assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

background: a comprehensive database, comprising geometry and properties of human teeth, is needed for dentistry education and dental research. the aim of this study was to create a three-dimensional model of human teeth to improve the dental e-learning and dental research.   methods: in this study, a cross-section picture of the three-dimensional model of the teeth was used. ct-scan images wer...

introduction: mandibular first molar is the most important tooth with complicated morphology. in finite element (fe) studies, investigators usually prefer to model anterior teeth with a simple and single straight root; it makes the results deviate from the actual case. the most complicated and time-consuming step in fe studies is modeling of the desired tooth, thus this study was performed to e...

We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics. Starting with the finite-dimensional case of landmarks, we prove that the random solutions do not blow up in finite time. We then prove the consistency of the ...

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitiansymmetric space of compact type, which is a particular example of an Hilbert manifold, is transitively acted upon by a Hilbert Lie group of isometries. In this paper we give the classification ...

In this paper we construct an L∞ structure on polyvector fields on a vector space V over C where V may be infinite-dimensional. We prove that the constructed L∞ algebra of polyvector fields is L∞ equivalent to the Hochschild complex of polynomial functions on V , even in the infinite-dimensional case. For a finite-dimensional space V , our L∞ algebra is equivalent to the classical Schouten-Nije...

Many natural spaces of functions form infinite-dimensional vector spaces. Examples are the space of polynomials and the space of smooth functions. If we are interested in solving differential equations, then, it is important to understand analysis in infinite-dimensional vector spaces (over R or C). First of all, we should recognize the following straightforward fact about finite-dimensional ve...

In 1976 Ribe [R] proved that uniformly homeomorphic Banach spaces have uniformly linearly isomorphic finite-dimensional subspaces: that if there is a uniformly continuous homeomorphism between two Banach spaces, with uniformly continuous inverse, then every finite-dimensional subspace of one space, is linearly isomorphic to a subspace of the other, with an implied constant of isomorphism indepe...

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

Any higher dimensional shift space (X, d) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of d where r < d. We show here that any projectional entropy is bounded below by the d entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite p...