Table of contents

This issue of Proceedings gathers the papers presented at International Conference on Recent Inventions and Innovations in Mathematical Sciences (ICRIIMS-2019) held in department of Applied Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India during 28^th February & 1st March 2019. The Conference was attended by 260 participants representing several countries. Altogether, there were 165 oral presentations across the twelve conference topics.

It is well known that Mathematical Sciences plays a vital role in Physical, Chemical, Biological, Engineering and other Social Sciences. The main objective in organizing this conference is to exchange innovative research ideas, examine, promote and discuss issues related to the latest trend, importance, needs and future developments in Applied Mathematics in its own domain as well as it's applications in Mathematical Sciences.

Most problems of modern society are both complex and interdisciplinary. A large number of mathematical models have been developed to get an insight into the complexities of the problems and a variety of mathematical techniques have been employed to solve these models. Even though the problems are diverse in nature, the tools developed for one situation are often adaptable to an entirely different situation. The goal of differential equations is to understand the physical phenomena of nature and to develop mathematical models.

It is widely held view that a conference organized by bringing twelve research areas having interdisciplinary orientation will receive immense scientific attention. It's out come helps in the technical advancement for a fast developing country like ours. The aim of this International Conference is to direct all efforts to words unifying divergent trends by identifying the inter connection of many distinct and diverse scientific results.

The organization of the Conference would not have been possible without the help of many people. In particular, we would like to thank Prof. V.Uma Maheswara Rao, Chairman, ICRIIMS-2019, for his constant support. We thank the members of the Local Organizing Committee and the reviewers for their dedication and commitment to this event, without them the proven quality of the contributions would not have been possible. Also, we should express our thanks to all delegates, who showing the high level of international interest in the subject. It is exactly your participation that makes the conference to its success. We hope that these proceedings provide the reader with a contemporary vision of the teaching, research and learning process of Mathematical Sciences.

Andhra University,

Visakhapatnam, A.P., India.

Prof. M.Vijaya Santhi

Organizing Secretary, ICRIIMS-2019

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Bianchi type-I cosmological model for a cloud of a string with bulk viscosity is investigated in Lyra geometry. To get a deterministic model of universe, we assumed a unique form of constant deceleration parameter (CDP). Also, the bulk viscosity is presented as a linear combination of two positive constants ξ₀ & ξ₁ with Hubble parameter i.e ξ = ξ₀ + ξ₁H and studied the results resemblance with the constant and variable bulk viscosity in three different cases. Also, we conclude that the displacement vector used in Lyra geometry is vanishing in late time. The physical acceptability of the model is investigated.

In the present paper steady on MHD heat and mass transfer flow of a viscous incompressible fluid flow through a porous medium in the presence of radiation, heat source and chemical reaction effects are considered. The set of non linear differential equations can be solved analytically. Effects of various parameters like magnetic parameter, permeability parameter, Grashof number, modified Grashof number, radiation parameter, heat source parameter, Prandtl number, Schmidt number, chemical reaction and an angle of inclination on the velocity, temperature and concentration profiles as well as the skin friction, Nusselt number and Sherwood number are discussed qualitatively and shown graphically.

Cryptography algorithms provide confidentiality, integrity and authentication of communication channels. These algorithms and protocols are based on sophisticated mathe-matics such as computational and algorithmic algebraic geometry, coding theory, and generic algorithms for finite abelian groups. For secure encryption, establishing or transferring a shared key between the parties is an interesting challenge. Key management is an essential crypto-graphic primitive upon which other security primitives are built.

In this paper, we present a generic construction of asymmetric key Group key transfer protocol using one way function and coding theory technique. By guaranteeing the freshness of authentication messages, the authenticity of the generator of authentication messages and the completeness of the authenticator, the improved protocol can resist various passive and active attacks. The protocol allows the participants in the group to derive a common encryption key, provide the key security and unknown key share properties. Security analysis of proposed scheme is also discussed.

In this paper, we have investigated a spatially homogeneous locally rotationally symmetric Bianchi type-I space-time with cosmological term Λ in presence of perfect fluid distribution in f (R,T ) gravity theory. We have derived explicitly the field equations of the theory and obtained the exact solution of field equations by employing a periodic varying deceleration parameter, which is a unique feature of the model. We have also performed the analysis of the model such as the equation of state parameter, pressure, energy density, density parameter and jerk parameter which are significant in the discussion of cosmology. Some physical and geometrical properties of the model have also been discussed along with the graphical representation of various parameters. We obtained the presence of quintessence and phantom regions based on chosen parameters. It is observed that the deceleration parameter exhibits a smooth transition from early deceleration to late time acceleration of the universe and oscillate based on chosen parameters. We have observed that the presented model is compatible with the recent cosmological observations.

The present paper investigates the propagation of time harmonic waves in a two layered hollow poroelastic cylinder in contact with inviscid fluids. The hollow poroelastic two layered cylinder is assumed to be infinite in axial direction. The outer and inner surfaces of the two layered cylinder are in contact with fluids and at the interface stresses and displacements are continuous. The frequency equation for wave propagation for a pervious is obtained. Non-dimensional phase velocity is computed as a function of wave number and presented graphically for two types of two layered cylinder for arbitrary parameters of the fluid in contact. Numerical results show that, in general, phase velocity is more in absence of outer fluid compared to the case of absence of inner fluid. Several other particular cases are discussed.

This paper presents a Genetic Algorithm and Non-Linear Programming (GA-NLP) hybrid model to derive steady state optimal reservoir operating policies for a reservoir. In the present study, the objective is maximizing the yields of all the crops in the command area considering yield response to water deficit subject to constraints on reservoir water balance, storage bounds, channel capacities and minimum water requirements. Decision variables of the model are fortnight water allocations to each crop grown under left & right main canals and d/s releases. The model developed is applied to the Nagarjunasagar reservoir in Andhra Pradesh, India. Various levels of dependable inflows entering into the reservoir (75%, 80% & 85%) are considered in the present study. Optimal policy obtained by proposed model are validated through simulation and compared with Standard operating policy (SOP). The results obtained using the proposed model gives guidelines to reservoir managers to take decisions. Results reveal that GA-NLP model can be effectively used for optimal allocation of limited available water resources to any reservoir.

In this paper we give some characterization of minimal distributive semi lattice and proper filter in directed above semi lattice. Also this manuscript illustrates several principal results concerning congruence kernels of minimal distributive semi lattice S and provides a necessary and sufficient condition for a semi lattice congruence ≡ on Sis a * congruence. And also established a necessary and sufficient condition of an ideal of minimal distributive semi lattice S is a kernel ideal of semi lattice S.

The objective of the present paper is to investigate the soret and dufour effect of Kuvshinshiki fluid on MHD free convection flow past a vertical porous plate with heat and mass transfer in the presence of chemical reaction. The velocity, temperature and concentration are obtained by using a perturbation technique. The results have been discussed graphically and numerically for various values of the flow parameters by using Matlab.

Second order rotatable design (SORD) concepts will be more useful in developing the appropriate empirical relations. As the number of input variables are increasing (with the assigned levels to each variable), there is a need to conduct more number of experiments which may sometimes be practically impossible. Taguchi designs can solve the problem with less number of experiments and provides complete information useful for the applications of second order rotatable designs. This article provides a comparison of Central composite design and modified Taguchi approach and its validation by tracing the optimum process parameter on the experimental design. It is possible to get the required information and the expected range of process parameters from modified Taguchi design.

Signcryption is a cryptographic primitive that performs signature and encryption simultaneously at a cost significantly lower than the traditional signature-then-encryption methodology. An aggregate signature scheme is a digital signature scheme that combines n signatures on n different messages from n different users to a single signature. In this paper, we propose an aggregate signcryption scheme in the identity based setting using bilinear pairings over elliptic curves by combining aggregate signatures with signcryption schemes. We prove that our scheme is secure and satisfies the unforgeability and confidentiality in the random oracle model with the assumptions that the CBDHP and BDHP are hard. Also our scheme is public verifiable and requires constant number of pairings for aggregate verification. Comparing with previous schemes of this kind, our scheme is more efficient in computation and communication.

