In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

In this paper, we introduce intuitionistic fuzzy incline (IFI), intuitionistic fuzzy incline matrix (IFIM) and its determinant. Also the transitive closure, power of convergent, nilpotence of IFIM and adjoint of an IFIM are considered here. Some properties of determinant of IFIM and triangular IFIM are also introduced here. 2010 AMS Classification: 03E72, 15A15, 15B15

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N2 − 1)× (N2 − 1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N × N matrices in the fundamental representation.

We give a detailed description of the adjoint representation of Drinfeld's twist element, as well as of its coproduct, for suq(2). We also discuss, as applications, the computation of the universal R-matrix in this representation and the problem of symmetrization of identical-particle states with quantum su(2) symmetry.

This paper proposes a new method for estimating the error in the solution of matrix equations. The estimate is based on the adjoint method in combination with small sample statistical theory. It can be implemented simply and is inexpensive to compute. Numerical examples are presented which illustrate the power and effectiveness of the new method.  2004 IMACS. Published by Elsevier B.V. All rig...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker func...

We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener measure on phase space, as the diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian.

We show that, under a condition called minimality, if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, then the associated integrable twistor structure (or TERP structure, or non-commutative Hodge structure) is pure and polarized.

The first edition of these notes was written by Professor Dyson. The second edition was prepared by Michael J. Moravcsik; he is responsible for the changes made in the process of re-editing. A * : complex conjugate transposed (Hermitian conjugate) A + : complex conjugate (not transposed) A : A * β = A * γ 4 = adjoint A −1 = inverse A T = transposed I = identity matrix or operator i

Let H0 and H be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference φ(H)−φ(H0) for piecewise continuous functions φ. This description involves the scattering matrix for the pair H, H0.