Pre-trained language models (LMs) encode rich information about linguistic structure but their knowledge lexical polysemy remains unclear. We propose a novel experimental setup for analyzing this in LMs specifically trained different languages (English, French, Spanish, and Greek) multilingual BERT. perform our analysis on datasets carefully designed to reflect sense distributions, control para...

There are a few facts that can be read off from this expression immediately. We consider t > 0 here; t < 0 is similar. First, for t0 > 0, u(x0, t0) depends on the initial data φ just at the two points x0± ct0, while it depends on the values of ψ in the whole interval [x0 − ct0, x0 + ct0]. Thus, we call the interval [x0 − ct0, x0 + ct0] the domain of dependence of (x0, t0): if the initial condit...

We present the implementation of updated stellar evolution recipes in codes \texttt{Nbody6++GPU, MOCCA} and \texttt{McLuster}. test them through numerical simulations star clusters containing $1.1\times 10^5$ stars (with $2.0\times 10^4$ primordial hard binaries) performing high-resolution direct $N$-body (\texttt{Nbody6++GPU}) Monte-Carlo (\texttt{MOCCA}) to an age 10~Gyr. compare models imple...

In this work, the enzymatic synthesis of pentyl acetate obtained from acetic acid and pentan-1-ol using commercial immobilized lipase Lipozyme®435 was studied. Specifically, effects several variables process on kinetics were shown, such as initial concentration acid, alcohol/acid molar ratio, possible reuse enzyme, while other variables, temperature, agitation, enzyme/acid ratio held constant. ...

Certain solvable extensions of H-type groups provide noncompact counterexamples to a conjecture of Lichnerowicz, which asserted that “harmonic” Riemannian spaces must be rank 1 symmetric spaces. A Riemannian space M with Laplace-Beltrami operator ∆ is called harmonic if, given any function f(x) on M depending only on the distance d(x, x0) from a given point x0, then also ∆f(x) depends only on d...

Given a star product with separation of variables ⋆ on pseudo-Kähler manifold M and point x0∈M, we construct an associative algebra formal distributions supported at x0. We use this to express the oscillatory exponents family integrals related ⋆.