975 research outputs found
Complex cobordism of involutions
We give a simple and explicit presentation of the Z/2-equivariant complex
cobordism ring.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol5/paper11.abs.htm
Duality symmetry and the form fields of M-theory
In previous work we derived the topological terms in the M-theory action in
terms of certain characters that we defined. In this paper, we propose the
extention of these characters to include the dual fields. The unified treatment
of the M-theory four-form field strength and its dual leads to several
observations. In particular we elaborate on the possibility of a twisted
cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia
Equivariant Formal Group Laws
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135640/1/plms0355.pd
-Algebras, the BV Formalism, and Classical Fields
We summarise some of our recent works on -algebras and quasi-groups
with regard to higher principal bundles and their applications in twistor
theory and gauge theory. In particular, after a lightning review of
-algebras, we discuss their Maurer-Cartan theory and explain that any
classical field theory admitting an action can be reformulated in this context
with the help of the Batalin-Vilkovisky formalism. As examples, we explore
higher Chern-Simons theory and Yang-Mills theory. We also explain how these
ideas can be combined with those of twistor theory to formulate maximally
superconformal gauge theories in four and six dimensions by means of
-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
Π‘ΠΈΡΡΠ΅ΠΌΠ° ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ Ρ Π±Π΅ΡΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΠΉ Π·Π°ΡΡΠ΄ΠΊΠΎΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠ°ΡΡΡΠΊΠΈ Ρ ΠΊΡΠ΅ΡΡΠΎΠ²ΠΈΠ΄Π½ΠΎΠΉ ΠΏΠ΅ΡΠ΅ΠΌΡΡΠΊΠΎΠΉ ΠΈ Π°ΠΊΡΠΈΠ²Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π°ΠΊΠΊΡΠΌΡΠ»ΡΡΠΎΡΠΎΠΌ
The article presents a detection system with spider web coil-based wireless charging. Commonly available metal detectors are sold as handheld systems, which enable only progressive, lengthy, time-consuming search. Importantly, a part of the investigated area can thus be easily missed, and the probability that a metal object will not be found increases substantially. This problem, however, is eliminable via the automatic position tracking mode embedded in the solution obtained through our research. The proposed system facilitates using the spider web coil simultaneously for wireless charging and metal detection by pulse induction. The topology of the detector can emit variable pulse lengths, thus allowing the device to detect more types of metal and to adapt itself to the permeability of the soil. The coil has a branch in a relevant part of the winding to reduce undesirable electromagnetic interference during the charging. On the transmitting side of the topology, impedance matching is included to maintain the maximum spatial gap variability. By changing the