scholarly journals COENDOMORPHISM LEFT BIALGEBROIDS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250181
Author(s):  
A. ARDIZZONI ◽  
L. EL KAOUTIT ◽  
C. MENINI
Keyword(s):  
Explicit Description ◽  
Rigorous Proof ◽  
Generators And Relations

The main purpose of this paper is to give a rigorous proof of the construction of coendomorphism left bialgebroids as well as an explicit description of their structure maps. We also compute some concrete examples of these objects by means of their generators and relations.

scholarly journals THE UNIT MAP OF THE ALGEBRAIC SPECIAL LINEAR COBORDISM SPECTRUM

2019 ◽  
pp. 1-26
Author(s):  
Maria Yakerson
Keyword(s):  
Explicit Description ◽  
Homotopy Groups ◽  
Joint Work ◽  
Loop Spaces ◽  
Special Linear ◽  
Generators And Relations ◽  
Thom Spectra

In the joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^{1}$ -loop spaces of motivic Thom spectra using the technique of framed correspondences. This result allows us to express non-negative $\mathbb{G}_{m}$ -homotopy groups of motivic Thom spectra in terms of geometric generators and relations. Using this explicit description, we show that the unit map of the algebraic special linear cobordism spectrum induces an isomorphism on $\mathbb{G}_{m}$ -homotopy sheaves.

ON THE COHOMOLOGY OF $\bar{\mathcal M}_{0,n}({\mathbb P}^1,d)$

2002 ◽  
Vol 04 (04) ◽  
pp. 751-761 ◽  
Author(s):  
GILBERTO BINI ◽  
CLAUDIO FONTANARI
Keyword(s):  
Moduli Space ◽  
Cohomology Group ◽  
Betti Numbers ◽  
Projective Line ◽  
Explicit Description ◽  
Vanishing Theorems ◽  
Generators And Relations ◽  
Rational Cohomology ◽  
Complex Projective Line ◽  
Complex Projective

Here we investigate rational cohomology of the moduli space of stable maps to the complex projective line with a purely algebro-pgeometric approach. In particular, we prove vanishing theorems for all its odd Betti numbers, and we give an explicit description by generators and relations of its second cohomology group.

The Movement of Ezekiel’s “Living Beings” in 4Q405 Shirot ‘Olat Hashabbat. Part II: The Twelfth Song

2018 ◽  
Vol 27 (1) ◽  
Author(s):  
Annette Evans
Keyword(s):  
Explicit Description ◽  
Plural Form ◽  
The Law ◽  
Mount Sinai

In this article descriptions of angelic movement in the Twelfth Song are compared to descriptions of such activity arising from the throne of God in Ezekiel’s vision in Ezekiel 1 and 10, and to that in the Seventh Song as contained in scroll 4Q403. The penultimate Twelfth Song of the Songs of the Sabbath Sacrifice culminates in a more explicit description of angelic messenger activity and in other nuances. The Twelfth Song was intended to be read on the Sabbath immediately following Shavu’ot, when the traditional synagogue reading is Ezekiel 1 and Exodus 19–20. The possible significance for the author of Songs of the Sabbath Sacrifice of the connection between the giving of the Law at Mount Sinai and Ezekiel’s vision where merkebah thrones and seats appear in the plural form is considered in the conclusion

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals Quiver origami: discrete gauging and folding

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Bourget ◽  
Amihay Hanany ◽  
Dominik Miketa
Keyword(s):  
Gauge Theories ◽  
Generators And Relations

Abstract We study two types of discrete operations on Coulomb branches of 3d$$ \mathcal{N} $$ N = 4 quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers. Our methods explicitly describe Coulomb branches in terms of generators and relations including mass deformations.

Constraint-following servo control for an underactuated mobile robot under hard constraints

2021 ◽  
pp. 095965182110248
Author(s):  
Duo Fu ◽  
Jin Huang ◽  
Wen-Bin Shangguan ◽  
Hui Yin
Keyword(s):  
Mobile Robot ◽  
Control Problem ◽  
Servo Control ◽  
Robot Motion ◽  
Soft Constraints ◽  
Rigorous Proof ◽  
Control Approach ◽  
Hard Constraints

This article formulates the control problem of underactuated mobile robot as servo constraint-following, and develops a novel constraint-following servo control approach for underactuated mobile robot under both servo soft and hard constraints. Servo soft constraints are expressed as equalities, which may be holonomic or non-holonomic. Servo hard constraints are expressed as inequalities. It is required that the underactuated mobile robot motion eventually converges to servo soft constraints, and satisfies servo hard constraints at all times. Diffeomorphism is employed to incorporate hard constraints into soft constraints, yielding new soft constraints to relax hard constraints. By this, we design a constraint-following servo control based on the new servo soft constraints, which drives the system to strictly follow the original servo soft and hard constraints. The effectiveness of the proposed approach is proved by rigorous proof and simulations.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

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