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.     

Trends in the detection of pharmaceuticals and endocrine-disrupting compounds by Field-Effect Transistors (FETs)

Field-effect transistors (FETs) are one of the most widely-used electronic sensors for continuous monitoring and detection of contaminants such as pharmaceuticals and endocrine-disrupting compounds at low concentrations. FETs have been successfully utilized for the rapid analysis of these environmental pollutants due to their advantageous material properties like the disposability, rapid responses and simplicity. This paper presented an up-to-date overview of applied strategies with different bio-based materials in order to enhance the analytical performances of the designed sensors. Comparison and discussion were made between characteristics of recently engineered FET bio-sensors used for the detection of famous and selected pharmaceutical compounds in the literature. The recent progress in environmental research applications, comments on interesting trends, current challenge for future research in endocrine-disrupting chemicals’ (EDCs) detection using FETs biosensors were highlighted.     

One-step synthesis of new aluminum hydrides bearing a highly sterically hindered acenaphthene-1,2-diimine ligand

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A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment

Applications of Mathematics - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated...     

A quantitatively controllable mesoscopic reliability model of an interdependent public transit network considering congestion,time-delay interaction and self-organization effects

Nonlinear Dynamics - This paper establishes a multi-parameter controlling cascading failures (CFs) model for measuring interdependent public transit network (PTN) reliability under mesoscopic...     

Surface‐Enhanced Raman Scattering Based on Controllable‐Layer Graphene Shells Directly Synthesized on Cu Nanoparticles for Molecular Detection

Graphene shells with a controllable number of layers were directly synthesized on Cu nanoparticles (CuNPs) by chemical vapor deposition (CVD) to fabricate a graphene‐encapsulated CuNPs (G/CuNPs) hybrid system for surface‐enhanced Raman scattering (SERS). The enhanced Raman spectra of adenosine and rhodamine 6G (R6G) showed that the G/CuNPs hybrid system can strongly suppress background fluorescence and increase signal‐to‐noise ratio. In four different types of SERS systems, the G/CuNPs hybrid system exhibits more efficient SERS than a transferred graphene/CuNPs hybrid system and pure CuNPs and graphene substrates. The minimum detectable concentrations of adenosine and R6G by the G/CuNPs hybrid system can be as low as 10^?8 and 10^?10 M , respectively. The excellent linear relationship between Raman intensity and analyte concentration can be used for molecular detection. The graphene shell can also effectively prevent surface oxidation of Cu nanoparticles after exposure to ambient air and thus endow the hybrid system with a long lifetime. This work provides a basis for the fabrication of novel SERS substrates.     

Two new eudesmane-type glucopyranosides from the fruits of Daucus carota L.

Two new eudesmane-type glucopyranosides have been isolated from the fruits of Daucus carota L. On the basis of their spectroscopic and chemical evidence, the new compounds were elucidated as daucucarotol-10-O-β-d-glucopyranoside (1) and decahydro-7-[(2-O-β-d-glucopyranosyl)-isopropyl]-1β,4aα-dimethyl-(1α,4α,8aβ)-naphthalenetriol (2). Compounds 1 and 2 showed moderate antitumour activity against human ECA-109 and gave IC₅₀ values of 23.22 and 26.76 μM, respectively.     

Accurate Theoretical Study of LiS Radical and Its Singly Charged Cation and Anion in their Ground Electronic State

Potential energies of LiS(²Π), LiS^-(¹Σ⁺) and LiS⁺(³Σ^-) are calculated by using the multireference configuration interaction method including Davidson correction and the augmented correlation-consistent basis sets aug-cc-PV(X+d)Z (X=T, Q). Such obtained potential energies are subsequently extrapolated to the complete basis set limit. Both the core-valence correction and the relativistic effect are also considered. The analytical potential energy functions are then obtained by fitting such accurate energies utilizing a least-squares fitting procedure. By using such analytical potential energy functions, we obtain the accurate spectroscopic parameters, complete set of vibrational levels and classical turning points. The present results are compared well with the experimental and other theoretical work.