• Journal of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1355-1370
• /
• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• Journal of the Korean Magnetics Society
• /
• v.18 no.2
• /
• pp.67-70
• /
• 2008

$Tb_2Bi_1Ga_xFe_{5-x}O_{12}$(x=0, 1) fabricated by sol-gel and vacuum sealed annealing process. $Tb_2Bi_1Ga_xFe_{5-x}O_{12}$(x=0, 1) have been studied by x-ray diffraction(XRD), vibrating sample magnetometer, and $M\ddot{o}ssbauer$ spectroscopy. The crystal structures were found to be a cubic garnet structure with space group Ia3d. The determined lattice constants $a_0$ of x = 0, and 1 are $12.497\AA$, and $12.465\AA$, respectively. The distribution of gallium and iron in $Tb_2Bi_1Ga_xFe_{5-x}O_{12}$ is studied by Rietveld refinement. Based on Rietveld refinement results, the terbium and bismuth ions occupy the 24c site, iron ions occupy the 24d, l6a site, and nonmagmetic gallium ions occupy the 16a site. In order to verify the magnetic site occupancy of iron and gallium, we have taken $M\ddot{o}ssbauer$ spectra for $Tb_2Bi_1Ga_xFe_{5-x}O_{12}$(x=0, 1) at room temperature. From the results of $M\ddot{o}ssbauer$ spectra analysis, the absorption area ratios of Fe ions for $Tb_2Bi_1Fe_5O_{12}$ on 24d and 16a sites are 60.8 % and 39.2 %, respectively, and the absorption area ratios of Fe ions for $Tb_2Bi_1Fe_5O_{12}$ on 24d and 16a sites are 74.7 % and 25.3 %, respectively. It is noticeable that all of the nonmagnetic Ga atoms occupy the 16a site by vacuum annealing process.

• Journal of the Korean Magnetics Society
• /
• v.2 no.3
• /
• pp.216-221
• /
• 1992

Annealing effects on the permeability aftereffect(disaccommodation) of liquid quenched single strip $Fe_{73.5}Cu_1Nb_3Si_{16}B_{6.5}$ alloys were investigated with pulse method. The initial susceptibility X, $B_{10},$ (the flux density at 10 Oe) and disaccommodation intensity D (D = [X(1 s)-X(64 s)]/X(1 s), where X(1 s) and X(64 s) are the susceptibility of 1 and 64 s of rest time after A. C. demagnetization) were about 800, 0.8 T and 16 %, respectively. The soft magnetic properties were improved with isothermal annealing for 1 hour at $300{\sim}600^{\circ}C.$ X, $B_{10},$ and D at $570^{\circ}C$ of optimum annealing temperature were 15000, 1.2 T and 1.1 %, respectively. The origin of the change of characteristics were examined with fine crystalline structure and magnetostriction.

• Korean Journal of Mathematics
• /
• v.19 no.2
• /
• pp.163-169
• /
• 2011

Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.

• Journal of applied mathematics & informatics
• /
• v.33 no.1_2
• /
• pp.173-183
• /
• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.663-668
• /
• 2001

X and Y are Banach spaces for which K(X, Y), the space of compact operators from X to Y, is an M-ideal in L(X, Y), the space of bounded linear operators form X to Y. If Z is a closed subspace of Y such that L(X, Z) has property SU in L(X, Y) and d(T, K(X, Z)) = d(T, K(X, Y)) for all $T \in L(X, Z)$, then K(X, Z) is an M-ideal in L(X, Z) if and only if it has property SU is L(X, Z).

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.259-271
• /
• 1997

Let K be a nonempty subset of a normed linear space X and let x $\in$ X. An element k$_0$ in K satisfying $\$\mid$$x - k$_0$$\$\mid$$ = d(x, K) := (equation omitted) $\$\mid$$x - k$\$\mid$$ is called a best approximation to x from K. For any x $\in$ X, the set of all best approximations to x from K is denoted by P$_K$(x) = {k $\in$ K : $\$\mid$$ x - k $\$\mid$$ = d(x, K)}. (omitted)

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.1-11
• /
• 2020

In this paper, we introduce the notion of symmetric bi-f-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if D is a symmetric bi-f-derivation of L, then D(x → y, z) = f(x) → D(y, z) for all x, y, z ∈ L.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.123-128
• /
• 1998

The purpose of this paper is to prove the following result: Let A be a noncom mutative Banach algebra. Suppose that $D:A{\rightarrow}A$ is a continuous linear Jordan derivation such that $D^2(x)D(x)^2{\in}rad(A)$ for all $x{\in}A$. Then D maps A into its radical.

• Journal of the Korean Vacuum Society
• /
• v.13 no.2
• /
• pp.86-91
• /
• 2004

Transiton-metal gallides attract wide interest as a candidate for high-temperature structural materials. In a wide composition range, in which it was known that Co-Ga alloy have CsCl (B2) crystallographic structure, a systematic study on the correlation between physical properties and electronic structures of Co-gallides was performed. $Co_{l-x}Ga$ $_{x}$ alloys ($0.35\leq$x$\leq0.55$) were prepared by arc-melting method and were annealed at $1000 ^{\circ}C$ for 48hour to increase the homogeneity. In this composition range all the prepared alloys have the CsCl (B2) structure. The chemical states and the electronic structure were studied by using x-ray photoemission spectroscopy (XPS), and x-ray absorption near-edge structure (XANES), and exhibit different physical properties depending on the composition. During the annealing, a significant oxidation has happened and all the oxygen atoms are incorporated with the Ga atoms to form a $Ga_2O_3$ phase. In a view point of electronic structure, the $Co_{l-x}Ga$ $_{x}$ alloys were formed by the Ga(p) - Co(d) hybridization.