On Kernel Formulas and Dispersionless Hirota Equations

We rederive dispersionless Hirota equations of the dispersionless Toda hierarchy from the method of kernel formula provided by Carroll and Kodama. We then apply the method to derive dispersionless Hirota equations of the extended dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify associativity equations (WDVV equations) in the EdBKP hierarchy from dispersionless Hirota equations and give a realization of associative algebra with structure constants expressed in terms of residue formula.Comment: 30 pages, minor corrections, references adde

Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model

Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin-3/2 fermionic atoms in optical lattices. When the \textit{s}-wave scattering lengths for the total spin $S=2,0$ satisfy conditions $a_{2}>a_{0}>0$, we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a 2D square lattice, the saddle point solution yields a staggered spin-quadrupole ordering at zero temperature with symmetry breaking from SO(5) to SO(4). Both spin and spin-quadrupole static structure factors are calculated, displaying highly anisotropic spin antiferromagnetic fluctuations and antiferroquadrupole long-range correlations, respectively. When Gaussian fluctuations around the saddle point are taken into account, spin-quadrupole density waves with a linear dispersion are derived. Compared with the spin density waves in the half filled spin-1/2 Hubbard model, the quadrupole density wave velocity is saturated in the strong-coupling limit, and there are no transverse spin-quadrupole mode couplings, as required by the SO(4) invariance of the effective action. Finally, in the strong-coupling limit of the model Hamiltonian, we derive the effective hyperfine spin-exchange interactions for the Mott insulating phases in the quarter filled and half filled cases, respectively.Comment: 12 pages, 5 figure

Genetically engineered pre-microRNA-34a prodrug suppresses orthotopic osteosarcoma xenograft tumor growth via the induction of apoptosis and cell cycle arrest.

Osteosarcoma (OS) is the most common primary malignant bone tumor in children, and microRNA-34a (miR-34a) replacement therapy represents a new treatment strategy. This study was to define the effectiveness and safety profiles of a novel bioengineered miR-34a prodrug in orthotopic OS xenograft tumor mouse model. Highly purified pre-miR-34a prodrug significantly inhibited the proliferation of human 143B and MG-63 cells in a dose dependent manner and to much greater degrees than controls, which was attributed to induction of apoptosis and G2 cell cycle arrest. Inhibition of OS cell growth and invasion were associated with release of high levels of mature miR-34a from pre-miR-34a prodrug and consequently reduction of protein levels of many miR-34a target genes including SIRT1, BCL2, c-MET, and CDK6. Furthermore, intravenous administration of in vivo-jetPEI formulated miR-34a prodrug significantly reduced OS tumor growth in orthotopic xenograft mouse models. In addition, mouse blood chemistry profiles indicated that therapeutic doses of bioengineered miR-34a prodrug were well tolerated in these animals. The results demonstrated that bioengineered miR-34a prodrug was effective to control OS tumor growth which involved the induction of apoptosis and cell cycle arrest, supporting the development of bioengineered RNAs as a novel class of large molecule therapeutic agents

Mott insulating phases and quantum phase transitions of interacting spin-3/2 fermionic cold atoms in optical lattices at half filling

We study various Mott insulating phases of interacting spin-3/2 fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole/spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\pi$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.Comment: 11 pages, 4 figure

An easy approach to derive EOQ and EPQ models with shortage and defective items

Huang [Journal of Statistics and Management Systems, Vol. 6, No. 2, pp. 171-180, 2003.] studied the EOQ (Economic Order Quantity) and EPQ (Economic Production Quantity) models with backlogging and defective items using the algebraic approach. He assumed that a 100% inspection policy and the known proportion of defective items was removed after the screening process prior to storage or use. In this paper, we will offer another simple approach to find both the optimal lot size and backorder level under the minimized total relevant cost per unit time

An easy approach to derive EOQ and EPQ models with shortage and defective items

Huang [Journal of Statistics and Management Systems, Vol. 6, No. 2, pp. 171-180, 2003.] studied the EOQ (Economic Order Quantity) and EPQ (Economic Production Quantity) models with backlogging and defective items using the algebraic approach. He assumed that a 100% inspection policy and the known proportion of defective items was removed after the screening process prior to storage or use. In this paper, we will offer another simple approach to find both the optimal lot size and backorder level under the minimized total relevant cost per unit time

Metabolic labelling of cholesteryl glucosides in Helicobacter pylori reveals how the uptake of human lipids enhances bacterial virulence.

Helicobacter pylori infects approximately half of the human population and is the main cause of various gastric diseases. This pathogen is auxotrophic for cholesterol, which it converts upon uptake to various cholesteryl α-glucoside derivatives, including cholesteryl 6'-acyl and 6'-phosphatidyl α-glucosides (CAGs and CPGs). Owing to a lack of sensitive analytical methods, it is not known if CAGs and CPGs play distinct physiological roles or how the acyl chain component affects function. Herein we established a metabolite-labelling method for characterising these derivatives qualitatively and quantitatively with a femtomolar detection limit. The development generated an MS/MS database of CGds, allowing for profiling of all the cholesterol-derived metabolites. The subsequent analysis led to the unprecedented information that these bacteria acquire phospholipids from the membrane of epithelial cells for CAG biosynthesis. The resulting increase in longer or/and unsaturated CAG acyl chains helps to promote lipid raft formation and thus delivery of the virulence factor CagA into the host cell, supporting the idea that the host/pathogen interplay enhances bacterial virulence. These findings demonstrate an important connection between the chain length of CAGs and the bacterial pathogenicity