In this paper, we descend a variable mesh finite difference scheme based on non polynomial spline approximation for the solution of singular perturbation problems with twin boundary layers. We develop the discretization equation for the problem using the condition of continuity for the first order derivatives of the variable mesh non polynomial spline at the interior nodes. The discrete invariant imbedding algorithm is utilized to solve the tridiagonal system obtained by the method. Endeavor examples are illustrated and maximum absolute errors in comparison to the other methods in the literature are shown to vindicate the method.

In this paper we establish the existence of countably infinitely many positive solutions for coupled system of two point Riemann-Liouville integral fractional order boundary value problems. The main results are established by using the fixed point index theory in cone on a Banach space with increasing homeomorphism and positive homomorphism.

In this paper, a quadrature technique is employed for the solution of singularly perturbed delay differential equation. A first-order neutral type delay differential equation is achieved, which is asymptotically equivalent to the given singularly perturbed delay differential equation. Then Gaussian quadrature two-point formula is implemented on the first order equation to get a tridiagonal. Thomas algorithm is used to solve the resulting tri-diagonal system. The proposed method is implemented on model example, for different value of delay parameter and perturbation parameter. Maximum absolute errors are tabulated with a comparison to authorize the method. Theoretical convergence of the method is discussed. The layer behaviour is discussed using the graphical histrionics.

In this paper, we prove images of Fs-points are Fs-points under different kinds of Fsset functions and define Hausdroff space property on FsB-Toplogical Spaces.

In this paper an M/M/1 queueing system with server vacation, Startup, breakdowns and second optional service with impatient customer behavior is considered. All the customers will be given unique type of individual service in the first phase and then second phase service will be provided on option of the customer. We obtain some important system characteristics, such as the number of customers in the system, the probability that the server is idle, busy and broken down states, the expected waiting time in the system. Sensitivity analysis is also conducted with various parameters on system's performance measures.

Digital signature is one of the important primitive of public-key cryptography and has become an essential technique in providing security services in modern communications. Due to the limitations imposed by both the communication bandwidth and computational power of wireless communication devices, signature schemes with less bandwidth and less computational cost are desirable for practical applications. Signature schemes with message recovery provide a feature that the message is recoverable from the signature and hence does not need to be transmitted separately for signature verification. Recently many signature schemes with message recovery have been designed in traditional as well as Identity based settings and most of the schemes are constructed using bilinear pairings over elliptic curves. Nevertheless, the computational cost of a pairing is more expensive and is higher than the scalar multiplication. Thus, signature schemes without pairing would be more appealing in terms of efficiency. In this paper, we propose an efficient identity-based message recovery scheme without pairings. In our scheme the message itself is not required to be transmitted together with the signature and so it turns out to have the least data size of communication cost. Also, we compare our scheme with the existing ID-based signature schemes with message recovery in terms of computational and communicational point of view. With the pairing-free realization, the proposed scheme is efficient and applicable for resource constrained devices.

In this paper, we developed a new coding and decoding method followed from Pell-Lucas p numbers S_pAⁿ. We established the relations among the code matrix elements for p = 1 and i=1, error detection and correction for this coding theory. Correction ability of this method is 93.33% for p = 1,i=1 and for p = 2,i=2 the correction ability is 99.80%. In general, correction ability of this method increases as pincreases.

In this paper, we study an infinite capacity single server Markovian queue with a single working vacation and reneging of impatient customers in the queue during working vacation period. Customers arrive to the system following a Poisson distribution. The server goes to vacation when the system is empty and stay in vacation for a random period of time that is exponentially distributed. During the working vacation period, the server still continue providing service with a slow service rate. After the completion of the vacation, the server returns back to the regular service period and continue providing service with the regular busy period service rate if there are one or more customers in the system or it will stay idle until a new customer arrives to the system. During working vacation, customers in the queue get impatient and renege from the system and the reneging time is assumed to follow an exponential distribution. The system is modeled as a quasi-birth-death process and the stationary probabilities of the model are obtained using probability generating function approach. Some numerical analysis is also carried out to show the effect of some of the parameters on some selected performance measures of the system.

In this paper, we have defined summability of improper integrals and have established a theorem on indexed absolute Nörlund summability factors of improper integrals under sufficient conditions, generalizing the result of Ozgen [9] and Mishra et al. [8].

