scholarly journals MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS

2020 ◽  
Vol 8 ◽  
Author(s):  
ADAM J. HARPER
Keyword(s):  
Large Deviations ◽  
Multiplicative Function ◽  
Multiplicative Functions ◽  
Order Of Magnitude ◽  
Introductory Discussion ◽  
First Moment ◽  
Better Than

We determine the order of magnitude of $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$ , where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, and $0\leqslant q\leqslant 1$ . In the Steinhaus case, this is equivalent to determining the order of $\lim _{T\rightarrow \infty }\frac{1}{T}\int _{0}^{T}|\sum _{n\leqslant x}n^{-it}|^{2q}\,dt$ . In particular, we find that $\mathbb{E}|\sum _{n\leqslant x}f(n)|\asymp \sqrt{x}/(\log \log x)^{1/4}$ . This proves a conjecture of Helson that one should have better than squareroot cancellation in the first moment and disproves counter-conjectures of various other authors. We deduce some consequences for the distribution and large deviations of $\sum _{n\leqslant x}f(n)$ . The proofs develop a connection between $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$ and the $q$ th moment of a critical, approximately Gaussian, multiplicative chaos and then establish the required estimates for that. We include some general introductory discussion about critical multiplicative chaos to help readers unfamiliar with that area.

Second Paper: Deep Drawing and Free Forming Using a Water Hammer Technique

1964 ◽  
Vol 179 (1) ◽  
pp. 222-233 ◽  
Author(s):  
A. P. Vafiadakis ◽  
W. Johnson ◽  
I. S. Donaldson
Keyword(s):  
Deep Drawing ◽  
Time History ◽  
Water Hammer ◽  
High Rate ◽  
Pressure Time ◽  
Order Of Magnitude ◽  
History Of ◽  
Overall Efficiency ◽  
Initial Movement ◽  
Better Than

Earlier work on a water-hammer technique for high-rate forming of sheet metal has been extended to include work on deep drawing using lead plugs. A study of the pressure-time history of a deforming blank during its initial movement is reported. An assessment of the overall efficiency of the process has been made and is found to be about 50 per cent; this is an order of magnitude better than that found with comparable electro-hydraulic and explosive methods.

A method of precise misorientation determination

2003 ◽  
Vol 36 (6) ◽  
pp. 1319-1323 ◽  
Author(s):  
A. Morawiec
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Spatial Resolution ◽  
Standard Procedure ◽  
Good Spatial Resolution ◽  
Transmission Electron ◽  
Order Of Magnitude ◽  
Achievable Accuracy ◽  
Better Than

A method that improves the accuracy of misorientations determined from Kikuchi patterns is described. It is based on the fact that some parameters of a misorientation calculated from two orientations are more accurate than other parameters. A procedure which eliminates inaccurate elements is devised. It requires at least two foil inclinations. The quality of the approach relies on the possibility to set large sample-to-detector distances and the availability of good spatial resolution of transmission electron microscopy. Achievable accuracy is one order of magnitude better than the accuracy of the standard procedure.

scholarly journals REINFORCEMENT LEARNING BASED ANTI-COLLISION ALGORITHM FOR RFID SYSTEMS

2019 ◽  
pp. 155-168
Author(s):  
Murukesan Loganathan ◽  
Thennarasan Sabapathy ◽  
Mohamed Elobaid Elshaikh ◽  
Mohamed Nasrun Osman ◽  
Rosemizi Abd Rahim ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Radio Frequency Identification ◽  
Energy Efficient ◽  
Current Standard ◽  
Tag Identification ◽  
Rfid Systems ◽  
Order Of Magnitude ◽  
Control Message ◽  
Frequency Identification ◽  
Better Than

Efficient collision arbitration protocol facilitates fast tag identification in radio frequency identification (RFID) systems. EPCGlobal-Class1-Generation2 (EPC-C1G2) protocol is the current standard for collision arbitration in commercial RFID systems. However, the main drawback of this protocol is that it requires excessive message exchanges between tags and the reader for its operation. This wastes energy of the already resource-constrained RFID readers. Hence, in this work, reinforcement learning based anti-collision protocol (RL-DFSA) is proposed to address the energy efficient collision arbitration problem in the RFID system. The proposed algorithm continuously learns and adapts to the changes in the environment by devising an optimal policy. The proposed RL-DFSA was evaluated through extensive simulations and compared with the variants of EPC-C1G2 algorithms that are currently being used in the commercial readers. Based on the results, it is concluded that RL-DFSA performs equal or better than EPC-C1G2 protocol in delay, throughput and time system efficiency when simulated for sparse and dense environments while requiring one order of magnitude lesser control message exchanges between the reader and the tags.

