Romanian Academy

About: Romanian Academy is a archive organization based out in Bucharest, Romania. It is known for research contribution in the topics: Population & Nonlinear system. The organization has 3662 authors who have published 10491 publications receiving 146447 citations. The organization is also known as: Academia Română & Societatea Literară Română.

Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach

Abstract: We prove well-posedness results for stochastic nonlinear Schrodinger equations with linear multiplicative Wiener noise, including the nonconservative case. Our approach is different from the standard literature on stochastic nonlinear Schrodinger equations. By a rescaling transformation we reduce the stochastic equation to a random nonlinear Schrodinger equation with lower-order terms and treat the resulting equation by a fixed point argument based on generalizations of Strichartz estimates proved by Marzuola et al. (J Funct Anal 255(6):1479–1553, 2008). This approach makes it possible to improve earlier well-posedness results obtained in the conservative case by a direct approach to the stochastic Schrodinger equation. In contrast to the latter, we obtain well-posedness in the full range \([1, 1 + 4/d)\) of admissible exponents in the nonlinear part (where \(d\) is the dimension of the underlying Euclidean space), i.e., in exactly the same range as in the deterministic case.

The structure of F-pure rings

Abstract: For a reduced F-finite ring R of characteristic p>0 and q=pe one can write Open image in new window where Mq has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers aq grow with respect to q. This growth is quantified by the splitting dimension and the splitting ratios of R which we study in detail. We also prove the existence of a special prime ideal Open image in new window(R) of R, called the splitting prime, that has the property that R/Open image in new window(R) is strongly F-regular. We show that this ideal captures significant information with regard to the F-purity of R.

On iterated twisted tensor products of algebras

Abstract: We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors and give some examples of algebras that can be described within our theory. We prove a certain result (called "invariance under twisting") for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrel...

WO3-Based Gas Sensors: Identifying Inherent Qualities and Understanding the Sensing Mechanism.

Abstract: Semiconducting metal oxide-based gas sensors are an attractive option for a wide array of applications. In particular, sensors based on WO3 are promising for applications varying from indoor air qu...