Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

Radiological Features of Microvascular Invasion of Hepatocellular Carcinoma in Patients with Non-Alcoholic Fatty Liver Disease

Background: The aim of the present study was to evaluate the presence and the prognostic value of the radiological signs of microvascular invasion (MVI) of hepatocellular carcinoma (HCC) in patients with non-alcoholic fatty liver disease (NAFLD). Methods: Between January 2015 and December 2017, all patients (91 patients) with de novo HCC or HCC recurrence occurring at least 2 years after the last treatment in NAFLD (36 patients) or with hepatitis C virus (HCV) liver disease (55 patients) were included. Each HCC was treated with liver resection and transplantation to obtain the anatomopathological confirmation of MVI. All patients had at least one available computed tomography (CT) scan or magnetic resonance imaging (MRI) performed no more than one month prior to the treatment. The clinical data of each patient, tumor burden (diameter, margins, two-trait predictor of venous invasion (TTPVI), and peritumoral enhancement), the recurrence rate (RR) after a 1-year follow-up, and the time to recurrence (TTR) were collected. Results: The NAFLD–HCC nodules were larger as compared to HCV–HCC (51 mm vs. 36 mm, p = 0.004) and showed a higher prevalence of TTPVI (38.9 vs. 20.0%, p = 0.058). At multivariate analysis, nodule diameter &gt;50 mm was found to be the only independent prognostic factor of TTPVI (hazard ratio: 21.3, 95% confidence interval: 4.2–107.7, p &lt; 0.001), and the presence of TTPVI was confirmed to be the only independent prognostic factors of recurrence (hazard ratio: 2.349, 95% confidence interval: 1.369–4.032, p = 0.002). No correlations were found between TTR and irregular tumor margins or peritumoral enhancement. Conclusion: The NAFLD–HCC patients had larger tumors at diagnosis and showed a more frequent presence of radiological signs of MVI as compared to the HCV–HCC patients. The MVI was related to a more rapid recurrence after curative treatments, demonstrating the prognostic value of this radiological diagnosis

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Status of Intraductal Therapy for Ductal Carcinoma in Situ

The intraductal approach is particularly appealing in the setting of ductal carcinoma in situ (DCIS), a preinvasive breast neoplasm that is thought to be entirely intraductal in its extent. Based on an emerging understanding of the anatomy of the ductal system as well as novel techniques to leverage the access accorded by the intraductal approach, researchers are actively exploring how ductal lavage, ductoscopy, and intraductal infusion of therapeutic agents may enhance breast cancer treatment. Both cytologic and molecular diagnostics continue to improve, and work is ongoing to identify the most effective diagnostic biomarkers for DCIS and cancer, although optimal targeting of the diseased duct remains an important consideration. Ductoscopy holds potential in detection of occult intraductal lesions, and ductoscopically guided lumpectomy could increase the likelihood of a more comprehensive surgical excision. Exciting pilot studies are in progress to determine the safety and feasibility of intraductal chemotherapy infusion. These studies are an important starting point for future investigations of intraductal ablative therapy for DCIS, because as our knowledge and techniques evolve, it is likely that DCIS may be the target most amenable to treatment by intraductal therapy. If such studies are successful, these approaches will allow an important and meaningful transformation in treatment options for women diagnosed with DCIS

Effect of jenny milk addition on the inhibition of late blowing in semihard cheese

The occurrence of late blowing defects in cheese produces negative effects on the quality and commercial value of the product. In this work, we verified whether the addition of raw jenny milk to bulk cow milk reduced the late blowing defects in semihard cheeses. During cheesemaking, different aliquots of jenny milk were poured into 2 groups of 4 vats, each containing a fixed amount of cow milk. A group of cheeses was created by deliberately contaminating the 4 vats with approximately 3 log10 cfu/mL milk of Clostridium tyrobutyricum CLST01. The other 4 vats, which were not contaminated, were used for a second group of cheeses. After 120 d of ripening, some physical, chemical, and microbiological parameters were evaluated on the obtained semihard cheeses. Differences in sensory properties among cheeses belonging to the uncontaminated group were evaluated by 80 regular consumers of cheese. Our results showed that the increasing addition of jenny milk to cow milk led to a reduction of pH and total bacterial count in both cheese groups, as well as C. tyrobutyricum spores that either grew naturally or artificially inoculated. We observed a progressive reduction of the occurrence of late blowing defects in cheese as consequence of the increasing addition of jenny milk during cheese making. Moreover, the addition of jenny milk did not affect the acceptability of the product, as consumers found no difference among cheeses concerning sensorial aspects. In conclusion, the important antimicrobial activity of lysozyme contained in jenny milk has been confirmed in the current research. It is recommend for use as a possible and viable alternative to egg lysozyme for controlling late blowing defects in cheese

Bringing analysis of gender and social–ecological resilience together in small-scale fisheries research: Challenges and opportunities

The demand for gender analysis is now increasingly orthodox in natural resource programming, including that for small-scale fisheries. Whilst the analysis of social–ecological resilience has made valuable contributions to integrating social dimensions into research and policy-making on natural resource management, it has so far demonstrated limited success in effectively integrating considerations of gender equity. This paper reviews the challenges in, and opportunities for, bringing a gender analysis together with social–ecological resilience analysis in the context of small-scale fisheries research in developing countries. We conclude that rather than searching for a single unifying framework for gender and resilience analysis, it will be more effective to pursue a plural solution in which closer engagement is fostered between analysis of gender and social-ecological resilience whilst preserving the strengths of each approach. This approach can make an important contribution to developing a better evidence base for small-scale fisheries management and policy