Some Applications of the Poincaré–Bendixson Theorem

We consider a $${\mathcal {C}}^1$$ C 1 vector field X defined on an open subset U of the plane with compact closure. If X has no singular points and if U is simply connected, a weak version of the Poincaré–Bendixson theorem says that the limit sets of X in U are empty but that one can define non empty extended limit sets contained in the boundary of U. We give an elementary proof of this result, independent of the classical Poincaré–Bendixson theorem. A trapping triangle $${\mathcal {T}}$$ T based at p, for a $${\mathcal {C}}^1$$ C 1 vector field X defined on an open subset $${\mathcal {U}}$$ U of the plane, is a topological triangle with a corner at a point p located on the boundary $$\partial {\mathcal {U}}$$ ∂ U and a good control of the tranversality of X along the sides. The principal application of the weak Poincaré–Bendixson theorem is that a trapping triangle at p contains a separatrix converging toward the point p. This does not depend on the properties of X along $$\partial {\mathcal {U}}$$ ∂ U . For instance, X could be non differentiable at p, as in the example presented in the last section.

Category of theme in the genre of essay (on the materials of V. M. Peskov’s essays)

The subject of this research is the category of theme – one of the leading text categories that reflects the subject matter of speech and extra-textual reality. Analysis of the category of theme in the essay genre is a relevant trend in modern linguistics. The essays by V. M. Peskov, whose works are considered exemplary and representative for the scientific research in the field of humanities, serve as the materials for this article. Among the essays of the Soviet period, the essays of V. M. Peskov rightfully hold a special place and retain its relevance. The research methodology contains categorical-textual analysis based on the category of communicativeness. The novelty consists in application of the categorical-textual method towards analyzing the genre of essay, which implies a combination of uniform by means of explication textual categories, and with a high degree of objectivity, allows to determine the characterological features of the genre and functional style. The means of explication of the category of theme in the genre of essay have the following peculiarities: incorporation of several functions in a single nomination (primary, basic, principal); application of diverse additional nominations (referentially identical nominations, synonyms, taxonomic nominations, substitutions, grammatical transformations, zero nominations). The analysis of a wide range of additional nominations demonstrates that the essays by V. M. Peskov with a high degree of confidence can be attributed to the field of publicistic, fiction and colloquial styles; or in other words, the genre is at the intersection of several functional styles.

Compilation by stochastic Hamiltonian sparsification

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.

Fusion Imaging in the Guidance of Thermal Ablations

Image-guided thermal ablations are having an increasingly widespread effect on the treatment of several different abdominal conditions, and particularly on the treatment of liver and kidney tumors. In other conditions, such as in the case of pancreatic cancers, image-guided thermal ablations are still under investigation, but some studies showed promising results. Regardless the target organ to be treated, imaging represents one of the most important aspects for a safe and effective application of these techniques. To improve the image guidance in thermal ablations, some systems have been developed to fuse together two or more imaging modalities, providing the operator a real-time visualization of different information during the treatment. In the present review, the principles of fusion imaging will be described, and the principal application in the abdomen will be illustrated.

An Interdisciplinary Review of Smart Vehicular Traffic and Its Applications and Challenges

Sensors and intelligent applications enabling smart vehicular traffic create an opportunity for improving the welfare of people, from the viewpoints of efficiency, sustainability, and social inclusivity. Like the opportunities, challenges of such an endeavour are multifaceted, including the scalable collection and processing of the hefty data volumes generated by sensors, and the coordinated operation between selfish agents. The purpose of this work is to survey recent literature with an emphasis on applications and a multidisciplinary eye, with the aim of stimulating discussion and reflection in the scientific communities. The principal application areas of smart traffic and smart mobility are discussed, synthesizing different perspectives. Many intriguing areas for future research exist besides those relative to connectivity, data fusion, and privacy. Some research challenges pertinent to sustainability, insurance, simulation and the handling of ambiguous information are highlighted.

Floating-point exception handling

Exception handling is required for the development of robust and efficient numerical software, a principal application of Fortran. Indeed, the existence of such a facility makes it possible to develop more efficient software than would otherwise be possible. Most computers nowadays have hardware based on the IEEE standard for binary floating-point arithmetic, which later became an ISO standard. Therefore, the Fortran exception handling features are based on the ability to test and set the five flags for floating-point exceptions that the IEEE standard specifies.

Observation and Analysis of Affinity Law Deviations through Tested Performance of Liquefied Gas Reaction Turbines

Liquefied gas reaction turbines are subject to the hydraulic affinity laws. Particularly for liquefied hydrocarbon gas-driven turbines, deviations from the affinity laws are encountered. In the case of reaction turbines, where the geometry is fixed, the affinity law relationships between flow, head, and rotational speed are relevant. Field experience confirms that the affinity law relationships are adequate, but that the predictions made also tend to deviate from real turbine performance. Part of the deviations seen may be attributed to the nonideal fluid; however, further examination is warranted. This paper presents an investigation into the affinity law relationships between head, flow, and rotational speed in conjunction with actual turbine performance. The three basic affinity law relationships are combined to form the most general performance equation. This equation subsequently incorporates both the affinity law relationships and the conservation of energy principal. Application of real turbine test data shows that this general performance equation presents a more accurate representation of turbine performance than the affinity law relationships alone.

Model Reduction in Structural Analysis Using a Multiresolution Analysis

A method is presented to reduce the size of models used in analysis of elastic systems. The reduction is accomplished using a multiresolution analysis applied to elasticity operators to average fine scale properties and behavior while limiting loss of information. In discretized form, the method results in smaller matrices that can be used as building blocks to construct larger systems. The principal application envisioned is in design problems involving complex structural systems, such as crash-worthiness design, where very intensive computations demand computational efficiency.

Increasing Physician Acceptance of Technology Assessment Through a Focused Training Program

This paper presents the framework for a one-semester course to give physicians a better understanding of the core concepts of technology assessment, using medical instrumentation technology as a vehicle to stimulate the discussion of technology assessment and its applications. An assessment matrix has been developed as an organizational tool to identify issues in assessment to be addressed under each topic and to identify those issues that are of key importance to particular technologies. At the end of the class, the physician-student should be able to identify major types of medical instrumentation and the instrument's principal application(s), to identify the techniques of technology assessment, and to analyze the economic, ethical, and legal issues that are applicable to instrumentation.