Mathematical analysis of the guided waves in photonic crystal fibers

AbstractThe propagation of guided waves in photonic crystal fibers (PCFs) is studied. The structure of a PCF can be regarded as a perfect two-dimensional photonic crystal with a line defect along the invariant direction. This problem can be treated as an eigenvalue problem for a family of noncompact self-adjoint operators. We prove that line defects do not change the essential spectrum of the associated “background” medium. This result plays a key role for studying the influence of line defects on the “background” spectrum. A modified Combes–Thomas estimate is also formulated

A Herglotz wavefunction method for solving the inverse Cauchy problem connected with the Helmholtz equation

AbstractThis paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

A problem modeling Hall effect in a semiconductor film from an electrode of arbitrary shape is considered, which is a skew-derivative problem. Boundary Galerkin method for solving the problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented

Mach cone induced by γ\gamma-triggered jets in high-energy heavy-ion collisions

MMedium excitation by jet shower propagation inside a quark-gluon plasma is studied within a linear Boltzmann transport and a multiphase transport model. Contrary to the naive expectation, it is the deflection of both the jet shower and the Mach-cone-like excitation in an expanding medium that is found to gives rise to a double-peak azimuthal particle distribution with respect to the initial jet direction. Such deflection is the strongest for hadron-triggered jets which are often produced close to the surface of dense medium due to trigger-bias and travel against or tangential to the radial flow. Without such trigger bias, the effect of deflection on $\gamma$-jet showers and their medium excitation is weaker. Comparative study of hadron and $\gamma$-triggered particle correlations can therefore reveal the dynamics of jet-induced medium excitation in high-energy heavy-ion collisions.Comment: 4 pages in RevTeX with 5 figures, finally version in PR

Percutaneous cryoablation of subcapsular hepatocellular carcinoma: a retrospective study of 57 cases

PURPOSEThis study aims to evaluate the safety and effectiveness of the percutaneous cryoablation for subcapsular hepatocellular carcinoma (HCC).METHODSA total of 57 patients with subcapsular (<1 cm form the liver edge) HCCs (68 lesions), who were treated with CT-guided percutaneous cryoablation in the Department of Interventional Radiology of our hospital between July 1, 2016 and September 1, 2018, were retrospectively included. Complete ablation rate, local tumor progression (LTP) and treatment-related complications were evaluated. Furthermore, the degree of intraoperative and postoperative pain was measured with the visual analog scale (VAS), and laboratory findings were compared before and after the procedure.RESULTSAll patients successfully completed the treatment. The mean follow-up period was 12.8 months (range, 3–27 months), and the complete ablation rate was 97% (66/68). Local tumor progression occurred in 11 lesions (16.2%), and the 6-, 12- and 18-month cumulative LTP rates were 4.0%, 8.2% and 20.5%, respectively. Two patients (3.5%, 2/57) developed major complications, and 12 patients had minor complications (22.8%, 12/57). The mean VAS score during the operation was 1.65 points (range, 1–3 points). Postoperative pain worsened in 3 patients, and the VAS scores reached 4–5. Transient changes in biochemical and hematologic markers were observed.CONCLUSIONPercutaneous cryoablation for subcapsular HCC is safe and effective, the procedure is simple and the patients suffer less pain

BTG2 suppresses renal cell carcinoma progression through N6-methyladenosine

The biological functions of N6-methyladenosine (m6A) modification of mRNA have recently received a great deal of attention. In previous studies, m6A methylation modification has been shown to regulate mRNA fate and to be crucial for the progression and development of tumors. BTG2 (B-cell translocation gene 2) is a member of BTG/TOB anti-proliferative protein family. BTG2 could inhibit cell proliferation and migration and regulate the cell cycle progression. In this study, we confirm that BTG2 is frequently down-regulated in renal cell carcinoma (RCC) tissues and its low expression is associated with unfavorable prognosis and decreased m6A level. Moreover, we found that m6A methylation modifies the 5’UTR of BTG2 to promote its mRNA stability by binding to IGF2BP2. It has been shown that CRISPR/dCas13b-METLL3 can specifically increase BTG2 m6A modification to significantly increase its m6A and expression levels. Then m6A hypermethylation in BTG2 mRNA could dramatically inhibit RCC cells proliferation and migration, and induce cells apoptosis. Taken together, our data show that BTG2 functions as a tumor suppressor and is frequently silenced via m6A modification in RCC