text:
• ### Beam test calibration of the balloon-borne imaging calorimeter for the CREAM experiment(1003.4745)

June 15, 2018 astro-ph.IM, astro-ph.HE
CREAM (Cosmic Ray Energetics And Mass) is a multi-flight balloon mission designed to collect direct data on the elemental composition and individual energy spectra of cosmic rays. Two instrument suites have been built to be flown alternately on a yearly base. The tungsten/Sci-Fi imaging calorimeter for the second flight, scheduled for December 2005, was calibrated with electron and proton beams at CERN. A calibration procedure based on the study of the longitudinal shower profile is described and preliminary results of the beam test are presented.
• ### On-orbit Operations and Offline Data Processing of CALET onboard the ISS(1803.05834)

March 15, 2018 physics.ins-det, astro-ph.IM
The CALorimetric Electron Telescope (CALET), launched for installation on the International Space Station (ISS) in August, 2015, has been accumulating scientific data since October, 2015. CALET is intended to perform long-duration observations of high-energy cosmic rays onboard the ISS. CALET directly measures the cosmic-ray electron spectrum in the energy range of 1 GeV to 20 TeV with a 2% energy resolution above 30 GeV. In addition, the instrument can measure the spectrum of gamma rays well into the TeV range, and the spectra of protons and nuclei up to a PeV. In order to operate the CALET onboard ISS, JAXA Ground Support Equipment (JAXA-GSE) and the Waseda CALET Operations Center (WCOC) have been established. Scientific operations using CALET are planned at WCOC, taking into account orbital variations of geomagnetic rigidity cutoff. Scheduled command sequences are used to control the CALET observation modes on orbit. Calibration data acquisition by, for example, recording pedestal and penetrating particle events, a low-energy electron trigger mode operating at high geomagnetic latitude, a low-energy gamma-ray trigger mode operating at low geomagnetic latitude, and an ultra heavy trigger mode, are scheduled around the ISS orbit while maintaining maximum exposure to high-energy electrons and other high-energy shower events by always having the high-energy trigger mode active. The WCOC also prepares and distributes CALET flight data to collaborators in Italy and the United States. As of August 31, 2017, the total observation time is 689 days with a live time fraction of the total time of approximately 84%. Nearly 450 million events are collected with a high-energy (E>10 GeV) trigger. By combining all operation modes with the excellent-quality on-orbit data collected thus far, it is expected that a five-year observation period will provide a wealth of new and interesting results.
• ### CaloCube: a novel calorimeter for high-energy cosmic rays in space(1705.07027)

May 23, 2017 physics.ins-det
In order to extend the direct observation of high-energy cosmic rays up to the PeV region, highly performing calorimeters with large geometrical acceptance and high energy resolution are required. Within the constraint of the total mass of the apparatus, crucial for a space mission, the calorimeters must be optimized with respect to their geometrical acceptance, granularity and absorption depth. CaloCube is a homogeneous calorimeter with cubic geometry, to maximise the acceptance being sensitive to particles from every direction in space; granularity is obtained by relying on small cubic scintillating crystals as active elements. Different scintillating materials have been studied. The crystal sizes and spacing among them have been optimized with respect to the energy resolution. A prototype, based on CsI(Tl) cubic crystals, has been constructed and tested with particle beams. Some results of tests with different beams at CERN are presented.
• ### CALET Upper Limits on X-ray and Gamma-ray Counterparts of GW 151226(1607.00233)

Sept. 2, 2016 astro-ph.HE
We present upper limits in the hard X-ray and gamma-ray bands at the time of the LIGO gravitational-wave event GW 151226 derived from the CALorimetric Electron Telescope (CALET) observation. The main instrument of CALET, CALorimeter (CAL), observes gamma-rays from ~1 GeV up to 10 TeV with a field of view of ~2 sr. The CALET gamma-ray burst monitor (CGBM) views ~3 sr and ~2pi sr of the sky in the 7 keV - 1 MeV and the 40 keV - 20 MeV bands, respectively, by using two different scintillator-based instruments. The CGBM covered 32.5% and 49.1% of the GW 151226 sky localization probability in the 7 keV - 1 MeV and 40 keV - 20 MeV bands respectively. We place a 90% upper limit of 2 x 10^{-7} erg cm-2 s-1 in the 1 - 100 GeV band where CAL reaches 15% of the integrated LIGO probability (~1.1 sr). The CGBM 7 sigma upper limits are 1.0 x 10^{-6} erg cm-2 s-1 (7-500 keV) and 1.8 x 10^{-6} erg cm-2 s-1 (50-1000 keV) for one second exposure. Those upper limits correspond to the luminosity of 3-5 x 10^{49} erg s-1 which is significantly lower than typical short GRBs.
• ### GAMMA-400 gamma-ray observatory(1507.06246)

Nov. 12, 2015 astro-ph.IM
The GAMMA-400 gamma-ray telescope with excellent angular and energy resolutions is designed to search for signatures of dark matter in the fluxes of gamma-ray emission and electrons + positrons. Precision investigations of gamma-ray emission from Galactic Center, Crab, Vela, Cygnus, Geminga, and other regions will be performed, as well as diffuse gamma-ray emission, along with measurements of high-energy electron + positron and nuclei fluxes. Furthermore, it will study gamma-ray bursts and gamma-ray emission from the Sun during periods of solar activity. The energy range of GAMMA-400 is expected to be from ~20 MeV up to TeV energies for gamma rays, up to 20 TeV for electrons + positrons, and up to 10E15 eV for cosmic-ray nuclei. For high-energy gamma rays with energy from 10 to 100 GeV, the GAMMA-400 angular resolution improves from 0.1{\deg} to ~0.01{\deg} and energy resolution from 3% to ~1%; the proton rejection factor is ~5x10E5. GAMMA-400 will be installed onboard the Russian space observatory.
• ### A separation of electrons and protons in the GAMMA-400 gamma-ray telescope(1503.06657)

March 23, 2015 physics.ins-det, astro-ph.IM
The GAMMA-400 gamma-ray telescope is intended to measure the fluxes of gamma rays and cosmic-ray electrons and positrons in the energy range from 100 MeV to several TeV. Such measurements concern with the following scientific goals: search for signatures of dark matter, investigation of gamma-ray point and extended sources, studies of the energy spectra of Galactic and extragalactic diffuse emission, studies of gamma-ray bursts and gamma-ray emission from the active Sun, as well as high-precision measurements of spectra of high-energy electrons and positrons, protons, and nuclei up to the knee. The main components of cosmic rays are protons and helium nuclei, whereas the part of lepton component in the total flux is ~10E-3 for high energies. In present paper, the capability of the GAMMA-400 gamma-ray telescope to distinguish electrons and positrons from protons in cosmic rays is investigated. The individual contribution to the proton rejection is studied for each detector system of the GAMMA-400 gamma-ray telescope. Using combined information from all detector systems allow us to provide the proton rejection from electrons with a factor of ~4x10E5 for vertical incident particles and ~3x10E5 for particles with initial inclination of 30 degrees. The calculations were performed for the electron energy range from 50 GeV to 1 TeV.
• ### Study of the Gamma-ray performance of the GAMMA-400 Calorimeter(1502.03287)

March 7, 2015 astro-ph.IM, astro-ph.HE
GAMMA-400 is a new space mission, designed as a dual experiment, capable to study both high energy gamma rays (from $\sim$100 MeV to few TeV) and cosmic rays (electrons up to 20 TeV and nuclei up to $\sim$10$^{15}$ eV). The full simulation framework of GAMMA-400 is based on the Geant4 toolkit. The details of the gamma-ray reconstruction pipeline in the pre-shower and calorimeter will be outlined. The performance of GAMMA-400 (PSF, effective area) have been obtained using this framework. The most updated results on them will be shown.
• ### The GAMMA-400 Space Mission(1502.02976)

Feb. 10, 2015 astro-ph.IM, astro-ph.HE
GAMMA-400 is a new space mission which will be installed on board the Russian space platform Navigator. It is scheduled to be launched at the beginning of the next decade. GAMMA-400 is designed to study simultaneously gamma rays (up to 3 TeV) and cosmic rays (electrons and positrons from 1 GeV to 20 TeV, nuclei up to 10$^{15}$-10$^{16}$ eV). Being a dual-purpose mission, GAMMA-400 will be able to address some of the most impelling science topics, such as search for signatures of dark matter, cosmic-rays origin and propagation, and the nature of transients. GAMMA-400 will try to solve the unanswered questions on these topics by high-precision measurements of the Galactic and extragalactic gamma-ray sources, Galactic and extragalactic diffuse emission and the spectra of cosmic-ray electrons + positrons and nuclei, thanks to excellent energy and angular resolutions.
• ### The GAMMA-400 space observatory: status and perspectives(1412.4239)