position of the receiving side, the output voltage changes; therefore, a high efficiency DC/DC converter is employed. The individual battery cells demonstrate different internal resistances, requiring us to apply a new method to balance the cells voltage. The system can be utilized on self-guided vehicles or drones; advantageously, a GPS resending the coordinates to a mesh radio allows for accurate positioning. With the mesh topology, potential cooperation between the multiple systems is possible. The setup utilizes the same coil for wireless power transfer and detection.Π ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ Ρ Π±Π΅ΡΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΠΉ Π·Π°ΡΡΠ΄ΠΊΠΎΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠ°ΡΡΡΠΊΠΈ Ρ ΠΊΡΠ΅ΡΡΠΎΠΎΠ±ΡΠ°Π·Π½ΠΎΠΉ ΠΏΠ΅ΡΠ΅ΠΌΡΡΠΊΠΎΠΉ. ΠΠ±ΡΡΠ½ΠΎ Π΄ΠΎΡΡΡΠΏΠ½ΡΠ΅ ΠΌΠ΅ΡΠ°Π»Π»ΠΎΠΈΡΠΊΠ°ΡΠ΅Π»ΠΈ ΠΏΡΠΎΠ΄Π°ΡΡΡΡΒ Π² Π²ΠΈΠ΄Π΅ ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ ΠΏΠΎΡΡΠ΅ΠΏΠ΅Π½Π½ΡΠΉ, Π΄Π»ΠΈΡΠ΅Π»ΡΠ½ΡΠΉ ΠΈ ΡΡΡΠ΄ΠΎΠ΅ΠΌΠΊΠΈΠΉ ΠΏΠΎΠΈΡΠΊ. ΠΠ°ΠΆΠ½ΠΎ ΠΎΡΠΌΠ΅ΡΠΈΡΡ, ΡΡΠΎ ΡΠ°ΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΠΎΠΉ Π·ΠΎΠ½Ρ, ΡΠ°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ Π»Π΅Π³ΠΊΠΎ ΠΏΡΠΎΠΏΡΡΠ΅Π½Π°, ΠΈ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΡ ΡΠΎΠ³ΠΎ, ΡΡΠΎ ΠΌΠ΅ΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΎΠ±ΡΠ΅ΠΊΡ Π½Π΅ Π±ΡΠ΄Π΅Ρ Π½Π°ΠΉΠ΄Π΅Π½, ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π²ΠΎΠ·ΡΠ°ΡΡΠ°Π΅Ρ. ΠΡΠ° ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° ΡΡΡΡΠ°Π½ΡΠ΅ΡΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΎΡΡΠ»Π΅ΠΆΠΈΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΡΠΎΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ, Π²ΡΡΡΠΎΠ΅Π½Π½ΠΎΠ³ΠΎ Π² ΡΠ΅ΡΠ΅Π½ΠΈΠ΅, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΠΎΠ΅ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π½Π°ΡΠΈΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ. ΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠ°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° ΠΎΠ±Π»Π΅Π³ΡΠ°Π΅Ρ ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΊΠ°ΡΡΡΠΊΠΈ Ρ ΠΊΡΠ΅ΡΡΠΎΠΎΠ±ΡΠ°Π·Π½ΠΎΠΉ ΠΏΠ΅ΡΠ΅ΠΌΡΡΠΊΠΎΠΉ Π΄Π»Ρ Π±Π΅ΡΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΠΉ Π·Π°ΡΡΠ΄ΠΊΠΈ ΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΌΠ΅ΡΠ°Π»Π»Π° Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠΌΠΏΡΠ»ΡΡΠ½ΠΎΠΉ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ. Π’ΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡ Π΄Π΅ΡΠ΅ΠΊΡΠΎΡΠ° ΠΌΠΎΠΆΠ΅Ρ ΠΈΠ·Π»ΡΡΠ°ΡΡ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ Π΄Π»ΠΈΠ½Ρ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ², ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΡΡΡΠΎΠΉΡΡΠ²Ρ ΠΎΠ±Π½Π°ΡΡΠΆΠΈΠ²Π°ΡΡ Π±ΠΎΠ»ΡΡΠ΅ ΡΠΈΠΏΠΎΠ² ΠΌΠ΅ΡΠ°Π»Π»ΠΎΠ² ΠΈ Π°Π΄Π°ΠΏΡΠΈΡΠΎΠ²Π°ΡΡΡΡ ΠΊ ΠΏΡΠΎΠ½ΠΈΡΠ°Π΅ΠΌΠΎΡΡΠΈ ΠΏΠΎΡΠ²Ρ. ΠΠ°ΡΡΡΠΊΠ° ΠΈΠΌΠ΅Π΅Ρ ΠΎΡΠ²Π΅ΡΠ²Π»Π΅Π½ΠΈΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠ΅ΠΉ ΡΠ°ΡΡΠΈ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ, ΡΡΠΎΠ±Ρ ΡΠΌΠ΅Π½ΡΡΠΈΡΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΡΠ΅ ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ°Π³Π½ΠΈΡΠ½ΡΠ΅ ΠΏΠΎΠΌΠ΅Ρ
