Search results for " Algebra"

Existence of dynamical low-rank approximations to parabolic problems

2021

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

Complex powers of elliptic pseudodifferential operators

1986

The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and kS (x,x) can not always be extended to337-2. An example is given where kS (x,x) has a vertical line as natural boundary.

Varieties with at most cubic growth

2019

Abstract Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c n ( V ) , n = 1 , 2 , … , and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x ( y z ) ≡ 0 such that c n ( V ) C n α , with 1 ≤ α 3 , for some constant C. We prove that if 1 ≤ α 2 then c n ( V ) ≤ C 1 n , and if 2 ≤ α 3 , then c n ( V ) ≤ C 2 n 2 , for some constants C 1 , C 2 .

The enveloping algebra of the Lie superalgebra osp(1,2)

1990

International audience

Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations

2014

Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.

Actions of complex Lie groups on analytic ?-algebras

1987

On a reduced analytic .ℂ-algebraR there are faithful analytic actions of complex Lie groups of arbitrarily high dimension if and only ifR has Krull dimension ≥2.

Conditioning on MV-algebras and additive measures —I

1997

Abstract We present a lattice-ordered semigroup approach for the foundation of conditional events which covers the special situations where the underlying (unconditional) events are Boolean or fuzzy, respectively. Our proposal is quite different from other, ring theoretical, approaches. The problem of extending additivity of uncertainty measures from unconditional to conditional events will be discussed.

On the loewy series of the group algebra of groups of smallp-Length∗

1989

(1989). On the loewy series of the group algebra of groups of small p-Length. Communications in Algebra: Vol. 17, No. 5, pp. 1249-1274.

Absolute and monotonic norms

1961

Quasi-Projective Varieties

2000

We have developed the theory of affine and projective varieties separately. We now introduce the concept of a quasi-projective variety, a term that encompasses both cases. More than just a convenience, the notion of a quasi-projective variety will eventually allow us to think of an algebraic variety as an intrinsically defined geometric object, free from any particular embedding in affine or projective space.