Mackey-Glass type delay differential equations near the boundary of absolute stability

For equations $x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero when both $\zeta -1 >0$ and $h(\zeta-1)^{1/8}$ are less than some constant (independent on $h,\zeta$). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of Mathematical Analysis and Application

The Importance of the Study of the Hemodynamics of the Uterine Tumors by the Method of Dopplerometry in the Two- and Three-dimensional Echography Modes for Differential Diagnostics of Simple, Proliferating Leiomyomas and Uterine Sarcomas (Review of Litera

The article analyzes modern literature data on the importance of studying the hemodynamics of uterine tumors with dopplerometry in two - and three - dimensional regimens of echography for differential diagnosis of simple proliferating leiomyomas and sarcomas of the uterus. It is shown that the differential diagnosis of benign and Malignant tumors using the dopplerometry is based on various features of the blood supply of these tumors. On the basis of the analysis of literature data, it was concluded that in the dopplerometry evaluation of benign, borderline and Malignant tumors of myometrium in the two-dimensional regime, there were differences in the localization of the detected vessels in the CDM regimen, in the rates of vascular blood flow and vascular resistance in pulse dopplerometry. For a simple leiomyoma, the absence of a central intra-node localization of blood vessels in the CDM regimen, a low rate of arterial and venous blood flow, as well as an average resistance of arterial blood flow in the regime of impulsive dopplerometry are most typical; in a leiomyoma with eating disorders, the absence of a central intra-node localization of blood vessels, a low rate of arterial and venous blood flow in combination with high arterial resistance were more often observed. For the proliferating leiomyoma, the central intra-node localization of the vessels and the average blood flow velocities with low and medium resistance are characteristic. For sarcoma of the uterus, there is abundant vascularization both around the periphery and in the center, high blood flow rates and low resistance. The authors emphasize that there is information about the low specificity of this gradation, since the detection of a central type of vascularization and low resistance values can be in simple myomatous nodes with edema, eating disorders and destruction, and leads to diagnostic errors and suspicion of Malignancy. In the three-dimensional dopplerometry mode for simple leiomyomas, low indices of volume perfusion indices were characteristic, and for proliferating leiomyomas and sarcomas of the uterus – high indices of volume perfusion indices exceeding those in the uterus as a whole.Based on the review of the literature, the authors concluded that the presently available echographic and dopplerometric two- and three-dimensional markers are characterized by high sensitivity, but very low specificity. The low specificity of the known ultrasonic and dopplerometric criteria combined with the rarity of cases of sarcoma in the uterus against the background of a large number of similar echographically and dopplerometrically leiomyomas lead to low diagnostic accuracy of ultrasound diagnostics. This situation requires a further continuation of the scientific search for differential diagnostic ultrasound criteria by leiomyomas and sarcomas of the uterus using modern technologies, including three-dimensional echography

Assessing digital preservation frameworks: the approach of the SHAMAN project

How can we deliver infrastructure capable of supporting the preservation of digital objects, as well as the services that can be applied to those digital objects, in ways that future unknown systems will understand? A critical problem in developing systems is the process of validating whether the delivered solution effectively reflects the validated requirements. This is a challenge also for the EU-funded SHAMAN project, which aims to develop an integrated preservation framework using grid-technologies for distributed networks of digital preservation systems, for managing the storage, access, presentation, and manipulation of digital objects over time. Recognising this, the project team ensured that alongside the user requirements an assessment framework was developed. This paper presents the assessment of the SHAMAN demonstrators for the memory institution, industrial design and engineering and eScience domains, from the point of view of user’s needs and fitness for purpose. An innovative synergistic use of TRAC criteria, DRAMBORA risk registry and mitigation strategies, iRODS rules and information system models requirements has been designed, with the underlying goal to define associated policies, rules and state information, and make them wherever possible machine-encodable and enforceable. The described assessment framework can be valuable not only for the implementers of this project preservation framework, but for the wider digital preservation community, because it provides a holistic approach to assessing and validating the preservation of digital libraries, digital repositories and data centres