An Algebraic Approach to Regular Sets

2006 ◽  
pp. 449-458
Author(s):  
Horst Reichel
Keyword(s):  
Algebraic Approach ◽  
Regular Sets

Multilevel Algebraic Approach for Performance Analysis of Parallel Algorithms

2019 ◽  
Vol 38 (4) ◽  
pp. 817-850 ◽  
Author(s):  
Luisa D'Amore ◽  
Valeria Mele ◽  
Diego Romano ◽  
Giuliano Laccetti
Keyword(s):  
Performance Analysis ◽  
Parallel Algorithms ◽  
Algebraic Approach

scholarly journals Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Interest Rate ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Bond Pricing ◽  
Model Parameters ◽  
Time Varying ◽  
Single Factor ◽  
Bond Price ◽  
Interest Rate Models ◽  
Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

scholarly journals Prox-regular sets and Legendre-Fenchel transform related to separation properties

Optimization ◽  
2020 ◽  
pp. 1-33
Author(s):  
Samir Adly ◽  
Florent Nacry ◽  
Lionel Thibault
Keyword(s):  
Fenchel Transform ◽  
Regular Sets

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals Plenty of big projections imply big pieces of Lipschitz graphs

2021 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Lipschitz Graphs ◽  
Regular Sets ◽  
Big Pieces

AbstractI prove that closed n-regular sets $$E \subset {\mathbb {R}}^{d}$$ E ⊂ R d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

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