scholarly journals Defect-Tolerant Architectures for Nanoelectronic Crossbar Memories

2007 ◽  
Vol 7 (1) ◽  
pp. 151-167 ◽  
Author(s):  
Dmitri B. Strukov ◽  
Konstantin K. Likharev
Keyword(s):  
Upper Bound ◽  
Memory Cell ◽  
Error Correcting Codes ◽  
Cell Fraction ◽  
Access Time ◽  
Initial Stage ◽  
Order Of Magnitude ◽  
Pitch Ratio ◽  
Better Than

We have calculated the maximum useful bit density that may be achieved by the synergy of bad bit exclusion and advanced (BCH) error correcting codes in prospective crossbar nanoelectronic memories, as a function of defective memory cell fraction. While our calculations are based on a particular ("CMOL") memory topology, with naturally segmented nanowires and an area-distributed nano/CMOS interface, for realistic parameters our results are also applicable to "global" crossbar memories with peripheral interfaces. The results indicate that the crossbar memories with a nano/CMOS pitch ratio close to 1/3 (which is typical for the current, initial stage of the nanoelectronics development) may overcome purely semiconductor memories in useful bit density if the fraction of nanodevice defects (stuck-on-faults) is below ∼15%, even under rather tough, 30 ns upper bound on the total access time. Moreover, as the technology matures, and the pitch ratio approaches an order of magnitude, the crossbar memories may be far superior to the densest semiconductor memories by providing, e.g., a 1 Tbit/cm2 density even for a plausible defect fraction of 2%. These highly encouraging results are much better than those reported in literature earlier, including our own early work, mostly due to more advanced error correcting codes.

New Instrumentation in Argonne's Hvem-Tandem Facility: Expanded Capability for in Situ Ion Beam Studies+

1995 ◽  
Vol 396 ◽  
Author(s):  
Charles W. Allen ◽  
Loren L. Funk ◽  
Edward A. Ryan
Keyword(s):  
Scientific Community ◽  
State Of The Art ◽  
Ion Irradiation ◽  
Ion Beam ◽  
Voltage Electron ◽  
User Facility ◽  
Order Of Magnitude ◽  
New Instrumentation ◽  
Better Than

AbstractDuring 1995, a state-of-the-art intermediate voltage electron microscope (IVEM) has been installed in the HVEM-Tandem Facility with in situ ion irradiation capabilities similar to those of the HVEM. A 300 kV Hitachi H-9000NAR has been interfaced to the two ion accelerators of the Facility, with a spatial resolution for imaging which is nearly an order of magnitude better than that for the 1.2 MV HVEM which dates from the early 1970s. The HVEM remains heavily utilized for electron- and ion irradiation-related materials studies, nevertheless, especially those for which less demanding microscopy is adequate. The capabilities and limitations of this IVEM and HVEM are compared. Both the HVEM and IVEM are part of the DOE funded User Facility and therefore are available to the scientific community for materials studies, free of charge for non-proprietary research.

scholarly journals Moments of the Critical Values of Families of Elliptic Curves, with Applications

2010 ◽  
Vol 62 (5) ◽  
pp. 1155-1181 ◽  
Author(s):  
Matthew P. Young
Keyword(s):  
Elliptic Curves ◽  
Large Family ◽  
Critical Values ◽  
Central Values ◽  
The Family ◽  
Order Of Magnitude ◽  
Rank 2 ◽  
Family Based ◽  
First Moment ◽  
Positive Rank

AbstractWe make conjectures on the moments of the central values of the family of all elliptic curves and on themoments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of L-functions. Notably, we predict that the critical values of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves in the positive rank family.Furthermore, as arithmetical applications, we make a conjecture on the distribution of ap's amongst all rank 2 elliptic curves and show how the Riemann hypothesis can be deduced from sufficient knowledge of the first moment of the positive rank family (based on an idea of Iwaniec).

scholarly journals The Radio Properties of SNRs in the Magellanic Clouds

1983 ◽  
Vol 101 ◽  
pp. 551-558 ◽  
Author(s):  
B. Y. Mills
Keyword(s):  
Supernova Remnants ◽  
Average Distance ◽  
Hii Regions ◽  
Magellanic Clouds ◽  
Selection Effects ◽  
Absolute Distance ◽  
Major Difficulty ◽  
Order Of Magnitude ◽  
Thermal Sources ◽  
Better Than

