Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group

We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz [6]. Key new features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence of sequences of biholomorphic mappings of domains in Banach spaces.     

Depth-enhanced integral imaging by use of optical path control

The image depth of integral imaging is enhanced by doubling the number of central depth planes by use of optical path control. To accomplish this, the optical path lengths are changed by controlling whether reflections occur behind the lens array. We propose three schemes that use mirrors, a combination of beam splitters and polarizers, and polarization beam splitters, respectively. In experiments we implement the systems that are completely electronically controllable, are compact, and provide two central depth planes with 50.4-mm separation.     

Phase-only hologram generation based on integral imaging and its enhancement in depth resolution

We introduce a phase-only hologram generation method based on an integral imaging,and propose an enhancement method in representable depth interval.The computational integral imaging reconstruction method is modified based on optical flow to obtain depth-slice images for the focused objects only.A phaseonly hologram for multiple plane images is generated using the iterative Fresnel transform algorithm.In addition,a division method in hologram plane is proposed for enhancement in the representable minimum depth interval.     

On the Automorphism Group of the Kohn-Nirenberg Domain

In this paper, we prove that there are no automorphism orbits of the Kohn-Nirenberg domain accumulating at the origin.     

An application of comonotonicity theory in a stochastic life annuity framework

A life annuity contract is an insurance instrument which pays pre-scheduled living benefits conditional on the survival of the annuitant. In order to manage the risk borne by annuity providers, one needs to take into account all sources of uncertainty that affect the value of future obligations under the contract. In this paper, we define the concept of annuity rate as the conditional expected present value random variable of future payments of the annuity, given the future dynamics of its risk factors. The annuity rate deals with the non-diversifiable systematic risk contained in the life annuity contract, and it involves mortality risk as well as investment risk. While it is plausible to assume that there is no correlation between the two risks, each affects the annuity rate through a combination of dependent random variables. In order to understand the probabilistic profile of the annuity rate, we apply comonotonicity theory to approximate its quantile function. We also derive accurate upper and lower bounds for prediction intervals for annuity rates. We use the Lee-Carter model for mortality risk and the Vasicek model for the term structure of interest rates with an annually renewable fixed-income investment policy. Different investment strategies can be handled using this framework.     

Unique X-ray sheet structure of 1,8-bis(imidazolium) anthracene and its application as a fluorescent probe for DNA and DNase

A new imidazolium anthracene derivative 1 was synthesized, and its unique X-ray crystal structure was examined. In aqueous solutions, probe 1 exhibited a selective fluorescent quenching effect only with DNA among various anions including the nucleotides investigated. This probe was further applied to monitor the activity of DNase.     

Removal of arsenic from aqueous solution: A study of the effects of pH and interfering ions using iron oxide nanomaterials

Nanophase Fe₃O₄ and Fe₂O₃ were synthesized through a precipitation method and were utilized for the removal of either arsenic (III) or (V) from aqueous solution as a possible method for drinking water treatment. The synthesized nanoparticles were characterized using X-ray diffraction, which showed that the Fe₃O₄ and the Fe₂O₃ nanoparticles had crystal structures of magnetite and hematite, respectively. In addition, Secherrer's equation was used to determine that the grain size nanoparticles were 12 ± 1.0 nm and 17 ± 0.5 nm for the Fe₂O₃ and Fe₃O₄, respectively. Under a 1 h contact time, batch pH experiments were performed to determine the optimum pH for binding using 300 ppb of either As(III) or (V) and 10 mg of either Fe₃O₄ or Fe₂O₃. The binding was observed to be pH independent from pH 6 through pH 9 and a significant drop in the binding was observed at pH 10. Furthermore, batch isotherm studies were performed using the Fe₂O₃ and Fe₃O₄ to determine the binding capacity of As(III) and As(V) to the iron oxide nanomaterials. The binding was found to follow the Langmuir isotherm and the capacities (mg/kg) of 1250 (Fe₂O₃) and 8196 (Fe₃O₄) for As(III) as well as 20,000 (Fe₂O₃) and 5680 (Fe₃O₄) for As(III), at 1 and 24 h of contact time, respectively. The As(V) capacities were determined to be 4600 (Fe₂O₃), 6711(Fe₃O₄), 4904 (Fe₂O₃), and 4780 (Fe₃O₄) mg/kg for nanomaterials at contact times of 1 and 24 h respectively.