scholarly journals Student Objections to and Understanding of Non-Cartesian Unit Vector Notation in Upper-Level E&M

2018 ◽  
Author(s):  
Brant E. Hinrichs
Keyword(s):  
Unit Vector ◽  
Upper Level

State special primary acceleration measurement standard for gravimetry GET 190-2019

2020 ◽  
pp. 3-8
Author(s):  
L.F. Vitushkin ◽  
F.F. Karpeshin ◽  
E.P. Krivtsov ◽  
P.P. Krolitsky ◽  
V.V. Nalivaev ◽  
...  
Keyword(s):  
High Precision ◽  
Free Fall ◽  
Measurement Range ◽  
Measurement Standard ◽  
Acceleration Measurement ◽  
Measurement Systems ◽  
Free Fall Acceleration ◽  
Investigation Methods ◽  
Measurement Results ◽  
Upper Level

The State special primary acceleration measurement standard for gravimetry (GET 190-2019), its composition, principle of operation and basic metrological characteristics are presented. This standard is on the upper level of reference for free-fall acceleration measurements. Its accuracy and reliability were improved as a result of optimisation of the adjustment procedures for measurement systems and its integration within the upgraded systems, units and modern hardware components. A special attention was given to adjusting the corrections applied to measurement results with respect to procedural, physical and technical limitations. The used investigation methods made it possibled to confirm the measurement range of GET 190-2019 and to determine the contributions of main sources of errors and the total value of these errors. The measurement characteristics and GET 90-2019 were confirmed by the results obtained from measurements of the absolute value of the free fall acceleration at the gravimetrical site “Lomonosov-1” and by their collation with the data of different dates obtained from measurements by high-precision foreign and domestic gravimeters. Topicality of such measurements ensues from the requirements to handle the applied problems that need data on parameters of the Earth gravitational field, to be adequately faced. Geophysics and navigation are the main fields of application for high-precision measurements in this field.

The smooth case

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Homotopy Type ◽  
Unit Vector ◽  
Smooth Case ◽  
Open Set ◽  
Birational Invariant

This chapter examines the simplifications occurring in the proof of the main theorem in the smooth case. It begins by stating the theorem about the existence of an F-definable homotopy h : I × unit vector X → unit vector X and the properties for h. It then presents the proof, which depends on two lemmas. The first recaps the proof of Theorem 11.1.1, but on a Zariski dense open set V₀ only. The second uses smoothness to enable a stronger form of inflation, serving to move into V₀. The chapter also considers the birational character of the definable homotopy type in Remark 12.2.4 concerning a birational invariant.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Overpressure Identification Using The Eaton Method on The Gumai Formation of Geragai Graben, Jambi Sub Basin

2020 ◽  
Author(s):  
A. O. Marnila
Keyword(s):  
Pressure Data ◽  
Stratigraphic Sequence ◽  
Fine Grained ◽  
Marine Sedimentation ◽  
Plot Analysis ◽  
Significant Reversal ◽  
Porosity And Permeability ◽  
Upper Level ◽  
Type Data ◽  
Fine Grained Sand

Geragai graben is located in the South Sumatera Basin. It was formed by mega sequence tectonic process with various stratigraphic sequence from land and marine sedimentation. One of the overpressure indication zones in the Geragai graben is in the Gumai Formation, where the sedimentation is dominated by fine grained sand and shale with low porosity and permeability. The aim of the study is to localize the overpressure zone and to analyze the overpressure mechanism on the Gumai Formation. The Eaton method was used to determine pore pressure value using wireline log data, pressure data (RFT/FIT), and well report. The significant reversal of sonic and porosity log is indicating an overpressure presence. The cross-plot analysis of velocity vs density and fluid type data from well reports were used to analyze the causes of overpressure in the Gumai Formation. The overpressure in Gumai Formation of Geragai graben is divided into two zones, they are in the upper level and lower level of the Gumai Formation. Low overpressure have occurred in the Upper Gumai Formation and mild overpressure on the Lower Gumai Formation. Based on the analyzed data, it could be predicted, that the overpressure mechanism in the Upper Gumai Formation might have been caused by a hydrocarbon buoyancy, whereas in the Lower Gumai Formation, might have been caused by disequilibrium compaction as a result of massive shale sequence.

Sign in / Sign up

Export Citation Format

Share Document