Equivalent conditions of polynomial growth of a variety of Poisson algebras

In this paper we study commutative Leibniz-Poisson algebras. We prove that a variety of commutative Leibniz-Poisson algebras has either polynomial growth or growth with exponential not less than 2, the ﬁeld being arbitrary. We prove that every variety of commutative Leibniz-Poisson algebras of polynomial growth over a ﬁeld of characteristic 0 has a ﬁnite basis for its polynomial identities. Also we construct a variety of commutative Leibniz-Poisson algebras with almost polynomial growth.

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Scanning Microscopy of Human Intestinal Explants in Organ Culture

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100095248 ◽

1972 ◽

Vol 30 ◽

pp. 396-397

Author(s):

Bruce Wetzel ◽

Robert Buscho ◽

Raphael Dolin

Keyword(s):

Electron Microscopy ◽

Room Temperature ◽

Culture Conditions ◽

Human Fetuses ◽

Enteric Disease ◽

Organ Cultures ◽

Growth Of A Variety ◽

Normal Human ◽

Fetal Intestine ◽

Scanning Electron

It has been reported that explants of human fetal intestine can be maintained in culture for up to 21 days in a viable condition and that these organ cultures support the growth of a variety of known viral agents responsible for enteric disease. Scanning electron microscopy (SEM) has been undertaken on several series of these explants to determine their appearance under routine culture conditions.Fresh specimens of jejunum obtained from normal human fetuses were washed, dissected into l-4mm pieces, and cultured in modified Leibowitz L-15 medium at 34° C as previously described. Serial specimens were fixed each day in 3% glutaraldehyde for 90 minutes at room temperature, rinsed, dehydrated, and dried by the CO2 critical point method in a Denton DCP-1 device. Specimens were attached to aluminum stubs with 3M transfer tape No. 465, and one sample on each stub was carefully rolled along the adhesive such that villi were broken off to expose their interiors.

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Affine Subspaces of Curvature Functions from Closed Planar Curves

Results in Mathematics ◽

10.1007/s00025-021-01378-6 ◽

2021 ◽

Vol 76 (2) ◽

Author(s):

Leonardo Alese

Keyword(s):

Arc Length ◽

Planar Curves ◽

Affine Subspaces ◽

Planar Curve ◽

Real Functions ◽

Discrete Counterpart ◽

Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

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Weakly associative algebras, Poisson algebras and deformation quantization

Communications in Algebra ◽

10.1080/00927872.2021.1909058 ◽

2021 ◽

pp. 1-33

Author(s):

Elisabeth Remm

Keyword(s):

Deformation Quantization ◽

Associative Algebras ◽

Poisson Algebras

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Quasi-ideal Ehresmann transversals: The spined product structure

Open Mathematics ◽

10.1515/math-2020-0071 ◽

2021 ◽

Vol 19 (1) ◽

pp. 77-86

Author(s):

Xiangjun Kong ◽

Pei Wang ◽

Jian Tang

Keyword(s):

Structure Theorem ◽

Product Structure ◽

Abundant Semigroup ◽

Spined Product ◽

Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

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BSDEs with polynomial growth generators

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953300000216 ◽

2000 ◽

Vol 13 (3) ◽

pp. 207-238 ◽

Cited By ~ 41

Author(s):

Philippe Briand ◽

René Carmona

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Existence And Uniqueness ◽

Polynomial Growth ◽

Probabilistic Representation ◽

Existence And Uniqueness Results ◽

State Variable ◽

Cahn Equation ◽

Uniqueness Results ◽

Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

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Some estimates for the commutators of multilinear maximal function on Morrey-type space

Open Mathematics ◽

10.1515/math-2021-0031 ◽

2021 ◽

Vol 19 (1) ◽

pp. 515-530

Author(s):

Xiao Yu ◽

Pu Zhang ◽

Hongliang Li

Keyword(s):

Maximal Function ◽

Morrey Space ◽

Morrey Spaces ◽

Bounded Mean Oscillation ◽

Generalized Morrey Spaces ◽

Type Space ◽

Bmo Function ◽

Mean Oscillation ◽

Multilinear Maximal Function ◽

Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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