Tube Domains Research Articles

Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains

Abstract We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains. The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry of non-Gromov hyperbolic convex domains. A connection between the Hilbert metric of a convex domain Ω in ℝ n {\mathbb{R}^{n}} with the Kobayashi distance of the tube domain over the domain Ω is also shown. Moreover, continuity properties up to the boundary of complex geodesics in tube domains with a smooth convex bounded base are also studied in detail.

Convex floating bodies as approximations of Bergman sublevel sets on tube domains

For a pseudoconvex tube domain, we prove estimates that relate the sublevel sets of its diagonal Bergman kernel to the floating bodies of its convex base. This allows us to associate a new affine invariant to any convex body.

Computational Modeling and Dynamics of the Oil and Water Flow Using the Galerkin Approximation

A Computational Fluid Dynamic (CFD) model is presented to analyze the flow dynamics of a two phase incompressible flow in the application sectors of different industries. The Finite Element method (FEM) which is based on the Galerkin approximation, has been implemented for this two phase flow model. Generally, two-phase flows can occur in different forms like gas-liquid, liquid-liquid and solid-liquid forms. The Oil and Water two-phase flow is an important phenomenon in petroleum industry for crude oil production and transportation. In our study, a laminar flow of liquid-liquid phase is considered to simulate the flow dynamics where the liquid phases are water and oil. The COMSOL Multiphysics software is used to perform the simulation including velocity profile, volume fraction, shear rate, pressure distributions and interfacial thicknesses at different times. A typical circular tube domain with radius 0.05 m and length 8 m is assumed for our simulation.

Improved Li+ Storage through Homogeneous N-Doping within Highly Branched Tubular Graphitic Foam.

A novel carbon structure, highly branched homogeneous-N-doped graphitic (BNG) tubular foam, is designed via a novel N, N-dimethylformamide (DMF)-mediated chemical vapor deposition method. More structural defects are found at the branched portions as compared with the flat tube domains providing abundant active sites and spacious reservoirs for Li+ storage. An individual BNG branch nanobattery is constructed and tested using in situ transmission electron microscopy and the lithiation process is directly visualized in real time.

The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure \(\mu \) so that the Hardy space \(H^{p}, 1\le p < \infty ,\) continuously embeds in the weighted Lebesgue space \(L^q (T_\Omega ,d\mu )\) with a larger exponent. Finally we use this result to characterize multipliers from \(H^{2m}\) to Bergman spaces for every positive integer m.

Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions

We consider a conservative system consisting of an elastic plate interacting with a gas filling a semi-infinite tube. The plate is placed on the bottom of the tube. The dynamics of the gas velocity potential is governed by the linear wave equation. The plate displacement satisfies the linear Kirchhoff equation. We show that this system possesses an infinite number of periodic solutions with the frequencies tending to infinity. This means that the well-known property of decaying of local wave energy in tube domains does not hold for the system considered.

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

WEIGHTED INTEGRAL REPRESENTATIONS IN TUBE DOMAIN OVER REAL UNIT BALL

Weighted spaces of functions holomorphic in tube domain over the real unit ball of R n are considered. For these classes reproducing kernels are constructed in an explicit form. Estimates for these kernels are obtained.

Bergman-type integral operators on semiproducts of the tube domains over symmetric cones and multifunctional analytic spaces

Bergman-type integral operators on semiproducts of the tube domains over symmetric cones and multifunctional analytic spaces

Towards Oka–Cartan theory for algebras of holomorphic functions on coverings of Stein manifolds. II

We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H^{\infty} ). In particular, in this context we obtain results on holomorphic extension from complex sub manifolds, properties of divisors, corona-type theorems, holomorphic analogues of the Peter–Weyl approximation theorem, Hartogs-type theorems, characterizations of uniqueness sets, etc. Our proofs are based on analogues of Cartan theorems A and B for coherent-type sheaves on maximal ideal spaces of these algebras proved in Part I.

