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WEIGHTED ESTIMATES FOR CERTAIN ROUGH OPERATORS WITH APPLICATIONS TO VECTOR VALUED INEQUALITIES 若干粗糙算子的加权估计及其在向量值不等式上的应用
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200450
Feng Liu, Qingying Xue
{"title":"WEIGHTED ESTIMATES FOR CERTAIN ROUGH OPERATORS WITH APPLICATIONS TO VECTOR VALUED INEQUALITIES","authors":"Feng Liu, Qingying Xue","doi":"10.4134/JKMS.J200450","DOIUrl":"https://doi.org/10.4134/JKMS.J200450","url":null,"abstract":". Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ON ℤ p ℤ p [u]/ k >-CYCLIC CODES AND THEIR WEIGHT ENUMERATORS 关于p [u]/ k >-循环码及其权枚举数
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J190536
Maheshanand Bhaintwal, Soumak Biswas
{"title":"ON ℤ p ℤ p [u]/ k >-CYCLIC CODES AND THEIR WEIGHT ENUMERATORS","authors":"Maheshanand Bhaintwal, Soumak Biswas","doi":"10.4134/JKMS.J190536","DOIUrl":"https://doi.org/10.4134/JKMS.J190536","url":null,"abstract":"In this paper we study the algebraic structure of ZpZp[u]/ 〈uk〉-cyclic codes, where uk = 0 and p is a prime. A ZpZp[u]/〈u〉-linear code of length (r + s) is an Rk-submodule of Zp × Rs k with respect to a suitable scalar multiplication, where Rk = Zp[u]/〈u〉. Such a code can also be viewed as an Rk-submodule of Zp[x]/〈x−1〉×Rk[x]/〈x−1〉. A new Gray map has been defined on Zp[u]/〈u〉. We have considered two cases for studying the algebraic structure of ZpZp[u]/〈u〉-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) 6= 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ZpZp[u]/〈u〉-linear codes. Examples have been given to construct ZpZp[u]/〈u〉-cyclic codes, through which we get codes over Zp using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
CONSTRUCTION OF TWO- OR THREE-WEIGHT BINARY LINEAR CODES FROM VASIL'EV CODES 用vasil 'ev码构造二权或三权二进制线性码
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J190429
J. Hyun, Jaeseon Kim
{"title":"CONSTRUCTION OF TWO- OR THREE-WEIGHT BINARY LINEAR CODES FROM VASIL'EV CODES","authors":"J. Hyun, Jaeseon Kim","doi":"10.4134/JKMS.J190429","DOIUrl":"https://doi.org/10.4134/JKMS.J190429","url":null,"abstract":". The set D of column vectors of a generator matrix of a linear code is called a defining set of the linear code. In this paper we consider the problem of constructing few-weight (mainly two- or three-weight) linear codes from defining sets. It can be easily seen that we obtain an one- weight code when we take a defining set to be the nonzero codewords of a linear code. Therefore we have to choose a defining set from a non-linear code to obtain two- or three-weight codes, and we face the problem that the constructed code contains many weights. To overcome this difficulty, we employ the linear codes of the following form: Let D be a subset of F n 2 , and W (resp. V ) be a subspace of F 2 (resp. F n 2 ). We define the linear code C D ( W ; V ) with defining set D and restricted to W,V by C D ( W ; V ) = { ( s + u · x ) x ∈ D ∗ | s ∈ W,u ∈ V } . We obtain two- or three-weight codes by taking D to be a Vasil’ev code of length n = 2 m − 1( m ≥ 3) and a suitable choices of W . We do the same job for D being the complement of a Vasil’ev code. The constructed few-weight codes share some nice properties. Some of them are optimal in the sense that they attain either the Griesmer bound or the Grey-Rankin bound. Most of them are minimal codes which, in turn, have an application in secret sharing schemes. Finally we obtain an infinite family of minimal codes for which the sufficient condition of Ashikhmin and Barg does not hold.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70512066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
WEIGHTED L p -BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACES 曲面上粗糙核奇异积分的加权L - p有界性
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J190845
Ronghui Liu, Huo-xiong Wu
{"title":"WEIGHTED L p -BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACES","authors":"Ronghui Liu, Huo-xiong Wu","doi":"10.4134/JKMS.J190845","DOIUrl":"https://doi.org/10.4134/JKMS.J190845","url":null,"abstract":". In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ (cid:52) γ ( R + ) and Ω ∈ WG β (S n − 1 ) for some γ > 1 and β > 1. Here Ω ∈ WG β (S n − 1 ) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70513172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS 随机变量加权和的完全收敛性及其在非参数回归模型中的应用
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200029
A. Shen, Yajing Zhang
{"title":"COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS","authors":"A. Shen, Yajing Zhang","doi":"10.4134/JKMS.J200029","DOIUrl":"https://doi.org/10.4134/JKMS.J200029","url":null,"abstract":"In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70513813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
