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## Korean Journal of mathematics

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자료건수 (398건)
No
398

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.537-544

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There is a standard construction of lifting cyclic codes over the prime finite field ${\mathbb{Z}}_p$ to the rings ${\mathbb{Z}}_{p^e}$ and to the ring of p-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields ${\mathbb{F}}_{p^r}$ to codes over Galois rings GR($p^e$, r). We give concrete examples with all of the lifts.

397

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.519-535

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Let ${\mathcal{R}}$ denote the Galois ring of characteristic $p^n$, where p is a prime. In this paper, we investigate the elementary properties of Gauss sums over ${\mathcal{R}}$ in accordance with conditions of characters of Galois rings, and we restate results for Gauss sums in [1, 2, 3, 7, 12, 13]. Also, we compute the modulus of the Gauss sums.

396

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.503-517

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Keeping in view the expediency of soft sets in algebraic structures and as a mathematical approach to vagueness, in this paper the concept of lattice ordered soft near rings is introduced. Different properties of lattice ordered soft near rings by using some operations of soft sets are investigated. The concept of idealistic soft near rings with respect to lattice ordered soft near ring homomorphisms is deliberated.

395

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.483-501

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In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.

394

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.467-481

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In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

393

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.459-465

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Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $${\Phi}([[A,B]_*,C]_*)=[[{\Phi}(A),B]_*,C]_*+[[A,{\Phi}(B)]_*,C]_*+[[A,B]_*,{\Phi}(C)]_*$$ where $[A,B]_*=AB-BA^*$ for all $A,B{\in}{\mathcal{A}}$, is additive ${\ast}-derivation$. In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$.

392

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.439-458

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In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category C of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in C. Further, we characterize the derivations of crossed modules in a category C and obtain new crossed modules using regular derivations of old one.

391

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.425-437

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In this paper, we linked the motion of spherical images with the motion of their curves. Surfaces generated by the evolution of spherical image of a space curve are constructed. Also geometric proprieties of these surfaces are obtained.

390

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.405-424

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In this paper we study some comparative growth properties of composite entire functions on the basis of relative (p, q)-th order and relative (p, q)-th lower order of entire function with respect to another entire function where p and q are any two positive integers.

389

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.387-403

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Shifting, scaling and modulation proprerties for the convolution product of the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A1,A2}$ are given. These properties help us to obtain convolution product of new functionals from the convolution product of old functionals which we know their convolution product.

388

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.373-385

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In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.

387

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.3 2018 pp.349-371

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Some inequalities for quantum f-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and ${\chi}^2-distance$ are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

386

BEGINNER'S GUIDE TO NEURAL NETWORKS FOR THE MNIST DATASET USING MATLAB

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.337-348

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MNIST dataset is a database containing images of handwritten digits, with each image labeled by an integer from 0 to 9. It is used to benchmark the performance of machine learning algorithms. Neural networks for MNIST are regarded as the starting point of the studying machine learning algorithms. However it is not easy to start the actual programming. In this expository article, we will give a step-by-step instruction to build neural networks for MNIST dataset using MATLAB.

385

SRB MEASURES IN CHAOTIC DYNAMICAL SYSTEMS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.327-335

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In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.

384

FIXED POINT THEOREMS IN FUZZY METRIC SPACES FOR MAPPINGS WITH SOME CONTRACTIVE TYPE CONDITIONS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.307-326

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In this paper, we derive some fixed point theorems in fuzzy metric spaces for self mappings satisfying different contractive type conditions. Some of these theorems generalize some results of Wairojjana et al. (Fixed Point Theory and Applications (2015) 2015:69). Several examples in support of the theorems are also presented here.

383

SOLUTIONS OF VECTOR VARIATIONAL INEQUALITY PROBLEMS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.299-306

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In this paper, we prove the existence results of the solutions for vector variational inequality problems by using the ${\parallel}{\cdot}{\parallel}$-sequentially continuous mapping.

382

CONSTRUCTION OF THE HILBERT CLASS FIELD OF SOME IMAGINARY QUADRATIC FIELDS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.293-297

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In the paper [4], we constructed 3-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by 3. In this paper, we extend the result for any odd prime p.

381

A CHARACTERIZATION OF ADDITIVE DERIVATIONS ON C*-ALGEBRAS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.285-291

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Let $\mathcal{A}$ be a unital $C^*$-algebra. It is shown that additive map ${\delta}:{\mathcal{A}}{\rightarrow}{\mathcal{A}}$ which satisfies $${\delta}({\mid}x{\mid}x)={\delta}({\mid}x{\mid})x+{\mid}x{\mid}{\delta}(x),\;{\forall}x{{\in}}{\mathcal{A}}_N$$ is a Jordan derivation on $\mathcal{A}$. Here, $\mathcal{A}_N$ is the set of all normal elements in $\mathcal{A}$. Furthermore, if $\mathcal{A}$ is a semiprime $C^*$-algebra then ${\delta}$ is a derivation.

380

SOME RESULTS ABOUT THE REGULARITIES OF MULTIFRACTAL MEASURES

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.271-283

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In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 118, (2008), pp. 273-279.). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.

379

SOME RESULTS RELATING TO SUM AND PRODUCT THEOREMS OF RELATIVE (p, q, t) L-TH ORDER AND RELATIVE (p, q, t) L-TH TYPE OF ENTIRE FUNCTIONS

[Kisti 연계] 강원경기수학회 Korean Journal of mathematics Vol.26 No.2 2018 pp.215-269

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Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of relative (p, q, t) L-th order, relative (p, q, t) L-th type, and relative (p, q, t) L-th weak type of entire functions with respect to another entire function where $p,q{\in}{\mathbb{N}}$ and $t{\in}{\mathbb{N}}{\cup}\{-1,0\}$.

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