• The Journal of the Acoustical Society of Korea
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• v.17 no.1E
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• pp.70-75
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• 1998

The analysis of dynamic responses are carried out on several anisotropic systems due to buried pulsating line sources. These include infinite, semi-infinite spaces. The media possess orthotropic or higher symmetry. The load is in the from of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for infinite media. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions, thereby leading to the complete solutions. The solutions are simplified to the systems possessing of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic symmetry.

• Coupled systems mechanics
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• v.7 no.1
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• pp.61-77
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• 2018

This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

• Bulletin of the Korean Chemical Society
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• v.12 no.5
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• pp.544-554
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• 1991

Using the Huckel method, we obtain the analytical expressions for eigenvalues and eigenvectors of s.c., f.c.c. and b.c.c. clusters of rectangular parallelepiped shape, and of an arbitrary size. Our formula converage to those derived from the Bloch sum, in the limit of infinite extension. DOS and LDOS reveal that the major contribution of the states near Fermi level originates from the surface atoms, also symmetry of DOS curves disappears by the introduction of 2nd nearest neighbor interactions, in all the cubic lattices. An accumulation of the negative charges on surface of cluster is observed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.97-104
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• 2007

Vibration analysis of a rigid body supported by in-parallel linear springs can be greatly simplified by utilizing the conditions for a plane of symmetry. The vibration modes of an oscillatory system having plane of symmetry are classified into the in-plane and out-of-plane modes. From the viewpoint of screw theory, they represent respectively the vibration axes perpendicular to the plane of symmetry and lying in the plane of symmetry. In this paper, the sets of orthogonal and mutually intersecting three springs are used as resilient support of a rigid body. The geometrical conditions for the system to have a plane of symmetry and diagonalized stiffness matrix are presented. From the orthogonality of the vibration modes with respect to the inertia matrix, the geometrical relation between the reaction wrenches and the vibration modes are derived. This geometrical relation is then used to get the cubic design equation for the design of out-of-plane modes. The numerical design example of engine mounts is presented in order to explain the suggested design technique.

• Applied Chemistry for Engineering
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• v.4 no.2
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• pp.342-348
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• 1993

At 1473 K under atmospheric pressure, the homogeneous samples of the $Sm_{1-x}Sr_xFe^{3+}{_{1-t}}Fe^{4+}{_t}O_{3-y}$ ($0.00{\leq}x{\leq}1.00$) ferrite system were prepared. With the increase in x value, the amount of $Fe^{4+}$ ion increased and the crystallographic structure was changed from orthorhombic symmetry to cubic symmetry. The electrical conductivity at constant temperature sharply increases and the activation energy decreases with the increase of $Fe^{4+}$ ion. $M{\ddot{o}}ssbauer$ spectrum of the sample x=0.00 shows six-line pattern indicating the presence of $Fe^{3+}$ ion in the octahedral sites.

• Journal of the Korean Society for Heat Treatment
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• v.31 no.5
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• pp.237-243
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• 2018

In-rich InGaN epilayers were grown on (0001) sapphire substrates by radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). InGaN epilayers grown at various growth condition were observed by SEM, XRD, and RHEED. When plasma power of nitrogen increased from 290 to 350 W, surface morphology and crystal quality became worse according to more active nitrogen on the surface of InGaN at N-rich growth condition. As In composition was reduced from 89 to 71% by changing the incoming flux of In and Ga, surface morphology and crystal quality became worse. In addition, weak peaks of cubic InGaN phase was observed from InGaN layer with 71% In composition by XRD ${\Phi}$ scan measurement. When growth temperature decreased from 500 to $400^{\circ}C$, RHEED diffraction pattern was changed to be from streaky to spotty which means atomically rough surface, and spotty pattern showed cubic symmetry of InGaN clearly. XRD ${\Phi}$ scan measurement gave clear evidence that more cubic InGaN phase was formed at low growth temperature. All these results indicates that extremely low surface mobility of Ga adatom caused inferior crystal quality and cubic InGaN phase.

• Journal of the Korean Society for Advanced Composite Structures
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• v.2 no.3
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• pp.1-11
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• 2011

The typical truss-lattice material successively packed by repeated cubic symmetric unit cells consists of sub-elements (SE) proposed in this study. The representative continuum model for this truss-lattice material such as the effective strain and stress relationship can be formulated by the homogenization procedure based on the notation of averaged mechanical properties. The volume fractions of micro-scale struts have a significant influence on the effective strength as well as the relative density in the lattice plate with replicable unit cell structures. Most of the strength contribution in the lattice material is induced by axial stiffness under uniform stretching or compression responses. Therefore, continuum based constitutive models composed of homogenized member stiffness include these mechanical characteristics with respect to strength, internal stress state, material density based on the volume fraction and even failure modes. It can be also recognized that the stress state of micro-scale struts is directly associated with the continuum constitutive model. The plastic flow at the micro-scale stress can extend the envelope of the analytical stress function on the surface of macro-scale stress derived from homogenized constitutive equations. The main focus of this study is to investigate the basic topology of unit cell structures with the cubic symmetric system and to formulate the plastic models to predict pressure dependent macro-scale stress surface functions.

• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• Journal of the Korean Magnetic Resonance Society
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• v.16 no.2
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• pp.111-121
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• 2012

The spin-lattice relaxation times, $T_1$, and spin-spin relaxation times, $T_2$, of the $^{27}Al$ and $^{87}Rb$ nuclei in $RbAl(CrO_4)_2{\cdot}2H_2O$ crystals were investigated. The presence of only one resonance line for the $^{27}Al$ nuclei indicates that the results in a dynamical averaging of the crystal electric field that produces a cubic symmetry field. The changes in the temperature dependence of $T_1$ are related to variations in the symmetry of the octahedra of water molecules surrounding $Al^+$ and $Rb^+$. The $T_1$ values for the $^{27}Al$ and $^{87}Rb$ nuclei are different due to differences in the local environments of these ions. We also compared these $^{27}Al$ and $^{87}Rb$ NMR results with those obtained for $RbAl(CrO_4)_2{\cdot}2H_2O$ crystals. The relaxation mechanisms of $RbAl(XO_4)_2{\cdot}nH_2O$ (X=Cr and S) crystals are characterized by completely different NMR behaviors.

• Journal of the Korean Chemical Society
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• v.34 no.5
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• pp.413-417
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• 1990

The structural variation process of amorphous SiO$_2$ gel upon heat-treatment conditions of 80, 250, 450 and 1000$^{\circ}C$ has been studied by using the radial distribution functions (RDF$_{obs}$) estimated from the X-ray diffraction intensities. The expected gel structure was determined by comparing the RDF$_{obs}$ with those for the other six standard samples selected appropriately. The structure of specimens prepared by sol-gel method is well consistent with that of fused SiO$_2$ (${\beta}$-cristobalite with cubic symmetry) except a slight difference in O-O band distance.