A fixed point theoremfor nonexpansive compact self-mapping

A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B. B. Williams [J. Math. Anal. Appl. 74 (1980), 382-387] and of Yoichi Kijima and Wataru Takahashi [Kodai Math Sem. Rep. 21 (1969), 326-330]

Metrically Round and Sleek Metric Spaces

A round metric space is the one in which closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which interior of each closed ball is the corresponding open ball. In this, article we establish some results on round metric spaces and sleek metric spaces.Comment: 13 pages, 10 Figure

On strong proximinality in normed linear spaces

The paper deals with strong proximinality in normed linear spaces. It is proved that in  a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and  approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed

Round and sleek subspaces of linear metric spaces and metric spaces

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the present article discusses more results on such spaces along with identification of round and sleek subsets of linear metric spaces and metric spaces in the subspace topology.Comment: 14 pages, 1figur

In silico evolution of diauxic growth

The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture. Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves. As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited. However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency. Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression

Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré superlattice

The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other