All posts under tag "Mathematics"
Let $K$ be a totally real number field with Galois closure $L$. We prove that if $f in mathbb Q[x_1,...,x_n]$ is a sum of $m$ squares in $K[x_1,...,x_n]$, then $f$ is a sum of [4m cdot 2^{[L: mathbb Q]+1} {[L: mathbb Q] +1 choose 2}] squares in $mathbb Q[x_1,...,x_n]$. Moreover, our argument is cons
We show that the image of Connes-Karoubi-Chern character, restricted to the image of the Baum-Connes assembly map in the Bott-periodized topological K-theory of the complex group algebra, lies in the elliptic summand of the (periodic) cyclic homology of the group algebra. This implies that for any (
The results of J. F. Qiann et al. [4] on $(1-gamma)$-cyclic codes over finite chain rings of nilpotency index 2 are extended to $(1-gamma^e)$-cyclic codes over finite chain rings of arbitrary nilpotency index $e+1$. The Gray map is introduced for this type of rings. We prove that the Gray image of a
A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. We define
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes of compact subsets of Euclidean space $R^d$. However, the com
We calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in locally constant systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a Fock space representation to the twisted case. We further ge
Uplink synchronization in orthogonal frequency-division multiple-access (OFDMA) systems is a challenging task. In IEEE 802.16-based networks, users that intend to establish a communication link with the base station must go through a synchronization procedure called Initial Ranging (IR). Existing IR
One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M'ezard have proposed an interesting model of economy [Bouchaud and M'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribu
Let X be a geodesic metric space. Gromov proved that there exists k>0 such that if every sufficiently large triangle T satisfies the Rips condition with constant k times pr(T), where pr(T) is the perimeter T, then X is hyperbolic. We give an elementary proof of this fact, also giving an estimate for
A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to soluti
A point-to-point discrete-time scheduling problem of transmitting $B$ information bits within $T$ hard delay deadline slots is considered assuming that the underlying energy-bit cost function is a convex monomial. The scheduling objective is to minimize the expected energy expenditure while satisfyi
Let $K$ be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X,K)$ of $X$ in the class $K$ is an $R^infty$-manifold if and only if $X$ has no isolated points and $F(X,K)$ is a retrac
In ``Rips complexes and covers in the uniform category'' the authors define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are give
Bott periodicity plays an important role in topological K-theory. The purpose of this paper is to extend the periodicity theorem in a discrete context, where all classical groups are involved and not just the general linear group. The present paper generalizes previous results of the author [K1] and
We investigate the delay limited secrecy capacity of the flat fading channel under two different assumptions on the available transmitter channel state information (CSI). The first scenario assumes perfect prior knowledge of both the main and eavesdropper channel gains. Here, upper and lower bounds
We investigate the perfect derived category dgPer(A) of a positively graded differential graded (dg) algebra A whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of dgPer(A) whose objects are easy to describe, define a t-structure on dgPer(A) a
Make an exponential transformation in the integral formulation of Riemann's zeta-function zeta(s) for Re(s) > 0. Separately, in addition make the substitution s -> 1 - s and then transform back to s again using the functional equation. Using residue calculus, we can in this way get two alternative,
We show that for every injective continuous map f: S^2 --> R^3 there are four distinct points in the image of f such that the convex hull is a tetrahedron with the property that two opposite edges have the same length and the other four edges are also of equal length. This result represents a partia
This is an old paper put here for archeological purposes. We derive a general formula expressing the second homology of a Lie algebra of the form Lotimes A with coefficients in the trivial module through homology of $L$, cyclic homology of $A$, and other invariants of $L$ and $A$. This is achieved b
We describe a non-extensional variant of Martin-L'of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.
In this article we further the study of non-commutative motives. Our main result is the construction of a simple model, given in terms of infinite matrices, for the suspension in the triangulated category of non-commutative motives. As a consequence, this simple model holds in all the classical inva
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