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# Nodal Translational Inertia

Computes the interial forces and mass proportional damping terms corresponding to nodal mass.

# Description

This NodalKernel computes the component of translational inertial force proportional to nodal mass. Mass proportional Rayleigh damping is also computed by this NodalKernel. A constant mass for all the nodes in the given boundary can be provided using the mass parameter. Otherwise, a CSV file containing nodal positions and the corresponding nodal masses can also be provided using the nodal_mass_file parameter. Please refer to C0TimoshenkoBeam for details.

For example, the below csv file has two rows with 4 columns. The first three columns correspond to the nodal positions in the global coordinate system and the last column corresponds to the nodal mass. Each row contains position and mass information for one node.

0.0, 0.0, 0.0, 2.0
4.0, 0.0, 0.0, 0.01899772

(modules/tensor_mechanics/test/tests/beam/dynamic/nodal_mass.csv)

## Input Parameters

• variableThe name of the variable that this boundary condition applies to

C++ Type:NonlinearVariableName

Options:

Description:The name of the variable that this boundary condition applies to

### Required Parameters

• accelerationacceleration variable

C++ Type:std::vector

Options:

Description:acceleration variable

• save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Options:

Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Options:

Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• velocityvelocity variable

C++ Type:std::vector

Options:

Description:velocity variable

• betabeta parameter for Newmark Time integration

C++ Type:double

Options:

Description:beta parameter for Newmark Time integration

• eta0Constant real number defining the eta parameter for Rayleigh damping.

Default:0

C++ Type:double

Options:

Description:Constant real number defining the eta parameter for Rayleigh damping.

• massMass associated with the node

C++ Type:double

Options:

Description:Mass associated with the node

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Options:

Description:The list of block ids (SubdomainID) that this object will be applied

• nodal_mass_fileThe file containing the nodal positions and the corresponding nodal masses.

C++ Type:FileName

Options:

Description:The file containing the nodal positions and the corresponding nodal masses.

• alpha0Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme

Default:0

C++ Type:double

Options:

Description:Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Options:

Description:The list of boundary IDs from the mesh where this boundary condition applies

• gammagamma parameter for Newmark Time integration

C++ Type:double

Options:

Description:gamma parameter for Newmark Time integration

### Optional Parameters

• vector_tagstimeThe tag for the vectors this Kernel should fill

Default:time

C++ Type:MultiMooseEnum

Options:nontime time

Description:The tag for the vectors this Kernel should fill

• extra_vector_tagsThe extra tags for the vectors this Kernel should fill

C++ Type:std::vector

Options:

Description:The extra tags for the vectors this Kernel should fill

• matrix_tagssystemThe tag for the matrices this Kernel should fill

Default:system

C++ Type:MultiMooseEnum

Options:nontime system

Description:The tag for the matrices this Kernel should fill

• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

C++ Type:std::vector

Options:

Description:The extra tags for the matrices this Kernel should fill

### Tagging Parameters

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Options:

Description:Determines whether this object is calculated using an implicit or explicit form

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Options:

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.


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# Elementary Cryptanalysis: A Mathematical Approach

### By Abraham Sinkov, Revised and Updated by Todd Feil

2nd Edition
Catalog Code: NML-22E2
Print ISBN: 978-0-88385-647-5
Electronic ISBN: 978-0-88385-937-7
232 pp., Hardbound, 2009
List Price: $58.95 MAA Member:$47.50
Series: MAA Textbooks

The revised and updated version of Elementary Cryptanalysis, originally published in the New Mathematical Library almost half a century ago, explains how to solve cryptograms based on elementary mathematical principles, starting with Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.

Exercises are given throughout the text that will help the reader understand the concepts and practice the techniques presented. The book assumes minimal mathematical prerequisites and therefore explains from scratch such concepts as summation notation, matrix multiplication, and modular arithmetic.

### Table of Contents

Preface to the First Edition
Preface to the Second Edition
1. Monoalphabetic Ciphers Using Additive Alphabets
2. General Monoalphabetic Substitution
3. Polyalphabetic Substitution
4. Polygraphic Systems
5. Transposition
6. RSA Encryption
7. Perfect Security—One-time Pads
Appendix A: Tables
Appendix B: ASCII Codes
Appendix C: Binary Codes
Solutions to Exercises
Further Reading
Index
About the Authors

### About the Authors

Abraham Sinkov was born in 1907 in Philadelphia but moved to New York City when young. He graduated from City College of New York and received his master’s in mathematics from Columbia University. Later he received his doctorate in mathematics from George Washington University. After briefly teaching in the New York City schools, he took a civil service examination in 1930 that resulted in his being offered a job as a cryptanalyst by William Friedman, one of the first three hired to form the Army’s new Signal Intelligence Service (SIS). Sinkov was instrumental in breaking the Japanese diplomatic codes in the mid 1930’s.

After World War II Sinkov continued to work for SIS. This organization eventually became the Armed Forces Security Agency and then the National Security Agency (NSA). Sinkov held high positions in the NSA until his retirement in 1963. After his retirement he taught mathematics at Arizona State University. In 1966, he wrote the original edition of this book for the MAA, one of the first books on cryptology for the general public.

Todd Feil was born in Findlay, Ohio, in 1951. He graduated from Millikin University and received his doctorate from Bowling Green State University. He has taught mathematics at Denison University since 1982. Feil has published Lattice-Ordered Groups (Reidel) and A First Course in Abstract Algebra (2nd edition by Chapman & Hall/CRC), both coauthored with Marlow Anderson, and Essential Discrete Mathematics for Computer Science (Prentice Hall), coauthored with Joan Krone. He is an avid cyclist and lives in Granville, Ohio, with his wife Robin. They have two daughters, Halley and Emma.

Book Series:

format: plain


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# TAUP 2013 - Young Researcher Poster Session

