Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method

In this article, the sub‐equation method is presented for finding the exact solutions of a nonlinear fractional partial differential equations. For this, the fractional complex transformation method has been used to convert fractional‐order partial differential equation to ordinary differential equation. The fractional derivatives are described in Jumarie's the modified Riemann–Liouville sense. We apply to this method for the nonlinear time fractional differential equations. With the aid of symbolic computation, a variety of exact solutions for them are obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Counting and enumerating aggregate classifiers

We propose a generic model for the “weighted voting” aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to enumerate the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions.     

Identification of Natural Compounds as Inhibitors of Pyruvate Kinase M2 for Cancer Treatment

The reliance of tumor cells on aerobic glycolysis is one of the emerging hallmarks of cancer. Pyruvate kinase M2 (PKM2), an important enzyme of glycolytic pathway, is highly expressed in a number of cancer cells. Tumor cells heavily depend on PKM2 to fulfill their divergent energetic and biosynthetic requirements, suggesting it as novel drug target for cancer therapies. Based on this context, we performed enzymatic-assay-based screening of the in-house phenolic compounds library for the identification of PKM2 inhibitors. This screening identified silibinin, curcumin, resveratrol, and ellagic acid as potential inhibitors of PKM2 with IC₅₀ values of 0.91 µM, 1.12 µM, 3.07 µM, and 4.20 µM respectively. For the determination of Ki constants and the inhibition type of hit compounds, Lineweaver–Burk graphs were plotted. Silibinin and ellagic acid performed the competitive inhibition of PKM2 with Ki constants of 0.61 µM and 5.06 µM, while curcumin and resveratrol were identified as non-competitive inhibitors of PKM2 with Ki constants of 1.20 µM and 7.34 µM. The in silico screening of phenolic compounds against three binding sites of PKM2 provided insight into the binding pattern and functionally important amino residues of PKM2. Further, the evaluation of cytotoxicity via MTT assay demonstrated ellagic acid as potent inhibitor of cancer cell growth (IC₅₀ = 20 µM). These results present ellagic acid, silibinin, curcumin, and resveratrol as inhibitors of PKM2 to interrogate metabolic reprogramming in cancer cells. This study has also provided the foundation for further research to validate the potential of identified bioactive entities for PKM2 targeted-cancer therapies.     

Electrochemical Detection of Epinephrine Based on a Screen-printed Electrode Modified with NiO−ERGO Nanocomposite Film

This study presents a new electrochemical sensor (NiO−ERGO/SPE) for sensitive and selective detection of epinephrine (EPI) on the screen-printed electrode (SPE) which is modified with a nanocomposite film consisting of electrochemically reduced graphene oxide and NiO nanoparticles. After surface functionalization, structural and electrochemical characterization of NiO−ERGO film, DPV signals of NiO−ERGO/SPE towards the oxidation of EPI exhibited a linear correlation in the concentration range of 0.025 μM to 175 μM with a detection limit of 0.015 μM, which reveals NiO−ERGO film is manifested a good electrocatalytic activity for EPI detection compared with the previous reports. The selectivity of NiO−ERGO film was also tested on a very wide scale of possible interferents (ascorbic acid, uric acid, dopamine, lactic acid, phenylalanine, tyrosine, tryptophan, Li⁺, Na⁺, K⁺, Ca²⁺, and Zn²⁺). Moreover, to evaluate the applicability of the proposed sensor for real sample analysis, NiO−ERGO/SPE was successfully utilized for the determination of EPI in pharmaceutical samples.     

Determination of the Rheological Properties of Polypropylene Filled with Colemanite

Colemanite (Ca₂B₆O₁₁.H₂O) in powder form was filled to polypropylene (PP) at concentrations of 5, 7.5, 11.25, 16.875, and 25.312 wt%, and filled PP granules were obtained. To prevent oxidation, an antioxidant (Songnox 1010) was added to the colemanite‐filled polypropylene mixture at a ratio of 0.2 wt%. The rheological properties of the resulting composite material were determined using a Melt Flow Index testing device, at four separate pressure settings (298.2, 524, 689.5, and 987.4 kPa) and four separate temperature settings (190°C, 200°C, 210°C, and 220°C). The viscosity, shear rate, shear stress, and power law index (n) values of the colemanite‐filled PP were measured as part of the testing conducted. The study determined that viscosity values increased by approximately 60% in response to increasing colemanite content in the resulting filled material, while shear rate values decreased by 62%. The viscosity values were found to decrease with increasing temperature and pressure values, while shear rate values were found to increase. Additionally, Power Law Index value was found to vary between 0.561 and 0.687, with an average value of 0.608 based on the colemanite content used. Copyright © 2017 John Wiley & Sons, Ltd.     

Comparison of irradiation effects of electrons and gamma rays on PVC samples

Samples of polyvinyl chloride (PVC) were irradiated at a dose of 15 MGy using both electrons and gamma rays. The resultant material shows differences attributed to the very different dose rates in each type of radiation. In addition, a method useful in separating the highly cross-linked portion of the sample has been tested. Transmission electron microscopy, electron stimulated desorption and energy dispersive spectroscopy have been applied in the characterization of the irradiated material. We show that this resultant material, after irradiation, consists mainly of carbon-like material with distinct crystallographic phases which, in some cases, resemble graphitic structures.     

Compatibilization of recycled and virgin PET with radiation-oxidized HDPE

Blends of high-density polyethylene (HDPE), which cross-links on radiation, and both, recycled and pristine polyethylene terephtalate (PET), one of the most radiation-stable polymers, that contain aromatic groups, which are effective at dissipation of the energy of the ionizing radiation, were irradiated with gamma rays, in order to form a copolymer capable of improving the compatibility of the blend HDPE/PET. Due to the low content of the PET in the resulting copolymer, blends PET and radiation-oxidized HDPE, were also studied. The tensile and flexural properties were improved when the PET content was increased and when the HDPE was pre-irradiated; the largest increase in the mechanical properties was observed for PET contents between 10% and 20% (w/w). The improvement in the properties is believed to occur because of a percolation effect of the PET in the HDPE matrix and the radiation-improved compatibility by means of polar groups formed in the polyethylene. However, impact properties were observed to decrease when the PET content increased in spite of the irradiation.     

Electron beam irradiation effects on poly(ethylene terephthalate)

Changes in poly(ethylene terephthalate) subjected to electron beam irradiation at doses up to 15 MGy and dose rate of 1.65 MGy/h, were investigated by differential scanning calorimetry, molecular weight measurement, X-ray photoelectron spectroscopy, and scanning electron microscopy. Irradiated samples showed a decrease of molecular weight with a minimum at 5 MGy, which is attributed to chain scission of the macromolecules and then an increase at further doses due to branching and some degradation effect. Irradiation in air is not an important factor because the high dose rate of irradiation inhibits oxygen diffusion in the samples.     

On the non-commutative neutrix product (x + r lnx +) ox − −s

The non-commutative neutrix product of the distributionsx ₊ ^r lnx ₊ andx _– ^–s is evaluated forr=0, 1, 2, ands=1, 2, . Further neutrix products are then deduced.