DSpace Community: KAIST College of Natural SciencesKAIST College of Natural Scienceshttp://hdl.handle.net/10203/112018-02-12T18:23:48Z2018-02-12T18:23:48ZA sextuple equidistribution arising in Pattern AvoidanceLin, ZhicongKim, Dongsuhttp://hdl.handle.net/10203/2376612018-01-22T08:59:55Z2018-04-01T00:00:00ZTitle: A sextuple equidistribution arising in Pattern Avoidance
Authors: Lin, Zhicong; Kim, Dongsu
Abstract: We construct an intriguing bijection between 021-avoiding inversion sequences and (2413,4213)-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length 4 whose descent polynomial equals that of separable permutations.2018-04-01T00:00:00ZGrooving of nanoparticles using sublimable liquid crystal for transparent omniphobic surfaceKim, Dae SeokSuh, AhramYang, ShuYoon, Dong Kihttp://hdl.handle.net/10203/2381502018-01-30T02:39:18Z2018-03-01T00:00:00ZTitle: Grooving of nanoparticles using sublimable liquid crystal for transparent omniphobic surface
Authors: Kim, Dae Seok; Suh, Ahram; Yang, Shu; Yoon, Dong Ki
Abstract: Hierarchical assembly of nanoparticles (NPs) is of interest for omniphobic surfaces in the way that hierarchical scale roughness possibly provides effective liquid repellency and also it is relatively easy to build large-area coatings via the bottom-up assembly process. However, all NP assemblies often lacks mechanical robustness. Hence, the development of the effective fabrication method to make well-deposited hierarchical NPs assembly is demanded.
In this report, we have demonstrated an all-NP three-dimensional hierarchical surface that is omniphobic yet highly transparent and mechanically robust. By taking advantage of sublimation and recondensation of smectic A liquid crystals (LCs) in a simple thermal annealing process, we patterned NP aggregates in one-dimensional grooves directed by LCs. The resultant groove-like NP-assembled surface showed omniphobicity, repelling water, glycerol, ethylene glycol, and olive oil (with contact angle of 156.5°, 147°, 136.5°, and 123.2°, respectively) because of the low surface energy of the fluorinated NPs and dual roughness. The coating is highly transparent with ∼90% transmittance in the visible wavelength. We investigate the mechanical robustness of the all NP coatings by sand abrasion, which shows nearly identical omniphobicity and transparency after the sand abrasion.2018-03-01T00:00:00ZRank gain of Jacobian varieties over finite Galois extensionsIm, Bo-HaeWallace, Erikhttp://hdl.handle.net/10203/2371442018-01-30T08:54:59Z2018-03-01T00:00:00ZTitle: Rank gain of Jacobian varieties over finite Galois extensions
Authors: Im, Bo-Hae; Wallace, Erik
Abstract: Let K be a number field, and let X -> P-K(1) be a degree p covering branched only at 0, 1, and infinity. If K is a field containing a primitive p-th root of unity then the covering of P-1 is Galois over K, and if p is congruent to 1 mod 6, then there is an automorphism sigma of X which cyclically permutes the branch points. Under these assumptions, we show that the Jacobian of both X and X/<sigma > gain rank over infinitely many linearly disjoint cyclic degree p-extensions of K. We also show the existence of an infinite family of elliptic curves whose j-invariants are parametrized by a modular function on Gamma(0)(3) and that gain rank over infinitely many cyclic degree 3-extensions of Q.2018-03-01T00:00:00ZAll-fiber-based selective mode multiplexer and demultiplexer for weakly-coupled mode-division multiplexed systemsIgarashi, KojiPark, Kyung JunTsuritani, TakahiroMorita, ItsuroKim, Byoung Yoonhttp://hdl.handle.net/10203/2285002018-01-30T08:54:56Z2018-02-01T00:00:00ZTitle: All-fiber-based selective mode multiplexer and demultiplexer for weakly-coupled mode-division multiplexed systems
Authors: Igarashi, Koji; Park, Kyung Jun; Tsuritani, Takahiro; Morita, Itsuro; Kim, Byoung Yoon
Abstract: We show all-fiber-based selective mode multiplexers and demultiplexers for weakly-coupled mode-division multiplexed systems. We fabricate a set of six-mode multiplexer and demultiplexer based on fiber mode selective couplers, and experimentally evaluate the performance for the six-mode dual-polarization (DP) quadrature phase shift keying (QPSK) optical signals. In the mode multiplexer and demultiplexer, the mode couplings between the lower three modes and the higher three modes are suppressed to be less than -20 dB, which enables us to apply partial 6x6 MIMO equalizers even for the six-mode demultiplexing. For the six-mode DP-QPSK signals, the penalty of optical signal-to-noise ratio by replacing the full 12x12MIMO to the partial 6x6 MIMO is suppressed by less than 1 dB. (C) 2017 Elsevier B.V. All rights reserved.2018-02-01T00:00:00Z