Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the sphere S. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections taking values in a spinor bundle and annihilated by a Dirac operator, or generalized Cauchy-Riemann operator. Basic properties of this kernel are examined, in particular we exa...

M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...

This paper considers a scheduling problem in which a single operator completes a set of n jobs requiring operations on two machines. The operator can perform only one operation at a time, so when one machine is in use the other is idle. After developing general properties of optimal schedules, the paper develops e cient algorithms for minimizing maximum lateness. The algorithm has time complexi...

We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...

The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in open string theory and boundary conformal field theory. We present some results, problems, conjectures, their conceptual implications and meanings in a program...

Let E be a Banach space, with unit ball BE . We study the spectrum and the essential spectrum of a composition operator on H∞(BE) determined by an analytic symbol with a fixed point in BE . We relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point. We extend a theorem of Zheng to the context of analytic symbols on the open unit ball of a Hilbe...

We show that the knowledge of the set of the Cauchy data on the boundary of a C bounded open set in R, n ≥ 3, for the Schrödinger operator with continuous magnetic and bounded electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives.

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

"Let $\B_X$ be a bounded symmetric domain realized as the open unit ball of JB*-triple $X$ which may infinite dimensional. In this paper, we characterize weighted composition operators from Hardy space $H^{\infty}(\mathbb{B}_X)$ into $\alpha $-Bloch $\mathcal{B}^\alpha (\B_X)$ on $\mathbb{B}_X$. Later, show multiplication operator is bounded. Also, give norm operator."

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...