scholarly journals An algebraic formula for the index of a ‐form on a real quotient singularity

2018 ◽  
Vol 291 (17-18) ◽  
pp. 2543-2556
Author(s):  
Wolfgang Ebeling ◽  
Sabir M. Gusein‐Zade
Keyword(s):  
Quotient Singularity ◽  
Algebraic Formula

Optimal Duration of the Preincubation Phase in Enzyme Inhibition Experiments

2020 ◽  
Author(s):  
Petr Kuzmic
Keyword(s):  
Enzyme Inhibition ◽  
Dose Response ◽  
Enzyme Inhibitor ◽  
Single Point ◽  
Association Rate ◽  
Weakly Bound ◽  
Inhibitor Complex ◽  
Dissociation Equilibrium ◽  
Optimal Duration ◽  
Algebraic Formula

This report describes an algebraic formula to calculate the optimal duration of the pre-incubation phase in enzyme-inhibition experiments, based on the assumed range of expected values for the dissociation equilibrium constant of the enzyme–inhibitor complex and for the bimolecular association rate constant. Three typical experimental scenarios are treated, namely, (1) single-point primary screening at relatively high inhibitor concentrations; (2) dose-response secondary screening of relatively weakly bound inhibitors; (3) dose-response screening of tightly-bound inhibitors.

scholarly journals An algebraic formula for the intersection number of a polynomial immersion

2010 ◽  
Vol 214 (3) ◽  
pp. 269-280 ◽  
Author(s):  
Iwona Karolkiewicz ◽  
Aleksandra Nowel ◽  
Zbigniew Szafraniec
Keyword(s):  
Intersection Number ◽  
Algebraic Formula

scholarly journals A software package for Mori dream spaces

2015 ◽  
Vol 18 (1) ◽  
pp. 647-659 ◽  
Author(s):  
Jürgen Hausen ◽  
Simon Keicher
Keyword(s):  
Software Package ◽  
Toric Varieties ◽  
Quotient Singularity ◽  
Algebraic Varieties ◽  
Cox Rings ◽  
Cox Ring ◽  
Mori Dream Spaces ◽  
The Common ◽  
Symplectic Resolutions

Mori dream spaces form a large example class of algebraic varieties, comprising the well-known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample computations. The software package is accompanied by a Cox ring database which delivers defining data for Cox rings and Mori dream spaces in a suitable format. As an application of the package, we determine the common Cox ring for the symplectic resolutions of a certain quotient singularity investigated by Bellamy–Schedler and Donten-Bury–Wiśniewski.

scholarly journals ON WłODARCZYK'S EMBEDDING THEOREM

2000 ◽  
Vol 11 (06) ◽  
pp. 811-836
Author(s):  
JÜRGEN HAUSEN
Keyword(s):  
Embedding Theorem ◽  
Normal Complex ◽  
Closed Embedding ◽  
Algebraic Formula

We prove the following version of Włodarczyk's Embedding Theorem: Every normal complex algebraic [Formula: see text]-variety Y admits an equivariant closed embedding into a toric prevariety X on which [Formula: see text] acts as a one-parameter-subgroup of the big torus T⊂X. If Y is ℚ-factorial, then X may be chosen to be simplicial and of affine intersection.

scholarly journals On polynomials with simple trigonometric formulas

2004 ◽  
Vol 2004 (63) ◽  
pp. 3419-3422 ◽  
Author(s):  
R. J. Gregorac
Keyword(s):  
Inner Product ◽  
Algebraic Numbers ◽  
Algebraic Formula ◽  
Orthogonal Sequences

We show that the sequences of polynomials with zeroscot(mπ/(n+2))andtan(mπ/(n+2))are not orthogonal sequences with respect to any integral inner product. We give an algebraic formula for these polynomials, that is simpler than the formula originally derived by Cvijovic and Klinowski (1998). New sequences of polynomials with algebraic numbers as roots and closed trigonometric formulas are also derived by these methods.

scholarly journals Algebras with two multiplications and their cumulants

2019 ◽  
Vol 52 (2) ◽  
pp. 157-186
Author(s):  
Adam Burchardt
Keyword(s):  
Probability Theory ◽  
Linear Space ◽  
Structure Constant ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Sum Of Products ◽  
Probabilistic Concept ◽  
Algebraic Formula

Abstract Cumulants are a notion that comes from the classical probability theory; they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication structures. We present an algebraic formula which involves those two multiplications as a sum of products of cumulants. In our approach, beside cumulants, we make use of standard combinatorial tools as forests and their colourings. We also show that the resulting statement can be understood as an analogue of Leonov–Shiryaev’s formula. This purely combinatorial presentation leads to some conclusions about structure constant of Jack characters.

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