Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation

In this Letter we propose a new generalization of the two-dimensional differential transform method that will extend the application of the method to a diffusion-wave equation with space- and time-fractional derivatives. The new generalization is based on generalized Taylor's formula and Caputo fractional derivative. Theorems that are never existed before are introduced with their proofs. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The results reveal that the technique introduced here is very effective and convenient for solving partial differential equations of fractional order.     

On the orientation of a designed transmembrane peptide: toward the right tilt angle?

The orientation of the transmembrane peptide WALP23 under small hydrophobic mismatch has been assessed through long-time-scale molecular dynamics simulations of hundreds of nanoseconds. Each simulation gives systematically large tilt angles (>30 degrees). In addition, the peptide visits various azimuthal rotations that mostly depend on the initial conditions and converge very slowly. In contrast, small tilt angles as well as a well-defined azimuthal rotation were suggested by recent solid-state 2H NMR studies on the same system. To optimally compare our simulations with NMR data, we concatenated the different trajectories in order to increase the sampling. The agreement with 2H NMR quadrupolar splittings is spectacularly better when these latter are back-calculated from the concatenated trajectory than from any individual simulation. From these ensembled-average quadrupolar splittings, we then applied the GALA method as described by Strandberg et al. (Biophys J. 2004, 86, 3709-3721), which basically derives the peptide orientation (tilt and azimuth) from the splittings. We find small tilt angles (6.5 degrees), whereas the real observed tilt in the concatenated trajectory presents a higher value (33.5 degrees). We thus propose that the small tilt angles estimated by the GALA method are the result of averaging effects, provided that the peptide visits many states of different azimuthal rotations. We discuss how to improve the method and suggest some other experiments to confirm this hypothesis. This work also highlights the need to run several and rather long trajectories in order to predict the peptide orientation from computer simulations.     

Self-organization of double-C60 end-capped poly(ethylene oxide) in chloronaphthalene and benzene solvent mixtures

Well-defined and narrowly distributed double-C60 end-functionalized poly(ethylene oxide) (C60-PEO-C60) was prepared by reacting azido-terminated PEO with C60. The self-organization behavior of such C60-modified copolymers in different mixtures of chloronaphthalene (CN) and benzene (BN) was studied by a combination of static and dynamic laser light scattering. For C60-PEO-C60 in pure CN, a selective solvent only for C60, self-organization occurred to form a large micelle-like core-shell aggregate, probably with some C60 interlocking with each other with the collapsed PEO chains as the core. The addition of BN, a second selective solvent for core-forming PEO chains, has a significant effect on the structures and compactness of the resultant aggregates because the introduction of BN increases the stretching of the PEO chains inside the core and modifies the interfacial energy of the core-corona interface. On the other hand, for C60-PEO-C60 in pure BN, a non-solvent of C60, several smaller flower-like micelles may self-organize to form a large spherical-like aggregation complex.     

Epithelial-to-Mesenchymal Transition Is Not a Major Modulating Factor in the Cytotoxic Response to Natural Products in Cancer Cell Lines

Numerous natural products exhibit antiproliferative activity against cancer cells by modulating various biological pathways. In this study, we investigated the potential use of eight natural compounds (apigenin, curcumin, epigallocatechin gallate, fisetin, forskolin, procyanidin B2, resveratrol, urolithin A) and two repurposed agents (fulvestrant and metformin) as chemotherapy enhancers and mesenchymal-to-epithelial (MET) inducers of cancer cells. Screening of these compounds in various colon, breast, and pancreatic cancer cell lines revealed anti-cancer activity for all compounds, with curcumin being the most effective among these in all cell lines. Although some of the natural products were able to induce MET in some cancer cell lines, the MET induction was not related to increased synergy with either 5-FU, irinotecan, gemcitabine, or gefitinib. When synergy was observed, for example with curcumin and irinotecan, this was unrelated to MET induction, as assessed by changes in E-cadherin and vimentin expression. Our results show that MET induction is compound and cell line specific, and that MET is not necessarily related to enhanced chemosensitivity.     

Cyclic codes over $${{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}$$

In this work, we focus on cyclic codes over the ring \mathbbF₂+u\mathbbF₂+v\mathbbF₂+uv\mathbbF₂{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} , which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273–287, 2007) to characterize the ring (\mathbbF₂+u\mathbbF₂+v\mathbbF₂+uv\mathbbF₂)/(xⁿ-1){({{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2})/(x^n-1)} and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over \mathbbF₂+u\mathbbF₂+v\mathbbF₂+uv\mathbbF₂{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} under two Gray maps that are defined. We also characterize the binary images of cyclic codes over \mathbbF₂+u\mathbbF₂+v\mathbbF₂+uv\mathbbF₂{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} in general.     

On the perturbation determinants of a singular dissipative boundary value problem with finite transmission conditions

In this paper a singular dissipative boundary value problem with finite transmission conditions is investigated. Using Livšic’s theorem, it is proved that the system of all eigen and associated functions of this problem is complete in the Hilbert space.     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

Solving systems of fractional differential equations using differential transform method

This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.     

Application of generalized differential transform method to multi-order fractional differential equations

In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential transform method that would extended the application of the method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y^(μ)(t)=f(t,y(t),y^(β₁)(t),y^(β₂)(t),…,y^(β_n)(t)) with μ>β_n>β_n-1>…>β₁>0, combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization.