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Graph theory is employed in this study to examine the Paate clan of the Nyishi tribe’s unique naming system. The network represented by the Parental graph is a directed acyclic graph with 1388 nodes which represent individuals of the clan, and 1387 arcs indicate father–son relationships and the transfer of the naming system. Centrality measures show that individual Kadu is the most essential node for linking others, while individual Nina is capable of communicating more efficiently with other nodes in the network. No clusters or cliques were observed in the network. The network exhibits characteristics of a scale-free network. No relinking marriages were observed in the genealogical network. [ABSTRACT FROM AUTHOR]

In this paper, we have established a theorem by using the elliptic WP-Bailey lemma. Certain transformation formulae for elliptic hypergeometric series have also been obtained by making use of the theorem established herein. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of a family of... Finsler metrics, defined as F = ..., where ... is a Riemannian metric; ... are constants. We study some important properties for this family of (α; β)-metric, such as: the projectively atness for the Finsler space endowed with a type of this metric, the nonholonomic frame for the Finsler space endowed with this family of (α; β)-metrics; the S-curvature, the Landsberg curvature and also the bounded Cartan torsion. [ABSTRACT FROM AUTHOR]

Some results have been established on absolute index Riesz summability factor of an infinite series. Furthermore, these kind of results can be extended by taking other parameters and an absolute index matrix summability factor of an infinite series or some weaker conditions. In the present paper a new result on generalized absolute index matrix summability factor of an infinite series has been established. [ABSTRACT FROM AUTHOR]

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghius sense on spaces endowed with a family of vector valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector valued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations. [ABSTRACT FROM AUTHOR]

The present paper investigates the effects of thermal radiation, joule heating on an unsteady hydro magnetic free convective flow of a viscous electrically conductive Newtonian and polar fluid past a semi-infinite vertical plate embedded in a porous media in the presence of heat absorption, chemical reaction, slip flow and Dufour effect. Analytical perturbation solutions are obtained for the velocity, temperature and concentration fields as well as for the skin friction coefficient, Nusselt number and Sharewood number. The results are presented in graphical forms to study the effects of various parameters. [ABSTRACT FROM AUTHOR]

In this paper we introduce the backward operator is ∇ and study the notion of ∇ -- Cauchy sequence using by almost (λmµn) convergence in χ² -- Riesz space and also some inclusion theorems are discussed. [ABSTRACT FROM AUTHOR]

We establish a common coupled fixed point theorem for hybrid pair of map- pings under weak #968;-φ contraction on a non-complete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not em- ploy the condition of continuity of any mapping involved therein. Moreover, an example and an application to integral equations are given here to illustrate the usability of the obtained results. We improve, extend, and generalize several known results. [ABSTRACT FROM AUTHOR]

In this paper, we prove some n-tupled coincidence point theorems for a pair of mappings in partially ordered complete G-metric spaces satisfying weakly contractive type conditions. Our results generalize the results of several authors. Also, we discuss an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new concept for Riesz almost lacunary χ³sequence sequence spaces strong P-convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary χ³ sequence spaces and also some inclusion theorems are discussed. [ABSTRACT FROM AUTHOR]

In the present paper, a new theorem on the degree of approximation of a function [InlineEquation not available: see fulltext.], conjugate to a 2 π periodic function f belonging to the Lip α ([InlineEquation not available: see fulltext.]) class without the monotonicity condition on the generating sequence [InlineEquation not available: see fulltext.] has been established, which in turn generalizes the results of Lal (Appl. Math. Comput. 209: 346-350, 2009) on a Fourier series. MSC: 40G05, 41A10, 42B05, 42B08. [ABSTRACT FROM AUTHOR]

Recently, Lal (Appl. Math. Comput. 209:346-350, 2009) has determined the degree of approximation of a function belonging to Lip α and weighted [InlineEquation not available: see fulltext.]-classes using product [InlineEquation not available: see fulltext.] summability with non-increasing weights [InlineEquation not available: see fulltext.]. In this paper, we determine the degree of approximation of function [InlineEquation not available: see fulltext.], conjugate to a 2 π-periodic function f belonging to weighted [InlineEquation not available: see fulltext.]-class by dropping the monotonicity on the generating sequence [InlineEquation not available: see fulltext.] with a new (proper) set of conditions, which in turn generalizes the results of Mishra et al. (Bull. Math. Anal. Appl., 2013) on [InlineEquation not available: see fulltext.]-class and rectifies (removes) the errors of Mishra et al. (Mat. Vesn., 2013). Few examples and applications are also highlighted in this manuscript. MSC: Primary 42B05, 42B08, 40G05, 41A10. [ABSTRACT FROM AUTHOR]

