Nonlinear Schroedinger equation with two symmetric point interactions in one dimension

We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric potential double well represented by two delta interactions. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem

The importance of circulating tumor products as „liquid biopsies” in colorectal cancer

Liquid biopsies represent an array of plasma analysis tests that are studied to evaluate and identify circulating tumor products, especially circulating tumor cells (CTCs) and circulating tumor DNA (ctDNA). Examining such biomarkers in the plasma of colorectal cancer patients has attracted attention due to its clinical significance in the treatment of malignant diseases. Given that tissue samples are sometimes challenging to procure or unsatisfactory for genomic profiling from patients with colorectal cancer, trustworthy biomarkers are mandatory for guiding treatment, monitoring therapeutic response, and detecting recurrence. This review considers the relevance of flowing tumor products like circulating tumor cells (CTCs), circulating tumor DNA (ctDNA), circulating messenger RNA (mRNA), circulating micro RNA (miRNA), circulating exosomes, and tumor educated platelets (TEPs) for patients with colorectal cancer

DC magnetron discharge fluid model using a new numerical scheme

Numerical modelling of an electrical discharge by fluid model can be accomplished through different procedures and approaches. A 2D time-dependent one was applied in order to describe a cylindrical symmetry Argon DC planar magnetron discharge. All transport equations, which means continuity and momentum transfer equations for electrons and ions and electron mean energy transport equation are solved in the same manner, using corrected classical drift-diffusion expressions for fluxes. For the validity of this last approach, the presence of magnetic field has been introduced as a correction in the electronic flux expression, while for ions an effective electric field has been considered. Plasma potential is given by Poisson equation

2D fluid approaches of DC magnetron discharge

A two dimensional (r,z) time-dependent fluid model was developed and used to describe a DC planar magnetron discharge with cylindrical symmetry. The transport description of the charged species uses the corresponding first three moments of Boltzmann equation: continuity, momentum transfer and mean energy transfer (the latter one only for electrons), coupled with Poisson equation. An original way is proposed to treat the transport equations. Electron and ion momentum transport equations are reduced to the classical drift-diffusion expression of the fluxes since the presence of the magnetic field is introduced as an additional part in the electron flux, while for ions an effective electric field was considered. Thus, both continuity and mean energy transfer equations are solved in a classical manner. Numerical simulations were performed considering Argon as buffer gas, with a neutral pressure varying between 5 and 30 mtorr, a gas temperature from 300 to 350 K and cathode voltages lying from -200 up to -600 V. Results obtained for densities of the charged particle, fluxes and plasma potential are in good agreement with previous works.Laboratoire de Physique des Gaz el des Plasmas (LPGP).Consiliul National al Cercetarii Stiintifice din Invatamantul Superior (CNCSIS) - A/1344/40213/2003

Two-dimensional fluid approach to the dc magnetron discharge

A two-dimensional (r, z) time-dependent fluid model was developed and used to describe a dc planar magnetron discharge with cylindrical symmetry. The transport description of the charged species uses the corresponding first three moments of the Boltzmann equation: continuity, momentum transfer and mean energy transfer (the last one only for electrons), coupled with the Poisson equation. An original method is proposed to treat the transport equations. Electron and ion momentum transport equations are reduced to the classical drift-diffusion expression for the fluxes since the presence of the magnetic field is introduced as an additional part in the electron flux, while for ions an effective electric field was considered. Thus, both continuity and mean energy transfer equations are solved in a classical manner. Numerical simulations were performed considering argon as a buffer gas, with a neutral pressure varying between 5 and 30 mTorr, for different voltages applied on the cathode. Results obtained for densities of the charged particle, fluxes and plasma potential are in good agreement with those obtained in previous studies.C Costin would like to thank the French Government for his PhD fellowship at Laboratoire de Physique des Gaz et des Plasmas. We are also grateful to Dr T Minea for very helpful discussions. This work was partly supported by CNCSIS Romania, grant A/1344/2003

Clinical-evolutional particularities of the cryoglobulinemic vasculitis in the case of a patient diagnosed with hepatitis C virus in the predialitic phase

Hepatitis C virus (HCV) represents a fundamental issue for public health, with long term evolution and the gradual appearance of several complications and associated pathologies. One of these pathologies is represented by cryoglobulinemic vasculitis, a disorder characterized by the appearance in the patient’s serum of the cryoglobulins, which typically precipitate at temperatures below normal body temperature (37°C) and dissolve again if the serum is heated. Here, we describe the case of a patient diagnosed with HCV that, during the evolution of the hepatic disease, developed a form of cryoglobulinemic vasculitis. The connection between the vasculitis and the hepatic disorder was revealed following treatment with interferon, with the temporary remission of both pathologies and subsequent relapse at the end of the 12 months of treatment, the patient becoming a non-responder. The particularity of the case is represented by both the severity of the vasculitic disease from its onset and the deterioration of renal function up to the predialitic phase, a situation not typical of the evolution of cryoglobulinemia. Taking into account the hepatic disorder, the inevitable evolution towards cirrhosis, and the risk of developing the hepatocellular carcinoma, close monitoring is necessary