Let $$\mathcal {H}$$ be a Hilbert space, A positive definite operator in and $$\langle f,g\rangle _A=\langle Af,g\rangle $$ , $$f,g\in \mathcal the A-inner product. This paper studies geometry of set $$\begin{aligned} {I}_A^a:=\{\text { adjointable isometries for } \langle \ \rangle _A\}. \end{aligned}$$ It is proved that {I}_A^a$$ submanifold Banach algebra operators, homogeneous space group i...

In this paper we present an a priori error estimate of the Runge-Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge-Kutta method and the finite element space is made up of piecewise polynomials of degree k ≥ 2. Quasi-optimal error estimate is obtained by energy techniques,...

We consider the first-order Cauchy problem ∂zu + a(z, x,Dx)u = 0, 0 < z ≤ Z, u |z=0 = u0, with Z > 0 and a(z, x,Dx) a k×k matrix of pseudodifferential operators of order one, whose principal part a1 is assumed symmetrizable: there exists L(z, x, ξ) of order 0, invertible, such that a1(z, x, ξ) = L(z, x, ξ) (−iβ1(z, x, ξ) + γ1(z, x, ξ)) (L(z, x, ξ))−1, where β1 and γ1 are hermitian symmetric and...

We introduce the notion of a symmetrizable finite difference operator and prove that such operators are stable. We then present some sufficient conditions for symmetrizability. One of these extends H.-O. Kreiss' theorem on dissipative difference schemes for hyperbolic equations to a more general case with full (jc , invariable coefficients.

in this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎some results in [a. v‎. ‎arhangel'skii and j‎. ‎van mill‎, ‎on topological groups with a first-countable remainder‎, ‎topology proc. 42 (2013...

We consider a general parabolic category OS over symmetrizable Kac-Moody algebras. introduce reduction rule of hom-spaces between Verma modules different algebras which yield some applications on module homomorphisms.