Intersection theory and the Horn inequalities for invariant subspaces

We provide a direct, intersection theoretic, argument that the Jordan models of an operator of class C_{0}, of its restriction to an invariant subspace, and of its compression to the orthogonal complement, satisfy a multiplicative form of the Horn inequalities, where `inequality' is replaced by `divisibility'. When one of these inequalities is saturated, we show that there exists a splitting of the operator into quasidirect summands which induces similar splittings for the restriction of the operator to the given invariant subspace and its compression to the orthogonal complement. The result is true even for operators acting on nonseparable Hilbert spaces. For such operators the usual Horn inequalities are supplemented so as to apply to all the Jordan blocks in the model

All\u27s right with the world = 歌舞昇平

Film Director: Cheung King Wai (張經緯) Film Release Year: 2007https://commons.ln.edu.hk/ccs_worksheet/1002/thumbnail.jp

Production of high temperature grease from waste lubricant sludge and silicone oil

This research was carried out to study the production of high temperature grease from waste lubricant sludge and silicone oil. The effects of different ratios of waste lubricant sludge to fumed silica and mixing time on grease characteristics were investigated. The ratios of waste lubricant sludge and fumed silica used were 100:0, 90:10, 80:20, 70:30, 60:40, 50:50 and 40:60. In terms of mixing time, it was varied at 1, 2, 3, 4 and 5 hours. Throughout the experiment, the grease was prepared by using the heating and mixing technique. The grease produced was analysed according to the ASTM and NLGI standard via penetration test, dropping point test, copper corrosion test, FTIR and AAS.Fourier transform infra red (FTIR) analysis was carried out to study on the functional groups present in the grease. Atomic absorption spectroscopy analysis was also carried out to determine the concentration of a specific metal element in the grease. The results showed that the grease produced with a minimum ratio of fumed silica to sludge (10:90) was able to produce high temperature grease with a dropping point of 272.5.C.Further analysis verified that the grease is a high temperature grease, has worked penetration of 270-290 which makes the grease fall into the common grease category, has a low tendency to corrode copper and very little metal element was present in the grease. It can be concluded that the ratio of fumed silica to sludge and the mixing time of the grease produced significant effect on worked penetration and dropping point of the grease

Structural Analysis of a Peptide (CTLTTKLYC) that Interacts with Newcastle Disease Virus

A peptide with the sequence Cys-Thr-Leu-Thr-Thr-Lys-Leu-Tyr-Cys (CTLTTKLYC) has previously been identified to inhibit the propagation of Newcastle disease virus (NDV) in embryonated chicken eggs and tissue culture. It has two different dissociation constants (&"I), in which the first constant can be used as a determinant to classifjr NDV strains into two groups: the velogenic strains in the first group, whereas the mesogenic and lentogenic strains are in the second group. The peptide, C 1T 2L3 P T5K 6 L7 Y8 C9 ,d isplayed on the pIII protein of a filamentous M13 phage was mutated by oligonucleotide-directed mutagenesis in order to identify the amino acid residues involved in the interactions with NDV. Mutations of Cys at first position (c')a nd Lys at the sixth position of the peptide ( K ~t)o Ala (A), which produced mutants C'A and K~Ad,i d not affect the binding between the peptide and the virus significantly, but substitution of Tyr at eighth position (Y8) alone with Ala (A) dramatically reduced the interaction. This suggests that y8 couid play an important role in the peptide-virus interaction. Double mutations were carried out on K~ and y8 to produce mutants K~A-Y~AK,~ R-Y~AK,~ A-Y'F, and K ~ - Y ~ Fto, determine whether the mutated amino acids could improve the binding capability. However, the mutations did not improve the binding capability significantly. Fmoc-solid phase peptide synthesis was employed to synthesize the peptide, CTLTTKLYC. Crude peptide was purified with HPLC and analysed with a mass spectrometer. The secondary structure of the peptide was analysed with circular dichroism (CD) and the three dimensional conformation of the peptide was determined by nuclear magnetic resonance (NMR) and molecular modelling. A mixture conformation of p-turn and P-sheet (intermolecular interaction) was observed for the linear peptide by using CD. However, the three-dimensional structure of the linear peptide could not be arrived due to the mixture of conformation which made the sequence assignment of NMR extremely difficult. On the other hand, the disulfide-constrained cyclic peptide, which has a more rigid structure, exhibited only a P-turn structure. Two models were obtained: one of it consists of a p-turn and a distorted p-turn, while the other structure is an extended structure

TOX3 mutations in breast cancer

TOX3 maps to 16q12, a region commonly lost in breast cancers and recently implicated in the risk of developing breast cancer. However, not much is known of the role of TOX3 itself in breast cancer biology. This is the first study to determine the importance of TOX3 mutations in breast cancers. We screened TOX3 for mutations in 133 breast tumours and identified four mutations (three missense, one in-frame deletion of 30 base pairs) in six primary tumours, corresponding to an overall mutation frequency of 4.5%. One potentially deleterious missense mutation in exon 3 (Leu129Phe) was identified in one tumour (genomic DNA and cDNA). Whilst copy number changes of 16q12 are common in breast cancer, our data show that mutations of TOX3 are present at low frequency in tumours. Our results support that TOX3 should be further investigated to elucidate its role in breast cancer biology.Breast Cancer Research Foundation grant; University of Cambridge; Cancer Research UK; Hutchison Whampoa Limited; NIHR Cambridge Biomedical Research Centre; Marie Curie Career Integration Grant; Cancer Research UK [16942]; National Institute for Health Research [NF-SI-0611-10154