On the Local Coefficients Matrix for Coverings of $$\mathrm{SL}_2$$SL2

2018 ◽  
pp. 207-244 ◽  
Author(s):  
Fan Gao ◽  
Freydoon Shahidi ◽  
Dani Szpruch
Keyword(s):  
Local Coefficients

Mathematical Formulation of the Global Coefficients of Transmission and Reflection of Ultrasonic Waves in Bi-Phase Porous Medium

2015 ◽  
Vol 1101 ◽  
pp. 471-479
Author(s):  
Georges Freiha ◽  
Hiba Othman ◽  
Michel Owayjan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Mathematical Formulation ◽  
Ultrasonic Waves ◽  
Ultrasonic Wave Propagation ◽  
Local Coefficients ◽  
Important Field ◽  
New Formulation ◽  
Transmission And Reflection

The study of signals propagation inside porous media is an important field especially in the biomedical research related to compact bones. The purpose of this paper is to determine a mathematical formulation of the global coefficients of transmission and reflection of nondestructive ultrasonic waves in any bi-phase porous medium. Local coefficients of transmission and reflection on the interface of the porous medium will be determined based on a study of boundary conditions. The behavior of different waves inside the porous medium will be developed so that we can derive a new formulation of global coefficients that takes interior phenomena into consideration. Results are found independently of the geometrical and physical characteristics of the medium. Note that this study is based on normal incident ultrasonic wave propagation.

scholarly journals Boundary behaviour of special cohomology classes arising from the Weil representation

2012 ◽  
Vol 12 (3) ◽  
pp. 571-634 ◽  
Author(s):  
Jens Funke ◽  
John Millson
Keyword(s):  
Modular Forms ◽  
Symmetric Spaces ◽  
Theta Functions ◽  
Theta Series ◽  
Siegel Modular Forms ◽  
Boundary Behaviour ◽  
Orthogonal Groups ◽  
Local Coefficients ◽  
Generating Series ◽  
Vector Valued

AbstractIn our previous paper [J. Funke and J. Millson, Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms, American J. Math. 128 (2006), 899–948], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces $X$ attached to real orthogonal groups of type $(p, q)$. This correspondence is realized using theta functions associated with explicitly constructed ‘special’ Schwartz forms. Furthermore, the theta functions give rise to generating series of certain ‘special cycles’ in $X$ with coefficients.In this paper, we study the boundary behaviour of these theta functions in the non-compact case and show that the theta functions extend to the Borel–Sere compactification $ \overline{X} $ of $X$. However, for the $ \mathbb{Q} $-split case for signature $(p, p)$, we have to construct and consider a slightly larger compactification, the ‘big’ Borel–Serre compactification. The restriction to each face of $ \overline{X} $ is again a theta series as in [J. Funke and J. Millson, loc. cit.], now for a smaller orthogonal group and a larger coefficient system.As an application we establish in certain cases the cohomological non-vanishing of the special (co)cycles when passing to an appropriate finite cover of $X$. In particular, the (co)homology groups in question do not vanish. We deduce as a consequence a sharp non-vanishing theorem for ${L}^{2} $-cohomology.

scholarly journals MEASUREMENT OF THERMAL EFFICIENCY OF HEATING BOILER WITH FURNACE WALL WATERFLOW

2019 ◽  
pp. 169-176
Author(s):  
A. S. Klimov ◽  
R. T. Emelyanov ◽  
A. F. Aleksandrov ◽  
V. A. Taranov
Keyword(s):  
Thermal Efficiency ◽  
Lower Boundary ◽  
Heating Surface ◽  
Large Error ◽  
Furnace Wall ◽  
Temperature Fields ◽  
Thermal Probe ◽  
Local Coefficients ◽  
Measurement Results ◽  
Boiler Design

This article deals with the improvement of thermal efficiency of heating boilers with furnace wall waterflow. During one cycle in a PK-38 boiler the average level of the heat flow decreases by 25–30 %. The incident heat flux is measured with a thermal probe which, however, gives a large error in the measurement results. Experiments show that the error depends on the penetration of the thermal probe into the outer surface of thermal zone as well as on cavities in sealing the thermal probe, and different thermophysical properties of the latter and metal material of the heating surface. The accuracy of the measured parameters is affected by the thermal probe sealing. It is found that the distortion of temperature fields is more significant at the lower boundary of the thermal probe junction at frequently used sealing. Studies show that the waterflow leads to the restoration of local coefficients of thermal efficiency to the previous values. The obtained results can be used in boiler design and allow improving the measurement methods for thermal efficiency of heating boilers with furnace wall waterflow.

scholarly journals Cohomology of Homotopy Colimits of Simplicial Sets and Small Categories

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 981
Author(s):  
Antonio M. Cegarra
Keyword(s):  
Simplicial Sets ◽  
Local Coefficients ◽  
Weak Homotopy

This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of small categories and simplicial sets. We show that these weak homotopy equivalences have stronger cohomology-preserving properties than for local coefficients.

scholarly journals Local coefficients and Euler class groups

2009 ◽  
Vol 322 (12) ◽  
pp. 4295-4330 ◽  
Author(s):  
Satya Mandal ◽  
Albert J.L. Sheu
Keyword(s):  
Euler Class ◽  
Class Groups ◽  
Local Coefficients
Sign in / Sign up

Export Citation Format

Share Document