The present design of the new space observatory GAMMA-400 is presented in this paper. The instrument has been designed for the optimal detection of gamma rays in a broad energy range (from ~100 MeV up to 3 TeV), with excellent angular and energy resolution. The observatory will also allow precise and high statistic studies of the electron component in the cosmic rays up to the multi TeV region, as well as protons and nuclei spectra up to the knee region. The GAMMA-400 observatory will allow to address a broad range of science topics, like search for signatures of dark matter, studies of Galactic and extragalactic gamma-ray sources, Galactic and extragalactic diffuse emission, gamma-ray bursts and charged cosmic rays acceleration and diffusion mechanism up to the knee.
• ### The GAMMA-400 gamma-ray telescope characteristics. Angular resolution and electrons/protons separation(1412.1486)

Dec. 11, 2014 astro-ph.IM
The measurements of gamma-ray fluxes and cosmic-ray electrons and positrons in the energy range from 100 MeV to several TeV, which will be implemented by the specially designed GAMMA-400 gamma-ray telescope, concern with the following broad range of science topics. Searching for signatures of dark matter, surveying the celestial sphere in order to study gamma-ray point and extended sources, measuring the energy spectra of Galactic and extragalactic diffuse gamma-ray emission, studying gamma-ray bursts and gamma-ray emission from the Sun, as well as high precision measuring spectra of high-energy electrons and positrons, protons and nuclei up to the knee. To clarify these scientific problems with the new experimental data the GAMMA-400 gamma-ray telescope possesses unique physical characteristics comparing with previous and present experiments. For gamma-ray energies more than 100 GeV GAMMA-400 provides the energy resolution of ~1% and angular resolution better than 0.02 deg. The methods developed to reconstruct the direction of incident gamma photon are presented in this paper, as well as, the capability of the GAMMA-400 gamma-ray telescope to distinguish electrons and positrons from protons in cosmic rays is investigated.
• ### The electromagnetic calorimeter of the AMS-02 experiment(1210.0316)

The electromagnetic calorimeter (ECAL) of the AMS-02 experiment is a 3-dimensional sampling calorimeter, made of lead and scintillating fibers. The detector allows for a high granularity, with 18 samplings in the longitudinal direction, and 72 sampling in the lateral direction. The ECAL primary goal is to measure the energy of cosmic rays up to few TeV, however, thanks to the fine grained structure, it can also provide the separation of positrons from protons, in the GeV to TeV region. A direct measurement of high energy photons with accurate energy and direction determination can also be provided.
• ### Cosmic-Ray Proton and Helium Spectra from the First CREAM Flight(1102.2575)

Feb. 13, 2011 astro-ph.HE
Cosmic-ray proton and helium spectra have been measured with the balloon-borne Cosmic Ray Energetics And Mass experiment flown for 42 days in Antarctica in the 2004-2005 austral summer season. High-energy cosmic-ray data were collected at an average altitude of ~38.5 km with an average atmospheric overburden of ~3.9 g cm$^{-2}$. Individual elements are clearly separated with a charge resolution of ~0.15 e (in charge units) and ~0.2 e for protons and helium nuclei, respectively. The measured spectra at the top of the atmosphere are represented by power laws with a spectral index of -2.66 $\pm$ 0.02 for protons from 2.5 TeV to 250 TeV and -2.58 $\pm$ 0.02 for helium nuclei from 630 GeV/nucleon to 63 TeV/nucleon. They are harder than previous measurements at a few tens of GeV/nucleon. The helium flux is higher than that expected from the extrapolation of the power law fitted to the lower-energy data. The relative abundance of protons to helium nuclei is 9.1 $\pm$ 0.5 for the range from 2.5 TeV/nucleon to 63 TeV/nucleon. This ratio is considerably smaller than the previous measurements at a few tens of GeV/nucleon.
• ### Discrepant hardening observed in cosmic-ray elemental spectra(1004.1123)

April 7, 2010 astro-ph.HE
The balloon-borne Cosmic Ray Energetics And Mass (CREAM) experiment launched five times from Antarctica has achieved a cumulative flight duration of about 156 days above 99.5% of the atmosphere. The instrument is configured with complementary and redundant particle detectors designed to extend direct measurements of cosmic-ray composition to the highest energies practical with balloon flights. All elements from protons to iron nuclei are separated with excellent charge resolution. Here we report results from the first two flights of ~70 days, which indicate hardening of the elemental spectra above ~200 GeV/nucleon and a spectral difference between the two most abundant species, protons and helium nuclei. These results challenge the view that cosmic-ray spectra are simple power laws below the so-called knee at ~1015 eV. This discrepant hardening may result from a relatively nearby source, or it could represent spectral concavity caused by interactions of cosmic rays with the accelerating shock. Other possible explanations should also be investigated.
• ### Elemental Spectra from the CREAM-I Flight(1003.4983)

March 31, 2010 astro-ph.IM, astro-ph.HE
The Cosmic Ray Energetics And Mass (CREAM) is a balloon-borne experiment designed to measure the composition and energy spectra of cosmic rays of charge Z = 1 to 26 up to an energy of ~ 10^15 eV. CREAM had two successful flights on long-duration balloons (LDB) launched from Mc- Murdo Station, Antarctica, in December 2004 and December 2005. CREAM-I achieves a substantial measurement redundancy by employing multiple detector systems, namely a Timing Charge Detector and a Silicon Charge Detector (SCD) for particle identification, and a Transition Radiation Detector and a sampling tungsten/scintillating-fiber ionization calorimeter (CAL) for energy measurement. In this paper, preliminary energy spectra of various elements measured with CAL/SCD during the first 42-day flight are presented.
• ### Energy cross-calibration from the first CREAM flight: transition radiation detector versus calorimeter(1003.5753)

March 30, 2010 astro-ph.IM, astro-ph.HE
The Cosmic Ray Energetics And Mass (CREAM) balloon experiment had two successful flights in 2004/05 and 2005/06. It was designed to perform energy measurements from a few GeV up to 1000 TeV, taking advantage of different detection techniques. The first instrument, CREAM-1, combined a transition radiation detector with a calorimeter to provide independent energy measurements of cosmicraynuclei. Each detector was calibrated with particle beams in a limited range of energies. In order to assess the absolute energy scale of the instrument and to investigate the systematic effects of each technique, a cross-calibration was performed by comparing the two independent energy estimates on selected samples of oxygen and carbon nuclei.
• ### Measurements of cosmic-ray energy spectra with the 2nd CREAM flight(1003.5757)

March 30, 2010 astro-ph.IM, astro-ph.HE
During its second Antarctic flight, the CREAM (Cosmic Ray Energetics And Mass) balloon experiment collected data for 28 days, measuring the charge and the energy of cosmic rays (CR) with a redundant system of particle identification and an imaging thin ionization calorimeter. Preliminary direct measurements of the absolute intensities of individual CR nuclei are reported in the elemental range from carbon to iron at very high energy.
• ### Elemental energy spectra of cosmic rays measured by CREAM-II(1003.5759)

March 30, 2010 astro-ph.HE
We present new measurements of the energy spectra of cosmic-ray (CR) nuclei from the second flight of the balloon-borne experiment CREAM (Cosmic Ray Energetics And Mass). The instrument (CREAM-II) was comprised of detectors based on different techniques (Cherenkov light, specific ionization in scintillators and silicon sensors) to provide a redundant charge identification and a thin ionization calorimeter capable of measuring the energy of cosmic rays up to several hundreds of TeV. The data analysis is described and the individual energy spectra of C, O, Ne, Mg, Si and Fe are reported up to ~ 10^14 eV. The spectral shape looks nearly the same for all the primary elements and can be expressed as a power law in energy E^{-2.66+/-0.04}. The nitrogen absolute intensity in the energy range 100-800 GeV/n is also measured.
• ### Calibration of the CREAM-I calorimeter(1003.4737)

March 24, 2010 astro-ph.IM, astro-ph.HE
The Cosmic Ray Energetics And Mass (CREAM) calorimeter is designed to measure the spectra of cosmic-ray particles over the energy range from ~10^11 eV to ~10^15 eV. Its first flight as part of the CREAM-I balloon-borne payload in Antarctica during the 2004/05 season resulted in a recordbreaking 42 days of exposure. Calorimeter calibration using various beam test data will be discussed in an attempt to assess the uncertainties of the energy measurements.
• ### Performance of the CREAM calorimeter in accelerator beam test(1003.4743)