Recently, Lal [9] has determined the degree of approximation of function belonging to Lip α and weighted classes using Product C¹. Np summability with non-increasing weights{pn}. In this paper, we determine the degree of approximation of function f, conjugate to a 2π-periodic function f belonging to Lip (ξ (t), r)-class using semi-monotonicity on the generating sequence {pn} with proper set of conditions. Few applications of approximation of functions will also be highlighted. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the mixed summationintegral type operators having Baskakov and Beta basis functions in summation and integration, respectively. First, we estimate moments of these operators using hypergeometric series. Next, we obtain an error estimation in simultaneous approximation for Baskakov-Durrmeyer-Stancu operators. [ABSTRACT FROM AUTHOR]

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme. [ABSTRACT FROM AUTHOR]

In this research work, a soft computing optimization operating approach is developed for a multi-objective aspirational level fractional transportation problem. In the proposed technique, a mathematical model is formulated for the multi-objective aspirational level fractional transportation problem (MOFTP) based on the highest value of one and all objectives of the model. We also used the symmetry concept over our model to identify the best optimum solution based on symmetrical data. We constructed the membership grades for the set of fetched parameters having symmetry. In this work, we also used the concept of ranking function in our mathematical model to obtain the optimum solution of the fuzzy multi-objective fractional transportation. In this proposed algorithm, the aspiration levels are also associated with the objective function of MOFTP. We are also proposing a new approach for the optimization of fractional problems in which the objectives are being optimized by using the numerator function and denominator function simultaneously. Further, a methodology is also developed to find the average cost for each fractional objective of the model. After that, we will find the ranking function for each parameter by using the defuzzification method. By this methodology, we will be able to convert the MOFTP into a bi-objective transportation problem. The provided technique is elaborated with the help of numerical computations to prove the beauty and power of the proposed technique. [ABSTRACT FROM AUTHOR]

Let ( Amnuv) be a sequence of bounded linear operators from a separable Banach metric space of (X, 0) into a Banach metric space ( Y, 0). Suppose that φ ∈ Φ is a countable fundamental set of X and the ideal I - of subsets ℕ x ℕ has property (AP). The sequence (Amnuv) is said to be b* I - convergent if it is pointwise I - convergent and there exists an index set K such that ℕ x ℕ / K ∈ I and ( Amnuv x)m,n∈K is bounded for any x ∈ X, the concept of lacunary vector valued of χ² and the concept of Δ11 - lacunary statistical convergent vector valued of χ² of difference sequences have been introduced. In addition, we introduce interval numbers of asymptotically ideal equivalent sequences of vector valued difference by Musielak fuzzy real numbers and established some relations related to this concept. Finally we introduce the notion of interval numbers of Cesáro Orlicz asymptotically equivalent sequences vector valued difference of Musielak Orlicz function and establish their relationship with other classes. [ABSTRACT FROM AUTHOR]

In this article we introduce the sequence spaces [Xƒ3FI, ∥(d(xi), d(x2), ..., d(Xn-1))∥p] and ［1Λ3FIƒ, ∥(d(x1), d(x2), ..., d (xn-1))∥p］, and study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces and some of their properties like solidity, symmetricity, convergence free etc., and also investigate some inclusion relations related to these spaces. [ABSTRACT FROM AUTHOR]

In this study, Data Envelopment Analysis (DEA) models are improved by employing spherical fuzzy sets (SFSs), which is an extension of generalized fuzzy sets. SFSs were recently introduced as a novel type of fuzzy set that allows decision-makers to express their level of uncertainty directly. As a result, SFSs provide a more preferred domain for decision-makers. Fundamental Charnes-Cooper-Rhodes (CCR) model is discussed on the context of spherical trapezoidal fuzzy numbers (STrFNs), which consider each data value’s truth, indeterminacy, and falsehood degrees, and a unique solution technique is implemented. This method converts a spherical fuzzy DEA (SF-DEA) model into three pair of crisp DEA model, which may then be solved using one of many existing approaches. The largest optimal interval is determined for each DMU such that the efficiency score lies inside that interval. Furthermore, an example demonstrates this novel method and clearly explains the DMUs’ ranking technique. [ABSTRACT FROM AUTHOR]

We study some connections between -lacunary strong -convergence with respect to a mnk sequence of moduli Musielak-Orlicz function and -lacunary -statistical convergence, where A is a sequence of four-dimensional matrices of complex numbers. [ABSTRACT FROM AUTHOR]