Modeling Scatter in Multiple Energy Windows to Incorporate Scattered Radiation Information in Single Photon Emission Computed Tomography Imaging

Using scattered radiation as useful information to improve radioisotope image quality is a topic attracting many researchers. Some reports showed that incorporating scattered components offers a possibility to improve image quality. The general method is modeling scatter in multiple energy windows and incorporating that information into the reconstruction process. However, what the performance will be and how noise will behave when using scattered radiation in reconstruction are not yet well answered. In this paper, we investigate a method of modeling scatter in multiple energy windows in cases of a few projection views. The system performance is analyzed using singular value decomposition and resolution kernels. For noise behavior investigation, reconstructions are accomplished by estimating the variance of reconstructed voxel values and the effectiveness of using scatter is evaluated by resolution kernel analysis. The results show there are improvements in normalized mean-square error of the images and the resolution kernels. When photon counts fall below about one million, it is still effective to use scatter for some cases of a few projections     

Eicosapentaenoic acid release from the red alga Pachymeniopsis lanceolata by enzymatic degradation

Forty-eight species of seaweeds from Japanese waters were screened for the valuable polyunsaturated fatty acids eicosapentaenoic acid (EPA). The eight species that contained the highest levels of these compounds were analyzed in detail. Of all species tested the red alga Pachymeniopsis lanceolata contained the highest EPA concentration, and it was present as both the free and bound forms. EPA constituted 38.7% of total fatty acids, and polar lipids were the main constituent of the total lipids in P. lanceolata. EPA was obtained from the marine algae P. lanceolata by enzymatic hydrolysis of the total lipids extract using phospholipase A₂(PLA₂). The release of EPA reached a plateau after 10 min of enzymatic treatment. These results suggest that P. lanceolata is a useful natural source of EPA and that PLA₂ treatment is a convenient method for obtaining EPA from the red alga.     

Does truth-table of linear norm reduce the one-query tautologies to a random oracle?

In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent to the assertion that the probabilistic complexity class R is not equal to NP; The hypothesis for p-tt (polynomial-time truth-table) reduction implies that P is not NP; The hypothesis holds for each of the following: disjunctive reduction, conjunctive reduction, and p-btt (polynomial-time bounded-truth-table) reduction. In this paper, we show the following three results: (1) Let c be a positive real number. We consider a concept of truth-table reduction whose norm is at most c times size of input, where for a relativized propositional formula F, the size of F denotes the total number of occurrences of propositional variables, constants and propositional connectives. Then, our main result is that the hypothesis holds for such tt-reduction, provided that c is small enough. How small c can we take so that the above holds? It depends on our syntactic convention on one-query tautologies. In our setting, the statement holds for all c < 1. (2) The hypothesis holds for monotone truth-table reduction (also called positive reduction). (3) Dowd (in Inf. Comput. 96, 65–76, 1992) shows a polynomial upper bound for the minimum sizes of forcing conditions associated with a random oracle. We apply the above result (1), and get a linear lower bound for the sizes.     

An efficient total synthesis of (+)-heliannuol D

An efficient total synthesis of (+)-heliannuol D was accomplished in 14 steps and in 12% overall yield by employing a diastereoselective conjugate addition reaction to create a tertiary benzylic stereogenic center and simple assembly of the functionalized oxepane framework by an efficient one-pot transformation procedure as the key steps.     

A characterization of Hyers-Ulam stability of first order linear differential operators

Let X be a complex Banach space and a continuous function. Let be the linear differential operator defined by T_hu=u′+hu. We give a necessary and sufficient condition in order that the operator T_h has the Hyers-Ulam stability.     

Donor-substituted cyanoethynylethenes: powerful chromophores for opto-electronic applications

Donor-substituted cyanoethynylethenes (CEEs) were synthesised, structurally characterised and investigated for their electronic and two-photon absorption properties, revealing exceptionally strong intramolecular charge-transfer interactions.     

Transacylation of alpha-aryl-beta-keto esters

The acyl group of an alpha-aryl-beta-keto ester was readily transferred to N-, O-, and S-nucleophiles. The transacylation from arylated diethyl 3-oxoglutarate to amines led to unsymmetrical malonic acid amide esters in high yields. The present reaction proceeded under mild conditions without formation of detectable byproducts. Only simple experimental manipulations were required. This reaction was also found to be sensitive to steric factors, which enabled the chemoselective monoacylation of diamines and amino alcohols without any modifications such as protection.