293 research outputs found
The construction of translation planes from projective spaces
AbstractCan every (nonDesarguesian) projective plane be imbedded (in some natural, geometric fashion) in a (Desarguesian) projective space? The question is new but important, for, if the answer is yes, two entirely separate fields of research can be united. This paper provides a conceptually simple geometric construction which yields an affirmative answer for a broad class of planes. A plane Ï is given by the construction precisely when Ï is a translation plane with a coordinatizing right Veblen-Wedderburn system which is finite-dimensional over its left-operator skew-field. The condition is satisfied by all known translation planes, including all finite translation planes
Some results on the Krein parameters of an association scheme
We consider association schemes with d classes and the underlying Bose-
Mesner algebra, A. Then, by taking into account the relationship between the
Hadamard and the Kronecker products of matrices and making use of some matrix
techniques over the idempotents of the unique basis of minimal orthogonal idempotents
of A , we prove some results over the Krein parameters of an association
scheme
Further results on error correcting binary group codes
The present paper is a sequel to the paper âOn a class of error-correcting binary group codesâ, by R. C. Base and D. K. Ray-Chaudhuri, appearing in Information and Control in which an explicit method of constructing a t-error correcting binary group code with n = 2m â 1 places and k = 2m â 1 â R(m,t) ⧠2m â 1 â mt information places is given. The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n â R(m,t) ⧠[(2m â 1)/c] â mt information places where m is the least integer such that cn = 2m â 1 for some integer c. A second method of constructing t-error correcting codes for n places when n is not of the form 2m â 1 is also given
A generalization of bounds for cyclic codes, including the HT and BS bounds
We use the algebraic structure of cyclic codes and some properties of the
discrete Fourier transform to give a reformulation of several classical bounds
for the distance of cyclic codes, by extending techniques of linear algebra. We
propose a bound, whose computational complexity is polynomial bounded, which is
a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the
majority of computed cases, our bound is the tightest among all known
polynomial-time bounds, including the Roos bound
Hard Instances of the Constrained Discrete Logarithm Problem
The discrete logarithm problem (DLP) generalizes to the constrained DLP,
where the secret exponent belongs to a set known to the attacker. The
complexity of generic algorithms for solving the constrained DLP depends on the
choice of the set. Motivated by cryptographic applications, we study sets with
succinct representation for which the constrained DLP is hard. We draw on
earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such
as generalized Menelaus' theorem for proving lower bounds on the complexity of
the constrained DLP, and construct sets with succinct representation with
provable non-trivial lower bounds
Two-dimensional quantum-corrected black hole in a finite size cavity
We consider the gravitation-dilaton theory (not necessarily exactly
solvable), whose potentials represent a generic linear combination of an
exponential and linear functions of the dilaton. A black hole, arising in such
theories, is supposed to be enclosed in a cavity, where it attains thermal
equilibrium, whereas outside the cavity the field is in the Boulware state. We
calculate quantum corrections to the Hawking temperature , with the
contribution from the boundary taken into account. Vacuum polarization outside
the shell tend to cool the system. We find that, for the shell to be in the
thermal equilibrium, it cannot be placed too close to the horizon. The quantum
corrections to the mass due to vacuum polarization vanish in spite of non-zero
quantum stresses. We discuss also the canonical boundary conditions and show
that accounting for the finiteness of the system plays a crucial role in some
theories (e.g., CGHS), where it enables to define the stable canonical
ensemble, whereas consideration in an infinite space would predict instability.Comment: 21 pages. In v.2 misprints corrected. To appear in Phys. Rev.
Families of twisted tensor product codes
Using geometric properties of the variety \cV_{r,t}, the image under the
Grassmannian map of a Desarguesian -spread of \PG(rt-1,q), we
introduce error correcting codes related to the twisted tensor product
construction, producing several families of constacyclic codes. We exactly
determine the parameters of these codes and characterise the words of minimum
weight.Comment: Keywords: Segre Product, Veronesean, Grassmannian, Desarguesian
spread, Subgeometry, Twisted Product, Constacyclic error correcting code,
Minimum weigh
Double quantum dot turnstile as an electron spin entangler
We study the conditions for a double quantum dot system to work as a reliable
electron spin entangler, and the efficiency of a beam splitter as a detector
for the resulting entangled electron pairs. In particular, we focus on the
relative strengths of the tunneling matrix elements, the applied bias and gate
voltage, the necessity of time-dependent input/output barriers, and the
consequence of considering wavepacket states for the electrons as they leave
the double dot to enter the beam splitter. We show that a double quantum dot
turnstile is, in principle, an efficient electron spin entangler or
entanglement filter because of the exchange coupling between the dots and the
tunable input/output potential barriers, provided certain conditions are
satisfied in the experimental set-up.Comment: published version; minor error correcte
Viking Afterbody Heating Computations and Comparisons to Flight Data
Computational fluid dynamics predictions of Viking Lander 1 entry vehicle afterbody heating are compared to flight data. The analysis includes a derivation of heat flux from temperature data at two base cover locations, as well as a discussion of available reconstructed entry trajectories. Based on the raw temperature-time history data, convective heat flux is derived to be 0.63-1.10 W/sq cm for the aluminum base cover at the time of thermocouple failure. Peak heat flux at the fiberglass base cover thermocouple is estimated to be 0.54-0.76 W/sq cm, occurring 16 seconds after peak stagnation point heat flux. Navier-Stokes computational solutions are obtained with two separate codes using an 8-species Mars gas model in chemical and thermal non-equilibrium. Flowfield solutions using local time-stepping did not result in converged heating at either thermocouple location. A global time-stepping approach improved the computational stability, but steady state heat flux was not reached for either base cover location. Both thermocouple locations lie within a separated flow region of the base cover that is likely unsteady. Heat flux computations averaged over the solution history are generally below the flight data and do not vary smoothly over time for both base cover locations. Possible reasons for the mismatch between flight data and flowfield solutions include underestimated conduction effects and limitations of the computational methods
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