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.$

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

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

The Use of Ropivacaine in Therapeutic Treatment of Oral Aphthosis

The use of anaesthetic drugs in the treatment of oral aphthosis is one of the pharmaceutical possibilities that a doctor can use for the most painful forms. Normally, Lidocaine or Diclofenac is used to treat this disease, but they can be used for a very limited time and so they are of little practical use. In this study, the authors have used Ropivacaine whose pharmaceutical kinetics allows the analgesic effect to be active for 60 to 90 minutes. In our research, we compared 8 groups of patients who have been given 3 principal pharmaceutical products: one group was given an anaesthetic drug, one had a topical medication administered which is often used for the treatment of aphthous lesions, and the last group was given a multivitamin. These pharmaceutical products were used alone and in various possible combinations in the 8 groups. The results of this study are very interesting and show that in all the groups that used anaesthetics there was more satisfaction on the patients' part because their pain level became more manageable right after the first application of the drug and the patients could carry on with their normal lives

Biodiversità e innovazione: la percezione del consumatore per il prodotto onocosmetico.

Nel presente studio si è valutata la percezione del consumatore verso una crema viso a base di latte di asina proveniente da allevamenti montani del Parco Nazionale dell'Appennino Lucano Val d'Agri Lagonegrese. Il latte presentava la seguente composizione chimica: proteine 13,5 g/l; grasso 2,9 g/l, lattosio 59,8 g/l, sostanza secca 80,6 g/l, ceneri 4,5 g/l. L’attività antiossidante, espressa come percentuale di inibizione, è risultata del 79,54% con saggio ABTS e del 58,84% con saggio DPPH. Al consumer test hanno partecipato 80 soggetti reclutati in modo casuale tra maschi e femmine e suddivisi in base al tipo di pelle (secca e grassa) e di età compresa fra 30 e 50 anni. Il test è stato condotto "at home" e i partecipanti sono stati invitati ad applicare la crema ogni sera per 15 giorni. Gli aspetti sensoriali della crema sono stati valutati, con un punteggio da 1 a 10, a 7 e a 15 giorni dall'inizio del trattamento. L'analisi della varianza ha evidenziato l'effetto del tipo di pelle. A 7 giorni dall'inizio del trattamento, il giudizio totale dell’aspetto della crema ha riportato il punteggio più alto nei consumatori (+1,15, P<0,05) e nelle consumatrici (+1,40, P<0,05) con pelle grassa. Queste ultime hanno espresso un punteggio più elevato sul giudizio totale relativo al profumo (+1,7, P<0,05). A 15 giorni i giudizi complessivi sull'aspetto e sul profumo della crema sono risultati migliori nelle consumatrici con pelle grassa (+1,53, P<0,01 e +1,38, P<0,05, rispettivamente). I consumatori con pelle secca hanno apprezzato maggiormente il profumo (+1,03, P<0,05) e l’efficacia della crema (1,06, P<0,05)

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