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In this paper existence and uniqueness of fixed points are proved for self maps, satisfying a new contraction without assuming the compatibility and commutative property of maps. Some remarks and applications to integral type contraction are given to illustrate the importance of our results. An open problem for future research is also given.

The selective laser sintering (SLS) of an yttria (Y2O3) ceramic powder was studied to understand both the effects of i) the initial yttria particle characteristics on the powder bed behaviour and ii) the process conditions (laser power, scanning speed, hatching space) on the sintering/melting of three-dimensionally printed objects. The roughness of the powder bed, a sensitive indicator of the layer bed quality, was determined through three-dimensional optical profilometry and the powder bed packing density was modelled using the discrete-element method. Complex shaped objects including spheres and open rings were successfully fabricated by the SLS three-dimensional printing. In addition, SLS cube-shaped samples were characterized by X-ray diffraction and scanning electron microscopy. The open pore volume fraction significantly decreased from 41% without a post-SLS heat treatment to 31% with a post-SLS heat treatment at 1750 °C for 20 h under secondary vacuum. Finally, an anisotropy in elastic properties has been highlighted, Young's modulus reaches 11 GPa in the stiffest direction.

In this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.

Our aim in this communication is to present a new type of contraction and common fixed point results for non-continuous self mappings without using the compatibility and commutative property. Moreover, we have found common fixed point without using the Cauchy's criterion for convergence. Some illustrative examples with graphical representation and remarks are given to justify that the contraction introduced in the main result is new and unique, which will be useful for future researches.

Time period of natural transverse vibration of a nonhomogeneous skew (parallelogram) plate with variable thickness and temperature field has been investigated on clamped CCCC and combination of clamped and simply supported CSCS edge conditions. The thickness variation on the plate is assumed to be linear in two dimensions, and the temperature variation on the plate is considered to be parabolic in two dimensions. For nonhomogeneity, authors considered circular variation in density. The Rayleigh–Ritz technique is applied to solve the differential equation of motion. A comparative analysis of frequency modes of the present study with the available published result is also given to support the present findings. The convergence study of obtained results is also presented with the help of figures.

Frequencies comprising two-dimensional circular thickness impacts are computed for the first time, for clamped rectangle plate under nonhomogeneity and temperature field. The study also comprises the two-dimensional temperature and one-dimensional density effect, on frequencies computation, utilizing the Rayleigh–Ritz technique. The objective of the study is to reduce the frequencies of the plate as well as to provide the effect of various plate parameters on frequencies. Numerical illustration and comparative study of the frequencies with other available results well authenticate the objective of the study. A comparison of frequency modes done for the clamped rectangle and square plate corresponding to tapering and aspect ratio and nonhomogeneity concludes that frequency obtained for the present study is very less in comparison with other studies done. A convergence study of the obtained results is also presented with the help of figures. The convergence study done concludes that rate of convergence in case of circular variation is faster than the other variations.

Fuzzy sets, as well as their extension intuitionistic fuzzy sets (IFS), are more effective and appealing tools for expressing quantitative complexity throughout the decision-making process, and they have gotten greater attention from researchers in recent years for new study directions. Keeping the advantages of IFS, this chapter proposes a novel information measure to measure the fuzziness of IFS known as entropy measure (EM). The various notable features of the proposed EM are also presented. EM is a very useful tool to determine the attribute's weight during the multi-attribute decision-making (MADM) process. Therefore, in this chapter, the authors propose a new MADM approach by using the proposed EM where the attribute's weights are absolutely unknown. Finally, the proposed MADM methodology is applied to solve the real-life MADM examples. Comparative studies are also given to show the advantages of the proposed MADM methodology. The proposed MADM methodology can overcome the weaknesses of the existing MADM approaches.

The significance of the acceleration zone is expressed in designing a straight pipeline that follows the feeding point or a bend of a pneumatic conveying system. Although there are various publications that suggest a mean for evaluating the primary acceleration length, no correlation has been presented for evaluating the re-acceleration length following a bend. The current paper presents a thorough experimental investigation of the particles velocity reduction due to the flow in bends and the re-acceleration velocity profile that follows various bends. The experimental results have been obtained from a 2″ dilute phase pneumatic conveying systems with a wide range of operating conditions, conveyed materials and six different bend geometries. The research resulted in a new correlation for the particle velocity reduction due to the flow in the bends, and accordingly we derived an expression for calculating the re-acceleration length following a bend, and the energy loss in the bend.

In this paper, we prove fixed point results employing mixed weakly monotone maps, C-class functions and altering distance function in the framework of S-metric space. Here, integral application has additionally been given.

The present model describes the vibrational analysis of skew (parallelogram) plate made up of non-homogeneous material with variable thickness and temperature on clamped edges. One dimensional thickness and two-dimensional temperature variation is taken into consideration. The non-homogeneity of the plate varies circular in one dimension. The governing differential equation of motion for vibration analysis is solved by using Rayleigh Ritz technique and time period is calculated for the combination of different variation of plate parameters. The obtained results are presented in tabular form.

