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20 March 2014, Volume 34 Issue 2 Previous Issue    Next Issue

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THE BOREL DIRECTIONS OF ALGEBROIDAL FUNCTION AND ITS COEFFICIENT FUNCTIONS ZHANG Shao-Hua, ZHANG Xiao-Mei, SUN Dao-Chun Acta mathematica scientia,Series B. 2014, 34 (2):  241-251.  DOI: 10.1016/S0252-9602(14)60001-1 Abstract ( 250 )   RICH HTML PDF (178KB) ( 584 )   Save In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained. References | Related Articles | Metrics

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CONSTRUCTING POINTED WEAK HOPF ALGEBRAS BY ORE-EXTENSION CAO Hai-Jun, LI Fang, ZHANG Mian-Mian Acta mathematica scientia,Series B. 2014, 34 (2):  252-262.  DOI: 10.1016/S0252-9602(14)60002-3 Abstract ( 203 )   RICH HTML PDF (204KB) ( 960 )   Save The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra At = ni=0A αt from a Clifford monoid S = [Y ; Gα, φα, β ]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal. References | Related Articles | Metrics

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THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS Afif BEN AMAR Acta mathematica scientia,Series B. 2014, 34 (2):  263-273.  DOI: 10.1016/S0252-9602(14)60003-5 Abstract ( 204 )   RICH HTML PDF (185KB) ( 1893 )   Save The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations. References | Related Articles | Metrics

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A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES Peyman SALIMI, Pasquale VETRO Acta mathematica scientia,Series B. 2014, 34 (2):  274-284.  DOI: 10.1016/S0252-9602(14)60004-7 Abstract ( 196 )   RICH HTML PDF (164KB) ( 1617 )   Save Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki´s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point. References | Related Articles | Metrics

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A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS LI You-Fa, YANG Shou-Zhi Acta mathematica scientia,Series B. 2014, 34 (2):  285-300.  DOI: 10.1016/S0252-9602(14)60005-9 Abstract ( 273 )   RICH HTML PDF (232KB) ( 350 )   Save This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R*, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(R*). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(R*) and their biorthogonal (orthogo-nal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L2(R*) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L2(R*), we can get dual (tight) two-direction wavelet frames in L2(Rm), where m ≤s. From the projected dual (tight) two-direction wavelet frames in L2(Rm), symmetric dual (tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results. References | Related Articles | Metrics

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ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES ZHAO Yue-Xu Acta mathematica scientia,Series B. 2014, 34 (2):  301-312.  DOI: 10.1016/S0252-9602(14)60006-0 Abstract ( 201 )   RICH HTML PDF (180KB) ( 765 )   Save It is well-known that the complete convergence theorem for i.i.d. random vari-ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ε  goes to zero, so it is of interest to investigate the asymptotic behavior of the series as ε goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables. References | Related Articles | Metrics

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SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS ZHANG Qing-Cheng, WEI Zhu, CHU Ying-Na, ZHANG Yong-Ping Acta mathematica scientia,Series B. 2014, 34 (2):  313-330.  DOI: 10.1016/S0252-9602(14)60007-2 Abstract ( 194 )   RICH HTML PDF (217KB) ( 1021 )   Save In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland´s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations. References | Related Articles | Metrics

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INVOLUTIONS WITH FIXED POINT SET RP(2m) ? P(2m, 2n + 1) MENG Yuan-Yuan, WANG Yan-Yang Acta mathematica scientia,Series B. 2014, 34 (2):  331-342.  DOI: 10.1016/S0252-9602(14)60008-4 Abstract ( 176 )   RICH HTML PDF (186KB) ( 964 )   Save Let (M, T) be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of (M, T) are determined. References | Related Articles | Metrics

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I2-CONVERGENCE AND I2-CAUCHY DOUBLE SEQUENCES ErdinC DUNDAR, Bilal ALTAY Acta mathematica scientia,Series B. 2014, 34 (2):  343-353.  DOI: 10.1016/S0252-9602(14)60009-6 Abstract ( 171 )   RICH HTML PDF (168KB) ( 1120 )   Save In this article, we prove a decomposition theorem for I2-convergent double sequences and introduce the notions of I2-Cauchy and I*2 -Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I2, I)-convergence and (I2, I)-Cauchy double sequence. References | Related Articles | Metrics

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ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX Murat CANDAN Acta mathematica scientia,Series B. 2014, 34 (2):  354-366.  DOI: 10.1016/S0252-9602(14)60010-2 Abstract ( 198 )   RICH HTML PDF (206KB) ( 1788 )   Save The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80(1948), 167–190]. Let f0(B) and f(B) be the domain of the double sequentialband matrix B(r, s) in the sequence spaces f0 and f. In this article, the β− and −duals of the space f(B) are determined. Additionally, we give some inclusion theorems concerning with the spaces f0(B) and f(B). Moreover, the classes (f(B) : μ) and (μ : f(B)) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space. References | Related Articles | Metrics

