Interpolation of Sparse Multivariate Polynomials over Large Finite Fields with Applications

We develop a Las Vegas-randomized algorithm which performs interpolation of sparse multivariate polynomials over finite fields. Our algorithm can be viewed as the first successful adaptation of the sparse polynomial interpolation algorithm for the complex field developed by M. Ben-Or and P. Tiwari (1988, in “Proceedings of the 20th ACM Symposium on the Theory of Computing,” pp. 301–309, Assoc. Comput. Mach., New York) to the case of finite fields. It improves upon a previous result by D. Y. Grigoriev, M. Karpinski, and M. F. Singer (1990, SIAM J. Comput.19, 1059–1063) and is by far the most time efficient algorithm (time and processor efficient parallel algorithm) for the problem when the finite field is large. As applications, we obtain Monte Carlo-randomized parallel algorithms for sparse multivariate polynomial factorization and GCD over finite fields. The efficiency of these algorithms improves upon that of the previously known algorithms for the respective problems.     

Retraction Note to: Nano Pt–TiO2 for an efficient one-pot photocatalytic synthesis of quinaldines from anilines and ethanol

Research on Chemical Intermediates - This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s11164-020-04374-7     

Thermal and optical properties of Cd2SnO4 thin films using photoacoustic spectroscopy

Cadmium stannate (Cd₂SnO₄) thin films were prepared by the RF magnetron sputtering technique on glass substrates with substrate temperatures of room temperature (RT), 100°C, 200°C and 300°C. Photoacoustic analyses were made to obtain the thermal diffusivity and the optical bandgap values of the Cd₂SnO₄ thin films. The change in thermal diffusivity of the films with the substrate temperature was analyzed. The optical bandgap values obtained from the photoacoustic spectroscopy were compared with the values obtained from the optical transmittance spectra. X-ray photoelectron spectroscopic (XPS) studies confirm the formation of stoichiometric films. Surface morphological studies by atomic force microscopy (AFM) revealed the crystalline nature of the films deposited at 100°C.     

Direct electrochemical nanopatterning of polycarbazole monomer and precursor polymer films: ambient formation of thermally stable conducting nanopatterns

The direct nanopatterning of polycarbazole on ultrathin films of a "precursor polymer" and monomer under ambient conditions is reported. In contrast to previous reports on electrochemical dip-pen nanolithography using monomer ink or electrolyte-saturated films in electrostatic nanolithography, these features were directly patterned on spin-cast films of carbazole monomer and poly(vinylcarbazole) (PVK) under room temperature and humidity conditions. Using a voltage-biased atomic force microscope (AFM) tip, electric-field-induced polymerization and cross-linking occurred with nanopatterning in these films. Different parameters, including writing speed and bias voltages, were studied to demonstrate line width and patterning geometry control. The conducting property (current-voltage (I-V) curves) of these nanopatterns was also investigated using a conducting-AFM (C-AFM) setup, and the thermal stability of the patterns was evaluated by annealing the polymer/monomer film above the glass transition (T(g)) temperature of the precursor polymer. To the best of our knowledge, this is the first report in which thermally stable conducting nanopatterns were drawn directly on monomer or polymer film substrates using an electrochemical nanolithography technique under ambient conditions.     

Stereoselective Lewis acid-catalyzed alpha-acylvinyl additions

Silyloxyallenes derived from alpha-hydroxypropargylsilanes undergo efficient addition to aldehydes with catalytic amounts of Lewis acids. The allenes are accessed from the corresponding propargylsilanes in a base-catalyzed 1,2-Brook rearrangement/SE2' process. Enantioenriched propargylsilanes are synthesized by a new zinc-promoted addition of alkynes to acylsilanes in up to 74% ee. This work demonstrates that conversion to the silyloxyallenes occurs with minimal erosion in optical activity. The use of a chiral chromium(III) Lewis acid effects the catalytic asymmetric addition of racemic silyloxyallenes to aromatic aldehydes in up to 92% ee. The overall reaction is broad in scope and accommodates a wide variety of aromatic and aliphatic substituents on both the propargylsilane and aldehyde.     