A partial Γ-semiring is a structure possessing an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a partial Γ-semiring. In this paper we introduce of notions of left/right operator partial semirings of a partial -semiring and obtained a correspondence between the partial ideals of partial Γ-semiring R and its operator partial semirings.

In this paper general expression of reliability has been derived for time dependent stress strength model if stress is random independent and strength is random fixed for the following cases. (i).Stress follow Pareto distribution and strength follow finite mixture of exponential distribution. (ii).Stress follow exponential distribution and strength follow finite mixture of Pareto distribution.

Numerical expression for steady 2D natural convection magnetohydrodynamics flow of micropolar fluid past along a vertical surface embedded through non-Darcian porous medium in the presence of heat source, chemical reaction, viscous dissipation and thermal radiation is obtained. Variable wall temperature and concentration in a doubly stratified are taken into account. The initial governing boundary layer equations are transformed to a system of ODEs, which are then solved numerically by using the Runge– Kutta–Fehlberg fourth–fifth order method along shooting technique. A parametric study is conducted and so that numerical result are obtained for the velocity, micro-rotation, temperature and concentration as well as the local friction factor coefficient, local couple stress, local Nusselt and Sherwood numbers for different values of the governing parameters, namely, the magnetic parameter, material parameter, Prandtl number, radiation parameter, chemical reaction parameter and viscous dissipation and discussed in detail. Comparison in limiting case is also part of present study to validate the obtained results.

In this paper with the help of soft set theory the notion of soft ternary Γ-semiring and soft ternary Γ-sub semiring are introduced. Some of the properties of soft ternary Γ-semiring are discussed and some illustrations are also given. It is proved that (1) a soft set (q, P1, Γ) over a ternary Γ-semiring T is a soft ternary Γ-semiring over T if and only if for all x ∈ P₁; q(x) ≠ Ø a ternary Γ-subsemiring of T. (2) A soft set (r, P1, Γ) over T is a soft L(R, M) Γ-ideal over T iff ∀ p₁ ∈ P₁; r(p₁) ≠ Ø is a L(R, M) Γ-ideal of T. (3) Let (q, P1, Γ) and (r, P2, Γ) be two soft ternary Γ-semirings over T, such that P₁ ∩ P₂ ≠ Ø Then (q, P1, Γ) ∩_r(r, P2, Γ) is a soft ternary Γ-semiring over T. (4) Let (q, P1, Γ) and (r, P2, Γ) are two soft ternary Γ-semirings over T, such that P₁ ∩ P₂ ≠ Ø Then (q, P1, Γ) ∪_E(r, P2, Γ) is a soft ternary Γ-semiring over T. (5) Let (q, P1, Γ) and (r, P2, Γ) are two soft ternary Γ-semirings over T. Then (q, P1, Γ) Λ(r, P2, Γ) is a soft ternary Γ-semiring over T. (6) Let (q, P1, Γ) and (r, P2, Γ) are two soft ternary Γ-semirings over T. Then (q, P1, Γ) Λ(r, P2, Γ) is a soft ternary Γ-semiring over T. (7) Let (q, P1, Γ), (r, P2, Γ) and (s, P3, Γ) are any three soft ternary Γ-semirings over a commutative ternary Γ-semiring T. Then (q, P1, Γ) ⊚(r, P2, Γ) ⊚(s, P3, Γ)is a soft ternary Γ-semiring over T. (8) Let (q, P₁, Γ), (r, P₂, Γ) are any two soft Γ-ideals over a ternaryΓ-semiring T with P₁ ∩ P₂ ≠ Ø Then (q, P₁, Γ) ∪R (r, P₂, Γ) is a soft Γ-ideal over T contained in both (q, P₁, Γ), (r, P₂, Γ). (9) Let (q, P₁, Γ), (r, P₂, Γ) are any two soft Γ-ideals over a ternary Γ-semiring T. Then (q, P₁, Γ). E (r, P₂, Γ) is also soft Γ-ideal over T contained in both (q, P₁, Γ) and(r, P₂, Γ).

In section 5, the term soft ternary Γ-sub semiring is introduced and some examples are given and characterized the soft ternary Γ-semirings.

