Method for measuring the self-assembly of alkanethiols on gold at femtomolar concentrations

We describe a cantilever-based method for measuring the self-assembly of alkanethiols on a gold surface in a flow system that permits easy step changes in concentration and acquire a continuous in situ measure of the resulting chemisorption through the change in resonance frequency. A gold-coated (2.2 mm2), piezoelectric-excited, millimeter-sized cantilever (PEMC) sensor was exposed to 1-hexadecanethiol (HDT) in ethanol at concentrations ranging from 1 fM to 1 mM, sequentially and separately. A high-order flexural mode at approximately 850 kHz was monitored during the self-assembly. The resonance frequency decreases as a result of increased mass as chemisorption occurs on the surface. We show for the first time that the chemisorption of HDT at 1 fM is readily measurable and gave a response of 220 +/- 13 Hz (n = 4). At higher concentrations (10 and 100 fM; 1, 10, and 100 pM; 1, 10, and 100 nM; 1 microM; and 1 mM), the responses were proportionately, but nonlinearly, higher. At high concentrations (1 mM), the responses to C4, C8, C11, C16, and C18 alkanethiols were linearly proportional and were complete in approximately 25 min. We report for the first time that, once the Au surface is equilibrated at 1 pM, further chemisorption at a lower HDT concentration does not take place, even though over 99% of surface adsorption sites are available. At 1 fM, the overall chemisorption rate did not increase with a 2-fold increase in the HDT flow rate, suggesting that chemisorption at 1 fM is not transport-limited. The measured overall chemisorption rate constant at 1 fM was more rapid than 0.1 min-1.     

Vector valued double sequence spaces defined by Orlicz function

In this article we introduce some vector valued double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness etc. and prove some inclusion results.     

Strongly almost convergent generalized difference sequences associated with multiplier sequences

Let Λ = (λ _k ) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w ₀[A,Δ ^m ,Λ,p], w ₁[A,Λ ^m ,Λ,p], w _∞[A,Δ ^m ,Λ,p] and study their different properties. We also introduce Δ _Λ ^m -statistically convergent sequences and give some inclusion relations between w ₁[Δ ^m ,λ,p] convergence and Δ _Λ ^m -statistical convergence. Communicated by Pavel Kostyrko     

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral radius? Let U _n,g be the lollipop graph obtained by appending a pendent vertex of a path on n ? g (n > g) vertices to a vertex of a cycle on g ? 3 vertices. We prove that the graph U _n,g uniquely minimizes the Laplacian spectral radius for n ? 2g ? 1 when g is even and for n ? 3g ? 1 when g is odd.     

On the spectrum of the Cesàro operator C 1 on b\bar v_0 \cap \ell _\infty

In this paper we have investigated the spectrum of the Cesàro operator C ₁ which is regarded as an operator on the sequence space $b\bar v_0 \cap \ell _\infty $ the space of statistically null bounded variation sequences.     

Synthesis and mycobacterial growth inhibition activities of bivalent and monovalent arabinofuranoside containing alkyl glycosides

Arabinofuranosides constitute one of the important components of cell wall structures of mycobacteria. With this importance of arabinofuranosides in mind, alkyl glycosides bearing arabinofuranoside trisaccharides were prepared, wherein the sugars were presented either in the monovalent or bivalent forms. Following the synthesis, the monovalent and bivalent alkyl glycosides were tested for their activities in a mycobacterial growth assay. The growth of the mycobacterial strain M. smegmatis was assessed in the presence of the alkyl glycosides and it was realized that the alkyl glycosides acted as inhibitors of the mycobacterial growth. The inhibition of the growth, caused by the above alkyl glycosides, was not observed for the arabinofuranose trisaccharide alone, without the alkyl groups, and for an alkyl glycoside bearing maltose as the sugar component.