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SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH Acta mathematica scientia,Series B. 2014, 34 (2):  367-379.  DOI: 10.1016/S0252-9602(14)60011-4 Abstract ( 223 )   RICH HTML PDF (191KB) ( 769 )   Save The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator  Ω( λ, p). References | Related Articles | Metrics

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AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS WU Zhao-Jun Acta mathematica scientia,Series B. 2014, 34 (2):  380-386.  DOI: 10.1016/S0252-9602(14)60012-6 Abstract ( 183 )   RICH HTML PDF (154KB) ( 554 )   Save The author proves that if f : C→Cn is a transcendental vector valued mero-morphic function of finite order and assume ∑a∈Cn∪{∞}δ(a) = 2, then, 1 − δ(∞)/2 − δ(∞)≤K(f′) ≤2(1 − δ(∞)/2 − δ(∞), where K(f ′) = limsup r→+∞N(r, f ′) + N (r, 0, f′)T(r, f ′). This result extends the related results for meromorphic function by Singh and Kulkarni. References | Related Articles | Metrics

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ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS YANG Jie, WANG Yu-Zhao, CHEN Wen-Yi Acta mathematica scientia,Series B. 2014, 34 (2):  387-393.  DOI: 10.1016/S0252-9602(14)60013-8 Abstract ( 233 )   RICH HTML PDF (165KB) ( 703 )   Save It is well known that the commutator Tb of the Calder´on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 < p < +∞ if and only if b ∈ BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is S01,δ with 0 ≤δ < 1, if b∈ LMO1, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L1(Rn) into BMO(Rn); If [b, Tσ ] is bounded from H1(Rn) into L1(Rn) or L1(Rn) into BMO(Rn), then, b ∈ LMOloc. References | Related Articles | Metrics

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DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES Faruk OZGER, Feyzi BASAR Acta mathematica scientia,Series B. 2014, 34 (2):  394-408.  DOI: 10.1016/S0252-9602(14)60014-X Abstract ( 231 )   RICH HTML PDF (220KB) ( 1200 )   Save The domain of generalized difference matrix B(r, s) in the classical spaces l∞, c, and c0 was recently studied by Kiri¸s¸ci and Ba¸sar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞(B, p), c( B, p), and c0(B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞(B, p), c(B, p), and c0(eB , p) are computed and the bases of the spaces c(B , p) and c0(B, p) are constructed. The final section of this article is devoted to the characterization of the classes (λ(B, p) : μ) and (μ : λ(B, p)), where λ∈ {c, c0, l∞} and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma. References | Related Articles | Metrics

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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES Yekini SHEHU Acta mathematica scientia,Series B. 2014, 34 (2):  409-423.  DOI: 10.1016/S0252-9602(14)60015-1 Abstract ( 192 )   RICH HTML PDF (208KB) ( 1133 )   Save Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gˆateaux differentiable norm. Assume that every nonempty closed con-vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map-pings which is also a unique solution to variational inequality problem involving-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con-vex optimization problems, and split feasibility problems. Our result extends many recent important results. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING ZHANG Ying-Hui, WU Guo-Chun Acta mathematica scientia,Series B. 2014, 34 (2):  424-434.  DOI: 10.1016/S0252-9602(14)60016-3 Abstract ( 286 )   RICH HTML PDF (187KB) ( 1047 )   Save We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods. References | Related Articles | Metrics

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UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL Bn FENG Shu-Xia, LIU Tai-Shun Acta mathematica scientia,Series B. 2014, 34 (2):  435-443.  DOI: 10.1016/S0252-9602(14)60017-5 Abstract ( 169 )   RICH HTML PDF (165KB) ( 1123 )   Save In this article, we extend the definition of uniformly starlike functions and uni-formly convex functions on the unit disk to the unit ball in Cn, give the discriminant criterions for them, and get some inequalities for them. References | Related Articles | Metrics

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UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS LIU Yong, QI Xiao-Guang Acta mathematica scientia,Series B. 2014, 34 (2):  444-452.  DOI: 10.1016/S0252-9602(14)60018-7 Abstract ( 248 )   RICH HTML PDF (158KB) ( 1179 )   Save In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. References | Related Articles | Metrics

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CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY GUO Wan-Li, XIAO Hai-Jun, CHEN Shi-Hua Acta mathematica scientia,Series B. 2014, 34 (2):  453-465.  DOI: 10.1016/S0252-9602(14)60019-9 Abstract ( 190 )   RICH HTML PDF (421KB) ( 446 )   Save This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis. References | Related Articles | Metrics

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MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION Jacek DZIOK Acta mathematica scientia,Series B. 2014, 34 (2):  466-472.  DOI: 10.1016/S0252-9602(14)60020-5 Abstract ( 200 )   RICH HTML PDF (144KB) ( 750 )   Save In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given. References | Related Articles | Metrics