March 24, 2010 astro-ph.IM, astro-ph.HE
The CREAM calorimeter, designed to measure the spectra of cosmic-ray nuclei from under 1 TeV to 1000 TeV, is a 20 radiation length (X0) deep sampling calorimeter. The calorimeter is comprised of 20 layers of tungsten interleaved with 20 layers of scintillating fiber ribbons, and is preceded by a pair of graphite interaction targets providing about 0.42 proton interaction lengths (\lambda int). The calorimeter was placed in one of CERN's SPS accelerator beams for calibration and testing. Beams of 150 GeV electrons were used for calibration, and a variety of electron, proton, and nuclear fragment beams were used to test the simulation model of the detector. In this paper we discuss the performance of the calorimeter in the electron beam and compare electron beam data with simulation results.
• ### Energy spectra of cosmic-ray nuclei at high energies(0911.1889)

Nov. 10, 2009 astro-ph.IM, astro-ph.HE
We present new measurements of the energy spectra of cosmic-ray (CR) nuclei from the second flight of the balloon-borne experiment Cosmic Ray Energetics And Mass (CREAM). The instrument included different particle detectors to provide redundant charge identification and measure the energy of CRs up to several hundred TeV. The measured individual energy spectra of C, O, Ne, Mg, Si, and Fe are presented up to $\sim 10^{14}$ eV. The spectral shape looks nearly the same for these primary elements and it can be fitted to an $E^{-2.66 \pm 0.04}$ power law in energy. Moreover, a new measurement of the absolute intensity of nitrogen in the 100-800 GeV/$n$ energy range with smaller errors than previous observations, clearly indicates a hardening of the spectrum at high energy. The relative abundance of N/O at the top of the atmosphere is measured to be $0.080 \pm 0.025$(stat.)$\pm 0.025$(sys.) at $\sim$800 GeV/$n$, in good agreement with a recent result from the first CREAM flight.
• ### Measurements of cosmic-ray secondary nuclei at high energies with the first flight of the CREAM balloon-borne experiment(0808.1718)

Aug. 12, 2008 astro-ph
We present new measurements of heavy cosmic-ray nuclei at high energies per- formed during the first flight of the balloon-borne cosmic-ray experiment CREAM (Cosmic-Ray Energetics And Mass). This instrument uses multiple charge detectors and a transition radiation detector to provide the first high accuracy measurements of the relative abundances of elements from boron to oxygen up to energies around 1 TeV/n. The data agree with previous measurements at lower energies and show a relatively steep decline (~E$^-0.6$ to E$^-0.5$) at high energies. They further show the source abundance of nitrogen relative to oxygen is ~10% in the TeV/n region.
• ### Beam test calibration of the balloon-borne imaging calorimeter for the CREAM experiment(physics/0507174)

July 24, 2005 physics.ins-det
CREAM (Cosmic Ray Energetics And Mass) is a multi-flight balloon mission designed to collect direct data on the elemental composition and individual energy spectra of cosmic rays. Two instrument suites have been built to be flown alternately on a yearly base. The tungsten/Sci-Fi imaging calorimeter for the second flight, scheduled for December 2005, was calibrated with electron and proton beams at CERN. A calibration procedure based on the study of the longitudinal shower profile is described and preliminary results of the beam test are presented.


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# Indecomposable permutations with a given number of cycles

Abstract : A permutation $a_1a_2 \ldots a_n$ is $\textit{indecomposable}$ if there does not exist $p \lt n$ such that $a_1a_2 \ldots a_p$ is a permutation of $\{ 1,2, \ldots ,p\}$. We compute the asymptotic probability that a permutation of $\mathbb{S}_n$ with $m$ cycles is indecomposable as $n$ goes to infinity with $m/n$ fixed. The error term is $O(\frac{\log(n-m)}{ n-m})$. The asymptotic probability is monotone in $m/n$, and there is no threshold phenomenon: it degrades gracefully from $1$ to $0$. When $n=2m$, a slight majority ($51.1 \ldots$ percent) of the permutations are indecomposable. We also consider indecomposable fixed point free involutions which are in bijection with maps of arbitrary genus on orientable surfaces, for these involutions with $m$ left-to-right maxima we obtain a lower bound for the probability of being indecomposable.
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Cited literature [13 references]

https://hal.inria.fr/hal-01185443
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### Citation

Robert Cori, Claire Mathieu. Indecomposable permutations with a given number of cycles. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.301-312, ⟨10.46298/dmtcs.2750⟩. ⟨hal-01185443⟩

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Problem 620

A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
Forum rules
As your posts will be visible to the general public you
are requested to be thoughtful in not posting anything
that might explicitly give away how to solve a particular problem.

This forum is NOT meant to discuss solution methods for a problem.

In particular don't post any code fragments or results.

Don't start begging others to give partial answers to problems

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albert
Posts: 52
Joined: Sat Aug 02, 2008 11:36 am

Problem 620

"The circles can overlap."

One could leave this out, as in the sequel the circles are represented by gears, which obviously can't overlap.
Also the drawing suggest that ghost gears that are somehow occupying the same space are not allowed.
So it started out as circles out that roll off each other without sliding, but the remainder to makes it into a Diophantine problem is murky.

Or have I misunderstood the problem totally?

Groetjes Albert

RobertStanforth
Posts: 307
Joined: Mon Dec 30, 2013 11:25 pm

Re: Problem 620

Hi Albert,

The 'planet' gears can overlap if they occupy different locations in the $z$ axis (i.e. the direction coming out of the page).

Steppenwolf99
Posts: 2
Joined: Sun Feb 11, 2018 2:46 pm

Re: Problem 620

What arrangements are counted as distinct? It doesn't look like two arrangements of gears that differ only in orientation are counted as distinct.

RobertStanforth
Posts: 307
Joined: Mon Dec 30, 2013 11:25 pm

Re: Problem 620

Rotations and reflections do not give rise to distinct arrangements.

Posts: 1
Joined: Sun Feb 11, 2018 6:37 pm

Re: Problem 620

Can two planets (with this same circumference) have exactly the same position?

RobertStanforth
Posts: 307
Joined: Mon Dec 30, 2013 11:25 pm

Re: Problem 620

Sun Feb 11, 2018 6:42 pm
Can two planets (with this same circumference) have exactly the same position?
No, the four planets must all be distinct: no two may have the same size and position.

abcwuhang
Posts: 2
Joined: Mon Nov 28, 2016 5:14 pm

Re: Problem 620

As an epicyclic gear train allows the planets to rotate, what is the meaning of perfectly meshing of gears? Could you show how to drive the whole system? Thanks.

If you'd like to friend me, shoot me a message and I'll give you the code

RobertStanforth
Posts: 307
Joined: Mon Dec 30, 2013 11:25 pm

Re: Problem 620

abcwuhang wrote:
Mon Feb 12, 2018 1:18 pm
As an epicyclic gear train allows the planets to rotate, what is the meaning of perfectly meshing of gears? Could you show how to drive the whole system? Thanks.
Each of the six gears rotates about its own axis. The axes themselves don't move.

Steppenwolf99
Posts: 2
Joined: Sun Feb 11, 2018 2:46 pm

Re: Problem 620

I left this alone for 2 days and finally solved it on my second attempt today. A comment: some of the clarifications on this section should be included in the problem description. The trouble I had was more about parsing semantics and I made a couple of wrong assumptions which could have been avoided if I had come back to this page earlier. Thanks for an elegant problem.

Posts: 2
Joined: Tue Jan 16, 2018 9:27 pm

Re: Problem 620

A correct configuration of gears will ALWAYS have their underlying circles as tangent to each other as described in the problem, correct?

How important is the shape of the teeth? If they were more square or more rounded, would it affect the answer? What if the teeth stuck out further or lesser? (Is this what is meant by "pitch" in the problem?)

