2,339 research outputs found
A functional interpretation for nonstandard arithmetic
We introduce constructive and classical systems for nonstandard arithmetic
and show how variants of the functional interpretations due to Goedel and
Shoenfield can be used to rewrite proofs performed in these systems into
standard ones. These functional interpretations show in particular that our
nonstandard systems are conservative extensions of extensional Heyting and
Peano arithmetic in all finite types, strengthening earlier results by
Moerdijk, Palmgren, Avigad and Helzner. We will also indicate how our rewriting
algorithm can be used for term extraction purposes. To conclude the paper, we
will point out some open problems and directions for future research and
mention some initial results on saturation principles
TPC tracking and particle identification in high-density environment
Track finding and fitting algorithm in the ALICE Time projection chamber
(TPC) based on Kalman-filtering is presented. Implementation of particle
identification (PID) using d/d measurement is discussed. Filtering and
PID algorithm is able to cope with non-Gaussian noise as well as with ambiguous
measurements in a high-density environment. The occupancy can reach up to 40%
and due to the overlaps, often the points along the track are lost and others
are significantly displaced. In the present algorithm, first, clusters are
found and the space points are reconstructed. The shape of a cluster provides
information about overlap factor. Fast spline unfolding algorithm is applied
for points with distorted shapes. Then, the expected space point error is
estimated using information about the cluster shape and track parameters.
Furthermore, available information about local track overlap is used. Tests are
performed on simulation data sets to validate the analysis and to gain
practical experience with the algorithm.Comment: 9 pages, 5 figure
The strength of countable saturation
We determine the proof-theoretic strength of the principle of countable
saturation in the context of the systems for nonstandard arithmetic introduced
in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the
conclusio
Magnetic fluid modified peanut husks as an adsorbent for organic dyes removal
AbstractMagnetically responsive nanocomposite materials, prepared by modification of diamagnetic materials by magnetic fluids (ferrofluids), have already found many important applications in various areas of biosciences, medicine, biotechnology, environmental technology etc. Ferrofluid modified biological waste (peanut husks) has been successfully used for the separation and removal of water soluble organic dyes and thus this low cost adsorbent could be potentially used for waste water treatment
Magnetic techniques for the isolation and purification of proteins and peptides
Isolation and separation of specific molecules is used in almost all areas of biosciences and biotechnology. Diverse procedures can be used to achieve this goal. Recently, increased attention has been paid to the development and application of magnetic separation techniques, which employ small magnetic particles. The purpose of this review paper is to summarize various methodologies, strategies and materials which can be used for the isolation and purification of target proteins and peptides with the help of magnetic field. An extensive list of realised purification procedures documents the efficiency of magnetic separation techniques
The cohesive principle and the Bolzano-Weierstra{\ss} principle
The aim of this paper is to determine the logical and computational strength
of instances of the Bolzano-Weierstra{\ss} principle (BW) and a weak variant of
it.
We show that BW is instance-wise equivalent to the weak K\"onig's lemma for
-trees (-WKL). This means that from every bounded
sequence of reals one can compute an infinite -0/1-tree, such that
each infinite branch of it yields an accumulation point and vice versa.
Especially, this shows that the degrees d >> 0' are exactly those containing an
accumulation point for all bounded computable sequences.
Let BW_weak be the principle stating that every bounded sequence of real
numbers contains a Cauchy subsequence (a sequence converging but not
necessarily fast). We show that BW_weak is instance-wise equivalent to the
(strong) cohesive principle (StCOH) and - using this - obtain a classification
of the computational and logical strength of BW_weak. Especially we show that
BW_weak does not solve the halting problem and does not lead to more than
primitive recursive growth. Therefore it is strictly weaker than BW. We also
discuss possible uses of BW_weak.Comment: corrected typos, slightly improved presentatio
- …