Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

The Kramer sampling theorem revisited

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space through an -valued kernel K defined on an appropriate domain.This work has been supported by the grant MTM2009–08345 from the Spanish Ministerio de Ciencia e Innovación (MICNN).Publicad

Designing the physical metallurgy of a bainitic microalloyed steel with a dilatometer

During the past decade, medium carbon microalloyed steels have become increasingly important in the automotive sector. These steels are especially suitable for automobile components such as connecting rods, crankshafts and wheel hubs. Their mechanical properties are generally adequate in most cases although their toughnesses are consistently low. High toughness can be obtained in medium carbon microalloyed bainitic steel (38MnV7) after a careful control of the chemistry and heat thermal treatment. An specific chemical composition of a 38MnV7 steel has been developed, providing impact energies after Charpy-V tests at room temperature as high as 40J (the steel in bainitic state). Present work is oriented to an optimization of the above chemical composition by control of the Transformation Time Temperature (TTT) curves as well as the Precipitation Time Temperatures (PTT) curves of the present microallying elements. To attain this purpose six different casting were prepared, ranging the chemical composition as follows %C: 0.35-0.46, %Mn: 1.33-1.84, %V: 0.066-0.14% and %Ti: 0.010- 0.025. To appropriate design the thermal cycle, TTT curves were determined for each steel at two austenitization conditions, in order to promote fine and large initial grain sizes.. PTT curves were determined by the stress relaxation technique, a method which can be also be used to derive recrystrallization kinetics. All curves, TTT and PTT curves where derived by using a quenching dilatometer Bahr DIL805A/D. While the TTT curves were obtained in a classical way, the relaxation test consist in sample austenization followed by cooling down to the testing temperature. After a short stabilization period of 10s, samples are deformed to different strain levels and then relaxed, i.e. deformation is kept constant and the variation of the stress with the time is recorded. The different deformation levels are selected to evaluate the effect of deformation on precipitation characteristics. The relaxation curves under these conditions gave information about the kinetics of precipitation when there is no plastic deformation and, thus, generation of dislocations involved. Results are finally discussed in terms of the chemical composition, initial microstructure and precipitates interaction.Peer Reviewe

On Some Sampling-Related Frames in U-Invariant Spaces

This paper is concerned with the characterization as frames of some sequences in -invariant spaces of a separable Hilbert space H where U denotes an unitary operator defined on H ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2(R) , where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In doing so, we need the unitary operator to belong to a continuous group of unitary operators

Genetics: Is LADA just late onset type 1 diabetes?

Background: There is a controversy regarding Latent Autoimmune Diabetes in Adults (LADA) classification and whether it should be considered a slowly progressing form of type 1 (T1) diabetes (DM) or a distinct type of DM altogether. Methods: This cross-sectional study assessed major genes associated with T1DM (class II Results: A total of 578 participants were included: 248 with T1DM (70 diagnosed after the age of 30), 256 with T2DM and 74 with LADA. High risk HLA alleles were significantly more frequent in LADA than in T2DM, whereas the opposite was true for protective alleles. We found a lower frequency of the high-risk DRB1*04-DQB1*03:02-DQA1*03:01 haplotype in LADA (21.1%) than in the overall T1DM (34.7%) (p\u3c0.05), whereas no differences were found between these groups for DRB1*03-DQB1*02:01-DQA1*05:01 or for protective alleles. Only 12% the overall T1DM group had no risk alleles vs 30% of LADA (p\u3c0.0005). However, HLA allele distribution was similar in LADA and T1DM diagnosed after the age of 30. A total of 506 individuals (195 with T1DM [21 diagnosed after age 30] 253 with T2DM and 58 with LADA) were genotyped for the Conclusion: In this relatively small cross-sectional study, the genetic profile of subjects with LADA showed a similar T1DM-related risk allele distribution as in participants with T1DM diagnosed after the age of 30, but fewer risk alleles than those diagnosed before 30. Differences were present for HLA, as well a

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros