Corrections and Extensions in Left and Right Almost Semigroups

In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup (RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally associative LA-Semigroup explained in [20, 21] towards LA-Semigroup and RA-Semigroup with left zero and right zero respectively. We also discussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three left or right identities and finite as well as infinite commutative idempotent medials not studied in literature.

OSTROWSKI-TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR r−TIMES DIFFERENTIABLE h−CONVEX FUNCTIONS

The authors have tried to prove some Ostrowski-type fractional integral inequalities for r−times differentiable functions and generalized some results which were carried out in both [6, 25]. Some applications to special means are given. The methods and techniques of this paper could further stimulate the research conducted in the field of fractional integral inequalities.

Theory of Bijective Hypersoft Set with Application in Decision Making

Hypersoft set (an extension of soft set) is a new mathematical tool to tackle the inadequacy of soft set for attribute-valued sets. In this study, concept of bijective hypersoft set is proposed and some of its set theoretic operations like restricted-AND and relaxed-AND, are characterized. Moreover, new operations of bijective hypersoft set such as dependency, decision system, significance of decision system, reduced decision system and decision rules in decision system, are discussed with illustrated examples. A decision making algorithm and application are discussed with the support of these proposed operations.

An Efficient Two-Step Iterative Technique for Solving Non-Linear Equations

We use the homotopy perturbation method (HPM) to construct a new iterative system for solving non-linear equations in this article. The criteria for convergence in the scheme developed are also imposed. To show the validity and reliability of our process, we compare our regime with other current procedures by looking at various test problems.

Mathematical Model for Single and Multiple Object Extraction

In the image processing, noise is referred to as the visual distortion. This undesirable by-product may be captured in an image due to unpreventable assorted reasons. The interference of natural phenomena and technical problem, such as small sensor size, long exposure time, low ISO, shadow noise etc., can pollute image. The presence of noise images affects image processing outputs that include segmentation. Segmentation for noisy images is the major concern. To tackle this issue, we propose a modernistic model that is able neutralize the negative effects of outlier using the characteristic of kernel function by different approaches such as linear approach and quadratic approach for global segmentation. Moreover the weight function is used for local segmentation of noisy images. Comparing with classical models, the proposed technique shows robust performance. In comparison with the wellknown models such as Chan-Vese (CV) model , Yongfei Wu and Chuanjiang He (Wu-He) model and Chunming Li (Li) model we conclude that performance of our new model is much better.

Exact Analytical Solutions of Linear Dissipative Wave Equations via Laplace Transform Method

A wave phenomena evolved day after day, as various concepts regarding waves appeared with the passage of time. These phenomena are generally modelled mathematically by partial differential equations (PDEs). In this research, we investigate the exact analytical solutions of one and two dimensional linear dissipative wave equations which are modelled by second order PDEs with use of some initial and boundary conditions. We use double Laplace transform (DLT) and triple Laplace transform (TLT) methods to determine these exact analytical solutions. We provide examples with figures to test effectiveness of this scheme of Laplace transform

Relations on topologized groups

: In our present paper, topological groups are being discussed, where the relations with counter examples built the interest in the generalized structure. Some of these structures have also been converted into the other structures using topological isomorphism. In our work, the identity element plays the important role in lieu of arbitrary element. The role of topology has the more interest in our discipline.

An extension of TOPSIS based on linguistic terms in triangular intuitionistic fuzzy structure

Chen [24] introduced the extension of TOPSIS in the fuzzy structure, while this article stretches the modern approach of TOPSIS to the intuitionistic fuzzy framework. Linguistic terms are used in this study to evaluate the weight of each criterion and the rating of alternatives in the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both (IFPIS) and (IFNIS). The proposed model’s mechanism is presented with the help of an algorithm, and then it is applied to the personal selection problem. Finally, a comparative study is given between this model and other TOPSIS techniques.

A variety of multivalently analytic functions with complex coefficients and some argument properties of their applications

The principal goal of this scientific note is first to compose various rational types functions directly connecting to a variety of multivalently functions with complex coefficients, which are regular in certain domains in the complex plane, and then to designate numerous argument properties associating with certain applications of those (multivalent) functions

Bielecki–Ulam–Hyers stability of non–linear Volterra impulsive integro–delay dynamic systems on time scales

In this manuscript, the stability in terms of Bielecki–Ulam– Hyers and stability in terms of Bielecki–Ulam–Hyers–Rassias of non– linear Volterra impulsive integro–delay dynamic systems on time scales are obtained using the fixed point approach along with Gronwall inequal- ¨ ity and Lipschitz condition.