An understanding of the radio properties and evolution of Galactic supernova remnants has always been hampered by the difficulty of measuring distances. A conventional wisdom has developed around a set of ‘good’ calibrators but most workers involved have drawn attention to the uncertainties and the possibility of selection effects distorting results. This major difficulty is completely overcome by studying SNRs in the Magellanic Clouds. Although there is uncertainty in the absolute distance scale, relative distances can be determined to better than 10% and differences of this magnitude are not significant when intercomparing SNRs. There is, however, another set of problems associated with sensitivity and resolution. The Clouds are an order of magnitude more distant than the average distance of Galactic SNRs, thus many of the SNRs are close to or below the sensitivity limits of most of the southern radiotelescopes and, until recently, the resolution available has often been inadequate to separate non-thermal sources from thermal HII regions, so that both flux densities and spectra have been subject to error. Also there are ∼ 1000 extragalactic background sources which can mimic the flux density and spectra of SNRs in the Clouds, particularly when close to or behind HII regions; as a result numerous incorrect or doubtful SNR identifications have been suggested.

scholarly journals Device for Contact Measurement of Turbine Blade Geometry in Robotic Grinding Process

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7053
Author(s):  
Dariusz Szybicki ◽  
Andrzej Burghardt ◽  
Krzysztof Kurc ◽  
Piotr Gierlak
Keyword(s):  
Turbine Blade ◽  
Feedback Loop ◽  
Aircraft Engine ◽  
Grinding Process ◽  
Measuring Device ◽  
Robotic Grinding ◽  
Order Of Magnitude ◽  
Accuracy And Repeatability ◽  
Output Interface ◽  
Better Than

The article discusses the design, implementation, and testing of the accuracy of a measuring device used to measure the thickness of aircraft engine blades subjected to a robotic grinding process. The assumptions that the measuring device should meet were presented. The manufactured device was subjected to accuracy and repeatability tests using a standard workpiece. The analysis of research results proved that the measuring device exhibits an accuracy of one order of magnitude better than the accuracy required for blades. For control of the grinding process, the results should be perceived as appropriate. Then, the device was subjected to verification consisting in using it to measure the thickness of aircraft engine blades. The constructed device can be used, not only for inspection of final products, but also for control of the robotic grinding process because thanks to the output interface it can be used in the robotic station’s feedback loop.

scholarly journals mm-VLBI observations of SiO masers: Further support for radiative pumping and rotation of the inner shell

2002 ◽  
Vol 206 ◽  
pp. 286-289
Author(s):  
Jean-François Desmurs ◽  
Valentín Bujarrabal ◽  
Francisco Colomer ◽  
Javier Alcolea
Keyword(s):  
Spatial Distribution ◽  
High Spatial Resolution ◽  
Agb Stars ◽  
Polarization Pattern ◽  
Vlbi Observations ◽  
Very High Spatial Resolution ◽  
Order Of Magnitude ◽  
Circumstellar Shells ◽  
Very High ◽  
Better Than

We have performed VLBA observations of the SiO v = 1 and v = 2 J = 1-0 masers in two AGB stars, TX Cam and IRC +10011. We confirm the ring-like spatial distribution, previously found in several AGB objects, as well as the tangential polarization pattern, already reported for TX Cam. Both properties, that seem to be systematic in this kind of objects, are characteristic of radiatively pumped SiO masers. On the contrary, we do not confirm the previous report on the spatial coincidence between the J = 1-0 v = 1 and 2 masers, a result that would have argued in favor of collisional pumping. We find that both lines sometimes arise from nearby spots, typically separated by 1-2 mas, but are rarely coincident. The discrepancy with previous results is explained by the very high spatial resolution of our observations, ∼ 0.5 mas, an order of magnitude better than in the relevant previously published experiment. Moreover, we have been able to measure a probable rotation of the inner shell of a few km/s. Rotation of circumstellar shells is assumed by the most convincing models explaining the drastic change of symmetry between the AGB envelopes (spherical symmetry) and Proto Planetary Nebulae (axial symmetry).

scholarly journals Some characterizations of totients

1996 ◽  
Vol 19 (2) ◽  
pp. 209-217 ◽  
Author(s):  
Pentti Haukkanen
Keyword(s):  
Multiplicative Function ◽  
Arithmetical Function ◽  
Multiplicative Functions ◽  
Dirichlet Convolution

An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient. All completely multiplicative functions are also totients. There is a large number of characterizations of completely multiplicative functions in the literature, while characterizations of totients have not been widely studied in the literature. In this paper we present several arithmetical identities serving as characterizations of totients. We also introduce a new concrete example of a totient.

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