ΠΈ Π²ΠΎ Π²ΡΠ΅ΠΌΡ Π·Π°ΡΡΠ΄ΠΊΠΈ. ΠΠ° ΠΏΠ΅ΡΠ΅Π΄Π°ΡΡΠ΅ΠΉ ΡΡΠΎΡΠΎΠ½Π΅ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΠΈ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΎ ΡΠΎΠ³Π»Π°ΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠΌΠΏΠ΅Π΄Π°Π½ΡΠ° Π΄Π»Ρ ΠΏΠΎΠ΄Π΄Π΅ΡΠΆΠ°Π½ΠΈΡ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠΉ ΠΈΠ·ΠΌΠ΅Π½ΡΠΈΠ²ΠΎΡΡΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ Π·Π°Π·ΠΎΡΠ°. ΠΡΠΈ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΈ ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΈΠ΅ΠΌΠ½ΠΎΠΉ ΡΡΠΎΡΠΎΠ½Ρ ΠΈΠ·ΠΌΠ΅Π½ΡΠ΅ΡΡΡ Π²ΡΡ
ΠΎΠ΄Π½ΠΎΠ΅ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠ΅, ΠΏΠΎΡΡΠΎΠΌΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ Π²ΡΡΠΎΠΊΠΎΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΉ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»Ρ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ ΡΠΎΠΊΠ° Π² ΠΏΠΎΡΡΠΎΡΠ½Π½ΡΠΉ. ΠΡΠ΄Π΅Π»ΡΠ½ΡΠ΅ ΡΠ»Π΅ΠΌΠ΅Π½ΡΡ Π±Π°ΡΠ°ΡΠ΅ΠΈ Π΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΡΡΡ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠ΅ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΡ, ΡΡΠΎ ΡΡΠ΅Π±ΡΠ΅Ρ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ Π½ΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° Π΄Π»Ρ Π±Π°Π»Π°Π½ΡΠΈΡΠΎΠ²ΠΊΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π‘ΠΈΡΡΠ΅ΠΌΠ° ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½Π° Π½Π° ΡΠ°ΠΌΠΎΠ½Π°Π²ΠΎΠ΄ΡΡΠΈΡ
ΡΡ ΡΡΠ°Π½ΡΠΏΠΎΡΡΠ½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ²Π°Ρ
ΠΈΠ»ΠΈ Π±Π΅ΡΠΏΠΈΠ»ΠΎΡΠ½ΡΡ
Π»Π΅ΡΠ°ΡΠ΅Π»ΡΠ½ΡΡ
Π°ΠΏΠΏΠ°ΡΠ°ΡΠ°Ρ
; GPS, ΡΡΠΏΠ΅ΡΠ½ΠΎ ΠΎΡΠΏΡΠ°Π²Π»ΡΡΡΠΈΠ΅ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°ΡΡ Π½Π° ΠΌΠ½ΠΎΠ³ΠΎΠΊΠ°Π½Π°Π»ΡΠ½ΠΎΠ΅ ΡΠ°Π΄ΠΈΠΎ, ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡ ΡΠΎΡΠ½ΠΎΠ΅ ΠΏΠΎΠ·ΠΈΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅. ΠΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΠ°Π½Π°Π»ΡΠ½ΠΎΠΉ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠ΅ ΡΠΎΡΡΡΠ΄Π½ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠ°Π·Π½ΠΎΠΎΠ±ΡΠ°Π·Π½ΡΠΌΠΈ ΡΠΈΡΡΠ΅ΠΌΠ°ΠΌΠΈ. Π ΡΡΡΠ°Π½ΠΎΠ²ΠΊΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ ΠΎΠ΄Π½Π° ΠΈ ΡΠ° ΠΆΠ΅ ΠΊΠ°ΡΡΡΠΊΠ° Π΄Π»Ρ Π±Π΅ΡΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ
Twisted topological structures related to M-branes
Studying the M-branes leads us naturally to new structures that we call
Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which
we show can also have twisted counterparts. We study some of their basic
properties, highlight analogies with structures associated with lower levels of
the Whitehead tower of the orthogonal group, and demonstrate the relations to
M-branes.Comment: 17 pages, title changed on referee's request, minor changes to
improve presentation, typos correcte
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