scholarly journals Some Properties of Fuzzy Neutrosophic Generalized Semi Continuous Mapping and Alpha Generalized Continuous Mapping

2021 ◽  
Vol 19 (3) ◽  
Keyword(s):  
Continuous Mapping

Cerebellopontine Angle Surgery Assisted by Continuous Mapping of the Facial Nerve Via the Ultrasonic Aspirator

2020 ◽  
Author(s):  
Marco Cenzato ◽  
Roberto Stefini ◽  
Francesco Zenga ◽  
Maurizio Piparo ◽  
Alberto Debernardi ◽  
...  
Keyword(s):  
Electrical Stimulation ◽  
Facial Nerve ◽  
Cerebellopontine Angle ◽  
Continuous Mapping ◽  
Cost Effective ◽  
Current Intensity ◽  
Vestibular Schwannomas ◽  
Constant Current ◽  
Surgical Workflow ◽  
Ultrasonic Aspirator

Abstract Background Cerebellopontine angle (CPA) surgery carries the risk of lesioning the facial nerve. The goal of preserving the integrity of the facial nerve is usually pursued with intermittent electrical stimulation using a handheld probe that is alternated with the resection. We report our experience with continuous electrical stimulation delivered via the ultrasonic aspirator (UA) used for the resection of a series of vestibular schwannomas. Methods A total of 17 patients with vestibular schwannomas, operated on between 2010 and 2018, were included in this study. A constant-current stimulator was coupled to the UA used for the resection, delivering square-wave pulses throughout the resection. The muscle responses from upper and lower face muscles triggered by the electrical stimulation were displayed continuously on multichannel neurophysiologic equipment. The careful titration of the electrical stimulation delivered through the UA while tapering the current intensity with the progression of the resection was used as the main strategy. Results All operations were performed successfully, and facial nerve conduction was maintained in all patients except one, in whom a permanent lesion of the facial nerve followed a miscommunication to the neurosurgeon. Conclusion The coupling of the electrical stimulation to the UA provided the neurosurgeon with an efficient and cost-effective tool and allowed a safe resection. Positive responses were obtained from the facial muscles with low current intensity (lowest intensity: 0.1 mA). The availability of a resection tool paired with a stimulator allowed the surgeon to improve the surgical workflow because fewer interruptions were necessary to stimulate the facial nerve via a handheld probe.

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

Perturbation of the fixed point problem for continuous mappings

2020 ◽  
pp. 241-249
Author(s):  
Zukhra T. Zhukovskaya ◽  
Sergey E. Zhukovskiy
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Continuous Mapping ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Bounded Subset ◽  
Completely Continuous ◽  
Continuous Map ◽  
Continuous Mappings

We consider the problem of a double fixed point of pairs of continuous mappings defined on a convex closed bounded subset of a Banach space. It is shown that if one of the mappings is completely continuous and the other is continuous, then the property of the existence of fixed points is stable under contracting perturbations of the mappings. We obtain estimates for the distance from a given pair of points to double fixed points of perturbed mappings. We consider the problem of a fixed point of a completely continuous mapping on a convex closed bounded subset of a Banach space. It is shown that the property of the existence of a fixed point of a completely continuous map is stable under contracting perturbations. Estimates of the distance from a given point to a fixed point are obtained. As an application of the obtained results, the solvability of a difference equation of a special type is proved.

scholarly journals On Soft Rough Topology with Multi-Attribute Group Decision Making

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 67 ◽  
Author(s):  
Muhammad Riaz ◽  
Florentin Smarandache ◽  
Atiqa Firdous ◽  
Atiqa Fakhar
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Topological Structure ◽  
Group Decision ◽  
Continuous Mapping ◽  
Product Topology ◽  
Closed Sets ◽  
Open Set ◽  
Soft Rough Set

Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set ( SR -set) by using pairwise SR -approximations. We define SR -open set, SR -closed sets, SR -closure, SR -interior, SR -neighborhood, SR -bases, product topology on SR -sets, continuous mapping, and compactness in soft rough topological space ( SRTS ). The developments of the theory on SR -set and SR -topology exhibit not only an important theoretical value but also represent significant applications of SR -sets. We applied an algorithm based on SR -set to multi-attribute group decision making (MAGDM) to deal with uncertainty.

scholarly journals A new methodology for monitoring P. oceanica meadows in Tavolara Punta Coda Cavallo MPA using GIS

2015 ◽  
Author(s):  
Pieraugusto Panzalis ◽  
Andrea Deiana ◽  
Sarah Caronni ◽  
Augusto Navone
Keyword(s):  
Scale Up ◽  
Continuous Mapping ◽  
Detailed Knowledge ◽  
Regular Grid ◽  
Side Scan Sonar ◽  
Sea Bottom ◽  
The Status ◽  
Square Cells ◽  
Set Up ◽  
The Many

Marine Protected Areas (MPAs) are acknowledged globally as effective tools for the protection and management of the marine environment; however, to get effective results it is necessary to set up a proper and continuous mapping of the marine territory, in order to gain detailed knowledge of its different aspects. Therefore, the implementation and maintenance of a modern GIS (Geographic Information System) has become an indispensable task for the MPA of Tavolara - Punta Coda Cavallo to collect, aggregate, classify, and track the conducted mapping activities. Between 2011 and 2012 the sea bottom of the MPA was surveyed using different methods: by means of a multi-beam echo sounder and of a side scan sonar, as well as conducting fast scientific scuba divings with re-breathers and underwater position system technologies. High resolution geodatasets, characterized by a significantly high quality in representing and describing the sea bottom and its habitats, were produced in both feature (scale up to 1:1.250) and raster formats (up to 30cm/pixel for sonar images and 1m/pixel for bathymetry) and they currently constitute the basis of the MPA's GIS, including its 3D applications and its web map services for desktop and mobile devices (iPhone & Android). To update the above described geodatasets during time, acquiring new data on the conservation targets considered in monitoring activities, among which the status of P. oceanica meadows is of the most important ones, a long term mapping plan was realized on the basis of an innovative methodology elaborated by the MPA considering both the wideness of the area and the limited funds available at present. The whole MPA was divided in territorial units by means of a regular grid of square cells having a 100m side with the logic of starting the mapping activities from the mainly important areas and then to spread the surveys up to fill the whole mosaic. All the new data acquired with this methodology could then be mixed, compared and indexed within the same cell and/or in the many already available geodatases, starting from those dated 2006 having a regular grid with square cells of 500m per side.

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