The eigenproblems of the rank-one updates of the matrices have lots of applications in scientific computation and engineering such as the symmetric tridiagonal eigenproblems by the divide-andconquer method and Web search engine. Many researchers have well studied the algorithms for computing eigenvalues of Hermitian matrices updated by a rank-one matrix [1–6]. Recently, Ding and Zhou studied a ...

in terms of the Langlands parametrization of Irr(G). More precisely, the Gan-Gross-Prasad triples come from certain pairs W ⊂ V of quadratic spaces or hermitian spaces (over a fixed quadratic extension E/F ). We will denote uniformly by h the underlying quadratic or hermitian form on these spaces. To get a GGP triple, you need the following two conditions to be satisfied : – W⊥ (the orthogonal ...

For any natural number l and any prime p ≡ 1 (mod 4) not dividing l there is a Hermitian modular form of arbitrary genus n over L := Q[ √ −l] that is congruent to 1 modulo p which is a Hermitian theta series of an OL-lattice of rank p− 1 admitting a fixed point free automorphism of order p. It is shown that also for non-free lattices such theta series are modular forms.

The work contains a detailed investigation of free neutral (Hermitian) or charged (non-Hermitian) scalar fields and the describing them (system of) Klein-Gordon equation(s) in momentum picture of motion. A form of the field equation(s) in terms of creation and annihilation operators is derived. An analysis of the (anti-)commutation relations on its base is presented. The concept of the vacuum a...

We analyze a class of non-Hermitian quadratic Hamiltonians, which are of the form H = A†A + αA2 + βA† 2, where α , β are real constants, with α 6= β, and A† and A are generalized creation and annihilation operators. Thus these Hamiltonians may be classified as generalized Swanson models. It is shown that the eigenenergies are real for a certain range of values of the parameters. A similarity tr...

The generalized Kähler structures were introduced and studied by M. Gualtieri in his PhD thesis [16] in the more general context of generalized geometry started by N. Hitchin in [20]. There are many explicit constructions of non-trivial generalized-Kähler structures [1, 2, 21, 24, 25, 4, 7]. For instance Gualtieri proved that all compact-even dimensional semisimple Lie groups are generalized Kä...

We propose a method for explicit computation of the Chern character form of a holomorphic Hermitian vector bundle (E, h) over a complex manifold X in a local holomorphic frame. First, we use the descent equations arising in the double complex of (p, q)-forms on X and find the explicit degree decomposition of the Chern–Simons form csk associated to the Chern character form chk of (E, h). Second,...

we observe that the variable φ enters the expression in the form of the operator ∂2/∂φ2. This operator—1D Laplace operator with respect to the variable φ—is a Hermitian operator in the space of single-valued functions of the angle φ, because single-valuedness is equivalent to the 2π-periodicity, and Laplace operator is Hermitian in the space of periodic functions. Hence, we have ONB of the eige...