The adjoint curve of any Frenet curve r=r(s) is defined as the integral of binormal vector with any parameter s, of a curve r. In this paper,we analyzed the problem of finding a surfaces pencil through a given the spacelike adjoint curve as an asymptotic curve, geodesic or a line of curvature in Minkowski 3-space, respectively. We find necessary and sufficient condition for a surface pencil possessing the spacelike adjoint curve as an asymptotic curve, geodesic or line of curvature. We illustrate this method by presenting some examples.

An investigation into the representation of integrals involving the product of the logarithm and the $\tanh ^{-1}$ functions will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann Zeta function, the Dirichlet Eta function, Dirichlet Lambda function and many other special functions. Some examples illustrating the theorems will be detailed.

In this paper, we study the initial value problem for a semi-linear nonclassical diffusion equations with fading memory in $\mathbb{R}^{n}$. Under smallness conditions on the initial data, the global existence and decay estimates of the solutions are established. Furthermore, time decay estimates in higher Sobolev space of the solution are provided. The proof is carried out by means of the pointwise decay estimates of the solution in the Fourier space and a fixed point-contraction mapping argument.

In this article, we examine the combined Jacobsthal-Padovan (CJP) generalized quaternions with four special cases: Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan and modified Jacobsthal-Padovan generalized quaternions. Then, recurrence relation, generating function, Binet-like formula and exponential generating function of these quaternions are examined. In addition to this, some new properties, special determinant equations, matrix formulas and summation formulas are discussed.

In this paper, we derive Hölder's inequality (weighted standard as well as reverse), Minkowski's inequality, Grüss-integral inequality and Hermite-Hadamard inequalities for fractional $(p,q)$-calculus.

A Gröbner-Shirshov basis and classification of the normal forms for the infinite Coxeter group of type $\widetilde{C}_n$ are obtained. A new algorithm for getting normal forms of elements of this groups is also given.

This research article aims to staunchly study the approximation using Lagrange interpolation on the unit circle. Nodal system constitutes the vertically projected zeros of Jacobi polynomial onto the unit circle with boundary points at $ \pm $1. Moreover, convergence is obtained by considering analytic functions on a suitable domain accompanied by some numerical experiments.