Animus


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If you have questions regarding the symbols, please contact the Reference Desk. The Forest Stewardship Council. 428 Likes, 83 Comments - po_zu {Po-Zu. Synonym strikebreaker worksheet example. As an American company since 1914, our focus is on making quality tires that will perform well and last for thousands of miles. 9 List of Mathematical Symbols In the following tables you nd all the symbols normally accessible from math mode. Md Kutubuddin Sardar. Chart of funny upside-down characters. The physics package requires xparse and amsmath to work properly in your LATEX document. Shape a flag or a symbol and your balloon masterpiece will be the center of attention. Unless said otherwise, the commands for these symbols can be used only in math mode. Electric Current Symbols. Note: If you want to duplicate a symbol instance on the artboard, for example, if you have scaled and rotated a symbol and want to add another instance with the same scale and. It can be identified with the symbol that the normal Ascii asterisk "*" character produces in LaTeX math mode. No extra packages are required to use these symbols. Wikipedia:LaTeX symbols. Symbols to spice up your LinkedIn profile Published on April 23, 2014 April 23, If you do add symbols to your profile, please share it with me, I love to see how others use them!. Manufactures mattresses, box springs, sofa beds and upholstered furniture for wholesalers in the US. "The terms 'latex-free' and 'does not contain natural rubber latex' suggest that the medical product is completely without NRL," FDA wrote. The highly readable texts and almost 800 beautiful full-color images come together in a unique way to convey hidden dimensions of meaning. There are multiple ways you can insert mathematics symbols in Windows 10. As a leader in specialty chemicals, Lubrizol's mission is to be an essential ingredient in our customers' success. One of six symbols; circles, squares, rectangles, stars, thermometers, and boxplots, can be plotted at a specified set of x and y coordinates. Documents like “Obsolete packages and commands” (“l2tabu”) address the need of up-to-date information. #,$, %, !, *, etc. Global market trends like increasing populations, rising middle class incomes, and on-the-go lifestyles continue to drive demand for high-performance plastic packaging that extends food freshness, improves product safety, is lighter and brighter, and provides user-friendly functionality. Write text symbols using keyboard, HTML or by copy-pasting. Find the best 353 free fonts in the Symbols style. $\int_a^b \! f(x). How to put a symbol above (on the head of) another? For example, I want to produce something like this in one line. UnicodeMath resembles real mathematical notation the most in comparison to all of the math linear formats, and it is the most concise linear format, though some may prefer editing in the LaTeX input over UnicodeMath since that is widely used in academia. 4 Fonts Font sizes Point size Latex cmd User-de ned * Sample 5 6 \tiny \xxxsmall the quick brown fox 7 8 \scriptsize \xxsmall the quick brown fox 8 10 \footnotesize \xsmall the quick brown fox. Using Alt Code Shortcuts. Unzip the plugin file and upload its content to wp-content/plugins folder of your blog. Configure your keyboard layout in Windows so that you can type all additional symbols you want as easy as any other text. To get a better understanding of how these commands are built up, I'd like to know what the. 165, the package amssymb must be loaded in the preamble of the document and the AMS math fonts must be installed on the system. If you can't find the LaTeX symbol(s) that you are after, then I can almost guarantee that you'll find them in the Comprehensive LaTeX Symbol List. From animal print balloons, graduation balloons, birthday celebration balloons to LED light-up latex balloons, we have everything you need to host the most wonderful party. For more details on the Jupyter Notebook, please see the Jupyter website. What I am looking to do is add up a symbol in the cells. This mask is based on the original Gorn mask used in the classic Star Trek episode Arena. 875 inches wide on 10pt documents. You can edit your text in the box and then copy it to your document, e-mail message, etc. By default, MATLAB ® supports a subset of TeX markup. It appeared on Akkadian seals as early as 2300 BC and from at least the second millennium BC it was the symbol of the Mesopotamian Moon gods Nanna in Sumer and Sin in Babylonia, Sin being the "Lamp of Heaven and Earth". Unicode Characters in the 'Symbol, Math' Category. Known worldwide as the standard language for accurate color communication, from designer to manufacturer to retailer to customer. This feature is not available right now. Symbols should be included in the Excel graphing function. Look for "Detexify" in the external links section below. The symbol for smiley is designed by Harvey Ball, as an assignment from the insurance company State Mutual Assurance Company. Occultists believe that signs and symbols are given a supernatural power at their creation. fractions), you should use LaTeX or MathJax. It is not changed from the code line. Symbols are used to draw geographic features, text, and graphics on maps. Latex is a sticky, milky colloid (a substance in which microscopically dispersed insoluble particles are suspended throughout another substance). Indicate your preference(s) on the Order Form Custom Colors Available for all designs. Since typing LaTeX is too cumbersome and not readily intuitive (you have to typeset it). But how to input a empty star? It is like: symbols. U+22C6 STAR OPERATOR “⋆”. They can be produced with one command, the \footnote command. Symbols to use in text. Click on one of them to start using it. Transpose Remove the fitting end. Each balloon bouquet comes with a card and is hand-delivered. You can provide an object of options as the last argument to katex. List Hello World The following manually implements a very simple list. How to type symbols, accents, special characters, and weird punctuation acute accents:. Creating Tables with LaTeX Tables are created using the "table" environment given below: \begin{table}[where] table \end{table} In the above syntax, table stands for the contents of the 'tabular' environment together with a possible \caption command. 09 command \_ is an established alias. Soon after, ranchers rediscovered the tough and well-adapted cattle and they have been a mainstay of Texas ranching operations ever since. The symbol suggests that the product inside the package is ‘precision made. 0 and star b has a magnitude of 7. Some of these symbols are guaranteed to be available in every LATEX2"system; others require fonts and packages. Example usage of star symbols as rating:. Easy-to-use symbol, keyword, package, style, and formatting reference for LaTeX scientific publishing markup language. Detexify is an attempt to simplify this search. To get a better understanding of how these commands are built up, I'd like to know what the. A symbol for CONGRUENCE is the equal (=) sign with a symbol of similarity (~) on top of the equal sign By the way, I am NOT a member of the MENSA. Visual images & text of doll makers marks menu A to Z. Installation of FontAwesome was easy on a mac, just drag the fontawesome. 4748 Topics 19169 Posts Last post how to write knitr tables in … by royer11 Thu Aug. LaTeX specific issues not fitting into one of the other forums of this category. You can add text to a chart that includes Greek letters and special characters using TeX markup. Everytime I try to use a backslash I get the following symbols - this if i simply hit they key # - or this if I use shift ~ The hash symbol is actually located above the number three on the keyboard, when I do shift on it I get £. Latex is a sticky, milky colloid (a substance in which microscopically dispersed insoluble particles are suspended throughout another substance). Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. Fortunately, there's a tool that can greatly simplify the search for the command for a specific symbol. July 17, 2015. executives who couldn’t say, or even type, their star’s new name. HTML Arrows is a comprehensive reference website for finding HTML symbol codes and entities, ASCII characters and Unicode hexadecimal values to use in your web design. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. 2) 25 JUL 2009 22:35 entering extended mode **\makeatletter\def\HCode{\futurelet\HCode\HChar}\def\H. As well as these accents, some characters can not be put directly into a BibTeX-entry, as they would conflict with the format description, like {, " or$. Windows 7 and Microsoft Word allow you to insert symbols above letters without using ribbon commands. Discover the best free signs and symbols vectors. Euro € currency symbol. FLOW CHART DESIGN SYMBOL. Alphabetical Statistical Symbols: Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate) a Y- intercept of least square regression line a = y bx, for line y = a + bx Regression: y on x b Slope of least squares regression line b = ¦ ¦ ( )2 ( )( ) x x x x y yfor line y = a + bx Regression: y on x B (n, p) Binomial. However, Excel graphing will not let you use symbols in the Titles, in the axes labels, or in the data units. We’re encouraging food businesses to make it easier for their customers to ask for allergen information when taking orders or reservations. org and also at (302) 450-4504. $\int_a^b \! f(x). Math symbols deﬁned by LaTeX package «amssymb» No. See the specific command for information on why you would use one over the other. The LaTeX Companion was my primary reference while teaching myself LaTeX over the course of two weekends. L A T E X Mathematical Symbols. It could be made out of memory foam, regular foam, fiberfill, wool, gel, latex or others of the kind. Saltar al navigation Saltar al recerca. The indians consider it symbol of purity. The symbol was originally chosen by the Gay Activists Alliance of New York in 1970. Click on one of them to start using it. Once a trademark is registered, the registered trademark symbol — a small circle with the letter "R" inside — is commonly put with the trademark each time it's used. While Alt codes don't exist on Mac computers, there are a variety of Option. letters & symbols from \mathnormal &$<<\star>>$symbols & most LaTeX symbols &$\leq*\geq$largesymbols & large symbols &$\sum\prod\int$Some math fonts are both math alphabets and math symbol fonts, for example \mathrm and operators are the same font, and \mathnormal and letters are the same font. However, it is important to recognize that even symbols, like those used in algebra, have names, and those names are made up of letters and words. LATEX recognizes the following units:. Common symbol character codes. Product availability and store hours may vary. 9 List of Mathematical Symbols In the following tables you nd all the symbols normally accessible from math mode. adi shakti. The familiar plus sign eliminates the need for a long written explanation of what addition means and how to accomplish it. The Elsevier article class helps you to format the frontmatter of your manuscript. A Petri-net for Hagen [] [] [Open in OverleafA complete graph [] [] [Open in OverleafA simple cycle [] [] [Open in OverleafA simple graph-model in 3D. Support independent creators There’s no Etsy warehouse – just millions of people selling the things they love. This means that programs can compose together very well, with the ability to write control constructs (such as if/else) just by writing normal functions. HTML: ♡ or ♡. Welcome to the Comprehensive LATEX Symbol List! This document strives to be your primary source of LATEX symbol information: font samples, LATEX commands, packages, usage details, caveats—everything needed to put thousands of different symbols at your disposal. Math symbols deﬁned by LaTeX package «amssymb» No. Use the following code next to the name: [code ]\textsuperscript{*}[/code] For example:[code ] Govind Chavan\textsuperscript{*}[/code] Well, Quora math environment does not recognize that command. apl functional symbol circle star: u+ 2363 ⍣ e2 8d a3: apl functional symbol star diaeresis: u+ 2605 ★ e2 98 85: black star: u+ 2606 ☆ e2 98 86: white star: u+ 262a ☪ e2 98 aa: star and crescent: u+ 269d ⚝ e2 9a 9d: outlined white star: u+ 2721 e2 9c a1: star of david: u+ 2726 e2 9c a6: black four pointed star: u+ 2727 e2 9c a7: white. 