Mathematics

We investigate the structure of quantum Markov generators that describe the reduced dynamics of a test particle interacting with a dilute Bose gas in the low density limit. These generators, called low density limit type generators (LDL), differ from the weak coupling limit type generators (WCL) studied in [4, 5] because of the presence of the T-operator that describes the change in momentum of the gas particle due to collisions with the test particle. We propose a general definition of Markov generator of stochastic limit type that includes (almost) all generators arising in the stochastic limit approach and we prove that the associated semigroups as well as their invariant states (or weights) have a very special structure which extends the explicit representation for the generic quantum Markov semigroups of weak coupling limit type, due to Accardi, Hachicha and Ouerdiane [7]. We also investigate the structure of invariant states and give conditions on the T - operator for the exis...

We review the Asymmetric Exclusion QMS in the light of new results, taking as a starting point the dynamics in the one particle space. We give a condition for the Asymmetric Exclusion QMS to be conservative, prove that an invariant state is necessarily diagonal and give conditions on eigenvalues of such an invariant state. We also give, a necessary condition to annul the generator of the predual semigroup; with this and the weighted detailed balance condition, we propose a method to construct some non-equilibrium invariant states.

The study deals with the complex systems in Nature by using of some specific numerical methods. First the method of the physical similarity is used for the characterization of the fluids flow regimes. Then, the method of the power laws and some of its multiple uses in Physics and another related fields are analyzed. The method of phenomenological universality, applied to the description of the growth processes is also discussed. The authors results presented in the paper were mainly obtained by computer simulations using the finite difference (FD) method and the classical gradient method (CGM).

"A set of log-rate models is proposed to transform Rogers and Wilson's accounting-based migration models into statistics-oriented migration models. This study demonstrates not only how log-rate models can be used to replicate results generated from Rogers-Wilson's cohort and multi-region mobility models, but also how log-rate models can be used to make statistical inferences and to derive more parsimonious models. Estimation issues and model fit are discussed, and case studies with U.S. mobility and interregional migration data are provided. The flexibility of log-rate models is emphasized, and possible uses for such models, such as the testing of various hypotheses and migration projection, are explored. Potential applications and limitations of log-rate models are also discussed." (EXCERPT)

In this paper, we introduce some classes of R-modules that are closely related to the classes of Prüfer, Dedekind and Bezout modules. Let R be a commutative ring with identity and set \mathbb{H}=\bigl{\{}M\mid M\text{ is an }R\text{-module and }\mathrm{Nil}(M)% \text{ is a divided prime submodule of }M\bigr{\}}. For an R-module {M\in\mathbb{H}} , set {T=(R\setminus Z(R))\cap(R\setminus Z(M))} , {\mathfrak{T}(M)=T^{-1}M} and {P=(\mathrm{Nil}(M):_{R}M)} . In this case, the mapping {\Phi:\mathfrak{T}(M)\to M_{P}} given by {\Phi(x/s)=x/s} is an R-module homomorphism. The restriction of Φ to M is also an R-module homomorphism from M into {M_{P}} given by {\Phi(x)=x/1} for every {x\in M} . A nonnil submodule N of M is said to be Φ-invertible if {\Phi(N)} is an invertible submodule of {\Phi(M)} . Moreover, M is called a Φ-Prüfer module if every finitely generated nonnil submodule of M is Φ-invertible. If every nonnil submodule of M is Φ-invertible, then we say that M is a Φ-Dedekind module...

Despite their differences, the NP/S, Relational/S and S/S Analyses face a number of problems which they share in common These problems arise from the following claim, which is made in all three analyses: If a sentence containing conjoined noun phrases is logically equivalent to a corresponding sentence containing conjoined clauses, then the original sentence is represented at LF by a structure containing sentential conjunction. For example, in all three analyses, the sentence John and Maly are asleep will receive a logical form essentially like John is asleep and Mary is asleep.

Among the plethora of techniques devised to curb the prevalence of noise in medical images, deep learning based approaches have shown the most promise. However, one critical limitation of these deep learning based denoisers is the requirement of high-quality noiseless ground truth images that are difficult to obtain in many medical imaging applications such as X-rays. To circumvent this issue, we leverage recently proposed approach of [7] that incorporates Stein's Unbiased Risk Estimator (SURE) to train a deep convolutional neural network without requiring denoised ground truth X-ray data. Our experimental results demonstrate the effectiveness of SURE based approach for denoising X-ray images.