Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high-frequency components and create undesirable imaging artifacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using smooth division...

Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite diff...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...

We discuss an age-sex-structured population dynamics deterministic model taking into account random mating of sexes, females’ pregnancy and its dispersal in whole space. This model can be derived from the previous one (Skakauskas, 1995) describing migration mechanism by the general linear elliptic operator of second order and includes the male, single (nonfertilized) female and fertilized femal...

The synthesis of 8-azido-2'-deoxyadenosine-5'-triphosphate is described. The photoreactive dATP analog was characterized by thin layer chromatography, proton resonance spectroscopy, infrared spectroscopy and UV spectroscopy. Its photolysis upon UV irradiation was studied. After incorporation of this dATP analog into DNA containing the tet operator sequence the investigation of the interactions ...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analys...

Application scenarios such as legacy-data migration, ETL processes, data cleaning and data-integration require the transformation of input tuples into output tuples. Traditional approaches for implementing these data transformations enclose solutions as Persistent Stored Modules (PSM) executed by an RDBMS or transformation code using a commercial ETL tool. Neither of these solutions is easily m...