Invariant circles and phase portraits of cubic vector fields on the sphere

In this paper, we characterize and study dynamical properties of cubic vector fields on the sphere $\mathbb{S}^2 = \{(x, y, z) \in \mathbb{R}^3 ~|~ x^2+y^2+z^2 = 1\}$. We start by classifying all degree three polynomial vector fields on $\mathbb{S}^2$ and determine which of them form Kolmogorov systems. Then, we show that there exist completely integrable cubic vector fields on $\mathbb{S}^2$ and also study the maximum number of various types of invariant circles for homogeneous cubic vector fields on $\mathbb{S}^2$. We find a tight bound in each case. Further, we also discuss phase portraits of certain cubic Kolmogorov vector fields on $\mathbb{S}^2$.Comment: 17 pages. Comments are welcom

Parameterized Approximation Scheme for Feedback Vertex Set

Feedback Vertex Set (FVS) is one of the most studied vertex deletion problems in the field of graph algorithms. In the decision version of the problem, given a graph G and an integer k, the question is whether there exists a set S of at most k vertices in G such that G-S is acyclic. It is one of the first few problems which were shown to be NP-complete, and has been extensively studied from the viewpoint of approximation and parameterized algorithms. The best-known polynomial time approximation algorithm for FVS is a 2-factor approximation, while the best known deterministic and randomized FPT algorithms run in time ?^*(3.460^k) and ?^*(2.7^k) respectively. In this paper, we contribute to the newly established area of parameterized approximation, by studying FVS in this paradigm. In particular, we combine the approaches of parameterized and approximation algorithms for the study of FVS, and achieve an approximation guarantee with a factor better than 2 in randomized FPT running time, that improves over the best known parameterized algorithm for FVS. We give three simple randomized (1+?) approximation algorithms for FVS, running in times ?^*(2^{?k}? 2.7^{(1-?)k}), ?^*(({(4/(1+?))^{(1+?)}}?{(?/3)^?})^k), and ?^*(4^{(1-?)k}) respectively for every ? ? (0,1). Combining these three algorithms, we obtain a factor (1+?) approximation algorithm for FVS, which has better running time than the best-known (randomized) FPT algorithm for every ? ? (0, 1). This is the first attempt to look at a parameterized approximation of FVS to the best of our knowledge. Our algorithms are very simple, and they rely on some well-known reduction rules used for arriving at FPT algorithms for FVS

Designing of Chitosan-Based Scaffolds for Biomedical Applications

Thesis (Ph.D.)--University of Washington, 2012Chitosan is a favorable natural polymer for biomedical application for its biocompatible, biodegradable, non-toxic, and hydrophilic properties. It has a chemical structure analogous to glycosaminoglycans, a component of extracellular matrix, indicating its potential bioactivity. However, chitosan's low mechanical strength precludes pristine chitosan scaffolds from tissue engineering. To achieve higher mechanical strength, different reinforcing agents are incorporated into the scaffold system; however, improved mechanical properties are obtained at the cost of compromised structure, porosity, and biological properties of the scaffold. Therefore, pristine chitosan is often preferred over its composites in biomedical applications due to its superior biological properties. This dissertation research presents several novel approaches such as controlling chitosan concentration in scaffold, applying the right temperature gradient, and developing a modular-collector electrospinning system to fabricate chitosan scaffolds with higher mechanical properties and appropriate morphology, pore size, and porosity for different tissue engineering uses, including bone and muscle. In the first approach, we controlled chitosan concentration in acidic solution to increase the crystallinity of chitosan scaffolds and thus fabricate stiffer scaffolds. Scaffolds of increased chitosan concentration, i.e., with greater mechanical strength, showed efficient bone tissue engineering with improved adhesion, proliferation, and osteogenic activity of MG-63 osteoblast cells. In the second approach, we applied appropriate temperature gradients to control pore size and porosity of the scaffold by regulating the rate of ice crystal formation in chitosan solution. Thus, we produced uniaxial tubular porous chitosan scaffolds with pore size and mechanical properties comparable to those of native skeletal muscle tissues. These scaffolds demonstrated the ability to align muscle cells, guide and promote cell fusion, and produce thick myotubes. In the third approach, we developed a novel portable electrospinning system with a modular-collector to control scaffold shape. This approach produced chitosan-based aligned nanofibrous cylindrical, tubular, and membrane scaffolds for different tissue engineering. In a model application, muscle cells cultured on chitosan-based cylindrical and tubular scaffolds showed their effectiveness in producing highly aligned and densely populated myotubes required for muscle tissue engineering. In the fourth approach, we developed a novel hybrid substrate in which a stripe-pattern chitosan substrate, several microns in thickness, is overlaid on a chitosan-based aligned nanofibrous membrane paralally to mimic native micro/nano environment. The results from muscle cell culture showed a higher level of expression of later-stage differentiation genes such as myogenin and myosin heavy chain on the hybrid substrate compared to that found on only nanofibrous membrane or stripe-pattern chitosan substrate. Finally, we stacked cell-cultured substrates to produce 3D tissue-engineered scaffold constructs. These findings prove chitosan's effectiveness as a material that can be used to design and develop scaffolds of required native forms with controlled structure, size, porosity, and mechanical properties for different tissue engineering needs

Interaction of DNA bases with silver nanoparticles: Assembly quantified through SPRS and SERS