US/Pacific
Asilomar, California
Description
13th International Conference on Topics in Astroparticle and Underground Physics
Young Researcher Poster Session
• 19:30 19:30
A Pedagogical Discussion on Neutrino Wave Packet Evolution
We present a pedagogical discussion on the time evolution of neutrino wave packet in free space. A common treatment is to keep terms up to quadratic order in the energy expansion so that the Fourier transform can be evaluated analytically via Gaussian integral. This leads to a solution representing a ”flat” Gaussian distribution with a constant longitudinal width and a spreading transverse width. It is tempting to conclude that special relativity is violated if the neutrino wave packet is detected on its edge. However, we demonstrate that by including higher order terms in the energy expansion the correct geometry of the wave packet will be restored. The corrected solution has a spherical wave front so that it complies with special relativity.
Speaker: Mr Cheng-Hsien Li (School of Physics and Astronomy, University of Minnesota at Twin Cities)
• 19:30 19:30
All particle cosmic ray energy spectrum with IceCube
We report on the measurement of the all-particle cosmic ray energy spectrum with the IceTop air shower array in the energy range from 1.58 PeV to 1.26 EeV. The IceTop air shower array is the surface component of the IceCube Neutrino Observatory at the geographical South Pole. The analysis was performed using only information from IceTop. The data used in this work were taken from June 1, 2010 to May 13, 2011. During that period the IceTop array consisted of 73 stations, compared to 81 in its final configuration. The measured spectrum exhibits a clear deviation from a single power law above the knee around 4 PeV and below 1 EeV. We observe spectral hardening around 18 PeV and steepening around 130 PeV.
Speaker: Dr Bakhtiyar Ruzybayev (University of Delaware)
• 19:30 19:30
Characterization of the Ge detectors for the Majorana Demonstrator
High purity germanium (HPGe) crystals will be used for the Majorana Demonstrator, where they serve as both the source and the detector for neutrinoless double beta decays. It is crucial for the experiment to understand the performances of the HPGe crystals. A variety of crystal properties are being investigated, including both basic properties such as energy resolution, efficiency, uniformity, capacitance, leakage current and crystal axis orientation, as well as more sophisticated properties, e.g. pulse shapes and dead layer and transition layer distribution. In this talk, we will present our measurements to characterize the HPGe crystals and discuss the results. Since additional information regarding the crystals can be learned by data-simulation comparison, we will also discuss the experiment's simulation package for the detector characterization setup and for the prototype cryostat of the Demonstrator. This work is supported by grants from the DOE Office of Nuclear Physics and the NSF Particle Astrophysics program.
Speaker: Dr Wenqin Xu (LANL)
• 19:30 19:30
Constraining the nature of bow shocks of runaway stars through Fermi-LAT observations
Bow shocks of runaway stars were suggested as possible sources of high-energy gamma-ray emission. In addition to the detection at infrared wavelengths, there have recently been claims for detection in X-rays and radio, indicating a spectrally wide non-thermal component. For the first time we systematically analyzed nearly five years of Fermi-LAT data from the regions of 28 bow shock candidates. These candidates are the ones listed in the E-BOSS catalogue of stellar bow shocks. Since no significant emission was found, we calculated flux upper limits. For one of the candidates (Zeta Ophiuchi) a recent prediction of gamma-ray emission can be robustly ruled out by our data. Our flux upper limits on the gamma-ray emission from any of the known stellar bow shocks strongly constrain the possible gamma-ray component that these objects may have.
Speaker: Anneli Schulz (DESY)
• 19:30 19:30
Cosmic Rays from Heavy Dark Matter from the Galactic Center
The gamma-ray fluxes observed by the High Energy Stereoscopic System (H.E.S.S.) from the J1745-290 Galactic Center source is well fitted by the secondary photons coming from dark matter (DM) annihilation in particle-antiparticle standard model pairs over a diffuse power-law background. The spectral features of the signal are consistent with different channels: light quarks, electro-weak gauge bosons and the top-antitop channel. The amount of photons and morphology of the signal require compressed DM profiles as those resulting from baryonic contraction, which provides large enhancements in the signal over DM alone simulations. The fits return a heavy WIMP, with a mass above 10 TeV, but well below the unitary limit for thermal relic annihilations. The fitted background spectral index is compatible with the Fermi-Large Area Telescope (LAT) data from the same region. This possibility can be tested with future observations of other cosmic rays, whose amount and spectrum is unambiguously predicted for each channel. For example, high energy neutrinos could confirm this hypothesis at IceCube or ANTARES for angular resolutions smaller than 1º.
• 19:30 19:30
Development of ZnMoO4 scintillating bolometers for the LUMINEU project
The Luminescent Underground Molybdenum Investigation for NEUtrino mass and nature (LUMINEU), funded by ANR in France, aims at preparing the ground for a next-generation neutrinoless double beta decay experiment employing scintillating bolometers: these devices are in fact very promising tools in rare events search, in terms of efficiency, energy resolution and background control. In particular, they can tag alpha events, which are the dominant residual background for double beta decay candidates with a transition energy higher than 2615 keV. LUMINEU's goal is the operation of a pilot detector, consisting of four 400 g ZnMoO4 scintillating bolometers, probing an active 100Mo mass of about 0.7 kg, the energy transition of this isotope being 3034 keV. This preliminary investigation intends to be feasibility test for a next-generation neutrinoless double beta decay experiment, aiming at probing the inverted hierarchy region of the neutrino mass pattern. LUMINEU will help to fix the detailed structure of the single module of this future large-scale experiment and to develop the protocol for the synthetization of radiopure ZnMoO4 crystals. The crystals will be grown at the Nikolaev Institute for Inorganic Chemistry in Novosibirsk, Russia. LUMINEU foresees a systematic study of the crystal parameters, in order to optimize the bolometric performance, the light yield, the alpha particle rejection factor and the radiopurity of the scintillating bolometers. Previous tests with preliminary ZnMoO4 scintillating bolometers demonstrated the feasibility of aboveground tests for detector characterization: despite the dominating pile-up due to cosmic rays, it was possible to operate a 313 g bolometer and determine its sensitivity, energy resolution and particle discrimination power. This test was performed at the Centre de Sciences Nucléaires et de Sciences de la Matière (CSNSM), in Orsay, France, in a LHe dilution refrigerator. As a follow-up of these encouraging results, in view of future serial runs with LUMINEU's bolometers for a routine quality-control of the grown crystals, a dedicated aboveground facility was set up: this apparatus is based on a cryostat exploiting the Pulse-Tube (PT) technology, which allows to dispense with cryogenic fluids. In order to pave the way to the final pilot experiment, underground tests will have to be performed: 23.8 g and 313 g crystals have been operated in the EDELWEISS cryostat (where a direct dark matter search is performed with Ge hybrid detectors), at Laboratoire Souterrain de Modane (LSM), France, showing promising results, despite microphonic noise. In the incoming months, the test of the 313 g bolometer with a fully EDELWEISS-compatible holder will take place, looking forward to assess a noise improvement.
Speaker: Margherita Tenconi (CSNSM)
• 19:30 19:30
Development of a Low-Frequency Antenna for Detection of Ultra-High Energy Cosmic Rays with ANITA-III
The ANtarctic Impulsive Transient Antenna (ANITA) is a balloon-borne radiometer sensitive to broadband radiation from neutrinos interacting in ice and cosmic-ray air showers in the 200–1000 MHz range. The third flight of ANITA will achieve improved sensitivity through an upgraded triggering system and larger antenna array enabling the detection of an order of magnitude more ultra-high energy cosmic ray events over the first flight of ANITA and increased background rejection. Additionally, a prototypical drop-down antenna will record the first in-flight observations of cosmic-ray air showers at frequencies of 30–80 MHz. We report on the development of the low frequency antenna.
Speaker: Dr Stephanie Wissel (University of California, Los Angeles)
• 19:30 19:30
Dilution generated sterile neutrino dark matter
We present a model where a keV--MeV scale sterile neutrino plays the role of cold dark matter. This is accomplished by having a heavier (GeV--TeV scale) sterile neutrino decay out-of-equilibrium to generate vast amounts of entropy. This process of dilution modifies the number densities and spectra of the lighter neutrino, allowing it to evade existing constraints and behave as cold dark matter.
Speaker: Mr Amol Patwardhan (UC San Diego (Graduate student))
• 19:30 19:30
Efficiency Studies and Simulations for an Active Neutron Veto Detector for a Dark Matter Experiment
