Determinantal formula for the chow form of a toric surface

2002 ◽  
Author(s):  
Amit Khetan
Keyword(s):  
Toric Surface ◽  
Determinantal Formula ◽  
Chow Form

scholarly journals Differential resolvents of minimal order and weight

2004 ◽  
Vol 2004 (54) ◽  
pp. 2867-2893
Author(s):  
John Michael Nahay
Keyword(s):  
Upper Bound ◽  
Minimal Order ◽  
Determinantal Formula ◽  
Differential Field ◽  
Nonzero Coefficient ◽  
Univariate Polynomial ◽  
Linear Differential ◽  
Indicial Equation

We will determine the number of powers ofαthat appear with nonzero coefficient in anα-power linear differential resolvent of smallest possible order of a univariate polynomialP(t)whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of anα-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockleα-resolvent of a trinomial and finish with a related determinantal formula.

scholarly journals Explicit determinantal formula for a class of banded matrices

2020 ◽  
Vol 18 (1) ◽  
pp. 1227-1229
Author(s):  
Yerlan Amanbek ◽  
Zhibin Du ◽  
Yogi Erlangga ◽  
Carlos M. da Fonseca ◽  
Bakytzhan Kurmanbek ◽  
...  
Keyword(s):  
Short Note ◽  
Determinantal Formula ◽  
Banded Matrices

Abstract In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

scholarly journals Determinantal formula for generalized riffle shuffle

2021 ◽  
Vol 344 (12) ◽  
pp. 112599
Author(s):  
Fumihiko Nakano ◽  
Taizo Sadahiro
Keyword(s):  
Determinantal Formula

scholarly journals A quantum-trace determinantal formula for matrix commutators, and applications

2012 ◽  
Vol 436 (7) ◽  
pp. 2380-2397
Author(s):  
Dinesh Khurana ◽  
T.Y. Lam ◽  
Noam Shomron
Keyword(s):  
Determinantal Formula

Tool path optimal design for slow tool servo turning of complex optical surface

2016 ◽  
Vol 231 (5) ◽  
pp. 825-837 ◽  
Author(s):  
Xu Chen ◽  
Min Kang ◽  
Xingsheng Wang ◽  
Muhammad Hassan ◽  
Jun Yang
Keyword(s):  
Optimal Design ◽  
Tool Path ◽  
Tool Path Generation ◽  
Interpolation Error ◽  
Machining Accuracy ◽  
Calculation Error ◽  
Path Generation ◽  
Optical Surface ◽  
Toric Surface ◽  
Slow Tool Servo

In order to increase the machining accuracy of slow tool servo turning of complex optical surface, the optimal design for tool path was studied. A comprehensive tool path generation strategy was proposed to optimize the tool path for machining complex surfaces. A new algorithm was designed for tool nose radius compensation which had less calculation error. Hermite segment interpolation was analyzed based on integrated multi-axes controller, and a new interpolation method referred to as triangle rotary method was put forward and was compared with the area method and three-point method. The machining simulation indicated that the triangle rotary method was significant in error reduction. The interpolation error of toric surface was reduced to 0.0015 µm from 0.06 µm and sinusoidal array surface’s interpolation error decreases to 0.37 µm from 1.5 µm. Finally, a toric surface was machined using optimum tool path generation method to evaluate the proposed tool path generation method.

scholarly journals Chow form for projective differential variety

2012 ◽  
Vol 370 ◽  
pp. 344-360 ◽  
Author(s):  
Wei Li ◽  
Xiao-Shan Gao
Keyword(s):  
Chow Form ◽  
Differential Variety

scholarly journals Exceptional sequences of invertible sheaves on rational surfaces

2011 ◽  
Vol 147 (4) ◽  
pp. 1230-1280 ◽  
Author(s):  
Lutz Hille ◽  
Markus Perling
Keyword(s):  
Large Class ◽  
Complete Classification ◽  
Toric Surface ◽  
Structural Result ◽  
Toric Surfaces ◽  
Rational Surfaces ◽  
Exceptional Sequences

AbstractIn this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

scholarly journals MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS

2017 ◽  
Vol 5 ◽  
Author(s):  
ALEXANDER KASPRZYK ◽  
BENJAMIN NILL ◽  
THOMAS PRINCE
Keyword(s):  
Mirror Symmetry ◽  
Smooth Surface ◽  
Equivalence Classes ◽  
Del Pezzo Surfaces ◽  
Toric Surface ◽  
Del Pezzo

We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine representatives for all mutation-equivalence classes of such polygons. This is a key step in a program to classify orbifold del Pezzo surfaces using mirror symmetry. As an application, we classify all Fano polygons such that the corresponding toric surface is qG-deformation-equivalent to either (i) a smooth surface; or (ii) a surface with only singularities of type$1/3(1,1)$.

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