Modified simple equation method for nonlinear evolution equations

This paper reflects the implementation of a reliable technique which is called modified simple equation method (MSEM) for solving evolution equations. The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh-Nagumo equation and Sharma-Tasso-Olver equation. Numerical results are very encouraging.     

Study on the normalized Laplacian of a penta-graphene with applications

Let L _n denote a linear pentagonal chain with 2n pentagons. The penta-graphene (penta-C), denoted by R _n is the graph obtained from L _n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring is the graph obtained from the L _n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed-form formula of the multiplicative degree-Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R _n is obtained. Furthermore, it is interesting to see that the multiplicative degree-Kirchhoff index of R _n is approximately of its Gutman index. Based on our obtained results, all the corresponding results are obtained for .     

Oligosaccharide Analogues of Polysaccharides. Part 4. Synthesis of a monosaccharide-derived octamer

NaSMe in toluene leads to regioselective de-C-silylation of the bis[(trimethylsilyl)ethynyl]saccharide 2 , but to decomposition of butadiynes such as 1 or 12 . We have, therefore, combined the known reagent-controlled, regioselective desilylation of 2 and of 12 (AgNO₂/KCN) with a substrate-controlled regioselective de-C-silylation, based on C-silyl groups of different size. This combination was studied with the fully protected 3 which was mono-desilylated to 4 or to 5 (Scheme 1). Triethylsilylation of 5 (→ 6 ) was followed by removal of the Me₃Si group (→ 7 ), introduction of a (t-Bu)Me₂Si group (→ 8 ) and removal of the Et₃Si group yielded 9 ; these high-yielding transformations proceed with a high degree of selectivity. Iodination of 4 gave 10 . The latter was coupled with 5 to the homodimer 11 and the heterodimer 12 , which was desilylated to 13 . The second building block for the tetramer was obtained by coupling 14 (from 7 ) with 5 , leading to 15 and 16 . Removal of the Me₃Si group (→ 17 ) and iodination led to 18 which was coupled with 13 to the homotetramer 20 and the heterotetramer 19 (Scheme 2). Deprotection of 19 gave 21 , which was, on the one hand, iodinated to 22 , and, on the other hand, protected by the (t-Bu)Me₂Si group (→ 23 ). Removal of the Et₃Si group (→ 24 ) and coupling afforded the homooctamer 26 and the heterooctamer 25 . Yields of iodination, silylation, and desilylation were consistently high, while heterocoupling proceeded in only 50–55%. Cleavage of the (i-Pr)₃SiC and MeOCH₂O groups of 11 (→ 27 ), 15 (→ 28 ), 20 (→ 29 ) and 26 (→ 30 ) proceeded in high yields (Scheme 3). Complete deprotection in two steps of the heterocoupling products 16 (→ 31 → 32 ), 19 (→ 33 → 34 ), and 25 (→ 35 → 36 ) gave the unprotected dimer 32 , tetramer 34 , and octamer 36 in high yields (Scheme 4). Only the dimer 32 is soluble in H₂O; the ¹H-NMR spectra of 32 , 34 , and 36 in (D₆)DMSO (relatively low concentration) show no signs of association.     

Self-assembly, characterization, and chemical stability of isocyanide-bound molecular wire monolayers on gold and palladium surfaces

Self-assembled monolayers (SAMs) of the isocyano derivative of 4,4'-di(phenylene-ethynylene)benzene (1), a member of the "OPE" family of "molecular wires" of current interest in molecular electronics, have been prepared on smooth, {111} textured films of Au and Pd. For assembly in oxygen-free environments with freshly deposited metal surfaces, infrared reflection spectroscopy (IRS) indicates the molecules assume a tilted structure with average tilt angles of 18-24 degrees from the surface normal. The combination of IRS, X-ray photoelectron spectroscopy, and density functional theory calculations all support a single sigma-type bond of the -NC group to the Au surface and a sigma/pi-type of bond to the Pd surface. Both SAMs show significant chemical instability when exposed to typical ambient conditions. In the case of the Au SAM, even a few hours storage in air results in significant oxidation of the -NC moieties to -NCO (isocyanate) with an accompanying decrease in surface chemical bonding, as evidenced by a significant increase in instability toward dissolution in solvent. In the case of the Pd SAM, similar air exposure does not result in incorporation of oxygen or loss of solvent resistance but rather results in a chemically altered interface which is attributed to polymerization of the -NC moieties to quasi-2D poly(imine) structures. Conductance probe atomic force microscope measurements show the conductance of the degraded Pd SAMs can diminish by approximately 2 orders of magnitude, an indication that the SAM-Pd electrical contact has severely degraded. These results underscore the importance of careful control of the assembly procedures for aromatic isocyanide SAMs, particularly for applications in molecular electronics where the molecule-electrode junction is critical to the operational characteristics of the device.     

An authentication protocol based on chaos and zero knowledge proof

Nonlinear Dynamics - Port Knocking is a method for authenticating clients through a closed stance firewall, and authorising their requested actions, enabling severs to offer services to...     

Tuning the physical properties of a nematic liquid crystal elastomer actuator

In this report we demonstrate the ability to tune the physical properties of a liquid crystal elastomer (LCE) by varying the amount and type of crosslinking within the elastomer network. LCE films composed of a single mesogenic compound were capable of uniaxial contraction when thermally actuated through the nematic to isotropic phase of the material. We probed the physical properties of the LCE films while varying the amount and concentration of two crosslinking agents and measured actuation strains of 10-35%, elastic moduli of 3-14 MPa, and transition temperatures ranging between 75 and 60°C. The viscous losses of the elastomers and the estimated work capable of being produced by the films were also evaluated. The ability to tune the physical properties of the LCE films allows for a wide range of applications including robotics, microelectromechanical systems (MEMS), shape-changing membranes, and/or microfluidics.     

Laser irradiance of a homogeneous metal slab

Numerical calculations of the effect of laser irradiance was performed for three homogeneous slabs. The temperature profile and the temperature of the front surface for three metals, silver, steel, and aluminium was calculated. The formulation of the temperature distribution of the slab was carried out using Fourier series expansions for the case of time dependent laser irradiance. The exact expressions for the thermal penetration depth and the critical time required to initiate melting (i.e. damage) were found.