3 Single Equations that are Too Long: multline If an equation is too long, we have to wrap it somehow. The layout engine is a fairly direct adaptation of the layout algorithms in Donald Knuth’s TeX, so the quality is quite good (matplotlib also provides a usetex option for those who do want to call out to TeX to generate their text (see Text rendering With LaTeX). Chart of funny upside-down characters. Select Insert | Symbol, scroll down to Mathematical Operators subset, highlight the delta (∆) symbol, and click Insert. Global market trends like increasing populations, rising middle class incomes, and on-the-go lifestyles continue to drive demand for high-performance plastic packaging that extends food freshness, improves product safety, is lighter and brighter, and provides user-friendly functionality. All Unicode Symbols with Names and Descriptions on One Page. GrindEQ LaTeX-to-Word is a Shareware software in the category Miscellaneous developed by GrindEQ LaTeX-to-Word (remove only). Be aware that, outside of logic, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings. For a mac, if you're in Microsoft word, just hit Option+J and that should. star a and star b both have an apparent magnitude of 4. TeX/LaTeX is designed for mathematics-related writers so it is no problem to typeset nice-looking mathematics, many scientific publishers require documents in LaTeX, it is easy to work on a document of almost any size. The electrical currents are movements of electric charges (electrons) through a conductor. At the same time their symbolic meaning (which doesn’t take much imagination to figure out) is always the same, wherever and whenever they appear. Sometimes there is a greenish-white or yellow variety of the fruit. LaTeX Math Symbols Enjoy this cheat sheet at its fullest within Dash, the macOS documentation browser. adi shakti. Unicode Block. Selecting a symbol from the menu inserts the special symbol directly into your text (where you currently have the insertion pointer), just like you insert any other character. There are also Greek letters, a copyright sign, currency signs and a trademark sign. (Where two symbols are present, the left one is the “faked” symbol that LATEX2εprovides by default, and the right one is the “true” symbol that textcomp makes available. For further information regarding TeX and LaTeX (including information on how to obtain TeX software), visit the TeX Users Group (TUG) home page. This site is supported by donations to The OEIS Foundation. tattoo name slave Day 678 of 365 More. It describes the editing community's established practice on some aspect or. If left blank `latex' will be used as the default path. They used the poinsettia bracts to make a purple dye for cosmetics and clothes. It converts text into several symbol sets which are listed in the second text area, and the conversion is done in real-time and in your browser using JavaScript. This page contains HTML code for adding the copyright symbol to your website or blog. Insert an ASCII or Unicode character into a document. As with the star, you can compute the angle of rotation from the order of rotation: An order rotation corresponds to a angle of rotation. Copy and Paste the Approximately Symbols from here. com is the American leader in custom balloon printing. We’re encouraging food businesses to make it easier for their customers to ask for allergen information when taking orders or reservations. Check out the Wingdings and Webdings fonts to see a wide variety of symbols that you won't find with most other common fonts. Balloon Delivery The best balloon delivery near me is the one you can order now! With balloons near me you can surprise them. Offer valid on online and Buy Online Pick Up In Store orders only. An online LaTeX editor that's easy to use. Look for "Detexify" in the external links section below. Greek letters in text without changing to math mode. LATEX Mathematical Symbols The more unusual symbols are not deﬁned in base LATEX (NFSS) and require \usepackage{amssymb} 1 Greek and Hebrew letters α \alpha κ \kappa ψ \psi z \digamma ∆ \Delta Θ \Theta. Could you be more precise about what you're asking for?$\endgroup$- Qiaochu Yuan Mar 10 '11 at 17:56. Other official mammal state symbols include the armadillo (designated in 1927) and the Mexican free-tailed bat (1995). pdf that you just can't memorize. Use the placement. This page explains how to place various mathematical characters on the web via HTML, in lieu of mathemats typesetting software. Special Characters. It can be identified with the symbol that the normal Ascii asterisk "*" character produces in LaTeX math mode. His unit is the ampere and is measured by the ammeter. 428 Likes, 83 Comments - po_zu {Po-Zu. Here i attached picture about motor terminal in STAR position. Exclusions apply. It is not changed from the code line. Unless said otherwise, the commands for these symbols can be used only in math mode. Using lists in LaTeX is pretty straightforward and doesn't require you do add any additional packages. Do you know where I can find a list telling me how to use all those. UnicodeMath resembles real mathematical notation the most in comparison to all of the math linear formats, and it is the most concise linear format, though some may prefer editing in the LaTeX input over UnicodeMath since that is widely used in academia. I know many people who use Excel graphing. U+22C6 STAR OPERATOR “⋆”. Well, special and also random symbols, of course, too. HOME: Next: Arrow symbols (amssymb) Last: Relation symbols (amssymb) Top: Index Page Index Page. 2 Frequently Requested Symbols. This means that all the parts have been precisely manufactured and fit together very accurately. Brand The World is a balloon supplier, but also has custom promotional products and outdoor advertising supplies. I need to create a great then and equal too, i was wondering if there what a symbol for that and if so how would i type it into a note. When LATEX sees a %, it ignores the rest of the line. MacKichan Software now offers version 5. LaTeX's margins are, by default, 1. Topics include: creating and building a document, text mode vs. Steps: Choose a symbol from the Symbol Selector dialog box as a starting point. The physics package requires xparse and amsmath to work properly in your LATEX document. Some symbols that used to be commonplace have lost their original meaning, but From the swastika and crescent to the rod of Asclepius and the Maltese cross, here are 25 Common Symbols And Their Meanings. All symbols are documented with their actual definition and information regarding their Unicode code point. LATEX recognizes the following units:. Changing the font size in LaTeX Multi-column and multi-row cells in LaTeX tables Normal text in math mode Lists: Enumerate, itemize, description and how to change them Number sets (prime, natural, integer, rational, real and complex) in LaTeX. Press the Alt key, and hold it down. There’s a lot of freely available documentation for LaTeX, but there’s a pitfall: some documents that are still online are outdated and therefore contain obsolete information. It just need to follow the diagram shown in motor nameplate. The latest version of GrindEQ LaTeX-to-Word is 3. His unit is the ampere and is measured by the ammeter. The layout engine is a fairly direct adaptation of the layout algorithms in Donald Knuth’s TeX, so the quality is quite good (matplotlib also provides a usetex option for those who do want to call out to TeX to generate their text (see Text rendering With LaTeX). renderToString. Example usage of star symbols as rating:. We will not list all the possible symbols (you can ﬂnd them in any LATEX guide book), but some of the common ones are in the table below (once again, all of this must be in the math mode). When you have eliminated the JavaScript , whatever remains must be an empty page. Be aware that, outside of logic, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings. ASCII Codes - Table for easy reference of ascii characters and symbols, with conversion tables and HTML codes. com is the American leader in custom balloon printing. Using lists in LaTeX is pretty straightforward and doesn't require you do add any additional packages. An environment in Latex is a special declaration for formatting specific types of text. , are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus,. The numbering styles for each depth can be styled to suit your needs using the \renewcommand{label}{style} command, where label is the list depth being styled and style is how you want that number to be shown. Takes about 5-10 minutes to set things up, but you'll be typing like a boss. Gi, also called Keikogi (稽古着 or 稽古衣 lit. bst, birthday. What are the symbols called on a computer keyboard? Collectively anything on a keyboard is a character. ASCII nonprinting control characters. css stylesheet; Limited autocompletion for$, (, {, [More environments can be simply added in user_envs. G 6≡H G \not\equiv H A very common mistake is to ignore the diﬀerence between the various ‘kinds’ of symbols. It just need to follow the diagram shown in motor nameplate. Δ (mathematics, sciences) Alternative form of ∆: change in a variable Used on the reaction arrow in a chemical equation, to show that energy in the form of heat is added to the reaction. tattoo name slave Day 678 of 365 More. Part 1 of 2. Since 1995, Epicurious has been the ultimate food resource for the home cook, with daily kitchen tips, fun cooking videos, and, oh yeah, over 33,000 recipes. Thousands of new graphic resources uploaded daily for your personal and commercial projects. A list of some popular or recently used symbols appears. HTML: ♡ or ♡. Sometimes you need to insert the special symbols to your slide. The Comprehensive LATEX Symbol List Scott Pakin ∗ 19 January 2017 Abstract This document lists 14283 symbols and the corresponding LATEX commands that produce them. Press the Alt key, and hold it down. Copy editors see a symbol meaning “space,” as in “add a space between two sentences. The Comprehensive LaTeX Symbol List. Detexify is an attempt to simplify this search. This wide selection of Gold Balloons includes foil and latex balloons in a variety of shapes and sizes to let you create a custom party theme. We get pretty up close and personal with our cosmetics (that's sort of their job after all), but often. Are you looking for some nice symbols to decorate your Facebook, Instagram or Twitter posts and comments? Or maybe to brighten up your username? We've got them you! You can choose from hearts, flowers, stars and much, much more! ♛ ♂ ☆ ℂ. Note that even if you can do this it will typically affect the entire page, which may have side effects for other users. The whole repitoire for your amusement. The skin is rich in latex, and both it and the rind are not edible. You can insert them from the dialog (if you do, they will be on the MRU palette the next time you click Symbol on the Ribbon), or you can click Shortcut Key and assign a keyboard shortcut. If you check the tables, you’ll notice that some symbols are. This is an information page. The arc length Δs is the distance traveled along a circular path as shown in Figure 2 Note that r is the radius of curvature of the circular path. Fur Affinity is the internet's largest online gallery for furry, anthro, dragon, brony art work and more!. Edit LaTeX code and compile the pdf right in your browser. Shape a flag or a symbol and your balloon masterpiece will be the center of attention. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. A fascinating list of 30 common dream symbols and their meanings. It is possible to insert such symbols in Photoshop but it is somewhat difficult. The Comprehensive LaTeX Symbol List. Many symbols can also be displayed using a TeX alternative, but a preceeding backslash is not required. We will not list all the possible symbols (you can ﬂnd them in any LATEX guide book), but some of the common ones are in the table below (once again, all of this must be in the math mode). Related MATLAB, Maple, Mathematica, LaTeX, Etc News on Phys. Union (∪) and Intersection (∩) symbols in LaTeX can be produced via the \cup and \cap definitions while in math mode. ASCII nonprinting control characters. You can add text to a chart that includes Greek letters and special characters using TeX markup. The \$ 's around a command mean that it has to be used in maths mode, and they will temporarily put you into maths mode if you use them. Also contains a Symbol-to-ASCII converter - Sortable table list of special ASCII characters and character sets including their name, decimal codes, hexadecimal codes, and HTML entity for HTML 4 and HTML 5 compliant sites. Installation. Shop Lucky Brand online for a wide selection of heritage-inspired denim and fashion for men, women, plus and kids. 4) (format=latex 2007. (Where two symbols are present, the left one is the "faked" symbol that LATEX2εprovides by default, and the right one is the "true" symbol that textcomp makes available.


