We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith's method uses lattice basis reduction to construct an auxiliary polynomial that vanishes at the desired...
Since the geometrically linear response of thin medium-length cylinders under uniform meridional compression or uniform bending is relatively straightforward, these reference resistances can be defined on the basis of a simple beam or shell membrane theory treatment. The capacity curve then returns the ...
A theory solver must, as a minimum requirement, be able to assess an assignment to the Boolean abstraction of the given problem and decide whether that assignment makes the formula satisfiable in the theory’s interpretation of the Boolean values, and if so, produce an assignment for the ...
Using elastic theory for calculation, the normal stress at the edge of the cross-section σ is: (6.1)σ=MxWx where Mx is the bending moment about the x-axis; Wx is the elastic section modulus about the x-axis or simply called section modulus. Since the yield point is considered to be...
on discretizations of the boundaries (for example, our own method presented in Liesen et al. (Comput. Methods Funct. Theory17, 689–713, 2017)), while maintaining a very high level of accuracy. We study properties of the linear algebraic systems that arise in the CSM, and show how these...
For a general introduction about Multihorizon Stochastic Optimisation and Programming theory see [29]. Table 1. Nomenclature - parameters. Renewable Empty Cell R Unitary current investment cost of the renewable plant ($) RnL Long term multiplier that defines variations in the renewable investment ...
“A nonlinear theory of bending and buckling of thin elastic shallow spherical shells”, whose authors were Abner Kaplan and Yuan-Cheng Fung. This work contained both theoretical considerations and the results of the experimental studies conducted. These tests were conducted on a series of shallow ...
The central theory for the application of copulas is Sklar’s theorem [80], where 𝐻H is a joint CDF of random variables if it has a copula 𝐶C, as stated in Equation (16). 𝐻(𝑍𝐺,𝑍𝑇)=𝐶(𝛷(𝑍𝐺),𝛷(𝑍𝑇))H(ZG,ZT)=C(Φ(ZG),Φ(ZT)) (16) ...
Some Adaptations of Classical Plasticity Theory for Soil Stability Problems. In Proceedings of the Symposium on the Role of Plasticity in Soil Mechanics, Cambridge, UK, 13–15 September 1973; p. 24. [Google Scholar] Kusakabe, O.; Kimura, T.; Yamaguchi, H. Bearing Capacity of Slopes under ...
Some Adaptations of Classical Plasticity Theory for Soil Stability Problems. In Proceedings of the Symposium on the Role of Plasticity in Soil Mechanics, Cambridge, UK, 13–15 September 1973; p. 24. [Google Scholar] Kusakabe, O.; Kimura, T.; Yamaguchi, H. Bearing Capacity of Slopes under ...