Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Loss of Heterozygosity on Chromosomes 3p, 8p, 9p and 17p in the Progression of Squamous Cell Carcinoma of the Larynx

Previous molecular genetic studies of laryngeal squamous cell carcinoma (SCC)have shown certain chromosomal regions with recurring alterations. But studies of sequential molecular alterations and genetic progression model of laryngeal SCC have not been clearly defined. To identify the chromosomal alterations associated with the carcinogenesis of laryngeal SCC, we analyzed genomic DNA from microdissected squamous metaplasia, squamous dysplasia, invasive SCC, and metastatic carcinoma samples from 22 laryngeal SCC patients for loss of heterozygosity (LOH) at microsatellite loci. Ten microsatellite markers on chromosome 3p, 8p, 9p, and 17p were used. LOH at 9p21 was observed in the all stages including squamous metaplasia, squamous dysplasia, invasive SCC and metastatic carcinoma. LOH at 17p13.1, 3p25 and 3p14.2 was observed from the squamous dysplasia, invasive SCC and metastatic carcinoma. LOH at 8p21.3-p22 was observed mainly from the invasive SCC and metastatic carcinoma. The results suggest that 9p21 in the early event, 17p13.1, 3p25 and 3p14.2 in the intermediate event and 8p21.3-p22 in the late event may be involved in the laryngeal carcinogenesis

Medical-grade honey enriched with antimicrobial peptides has enhanced activity against antibiotic-resistant pathogens

Honey has potent activity against both antibiotic-sensitive and -resistant bacteria, and is an interesting agent for topical antimicrobial application to wounds. As honey is diluted by wound exudate, rapid bactericidal activity up to high dilution is a prerequisite for its successful application. We investigated the kinetics of the killing of antibiotic-resistant bacteria by RS honey, the source for the production of Revamil® medical-grade honey, and we aimed to enhance the rapid bactericidal activity of RS honey by enrichment with its endogenous compounds or the addition of antimicrobial peptides (AMPs). RS honey killed antibiotic-resistant isolates of Pseudomonas aeruginosa, Staphylococcus epidermidis, Enterococcus faecium, and Burkholderia cepacia within 2 h, but lacked such rapid activity against methicillin-resistant S. aureus (MRSA) and extended-spectrum beta-lactamase (ESBL)-producing Escherichia coli. It was not feasible to enhance the rapid activity of RS honey by enrichment with endogenous compounds, but RS honey enriched with 75 μM of the synthetic peptide Bactericidal Peptide 2 (BP2) showed rapid bactericidal activity against all species tested, including MRSA and ESBL E. coli, at up to 10–20-fold dilution. RS honey enriched with BP2 rapidly killed all bacteria tested and had a broader spectrum of bactericidal activity than either BP2 or honey alone