scholarly journals Weighted Bergman Kernels and Mathematical Physics

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 48
Author(s):  
Elisabetta Barletta ◽  
Sorin Dragomir ◽  
Francesco Esposito
Keyword(s):  
Transition Probability ◽  
Pseudoconvex Domains ◽  
Computational Tool ◽  
Open Problems ◽  
Weighted Version ◽  
Bergman Kernels ◽  
Classical State ◽  
Lorentzian Metric ◽  
Classical Phase Space ◽  
Fefferman’S Metric

We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems whose classical phase space is a complex manifold, and turn out to be an efficient computational tool that is useful for the calculation of transition probability amplitudes from a classical state (identified to a coherent state) to another. We review the weighted version (for weights of the form γ = | φ | m on strictly pseudoconvex domains Ω = { φ < 0 } ⊂ C n ) of Fefferman’s asymptotic expansion of the Bergman kernel and discuss its possible extensions (to more general classes of weights) and implications, e.g., such as related to the construction and use of Fefferman’s metric (a Lorentzian metric on ∂ Ω × S 1 ). Several open problems are indicated throughout the survey.

scholarly journals Estimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in C3

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Sanghyun Cho
Keyword(s):  
Kernel Function ◽  
Bergman Kernel ◽  
Pseudoconvex Domain ◽  
Tangential Direction ◽  
Pseudoconvex Domains ◽  
Bergman Kernel Function ◽  
Bergman Kernels ◽  
Optimal Estimates

Let Ω be a smoothly bounded pseudoconvex domain in C3 and assume that TΩreg(z0)<∞ where z0∈bΩ, the boundary of Ω. Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve” Cb(z0,δ0)⊂Ω∪z0.

Remarks on infinitesimal symmetries of geometrical structures of the classical phase space of general relativistic test particle

2015 ◽  
Vol 12 (08) ◽  
pp. 1560020 ◽  
Author(s):  
Josef Janyška
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Test Particle ◽  
Contact Structure ◽  
Jet Space ◽  
Geometrical Structures ◽  
Lorentzian Metric ◽  
Dimensional Phase Space ◽  
General Relativistic ◽  
Classical Phase Space

The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric and an electromagnetic field define the joined almost-cosymplectic-contact structure on the odd-dimensional phase space. In this paper, we study infinitesimal symmetries (ISs) of this phase structure. We prove that there are no hidden ISs.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

CAD Of Anticorrosive Protection Of Steel Structures

2019 ◽  
pp. 18-23
Keyword(s):  
Protective Coating ◽  
Computer Aided Design ◽  
Steel Structures ◽  
Cost Effective ◽  
Operating Conditions ◽  
Computational Tool ◽  
Protection Method ◽  
Cost Effective Method ◽  
The Cost ◽  
Aided Design

The choice of cost-effective method of anticorrosive protection of steel structures is an urgent and time consuming task, considering the significant number of protection ways, differing from each other in the complex of technological, physical, chemical and economic characteristics. To reduce the complexity of solving this problem, the author proposes a computational tool that can be considered as a subsystem of computer-aided design and used at the stage of variant and detailed design of steel structures. As a criterion of the effectiveness of the anti-corrosion protection method, the cost of the protective coating during the service life is accepted. The analysis of existing methods of steel protection against corrosion is performed, the possibility of their use for the protection of the most common steel structures is established, as well as the estimated period of effective operation of the coating. The developed computational tool makes it possible to choose the best method of protection of steel structures against corrosion, taking into account the operating conditions of the protected structure and the possibility of using a protective coating.

Regional household poverty and mobility analysis – a transition probability approach

2020 ◽  
Vol 63 (3) ◽  
pp. 286-302
Author(s):  
Damian Mowczan ◽  
Keyword(s):  
Transition Probability ◽  
General Level ◽  
Transition Matrices ◽  
Equivalent Unit ◽  
Central Statistical ◽  
Per Capita ◽  
Probability Matrices ◽  
General Mobility ◽  
One Year ◽  
The One

The main objective of this paper was to estimate and analyse transition-probability matrices for all 16 of Poland’s NUTS-2 level regions (voivodeship level). The analysis is conducted in terms of the transitions among six expenditure classes (per capita and per equivalent unit), focusing on poverty classes. The period of analysis was two years: 2015 and 2016. The basic aim was to identify both those regions in which the probability of staying in poverty was the highest and the general level of mobility among expenditure classes. The study uses a two-year panel sub-sample of unidentified unit data from the Central Statistical Office (CSO), specifically the data concerning household budget surveys. To account for differences in household size and demographic structure, the study used expenditures per capita and expenditures per equivalent unit simultaneously. To estimate the elements of the transition matrices, a classic maximum-likelihood estimator was used. The analysis used Shorrocks’ and Bartholomew’s mobility indices to assess the general mobility level and the Gini index to assess the inequality level. The results show that the one-year probability of staying in the same poverty class varies among regions and is lower for expenditures per equivalent units. The highest probabilities were identified in Podkarpackie (expenditures per capita) and Opolskie (expenditures per equivalent unit), and the lowest probabilities in Kujawsko-Pomorskie (expenditures per capita) and Małopolskie (expenditures per equivalent unit). The highest level of general mobility was noted in Małopolskie, for both categories of expenditures.

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