• Korean Journal of Materials Research
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• v.25 no.12
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• pp.713-718
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• 2015

A new method is proposed for the calculation of the unrelaxed surface energy of spinel ferrite. The surface energy calculation consists of (1) setting the central and computational domains in the semi-infinite real lattice, having a specific surface, and having an infinite real lattice; (2) calculation of the lattice energies produced by the associated portion of each ion in the relative domain; and (3) dividing the difference between the semi-infinite lattice energy and the infinite lattice energy on the exposed surface area in the central domain. The surface energy was found to converge with a slight expansion of the domain in the real lattice. This method is superior to any other so far reported due to its simple concept and reduced computing burden. The unrelaxed surface energies of the (100), (110), and (111) of $ZnFe_2O_4$ and $Fe_3O_4$ were evaluated by using in the semi-infinite real lattices containing only one surface. For the normal spinel $ZnFe_2O_4$, the(100), which consisted of tetrahedral coordinated $Zn^{2+}$ was electrostatically the most stable surface. But, for the inverses pinel $Fe_3O_4$, the(111), which consisted of tetrahedral coordinated $Fe^{3+}$ and octahedral coordinated $Fe^{2+}$ was electrostatically the most stable surface.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.491-502
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• 2016

In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.305-320
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• 2021

In this paper, the relations between L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using L-fuzzy semi-prime ideals.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.147-153
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• 2007

In this note, we obtained results related to multiparameter discrete exponential families on considering lattice or semi-lattice in place of N (Natural numbers) in view of Cacoullos-type inequalities via the same arguments in Papathanasiou (1990, 1993).

• Steel and Composite Structures
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• v.24 no.2
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• pp.249-264
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• 2017

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

• Applied Microscopy
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• v.25 no.3
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• pp.99-107
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• 1995

The morphological changes of primary solid particles as a function of process time on hypereutectic Al-15.5wt%Si alloy during semi-solid state processing with a shear rate of $200s^{-1}$ are studied. In this alloy, it was observed that primary Si crystals are fragmented at the early stage of stirring and morphologies of primary Si crystals change from faceted to spherical during isothermal shearing for 60 minutes. To understand the role of Al dissolved in the primary Si crystal by shear stress at high temperature, lattice parameters of the primary Si crystals are determined as a variation of high order Laue zone(HOLZ) line positions measured from convergent beam electron diffraction(CBED) pattern. The lattice parameter of the primary Si crystal in the rheocast Al-15.5wt%Si alloy shows tensile strain of about 5 times greater than that of the gravity casting. Increase of the lattice parameter by rheocasting is due to the increased amount of Al dissolved in the primary Si crystal accelerated by shear stress at high temperature. The amounts of solute Al in the primary Si crystal are measured quantitatively by EPMA method to confirm the CBED analysis.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.431-441
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• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.387-396
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• 2018

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a fixed topology on X and we will regard ${\tau}(X)$ a topological space. Our purpose of this study is to comparison new topologies on the family ${\tau}(X)$ of all topologies induced old one.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.285-299
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• 2018

Many generalizations of ideals of a lattice to an arbitrary poset have been studied by different scholars. In this paper, we introduce several L-fuzzy ideals of a poset which generalize the notion of an L-fuzzy ideal of a lattice and give several characterizations of them.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.5
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• pp.1264-1271
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• 1990

The vortex lattice method was adopted to predict the aerodynamic performance of a horizontal axis wind turbine. For this simulation. the rotor blade was divided into many panels both in chordwise and spanwise direction and then replaced by horseshoe vortices. The wake was divided into two parts of near wake and far wake : the near wake was assumed as helical vortex line elements and the far wake was modeled by semi-infinite circular vortex cylinder. The induced velocity components were calculated by the Biot-Savart law. By this way the power coefficient was obtained and represented as a function of the tip speed ratio. The numerical results obtained were compared with those of the other methods and experimental results and showed good agreement with experimental results.