GROUND STATE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SCHRÖDINGER-POISSON-KIRCHHOFF TYPEPROBLEMS WITH A CRITICAL NONLINEARITY IN ℝ 3 一类具有临界非线性的schrÖdinger-poisson-kirchhoff型问题的基态变符号解
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200497
Aixia Qian, M. Zhang
{"title":"GROUND STATE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SCHRÖDINGER-POISSON-KIRCHHOFF TYPEPROBLEMS WITH A CRITICAL NONLINEARITY IN ℝ 3","authors":"Aixia Qian, M. Zhang","doi":"10.4134/JKMS.J200497","DOIUrl":"https://doi.org/10.4134/JKMS.J200497","url":null,"abstract":"In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following SchrödingerPoisson-Kirchhoff system  − (1+b ∫ R3 |∇u|dx)4u+V (x)u+k(x)φu=λf(x)u+|u|u, in R, −4φ=k(x)u, in R, where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ1 and λ1 is the first eigenvalue of the problem −4u + V (x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ1. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ON THE RATIO OF BIOMASS TO TOTAL CARRYING CAPACITY IN HIGH DIMENSIONS 高维生物量与总承载力之比研究
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200538
Jun-Haeng Heo, Yeonho Kim
{"title":"ON THE RATIO OF BIOMASS TO TOTAL CARRYING CAPACITY IN HIGH DIMENSIONS","authors":"Jun-Haeng Heo, Yeonho Kim","doi":"10.4134/JKMS.J200538","DOIUrl":"https://doi.org/10.4134/JKMS.J200538","url":null,"abstract":"This paper is concerned with a reaction-diffusion logistic model. In [17], Lou observed that a heterogeneous environment with diffusion makes the total biomass greater than the total carrying capacity. Regarding the ratio of biomass to carrying capacity, Ni [10] raised a conjecture that the ratio has a upper bound depending only on the spatial dimension. For the one-dimensional case, Bai, He, and Li [1] proved that the optimal upper bound is 3. Recently, Inoue and Kuto [13] showed that the supremum of the ratio is infinity when the domain is a multi-dimensional ball. In this paper, we generalized the result of [13] to an arbitrary smooth bounded domain in Rn, n ≥ 2. We use the subsolution and super-solution method. The idea of the proof is essentially the same as the proof of [13] but we have improved the construction of sub-solutions. This is the complete answer to the conjecture of Ni.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
RESTRICTION OF SCALARS AND CUBIC TWISTS OF ELLIPTIC CURVES 椭圆曲线的标量限制和三次扭转
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J190867
Dongho Byeon, Keunyoung Jeong, N. Kim
{"title":"RESTRICTION OF SCALARS AND CUBIC TWISTS OF ELLIPTIC CURVES","authors":"Dongho Byeon, Keunyoung Jeong, N. Kim","doi":"10.4134/JKMS.J190867","DOIUrl":"https://doi.org/10.4134/JKMS.J190867","url":null,"abstract":". Let K be a number field and L a finite abelian extension of K . Let E be an elliptic curve defined over K . The restriction of scalars Res LK E decomposes (up to isogeny) into abelian varieties over K Res LK E ∼ (cid:77) F ∈ S A F , where S is the set of cyclic extensions of K in L . It is known that if L is a quadratic extension, then A L is the quadratic twist of E . In this paper, we consider the case that K is a number field containing a primitive third root of unity, L = K ( 3 √ D ) is the cyclic cubic extension of K for some D ∈ K × / ( K × ) 3 , E = E a : y 2 = x 3 + a is an elliptic curve with j invariant 0 defined over K , and E Da : y 2 = x 3 + aD 2 is the cubic twist of E a . In this case, we prove A L is isogenous over K to E Da × E D 2 a and a property of the Selmer rank of A L , which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ON SEMILOCAL KLEIN-GORDON-MAXWELL EQUATIONS 关于半局部klein-gordon-maxwell方程
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200463
Jongmin Han, Juhee Sohn, Yeong Seok Yoo
{"title":"ON SEMILOCAL KLEIN-GORDON-MAXWELL EQUATIONS","authors":"Jongmin Han, Juhee Sohn, Yeong Seok Yoo","doi":"10.4134/JKMS.J200463","DOIUrl":"https://doi.org/10.4134/JKMS.J200463","url":null,"abstract":"In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
ON GEOMETRIC PROPERTIES OF THE MITTAG-LEFFLER AND WRIGHT FUNCTIONS mittag-leffler和Wright函数的几何性质
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI: 10.4134/JKMS.J200333
Sourav Das, K. Mehrez
{"title":"ON GEOMETRIC PROPERTIES OF THE MITTAG-LEFFLER AND WRIGHT FUNCTIONS","authors":"Sourav Das, K. Mehrez","doi":"10.4134/JKMS.J200333","DOIUrl":"https://doi.org/10.4134/JKMS.J200333","url":null,"abstract":"The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70514473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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