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This paper is intended to explore the Rorty’s notion of truth and its vicinity and divergences with Putnam’s notion of truth. Rorty and Putnam, both the philosophers have developed their notion of truth against the traditional representational notion of truth but their strength lies in its distinctive characterization. For Putnam, truth is the property of a statement which cannot be lost but the justification of it could be. I will also examine the importance of Putnam’s idealized justificatory conditions without which he may succumb to the charge of relativism at the same time how does Putnam overcome the tension between metaphysical and relativistic stances of truth. For Rorty, truth is not representational rather it is social, which means the justification for a true belief is not external but internal to the community of believers. I would further examine how Rorty tries to dispel the charge of relativism which is hard to overcome. Finally, I shall try to defend the concept of truth which is free from metaphysical baggage and relativistic threats; and in this enterprise Rorty walks half the way and Putnam completes the journey.

Stable multistep schemes based on Caputo fractional derivative approximation are presented for solving 1D and 2D nonlinear fractional model arising from dielectric media. We approximate Caputo fractional derivatives in time with a multistep scheme of order O ( τ 3 − α ) & O ( τ 3 − β ) , 1 β α 2 , spatial Laplacian operator with a central difference scheme, and nonlinear source term g ( B ) by using Taylor series. The discretization of the problem results in a linear system of equations that is tridiagonal and penta-diagonal for 1D and 2D case, respectively. The unique solvability and unconditional stability are derived for both cases. The convergence of schemes is established with the help of optimal error bounds. Further, we establish that the order of convergence for 1D case is O ( τ 3 − α + τ 3 − β + h 2 ) and for 2D case is O ( τ 3 − α + τ 3 − β + h x 2 + h y 2 ) . Moreover, the stability of our schemes are verified numerically by adding some linear and nonlinear noisy inputs. Finally, four test functions are investigated to show the effectiveness and stability of our schemes. The method is simple, easy to implement, and yields very accurate results.

Present investigation evaluates the protective effect of vanillin against sepsis. Sepsis was induced by cecal ligation and puncture (CLP) in rat and vanillin was administered at dose of 100 and 200 mg/kg p.o. for five days after induction of sepsis. Effect of vanillin was observed on the percentage of survival, body weight and food intake were determined in CLP induced sepsis rats. Level of liver enzymes in the serum and organ weight was also observed in vanillin treated CLP induced rats. Moreover, histopathological changes were also observed in liver and lung tissue of hematoxylin and eosin (HE) staining. There was significant improvement in bodyweight and food intake in vanillin treated group than negative control group after the sepsis induction. Moreover, vanillin improves the percentage of survival rate and reduces the level of liver enzymes and spleen weight in CLP induced sepsis rat. It also improves the level of glutathione (GSH) compared to negative control group. In conclusion, data of investigation reveals that vanillin ameliorates the survival rate and oxidative stress in CLP induced sepsis rat model.

The current study is presented to develop two approaches and methodologies to find the numerical solution of linear and non-linear initial value problems such as Lane–Emden type equation, Riccati’s equation and Bessel’s equation of order zero based on approximation. The function approximations (scheme-I and scheme-II) are presented to find the numerical solutions of linear and non-linear initial value problems by using Gauss Legendre roots as node points and random node points in the domain [0, 1]. In the scheme-I, the roots of Legendre polynomial are used as node points for Lagrange polynomials and in scheme-II, we have taken random node points in the domain [0, 1] and orthogonalize the resulting Lagrange polynomials using Gram–Schmidt orthogonalization process. Firstly, we have introduced the function approximations by using generating interpolating scaling functions (ISF) and orthonormal Lagrangian basis functions (OLBF) over the space $$L^{2}[0,1]$$ then we have constructed the operational matrices of integration and product operational matrices based on newly designed approximations namely ISF and OLBF. These operational matrices convert given linear and non-linear initial value problems into the associated system of algebraic equations. Finally, we have established error bounds (Lemmas 1, 2) of both scheme-I and scheme-II including the function approximations. The efficiency of the proposed schemes has been confirmed with several test examples including numerical stability. So, the schemes are simple, efficient and produces very accurate numerical results in considerably small number of basis functions and hence reduces computational effort.

Heterocycles occupy a salient place in chemistry due to their wide range of activity in the fields of drug design, photochemistry, agrochemicals, dyes, and so on. Amongst all, indole scaffold is considered as one of the most promising heterocycles found in natural and synthetic sources and has been shown to possess various biological activity, including anti-inflammatory, anti-HIV, antitubercular, antimalarial, anticonvulsant, antidiabetic, antihypertensive, analgesics, antidepressant, anticancer, antioxidant, antifungal, and antimicrobial, etc. All the reported indole molecules bind to multiple receptors with high affinity, thus expedite the research on the development of novel biologically active compounds through the various approach. In this review, we aimed to highlight synthetic and medicinal perspective on the development of indole-based analogs. In addition, structural activity relationship (SAR) study to correlate for their biological activity also discussed.

In this article, multistep finite difference schemes are developed for solving one dimensional (1D) and two dimensional (2D) fractional differential models of electromagnetic waves (FDMEWs) arising from dielectric media which contain both initial and Dirichlet boundary conditions. The Caputo’s fractional derivatives in time are discretized by a difference scheme of order O ( τ 3 − α ) & O ( τ 3 − β ) , 1 β α 2 , and the Laplacian operator is approximated by central difference discretization. The proposed multistep schemes transform the FDMEWs into the tridiagonal system for 1D case and pentagonal system for 2D case. Theoretical unconditional stability, convergence analysis and error bounds are investigated. For 1D FDMEWs, accuracy of order O ( τ 3 − α + τ 3 − β + h 2 ) and for 2D FDMEWs, accuracy of order O ( τ 3 − α + τ 3 − β + h 1 2 + h 2 2 ) are investigated, where 1 β α 2 . Several test examples are included to verify the reliability and computational efficiency of the proposed schemes which support our theoretical findings for both 1D and 2D cases.

The key purpose of this study is to present two schemes based on Lagrange polynomials to deal with the numerical solution of second order two-dimensional telegraph equation (TDTE) with the Dirichlet boundary conditions. First, we convert the main equation into partial integro-differential equations (PIDEs) with the help of initial and boundary conditions. The operational matrices of differentiation and integration are then used to transform the PIDEs into algebraic generalized Sylvester equation. We compared the results obtained by the proposed schemes with Bernoulli matrix method and B-spline differential quadrature method which shows that the proposed schemes are accurate for small number of basis functions.