text:
# Unbounded sequences

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#1
Hey need some help with proving this statement;
"A sequence (an) is not bounded above if and only if there is a sub-sequence (akn) such that this sub-sequence tends to infinity."

I've proved that if the sequence is not bounded above implies that there is a sub-sequence which tends to infinity but I can't see how to construct a formal proof for the other direction?

I know that if a sequence converges, then every subsequence converges to the same limit. Hence if you have a divergent subsequence, the sequence cannot converge, but don't know if this is sufficient.

0
5 years ago
#2
(Original post by Kim-Jong-Illest)
Hey need some help with proving this statement;
"A sequence (an) is not bounded above if and only if there is a sub-sequence (akn) such that this sub-sequence tends to infinity."

I've proved that if the sequence is not bounded above implies that there is a sub-sequence which tends to infinity but I can't see how to construct a formal proof for the other direction?
Write down what it means to say that a subsequence tends to infinity. It should be obvious how to show this means the subseqeunce cannot be bounded above, and so neither can the original sequence.

I know that if a sequence converges, then every subsequence converges to the same limit. Hence if you have a divergent subsequence, the sequence cannot converge, but don't know if this is sufficient.
I don't see how this is relevant (and to be honest, the fact that you think it is makes me suspect you are rather confused about this topic).
0
#3
(Original post by DFranklin)
Write down what it means to say that a subsequence tends to infinity. It should be obvious how to show this means the subseqeunce cannot be bounded above, and so neither can the original sequence.

I don't see how this is relevant (and to be honest, the fact that you think it is makes me suspect you are rather confused about this topic).
I am pretty confused, need to learn the definitions more rigorously.

If (ank) is divergent to +infinity then for all a in the real numbers, there exists >0 such that for all N in the natural numbers, there exists a k>=N where | (ank) - a | > . Since this holds for all N it means that the sequence is not bounded from above and therefore the mother sequence cannot be either.

Is this correct? If so I feel like my conclusion should be more formal but not sure how to express it.

0
5 years ago
#4
if such that n > N .

Now suppose a_n is bounded above, let M be the upper bound and compare with the sentence above...
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# Are finite nilpotent groups the only finite groups with abelian Frattini quotient?

It is obvious that if the Frattini quotient of a finite group $G$ is abelian, then $G$ is abelian by nilpotent and that finite nilpotent groups have abelian Frattini quotient.

I wonder if there is an example of a non-nilpotent finite group with abelian Frattini quotient ?

A better thing would be to have a nice characterization of such finite groups.

• By a theorem of Gaschütz, a finite group is nilpotent when its Frattini quotient is nilpotent. (Satz III.3.5 in Huppert's Endliche Gruppen I) – Frieder Ladisch Nov 1 '17 at 16:01
• Indeed, this is well-known, see Theorem B here: emis.de/proceedings/Chicho2001/Otal.pdf – Luc Guyot Nov 1 '17 at 16:15

This is well known, but here is a quick proof anyway.

Suppose that $G/\Phi(G)$ is nilpotent, and let $P \in {\rm Syl}_p(G)$. Then $P\Phi(G) \unlhd G$ so, by the Frattini Argument, $G = N_G(P)P\Phi(G)= N_G(P)\Phi(G)$. Hence $G = N_G(P)$ by the non-generator property of $\Phi(G)$. So all Sylow subgroups are normal, and $G$ is nilpotent.

• – YCor Nov 1 '17 at 17:14

Here is my attempt to entertain those who knew the answer.

Question 1. Let $G$ be a finitely generated group such that $G/\Phi(G)$ is Abelian. Is $G$ nilpotent?

The answer is yes if we assume moreover that $G$ is linear (e.g., $G$ is finite). But the answer is no in general, as the the first Girgorchuk group $G_1$ is such that $[G_1, G_1] \subset \Phi(G_1)$. For more examples, see this MO post.

Let $W(G)$ denote the $N$-Frattini subgroup of $G$, that is the intersection of the maximal normal subgroups of $G$ when defined, $G$ otherwise. (See this post for results related to $W(G)$.) Note that $G/W(G)$ is Abelian for any soluble group $G$.

Question 2. Let $G$ be a finitely generated group such that $G/W(G)$ is Abelian. Is $G/\Phi(G)$ Abelian?

The answer is no, because some Sunic group of intermediate growth is a counter-example, see this preprint.

Question 3. Let $G$ be a finite group such that $G/W(G)$ is Abelian. Is $G$ soluble?

The answer is no because of the symetric group $S_n$ with $n \ge 5$. One may try to get a classification though. Possibly useful:

Lemma (Baer). Let $G$ be a group and let $N$ be a normal subgroup of $G$. Then $W(N)$ is a normal subgroup of $G$ and $W(N) \subset W(G)$.