In direct WIMP dark matter detection experiments, neutrons from cosmogenic sources and nuclear reactions in detector materials can provide backgrounds indistinguishable from WIMP signals. To reduce this background, an active neutron veto filled with a boron-loaded liquid scintillator is being developed. The scintillator will be pseudocumene, with trimethyl borate as a boron source, and PPO as a wavelength shifter. Such a veto would detect neutrons in the volume surrounding the detector, allowing coincident background events in the detector to be rejected. Neutrons are captured by the $^{10}$B with a high cross section, resulting in an alpha and $^{7}$Li. The energy from these products is heavily quenched, down to as low as 30-40 keVee. However, 96% of boron captures also produce a 478 keV gamma, which is much more easily detected. In order to efficiently detect the 4% of events that do not produce this gamma, the detector must have as high a light collection efficiency as possible. To model the neutron veto concept, light yield measurements were taken for a small prototype filled with the scintillator mixture and lined with a Lumirror reflector. These results were reproduced in GEANT4 and in an independent simulation. We then applied the simulations to the DarkSide-50 neutron veto to predicts its neutron rejection power.
Speaker: Mr Shawn Westerdale (Princeton University)
• 19:30 19:30
Evaluating Gadolinium's Action on Detector Systems
The proposed introduction of a soluble gadolinium [Gd] compound into water Cherenkov detectors can result in a high efficiency for the detection of free neutrons capturing on the Gd. The delayed 8 MeV gamma cascades produced by these captures in coincidence with a prompt positron signal serve to uniquely identify electron anti-neutrinos interacting via inverse beta decay. Such coincidence detection greatly reduces backgrounds, which should allow a large Gd-enhanced water Cherenkov detector to make the first observation of the diffuse supernova neutrino background and high precision measurements of Japan's reactor anti-neutrino flux, while still allowing for all current physics studies to be continued. Now a dedicated Gd test facility is operating in the Kamioka Mine, home of the Super-Kamiokande [SK] detector. This new facility houses a stainless steel tank, capable of holding 200 tons of water and lined with 240 50-cm photomultiplier tubes connected to a functioning data acquisition system, a specially designed water system for filtration and gadolinium recovery, and multiple devices for evaluating the quality of the water in the tank. Successful running of this new facility will demonstrate that adding Gd salt to SK is both safe for the detector and is capable of delivering the expected physics benefits.
Speaker: Andrew Renshaw (UC Irvine)
• 19:30 19:30
High Pressure Xenon Detectors for Rare Physics Searches
(On behalf of the NEXT collaboration) The existence of neutrinoless double beta decay and WIMP dark matter are both important questions that could be addressed by xenon gas-based detectors. We describe results obtained with the NEXT (Neutrino Experiment with a Xenon TPC) prototype for research and development towards the direct detection of neutrinoless Double Beta decay and Dark Matter (NEXT-DBDM). Good energy resolution (extrapolated to 0.5% FWHM at the 136Xe double beta Q-value) and tracking capabilities have been demonstrated in approximately 15 bar xenon gas. The ability to distinguish between electron and nuclear recoils in xenon gas using the simultaneous observation of primary scintillation (S1) and ionization (S2) has also been demonstrated.
Speaker: Joshua Renner
• 19:30 19:30
Ionization yield of 7 keV nuclear recoils in liquid argon
The response of liquid argon, and other low-background detector materials, to low-energy nuclear recoils is important for determining the sensitivity of these materials to light WIMPS and coherent neutrino-nucleus scattering. Using a small prototype dual-phase argon proportional scintillation counter at LLNL we have probed the response of liquid argon to sub-keV electronic recoils using 37Ar as an homogeneous internal calibration source. With this same detector we have measured the ionization yield of 7 keV nuclear recoils. This measurement was made using a near-threshold collimated Fe-filtered 7Li(p,n) source that provides a monoenergetic source of 70 keV neutrons.
Speaker: Mr Tenzing Joshi (University of California Berkeley)
• 19:30 19:30
Measurement of Neutrino and Antineutrino Oscillation Parameters Using the Complete Atmospheric and Beam Data Sets from MINOS
The MINOS detectors are used to collect data from the NuMI neutrino beam as well as atmospheric neutrino data. The atmospheric data taken by the Far Detector, located underground at a depth of 2070 meters-water-equivalent and at 735 km from the neutrino production target, is combined with beam data from both Near and Far Detectors to measure the neutrino and antineutrino mixing parameters. Because our detectors are magnetized, we are able to separate neutrinos and antineutrinos on an event-by-event basis. This allows us to analyze the complete MINOS data set under two possible scenarios: assuming neutrinos and antineutrinos have different oscillation parameters; and assuming their corresponding parameters are identical. We report the world-leading measurement of the neutrino and antineutrino atmospheric mass splitting parameter along with the most precise comparison to date of neutrino and antineutrino oscillation parameters.
Speaker: Ms Michelle Mesquita de Medeiros (Federal University of Goias)
• 19:30 19:30
Measurement of the diffuse neutrino flux by a global fit to multiple IceCube results
The IceCube Neutrino Observatory is the largest operating experiment searching for astrophysical neutrinos. Situated at the geographical South Pole, IceCube has been completed in 2010 and is entering its phase of discovery now. Several studies that have recently been performed in IceCube show an excess of events at high energies, indicating the presence of a non-atmospheric component in the diffuse neutrino flux. The aim of this study is to characterize the diffuse neutrino flux as measured by IceCube. To this end, a global likelihood fit to the results of multiple IceCube analyses has been performed. These analyses include both main detection channels (track-like and shower-like events) and use data taken between 2008 and 2012 with four different IceCube configurations (featuring 40, 59, 79 and 86 strings, respectively).
Speaker: Mr Lars Mohrmann (DESY)
• 19:30 19:30
Multivariate search for a diffuse astrophysical muon neutrino flux with ANTARES
The ANTARES Cherenkov detector is optimized for the detection of neutrino-induced muons in the TeV range with the aim to measure astrophysical neutrinos. A search for a diffuse astrophysical neutrino flux was performed on four years of ANTARES data through parameter space scanning and an upper limit is set on the expected muon neutrino flux.
Speaker: Ms Jutta Schnabel (ECAP Universität Erlangen-Nürnberg)
• 19:30 19:30
NEWAGE
NEWAGE is a direction sensitive WIMP search experiment using micro pixel chamber. After our first underground measurement at Kamioka (PLB686(2010)11), we constructed new detector. The size of new detector is twice than older one. And its drift-cage is made by PEEK material to reduce radon emanation. Also we constructed the gas circulation system using cooled charcoal to reduce radon gas. We confirmed detector performance with low pressure gas to lower energy threshold, then we applied to use gas with 76torr pressure. Then we performed underground measurement at Kamioka. We will report about result of underground measurements.
Speaker: Mr Kiseki Nakamura (Kyoto university)
• 19:30 19:30
Non Standard Neutrino Oscillation
Taup Abstract This work aims to propose a possible solution to the Gallium and Reactor Neutrino Problem, which verifies a difference between predictions and observations of neutrino flux originated from nuclear reactors. Based on non-standard neutrino interactions we could promote an instantaneous neutrino flavor changing at the moment of neutrino creation. The approach used is based on weak leptonic number violation, with the restriction of keeping the Lorentz invariance. That approach allow interactions like electron/muon-neutrino that create muon-neutrinos inside the reactor and give a better understanding of the quantum neutrino oscillation phenomenon for a region near to the reactor.
Speaker: Mr David Girardelli (Unicamp)
• 19:30 19:30
Non-Standard Models, Solar Neutrinos, and Large theta 13
Solar neutrino experiments have yet to see directly the transition region between matter-enhanced and vacuum oscillations. The transition region is particularly sensitive to models of non-standard neutrino interactions and propagation. We examine several such non-standard models, which predict a lower-energy transition region and a flatter survival probability for the 8B solar neutrinos than the standard large-mixing angle (LMA) model. We find that while some of the non-standard models provide a better fit to the solar neutrino data set, the large measured value of theta_13 and the size of the experimental uncertainties lead to a low statistical significance for these fits. We have also examined whether simple changes to the solar density profile can lead to a flatter 8B survival probability than the LMA prediction, but find that this is not the case for reasonable changes. We conclude that the data in this critical region is still too poor to determine whether any of these models, or LMA, is the best description of the data.
Speaker: Richard Bonventre (University of Pennsylvania)
• 19:30 19:30
Research potential of the Pyhasalmi Mine in Finland
We take this opportunity to advertise what kind of environment and existing infrastructure the Pyhasalmi mine could offer to the field of experimental astroparticle and underground physics. We summarize the status of the current research in the mine i.e. cosmic ray experiment EMMA and discuss the advantages of the mine in context of a large next-generation underground experiment, like LAGUNA-LBNO.
Speaker: Mr Kai Loo (University of Jyvaskyla)
• 19:30 19:30
Search for light WIMP captured in the Sun using contained events in Super-Kamiokande