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ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α Hacer SENGüL, Mikail ET Acta mathematica scientia,Series B. 2014, 34 (2):  473-482.  DOI: 10.1016/S0252-9602(14)60021-7 Abstract ( 207 )   RICH HTML PDF (177KB) ( 1280 )   Save In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacu-nary statistical convergence of order α and strong Nαθ (p)-summability. Furthermore, some relations between the spaces Nαθ (p)- and Sαθ are examined. References | Related Articles | Metrics

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EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS INVOLVING m CRITICAL HARDY-SOBOLEV EXPONENTS AND m SIGN-CHANGING WEIGHT FUNCTION Nemat NYAMORADI, Tsing-San HSU Acta mathematica scientia,Series B. 2014, 34 (2):  483-500.  DOI: 10.1016/S0252-9602(14)60022-9 Abstract ( 216 )   RICH HTML PDF (230KB) ( 949 )   Save In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods. References | Related Articles | Metrics

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CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME GAO Zhi-Qiang, LIU Quan-Sheng, WANG He-Song Acta mathematica scientia,Series B. 2014, 34 (2):  501-512.  DOI: 10.1016/S0252-9602(14)60023-0 Abstract ( 230 )   RICH HTML PDF (204KB) ( 655 )   Save We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi-ronment is supposed to be independent and identically distributed. For A （R, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization. References | Related Articles | Metrics

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3-LIE BIALGEBRAS BAI Rui-Pu, CHENG Yu, LI Jia-Qian, MENG Wei Acta mathematica scientia,Series B. 2014, 34 (2):  513-522.  DOI: 10.1016/S0252-9602(14)60024-2 Abstract ( 188 )   RICH HTML PDF (169KB) ( 1040 )   Save 3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided. References | Related Articles | Metrics

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THE SUPER-BIHAMILTONIAN REDUCTION ON C∞(S1, OSP(1|2)) ZHANG Ling, ZUO Da-Feng Acta mathematica scientia,Series B. 2014, 34 (2):  537-545.  DOI: 10.1016/S0252-9602(14)60026-6 Abstract ( 173 )   RICH HTML PDF (169KB) ( 1000 )   Save In this article, we will show that the super-bihamiltonian structures of the Kuper-KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16, 19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp(1|2). References | Related Articles | Metrics

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RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS Bilel KRICHEN Acta mathematica scientia,Series B. 2014, 34 (2):  546-556.  DOI: 10.1016/S0252-9602(14)60027-8 Abstract ( 264 )   RICH HTML PDF (183KB) ( 1414 )   Save In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter´s and approximate essential spectrum. References | Related Articles | Metrics

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ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS DENG Chun-Yuan Acta mathematica scientia,Series B. 2014, 34 (2):  523-536.  DOI: 10.1016/S0252-9602(14)60025-4 Abstract ( 174 )   RICH HTML PDF (197KB) ( 657 )   Save This note is to present some results on the group invertibility of linear combina-tions of idempotents when the difference of two idempotents is group invertible. References | Related Articles | Metrics

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RIEMANN-HILBERT CHARACTERIZATION FOR MAIN BESSEL POLYNOMIALS WITH VARYING LARGE NEGATIVE PARAMETERS DUAN Ping, DU Jin-Yuan Acta mathematica scientia,Series B. 2014, 34 (2):  557-567.  DOI: 10.1016/S0252-9602(14)60028-X Abstract ( 183 )   RICH HTML PDF (174KB) ( 979 )   Save In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters. References | Related Articles | Metrics

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LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS ZHAO Ji-Hong, LIU Qiao Acta mathematica scientia,Series B. 2014, 34 (2):  568-574.  DOI: 10.1016/S0252-9602(14)60029-1 Abstract ( 186 )   RICH HTML PDF (160KB) ( 538 )   Save This article proves the logarithmically improved Serrin´s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806–808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799–802). References | Related Articles | Metrics

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SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS Muhammad ARIF, Janusz SOK′O l, Muhammad AYAZ Acta mathematica scientia,Series B. 2014, 34 (2):  575-578.  DOI: 10.1016/S0252-9602(14)60030-8 Abstract ( 313 )   RICH HTML PDF (125KB) ( 1675 )   Save In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases. References | Related Articles | Metrics

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MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS TAN Qiu-Heng, JIANG Hang-Jin, DING Xi-Ming Acta mathematica scientia,Series B. 2014, 34 (2):  579-592.  DOI: 10.1016/S0252-9602(14)60031-X Abstract ( 303 )   RICH HTML PDF (791KB) ( 1975 )   Save The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar-ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coefficient (MIC), a recently proposed dependence measure, captures a wide range of associ-ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient (PMIC) is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given. References | Related Articles | Metrics