The behavior of particles in dilute phase pneumatic conveying is a rather complex phenomenon. For example, particle velocities and their trajectories owing to particle-particle and particle-wall collisions are unpredictable. In this study, we focus on particle velocity reduction in horizontal-vertical (H-V) and vertical-horizontal (V-H) bends. A new terminology, ‘bend point’, is introduced to compare different bends on common measures. A broad range of materials (Archimedes numbers = 102 to 106) was investigated using six different bends (blind-T, R/D = 1.5, 4.5, 6.6, 10, and 20) and wide range of conveying velocities (10 m/s

In this paper, authors studied the natural vibration of tapered non homogeneous rectangular plate on clamped edges. For tapering in plate, authors considered circular variation in thickness and for non-homogeneity (in plate’s material) Poisson’s ratio varies exponentially. Bilinear temperature (linear along both the axes) variation on the plate is being viewed. Rayleigh Ritz method is used to solve differential equation of motion. All the results are presented with the help of tables and graphs. A comparison of results is also given to support the present study.

In this paper, a theoretical analysis is carried out to investigate the effect of linear variation in density and circular variation in Poisson’s ratio on time period of frequency modes of rectangular plate with variable thickness under temperature field. The thickness variation is considered to be circular and temperature variation on the plate is assumed to be bi-linear. Rayleigh Ritz method is used to solve the differential equation. All the results (time period for first two modes of vibration) are presented with the help of tables.

Frequencies of nonuniform triangular plate (isosceles, right-angled, and scalene triangle) on clamped edges under temperature field are computed using Rayleigh–Ritz method. For non-uniformity, two-dimensional linear thickness variation on the plate is considered. The two-dimensional parabolic temperature is considered on the plate. First three modes of vibration are computed on different variation of plate parameters and presented with the help of tables. The objective of the study is to reduce the frequency of the plates. A comparative study of the frequencies with other available published results well presents the objective of the study.

The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.

An analysis was carried out to investigate the time period of the thermally induced vibration of clamped and simply supported circular plates with circular variation both in thickness and density. Prior to this study, the variations considered were either linear, quadratic, parabolic, or exponential in nature. To study thermal effect, one-dimensional linear temperature variation on the plates is taken into consideration. Rayleigh–Ritz method is applied to compute the time period of the first three modes of vibration for both plates by varying tapering parameter, thermal gradient, and density. Convergence study of frequency modes for both plates conducted suggests that the convergence rate in case of circular variation is faster than the other studies done. A comparison of time period with the available published results is done. The comparison done concludes that time period obtained in the present study by varying thermal gradient and tapering parameter is found to be less than the other studies done for the same set of parameters. This study helped to establish the fact that, by using circular variation in plate parameters, we can get less time period of frequency modes in comparison to other variations considered till date.

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

The significance of the acceleration zone is expressed when designing a straight pipeline that follows either the feeding point or a bend in a pneumatic conveying system. It is an effective and reliable system that takes into account the acceleration zone in the design process. The current paper presents a thorough experimental investigation of particle velocity profile at the acceleration region obtained from 3-in, 2-in and 1-in horizontal dilute phase pneumatic conveying systems with various operating conditions and conveyed materials. The velocity was obtained by using a high speed camera combined with image processing. Investigation of the statistical velocity distribution resulted in a new correlation for the particle velocity profile throughout the acceleration zone and the acceleration length in the range of the tested operating conditions.

Many parameters need to be investigated in order to reduce power consumption, product degradation and flawless operation of pneumatic conveying systems. Particle velocity in vertical conveying is one such parameter that we are focussing on in this study. Many correlations were developed to predict particle velocity in steady state zone. Still, they lacked in consistency for finding any correlation that would explain particle velocity in acceleration zone as well as in fully developed flow. In this study, an experimental system was developed with 5 m vertical test section having 50 mm ID of pipe. Materials selected were representing a large range of Archimedes number (102–107). Very small quantities (Diluted) of various materials were manually fed into the upward conveying airflow using a piston forced particle feeder. Particle velocities were measured in acceleration as well as in fully developed region. Visuals of particle flow were recorded using high-speed camera and analyzed by a Matlab programme, specially developed for this analysis. Terminal velocity analysis (up-ss = ua–uT) has been used to predict steady state velocity. Terminal velocity analysis was found to have good agreement with previously published data by using its (terminal velocity) true value. Correlation of particle velocity and acceleration length was developed based on the investigation of statistical velocity distribution at different locations in vertical test section. The developed parameters of vertical conveying in this study have been compared with horizontal conveying results of [1]. Different relative curves (horizontal and vertical) were developed and a new threshold velocity (VH-identical velocity) was added to the master curve developed by [2]. These developed correlations and curves will help in designing and operation of pneumatic conveying systems.