The Reversed q-Exponential Functional Relation

After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.Comment: 6 pages, LaTeX, no figure

On Fourier integral transforms for qq-Fibonacci and qq-Lucas polynomials

We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform

q-Analogue of Shock Soliton Solution

By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found.Comment: 13 pages, 5 figure

Carborane–β-cyclodextrin complexes as a supramolecular connector for bioactive surfaces

Supramolecular chemistry provides an attractive entry to generate dynamic and well-controlled bioactive surfaces. Novel host–guest systems are urgently needed to provide a broader affinity and applicability portfolio. A synthetic strategy to carborane–peptide bioconjugates was therefore developed to provide an entry to monovalent supramolecular functionalization of β-cyclodextrin coated surfaces. The β-cyclodextrin·carborane–cRGD surfaces are formed efficiently and with high affinity as demonstrated by IR-RAS, WCA, and QCM-D, compare favourable to existing bio-active host–guest surface assemblies, and display an efficient bioactivity, as illustrated by a strong functional effect of the supramolecular system on the cell adhesion and spreading properties. Cells seeded on the supramolecular surface displaying bioactive peptide epitopes exhibited a more elongated morphology, focal adhesions, and stronger cell adhesion compared to control surfaces. This highlights the macroscopic functionality of the novel supramolecular immobilization strategy

h analogue of Newton's binomial formula

In this letter, the $h$--analogue of Newton's binomial formula is obtained in the $h$--deformed quantum plane which does not have any $q$--analogue. For $h=0$, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to $\frac{n!}{(n-k)!}$ for $h=1$. \\ Some properties of the $h$--binomial coefficients are also given. \\ Finally, I hope that such results will contribute to an introduction of the $h$--analogue of the well--known functions, $h$--special functions and $h$--deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75

Nanodiamond quantum sensors reveal temperature variation associated to hippocampal neurons firing

Temperature is one of the most relevant parameters for the regulation of intracellular processes. Measuring localized subcellular temperature gradients is fundamental for a deeper understanding of cell function, such as the genesis of action potentials, and cell metabolism. Here, we detect for the first time temperature variations (1{\deg}C) associated with potentiation and depletion of neuronal firing, exploiting a nanoscale thermometer based on optically detected magnetic resonance in nanodiamonds. Our results provide a tool for assessing neuronal spiking activity under physiological and pathological conditions and, conjugated with the high sensitivity of this technique (in perspective sensitive to < 0.1{\deg}C variations), pave the way to a systematic study of the generation of localized temperature gradients. Furthermore, they prompt further studies explaining in detail the physiological mechanism originating this effect.Comment: 27 pages, 5 figures, 3 table

Central factorials under the Kontorovich-Lebedev transform of polynomials

We show that slight modifications of the Kontorovich-Lebedev transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of monomials to central factorial polynomials. A special attention is driven to the polynomial sequences whose KL-transform is the canonical sequence, which will be fully characterized. Finally, new identities between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August 201

Light-Responsive Hydrogel Microcrawlers, Powered and Steered with Spatially Homogeneous Illumination

Sub-millimeter untethered locomoting robots hold promise to radically change multiple areas of human activity such as microfabrication/assembly or health care. To overcome the associated hurdles of such a degree of robot miniaturization, radically new approaches are being adopted, often relying on soft actuating polymeric materials. Here, we present light-driven, crawling microrobots that locomote by a single degree of freedom actuation of their light-responsive tail section. The direction of locomotion is dictated by the robot body design and independent of the spatial modulation of the light stimuli, allowing simultaneous multidirectional motion of multiple robots. Moreover, we present a method for steering such robots by reversibly deforming their front section, using ultraviolet (UV) light as a trigger. The deformation dictates the robot locomotion, performing right- or left-hand turning when the UV is turned on or off respectively. The robots’ motion and navigation are not coupled to the position of the light sources, which enables simultaneous locomotion of multiple robots, steering of robots and brings about flexibility with the methods to deliver the light to the place of robot operation