Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Calculating the derivative of piecewise functions

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

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.

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.

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.

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.