• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.671-677
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• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• Bulletin of the Korean Chemical Society
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• v.30 no.3
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• pp.567-572
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• 2009

In this study, the effects of counter ion valency of the electrolyte on the colloidal repulsion between two parallel cylindrical particles were investigated. Electrostatic interactions of the cylindrical particles were calculated with the variation of counter ion valency. To calculate the electrical repulsive energy working between these two cylindrical particles, Derjaguin approximation was applied. The electrostatic potential profiles were obtained numerically by solving nonlinear Poission-Boltzmann (P-B) equation and calculating middle point potential and repulsive energy working between interacting surfaces. The electrical potential and repulsive energy were influenced by counter ion valency, Debye length, and surface potential. The potential profile and middle point potential decayed with the counter ion valency due to the promoted shielding of electrical charge. On the while, the repulsive energy increased with the counter ion valency at a short separation distance. These behaviors of electrostatic interaction agreed with previous results on planar or spherical surfaces.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.51-58
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• 2005

Interpreting a natural line drawing as a solid object requires simplifying assumptions in order to make the problem more tractable. Unfortunately, some of the assumptions made in the past have overly simplified the problem. Restricting the valency of vertices, and in particular allowing only trihedral vertices, distorts the problem, since algorithms which are satisfactory for the simplified problem are not satisfactory in the general case. This paper presents a test set of drawings of objects with higher-valency vertices. The intention in creating this test set is that it may be used to determine how effective various algorithms are in dealing with general (i.e. unrestricted) valency vertices.

• Vacuum Magazine
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• v.3 no.4
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• pp.8-13
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• 2016

The need of space-resolved x-ray photoelectron spectroscopy (XPS) has developed scanning photoelectron microscopy (SPEM). SPEM provides space-resolved XPS data from a spot of a sample as well as images of specific element, chemical state, valency distribution on the surface of a sample. Based on technical advancement of tight x-ray focusing, sample positioning accuracy, and electron analyzer efficiency, SPEM is now capable of providing ~100 nm space resolution for typical XPS functionality, and SPEM has become actively applied for the investigation of chemical state, valency, and electronic structure on the surface of newly discovered materials, such as graphene layers, dichalcogenide 2D-materials, and heterogenous new functional materials.

• Journal of the Korean Electrochemical Society
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• v.4 no.4
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• pp.176-181
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• 2001

This article covers the fundamentals of underpotential deposition (UPD), focussing on the importance of UPD in interfacial electrochemistry. Firstly, this article described the basic concepts of UPD, including underpotential shift and electrosorption valency. Secondly, the present article explained UPD of hydrogen, followed by hydrogen evolution or hydrogen absorption, giving special attention to the adsorption sites of hydrogen on metal surface and the absorption mechanism into Pd. Finally, this article briefly presented the important factors associated with UPD in various fields of interfacial electrochemistry from practical viewpoints.

• Journal of the Korean Chemical Society
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• v.35 no.2
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• pp.99-104
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• 1991

Nonstoichiometric solid solutions of Sr$_{1+x}Er _{1-x} FeO _{4-y}$ system (x = 0.00, 0.25, 0.50, 0.75 and 1.00) with layered $K_2NiF_4$ type structure were prepared at 1350$^{\circ}$C under atmospheric pressure. By the analysis of X-ray diffraction, the crystallographic structures of the solid solution of all compositions were found to be pseudo-tetragonal system. Nonstoichiometric chemical formulas have been determined by Mohr salt analysis. It shows that the amount of Fe$^{4+}$ increases with increasing x up to 0.50 and then decreases, and the value of oxygen nonstoichiometry increases with increasing x value. Mixed valency states of Fe$^{3+}$ and Fe$^{4+}$ in the sample were identified again by Mossbauer spectroscopic analysis at 298 K. Electrical conductivity varied within the semiconductivity range of 10-2 ∼ 10-7(${\Omega}$-1cm-1), activation energy for electrical conduction decreased with the increment of the mole ratio of Fe$^{4+}$ or ${\tau}$ value. The conduction mechanism could be explained by the hopping model of the conduction electrons between the valency states of Fe$^{3+}$ and Fe$^{4+}$.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.4
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• pp.107-116
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• 2013

This algorithm suggests a method in which a minimum spanning tree can be obtained fast by reducing the number of an algorithm execution. The suggested algorithm performs a select-and-delete process. In the select process, firstly, it performs Borůvka's first stage for all the vertices of a graph. Then it re-performs Borůvka's first stage for specific vertices and reduces the population of the edges. In the delete process, it deletes the maximum weight edge if any cycle occurs between the 3 edges of the edges with the reduced population. After, among the remaining edges, applying the valency concept, it gets rid of maximum weight edges. Finally, it eliminates the maximum weight edges if a cycle happens among the vertices with a big valency. The select-and-delete algorithm was applied to 9 various graphs and was evaluated its applicability. The suggested select process is believed to be the vest way to choose the edges, since it showed that it chose less number of big edges from 6 graphs, and only from 3 graphs, comparing to the number of edges that is to be performed when using MST algorithm. When applied the delete process to Kruskal algorithm, the number of performances by Kruskal was less in 6 graphs, but 1 more in each 3 graph. Also, when using the suggested delete process, 1 graph performed only the 1st stage, 5 graphs till 2nd stage, and the remaining till 3rd stage. Finally, the select-and-delete algorithm showed its least number of performances among the MST algorithms.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.145-155
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• 2002

In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1683-1709
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• 2015

Let (${\Omega}$, S) be an association scheme where ${\Omega}$ is a non-empty finite set and S is a partition of ${\Omega}{\times}{\Omega}$. For a positive integer k we say that (${\Omega}$, S) is k-equivalenced if each non-diagonal element of S has valency k. In this paper we focus on 4-equivalenced association schemes, and prove that they are transitive.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.329-335
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• 2007

A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the sphere and the torus, and we also present formula for such maps with four parameters: the root-valency, the number of isthmus, the number of planar loops and the number of essential loops.