Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Fractional Korovkin Theory Based on Statistical Convergence

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.

Fractional Trigonometric Korovkin Theory in Statistical Sense

2000 Mathematics Subject Classification: 41A25, 41A36.

Fiber Scaffolds of Poly (glycerol-dodecanedioate) and its Derivative via Electrospinning for Neural Tissue Engineering

Peripheral nerves have demonstrated the ability to bridge gaps of up to 6 mm. Peripheral Nerve System injury sites beyond this range need autograft or allograft surgery. Central Nerve System cells do not allow spontaneous regeneration due to the intrinsic environmental inhibition. Although stem cell therapy seems to be a promising approach towards nerve repair, it is essential to use the distinct three-dimensional architecture of a cell scaffold with proper biomolecule embedding in order to ensure that the local environment can be controlled well enough for growth and survival. Many approaches have been developed for the fabrication of 3D scaffolds, and more recently, fiber-based scaffolds produced via the electrospinning have been garnering increasing interest, as it offers the opportunity for control over fiber composition, as well as fiber mesh porosity using a relatively simple experimental setup. All these attributes make electrospun fibers a new class of promising scaffolds for neural tissue engineering. Therefore, the purpose of this doctoral study is to investigate the use of the novel material PGD and its derivative PGDF for obtaining fiber scaffolds using the electrospinning. The performance of these scaffolds, combined with neural lineage cells derived from ESCs, was evaluated by the dissolvability test, Raman spectroscopy, cell viability assay, real time PCR, Immunocytochemistry, extracellular electrophysiology, etc. The newly designed collector makes it possible to easily obtain fibers with adequate length and integrity. The utilization of a solvent like ethanol and water for electrospinning of fibrous scaffolds provides a potentially less toxic and more biocompatible fabrication method. Cell viability testing demonstrated that the addition of gelatin leads to significant improvement of cell proliferation on the scaffolds. Both real time PCR and Immunocytochemistry analysis indicated that motor neuron differentiation was achieved through the high motor neuron gene expression using the metabolites approach. The addition of Fumaric acid into fiber scaffolds further promoted the differentiation. Based on the results, this newly fabricated electrospun fiber scaffold, combined with neural lineage cells, provides a potential alternate strategy for nerve injury repair.

Table 1 Core site, fractional abundance of individual isoprenoid GDGTs and TEX86 values

TEXL86 and TEXH86 are organic palaeothermometers based on the lipids of Group 1 Crenarchaeota, recently proposed as a modified version of the original TEX86 index, but with significantly improved geographical coverage. Since few data from the global core top calibration are from the Pacific, this study was carried out to assess whether the global core top calibration is regionally biased or not. The result of principal components analysis of the fractional abundance of GDGTs, an analysis of variance (ANOVA) and the comparison of the residuals of TEXH 86 derived sea surface temperature (SST) estimates of the Pacific subset with that of the global data set suggest that the Pacific subset has a similar TEXH 86-SST relationship with the global data set. However, the regression line through the Pacific data and an ANOVA on the residuals of TEXL 86 derived SST estimates suggest otherwise. The contradictory findings are likely to stem from the large scatter in the Pacific TEXL 86 values in the mid temperature range. While regionality does not seem to exert a strong bias on TEXL 86 and TEXH 86 calibration, it appears that there is a strong need to resolve the large scatter in the global data set, especially in the mid and high latitudes, in order to improve the calibration for a better SST estimation.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Fractional order of poling period for broadly tunable second harmonic generation

We demonstrate the possibility to use a fractional order of poling period of nonlinear crystal waveguides for tunable second harmonic generation. This approach allows one to extend wavelength coverage in the visible spectral range by frequency doubling in a single crystal waveguide.

A transatlantic case: the derivative action as a corporate governance tool

The derivative action as a minority shareholder protection device seems to be almost a dead-letter law in the British Isles as compared with the United States. Whether it can or should be revived through legislative reform and judicial interpretation presents us with important governance questions at first instance, but also raises questions regarding the importance of law, as distinct from non-legally enforceable norms, to the development of corporate governance systems, in particular regarding the director-shareholder relationship.

Fractional abundances of isoprenoid and branched glycerol dialkyl glycerol tetraethers (GDGT) of cores SO201-2-12KL and SO201-2-114KL

It has been proposed that North Pacific sea surface temperature (SST) evolution was intimately linked to North Atlantic climate oscillations during the last glacial-interglacial transition. However, during the early deglaciation and the Last Glacial Maximum, the SST development in the subarctic northwest Pacific and the Bering Sea is poorly constrained as most existing deglacial SST records are based on alkenone paleothermometry, which is limited prior to 15 ka B.P. in the subarctic North Pacific realm. By applying the TEXL86 temperature proxy we obtain glacial-Holocene-SST records for the marginal northwest Pacific and the Western Bering Sea. Our TEXL86-based records and existing alkenone data suggest that during the past 15.5 ka, SSTs in the northwest Pacific and the Western Bering Sea closely followed millennial-scale climate fluctuations known from Greenland ice cores, indicating rapid atmospheric teleconnections with abrupt climate changes in the North Atlantic. Our SST reconstructions indicate that in the Western Bering Sea SSTs drop significantly during Heinrich Stadial 1 (HS1), similar to the known North Atlantic climate history. In contrast, progressively rising SST in the northwest Pacific is different to the North Atlantic climate development during HS1. Similarities between the northwest Pacific SST and climate records from the Gulf of Alaska point to a stronger influence of Alaskan Stream waters connecting the eastern and western basin of the North Pacific during this time. During the Holocene, dissimilar climate trends point to reduced influence of the Alaskan Stream in the northwest Pacific.

Targeting treatment resistant breast cancer stem cells with FKBPL and its peptide derivative, AD-01

FKBPL and its peptide derivative, AD-01, have already demonstrated well-established inhibitory effects on breast cancer growth and CD44 dependent anti-angiogenic activity1, 2, 3. Since breast cancer stem cells (BCSCs) are CD44 positive, we wanted to explore if AD-01 could specifically target BCSCs. FKBPL stable overexpression or AD-01 treatment were highly effective at reducing the BCSC population measured by inhibiting mammosphere forming efficiency (MFE) in cell lines and primary breast cancer samples from both solid breast tumours and pleural effusions. Flow cytometry, to assess the ESA+/CD44+/CD24- subpopulation, validated these results. The ability of AD-01 to inhibit the self-renewal capacity of BCSCs was confirmed across three generations of mammospheres, where mammospheres were completely eradicated by the third generation (p<0.001). Clonogenic assays suggested that AD-01 mediated BCSC differentiation, with a significant decrease in the number of holoclones and an associated increase in meroclones/paraclones. In support of this, the stem cell markers, Nanog and Oct4 were significantly reduced following AD-01 treatment, whilst transfection of FKBPL-targeted siRNAs led to an increase in these markers and in mammosphere forming potential, highlighting the endogenous role of FKBPL in stem cell signalling. The clinical relevance of this was confirmed using a publically available microarray data set (GSE7390), where, high FKBPL and low Nanog expression were independently associated with improved overall survival in breast cancer patients (log rank test p=0.03; hazard ratio=3.01). When AD-01 was combined with other agents, we observed synergistic activity with the Notch inhibitor, DAPT and AD-01 was also able to abrogate a chemo- and radiotherapy induced enrichment in BCSCs. Importantly, using ‘gold standard’ in vivo limiting dilution assays we demonstrated a delay in tumour initiation and reoccurrence in AD-01 treated xenografts. In summary, AD-01 appears to have dual anti-angiogenic and anti-BCSC activity which will be advantageous as this agent enters clinical trial.