Fissioned Triangular Schemes via the Cross-ratio

AbstractA construction of association schemes is presented; these are fission schemes of the triangular schemesT (n) where n=q+ 1 with q any prime power. The key observation is quite elementary, being that the natural action of PGL(2, q) on the 2-element subsets of the projective line PG(1, q) is generously transitive. In addition, some observations on the intersection parameters and fusion schemes of these association schemes are made

Fissioned Triangular Schemes Via the Cross-Ratio

A construction of association schemes is presented; these are fission schemes of the triangular schemes T(n) where n=q + 1with q any prime power. The key observation is quite elementary, being that the natural action of PGL(2,q) on the 2-element subsets of the projective line PG(1,q) is generously transitive. Also some observations on the intersection parameters and fusion schemes of these association schemes are made.

Nonexistence of Certain Skew-symmetric Amorphous Association Schemes

An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.Comment: 10 page

β-delayed fission and α decay of At196

A nuclear-decay spectroscopy study of the neutron-deficient isotope At196 is reported where an isotopically pure beam was produced using the selective Resonance Ionization Laser Ion Source and On-Line Isotope Mass Separator (CERN). The fine-structure α decay of At196 allowed the low-energy excited states in the daughter nucleus Bi192 to be investigated. A β-delayed fission study of At196 was also performed. A mixture of symmetric and asymmetric fission-fragment mass distributions of the daughter isotope Po196 (populated by β decay of At196) was deduced based on the measured fission-fragment energies. A βDF probability PβDF(At196)=9(1)×10−5 was determined

Piperine derivatives enhance fusion and axonal transport of mitochondria by activating mitofusins

Piperine (1-piperoylpiperidine) is the major pungent component of black pepper (Piper nigrum) and exhibits a spectrum of pharmacological activities. The molecular bases for many of piperine’s biological effects are incompletely defined. We noted that the chemical structure of piperine generally conforms to a pharmacophore model for small bioactive molecules that activate mitofusin (MFN)-mediated mitochondrial fusion. Piperine, but not its isomer chavicine, stimulated mitochondrial fusion in MFN-deficient cells with EC50 of ~8 nM. We synthesized piperine analogs having structural features predicted to optimize mitofusin activation and defined structure-activity relationships (SAR) in live-cell mitochondrial elongation assays. When optimal spacing was maintained between amide and aromatic groups the derivatives were potent mitofusin activators. Compared to the prototype phenylhexanamide mitofusin activator, 2, novel molecules containing the piperidine structure of piperine exhibited markedly enhanced passive membrane permeability with no loss of fusogenic potency. Lead compounds 5 and 8 enhanced mitochondrial motility in cultured murine Charcot-Marie-Tooth disease type 2A (CMT2A) neurons, but only 8 improved mitochondrial transport in sciatic nerve axons of CMT2A mice. Piperine analogs represent a new chemical class of mitofusin activators with potential pharmaceutical advantages