Complex geodesics in convex tube domains

We describe all the complex geodesics in convex tube domains. In the case where the base of a convex tube domain does not contain any real line, the obtained description involves the notion of boundary measure of a holomorphic map and it is expressed in the language of real Borel measures on the unit circle. Applying our result, we calculate all complex geodesics in convex tube domains with unbounded base covering a special class of Reinhardt domains.

Towards Oka–Cartan theory for algebras of holomorphic functions on coverings of Stein manifolds I

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona-type theorems, properties of divisors, holomorphic analogs of the Peter–Weyl approximation theorem, Hartogs-type theorems, characterization of uniqueness sets. The model examples of these algebras are: (1) Bohr’s algebra of holomorphic almost periodic functions on tube domains; (2) algebra of all fibrewise bounded holomorphic functions (e.g., arising in the corona problem for H^\infty ). Our approach is based on an extension of the classical Oka–Cartan theory to coherent-type sheaves on the maximal ideal spaces of these algebras – topological spaces having some features of complex manifolds.

Complex geodesics in convex tube domains II

Complex geodesics are fundamental constructs for complex analysis and as such constitute one of the most vital research objects within this discipline. In this paper, we formulate a rigorous description, expressed in terms of geometric properties of a domain, of all complex geodesics in a convex tube domain in \({\mathbb {C}}^n\) containing no complex affine lines. Next, we illustrate the obtained result by establishing a set of formulas stipulating a necessary condition for extremal mappings with respect to the Lempert function and the Kobayashi–Royden metric in a large class of bounded, pseudoconvex, complete Reinhardt domains: for all of them in \({\mathbb {C}}^2\) and for those in \({\mathbb {C}}^n\) whose logarithmic image is strictly convex in the geometric sense.

On the Kobayashi hyperbolicity of tube domains in [formula omitted

We construct elementary counterexamples to the criterion for Kobayashi hyperbolicity for a class of tube domains in C2 proposed by J.-J. Loeb.

Cauchy wavelet transform of ultra-distributions in tube domains

In this paper, Cauchy wavelet transform of ultra-distributions in tube domains is defined and its various properties are studied using the theory of Cauchy integrals and Poisson integrals of ultra-distributions.

Numerical prediction of the pressure fluctuations on small discharge condition of a pump-turbine at pump mode

The operational stability of the pump turbine at the pump mode will be greatly influenced by large pressure fluctuations when operated in the small-discharge conditions. Therefore, it is significant to analyse the flow characteristic under the small discharge operating conditions deeply. Study of the internal flow in the small discharge condition has been investigate in great detail combined with model experiments in this paper. The SST k-ω turbulence model is adopted to perform three-dimensional numerical simulation of the entire pump-turbine flow passage at optimal guide vanes opening. The numerical simulation results match well with experimental data. Then internal flow under the small discharge condition is analysed. The results show that the dominant frequency inside the flow passage is a relative low frequency. In addition, there are obvious complex flow phenomena inside the draft tube, runner and diffuser domains, such as secondary flow, backflow and even vortex, leading to strong unsteady flow and significant pressure fluctuation.

Carleson Embeddings and Two Operators on Bergman Spaces of Tube Domains over Symmetric Cones

We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Cesaro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Cesaro-type operators on weighted Hilbert-Bergman spaces.

Some questions related to the Bergman projection in symmetric domains

AbstractThis is essentially a survey on tube domains over irreducible symmetric cones or their bounded realizations. It includes the fact that in rank 2 these inequalities have now been proved for the whole range of possible exponents

A realization for a $\mathbb{Q}$-Hermitian variation of Hodge structure of Calabi-Yau type with real multiplication

We show that the $\mathbb{Q}$-descents of the canonical $\mathbb{R}$-variation of Hodge structure of Calabi-Yau type over a tube domain of type $A$ can be realized as sub-variations of Hodge structure of certain $\mathbb{Q}$-variations of Hodge structure which are naturally associated to abelian varieties of (generalized) Weil type.

ON EXTREMAL PROBLEMS IN TUBULAR DOMAINS OVER SYMMETRIC CONES

We prove new sharp distance theorems for analytic spaces in tube domains over symmetric cones extending our pre- vious results in this direction