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and Applied Analysis 3 Proof. As T and S form a K-Cyclic map, d x1, x2 d Tx0, Sx1 ≤ k d x0, Tx0 d x1, Sx1 1 − 2k d A,B k d x0, x1 d x1, x2 1 − 2k d A,B . 3.1 So, it follows that d x1, x2 ≤ k/ 1 − k d x0, x1 1 − k/ 1 − k d A,B . Similarly, it can be seen that d x2, x3 ≤ ( k 1 − k )2 d x0, x1 [ 1 − ( k 1 − k )2] d A,B . 3.2 Hence, it follows by induction that(More)
Let S : A→ B and T : A→ B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx = x and T x = x do not necessarily have a common solution, called a common fixed point of the mappings S and T . Therefore, in such cases of nonexistence of a common solution, it is attempted to find(More)
Assume that A and B are non-void subsets of a metric space, and that S : A −→ B and T : A −→ B are given non-self mappings. In light of the fact that S and T are non-self mappings, it may happen that the equations Sx = x and Tx = x have no common solution, named a common fixed point of the mappings S and T . Subsequently, in the event that there is no(More)
Huntington's disease (HD) is recognized as a currently incurable, inherited neurodegenerative disorder caused by the accumulation of misfolded polyglutamine (polyQ) peptide aggregates in neuronal cells. Yet, the mechanism by which newly formed polyQ chains interact and assemble into toxic oligomeric structures remains a critical, unresolved issue. In order(More)
OBJECTIVE We provide a contemporary account of the key pathologic events pertaining to autism: the theory of oxidative stress and inflammatory causes, ideas of immune dysfunction, the probable biomarkers that can be used for diagnostics, and the use of pharmaceuticals and stem cells as possible candidates for the treatment of autism spectrum disorders(More)
  • Aaron Tan, Reema Chawla, +5 authors Alexander M Seifalian
  • Journal of plastic, reconstructive & aesthetic…
  • 2016
The rapid ascent of nanotechnology and regenerative therapeutics as applied to medicine and surgery has seen an exponential rise in the scale of research generated in this field. This is evidenced not only by the sheer volume of papers dedicated to nanotechnology but also in a large number of new journals dedicated to nanotechnology and regenerative(More)
Vascularisation is often deemed the holy grail of tissue engineering because it is one of the key preconditions that determine the in vivo viability of tissue constructs. Given that a well-developed vascular network allows greater complexity in tissue design and helps regulate tissue metabolism, it appears that the overall outcome of engineered tissue(More)
Nanotechnology has the power to transform neurosurgery by facilitating intervention at the cellular and subcellular level. The unique properties of nanomaterials will not only improve the management of conditions traditionally treated through neurosurgery, but also make neurosurgical intervention possible for diseases where there are currently limited(More)
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