Super-Kamiokande can search for dark matter by detecting neutrinos and muons which are produced by WIMP pair annihilations occur inside the Sun. The huge gravity and hydrogen-rich composition of the Sun combined with high sensitivity of Super-Kamiokande for low-energy (few GeV) neutrinos allow us good sensitivity to light (few GeV to few 10 GeV) WIMP dark matter, especially for spin-dependent coupling case. In this analysis, we increased signal acceptance by using fully-contained and partially-contained neutrino events added to up-going muons in Super-Kamiokande. We also used minimum $\chi^2$ method to use energy, direction and flavor information. We fitted Super-Kamiokande I-IV data to find the allowed contribution of WIMP-induced neutrino events added to large background of atmospheric neutrino events. As a result, we found no signal observed and the null result was interpreted as upper limit on the spin-dependent (SD) WIMP-nucleon elastic scattering cross-section for $\chi\chi \rightarrow b\bar{b}$ and $\chi\chi \rightarrow \tau^+\tau^-$ WIMP annihilation channels. We set current best limit on SD WIMP-proton cross-section for WIMP mass below 100 GeV.
Speaker: Koun Choi (Nagoya University)
• 19:30 19:30
Systematics of Low Threshold Modulation Searches in CDMS-II
The Cryogenic Dark Matter Search experiment (CDMS-II) uses ground-based germanium and silicon detectors to search for the scattering of Weakly Interacting Massive Particles (WIMPs), which are among the leading candidates for the dark matter component of the universe. Using the ionization and athermal phonons measured in particle interactions, CDMS-II is able to achieve excellent discrimination between the nuclear recoils expected for WIMP interactions and radioactively produced electron recoils. With the rise of interest in the low energy interactions of light mass WIMPs, CDMS-II has undertaken a search for an annually modulating signal at low thresholds. Previous results detailed the analysis of data from eight germanium detectors over the course of six runs, to thresholds of 5 keVnr (nuclear recoil energy). We will discuss the impact of systematics at these low thresholds and their implications for thresholds down to 2.27 keVnr.
Speaker: Danielle Speller (UC Berkeley)
• 19:30 19:30
The Majorana Demonstrator
The Majorana experiment proposes to assemble an array of HPGe detectors to search for neutrinoless double-beta decay in ⁷⁶Ge. Neutrinoless double-beta decay searches play a major role in determining the Majorana/Dirac nature of neutrinos, and would have signiﬁcant implications for our understanding of the nature of neutrinos and matter in general. Initially, Majorana aims to construct a prototype system containing 40 kg of Ge detectors to demonstrate the feasibility and potential of a future tonne-scale experiment.
Speaker: Dr Clara Cuesta (University of Washington)
• 19:30 19:30
The POLARBEAR Cosmic Microwave Background Polarization Experiment
The POLARBEAR Cosmic Microwave Background (CMB) polarization experiment has been observing since early 2012 from its 17,000 ft site in the Atacama Desert in Northern Chile. Its measurements will characterize the expected CMB polarization due to gravitational lensing by large scale structure, and search for the possible B-mode polarization signature of inflationary gravitational waves. Its 250 mK focal plane detector array consists of 1,274 polarization-sensitive antenna-coupled bolometers, each with an associated lithographed band-defining filter and contacting dielectric lenslet, an architecture unique in current CMB experiments. We will present the status of the POLARBEAR instrument, its focal plane, and the analysis of its measurements.
Speaker: Darcy Barron (UC San Diego)
• 19:30 19:30
The TeV Cosmic-Ray Anisotropy from Local Dark Matter Annihilation
Several experiments, including Milagro and IceCube, have reported regions in the TeV sky with an excess of cosmic rays. I will discuss the consistency of these cosmic-ray excesses with dark matter annihilations in a nearby subhalo. The dark matter explanation of the TeV cosmic-ray excess naturally explains both its spatial and spectral features. I will show that the dark matter annihilation rate needed to produce the excess is consistent with current measurements of antiprotons, positrons, and gamma-rays. Additionally, I will show the predicted signatures from the dark matter subhalo in several cosmic-ray channels, several of which are measurable by the next generation of experiments.
Speaker: Dr J. Patrick Harding (Los Alamos National Laboratory)
• 19:30 19:30
The Tunka Radio Extension (Tunka-Rex): A new radio detector for cosmic ray air showers
Tunka-Rex is a new radio detector for extensive air showers from cosmic rays, built in 2012 as an extension to Tunka-133. The latter is a non-imaging air-Cherenkov detector, located near lake Baikal, Siberia. With its 25 radio antennas, Tunka-Rex extends over 1~km$^2$ with a spacing of 200~m and therefore is expected to be sensitive to an primary energy range of 10$^{17}$-10$^{18}$~eV. Using Trigger and DAQ from Tunka-133 this setup allows for a hybrid analysis with the air-Cherenkov and radio technique combined. The main goals of Tunka-Rex are to investigate the achievable precision in reconstruction of energy and composition of the primary cosmic rays by cross-calibrating to the well understood air-Cherenkov detector. While the focus in the first season was to understand the detector and develop frame conditions for future work, an early analysis already proves the detection of air-shower events with dependencies on energy and incoming direction as expected from a geomagnetic emission mechanism. Furthermore, in near future tests will be conducted for a joint operation of Tunka-Rex with Tunka-HiSCORE, a gamma ray observatory at the same site, and the upcoming scintillator extension of Tunka-133.
Speaker: Mr Roman Hiller (Karlsruhe Institute of Technology)
• 19:30 19:30
The importance of heavy-quark loops for dark matter searches
Effective operators are a convenient way to parameterise our ignorance of the interactions between Dark Matter (DM) particles and the Standard Model. However, if we want to apply the same effective operator to different processes (e.g. DM production at the LHC and DM direct detection in underground experiments), we need to worry about the large separation of scales. For example, to calculate direct detection cross sections, we need to evolve all effective operators from the TeV scale down to the MeV scale. In the process, new interactions may be induced at loop-level, leading to additional operators, which are absent at the TeV scale.
Speaker: Mr Felix Kahlhoefer (University of Oxford)
• 19:30 19:30
The test-facility GALATEA
The test-facility GALATEA is presented. GALATEA is a test-stand designed to study the properties of Germanium detectors in detail. It is a powerful high precision tool to investigate bulk and surface effects in germanium detectors. A vacuum tank hauses a cooled detector volume and a system of three stages which allow a complete scan of a detector. At current, a 19-fold segmented Germanium detector is under investigation. The main feature of GALATEA is that there is no material between source and detector. This allows the usage of alpha and beta sources as well as of a laser beam to study surface effects.
Speaker: Matteo Palermo (Max Plank Institut fur Physik, Munich)
• 19:30 19:30
Understanding the SNO+ Detector
The SNO+ detector is located in the Creighton Mine near Sudbury, Canada. It reuses the SNO detector for a broad neutrino-physics program, with emphasis on neutrinoless double beta decay. The heart of the SNO+ detector is a 12m-diameter acrylic sphere filled with liquid scintillator and the double beta decay isotope, 130Te. Light is emitted when charged particles pass through the scintillator, and is detected by an array of ~9,500 photomultiplier tubes. Event energies and positions are reconstructed using hit-level PMT information. Several aspects of the PMT response, a critical input to reconstruction resolution, are being calibrated as the detector is commissioned. During SNO, an aspect of PMT response called angular response was found to change over time. Modeling this time evolution to better understand the angular response is underway, and is essential for accurate energy reconstruction in SNO+. In addition, first runs of electronic calibration and comparison to SNO results show that SNO+ is accurately extracting the relevant constants.
Speaker: Ms Katayun Kamdin (UC Berkeley)
• 19:30 19:30
Using Gamma-Rays to Probe the EBL & New Physics
The Extragalactic Background Light (EBL) encompasses the light emitted by stars and other astrophysical objects throughout the history of the Universe. From this we can learn about star formation rate as well as galactic evolutionary traits. As gamma-rays travel from distant blazars they can maximally interact with this background light and create an electron-positron pair. This creates a measurable attenuation in the blazar's energy spectrum. As Cherenkov detectors become more prevalent, we are now finding more very high energy (VHE) blazars (E> 100s GeV). In turn we are now able to better probe the higher energy (UV) portion of the EBL. Using seven VHE blazars we test three different attenuation models and find they fit the sources well -- within one standard deviation in likelihood space. We also show a simple way to put constraints on the parameters of axion-like particles (ALPs) by the observation of high energy objects such as blazars. We consider the scenario of gamma-rays oscillating into ALPS over large distances in intergalactic magnetic fields. We know that gamma-rays are attenuated enroute to Earth due to interactions with background light, but here we also consider the spread in that attenuation to be due to ALP physics.
Speaker: Rebecca Reesman (The Ohio State University)