Taguchi approach is adopted to optimize the process parameters and improve the quality of components that are manufactured. Nature of the output response in any scientific investigation has to be understood through experimentation prior to the development of a suitable mathematical model. When several input variables are involved in the scientific problem, it is very difficult to develop a relation between the output responses in terms of input variables. The objective of this paper is to determine the expected range for the process parameters in the optimization process by introducing fictitious parameter.

This article presents optimalstrategy N-Policy M/E_k/1 vacation queueingsystem when the server is in Start-up, Time-out and Breakdown for two-phase. The individual arrivals considered to follow Poisson process and receive batch service of k-stages in the first phase, individual service in the second phase. During the service arrivals are allowed to enter the batch. On completion of the second phase service to all customers in the second phase, the server come back to the first phaseand do the service to the customers who have arrived by providing them first phase service of k-stages followed by second phase service. If there is no customer waiting in the phase one service, the server waits for a fixed time 'C' is called server Time-out. If units arrived during this fixed time, then the server provides first phase followed by second phase service, otherwise after expiration of fixed time he takes a vacation. After N-customers accumulate in the system the server returns from vacation. Before going to first phase service, the server spends a random startup period for pre-service after coming back from vacation. During individual service the server is susceptible to random breakdown according to a Poisson process and the repair time follows an exponential distribution. After repair the server resumes individual service. Exact notations for steady state distribution of the number of customers in the system are derived. Developed a cost model for determining the optimal operating policy at a minimum cost. By using numerical illustrations the sensitivity analysis is also presented.

This paper deals with the Bianchi type - II, VIII & IX metrics in presence of domain walls in the frame work of the modified f(R,T) theory of gravitation, where R is Ricci scalar and T is the trace of energy momentum tensor. Also, some important features of the models, thus obtained, have been discussed.

In this paper, we have introduced the concept of C−psosets and C−trellisesand their properties are studied. The notions of distributive and modular C−trellises are introduced and the properties of translations and derivations of C−trellises are discussed. It is proved that every derivation of a C−trellis L is a meet translation on L. It is also proved that a meet translation T of a C−trellis L is a derivation on L if and only if T is a join endomorphism.

We have investigated spatially homogeneous anisotropic Bianchi type-II, VIII & IX cosmological models in the presence of pressure less matter and modified holographic Ricci dark energy in the frame work of f(R, T) gravity in the context of late time accelerating expansion of the universe. The solutions of the field equations obtained using (i) a relation between metric potentials and (ii) the modified holographic Ricci dark energy. We have determined the cosmological parameters, namely, EoS parameter, matter energy density, anisotropic dark energy density, deceleration parameter. We discuss some physical and geometrical properties of the obtained models which are found to be consistent with recent observation

Dark energy cosmological models with variable equation of state (EoS) parameter in Brans-Dicke [1] scalar tensor theory of gravitation are obtained. The field equations have been solved by using the anisotropy feature of the universe in Bianchi type-III metric. Some important features of the models, thus obtained, have been discussed. We noticed that as a special case, it is always possible to obtain dark energy cosmological models in general relativity.

Any Municipal distribution system consists of pipe network, valves and pressure generating facilities etc. Around 70% of total cost of any water distribution system is towards cost of pipe network only. Therefore, the cost of pipe network is to be reduced by selecting the appropriate lengths of candidate diameter pipes between the nodes in a pipe network.

In the present study, a municipal looped water distribution network is designed for least cost by Genetic Algorithm – Non Linear Programming (GA-NLP) hybrid approach. In the present study, optimal lengths of sub pipes of various discrete diameters (sizes) available in the market making the link between the nodes are obtained by minimising the total cost of pipe network. In order to obtain the optimal solution of a looped network, non - linear hydraulic analysis and optimization of network is to be performed. In this study, non - linear hydraulic analysis is made a part of optimization by adding loop head loss and node continuity equations as constraints to the objective function. The model developed is solved by GA-NLP hybrid approach in MATLAB. Near optimal solution obtained by GA is taken as initial solution of NLP for obtaining optimal solution. By adopting GA-NLP hybrid approach, convergence is faster when compared to GA avoiding the complexity in selection of suitable trial values of GA parameters.

