28,584 research outputs found
F-threshold functions: syzygy gap fractals and the two-variable homogeneous case
In this article we study F-pure thresholds (and, more generally,
F-thresholds) of homogeneous polynomials in two variables over a field of
characteristic p>0. Passing to a field extension, we factor such a polynomial
into a product of powers of pairwise prime linear forms, and to this collection
of linear forms we associate a special type of function called a syzygy gap
fractal. We use this syzygy gap fractal to study, at once, the collection of
all F-pure thresholds of all polynomials constructed with the same fixed linear
forms. This allows us to describe the structure of the denominator of such an
F-pure threshold, showing in particular that whenever the F-pure threshold
differs from its expected value its denominator is a multiple of p. This
answers a question of Schwede in the two-variable homogeneous case. In
addition, our methods give an algorithm to compute F-pure thresholds of
homogenous polynomials in two variables.Comment: 42 pages; 6 figures. Section 6 was mostly rewritten; a new appendix
was included; other smaller changes throughout. Comments welcom
The lender of last resort in the european single financial market
The paper examines challenges in effectively implementing the lender-of-last-resort function in the EU single financial market. Briefly highlighted are features of the EU financial landscape that could increase EU systemic financial risk. Briefly described are the complexities of the EUâs financial-stability architecture for preventing and resolving financial problems, including lender-of-last-resort operations. The paper examines how the lender-of-last-resort function might materialize during a systemic financial disturbance affecting more than one EU Member State. The paper identifies challenges and possible ways of enhancing the effectiveness of the existing architecture
Classification of Energy Momentum Tensors in Dimensional Space-times: a Review
Recent developments in string theory suggest that there might exist extra
spatial dimensions, which are not small nor compact. The framework of a great
number of brane cosmological models is that in which the matter fields are
confined on a brane-world embedded in five dimensions (the bulk). Motivated by
this we review the main results on the algebraic classification of second order
symmetric tensors in 5-dimensional space-times. All possible Segre types for a
symmetric two-tensor are found, and a set of canonical forms for each Segre
type is obtained. A limiting diagram for the Segre types of these symmetric
tensors in 5-D is built. Two theorems which collect together some basic results
on the algebraic structure of second order symmetric tensors in 5-D are
presented. We also show how one can obtain, by induction, the classification
and the canonical forms of a symmetric two-tensor on n-dimensional (n > 5)
spaces from its classification in 5-D spaces, present the Segre types in n-D
and the corresponding canonical forms. This classification of symmetric
two-tensors in any n-D spaces and their canonical forms are important in the
context of n-dimensional brane-worlds context and also in the framework of 11-D
supergravity and 10-D superstrings.Comment: LaTex2e, 18 pages. To appear in Braz.J.Phys (2004
Slepton mass splittings and cLFV in the SUSY seesaw in the light of recent experimental results
Following recent experimental developments, in this study we re-evaluate if
the interplay of high- and low-energy lepton flavour violating observables
remains a viable probe to test the high-scale type-I supersymmetric seesaw. Our
analysis shows that fully constrained supersymmetric scenarios no longer allow
to explore this interplay, since recent LHC data precludes the possibility of
having sizeable slepton mass differences for a slepton spectrum sufficiently
light to be produced, and in association to BR(mu -> e gamma) within
experimental reach. However, relaxing the strict universality of supersymmetric
soft-breaking terms, and fully exploring heavy neutrino dynamics, still allows
to have slepton mass splittings O(few %), for slepton masses accessible at the
LHC, with associated mu -> e gamma rates within future sensitivity. For these
scenarios, we illustrate how the correlation between high- and low-energy
lepton flavour violating observables allows to probe the high-scale
supersymmetric seesaw.Comment: 19 pages, 12 eps figures. References updated; matches version
accepted by JHE
Linear Invariant Systems Theory for Signal Enhancement
This paper discusses a linear time invariant (LTI) systems approach to signal enhancement via projective subspace techniques. It provides closed form expressions for the frequency response of data adaptive finite impulse response eigenfilters. An illustrative example using speech enhancement is also presented.Este artigo apresenta a aplicação da teoria de sistemas lineares invariantes no tempo (LTI) na anĂĄlise de tĂ©cnicas de sub-espaço. A resposta em frequĂȘncia dos filtros resultantes da decomposição em valores singulares Ă© obtida aplicando as propriedades dos sistemas LTI
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