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# What do these new symbols mean...?I can't start this without knowing

by flyingpig
Tags: knowing, meani, start, symbols
 Share this thread:
 P: 2,568 Oh wait, there are n - k + 1 terms...shoot I forgot how to do this. I am guessing that means the sum sums to 1.
Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,726
 Quote by flyingpig So I must find $$P = \binom{n}{k} x^k (1 - x)^{n-k} = 1$$
Why? Where did you get this from?
P: 2,568
 Quote by vela Why? Where did you get this from?
Yeah scratch that I aws still thinking of multiplying and stuff. Forgot to get rid of it.
 P: 2,568 In $$\sum_{k=0}^{n} \binom{n}{k} x^k (1 - x)^{n-k}$$ It can only be 1 when k = 0, and n = 0... Is that what I Have to show? This is due tomorrow and I m still scratching my head
 P: 2,568 In the picture, f(x) was shown to be $$f(\frac{k}{n})$$ does this imply that k = n since f(x) = 1? If so then $$\frac{n!}{n!(0!)} x^n (1-x)^0 = x^n$$ Darn something is still off.
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,726 Do you understand sigma notation?
P: 2,568
 Quote by vela Do you understand sigma notation?
It means sum

EDIT: oh wait, are you referring when I said that n = k? Oh okay, so the sum is $$\sum_{n=0}^{n} \{whatever is here} = 1$$?

EDITING..not actually too sure of the property above. Looking through my old calc text
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,726 I'm asking you what is $$\sum_{k=0}^{n} \binom{n}{k} x^k (1 - x)^{n-k}$$ shorthand for? In other words, if you write the sum out, what do you get? I'm asking because you're making a bunch of guesses that make no sense if you understand what the notation means.
 P: 2,568 $$\binom{n}{k} x^k (1 - x)^{n-k} = P$$ $$\sum_{k=0}^{n} P$$ I am sorry for being so slow. wEDIT:writing out the sum...
 P: 2,568 I wrote the first three terms $$\sum_{k=0}^{n} \binom{n}{k} x^k (1 - x)^{n-k} = (1-x)^n + \frac{n!}{(n-1)!}x(1-x)^{n-1} + \frac{n!}{2!(n-2)!}x^2 (1-x)^{n-2}...$$
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,726 Ok, good. So you see how k isn't a variable you can really mess with, right? It takes on the values 0 to n just to generate the terms in the sum. In fact, when you expand the sum out, there is no k appearing anymore because it was just a dummy variable. So you can't do stuff like assume restrict k to just one value to try get the result you want. Similarly, you're asked to evaluate the sum for any value of n, so you can't set n to any one value. Now, are you familiar with the binomial theorem? That is, what is the expansion of (a+b)n?
 P: 2,568 $$(a + b)^n = \sum_{k=0}^{n}\binom{n}{k} a^{n-k} b^k$$ By observations I took x = b 1 - x = a So that a + b = 1 1^n = 1 forever, so that completes the problem!!! YES THANK YOU VELA, Kurt, and micro and all who helped *blows kisses*

 Related Discussions Special & General Relativity 4 General Physics 11 General Discussion 26 General Discussion 11 General Physics 2


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If you already have a Digi Embedded for Android version, go to Update Digi Embedded for Android.

## Install Digi Embedded for Android

If this is the first Digi Embedded for Android 9.0 installation, follow these steps:

1. Set up your environment following the steps at Set up your development computer.

2. Create an installation folder.

The installation folder requires user write permissions. For example, create the directory /usr/local/dea-9.0-r3.

``$sudo install -o <your-user> -g <your-group> -d /usr/local/dea-9.0-r3`` 3. Add execute permission. ``$ chmod +x 81000379_C.bin``
4. Execute the installer.

``$./81000379_C.bin`` 5. Accept the license agreement. The sources are installed inside a directory called dea-9.0-r3. ## Update Digi Embedded for Android  Regardless of your current version, you can only install the new Digi Embedded for Android 9.0-r3 using the source code installer. Follow the steps in Install Digi Embedded for Android to download the new version. Digi eventually will release hotfixes in the form of 9.0-r(x). To advance 9.0-r(x-1) to 9.0-r(x), sync your installation with the HEAD of the release branch: `$ repo sync -c -d --optimized-fetch -j<Number_Of_Jobs>`
 -j argument sets the number of projects to fetch simultaneously. The git servers have a limit on how many connections you can have open at the same time. It may make parallel 'repo sync' fail if '-j' parameter is too high.

You can Subscribe to the dea-manifest GitHub repository to receive Digi Embedded for Android update notifications.

New Digi Embedded for Android releases may include things like:

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text:
# mathematical expression to detect modulated data within a vector

Assume I have such modulated data which is, for example, $$x=0.7+0.7i$$. That modulated data is encapsulated in a vector as below:

OR

where $$c$$ is any constant number, let’s say, for example: $$c=0.7$$ . My question is how can I detect if the received vector is $$y_1$$ or $$y_2$$ ? I mean is there a mathematical expression I can apply for detection?

The same as you'd do for a scalar reception:

1. Build a stochastic model for your transmit vectors
2. Build a stochastic model for your noise
3. from 1. and 2., build a stochastic model for your received vectors
4. Define a metric on the error statistics that you want to minimize
5. from 3. and 4., derive a decider

For example:

1. $$x$$ are points from an amplitude-phase shift keying modulation $$\mathcal X$$, with two different amplitudes, and 4 points on the inner "circle", as well as 6 on the outer, and the inner points being chosen twice as often as the outer points; points on the same amplitude circle are equiprobable.
From that follows a statistic for $$\vec y_1=(y_{11},y_{12})^T$$, call it $$f_{y_{11},y_{12}}(\xi_1, \xi_2)$$.
In many cases this is relatively easy, since the possible points are discrete, in others you'll have to employ more complicated models e.g through random variable pdf transformations using the Jacobi determinant.
2. Noise $$\vec n = (n_1,n_2)^T$$ is uniform in phase over $$[0,\pi/2]$$, and exponentially distributed in amplitude, strongly stationary, white and independent from $$\vec y$$. That means it can be described by a single $$f_n(\chi)$$.
3. $$\vec r = (y_{11}+n_1, y_{12}+n_2)^T$$. If you modeled your noise to be independent from signal in 2., then the noise pdf is just the convolution of $$f_{\vec y}$$ and $$f_{n}$$.
4. You define that you want to minimize the symbol error probability for every receive point. Other choices might include minimizing bit error rate locally, or symbol error rate globally under constraints (e.g. complexity).
5. You hence decide to build an MAP decider that gives you an estimate $$\hat x$$ that gives you $$\hat x_{\vec r} = \operatorname*{\arg\max}\limits_x f(\vec r|x)$$. So, you write down the 2D density, and find a maximum.
• Thank you for your reply ... "stochastic model", does that mean like a matrix which includes all possible vectors ? second, could you please explain more what you mean by point 2 ？ I mean how to choose the noise. – Fatima_Ali Jan 30 at 6:14
• a stochastic model describes the thing stochastically, so, more something like probability densities (or probabilities in the discrete case), stationarity, ergodicity, correlation – Marcus Müller Jan 30 at 12:33


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# What is the difference between assignment, valuation and name binding?

I read that Name binding assigns some value (data/code/expression) to an identifier. Assignment and valuation seem to do the same thing. It is confusing. Can I just tell that free variable is one, which was not assigned a value whereas bound variable has its value assigned?

Binding has to do with giving names to things (or values) in a given well delimited context. Assignment is about storing things (or values) in some location (a variable). Another assignment can replace a previous value with a new one. Valuation consist in binding all the identifiers of a formal text with something (with a value). In mathematics these identifiers are often called variables, which causes a confusion with the concept of variable (i.e. memory storage) in computer science.

## Trying to give more intuitive details

Name binding attaches a meaning to identifiers within some part (called scope) of the concerned mathematical or programming text. This meaning can indeed be seen as a value in some domain when the text is interpreted.

For example, if you declare foo as an integer variable, the value attached to foo within the scope is an integer variable. An integer variable may be seen informally a a container that can carry an integer value, which may be changed. You can also see it as the address of a place in memory where the content may be stored.

But if you declare foo as the integer 25, then whithin the scope, any use of foo is identical to a use of 25. If you declare foo as an integer constant, it cannot change and thus its value must be specified.

Binding is attaching a name to some value that does not change within the scope of the name. An example is a legal documents stating that "for the purpose of this document, Mr. Brown, and the Smith family shall be called the beneficiary." The scope is the legal document. And everywhere in the document, the use of the word beneficiary means Mr. Brown, and the Smith family. You can see it as a definition of a local terminology. It has to do with giving names to things. Binding is about speaking, reading or writing. It is not about executing or moving values around: that corresponds to assignment.

A variable may be seen as a chunk of memory that can contain a value, When you have a variable, you can change the value contained in this variable contains with an assignment. If foo is bound to (or denotes) a variable in the current scope, you can assign a value to foo, i.e. to the variable denoted by foo, or read the value contained in that variable. And you can change that value with a new assignment.

So binding is an operation that tells what is the meaning of names in the text of the program or of the mathematical discourse. It is static, in the sense that the text does not change. But assignment is a programming concept that consist is storing a value in a variable, i.e. a container, which is usually a place in memory. It is a dynamic concept related to how (representations of) values are stored in memory, which changes as the program progresses.

Note that a variable may exist independently of any name to which it could be bound. This is the case for an element of an array, to take a simple example.

In various contexts, one may consider expressions or texts that use names that have not been defined. For example you can write $(a^2-b^2)/(a-b)$ which is an arithmetic expression. Then you may valuate the variables by associating an environment (you may read approximately a scope) where the variables $a$ and $b$ are bound to some values, for example 3 and 12, and be interested in the value taken by the exression. A valuation is such an association of a set of names, each with a specific value. The name valuation is used more in formal mathematics, while assigment is a programming concept.