Colloidal silver nanoparticles were prepared by reducing silver nitrate with sodium borohydride. The synthesized silver particles show an intense surface plasmon band in the visible region. The work reported here describes the interaction between nanoscale silver particles and various DNA bases (adenine, guanine, cytosine, and thymine), which are used as molecular linkers because of their biological significance. In colloidal solutions, the color of silver nanoparticles may range from red to purple to orange to blue, depending on the degree of aggregation as well as the orientation of the individual particles within the aggregates. Transmission electron microscopy (TEM), X-ray diffraction (XRD), and absorption spectroscopy were used to characterize the assemblies. DNA base-induced differential silver nanoparticle aggregation was quantified from the peak separation (relates to color) of surface plasmon resonance spectroscopy (SPRS) and the signal intensity of surface-enhanced Raman scattering (SERS), which rationalize the extent of silver–nucleobase interactions. © 2008 Published by Elsevier Inc

Electrical Conductivity Of Nanocomposites With Lithium Compound And Gold Nanoparticles

Electrical conductivity of polymers may be increased with the addition of conductive fillers as minor phases. We prepared nanocomposite films through the addition of lithium hexafluorophosphate (LiF6P), an alkali metal salt, and gold nanoparticles (AuNPs), as minor phase materials into poly (methyl methacrylate) (PMMA). Though an improved conductivity of the PMMA film specimen with LiF6P was observed, it did not occur with AuNPs. PMMA/LiF 6P and PMMA/AuNPs solutions were prepared separately in different ratios to achieve 0.20, 0.50, 0.75 and 1.00 wt % of LiF6P in PMMA and 0.2 wt% of AuNPs in PMMA. Electrical conductivity was measured on nanocomposite samples with the mentioned contents of LiF6P and AuNPs. The nanocomposite films with LiF6P show improved electrical conductivity, and the sample with 0.75 wt% LiF6P has the highest conductivity value with an improvement of three orders of magnitude compared to that of the pure PMMA film. However, the film sample with only AuNPs did not show any obvious change in its electrical conductivity. The mechanism of the conductivity improvement was examined by FTIR analysis

Bottom-up synthesis of bright fluorescent, moisture-resistant methylammonium lead bromide@poly(3-bromothiophene)

Colloidal organic-inorganic lead halide perovskites have gained tremendous attention due to their excellent optical properties and promising future in optoelectronic applications. However, the lack of large scale synthesis methods and structural instability in moisture conditions restrict their practical applications. We report, for the first time, a gram-scale aqueous synthesis of MAPbBr(3) (MA = CH3NH3+) using PbCO3, bottom-up synthesis of MAPbBr(3) NCs and in situ bottom-up synthesis of MAPbBr(3)@poly(3-bromothiophene) nanocomposite. The synthesized nanocomposite material exhibits bright green fluorescence and excellent water-resistivity. Together, the polymer-based bottom-up and in situ encapsulation strategy of MAPbBr(3) NCs will pave the way for synthesizing other lead halide water-resistant perovskites that will be used in thin-film based light-emitting devices

Redox-Active Nanoceria Depolarize Mitochondrial Membrane Of Human Colon Cancer Cells

Nanotherapeutics is emerging as a promising option to the various limitations and side effects associated with conventional chemotherapy. The present study investigates the cytotoxic effect of redox-active cerium oxide nanoparticles (nanoceria) on human colorectal adenocarcinoma-derived cell line (HCT 15). Exposure of these cells to nanoceria for 24 h with concentration ranging between 10 and 100 μM resulted in a significant reduction of cell viability in a dose-dependent manner. Further, at a concentration of 10 μM, nanoceria exhibited time-dependent cytotoxic effect when exposed to the cells for 24, 48, and 72 h. Upon treatment of the cells with nanoceria, reactive oxygen species (ROS) and lipid peroxidation which are indicators of oxidative stress and cytotoxicity increased significantly, in a dose-dependent manner. Nanoceria was also found to depolarize the mitochondrial membrane, thereby collapsing the membrane potential and leading to initiation of apoptosis. Scanning electron microscopic study of nanoceria-treated HCT 15 cells showed morphological changes and loss of filopodia and lamellipodia, indicating arrest of metastatic spread. Summarizing, when cultured HCT 15 cells are exposed to nanoceria, a dose-dependent cytotoxic effect mediated by ROS generation is observed. © Springer Science+Business Media 2014

Preparation And Properties Of Natural Sand Particles Reinforced Epoxy Composites

An epoxy composite using Cancun natural hydrophobic sand particle as filler material was fabricated in this study. Three point bending tests demonstrated an enhancement of 7.5 and 8.7% in flexural strength and flexural modulus, respectively, of epoxy composite containing 1 wt-% sand particles without any chemical treatment involved, compared to the pristine epoxy. Scanning electron microscopy (SEM) studies revealed that the fracture toughness of the epoxy matrix was enhanced owing to the presence of sand particles in an epoxy/sand composite. Through dynamic mechanical analysis (DMA) and thermal mechanical analysis (TMA) methods, it was found that the storage modulus (E′), glass transition temperature (Tg) and dimensional stability of the sand particles/ epoxy composites were increased compared to the pristine epoxy. The friction behavior of epoxy/sand system reflected that the microstructure of epoxy composites was steady. These experimental results suggest that Cancun sand, as a freshly found natural micron porous material, may find promising applications in composite materials. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA