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  1. Fundamentals and Applications
  2. Functional Analysis
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Presented from the point of view This book offers a self-contained introduction to partial differential equations PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. The Second Toggle navigation. New to eBooks. Cornerstones Series. Filter Results. Last 30 days Last 90 days All time. English Only. All PDF Epub. Add to Cart Add to Cart. Add to Wishlist Add to Wishlist. View More. Hermitian Analysis 2nd ed. Geometric Integration Theory Steven G.

Krantz , Harold R. Advanced Algebra Anthony W. Basic Algebra Anthony W. Well-dispersed NFAs were prepared through pyrolysis. Results and discussion: Transmission electron microscopy revealed the average nanoparticle size to be 7. Conclusion: The ability of NFA—MTX to dissociate under the influence of an applied magnetic field provides a new strategy to induce cancer cell death via hyperthermia. Applications in drug delivery, drug development, and cancer research are expected.

Keywords: iron—gold nanoparticles, methotrexate, hyperthermia, superparamagnetic, controlled drug release. Nanotechnology has recently emerged as an indispensable area of research, with applications in all fields of science.

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Nanoparticles, in particular, have revolutionized the medical industry by finding applications in pharmaceutics, 1 diagnostics, 2 and drug delivery. Single metal as well as metal alloy nanoparticles are exploited in the fields of catalysis, 5 imaging, 6 and biomedical 7 or tissue engineering. Additionally, the nano size of these particles makes it easier for them to be ingested by cells, where they can conveniently interact with cellular components and provide useful information about biological processes.

Cancer continues to be the leading cause of death in both developing and developed countries, with an estimated , deaths in in the USA alone. Such cells also show an increase in migration and invasion potential, 18 which may possibly lead to the establishment of fresh cancer colonies throughout the body. Various methods such as radiotherapy and chemotherapy have been proposed to induce cell apoptosis and limit cancer cell multiplication. Different cancer types display different characteristics because of variations in the cellular population, thereby rendering a single drug ineffective against multiple cancers.

This complicates the already challenging task of limiting cancer metastasis. Furthermore, while the nonspecific distribution of chemotherapy drugs in vivo, accompanied with rapid clearance, significantly limits the drug potency, administering drugs at higher dosage is undesirable as it often poses a serious cytotoxic threat. To overcome the conventional drawbacks of chemotherapy, a variety of drug carriers such as polymeric nanoparticles, 19 polymeric micelles, 20 dendrimers, 21 liposomes, 22 magnetic nanoparticles MNPs , 23 and silica 24 or gold nanoparticles 25 have been used to achieve targeted drug delivery TDD.

MNPs have gained considerable attention in recent years because of their superparamagnetic nature, 26 finding applications in gene delivery, 27 contrast-enhancing agents, 28 tissue repair, 29 and bioseparation. This is due to the ease of functionalization of drug molecules onto MNPs, after which they can be magnetically guided to the site of action, making them ideal candidates for TDD. A major benefit of TDD is that it ensures the safety of healthy cells or tissues surrounding the diseased stroma.

Another technique to limit cancer cell growth is hyperthermia, which triggers cell death through necrosis and apoptosis. An interesting yet unexplored alternative to hyperthermia in cancer therapy is the use of heat generated by MNPs under the influence of a magnetic field, which induces the release of chemotherapy drugs from the drug—MNP conjugate, ultimately triggering cancer cell death. This technique may act as a cornerstone in the use of hyperthermia for cancer therapy, whereby the magnetic field strength can be modulated to control the amount of drug release and ultimately improve the chemotherapeutic drug potency.

Our previous study showed the potential of iron—gold Fe—Au alloy nanoparticles NFAs to induce hyperthermia. We reported the generation of 1. To achieve this, methotrexate MTX , a chemotherapy drug, was covalently functionalized onto NFA via 2-aminoethanethiol grafting, and the effect of an external magnetic field on drug release was studied. The selectively higher absorption of the NFA—MTX conjugate by cancer cells in contrast to that by normal fibroblasts was also reported.

According to our results, the application of an external magnetic field can induce the degradation of the NFA—MTX conjugate. This leads to the active release of MTX, which is then selectively ingested by cancer cells, eventually triggering cell death. Thus, the ability of this NFA—drug conjugate to degrade as a function of the applied magnetic field provides an alternate way of utilizing hyperthermia in cancer therapy and presents a possible application of NFAs as drug carriers.

Applications in cancer research, biomedical engineering, and drug delivery are expected. Ferrous sulfate 7-hydrate and toluene were purchased from Echo Chemical Taiwan. Absolute ethanol was purchased from J. Baker Taiwan. NFAs were prepared using the pyrolysis method, as described elsewhere. Dimethylammonium bromide 0. Iron sulfate heptahydrate 0. After 2 min, 1. After another 20 min, 1. When the color of the above solution turned red, 1.

The color of the solution turned purple and slowly faded. The solution was stirred for 30 min, after which 0. The synthesized NFAs were mixed with ethanol and centrifuged at 7, rpm for 15 min. The precipitate was washed several times with ethanol and chloroform. The dark-green solid sample was collected, dried in vacuum for 10 h, and finally placed in the presence of a magnetic field for magnetic separation.

The magnetically induced portion was collected and characterized. At least 50 measurements were taken to calculate the average nanoparticle size. Laser light of nm was used for the analysis. In the first step, 1 mg of NFAs and 10 mg of 2-aminoethanethiol were mixed in anhydrous alcohol ethanol. The product was then washed three times with ethanol and purified.

Fundamentals and Applications

Subsequently, 1-ethyl 3-dimethylaminopropyl carbodiimide hydrochloride 75 mM and N -hydroxysuccinimide 15 mM were dissolved in 17 mL of DI water to form solution B. Solutions A and B were mixed together, the pH was adjusted to 8. The product was washed several times. Cell cultures were maintained for 24 h, after which they were washed three times with 1 mL of RPMI serum-free medium, trypsinized, and dissolved in 1 mL of nitric acid. Inductively coupled plasma mass spectrometry ICP-MS was then performed to measure the iron ion concentration. The cells were cultured for 24 h and exposed to an AC magnetic field for 20 min.

Five different experimental conditions were established at this point. Condition 1 consisted of cells cultured in NFAs.

Functional Analysis

Condition 2 consisted of cells cultured in NFAs and exposed to a magnetic field for 20 min. Condition 5 consisted of cells in MTX only. After treatment, the cell culture medium was removed and the WST-8 assay Sigma-Aldrich was performed. WST-8 is a water-soluble tetrazolium salt used to assess cell metabolic activity. Cells seeded in culture wells in standard medium were used as controls.

Unpaired-samples t -test SPSS Results from each group were first normalized with respect to the control group and then expressed as graphs. NFAs were synthesized through the pyrolysis process using iron sulfate heptahydrate and hydrogen tetrachloroaurate as sources of iron and gold, respectively. TEM was used to analyze the morphology and size of the nanoparticles Figure 2A , revealing that round NFAs had an average diameter of 2. In our previous study, we observed the average size of the NFA to be 3.

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  • [Full text] Iron–gold alloy nanoparticles serve as a cornerstone in hyperthe | IJN.

The estimated volume of the particles was Furthermore, the absence of any arbitrary peaks also confirmed the purity of the NFAs. Figure 2 Characterization of NFAs.

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An interesting aspect to consider at this point is the shape of the nanoparticles. Some studies have reported a modulation in the properties of nanoparticles with their shape. Further experiments will be required to confirm this hypothesis. NFA does not show any distinct peaks or bends because of the absence of any functional groups.

One of the key factors limiting the applications of chemotherapy drugs is the lack of techniques to control their release. The uncontrolled release of a drug can be lethal to the nearby healthy tissues. Therefore, to overcome this issue, in the next step, we analyzed the effect of the duration of AMF on drug release. The NFA—MTX conjugate was subjected to an external magnetic field frequency: —1, kHz for 10, 20, and 30 min, and absorption at nm was measured. Pure NFA did not show any representative peak at nm. However, after 10 min of exposure, a distinct MTX peak was observed at nm.

The absorption at this time point was 0. This is one of the key findings of this research, whereby controlled drug release using MNPs is demonstrated. Quantitative release of MTX was also observed. Absorption of free MTX at fixed concentrations of 0. Previous studies have reported the generation of 1. One of the major limitations of using chemotherapy drugs for cancer treatment is their nonspecific absorption by healthy stroma, leading to cell death.

To counter this, we chose MTX because of its proven higher absorption by cancer cells compared to that by normal cells. The 1. Notes: L and HepG2 cells were incubated in 0. As shown in the past by Kohler et al, 37 MTX uptake by breast cancer MCF-7 cells was nearly 16 folds higher compared to that by cardiomyocytes. Our results are consistent with the previous studies as we observed a 1. While the ratio of drug intake by HepG2 to L was not as high as that observed by Kohler et al, 37 the cell lines used in the two studies may be the explanation for this difference.

Nevertheless, the release of MTX via hyperthermia will evidently be ubiquitous. Another important aspect is the position of the bond at which cleavage occurs for active MTX release.

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  4. We hypothesize that after being ingested by cells, the NFAs find their way into the lysosomal compartment of the cells, wherein low pH and proteases degrade the amide bond, causing efficient release of MTX in its active form. This hypothesis is backed by similar experiments conducted by Kohler et al. All nanoparticle—drug conjugates possess a certain extent of cytotoxicity. A nanoparticle—drug conjugate with lower cytotoxicity will ensure less damage to the healthy stroma surrounding the cancer cells.

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    In contrast, at the same concentration 0. Similar results were also obtained after 48 h of incubation. Strikingly, at the same concentration 0. Figure 7 WST-8 assay performed to measure the relative cell viability. Notes: HepG2 cells were cultured in different concentrations 0.