Generalized P(N)-graded Lie superalgebras

We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction.     

Output feedback regulation of large-scale feedforward systems with discrete and distributed delays

Nonlinear Dynamics - This paper proposes an output feedback control strategy to achieve the global regulation of a class of large-scale feedforward nonlinear systems with discrete and distributed...     

Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels

Numerical Algorithms - The original solutions of highly oscillatory integral equations usually have rapid oscillation, which means that conventional numerical approaches used to solve these...     

Highly sensitive perylene tetra-(alkoxycarbonyl) based colorimetric and ratiometric probes for fluorine detection

Fluoride anion (F^?) affects environmental, biological, and chemical processes significantly. Therefore, its detection has received increasing attention, and sensitive, effective, and convenient probes for F^? detection need to be developed urgently. In this work, two perylene tetra-(alkoxycarbonyl) (PTAC) based colorimetric and ratiometric probes, P1 and P2, were developed for the detection of F^?. The interactions between F^? and these two probes were investigated by absorption, electrochemistry, ¹H NMR, and density functional methods. Both the two probes were complexed with F^? with a ratio of 1:1. The detection limits of P1 and P2 were 0.22 μM and 0.87 μM, respectively. It was worth noting that the absorption peak of P1 showed a 190 nm red shift when sensing F^?, and P1 is the largest red shift value reported in F^? probes based on PTAC derivatives. This phenomenon was resulted from the unique configuration and deprotonation of P1 that can promote the intramolecular charge transfer (ICT). This strategy provides an example for the development of other ion probes based on D-A type ICT mechanism.     

Sampled-data output voltage regulation for a DC–DC buck converter nonlinear system with actuator and sensor failures

Nonlinear Dynamics - This paper considers the distributed adaptive neural consensus tracking control problem for a class of uncertain nonaffine nonlinear multi-agent systems. By making use of the...     

Electron-donating methoxy group enhances the stability and efficiency of indole-based fluorescent probe for detecting Cu2+

Research on Chemical Intermediates - Two novel Schiff-base fluorescent probes bearing different substituents were synthesized by the reaction of indole derivatives with 4-aminoantipyrine. The...     

Cytosine-5 methylation-directed construction of a Au nanoparticle-based nanosensor for simultaneous detection of multiple DNA methyltransferases at the single-molecule level

DNA methylation at cytosine/guanine dinucleotide islands (CpGIs) is the most prominent epigenetic modification in prokaryotic and eukaryotic genomes. DNA methyltransferases (MTases) are responsible for genomic methylation, and their aberrant activities are closely associated with various diseases including cancers. However, the specific and sensitive detection of multiple DNA MTases has remained a great challenge due to the specificity of the methylase substrate and the rareness of methylation-sensitive restriction endonuclease species. Here, we demonstrate for the first time the cytosine-5 methylation-directed construction of a Au nanoparticle (AuNP)-based nanosensor for simultaneous detection of multiple DNA MTases at the single-molecule level. We used the methyl-directed endonuclease GlaI to cleave the site-specific 5-methylcytosine (5-mC). In the presence of CpG and GpC MTases (i.e., M.SssI and M.CviPI), their hairpin substrates are methylated at cytosine-5 to form the catalytic substrates for GlaI, respectively, followed by simultaneous cleavage by GlaI to yield two capture probes. These two capture probes can hybridize with the Cy5/Cy3–signal probes which are assembled on the AuNPs, respectively, to form the double-stranded DNAs (dsDNAs). Each dsDNA with a guanine ribonucleotide can act as the catalytic substrate for ribonuclease (RNase HII), inducing recycling cleavage of signal probes to liberate large numbers of Cy5 and Cy3 molecules from the AuNPs. The released Cy5 and Cy3 molecules can be simply quantified by total internal reflection fluorescence (TIRF)-based single-molecule imaging for simultaneous measurement of M.SssI and M.CviPI MTase activities. This method exhibits good specificity and high sensitivity with a detection limit of 2.01 × 10⁻³ U mL⁻¹ for M.SssI MTase and 3.39 × 10⁻³ U mL⁻¹ for M.CviPI MTase, and it can be further applied for discriminating different kinds of DNA MTases, screening potential inhibitors, and measuring DNA MTase activities in human serum and cell lysate samples, holding great potential in biomedical research, clinical diagnosis, drug discovery and cancer therapeutics.

Cytosine-5 methylation-directed construction of Au nanoparticle-based nanosensors enables specific and sensitive detection of multiple DNA methyltransferases.     

Uniform partition extensions,a generating functions perspective

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.