2, Theorem 6).

Journal ArticleDOI
TL;DR: In this article, the authors studied the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power of the positive mean curvature.
Abstract: This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive powerof the positive mean curvature. It is shown that the flow exists on a finite maximal inter- val, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

Journal ArticleDOI
TL;DR: In this article, the weighted Moore-Penrose inverse was introduced and studied in the context of Banach algebras, and weighted EP Ba- nach algebra elements were characterized.
Abstract: The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Ba- nach algebra elements will be characterized. The Banach space operator case will be also considered.

Journal ArticleDOI
TL;DR: In this article, the authors considered the case of the semi-hyperbolic patches arising from a transonic shock in simple waves interaction and constructed global solutions of the two-dimensional Riemann problem of the pressure gradient system.
Abstract: In this paper we consider a Riemann problem, in particular, the case of the presence of the semi-hyperbolic patches arising from a transonic shock in simple waves interaction. Under this circumstance, we construct global solutions of the two-dimensional Riemann problem of the pressure gradient system. We approach the problem as a Goursat boundary value problem and a mixed initial-boundary value problem, where one of the boundaries is the transonic shock.

Journal ArticleDOI
TL;DR: In this article, the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes were shown to imply the sharp 2-sided pointwise estimates for poisson kernels.
Abstract: In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica [5], our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

Journal ArticleDOI
TL;DR: In this article, it was shown that the factor ring of an Armendariz ring over its prime radical is also ARMENDERIZ, with the help of Antoine's results for nil-Armendariz rings.
Abstract: We observe from known results that the set of nilpotent ele- ments in Armendariz rings has an important role. The upper nilradical coincides with the prime radical in Armendariz rings. So it can be shown that the factor ring of an Armendariz ring over its prime radical is also Armendariz, with the help of Antoine's results for nil-Armendariz rings. We study the structure of rings with such property in Armendariz rings and introduce APR as a generalization. It is shown that APR is placed between Armendariz and nil-Armendariz. It is shown that an APR ring which is not Armendariz, can always be constructed from any Armen- dariz ring. It is also proved that a ring R is APR if and only if so is R(x), and that N(R(x)) = N(R)(x) when R is APR, where R(x) is the polynomial ring with an indeterminate x over R and N( ) denotes the set of all nilpotent elements. Several kinds of APR rings are found or constructed in the precess related to ordinary ring constructions.

Journal ArticleDOI
TL;DR: In this article, the authors established variational principle on cone metric spaces and gave some existence theorems of solutions for equilibrium problems on the cone metric space, and they gave some equivalences of an existence theorem of solution for the same problem.
Abstract: The aim of this paper is to establish variational principle on cone metric spaces and to give some existence theorems of solutions for equilibrium problems on cone metric spaces. We give some equivalences of an existence theorem of solutions for equilibrium problems on cone metric spaces.

Journal ArticleDOI
TL;DR: In this article, it was shown that a ring R is right Armendarizlike, if and only if R is strongly right McCoy if R was constructed by right annihilators.
Abstract: The concepts of reversible, right duo, and Armendariz rings are known to play important roles in ring theory and they are indepen- dent of one another. In this note we focus on a concept that can unify them, calling it a right Armendarizlike ring in the process. We first find a simple way to construct a right Armendarizlike ring but not Armendariz (reversible, or right duo). We show the difference between right Armen- darizlike rings and strongly right McCoy rings by examining the structure of right annihilators. For a regular ring R, it is proved that R is right Armendarizlike if and only if R is strongly right McCoy if and only if R is Abelian (entailing that right Armendarizlike, Armendariz, reversible, right duo, and IFP properties are equivalent for regular rings). It is shown that a ring R is right Armendarizlike, if and only if so is the polynomial ring over R, if and only if so is the classical right quotient ring (if any). In the process necessary (counter)examples are found or constructed. 1. Right Armendarizlike rings

Journal ArticleDOI
TL;DR: In this article, the authors considered a simply connected domain D with two marked boundary points q = q−, r = q+ and showed that all correlation functions of the fields in the OPE family of Gaussian free field with a certain boundary value are martingale-observables for dipolar SLE(4).
Abstract: We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condi- tion and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian free field with a certain boundary value are martingale-observables for dipolar SLE(4). In this paper we consider a version of dipolar conformal field theory with central charge one (c = 1) in a simply connected domain D with two marked boundary points q = q−, r = q+:More precisely, the theory we develop is based on a certain family of fields generated by the Gaussian free field in D with the Dirichlet boundary condition on _ and the Neumann boundary condition on the other boundary arc. We prove that the correlation functions of fields in this family under the insertion of a certain boundary condition changing operator form a collection of martingale-observables for dipolar SLE(4). We apply definitions and theories developed in (5) and (6) to a different conformal setting with a different boundary condition. In the chordal case ((5)) and the radial case ((6)), we consider a simply connected domain D with a marked boundary point and a marked interior point, respectively. Both theories are based on the Gaussian free field with the Dirichlet boundary condition. However, their central charge modifications are different. In this paper we do not discuss the central charge modification of dipolar conformal field theory with mixed boundary condition. We also explain the differences between the conformal field theory we con- sider in this paper and the other theories in (5) and (6). Unlike the chordal and the radial cases, the current field (the derivative of Gaussian free field) is

Journal ArticleDOI
TL;DR: In this paper, it was shown that the canonical functor of a preadditive category A is a weak equivalence between C and C/I. The advantage in passing from the category F to the category C lies in the fact that, although the two categories F and F/I are weakly equivalent, every endomorphism has a kernel and a cokernel in F/� which is not true in F.
Abstract: For an ideal I of a preadditive category A, we study when the canonical functor C: A ! A/I is local. We prove that there ex- ists a largest full subcategory C of A for which the canonical functor C: C ! C/I is local. Under this condition, the functor C turns out to be a weak equivalence between C and C/I. If A is additive (with splitting idempotents), then C is additive (with splitting idempotents). The cate- gory C is ample in several cases, such as the case when A = Mod-R and I is the idealof all morphisms with essential kernel. In this case, the category C contains, for instance, the full subcategory F of Mod-R whose objects are all the continuous modules. The advantage in passing from the category F to the category F/I lies in the fact that, although the two categories F and F/I are weakly equivalent, every endomorphism has a kernel and a cokernel in F/�, which is not true in F. In the final section, we extend our theory from the case of one ideal I to the case of n ideals I1,...,In.

Journal ArticleDOI
TL;DR: In this article, it was shown that a linear transformation from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks k and l. The term rank is the least number of lines (rows or columns) needed to include all the nonzero entries in A.
Abstract: The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks k and l.