We prove that there does not exist an orthonormal basis {bn} for L(R) such that the sequences {μ(bn)}, {μ(c bn)}, and {∆(bn)∆( bn)} are bounded. A higher dimensional version of this result that involves generalized dispersions is also obtained. The main tool is a time-frequency localization inequality for orthonormal sequences in L(R). On the other hand, for d > 1 we construct a basis {bn} for ...

Aerogels have numerous applications due to their high surface area and low densities. However, creating aerogels from a large variety of materials has remained an outstanding challenge. Here, we report a new methodology to enable aerogel production with a wide range of materials. The method is based on the assembly of anisotropic nano-objects (one-dimensional (1D) nanotubes, nanowires, or two-d...

Using variable temperature scanning tunneling microscopy and dI/dz barrier height spectroscopy, the structure of water on h-BN/Rh(111) nanomesh has been investigated. Below its desorption temperature, two distinct phases of water self-assemble within the 3.2 nm unit cell of the nanomesh. In the 2 nm holes, an ordered phase of nano-ice crystals with about 40 molecules is found. The ice crystals ...

The projection of neuronal processes is guided by a variety of soluble and insoluble factors, which are sensed by a fiber's growth cone. It is the differential distribution of such guidance cues that determine the direction in which neurites grow. The growth cone senses these cues on a fine scale, using extensible filopodia that range from a few to tens of mum in length. In order to study the e...

Angled nano-scale tunnels with high aspect ratio were fabricated on poly(methyl methacrylate) (PMMA) using a focused ion beam (FIB). The fabrication parameters such as ion fluence, incidence angle, and acceleration voltage of the Ga(+) ion beam were first studied on the PMMA surface to explore the formation of the nano-scale configurations such as nano-holes and cones with diameter in the range...

Human small cell lung cancers (SCLC) produce and secrete the regulatory peptide bombesin (BN) or its mammalian counterpart gastrin-releasing peptide (GRP). In addition, several SCLC tumor lines have been shown to express high affinity receptors for BN/GRP. On the basis of these findings, we investigated the effect of exogenously added BN and GRP on the soft agarose colony growth of a panel of h...

We give criteria for the rationality of Cantor series ∑ ∞ n=1 bn a1···an and series ∑ ∞ n=1 bn an where a1, a2, · · · and b1, b2, · · · are integers such that an > 0 and the series converge. We precisely say when ∑ ∞ n=1 bn a1···an is rational (i) if {an} ∞ n=1 is a monotonic sequence of integers and bn+1 − bn = o(an+1) or lim supn→∞( bn+1 an+1 − bn an ) ≤ 0, and (ii) if bn+1 an+1−1 ≤ bn an−1 f...

Electron beam lithography (EBL) has become a popular means to prepare a wide variety of nano-arrays for numerous studies and applications, including photonics and sensors. Their fabrications and characterizations are costly and time consuming, underscoring the importance of developing effective tools to rapidly study their physicochemical stabilities and properties over time. In this study, we ...

In the article structure and phase composition of material based on nano-and micro-sized cubic boron nitride (cBN) obtained under high pressure temperature conditions from mechanically activated graphite-like (hBN) in presence aluminum (Al), which plays role an initiator for transformation hBN → cBN, are investigated. It has been shown that use mechanical activation contributes to formation cBN...