There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Fixed point theorems for α–ψ-contractive type mappings

A comparative study of Casson fluid with homogeneous-heterogeneous reactions.

Ni-based metal organic frameworks (Ni-MOFs) with unique hierarchical hollow ball-in-ball nanostructure were synthesized by solvothermal reactions. After successive carbonization and oxidation treatments, hierarchical NiO/Ni nanocrystals covered with a graphene shell were obtained with the hollow ball-in-ball nanostructure intact. The resulting materials exhibited superior performance as the anode in lithium ion batteries (LIBs): they provide high reversible specific capacity (1144 mAh/g), excellent cyclability (nearly no capacity loss after 1000 cycles) and rate performance (805 mAh/g at 15 A/g). In addition, the hierarchical NiO/Ni/Graphene composites demonstrated promising performance as anode materials for sodium-ion batteries (SIBs). Such a superior lithium and sodium storage performance is derived from the well-designed hierarchical hollow ball-in-ball structure of NiO/Ni/Graphene composites, which not only mitigates the volume expansion of NiO during the cycles but also provides a continuous highly conductive graphene matrix to facilitate the fast charge transfer and form a stable SEI layer.

Metal Organic Frameworks Derived Hierarchical Hollow NiO/Ni/Graphene Composites for Lithium and Sodium Storage

MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation

Surface modification of carbon fibers with hydrophilic Fe3O4 nanoparticles for nickel-based multifunctional composites

Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms

The aim of this paper is to introduce new concepts of --complete metric space and --continuous function and establish fixed point results for modified ---rational contraction mappings in --complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for -graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

/pdf/fixed-point-theory-in-complete-metric-spaces-with-1gll2rf8s2.pdf

Fixed Point Theory in -Complete Metric Spaces with Applications

The aim of this paper is to establish some fixed point theorems for set-valued mappings in the context of b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature. An example is also given to support our main result. MSC: 46S40, 47H10, 54H25.

/pdf/some-fixed-point-results-for-multi-valued-mappings-in-b-toigdmjt9q.pdf

Marwan Amin Kutbi

Papers

MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation

Surface modification of carbon fibers with hydrophilic Fe3O4 nanoparticles for nickel-based multifunctional composites

Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms

Fixed Point Theory in -Complete Metric Spaces with Applications

Some fixed point results for multi-valued mappings in b-metric spaces