On the discrepancy between two Zagreb indices

We examine the quantity

$S\left(G\right)=\sum _{uv\in E\left(G\right)}min(degu,degv)$

over sets of graphs with a fixed number of edges. The main result shows the maximum possible value of $S\left(G\right)$ is achieved by three different classes of constructions, depending on the distance between the number of edges and the nearest triangular number. Furthermore we determine the maximum possible value when the set of graphs is restricted to be bipartite, a forest, or to be planar given sufficiently many edges. The quantity $S\left(G\right)$ corresponds to the difference between two well studied indices, the irregularity of a graph and the sum of the squares of the degrees in a graph. These are known as the first and third Zagreb indices in the area of mathematical chemistry.     

Managing new and differentiated remanufactured products

We study a firm that makes new products in the first period and uses returned cores to make remanufactured products (along with new products) in future periods. The remanufactured product is differentiated from the new product, so the firm needs to choose differentiated prices. We analyze the monopoly environment in two-period, multi-period (three, four and five) and infinite planning horizons, and characterize the optimal remanufacturing and pricing strategy for the firm. In the process, we identify remanufacturing savings thresholds that determine the production and pricing strategy for the firm. Among other results, we find—counter to intuition—that in a finite-horizon, multi-period setting, the optimal policy is not necessarily monotone in remanufacturing savings.     

Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

A novel microresonator operating on the principle of nonlinear modal interactions due to autoparametric 1:2 internal resonance is introduced. Specifically, an electrostatically actuated pedal-microresonator design, utilizing internal resonance between an out-of-plane torsional mode and a flexural in-plane vibrating mode is considered. The two modes have their natural frequencies in 1:2 ratio, and the design ensures that the higher frequency flexural mode excites the lower frequency torsional mode in an autoparametric way. A Lagrangian formulation is used to develop the dynamic model of the system. The dynamics of the system is modeled by a two degrees of freedom reduced-order model that retains the essential quadratic inertial nonlinearities coupling the two modes. Retention of higher-order model for electrostatic forces allows for the study of static equilibrium positions and static pull-in phenomenon as a function of the bias voltages. Then for the case when the higher frequency flexural mode is resonantly actuated by a harmonically varying AC voltage, a comprehensive study of the response of the microresonator is presented and the effects of damping, and mass and structural perturbations from nominal design specifications are considered. Results show that for excitation levels above a threshold, the torsional mode is activated and it oscillates at half the frequency of excitation. This unique feature of the microresonator makes it an excellent candidate for a filter as well as a mixer in RF MEMS devices.     

Bubbles pinned on electrodes: Friends or foes of aqueous electrochemistry?

Electrochemists and engineers regard adherent gas bubbles as redox-inactive and therefore blocking entities. Adhesion of bubbles at electrodes generally carries an energy penalty. But this is not always the case: bubbles pinned on an electrode surface initiate the oxidation of water-soluble species under conditions where such reactions would normally be considered impossible. Here we critically review the recent literature that is beginning to unveil the novel concept of on-water electrochemistry. Harnessing electrochemical reactivity of the water–gas–electrode interface has the potential to become a game-changer in organic electrosynthesis, accelerating the transition toward a sustainable chemical industry by simplifying the direct integration of renewable electricity into the production of commodity chemicals.     

Designing tubular conducting polymer actuators for wireless electropumping

Rational design and shaping of soft smart materials offer potential applications that cannot be addressed with rigid systems. In particular, electroresponsive elastic materials are well-suited for developing original active devices, such as pumps and actuators. However, applying the electric stimulus requires usually a physical connection between the active part and a power supply. Here we report about the design of an electromechanical system based on conducting polymers, enabling the actuation of a wireless microfluidic pump. Using the electric field-induced asymmetric polarization of miniaturized polypyrrole tubes, it is possible to trigger simultaneously site-specific chemical reactions, leading to shrinking and swelling in aqueous solution without any physical connection to a power source. The complementary electrochemical reactions occurring at the opposite extremities of the tube result in a differential change of its diameter. In turn, this electromechanical deformation allows inducing highly controlled fluid dynamics. The performance of such a remotely triggered electrochemically active soft pump can be fine-tuned by optimizing the wall thickness, length and inner diameter of the material. The efficient and fast actuation of the polymer pump opens up new opportunities for actuators in the field of fluidic or microfluidic devices, such as controlled drug release, artificial organs and bioinspired actuators.

Tubular conducting polymer actuators are used for developing a wireless electropumping device. Bipolar electrochemistry, allowing symmetry breaking in terms of polarization and electrochemical reactions, is the key ingredient for efficient pumping.