On unitary elements defined on Lorentz cone and their applications

2019 ◽  
Vol 565 ◽  
pp. 1-24 ◽  
Author(s):  
Chien-Hao Huang ◽  
Jein-Shan Chen
Keyword(s):  
Lorentz Cone

Heat Kernels of Lorentz Cones

1999 ◽  
Vol 42 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Hongming Ding
Keyword(s):  
Heat Kernel ◽  
Explicit Formula ◽  
Lower Bounds ◽  
Heat Kernels ◽  
Upper And Lower Bounds ◽  
Symmetric Cones ◽  
Lorentz Cone

AbstractWe obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of time t and two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.

NONCOMMUTATIVE BROWNIAN MOTIONS INDEXED BY PARTIALLY ORDERED SETS

2010 ◽  
Vol 13 (04) ◽  
pp. 629-661 ◽  
Author(s):  
ANNA KULA ◽  
JANUSZ WYSOCZAŃSKI
Keyword(s):  
Limit Theorems ◽  
Ordered Set ◽  
Positive Cone ◽  
Symmetric Matrices ◽  
Ordered Sets ◽  
Brownian Motions ◽  
Partially Ordered ◽  
Independent Increments ◽  
Lorentz Cone ◽  
The Given

We construct noncommutative Brownian motions indexed by partially ordered subsets of Euclidean spaces. The noncommutative independence under consideration is the bm-independence and the time parameter is taken from a positive cone in a vector space ([Formula: see text], the Lorentz cone or the positive definite real symmetric matrices). The construction extends the Muraki's idea of monotonic Brownian motion. We show that our Brownian motions have bm-independent increments for bm-ordered intervals. The appropriate version of the Donsker Invariance Principle is also proved for each positive cone. It requires the bm-Central Limit Theorems related to intervals in the given partially ordered set of indices.

scholarly journals Some inequalities for means defined on the Lorentz cone

2018 ◽  
pp. 1015-1028
Author(s):  
Yu-Lin Chang ◽  
Chie -Hao Huang ◽  
Jein-Shan Chen ◽  
Chu-Chin Hu
Keyword(s):  
Lorentz Cone

scholarly journals The Monotone Extended Second-Order Cone and Mixed Complementarity Problems

2021 ◽  
Author(s):  
Yingchao Gao ◽  
Sándor Zoltán Németh ◽  
Roman Sznajder
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Second Order ◽  
Mixed Complementarity Problem ◽  
Second Order Cone ◽  
Mixed Complementarity Problems ◽  
Lorentz Cone ◽  
Lyapunov Rank ◽  
Extended Second Order Cone

AbstractIn this paper, we study a new generalization of the Lorentz cone $$\mathcal{L}^n_+$$ L + n , called the monotone extended second-order cone (MESOC). We investigate basic properties of MESOC including computation of its Lyapunov rank and proving its reducibility. Moreover, we show that in an ambient space, a cylinder is an isotonic projection set with respect to MESOC. We also examine a nonlinear complementarity problem on a cylinder, which is equivalent to a suitable mixed complementarity problem, and provide a computational example illustrating applicability of MESOC.

scholarly journals The cone of Z-transformations on Lorentz cone

2019 ◽  
Vol 35 ◽  
pp. 387-393 ◽  
Author(s):  
Sandor Nemeth ◽  
Muddappa Gowda
Keyword(s):  
Structural Properties ◽  
Positive Cone ◽  
Linear Program ◽  
Completely Positive ◽  
Completely Positive Cone ◽  
Lorentz Cone ◽  
Semidefinite Cone

In this paper, the structural properties of the cone of $\calz$-transformations on the Lorentz cone are described in terms of the semidefinite cone and copositive/completely positive cones induced by the Lorentz cone and its boundary. In particular, its dual is described as a slice of the semidefinite cone as well as a slice of the completely positive cone of the Lorentz cone. This provides an example of an instance where a conic linear program on a completely positive cone is reduced to a problem on the semidefinite cone.

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