• To summarize, you basically confirm that all operations assign a value to variable/identifier/placeholder. The difference is the context. When we map guest (program) to host (machine), we say binding. When variable is bound to some value during program execution, we say it was assigned and we prefer to say valuated in the formal/cs context instead. I just started to look at the free/bound variables today and confused. It is like formal/cs context, yet, compiler/computer engeneer jargon is used? – Val Feb 18 '15 at 15:33
• @RecognizeEvilasWaste I have attempted to clarify. But there is a difficulty due to the fact that mathematical terminology conflicts with computer science terminology. A variable cannot be bound to some value, a variable is assigned a value. An identifier is bound to a meaning, but the formal notion of meaning is some value in a semantics domain. You do not assign identifiers, you do not bind variables. Identifiers are syntax, speech. Variables are memory, used to store information. Actually, it is computer jargon that was derived from the formal speech. – babou Feb 18 '15 at 16:37
• Your confusion is understandable. In lambda calculus, the word variable is used for what I call identifier. More generally, there is a whole branch of programming, called functional programming, that is not supposed to use assignment. So, in principle everything is done through binding, but it gives a very different style of programming. Lambda calculus is the basic formal example of that. However, they still talk of variables for what is identifiers. You question is fair, and the terminology is messy. Well I did my best. – babou Feb 18 '15 at 17:27
• @RecognizeEvilasWaste Your question is actually a very good one. I had not realized how much ambiguity this creates for beginners. – babou Feb 19 '15 at 12:10
• Not only for novice. I would say that I am quite experienced in these issues. I can understand what they mean. But I always have difficulty which term to use when I want to say similar things. I also like to see the relationships between things, en.wikipedia.org/wiki/User:Javalenok This helps understanding. – Val Feb 19 '15 at 13:29


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Contents

complex geometry

# Contents

## Idea

The complex projective plane $\mathbb{C}P^2$ is the complex projective space of complex dimension 2, hence the projective plane over the complex numbers.

## Properties

### Rational homotopy type

A Sullivan model is given by

$\array{ d\, \alpha_2 & = 0 \\ d\, \alpha_5 & = \alpha_2 \wedge \alpha_2 \wedge \alpha_2 }$
• Luc Menichi, Section 5.3 of: Rational homotopy – Sullivan models

### Quotient by complex conjugation is 4-sphere

###### Proposition

(Arnold-Kuiper-Massey theorem)

The 4-sphere is the quotient space of the complex projective plane by the action on homogeneous coordinates of complex conjugation:

$\mathbb{C}P^2 / (-)^* \simeq S^4$

### Blowup to del Pezzo surfaces

The blowup at generic points is a del Pezzo surface.


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# continuous linear recurrent relations

For a function $f:\mathbb{R}\rightarrow \mathbb{R}$ denote $f_0(x)=x$, $f_n(x)=f(f_{n-1}(x))$. Assume that $f$ satisfies a functional equation
$$f_n(x)+a_{n-1} f_{n-1}(x)+\dots+a_0 f_0(x)\equiv 0$$
for some constant real coefficients $a_{0},a_1,\dots,a_{n-1}$. Assume also that $f$ is continuous. What are conditions for polynomial $t^n+a_{n-1}t^{n-1}+\dots +a_0$ which allow to conclude that $f$ is linear?


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Public Group

# Multiple files error (c++) [Solved]

This topic is 4888 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hmmmm, I know this will be a really basic error but I just can't get rid of it. Google didn't help, and no matter how I change the code the error is still there. The errors are:
main.obj : error LNK2019: unresolved external symbol "public: int __thiscall Creature::GetStrength(void)const " (?GetStrength@Creature@@QBEHXZ) referenced in function _main
main.obj : error LNK2019: unresolved external symbol "public: class std::basic_string<char,struct std::char_traits<char>,class std::allocator<char> > __thiscall Creature::GetName(void)const " (?GetName@Creature@@QBE?AV?$basic_string@DU?$char_traits@D@std@@V?\$allocator@D@2@@std@@XZ) referenced in function _main

This is the code (I didn't comment it because it was just supposed to be a little experiment :P). Creature.h
#include <string>
using namespace std;

class Creature
{
private:

int Strength;
int Agility;
int Armor;
int RedDefence;
int BlueDefence;
int GreenDefence;
string Name;

public:

Creature(int iStrength, int iAgility, int iArmor, int iRedDefence, int iBlueDefence, int iGreenDefence, string iName);
~Creature();

int GetStrength() const;
int GetAgility() const;
int GetArmor() const;
int GetRedDefence() const;
int GetBlueDefence() const;
int GetGreenDefence() const;
string GetName() const;

void SetStrength(int iStrength);
void SetAgility(int iAgility);
void SetArmor(int iArmor);
void SetRedDefence(int iRedDefence);
void SetBlueDefence(int iBlueDefence);
void SetGreenDefence(int iGreenDefence);
void SetName(string iName);

};

Creature.cpp
#include "Creature.h"
Creature::Creature(int iStrength, int iAgility, int iArmor, int iRedDefence, int iBlueDefence, int iGreenDefence, std::string iName)
{
Strength = iStrength;
Agility = iAgility;
Armor = iArmor;
RedDefence = iRedDefence;
BlueDefence = iBlueDefence;
GreenDefence = iGreenDefence;
Name = iName;
}

Creature::~Creature() { }

inline int Creature::GetAgility() const {return Agility;}
inline int Creature::GetArmor() const {return Armor;}
inline int Creature::GetBlueDefence() const {return BlueDefence;}
inline int Creature::GetGreenDefence() const {return GreenDefence;}
inline string Creature::GetName() const {return Name;}
inline int Creature::GetStrength() const {return Strength;}
inline int Creature::GetRedDefence() const {return RedDefence;}

inline void Creature::SetAgility(int iAgility) {Agility = iAgility;}
inline void Creature::SetArmor(int iArmor) {Armor = iArmor;}
inline void Creature::SetBlueDefence(int iBlueDefence) {BlueDefence = iBlueDefence;}
inline void Creature::SetGreenDefence(int iGreenDefence) {GreenDefence = iGreenDefence;}
inline void Creature::SetName(std::string iName) {Name = iName;}
inline void Creature::SetRedDefence(int iRedDefence) {RedDefence = iRedDefence;}
inline void Creature::SetStrength(int iStrength) {Strength = iStrength;}

main.cpp
#include <iostream>
using namespace std;
#include "Creature.h"

int main()
{
Creature Dave(5,5,5,5,5,5,"Dave");

cout << Dave.GetName() << "/t/t is:" << endl;
cout << "/t/t " << Dave.GetStrength() << "/t points strong" << endl;
cout << endl;

cin.get();

return 0;
}

Any help would be appreciated. [Edit: Sorry for the crappy formatting] -Serano

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In the creature.cpp file, try removing the inline keyword in front of your function definitions.

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Thanks SiCrane. The problem now is how would I make them inline? Or should I just not bother?

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If you want to make them inline you should put the function definitions in the header. Only very smart linkers can inline functions defined in separate translation units; and if your linker is that smart it probably doesn't care if you've declared the function inline or not.

