A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers

We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano’s theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle’s theorem and Lagrange’s mean value theorem are also extended in soft setting

Optimizing the location of the colony of foragers with Collective Learning

Animal groups collaborate with one another throughout their lives to better comprehend their surroundings. Here, we try to model, using continuous random walks, how the entire process of birth, reproduction, and death might impact the searching process. We attempt to simulate an ecosystem where the post-reproductive foragers leave their colonies to discover where the targets are while others stay and breed at the base. Actually, a group of foragers searches for a location from where they access the targets for food supply. Particularly, we have explored a hypothetical situation in which the relocation to the new position depends on the agreement level of the species as well as an additional waiting time due to this agreement level. In this backdrop, detailed numerical results reveal that searching for an optimal position at an optimal mean time can be captured for a suitable range of the agreement level. We have also shown, for a given agreement level, the optimal mean time linearly increases with the Death-to-Birth ratio.Comment: 9 pages, 6 figure

Inside the plant: Bacterial endophytes and abiotic stress alleviation

Bacterial endophytes are the microbes internally associated with the plant, nourished in an isolated environment which is free from the external harsh and changeable ecological condition. They entered into the plant tissues and alleviate the biotic and abiotic stresses by producing numerous secondary metabolites. They are engaged with the de novo synthesis of structural compounds and stimulation of plant immunity. They are also involved in the process of exclusion of the pathogen by niche competition and actively take part in phenylpropanoid metabolism. Abiotic stresses in particular salinity problem, low pH, heavy metal toxicity and accumulation of recalcitrant complex compounds in the soil affecting the plant health are a major threat to the agriculture sector in crop production and stability of ecosystems. To cope with these problems agriculture productivity has been intensified by using synthetic chemicals and pesticides causes numerous problems worldwide. Endophytic bacteria are thus being utilized as a substitute to reduce the use of toxic chemicals and pesticides. They may be employed as a biological agent in the plant growth promotion and for the management of the global environment. There is a tremendous scope for the isolation and identification of new endophytic bacteria with excellent potential

Biocompatibility and cyclic fatigue response of surface engineered Ti6Al4V femoral heads for hip-implant application

A major problem with femoral head (FH) for hip implant (HI) applications is that it often fails in service. As a result, revision surgery becomes a must. The related trauma is tremendous for the patient, especially the aged ones. This also implies additional expenses. Keeping these aspects of the problem in view, here we report the development of wear, corrosion and fatigue resistant Ti6Al4V alloy based FH; by a duplex surface engineering (DSE) technique. Thus, the DSE based FHs are developed by a novel combination of plasma nitriding (PN) and Ti/TiN multilayer coating (MLC). The MLCs are formed by magnetron sputtering technique. The Ti6Al4V based FHs are called Ti. The only plasma nitrided FHs are called TiPN. The DSE based FHs are called TiPNML. The corrosion resistances are studied in hank's solution. The sliding wear resistance is studied in simulated body fluid (SBF). The biocompatibilities are studied by the standard MTT assay technique. The cyclic fatigue resistance behaviour up to one million walking cycles is studied in SBF in a HIP simulator with the UHMWPE acetabular cups used as the counter bodies in articulation. The results of the corrosion, biocompatibility, wear, and cyclic fatigue resposnses clearly reveal that the performances of the TiPNML and TiPN FHs are much better than that of the Ti based FHs. The reasons behind such spectacular improvement in biocompatibility as well as corrosion, wear and fatigue resistance are explained in terms of the prevalent phases, microstructural factors, wear mechanisms and surface roughness. The implications of the current results in terms of futuristic FH developments for HI applications are discussed. Such futuristic FH development could provide better HI. These prospects would minimize HI failure and hence, revision surgeries. Thus, the related trauma for numerous patients; especially the aged ones; could be significantly reduced

Bio-tribological response of duplex surface engineered SS316L for hip-implant application

Here we report on intelligently planned duplex surface engineering concept that utilizes a combination of plasma nitriding and multi-layering for optimizing cyclic fatigue resistance. This new concept of duplex surface engineering treatment is utilized to achieve improvement in cyclic fatigue as well as bio-tribological response of SS316L (SS) based hip-implants. The samples are SS316L (SS), Ti/TiN multi-layer-coated SS i.e., SSML and Ti/TiN multi-layer-coated plasma nitrided SS i.e., SSPNML. The samples are characterized by XRD, FESEM, TEM, nanoindentation, micro-scratch and sliding wear. In addition, cyclic fatigue behaviour up to 1 million cycles of SS and SSPNML femur heads against UHMWPE acetabular cups are studied using a hip simulator. The results prove that under comparable conditions, the nanohardness, micro-scratch resistance and sliding wear resistance of the SSPNML samples in SBF are much better than those of the corresponding SSML and SS samples. Further, as compared to the SS femoral head, the SSPNML femoral head is found to be much more resistant to cyclic fatigue. These results establish beyond doubt the superiority of the duplex surface engineering treatment utilized in the present work to achieve superb cyclic fatigue resistance in SS based femoral heads for bio-prosthetic hip implants

Nanotribological response of a plasma nitrided bio-steel

AISI 316L is a well known biocompatible, austenitic stainless steel (SS). It is thus a bio-steel. Considering its importance as a bio-prosthesis material here we report the plasma nitriding of AISI 316L (SS) followed by its microstructural and nanotribological characterization. Plasma nitriding of the SS samples was carried out in a plasma reactor with a hot wall vacuum chamber. For ease of comparison these plasma nitrided samples were termed as SSPN. The experimental results confirmed the formations of an embedded nitrided metal layer zone (ENMLZ) and an interface zone (IZ) between the ENMLZ and the unnitrided bulk metallic layer zone (BMLZ) in the SSPN sample. These ENMLZ and IZ in the SSPN sample were richer in iron nitride (FeN) chromium nitride (CrN) along with the austenite phase. The results from nanoindentation, microscratch, nanoscratch and sliding wear studies confirmed that the static contact deformation resistance, the microwear, nanowear and sliding wear resistance of the SSPN samples were much better than those. of the SS samples. These results were explained in terms of structure property correlations. (C) 2016 Elsevier Ltd. All rights reserved

Nano- and micro-tribological behaviours of plasma nitrided Ti6Al4V alloys

Plasma nitriding of the Ti-6Al-4V alloy (TA) sample was carried out in a plasma reactor with a hot wall vacuum chamber. For ease of comparison these plasma nitrided samples were termed as TAPN. The TA and TAPN samples were characterized by XRD, Optical microscopy, FESEM, TEM, EDX, AFM, nanoindentation, micro scratch, nanotribology, sliding wear resistance evaluation and in vitro cytotoxicity evaluation techniques. The experimental results confirmed that the nanohardness, Young's modulus, micro scratch wear resistance, nano wear resistance, sliding wear resistance of the TAPN samples were much better than those of the TA samples. Further, when the data are normalized with respect to those of the TA alloy, the TAPN sample showed cell viability about 11% higher than that of the TA alloy used in the present work. This happened due to the formation of a surface hardened embedded nitrided metallic alloy layer zone (ENMALZ) having a finer microstructure characterized by presence of hard ceramic Ti2N, TiN etc. phases in the TAPN samples, which could find enhanced application as a bioimplant material