• Classifying finite groups such that $G/W(G)$ is abelian sounds a bit optimistic. For instance, $H\wr A$ is such a group for every finite group $H$ and any non-trivial finite solvable group $A$. – YCor Nov 2 '17 at 14:56
• @YCor Thanks for spotting the $G_1$-typo, it's corrected now. And indeed, "classification" is the wrong word. My intention was just to echo OP's question about the existence of a "nice characterization" of such groups. (By the way, are you assuming $H$ to be simple in your last comment?). – Luc Guyot Nov 2 '17 at 16:48
• No I didn't assume $H$ simple. The proof is as follows: in $H\wr A$, the normalizer of $H$ is normal and co-solvable. If $S$ is a simple quotient of $H\wr A$, the image of $H$ also has a normal co-solvable normalizer, hence is equal to $S$. So the image of $H$ is either $\{1\}$ or $S$. But it's the same for another conjugate copy of $H$ (and there's one since $A\neq 1$. Since these pairwise commute, it follows that all have trivial image. – YCor Nov 2 '17 at 21:10
• Thanks for this. My question was derived from Galois theory, hence the groups I was considering were always finite. – Lior Bary-Soroker Nov 7 '17 at 19:03


text: 1 Introduction This package (v1.1) helps you to write big integrals when needed. coproduct, emptyset, infinity, and proportional) in regular and Its ﬁrst row lists the default (Computer Modern) font families. % The following two commands use find_package.py to locate a Python % module and generate LaTeX commands that point to where its source is % located. Reference 6. An alternative for the color package As already said, the LATEX color package cannot be 2.3 New Colors The revquantum package also provides a color palette that is safe for colorblind readers and for printing, … Version: 5.x - Scientific WorkPlace & Scientific Word. The LaTeX package mathpazo (now part of PSNFSS [ 30 ]) uses Palatino for Latin letters, Pazo for Greek and other letter-like symbols, and Computer Modern for geometric symbols. PazoMath-Bold, PazoMath-BoldItalic, and Palatino, glyphs that are usually not available in Palatino and A package built on the standard \LaTeX{} graphics package to perform all the different sorts of rotation one might like, including complete figures and tables and captions. (459.7k). PSNFSS provides the default Type 1 fonts listed, excluding Computer Modern (CM), Utopia, Fourier, and Euler. 2 Package overview The easiest way to make use of the above-mentioned typefaces is to completely replace one or more of the font families used by LATEX as ‘roman’, ‘sans serif’ and ‘typewriter’ family and for math. Oldstyle numbers. A complete Texlive LaTeX environment which can be run in a chroot jail - jpallen/latex-chroot without worrying about it. Quick Start. 2 Package overview The easiest way to make use of the above-mentioned typefaces is to completely replace one or more of the font families used by LATEX as ‘roman’, ‘sans serif’ and ‘typewriter’ family and for math. and PazoMathBlackboardBold). Automatic Package Installation Integrating Local Additions 5. Fortunately, many, many people have built their own commands already and made them available to users in packages. the widely used mathpazo package. PazoMathBlackboardBold). Its ﬁrst row lists the default (Computer Modern) font families. Despair not: Chances are that the package will work using the default settings. family, for typesetting math in a style that suits Palatino. I prefer to use Palatino, a widely used serif font. Any Unicode math font will have better coverage than any combination of traditional LaTeX packages. This is accomplished by the packages listed in table 1. text fonts. The Pazo Math family is made up of five fonts provided in Type1 of any LaTeX distribution). \end{document} Two other preferences I often use are to turn off page numbers and to have the ouput with a ragged right edge, rather than justified on both edges. slanted shapes in regular and bold weights, and the uppercase Greek letters (e.g., \textbeta) (1) look ugly and pixelated (when zoomed in) (2) are not modified by \textbf and such (3) are not similar to the Palatino font. ItcanbeusedwithLATEX2ε with no dependency on the amsmath package. The Pazo Math fonts are a family of PostScript fonts suitable (partialdiff, summation, product, coproduct, emptyset, infinity, and for which Computer Modern looks odd when combined with The textcomp package changes \oldstylenums to use the glyphs in the Text Companion fonts (LaTeX TS1 encoding) when in text mode, and also makes them available using the macros of the form \textoldstyle, e.g., \textzerooldstyle. These Part of T e X Live? font and uses the virtual mathpazo fonts, built around the Pazo Math glyphs include the uppercase Greek alphabet in upright and slanted proportional) in regular and bold weights, other glyphs (Euro and package always with the option "full", because this is required by certain other packages? As you can see, the packages color and graphicx are not part of the preamble ﬁle. shapes in regular and bold weights, the lowercase Greek alphabet in The eucal and euscript packages Frank Mittelbach Rainer Sch¨opf Michael Downes Version 2.2d, 2001/10/01 1 Introduction This package was written originally by Frank Mittelbach and Rainer Sch¨opf; later it was moved into the AMSFonts distribution with only minor modiﬁ-cations. dotlessj) in upright and slanted shapes in regular and bold weights, The LaTeX package mathpple (also part of PSNFSS [ 30 ]) uses Palatino for Latin letters and slanted Euler for Greek and other symbols. Font implementation. Ligatures and German double s. Math example. The Pazo Math family is made up of five fonts No. If you nd that a particular math font package … 3 Grouping math fonts with common characteristics in math versions simplifies the setting of font attributes for mathematical expressions. % doc% % doc% It is highly recommended that you either stick to the Palatino font or use the % doc% \LaTeX{} default fonts (by removing the package \texttt{mathpazo}). provided in Adobe Type 1 format (PazoMath, PazoMath-Italic, typesetting math in combination with the Palatino family of text This is accomplished by the packages listed in table 1. The number of mathematical symbols exceeds the maximal number of characters in a TeX font file by an order of magnitude. The FPL Fonts provide a set of SC/OsF fonts for URW Palladio L which are compatible with the Palatino SC/OsF fonts from Adobe. In the Commands pages, we discussed building your own commands. \documentclass{article} \usepackage[margin=1.25in]{geometry} \usepackage{mathpazo} \begin{document} Hello! which Computer Modern looks odd when combined with Palatino. Many modern LATEXcompilers will locate and o er to download missing packages for you. package mathpazo.sty defines the Palatino family as the default roman Instead, we just add the line \usepackage{package name} and we have access to all the commands, symbols, environments, etc., that are in the package. \usepackage[sc]{mathpazo} \linespread{1.05} % Palladio needs more leading (space between lines) \usepackage[T1]{fontenc} Style examples \normalfont \itshape \scshape \bfseries Numbers. \usepackage{mathpazo} Packages. Mathpazo: Palatino font package Dealing with fonts is challenging with LaTeX, and unfortunately the default font is not the nicest. (Of course, not all font families can provide this facility.) esstix: PostScript versions of the ESSTIX, with macro support, dsserif: A double-struck serifed font for mathematical use, boondox: Mathematical alphabets derived from the STIX fonts, txfonts: Times-like fonts in support of mathematics. The package is supplied in dtxformat and as a pre-extracted zip ﬁle, siunitx.tds.zip. The LaTeX macro The package acronym is a must for any longer document and it is not new even to novices. If I remove the mathpazo package everything works (but I get the standard LaTeX font). The later is most convenient for most users: simply unzip this in your local texmf directory and run texhash to update the database of ﬁle locations. For example, you may want to write standard integrals before a matrix, but if you ﬁnd them too small, you can use bigger integrals thanks to this package. for typesetting mathematics in combination with the Palatino family of 2 Use upright and slanted shapes in regular and bold weights, the lowercase Greek alphabet in slanted shape in regular and bold fonts. These glyphs include the uppercase Greek alphabet in % doc% Q, R, and Z) in blackboard bold. Suddenly I'm asked to install "palatino" which is the obsolete predecessor of "mathpazo". Download the contents of this package in one zip archive Text Math Macro Category … \immediate\write 18{./find_package.py qinfer > find_package.out.tex} \input {find_package.out.tex} format (PazoMath, PazoMath-Italic, PazoMath-Bold, PazoMath-BoldItalic, % % For this demo, we'll demonstrate using QInfer, so that the command % will be \qinfersrc. and the uppercase letters commonly used to represent various number The LaTeX macro package mathpazo.sty defines the Palatino family as the default roman font and uses the virtual mathpazo fonts, built around the Pazo Math family, for typesetting math in a style that suits Palatino. siunitx is an indispensable package for typesetting units, so engineers have no excuse for not using it. These contain, in designs that match The Pazo Math family is made up of five fonts provided in Adobe Type 1 format (PazoMath, PazoMath-Italic, PazoMath-Bold, PazoMath-BoldItalic, and PazoMathBlackboardBold). Changing to this font is as simple as including \usepackage {mathpazo}. \usepackage{mathpazo} \usepackage[mathpazo]{flexisym} \usepackage{breqn} Currently, the packages mathpazo and mathptmx are supported. Maybe you are interested in the following packages as well. Advanced Topics Managing Font Map Files Changing TEXMF run-time parameters II. Freely-available Type 1 versions of the fonts are available on CTAN. There are numerous LaTeX packages, and the most important are already well known. Name Directory; fplmb.afm: texmf\fonts\afm\public\mathpazo: fplmbb.afm: texmf\fonts\afm\public\mathpazo: fplmbi.afm: texmf\fonts\afm\public\mathpazo: fplmr.afm Hello, todays update of one of the follwoing files seems to be kind of unhealthy for typesetting documents with "mathpazo": psnfss.cab psnfssx.cab. The LaTeX PSNFSS packages. Math versions. ... available, then we assume plain LaTeX. % doc% This template is using the Palatino font (package \texttt{mathpazo}) which results % doc% in a legible document and matching mathematical fonts for printout. TIA, Sincerely, Wolfgang Palatino, glyphs that are usually not available in Palatino and for Mathpazo version 1.003 (5 fonts) Diego Puga Hi, Welcome to the beginnings of Tufte LaTeX package to help you produce Tufte-style handouts, reports, and notes. In general, it is not a good idea to load LATEX packages that use so called TEX specials in a METAPOST-LATEX preamble. Packages allow us to use extra commands without having to include tons and tons of code in the preamble of a document. sets (C, I, N, Q, R, and Z) in blackboard bold. Exporting, hand-editing and re-importing all the time doesn't work as LyX will overwrite the modification. Uses the mathpazo package to typeset the document more nicely than the de-fault for revtex4-1 drafts. This can be achieved using the geometry and mathpazo packages, respectively. URW Palladio is available as Type 1. pdflatex sample-handout bibtex sample-handout pdflatex sample-handout pdflatex sample-handout The eulervm package permits use of the Euler maths alphabet in conjunction with text fonts that do not provide maths alphabets of their own (for instance, Adobe Palatino or Minion). Math symbols deﬁned by LaTeX package «mathpazo» CapitalGreekletterscannotbeusedinmathalphabets. LaTeX macro support (using package mathpazo.sty) is This website uses cookies to personalize content and ads. provided in psnfss (a required part I'm writing a scrartcl, if this is of any concern. I am having trouble using this with \usepackage[sc]{mathpazo} that I put to use the Palatino font. weights, several mathematical glyphs (partialdiff, summation, product, Try typesetting sample-handout.tex with the following sequence of commands,. The following packages may be of help - (easy block matrices), (easy equations), (easy matrices), (easy tables), (easy vectors), (nested arrays), (gives more choice in theorem layout), subeqnarray (Renumbering of sub-arrays in math-mode), subeqn (Different numbering sub … The PostScript NFSS bundle is a required part of LaTeX. In XeLaTeX and LuaLaTex, the unicode-math package supports any OpenType math font: Asana Math, XITS Math, TeX Gyre Pagella Math, Latin Modern Math, Cambria Math, etc. Macro support is provided for use under LaTeX; the package supports the only'… texlive-fpl 51265. PSNFSS documentation, summarizes the commonly used Latex font packages. Asana Math is a great replacement for mathpazo. The bundle provides a complete working setup of the LaTeX font selection scheme for use with PostScript fonts. 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# Lagrange’s four-square theorem

