Abstract In this paper, we develop a class of methods based on exponential spline at off-step points for the solution of the nonlinear and linear fourth-order boundary value problems (BVPs). Spline relations and boundary equations are developed, and the methods of order two, four and six have been obtained. Convergence analysis of the method is discussed. Numerical examples for linear and nonlinear

Abstract The first general Zagreb index \(M^{\alpha }_{1}(G)\) of a graph G is equal to the sum of the \(\alpha \)th powers of the vertex degrees of G. For \(\alpha \ge 0\) and \(k \ge 1\), we obtain the lower and upper bounds for \(M^{\alpha }_{1}(G)\) and \(M^{\alpha }_{1}(L(G))\) in terms of order, size, minimum/maximum vertex degrees and minimal non-pendant vertex degree using some classical inequalities

Abstract Another proof of a supercongruence conjecture of Sun has been given in this paper, using tools of Gaussian hypergeometric series and the p-adic \(\Gamma\)-function together with a combinatorial identity.

Abstract In this paper, we present an efficient quartile paired double ranked set sampling (QPDRSS) scheme to estimate the population mean. QPDRSS provides an unbiased improved population mean estimator when the distribution is symmetric and bears negligible biasness for non-symmetric distribution. The performance of the proposed mean estimator is compared to its competitors in simple random sampling

Abstract A large number of the path key establishment schemes regard same probability of the node capture attack for each node in the wireless sensor networks. However, in certain critical applications this statement may not be right making such schemes less practical for many real-world applications like border surveillance and disaster management. In this paper, an attack matrix (AM) is designed

Abstract The cubic intuitionistic implicative ideals in BCK-algebras and the relationship between a cubic intuitionistic subalgebra, a cubic intuitionistic ideal and a cubic intuitionistic implicative ideal are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic implicative ideal are provided. Characterizations of a cubic intuitionistic implicative ideal are considered

Abstract The thermal and mass boundary layer flow of a time-dependent isochoric viscous fluid over an oscillating cylinder entrenched in a porous medium is investigated numerically. The governing problem contains a set of coupled nonlinear partial differential equations with significant initial and boundary conditions and are solved using an implicit finite difference scheme, namely Crank–Nicholson

Abstract In this paper, we have considered all the possible continuous subgroups of the Lie group \(SL(2;{\mathbb {R}})\) (upto conjugacy) from dimension zero to three. For each of the classification, we have defined group action on the same line as Kisil. Möbius transformation has been taken as the corresponding action. This action is defined on the homogeneous spaces of various dimensions generated

Abstract In this paper, we aim to establish the new integrals involving S-function and Laguerre polynomials. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formula involving the S-function and the Laguerre polynomials as their special cases .

Abstract In this paper, an attempt has been made to reduce the negative effect of random non-response in the estimation procedure of population variance in two-phase sampling. A difference-type imputation method has been considered to reduce the wrong impact of random non-response in the two-phase sampling. To build efficient estimation strategies, information on two auxiliary characters has been used

Abstract We present ultrasonic properties of lutetium monopnictides (LuPn: Pn = As and Sb) with the help of second and third order elastic constants in the temperature range 100–300 K. These elastic constants have been computed using Coulomb and Born–Mayer potential with the help of two basic parameters i.e., nearest neighbor distance and hardness parameter. First these elastic constants are applied

Abstract This paper deals with the study of Kantowski–Sachs universe in the presence of an anisotropic dark energy within the framework of Lyra geometry. A special form of time-varying deceleration parameter and present non-singular cosmological model were used to obtain exact solutions of Einstein's field equations. The physical and geometric features of the cosmological model were discussed. Under

Abstract Based on the \(\tan (\Phi (\xi )/2)\)-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup

Abstract Attempts have been made to discuss how successfully data can be delivered in vehicular ad hoc network which is a special kind of ad hoc network distinguished by its node movement characteristics, hybrid network architectures, and new application scenarios. The research shows that the application of fuzzy logic techniques in multi-hop greedy position-based routing helps in successfully delivering