Many researchers applied different techniques like linear programming, integer linear programming, linear programming gradient method and branch & bound algorithm etc. and optimized the looped pipe network by minimizing the cost. The results obtained by proposed model are compared with that of other investigators and found to be superior. It is also concluded that the proposed model may be applied to any larger municipal looped pipe network through demonstration by applying proposed model to a case study of Rajiv Gandhi Nagar of Guntur Municipal Corporation.

In this paper, we study a single server queueing system with variant working vacations wherein customers arrive according to a Poission process. The server takes variant working vacations as soon as the system becomes empty. The service time during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed and are mutually independent. During working vacation customer may renege due to impatience which follows exponential distribution. The steady state probabilities of number in the system are obtained using matrix geometric method. Numerical investigations showing the effect of model parameters on different performance measures are shown through tables and graphs. An optimization of cost function is performed to find the optimal service rate that minimizes the cost function.

In this paper we proposed a three species Ecological model with a Prey and Two predators. Distributed type of delay is incorporated in the interaction of prey and second predator is taken for investigation. The system dynamics is studied at its interior equilibrium point with exponential type of delay kernel. The effect of Time delay on the dynamical behavior of the system is studied using Numerical simulation. It is shown that the delay arguments with different weight parameters exhibit rich dynamics and the system is asymptotically stable.

The present work is based on group theoretic analysis of crystal structures. Group theory can be employed to a variety of problems in physics and chemistry. It plays a major role in the solution of solid state physics problems. The concept of symmetry plays an important role in our physical environment. The symmetry of a molecule can be used to determine various physical properties of a crystal using group theoretical methods. The applications of magneto-electric devices lie in the regions of millimeter and sub-millimeter wavelengths and in the areas of reducing electrical conductivity, improving dielectric magnetic or magneto-electric properties by solid solutions improving optical quality and obtaining larger crystals. Ferro-electric, Ferro-elastic and magneto-electric polarized domain pairs and tensor pairs are calculated using coset decomposition and double coset decomposition respectively for the crystal magnetite (Fe₃O₄). While considering Ferro-electric and Ferro-elastic properties only ordinary point group m3m is considered as prototypic point group since they are non-magnetic properties. In case of magneto-electric polarizability grey group m3m1 is taken as prototypic point group.

In this paper we have investigated the non-static plane symmetric model in the presence of dark energy and one dimensional cosmic string in the frame work of Barber's second self creation theory by using hybrid scale factor. We have discussed some physical and geometrical properties of the obtained model such as spatial volume(V ), deceleration parameter (q), expansion scalar(θ), Hubble parameter (H), shear scalar (σ), anisotropic parameter (A_h), EoS parameter (ω_de) and the state finder parameters (r, s). Here we have observed that our model is compatible with the present day cosmological observations.

In this paper we have studied the Kantowski-Sachs (KS) space time filled with generalized ghost dark energy (GGDE) and dark matter in the Saez-Ballester theory of gravitation. The equation of state (EoS) parameter of dark energy (ω_λ) has been formulated as a function of cosmic time and shows quintom like behavior. The properties of density of dark energy (ρ_λ) and the density of dark matter (ρ_m) indicate the accelerated expansion of the universe. The pressure of the dark energy is negative at present and late time evolution of the universe indicating the accelerated expansion of our universe during these periods. The physical and geometrical aspects of the statefinder parameters (r, s), squared speed of sound $({\upsilon }_{s}^{2})$ and ${\omega }_{\lambda }-{{\omega }^{\prime}}_{\lambda }$ plane are also discussed.

In this paper, we investigate bianchi type II, V III and IX Bulk viscous string cosmological models in the context of f(R) gravity. Here, we obtained the solutions of the field equations in the presence of cosmic strings under some specific possible physical conditions. Some physical and geometrical features of the models are also discussed.

In this paper, we have investigated flat Friedmann-Robertson-Walker type Kaluza-Klein model in the presence of ideal fluid with quadratic equation of state(EoS) with time dependent parameters ω(t) and (Λt). We have investigated the properties of ω(t) and found that for Little Rip model ω(t) = −1 and for Pseudo Rip model ω(t) <−1. Also, we have studied behaviour of Little Rip(LR) and Pseudo Rip(PR) for dark energy. For obtained LR and PR models we have estimated the disintegration time.