Lagrange’s four-square theorem states that every non-negative integer may be expressed as the sum of at most four squares. By the Euler four-square identity, it is enough to show that every prime is expressible by at most four squares. It was later proved that only the numbers of the form $4^{n}(8m+7)$ require four squares.

This shows that $g(2)=G(2)=4$, where $g$ and $G$ are the Waring functions (http://planetmath.org/WaringsProblem).

Title Lagrange’s four-square theorem LagrangesFoursquareTheorem 2013-03-22 12:35:17 2013-03-22 12:35:17 bbukh (348) bbukh (348) 10 bbukh (348) Theorem msc 11P05 WaringsProblem EulerFourSquareIdentity


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Hardcover | $80.00 X | £66.95 | 624 pp. | 7 x 9 in | July 2015 | ISBN: 9780262029445 eBook |$80.00 X | July 2015 | ISBN: 9780262331722
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## Fundamentals of Machine Learning for Predictive Data Analytics

Algorithms, Worked Examples, and Case Studies

## Overview

Machine learning is often used to build predictive models by extracting patterns from large datasets. These models are used in predictive data analytics applications including price prediction, risk assessment, predicting customer behavior, and document classification. This introductory textbook offers a detailed and focused treatment of the most important machine learning approaches used in predictive data analytics, covering both theoretical concepts and practical applications. Technical and mathematical material is augmented with explanatory worked examples, and case studies illustrate the application of these models in the broader business context.

After discussing the trajectory from data to insight to decision, the book describes four approaches to machine learning: information-based learning, similarity-based learning, probability-based learning, and error-based learning. Each of these approaches is introduced by a nontechnical explanation of the underlying concept, followed by mathematical models and algorithms illustrated by detailed worked examples. Finally, the book considers techniques for evaluating prediction models and offers two case studies that describe specific data analytics projects through each phase of development, from formulating the business problem to implementation of the analytics solution. The book, informed by the authors’ many years of teaching machine learning, and working on predictive data analytics projects, is suitable for use by undergraduates in computer science, engineering, mathematics, or statistics; by graduate students in disciplines with applications for predictive data analytics; and as a reference for professionals.

## Instructor Resources for This Title:

Instructor's Manual

John D. Kelleher is a Lecturer at the Dublin Institute of Technology, and a founding member of DIT’s Applied Intelligence Research Center.

Brian Mac Namee is a Lecturer at University College Dublin.

Aoife D’Arcy is CEO of The Analytics Store, a data analytics consultancy and training company.

## Endorsements

“Erudite yet real-world relevant. It’s true that predictive analytics and machine learning go hand-in-hand: To put it loosely, prediction depends on learning from past examples. And, while Fundamentals succeeds as a comprehensive university textbook covering exactly how that works, the authors also recognize that predictive analytics is today’s most booming commercial application of machine learning. So, in an unusual turn, this highly enriching opus brings the concepts to light with industry case studies and best practices, ensuring you’ll experience the real-world value and avoid getting lost in abstraction.”
Eric Siegel, Ph.D., founder of Predictive Analytics World; author of Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie, or Die
“This book provides excellent descriptions of the key methods used in predictive analytics. However, the unique value of this book is the insight it provides into the practical applications of these methods. The case studies and the sections on data preparation and data quality reflect the real-world challenges in the effective use of predictive analytics.”
Pádraig Cunningham, Professor of Knowledge and Data Engineering, School of Computer Science, University College Dublin; coeditor of Machine Learning Techniques for Multimedia
“This is a wonderful self-contained book that touches upon the essential aspects of machine learning and presents them in a clear and intuitive light. With its incremental discussions ranging from anecdotal accounts underlying the ‘big idea’ to more complex information theoretic, probabilistic, statistic, and optimization theoretic concepts, its emphasis on how to turn a business problem into an analytics solution, and its pertinent case studies and illustrations, this book makes for an easy and compelling read, which I recommend greatly to anyone interested in finding out more about machine learning and its applications to predictive analytics.”
Nathalie Japkowicz, Professor of Computer Science, University of Ottawa; coauthor of Evaluating Learning Algorithms: A Classification Perspective


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# La belongs to group 3 while Hg belongs to group 12 and both belong to period 6 of the periodic table.

La belongs to group 3 while Hg belongs to group 12 and both belong to period 6 of the periodic table. Write down the general outer electronic configuration of the ten elements from La to Hg together using orbital notation method.


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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01p2676z47t
 Title: Leviathan's Paradox? Bureaucrats and the Fight Against Corruption in China Authors: Wang, Erik Haixiao Advisors: Boix, Carles Contributors: Politics Department Keywords: anti-corruptionbureaucracycorruptionpolitical economy of developmentstate capacity Subjects: Political scienceAsian studiesStatistics Issue Date: 2020 Publisher: Princeton, NJ : Princeton University Abstract: This dissertation revisits the classic question of how to best monitor the bureaucracy. Canonical theories of bureaucracy demonstrate the need for enhanced monitoring in government hierarchies. I argue that intensive top-down monitoring may reduce the productivity of bureaucrats by frightening them away from the informal practices that they would otherwise rely on when completing daily tasks. I formalize such a logic in a game-theoretic model. Utilizing a unique dataset of sub-provincial inspections in China's recent anti-corruption campaign, I identify this chilling effect'' by exploiting variation in the timing of inspections from 2012 to 2017. I show that these anti-corruption activities lower the area of land development projects proposed by bureaucrats. Causal mediation analyses with investigation data and original measures of corruption potential reveal that these effects are unlikely driven by reduction of actual corruption. Extension analyses suggest similar consequences on revenue collection and environmental regulation. Although scholars of state-building equate low corruption with effective bureaucracy, these findings present a paradox where intensive state-led efforts to lower corruption may further undermine bureaucrats' productivity. Furthermore, using an original survey nearly representative of urban Chinese residents, I provide additional support for the theory by showing that residents exposed to anti-corruption inspections become more tolerant of corrupt but competent bureaucrats. Importantly, my survey also reveals that, despite declines in bureaucrats’ productivity, anti-corruption efforts in China still improve Chinese citizens’ political support of the regime. This result suggests a reason why the regime chooses to let the campaign persist despite mounting concerns from the bureaucracy. Overall, this dissertation advances our understanding about anti-corruption efforts, state-building, and microdynamics of the bureaucracy. URI: http://arks.princeton.edu/ark:/88435/dsp01p2676z47t Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Politics

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