1 edition of **Dual sets of envelopes and characteristic regions of quasi-polynomials** found in the catalog.

Dual sets of envelopes and characteristic regions of quasi-polynomials

S. S. Cheng

- 390 Want to read
- 13 Currently reading

Published
**2009**
by World Scientific in Hackensack, NJ
.

Written in English

- Polynomials,
- Special Functions

**Edition Notes**

Statement | Sui Sun Cheng, Yi-Zhong Lin |

Contributions | Lin, Yizhong, 1955-, ebrary, Inc |

Classifications | |
---|---|

LC Classifications | QA351 .C44 2009eb |

The Physical Object | |

Format | [electronic resource] / |

ID Numbers | |

Open Library | OL25554823M |

ISBN 10 | 9814277274 |

ISBN 10 | 9789814277273 |

OCLC/WorldCa | 647851120 |

Intersection of the dual sets of order 0 in (a) and (b) (see [4, Theorems and ]) to yield (c). The following result is easily deduced from Theorems and A.3 in [4]. Lecture notes 4: Duality Vincent Conitzer 1 Introduction Let us again consider the linear program for our original painting problem instance: maximize 3x 1 +2x 2 subject to 4x 1 +2x 2 ≤ 16 x 1 +2x 2 ≤ 8 x 1 +x 2 ≤ 5 x 1 ≥ 0;x 2 ≥ 0 We already know that the optimal solution is to set .

Chapter 7 Polynomial Functions Polynomial FunctionsMake this Foldable to help you organize your with five sheets of plain 8" 1 2 by 11" paper. Reading and WritingAs you read and study the chapter, use each page to write notes and examples. Prerequisite Skills To be successful in this chapter, you’ll need to master these skills and be able to apply them in problem-solving. Envelope of a family of curves. Let each curve C t in the family be given as the solution of an equation f t (x, y)=0 (see implicit curve), where t is a parameter. Write F(t, x, y)=f t (x, y) and assume F is differentiable.. The envelope of the family C t is then defined as the set of points (x,y) for which, simultaneously, (,,) = ∂ ∂ (,,) =for some value of t, where ∂ / ∂ is the.

Whereas polynomials are one-sided (i.e., involve increasing powers), quasi-polynomials are two-sided (i.e., involve both positive and negative powers). Crossing the line between two regions means that one real pole (or one complex pair of poles) crosses the imaginary axis. In the second step the stable region is found. If in one region the parameter set [τ 0 g 0] represents stable characteristic equation, then the stability is preserved under all continuous variations of [τ g] withinCited by:

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For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation.

In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. Dual sets of envelopes and characteristic regions of quasi-polynomials. [S S Cheng; Yi-Zhong Lin] -- In this book, we present this Cheng-Lin envelope method in a systematic manner, introduce sufficiently many technical tools related to this method, and show how they are used in handling.

Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials, pp.

() Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials. Metrics. Downloaded 2 times History. Loading Close Figure Viewer. Request PDF | Dual sets of envelopes and characteristic regions of quasi-polynomials | Existence and nonexistence of roots of functions involving one or more parameters has been the subject of.

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Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials, pp. i-viii () Free Access. Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials. Quick Search in Books.

Enter words / phrases / DOI / ISBN / keywords / authors / etc. Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials, pp. () No Access. C\(0, ∞)-Characteristic Regions of Real Polynomials Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials.

Metrics. Downloaded 1. Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations.

This book presents a formal theory of the Cheng-Lin envelope method. Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc.

Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials, pp. () No Access. C\(0,∞)-Characteristic Regions of Real Δ-Polynomials Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials.

As a result, we obtain a full description of the characteristic polynomials of the toric arrangements defined by these ideals.

As an application, we provide a combinatorial verification to the fact that the characteristic polynomial of every ideal subarrangement factors over the dual Author: Tan Nhat Tran. Dual sets of envelopes and characteristic regions of quasi-polynomials. [S S Cheng; Yi-Zhong Lin; World Scientific (Firm)] -- Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations.

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In the root system case, we present a beautiful formula for the generating function of the characteristic quasi-polynomial which has been essentially obtained by Ch. Athanasiadis and by A.

Blass and B. Sagan. On the other hand, it is hard to find the generating function of the characteristic quasi-polynomial in the mid-hyperplane arrangement by: «Back to Dual Sets of Envelopes and Characteristic Regions of Quasi-polynomials Find in a Library Find Dual Sets of Envelopes and Characteristic Regions of Quasi-polynomials near you.

CHARACTERISTIC QUASI-POLYNOMIALS OF IDEALS 3 to the factorization of the characteristic polynomial of every ideal subar-rangementinthe classicalcases withoutusingthefreeness (Theorem ).

PRELIMINARIES Characteristic quasi-polynomials. LetΓ:= Zℓ. LetAbeaﬁnitelist (multiset) of elements in Γ. Let q ∈ Z>: Tan Nhat Tran. It is not difficult to show that the quasi-polynomials having coefficients in either of the two smaller rings have the property that, if p is the quasi-period, then each coefficient c i is constant when restricted to a set on which gcd(k, p) is constant; equivalently, the quasi-polynomial is a polynomial on each such set Cited by: 4.

Absence of Real Roots of Characteristic Functions of Functional Differential Equations with Nine Real Parameters. Exact regions of oscillation for a neutral differential equation, Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials, World Scientific, Cited by: 1.

Abstract. Let q be a positive integer. In [], we proved that the cardinality of the complement of an integral arrangement, after the modulo q reduction, is a quasi-polynomial of q, which we call the characteristic this paper, we study general properties of the characteristic quasi-polynomial as well as discuss two important examples: the arrangements of reflecting Cited by: In this paper, we study the characteristic quasi-polynomial χS(q) or equivalently its generating function ΦS(t).

In Section 2, we discuss general properties of the characteristic quasi-polynomials and their generating functions. In the subsequent chapters, we deal. The Characteristic Polynomial 1. Coeﬃcients of the characteristic polynomial Consider the eigenvalue problem for an n ×n matrix A, A~v = λ~v, ~v 6= 0.

(1) The solution to this problem consists of identifying all possible values of λ (called the eigenvalues), and the corresponding non-zero vectors ~v (called the eigenvectors) that satisfy.

Books at Amazon. The Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch. Here you'll find current best sellers in books, new releases in books, deals in books, Kindle eBooks, Audible audiobooks, and so much more.In addition, the characteristic quasi-polynomials with respect to the root lattice have a nice expression in terms of the Ehrhart quasi-polynomials of the closed fundamental alcoves with respect to the coweight lattice, e.g., [18, Proposition ].Cited by: 1.Also, making corrections to the colors, gamma, contrast, and brightness had no effect.

In case there was any doubt, the resolution was set to x I have no way to test the connector. I did however created a x png with 1 pixel vertical lines in alternating colors/5(41).