365,942 research outputs found
Fourfolds
We have found a "non-purely-constructive" method of acquiring algebraic
cycles involving multiple steps. This note tries to present the main idea in
the last step by concentrating on an example of 4-folds. The method
demonstrates a contrast to traditional constructions
The cone construction via intersection theory
We show a method in constructing algebraic cycles via intersection theory. It
leads to a proof of the Lefschetz standard conjecture.Comment: arXiv admin note: text overlap with arXiv:1801.0532
Cone construction II
This is the second part of two parts, titled " cone construction". In this
part we prove the Lefschetz cohomologicity of the cone operator .Comment: It is combined with the revision of cone construction
Equivalence of Coniveaus
On a smooth projective variety over the complex numbers, there is the
coniveau from the coniveau filtration, which is called geometric coniveau. On
the same variety, there is another coniveau from the maximal sub-Hodge
structure, which is called Hodge coniveau. In this paper we show they are
equivalent
Leveled sub-cohomology
In this paper we define a functor-- leveled sub-cohomology. (It bears no
relation with the level of elliptic curves). It is based on leveled cycles on a
smooth projective variety, and will be expected to reveal a structure in the
level
Rational curves on complete intersection Calabi-Yau 3-folds
We prove the following results. If is a generic complete intersection
Calabi-Yau 3-fold, (1) then for each natural number there exists a rational
map \par\hspace{1 cc} of , (2) further more all such are immersions satisfying
\begin{equation} N_{c(\mathbf P^1)/ X_3}\simeq \mathcal O_{\mathbf
P^1}(-1)\oplus \mathcal O_{\mathbf P^1}(-1)
A remark on the local density approximation with the gradient corrections and the X method
We report that the solids with narrow valence bands cannot be described by
the local density approximation with the gradient corrections in the density
functional theory as well as the X method. In particular, in the case
of completely filled valence bands, the work function is significantly
underestimated by these methods for such types of solids. Also, we figured out
that these deficiencies cannot be cured by the
self-interaction-corrected-local-density-approximation method.Comment: 6 pages, 0 figure
Classical approach to the graph isomorphism problem using quantum walks
Given the extensive application of classical random walks to classical
algorithms in a variety of fields, their quantum analogue in quantum walks is
expected to provide a fruitful source of quantum algorithms. So far, however,
such algorithms have been scarce. In this work, we enumerate some important
differences between quantum and classical walks, leading to their markedly
different properties. We show that for many practical purposes, the
implementation of quantum walks can be efficiently achieved using a classical
computer. We then develop both classical and quantum graph isomorphism
algorithms based on discrete-time quantum walks. We show that they are
effective in identifying isomorphism classes of large databases of graphs, in
particular groups of strongly regular graphs. We consider this approach to
represent a promising candidate for an efficient solution to the graph
isomorphism problem, and believe that similar methods employing quantum walks,
or derivatives of these walks, may prove beneficial in constructing other
algorithms for a variety of purposes
Efficient quantum circuit implementation of quantum walks
Quantum walks, being the quantum analogue of classical random walks, are
expected to provide a fruitful source of quantum algorithms. A few such
algorithms have already been developed, including the `glued trees' algorithm,
which provides an exponential speedup over classical methods, relative to a
particular quantum oracle. Here, we discuss the possibility of a quantum walk
algorithm yielding such an exponential speedup over possible classical
algorithms, without the use of an oracle. We provide examples of some highly
symmetric graphs on which efficient quantum circuits implementing quantum walks
can be constructed, and discuss potential applications to quantum search for
marked vertices along these graphs
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