scholarly journals Generation of arbitrary vector beam based on optical holography

2015 ◽  
Vol 64 (12) ◽  
pp. 124202
Author(s):  
Xi Si-Xing ◽  
Wang Xiao-Lei ◽  
Huang Shuai ◽  
Chang Sheng-Jiang ◽  
Lin Lie
Keyword(s):  
Arbitrary Vector ◽  
Vector Beam

Single-Layer Noninterleaved Metasurface for Arbitrary Vector Beam Conversion in Triple Bands

2021 ◽  
Author(s):  
Linda Shao ◽  
Dajun Zhang ◽  
Ji Liu ◽  
Jin Zhang ◽  
Zhenfei Li ◽  
...  
Keyword(s):  
Single Layer ◽  
Arbitrary Vector ◽  
Vector Beam

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals Tight focusing of second-order cylindrical vector beam by Mikaelian lens

2021 ◽  
Vol 1745 ◽  
pp. 012013
Author(s):  
S. S. Stafeev ◽  
E. S. Kozlova ◽  
A. G. Nalimov ◽  
V. V. Kotlyar
Keyword(s):  
Second Order ◽  
Vector Beam ◽  
Tight Focusing ◽  
Cylindrical Vector Beam

An all-fiber laser for cylindrical vector beam

2010 ◽  
Author(s):  
Lixin Xu ◽  
Rui Zheng ◽  
Chun Gu ◽  
Anting Wang ◽  
Hai Ming
Keyword(s):  
Fiber Laser ◽  
Vector Beam ◽  
Cylindrical Vector Beam

scholarly journals Products of two idempotent transformations over arbitrary sets and vector spaces

1998 ◽  
Vol 57 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Rachel Thomas
Keyword(s):  
Vector Space ◽  
Transformation Semigroup ◽  
Vector Spaces ◽  
Endomorphism Monoid ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Full Transformation ◽  
Full Transformation Semigroup

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

Sign in / Sign up

Export Citation Format

Share Document