• Journal of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.627-639
• /
• 2011

Hopf corings are dened in this work as coring objects in the category of algebras over a commutative ring R. Using the Dieudonn$\'{e}$ equivalences from [7] and [19], one can associate coring structures built from the Hopf algebra $F_p[x_0,x_1,{\ldots}]$, p a prime, with Hopf ring structures with same underlying connected Hopf algebra. We have that $F_p[x_0,x_1,{\ldots}]$ coring structures classify thus Hopf ring structures for a given Hopf algebra. These methods are applied to dene new ring products in the Hopf algebras underlying known Hopf rings that come from connective Morava ${\kappa}$-theory.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.33 no.2
• /
• pp.94-103
• /
• 1991

This study was carried out to investigate the engineering characteristics of the R.C circular ring sector plate with various boundary conditions and then to propose a rational and paraical method for application of finite element method to R.C structures. The stiffness matrix of the circular ring sector plate was obtained by using the multi-base coordinate system in which the base-coordinate systems were constructed for each nodal point of the quadrilateral element in order to reflect the complicated boundary conditions conveniently and correctly. The R.C element stiffness matrix was constructed by adding the stiffness coefficients of the steel-bar element into the plate bending element stiffness matrix. Herein, the steel-bar element was treated as the common beam element. Using the above method, the effects of steel-bar can be considered without increasing of the numbers of element and nodal points.

• The Bulletin of The Korean Astronomical Society
• /
• v.39 no.1
• /
• pp.56.1-56.1
• /
• 2014

With the advent of high-resolution high-sensitivity observations, spiral patterns have been revealed around several asymptotic giant branch (AGB) stars. Such patterns can provide possible evidence for the existence of central binary stars embedded in outflowing circumstellar envelopes. It is, however, not generally recognized that the binary induced pattern, vertically extended from the orbital plane, exhibits a ring-like pattern with an inclined viewing angle. I will first review the binary-induced spiral-shell patterns on the AGB circumstellar envelopes with the effect of inclination angle with respect to the orbital plane, of which large inclination cases reveal incomplete ring-like patterns. I will describe a method of extracting such spiral-shell from the gas kinematics of an incomplete ring-like pattern to place constraints on the characteristics of the (unknown) central binary stars. This first success may open the possibility of connecting the ring-like patterns commonly found in the AGB circumstellar envelopes and in the outer parts of (pre-)planetary nebulae and pointing to the conceivable presence of central binary systems, which may give a clue for the onset of asymmetrical planetary nebulae.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.59 no.7
• /
• pp.1332-1339
• /
• 2010

This paper presents a large signal analysis of ring-type oscillators with feed forward and negative skewed delay scheme. The analysis yields the frequency increase factor due to two schemes. The large signal analysis is needed, because small signal model is limited to the initial stage of oscillation[1]. For verification of the frequency increase factor, simulation were done under the same conditions for the two different types of ring oscillators, i.e., with and without feed forward and negative skewed delay scheme. Simulation results are in good agreement with predictions based on analysis.

• Kyungpook Mathematical Journal
• /
• v.57 no.3
• /
• pp.401-417
• /
• 2017

Ever since their introduction, skew PBW ($Poincar{\acute{e}}$-Birkhoff-Witt) extensions of rings have kept growing in importance, as researchers characterized their properties (such as primeness, Krull and Goldie dimension, homological properties, etc.) in terms of intrinsic properties of the base ring, and studied their relations with other fields of mathematics, as for example quantum mechanics theory. Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW extensions. Our aim in this paper is to study skew PBW extensions of Baer, quasi-Baer, principally projective and principally quasi-Baer rings, in the case when the base ring R is not assumed to be reduced. We just impose some mild compatibleness over the base ring R, and prove that these properties are stable over this kind of extensions.

• Structural Engineering and Mechanics
• /
• v.15 no.2
• /
• pp.249-267
• /
• 2003

In this study, circular plates subjected to general type of loads and supported on a two-parameter elastic foundation are analysed. The stiffness, elastic bedding and soil shear effect matrices of a fully compatible ring sector plate element, developed by Saygun (1974), are obtained numerically assuming variable thickness of the element. Ring sector soil finite element is also defined to determine the deflection of the soil surface outside the domain of the plate in order to establish the interaction between the plate and the soil. According to Vallabhan and Das (1991) the elastic bedding (C) and shear parameters ($C_T$) of the foundation are expressed depending on the elastic constants ($E_s$, $V_s$) and the thickness of compressible soil layer ($H_s$) and they are calculated with a suitable iterative procedure. Using ring sector elements presented in this paper, permits the generalization of the loading and the boundary conditions of the soil outside the plate.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.975-979
• /
• 2012

Structure and Dynamics of dilute two-dimensional (2D) ring polymer solutions are investigated by using discontinuous molecular dynamics simulations. A ring polymer and solvent molecules are modeled as a tangent-hard disc chain and hard discs, respectively. Some of solvent molecules are confined inside the 2D ring polymer unlike in 2D linear polymer solutions or three-dimensional polymer solutions. The structure and the dynamics of the 2D ring polymers change significantly with the number ($N_{in}$) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration ($R^2$) increases with $N_{in}$ and scales as $R{\sim}N^{\nu}$ with the scaling exponent $\nu$ that depends on $N_{in}$. When $N_{in}$ is large enough, ${\nu}{\approx}1$, which is consistent with experiments. Meanwhile, for a small $N_{in}{\approx}0.66$ and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time ($\tau_{rot}$) are also sensitive to $N_{in}$: D decreases and $\tau$ increases sharply with $N_{in}$. D of 2D ring polymers shows a strong size-dependency, i.e., D ~ ln(L), where L is the simulation cell dimension. But the rotational diffusion and its relaxation time ($\tau_{rot}$) are not-size dependent. More interestingly, the scaling behavior of $\tau_{rot}$ also changes with $N_{in}$; for a large $N_{in}$ $\tau_{rot}{\sim}N^{2.46}$ but for a small $N_{in}$ $\tau_{rot}{\sim}N^{1.43}$.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.223-234
• /
• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• Bulletin of the Korean Chemical Society
• /
• v.7 no.5
• /
• pp.412-412
• /
• 1986

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.25 no.4
• /
• pp.245-252
• /
• 2016

Girth gears are applied in the mining, cement, and mineral processing industries and used in various types of horizontal mills, rotary dryers and kilns, and other heavy-gear ring applications. The large ring gears are normally fitted outside mills or kilns to provide the primary rotational drive. Recently, an external pinwheel gear set (e-PGS) was introduced to overcome manufacturing problems associated with girth gears. e-PGS is also suitable for low-speed, heavy-duty mechanical transmission and dusty and poor-lubrication conditions. This paper first presents a new profile modification of root relief for the e-PGS cam pinion. We then investigate load-stress factors to estimate the surface fatigue life by varying the shape design parameters. The results show that the contact fatigue life of an e-PGS can be extended significantly by increasing the profile shift coefficient. However, support bearing life of the pinwheel depends more on the contact force distribution than the profile shift coefficient.