Choi matrices revisited, II

In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between $k$-superpositivity and Schmidt number $\le k$ as well as $k$-positivity and $k$-block-positivity. We also compare de Pillis' definition [Pacific J. Math. 23 (1967), 129--137] and Choi's definition [Linear Alg. Appl. 10 (1975), 285--290], which arise from different bilinear forms.Comment: 17 page

Comment on ``Large Slip of Aqueous Liquid Flow over a Nanoengineered Superhydrophobic Surface'' by C-H Choi and C Kim

In a recent Letter (Phys. Rev. Lett. vol 96, 066001 (2006), ref [1]), Choi and Kim reported slip lengths of a few tens of microns for water on nanoengineered superhydrophobic surfaces, on the basis of rheometry (cone-and-plate) measurements. We show that the experimental uncertainty in the experiment of Ref. [1], expressed in term of slip lengths, lies in the range 20 - 100 micrometers, which is precisely the order of magnitude of the reported slip lengths. Moreover we point out a systematic bias expected on the superhydrophobic surfaces. We thus infer that it is not possible to draw out any conclusion concerning the existence of huge slip lengths in the system studied by Choi and Kim.Comment: to appear in Physical Review Letter

Impact of Low and Moderate Salinity Water on Plant Performance of Leafy Vegetables in a Recirculating NFT System

Two greenhouse experiments were conducted to examine the growth and mineral nutrition of four leafy vegetables in a nutrient film technique (NFT) system with water with low to moderate salinity. In Expt. 1, a nutrient solution was prepared using reverse osmosis (RO) water and treatments consisted of supplementing with RO water, tap water, or nutrient solution. In Expt. 2, nutrient solution was prepared using three different water sources (treatments), namely, RO water, tap water, or tap water, plus sodium chloride (NaCl), and supplementing solution was prepared using the same three water sources at one third strength. For both of the experiments, seeds of pac choi ‘Tokyo Bekana’, ‘Mei Qing Choi’, and ‘Rosie’ (Brassica rapa var. chinensis) and leaf lettuce ‘Tropicana’ (Lactuca sativa) were sown and were grown in a growth chamber. Two weeks after sowing, seedlings were transplanted to the NFT systems. Expt. 1 was conducted from 19 April to 19 May 2016 and Expt. 2 from 6 September to 12 October 2016. In Expt. 1, nitrate (NO3−) and phosphorus (P) levels in the tanks decreased, and potassium (K+) levels reached almost zero at the end of the experiment when supplemented with RO or tap water. However, calcium (Ca2+), magnesium (Mg2+), and sulfate (SO42−) either did not decrease or increased over time. Supplementing water type did not affect the growth of leaf lettuce and ‘Mei Qing Choi’ pac choi; however, fresh weight of ‘Rosie’ pac choi and both fresh and dry weight of ‘Tokyo Bekana’ pac choi were reduced when supplemented with RO water. Leaf sap NO3− was reduced in ‘Tokyo Bekana’ pac choi, but not in other varieties, when supplemented with RO or tap water. Leaf sap K+ decreased in ‘Tokyo Bekana’, but not in other varieties. The supplementing water type did not impact leaf sap Ca2+, regardless of vegetable varieties. In Expt. 2, NO3− in all of the treatments, P in RO water, and K+ in RO or tap water decreased in the last week of the experiment. Other macronutrients did not change substantially over time. The addition of NaCl significantly reduced the growth of all the vegetables. ‘Tropicana’ leaf lettuce was the least tolerant to NaCl, followed by ‘Rosie’ pac choi. Water source did not affect leaf Ca2+, K+, P, SO42−, and Mg2+ except for ‘Tokyo Bekana’ where NaCl addition decreased Ca2+ and Mg2+. Our results indicated that the tested leafy vegetables differed in response to various types of water used as supplementing or as source water. N, P, and especially K, should be supplemented in the late stage of the experiment, while replacing the whole tank nutrient solution is only necessary when Na+ and/Cl− build up to harmful levels

Generalized qudit Choi maps

Following the linear programming prescription of Ref. \cite{PRA72}, the $d\otimes d$ Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular $d\otimes d$ Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that thus obtained $d\otimes d$ BDEW's (consequently qudit Choi maps) are non-decomposable in certain range of their parameters.Comment: 22 page

A Method of Transformation for Generalized Hypergeometric Function 2F2

By employing an addition theorem for the confluent hypergeometric function, Paris R.B.[3], has obtained a Kummer-type transformation for a 2F2 (x) hypergeometric function with general parameters in the form of a sum of 2F2 (-x) functions. Recently, Choi Junesang and Rathie Arjun K.[1], has obtained the same result without using the addition theorem. The aim of this paper is to derive the result of Paris R.B.[3], with change in the general parameters without using the addition theorem in the line of Choi Junesang and Rathie Arjun K.[1]. Corresponding author E.mail:- [email protected], [email protected]

Entanglement witnesses arising from Choi type positive linear maps

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.Comment: 18 pages, 4 figures, 1 tabl

OT 501 Survey of Biblical Hebrew

Arnold, Bill T. and John H. Choi. A Guide to Biblical Hebrew Syntax. Cambridge: Cambridge University Press, 2003. [Guide, Arnold & Choi] Elliger, K., and W. Rudolph. Biblia Hebraica Stuttgartensia. Stuttgart: Deutsche Bibelgesellschaft, 1967-77. [BHS] Holladay, William L. A Concise Hebrew and Aramaic Lexicon of the Old Testament. Grand Rapids, Mich.: Eerdmans, 1971. [Holladay] Scott, William R. A Simplified Guide to BHS. Berkley, Calif.: BIBAL, 1987. [Scott] Seow, C. L. A Grammar for Biblical Hebrew. Rev. ed. Nashville: Abingdon, 1995. [Seow]https://place.asburyseminary.edu/syllabi/2298/thumbnail.jp