Related papers: Three-line derivation of the Thomas precession

We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is…

A fractional Adomian decomposition method for fractional nonlinear differential equations is proposed. The iteration procedure is based on Jumarie's fractional derivative. An example is given to elucidate the solution procedure, and the…

A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with…

We derive a symplectic analogue of A-directed immersion theorem.

We obtain some results related to Romanoff's theorem.

We consider the third order differential equation derived from the deformed Seiberg-Witten differential for pure ${\cal N}=2$ SYM with gauge group $SU(3)$ in Nekrasov-Shatashvili limit of $\Omega$-background. We show that this is the same…

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

In this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. In case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form.

I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…

In motion Kinematics, it is well-known that the time derivative of a 3x3rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix valued) function of the angular…

A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…

We settle in the affirmative the Graham-Sloane conjecture.

We give an explicit parameterization of the general 8k -3 instanton.

A very simple but useful almost sure convergence theorem of probability is given.

I present a brief update on the transverse polarization distributions, focusing on model calculations and phenomenological perspectives.

We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.

This is a reference volume on polyfold and Fredholm theory.