scholarly journals Inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree

2018 ◽  
Vol 26 (5) ◽  
pp. 673-680
Author(s):  
Alexander Mikhaylov ◽  
Victor S. Mikhaylov ◽  
Gulden Murzabekova

Abstract We consider inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as the matrix potentials on each edge. As inverse data we use the Weyl–Titchmarsh matrix function or the dynamic response operator.

2019 ◽  
Vol 39 (5) ◽  
pp. 645-673
Author(s):  
Kamila Dębowska ◽  
Leonid P. Nizhnik

The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on informations about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.


2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.


Author(s):  
Bilender Allahverdiev ◽  
Hüseyin Tuna

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).


2020 ◽  
Vol 8 (3) ◽  
pp. 202 ◽  
Author(s):  
Viktor P. Afanas’ev ◽  
Alexander Yu. Basov ◽  
Vladimir P. Budak ◽  
Dmitry S. Efremenko ◽  
Alexander A. Kokhanovsky

In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Foued Zitouni ◽  
Mario Lefebvre

The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.


2020 ◽  
Author(s):  
David Nagy ◽  
Annette E. Rosenbom ◽  
Bo V. Iversen ◽  
Mohamed Jabloun ◽  
Finn Plauborg

Abstract. The conceptual understanding of the preferential water flow is crucial and hence understanding the degree of water percolating rapidly through vertical macropores, or slowly through the low-permeable matrix, is vital in order to assess the risk of contaminants like nitrate and pesticides being transported through a variably-saturated macroporous clay till to drainage. This study compared six different model concepts, using the dual-permeability module of the one-dimensional model DAISY, incorporating three different macropore settings and two different groundwater tables set as lower boundary conditions. The three macropore settings included vertical macropores supplying water directly to (a) drainage, (b) drainage and matrix and (c) drainage and matrix including fractures supplying water to the matrix in the saturated zone. The model study was based on ten years of coherent climate, drainage, and groundwater data from an agricultural clay till field. The estimated drainage obtained with the six model concepts was compared to the measured drainage. No significant discrepancies between the estimated and measured drainage were identified. The model concept with the macropore setting (b) exposed to groundwater fluctuations measured in the southern part of the field, gave the best description of the drainage. Bromide leaching tests were used to evaluate the mass balance of the model concepts. The estimated water balance of all six concepts revealed that 70 % of the precipitation input to drainage was transported via macropores. According to the results of bromide leaching simulation, 54 % of the drainage was estimated to be transported via vertical macropores being initiated in the plow layer.


2007 ◽  
Author(s):  
R. Barkhudaryan ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nicola Gorini ◽  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Silvia Penati ◽  
Domenico Seminara ◽  
...  

Abstract We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.


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