The disjunctivities of ω-languages

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. Consider congruences IL and Pω, L on X* and a congruence OL on Xω introduced by an ω-language L. IL, Pω, L, and OL are called the infinitary syntactic-congruence, the principal congruence and the ω-syntactic congruence of L, respectively. If IL (Pω, L, OL) is the equality then L is called an I-disjunctive (P-disjunctive, O-disjunctive, respectively) ω- language. Properties concerning such ω-languages are explored and relations between these ω-languages are also studied

Unintended Consequences of Water Legislation

The population of Texas is expected to double by 2060. The Texas Lower Rio Grande Valley is one area in which alternative water sources and potable treatment methods are being sought to support a rapid population growth. An emerging and promising approach to expanding potable water supplies is brackish groundwater desalination. Due to recent technology developments in desalination membranes and increasing prices of surface water rights, the economics of desalination have become competitive with conventional treatment methods. The seemingly comparable competitive economics relationship between conventional and desalination treatments was impacted by Floor Amendment 60 of Texas Senate Bill 3, which was an attempt to meet the increased demand for municipal water. This amendment established the price at which irrigation water in the Valley can convert to municipal water, as a result of urban/residential development of agricultural land, at 68 percent of the market price, effective January 1, 2008. Preliminary economic and financial investigations suggest this legislation could affect the adoption of water treatment technology. This paper identifies and analyzes the economic and financial implications, both intended and unintended, of Floor Amendment 60 on the Valley water market, and the associated adoption of alternative technologies for producing potable water.Resource /Energy Economics and Policy,

Constructing exact symmetric informationally complete measurements from numerical solutions

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs and their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gr\"obner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of a SIC. Using this method we have calculated 69 new exact solutions, including 9 new dimensions where previously only numerical solutions were known, which more than triples the number of known exact solutions. In some cases the solutions require number fields with degrees as high as 12,288. We use these solutions to confirm that they obey the number-theoretic conjectures and we address two questions suggested by the previous work.Comment: 22 pages + 19 page appendix with many data tables. v2: published versio

Purification and Characterization of a Thermostable Xylanase Cloned from Bacillus Coagulans ST-6

The recombinant plasmid pBNX contains a xylanase gene cloned from a thermophilic Bacillus coagulans ST -6. It was found to produce a high level of intracellular xylanase activity in Escherichia coli HB 10 1. This xylanase enzyme was purified to homogeneity via a single step chromatography using a Sephadex G-50 column. SDS-PAGE analysis showed a single protein band having a molecular mass of 20 kDa. Zymogram analysis using agarose gel electrophoresis showed a single activity band for both crude and purified enzyme. Isoelectric point of the purified xylanase was pH 9.3. The optimum temperature and pH for xylanase activity was 55°C and pH 7.2 respectively. The enzyme was found to be stable and retained its activity after 30 min incubation at 60°C. The enzyme showed a broad range of pH stability, in that it retained its activity after a 1 hr incubation at pH 5 to pH 10.The apparent Km and Vmax of the enzyme was 2.18 mg/ml and 147.6 ).lmol xylose/min/mg protein respectively using oat spelt xylan as the suostrate. The purified enzyme was found to have very low CMCase activity after prolonged incubation of 5 hr to 24 hr (less than 5% that of xylanase activity after 24 hr incubation). No activity towards Avicel and filter paper was observed. No xylose, xylobiose or arabinose was found in the end product analysis using TLC indicating that the xylanase was a nondebranching endoxylanase. The effect of various metal ions on the measurement of reducing sugar by Somogyi-Nelson and DNS methods was examined. At 1 mM, Ca2+, Mn2+ and Pb2+ increased colour intensity of the standard glucose measured by DNS method while Mg2+, Zn2+, Hg2+ and EDTA decreased the colour formation. For the SomogyiNelson assay, only Mn2+ and Hg2+ decreased colour intensity of standard glucose measured while other compounds showed no effect. A subsequent study on the effect of metal ions on xylanase activity, taking into consideration of these results, showed that only Hg2+ was inhibitory while other metal ions (Li+, K+, Na+, Ca2+, Mg2+, Co2+, Mn2+, Cu2+, Zn2+, Pb2+ and Fe2), EDTA, urea and SDS had no effect

Financial Innovation for an Aging World

Over the last half-century, around the world, many nations have seen plummeting fertility rates and mounting life expectancies. These two factors are the engine behind unprecedented global aging. In this paper, we explore how the demographic transition may influence financial markets and, in turn, how financial market innovation might help resolve concerns flowing from global aging trends. We first provide context by reviewing the economics, finance, and insurance-related literature on how global aging patterns may influence capital markets. We then turn to insurance markets, and discuss a range of products and policies, including both retail and wholesale financial offerings for various forms of life annuities, long-term care benefits, reverse mortgages, securitization of longevity risk, inflation-protected assets, reinsurance, guarantees, derivative contracts on residential property price indices, mortality swaps and longevity derivative contracts. We also indicate how new public-private partnerships might be beneficial in enhancing the future environment for old-age risk management.

Modulation of COX2 and hTERT expression by Photodynamic Therapy in human colon cancer cells

Photodynamic therapy (PDT) was employed as a cancer therapy with photosensitizer (PS)-loaded cancer cells, eradicated by the reactive oxygen species after light activation. Cyclo-oxygenase 2 (COX2) is an enzyme expressed in 80% of colon adenocarcinoma and is one of the targets for effective cancer treatment. There is also uprising evidence that the human telomerase reverse transcriptase (hTERT), a catalytic component of telomerase, is reported as a promising indicator for monitoring cancer treatment. In this study, NPe6 mediated PDT on COX2 induced apoptosis in HT-29 was investigated. The cell cycle changes was analysed by flow cytometry and the hTERT expression at pre and post PDT was evaluated at transcription level by Taqman real time PCR. NPe6-PDT in HT-29 cells demonstrated anti-proliferating effect in a drug and light dose dependent manner. LD50 was achieved at 16μg/mL and 2J/cm2 at 4 hour-post treatment with a significant down-regulation of COX2 expression at LD30 and LD50 by immunohistochemical staining (IHC) (p<0.05, One-Way ANOVA). Membrane blebbing was detected in over 60% of cells. 35.2% of treated cells arrested in S-phase at LD50 after 24 hours by flow cytometry. A 0.25- and 0.6-fold down-regulation of hTERT mRNA expression was achieved at LD30 and LD50 respectively by TaqMan real-time PCR. To summarize, NPe6 mediated PDT down-regulated COX2 expression and triggered cell apoptosis. The hTERT can serve as an indicative marker for monitoring NPe6-PDT cancer treatment efficacy.published_or_final_versio