THE ASSESSMENT OF MARITIME SAFETY IN THE TURKISH STRAITS BASED ON THE PERFORMANCE OF FLAG STATES IN PORT STATE CONTROL REGIMES

The Turkish Straits are well known for theirs intensive maritime traffic. The average annual number of transit ships passing through this waterway is approximately 50000 and more than 100 flag states pass through it. Moreover, this waterway presents a navigational challenge owing to its inherent geographic and oceanographic characteristics. Also, sub-standard ships navigating in this region lead to an increased risk levels and pose a threat to the marine environment. Over the years, serious maritime accidents occurring in the straits region had resulted in losses of life and constituted environmental disasters. The high risk arising from maritime shipping in these regions had always endangered public health in the vicinity of the Turkish Straits. In this study, maritime safety in the Turkish Straits region had been assessed based on the performance in the Port State Control inspections of flag states passing through this region. For the assessment of the performance of passing flag states, detention and deficiency indices of these flag states were generated for the MOUs. According to these values, the risk level of these flag states had been determined by the weighted risk point methods. Hereby, in addition to the determination of the risk level of flag states, the relationships between the inspections of MOUs had been also discussed on the basis of both the detention and the deficiency rates of flag states.

Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

This paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

Spatiotemporal Analysis of Medical Resource Deficiencies in the U.S. under COVID-19 Pandemic

A data-driven approach is developed to estimate medical resource deficiencies or medical burden at county level during the COVID-19 pandemic from February 15, 2020 to May 1, 2020 in the U.S. Multiple data sources were used to extract local population, hospital beds, critical care staff, COVID-19 confirmed case numbers, and hospitalization data at county level. We estimate the average length of stay from hospitalization data at state level, and calculate the hospitalized rate at both state and county level. Then we develop two medical resource deficiency indices that measure the local medical burden based on the number of accumulated active confirmed cases normalized by local maximum potential medical resources, and the number of hospitalized patients that can be supported per ICU beds per critical care staff, respectively. The medical resources data, and the two medical resource deficiency indices are illustrated in a dynamic spatiotemporal visualization platform based on ArcGIS Pro Dashboards. Our results provide new insights into the U.S. pandemic preparedness and local dynamics relating to medical burdens in response to the COVID-19 pandemic.

Invariance of Deficiency Indices of Second-Order Symmetric Linear Difference Equations under Perturbations

This paper focuses on the invariance of deficiency indices of second-order symmetric linear difference equations under perturbations. By applying the perturbation theory of Hermitian linear relations, the invariance of deficiency indices of the corresponding minimal subspaces under bounded and relatively bounded perturbations is built. As a consequence, the invariance of limit types of second-order symmetric linear difference equations under bounded and relatively bounded perturbations is obtained.

On compressions of self-adjoint extensions of a symmetric linear relation with unequal deficiency indices

Let $A$ be a symmetric linear relation in the Hilbert space $\gH$ with unequal deficiency indices $n_-A <n_+(A)$. A self-adjoint linear relation $\wt A\supset A$ in some Hilbert space $\wt\gH\supset \gH$ is called an (exit space) extension of $A$. We study the compressions $C (\wt A)=P_\gH\wt A\up\gH$ of extensions $\wt A=\wt A^*$. Our main result is a description of compressions $C (\wt A)$ by means of abstract boundary conditions, which are given in terms of a limit value of the Nevanlinna parameter $\tau(\l)$ from the Krein formula for generalized resolvents. We describe also all extensions $\wt A=\wt A^*$ of $A$ with the maximal symmetric compression $C (\wt A)$ and all extensions $\wt A=\wt A^*$ of the second kind in the sense of M.A. Naimark. These results generalize the recent results by A. Dijksma, H. Langer and the author obtained for symmetric operators $A$ with equal deficiency indices $n_+(A)=n_-(A)$.