Abstract This paper presents a chaos-based cancelable biometric scheme for iris recognition. Instead of using original iris features, a masked version of the features is generated through chaotic map encryption for increasing the iris recognition system privacy. The proposed framework for iris recognition includes iris localization, normalization, and feature extraction with Gabor filter. Finally,

Abstract The efficient k-distance domination number \(\gamma ^{k}_{e}(G)\) is the minimum among the cardinalities of efficient k-distance dominating sets of G. Upper bound in terms of order and maximum degree of an independent set S of vertices in a graph \(G=(V,E)\) called an efficient k-distance dominating set if every vertex in \(V-S\) be distance k from exactly one vertex in S has been presented

Abstract The Discrete Cosine Transform (DCT) is an important transform in image and video processing systems. The perception of human visualization permits us to be numerically approximate rather than exact with slight compromise in accuracy. In this paper, we have proposed a digital implementation of 16-point approximate DCT architecture based on Modified Gate Diffusion Input (MGDI) technique. The

Abstract The hydrogeochemical study on glacial meltwater gives important information about the quality of meltwater and weathering processes controlling dissolved ions chemistry in the glacierized area. Anionic abundance in the Manimahesh Glacier meltwater shows a trend of HCO3− > SO42− > Cl− = NO3−, whereas cationic abundance in the meltwater shows a trend of Ca2+ > Mg2+ > K+ > Na+. On the basis of

Abstract The standard model (SM) of particle physics is a gauge-field theoretical model, produced of two non-abelian gauge groups and one abelian gauge group. This model has proved to be extremely successful during the past three decades. The Higgs boson which plays a unique role in the SM was the last part of the SM that was experimentally verified in 2012. In the SM, all observable particles are

Abstract Let \((s_n)\) be a sequence of real numbers. We say that \((s_n)\) is summable to \(\xi \) by the logarithmic power series method if $$\lim _{x\rightarrow 1^-}f(x)=\xi, \quad {\text{where}}\quad f(x)=-\frac{1}{\log (1-x)}\sum_{n=0}^{\infty }\frac{s_n}{n+1}x^{n+1}. $$It is well known that if the limit \(\lim_{n \rightarrow \infty }s_n=\xi \) exists, then the limit $$\lim _{x \rightarrow 1^-}

Abstract Attempts have been made to propose a software reliability growth model (SRGM) based on non-homogeneous Poisson process for NVP system. The proposed model concerns the combined effect of increasing fault detection rate and fault removal efficiency under imperfect debugging. Moreover, a cost model has been developed. Also, an optimal release policy based on the proposed cost model and the number

Abstract Transportation plays a major role in the industrial and corporate world and so as uncertainty. Several ways have been given in the literature to deal with the imprecision originated from various uncontrollable factors and conditions. In this paper, we consider transportation problems with uncertainty in transportation costs and propose an alternate algorithm to find its initial basic feasible

Abstract Lorentz hypersurfaces \(M_{1}^{4}\) is studied in \(E_{1}^{5}\) with non-diagonal shape operators having characteristic equation \((y-\lambda )^2(y-\lambda _3)(y-\lambda _4)\) or \((y-\lambda )^3(y-\lambda _4)\) or \(((y-\lambda )^2+\mu ^2)(y-\lambda _3)(y-\lambda _4)\). It is proved that if the mean curvature vector field \(\vec {H}\) of Lorentz hypersurfaces \(M_{1}^{4}\) in \(E_{1}^{5}\)

Abstract Carbon nanotubes are cylindrical carbon molecules which offer promising applications in nanotechnology due to high thermal conductivity. These carbon allotropes can be utilized as additives in various structural materials. Recent development in numerous technological and industrial sectors such as chemical bonding process, optics, and microelectronics requires a strong need to develop such