58,389 research outputs found
An Analysis of Factors Affecting the Royal Air Force Contribution to the Raid on Dieppe, 1942
This paper seeks to explain the limited options available to Air Marshal Sir Trafford Leigh-Mallory when planning the Royal Air Force (RAF) portion of the combined operation raid on Dieppe in 1942. It proposes that a number of constraining influences, some self-imposed, reduced the air support options, so that only an air umbrella over the attacking forces could be provided. It argues that these influences were a consequence of the RAF’s cultural and conceptual environment, which perpetuated Trenchardian notions of offensive spirit in RAF doctrine, together with the refusal to consider options to extend the range of its fighter aircraft. The paper rejects claims that the RAF’s effort at Dieppe was the natural evolution of combined operations doctrine and demonstrates that preemptive bombing of Dieppe was politically unacceptable
The maximum forcing number of polyomino
The forcing number of a perfect matching of a graph is the
cardinality of the smallest subset of that is contained in no other perfect
matchings of . For a planar embedding of a 2-connected bipartite planar
graph which has a perfect matching, the concept of Clar number of hexagonal
system had been extended by Abeledo and Atkinson as follows: a spanning
subgraph of is called a Clar cover of if each of its components is
either an even face or an edge, the maximum number of even faces in Clar covers
of is called Clar number of , and the Clar cover with the maximum number
of even faces is called the maximum Clar cover. It was proved that if is a
hexagonal system with a perfect matching and is a set of hexagons in a
maximum Clar cover of , then has a unique 1-factor. Using this
result, Xu {\it et. at.} proved that the maximum forcing number of the
elementary hexagonal system are equal to their Clar numbers, and then the
maximum forcing number of the elementary hexagonal system can be computed in
polynomial time. In this paper, we show that an elementary polyomino has a
unique perfect matching when removing the set of tetragons from its maximum
Clar cover. Thus the maximum forcing number of elementary polyomino equals to
its Clar number and can be computed in polynomial time. Also, we have extended
our result to the non-elementary polyomino and hexagonal system
The Farrell-Jones conjecture for hyperbolic and CAT(0)-groups revisited
We generalize the proof of the Farrell-Jones conjecture for CAT(0)-groups to
a larger class of groups in particular also containing all hyperbolic groups.
This way we give a unified proof for both classes of groups.Comment: 17 page
S-duality in Abelian gauge theory revisited
Definition of the partition function of U(1) gauge theory is extended to a
class of four-manifolds containing all compact spaces and certain
asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces.
The partition function is calculated via zeta-function regularization with
special attention to its modular properties. In the compact case, compared with
the purely topological result of Witten, we find a non-trivial curvature
correction to the modular weights of the partition function. But S-duality can
be restored by adding gravitational counter terms to the Lagrangian in the
usual way. In the ALF case however we encounter non-trivial difficulties
stemming from original non-compact ALF phenomena. Fortunately our careful
definition of the partition function makes it possible to circumnavigate them
and conclude that the partition function has the same modular properties as in
the compact case.Comment: LaTeX; 22 pages, no figure
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
We introduce some algebraic geometric models in cosmology related to the
"boundaries" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers
between aeons. We suggest to model the kinematics of Big Bang using the
algebraic geometric (or analytic) blow up of a point . This creates a
boundary which consists of the projective space of tangent directions to
and possibly of the light cone of . We argue that time on the boundary
undergoes the Wick rotation and becomes purely imaginary. The Mixmaster
(Bianchi IX) model of the early history of the universe is neatly explained in
this picture by postulating that the reverse Wick rotation follows a hyperbolic
geodesic connecting imaginary time axis to the real one. Penrose's idea to see
the Big Bang as a sign of crossover from "the end of previous aeon" of the
expanding and cooling Universe to the "beginning of the next aeon" is
interpreted as an identification of a natural boundary of Minkowski space at
infinity with the Big Bang boundary
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