scholarly journals On conformal capacity and Teichmüller’s modulus problem in space

1999 ◽  
Vol 79 (1) ◽  
pp. 201-214 ◽  
Author(s):  
Dimitrios Betsakos
Keyword(s):  
Conformal Capacity ◽  
Modulus Problem

scholarly journals Solution of the minimum modulus problem for covering systems

2015 ◽  
pp. 361-382 ◽  
Author(s):  
Bob Hough
Keyword(s):  
Minimum Modulus ◽  
Modulus Problem ◽  
Covering Systems

scholarly journals Extremal length definitions for the conformal capacity of rings in space.

1962 ◽  
Vol 9 (2) ◽  
pp. 137-150 ◽  
Author(s):  
F. W. Gehring
Keyword(s):  
Extremal Length ◽  
Conformal Capacity

Conformal capacity and the quasihyperbolic metric

1996 ◽  
Vol 45 (2) ◽  
pp. 0-0 ◽  
Author(s):  
David A. Herron ◽  
Pekka Koskela
Keyword(s):  
Conformal Capacity ◽  
Quasihyperbolic Metric ◽  
The Quasihyperbolic Metric

scholarly journals LWR-Based Fully Homomorphic Encryption, Revisited

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Fucai Luo ◽  
Fuqun Wang ◽  
Kunpeng Wang ◽  
Jie Li ◽  
Kefei Chen
Keyword(s):  
Tensor Product ◽  
Gaussian Noise ◽  
Homomorphic Encryption ◽  
Matrix Multiplication ◽  
Public Key ◽  
Multiparty Computation ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Private Key ◽  
Modulus Problem

Very recently, Costache and Smart proposed a fully homomorphic encryption (FHE) scheme based on the Learning with Rounding (LWR) problem, which removes the noise (typically, Gaussian noise) sampling needed in the previous lattices-based FHEs. But their scheme did not work, since the noise of homomorphic multiplication is complicated and large, which leads to failure of decryption. More specifically, they chose LWR instances as a public key and the private key therein as a secret key and then used the tensor product to implement homomorphic multiplication, which resulted in a tangly modulus problem. Recall that there are two moduli in the LWR instances, and then the moduli will tangle together due to the tensor product. Inspired by their work, we built the first workable LWR-based FHE scheme eliminating the tangly modulus problem by cleverly adopting the celebrated approximate eigenvector method proposed by Gentry et al. at Crypto 2013. Roughly speaking, we use a specific matrix multiplication to perform the homomorphic multiplication, hence no tangly modulus problem. Furthermore, we also extend the LWR-based FHE scheme to the multikey setting using the tricks used to construct LWE-based multikey FHE by Mukherjee and Wichs at Eurocrypt 2016. Our LWR-based multikey FHE construction provides an alternative to the existing multikey FHEs and can also be applied to multiparty computation with higher efficiency.

scholarly journals Estimates for conformal capacity

2000 ◽  
Vol 16 (4) ◽  
pp. 589-602 ◽  
Author(s):  
D. Betsakos ◽  
M. Vuorinen
Keyword(s):  
Conformal Capacity

The dependence on parameters of the modulus problem for families of several classes of curves

1987 ◽  
Vol 38 (4) ◽  
pp. 2131-2139 ◽  
Author(s):  
A. Yu. Solynin
Keyword(s):  
Modulus Problem

scholarly journals Conformal capacity and quasiregular mappings

1973 ◽  
Vol 1973 ◽  
pp. 1-8 ◽  
Author(s):  
Uri Srebro
Keyword(s):  
Quasiregular Mappings ◽  
Conformal Capacity

On the preservation of conformal capacity under meromorphic functions

2012 ◽  
Vol 184 (6) ◽  
pp. 699-702
Author(s):  
V. N. Dubinin
Keyword(s):  
Meromorphic Functions ◽  
Conformal Capacity

scholarly journals Impact of Vlasov Foundation Parameters on the Deflection of a Non-uniform Timoshenko Beam Subject to a Moving Load

2019 ◽  
Author(s):  
Magdalena Ataman
Keyword(s):  
Timoshenko Beam ◽  
Moving Load ◽  
Free Vibrations ◽  
Problem Solution ◽  
Moving Force ◽  
Dynamic Factors ◽  
Modulus Problem ◽  
Foundation Parameters ◽  
The Impact ◽  
Selection Of

Subject of the study is a Timoshenko beam with transverse-variable Young’s modulus. Problem of vibrations of the beam resting on an inertial Vlasov foundation and subjected to a moving force is solved analytically. The Timoshenko beam’s eigenproblem is discussed and the physical sense of the additional band of natural vibrations and the corresponding critical frequency is analytically explained. The impact of the foundation and its parameters on the Timoshenko beam’s vibrations forced by moving force is investigated. Dynamic factors relating to beam deflections are analyzed. Two vibration cases are discussed: forced vibrations (when a moving force is applied to the beam) and free vibrations (after the moving force has been left the beam). The damping effect on vibration is taken into account in the problem solution. The results indicate that appropriate selection of the foundation’s parameters allows for the beam deflection’s significant reduction, while the impact of the shear coefficient in the foundation on the reduction is more pronounced than the impact of other factors.

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