In this paper, we derive f(R) gravity field equations with the help of a spatially homogeneous and anisotropic Bianchi type-V I_h space-time, in the presence of a bulk-viscous fluid, containing one-dimensional cosmic strings. Here we obtained the solutions of the field equations, under some specific plausible physical conditions. In particular, cosmological model with bulk-viscous strings in f(R) theory of gravity is obtained by using the special law of variation for Hubble's parameter proposed by Berman (Nuovo Cimento, B74, 182 (1983)). Some physical and kinematical properties of the models are also discussed.

The aim of this paper is to introduce an effective fuzzy clustering technique based kernel function to find appropriate subgroups in heterogeneous databases. This paper introduces the effective fuzzy clustering that incorporates weighted bias field information, kernel distance, possibilistic memberships and fuzzy memberships into memberships equation and prototype equation. The effectiveness and efficiency of the proposed clustering techniques have been shown through the experimental results on benchmark heterogeneous databases.

This paper introduces a new notion to define equivalence to the non-reflexive fuzzy relation equation. The most important condition for the fuzzy equivalence relations is reflexive, but the condition of reflexive is unsuccessful in many cases of fuzzy relation in real life problems that creates problem to form partition tree. Therefore, this paper defines the equivalence for the cases of fuzzy relation that satisfies the symmetry, and transitive. That is, it proves the reflexive to non-reflexive fuzzy relations through alpha-cut relations. Further, this paper defines tolerance to the non-reflexive fuzzy relation equation through alpha-cut relations and it proves the entire upper left, lower right and centre sub matrices of every weakly-similarity relation matrix are weaklysimilarity relation matrices.

The present work deals with a spatially homogeneous and anisotropic Kantowski-Sachs space-time filled with bulk viscous fluid, containing one-dimensional cosmic strings. To obtain a deterministic solution of the field equations, we used the assumption of shear scalar is proportional to expansion scalar of the model. We have investigated geometric and kinematic properties of our bulk viscous string model and discussed the role of bulk viscosity in the evolution of Kantowski-Sachs universe within the framework of f(R) modified theory gravity. A detailed physical discussion of the dynamical parameters is presented through a graphical representation.

In this paper, we define an operation on Pythagorean fuzzy matrices (*) and discuss their properties in relation with standard operations available in the literature. Also, we prove some new results on Pythagorean fuzzy matrices. Further, we prove equalities and inequalities of Pythagorean fuzzy matrices.

Network theory deals with the study of graphs in which nodes connected by branches. It helps to determine the shortest route between two places, time schedule for the activities of a project and minimum cost flow in pipeline networks. In the present paper, we with the existing algorithms based on network theory and finding the shortest path from use the cluster algorithms to find the can be compare one to another and also shortest paths when the clusters are grouping based on cluster analysis the results which we obtain observed that the similarity levels of single, average and complete linkage methods. By applying the existing algorithms based on graph theory can analyze the shortest path from one to another where as clustering provides the shortest path as well as the similarity index for standardized and non-standardized variables.

In this paper we prove fixed point theorems for a self map satisfying certain contraction condition involving quadratic terms in the frame work of dislocated quasi b-metric spaces.Also, these results are extended to a pair of weakly compatible selfmaps. Examples are also furnished in support of our results. Our results unify and enrich the comparable results in the literature.

This paper elaborates the homogeneous and anisotropic Bianchi type-III, V and VI₀ space times filled with matter and generalized ghost dark energy components in the framework of Brans-Dicke (Phys. Rev. 124, 925 1961) theory of gravitation. The behavior of generalized ghost dark energy for Bianchi type-III, V and VI₀ background is discussed. The solutions of the field equations obtained using following two assumptions: (i) shear scalar of the model is proportional expansion scalar, which leads to a relation between the metric, (ii) scalar field in the Brans-Dicke theory is a function of average scale factor of the models. We have further established a correspondence between the generalized ghost dark energy models with the polytropic gas dark energy model. We also reconstructed the potential and dynamics of the scalar field. We discuss some physical and geometrical properties of the obtained models which are found to be consistent with recent observation.