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Thanks for the explanation. That was my first time using multiple files so I wasn't too sure about how I would have to change the code.

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When you mark a function inline, you ask the compiler to replace any call to that function with the contents of the function itself, instead of making that call. In most cases, that also means the function is not generated as a "out-of-line" function at all: there is no GetStrength function in your program.

When calling an inline function, it is necessary for the compiler to have access to the body of the function, so that the replacement can happen. That means you cannot bury a function in a single .cpp file, but really have to make the function code available to any .cpp file that calls that function. The simplest and most obvious way to do so is to put the whole inline function into a header file, which will get included in any translation unit that requires the function (remember that putting something in a header file and then including that header is strictly equivalent to manually writing out all of the header's contents in the file that includes the header - that's how preprocessor #include directives work).

In your case, you declared the functions in your class, telling the compiler that it was not an error to try and call them, but you never did provide the body for them. The compiler therefore assumed, when it processed main.cpp, that the function would be provided by another translation unit that would eventually get linked. However, in Creature.cpp, you did provide those functions as inline functions. Since C++ uses a separate compilation model, when processing Creature.cpp, the compiler is completely unaware of whatever needs main.cpp might have. It notices the functions have been marked inline and yet are never used in Creature.cpp -- it therefore just discards them completely. Once both files are compiled, the linker tries to reconciliate all the function calls, but never finds an actual GetStrength() function, and thus raises a stink.

You have several solutions to this problem. The first is to move the inline functions to the header file that contains the class definition. Any translation unit making use of the class is going to include the header anyway so, that way, they'll get the inline functions too. There are two ways you can do that. You can either simply cut and paste your code back to the header file or, given that member functions which are defined within a class definition are implicitely inline, you could turn the member function declarations into definitions:

class Foo{   int bar;public:   // int GetBar();                <--- That's a declaration   int GetBar() { return bar; } // <--- That's a definition};

The other solution, simpler but probably less satisfying for mere "accessor" functions (which, for such a simple class are in my opinion a terrible idea) is to just drop the inline. That way, actual functions will be generated and thus found by the linker.

edit: Bleh. Too slow... Curse you SiCrane, and your little dog too. [razz]

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Quote:
 Original post by SeranoAny recommended reading material?

Short of taking a course on the topic, your compiler documentation is actually probably one of the best place to start. gcc and ld's documentations are also online. They might help you get an idea of what kind of work they actually do. Beyond that, I am not aware of any tutorials explaining how such things work (your Google-Fu is probably as good as mine, you know what kind of things to search for). Then it's a question of experience, and trying to understand and remember why the compiler or linker might flag something as an error.

For example, along with "unresolved external" ('resolving' is the process by which the linker tries to associate a function call in an object file with the actual address of the function. An 'external' is a function (or a variable, for that matter) which has been declared in a translation unit (a .cpp file and all the headers it included), but not defined and thus assumed by the compiler as being provided by another translation unit), another very common error is "multiply defined symbol", where multiple translation units define, well, a symbol (a function, a variable...) and then, comes link time, the linker sees multiple copies and doesn't know which one to pick (it refuses to choose). A common source for that error is to have a non-inline (non-template) function (or a variable definition) in a header file ... which gets included into several .cpp files (thus multiple translation units).

Simple, really, if you keep track of what's going on. [smile]

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You can also read the C++ Standard and see what it says about defining things in multiple translation units and so on. It's fairly dry reading, but it does tell you how things are supposed to fit together. Section 7.1 is most relevant for this case.

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Quote:
 Original post by Frunymere "accessor" functions (which, for such a simple class are in my opinion a terrible idea)

Quoted for emphasis. Be aware that the current accessors and mutators do nothing that a public member access wouldn't, except add complication. Any time you find yourself writing that much for something simple - especially when it looks that repetitive - it should be adding a bunch of real value (protection, like sanity checks for values). Here, there is none.

Of course, public data isn't necessarily a good choice here either. Class interface design requires a fair bit of thought, and few people out there will make an effort to teach it, but basically you need to think about what changes will be valid during an objects lifetime, and what *patterns* of access are likely. In particular, most behaviour that uses Creature data should be represented with Creature member functions.

// badvoid levelUpCreature(Creature c) {  // or worse, writing the effective equivalent of this in-line somewhere else  if (coinFlip()) { c.strength++; sanityCheckStrengthOf(c); }  // And similarly for each other stat  // Worse yet, most people who write code like this won't even think to make  // a function for the sanity checks - they might not even think to make a   // function for the levelling-up, and instead copy-paste it a few times.  // One of the reasons OO works as a code organization tool is that it  // highlights more obvious places to put the common, reusable bits. :)}// also bad - in the case that there are no sanity checks at all, worse!int Creature::GetStrength() const {return Strength;}int Creature::SetStrength(int iStrength;) const {  Strength = iStrength;  sanityCheckStrength(); // normally this would be inline, but I just put  // a function stub here because I don't know what checks you're going to want}// and similarly for each statvoid levelUpCreature(Creature c) {  // or worse, writing the effective equivalent of this in-line somewhere else  if (coinFlip()) { c.setStrength(c.getStrength() + 1); }  // where appropriate sanity checks are done in setStrength  // And similarly for each other stat}// goodvoid Creature::levelUp() {  if (coinFlip()) { ++Strength; sanityCheckStrength(); }  // and so on}// Now we have way less code dedicated to moving data around in controlled ways,// because we're not moving the data around - but instead using it in the place// where it *should* be. We're also limiting the interface to what should be// available: a creature's stats only change in certain specific circumstances,// each of which has a logical name (like "levelUp()") and a specific set of// changes that may occur.

Of course, you may correctly point out that this approach will regardless leave duplication (not shown ;) ) in the levelling-up process, since each stat will probably be handled in a similar manner. Good! You're getting the idea now - what we need is to represent the concept of a "Stat" as a class (a very simple one probably), and then we can represent our Creature's data as an array (or some other container if appropriate; but do the simplest thing first) of Stats. Of course, for internal calculations (e.g. when we get to write something like Creature::use(const Item& i) ), we'll need to know which is which, so there will probably be an enumeration in class scope to give names to the array indices.

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# decibel carrier (dBc)

Decibel Carrier (dBc) corresponds to the transmit level of an instantaneous carrier signal. The signal strength of the modulated signal results from the tenfold logarithm of the power of the unmodulated transmit signal in relation to the power of the modulation signal. For positive dBc values, the instantaneous signal strength of the modulated signal is greater than that of the pure carrier signal; for negative dBc values, it is less.

Informations:
 Englisch: decibel carrier - dBc Updated at: 27.07.2017 #Words: 69 Links: level, carrier, signal, power (P), relation Translations: DE Sharing:


text:
# Complex Integration example

Suppose I'm asked to compute the value of the complex integral: $$\int_{C}^{}\frac{\operatorname{Log}(z)}{z}\,dz$$ with $C=[i,1].$

Is it possible to treat the complex integrand like a real one and apply the rules of integration with limits $i$ to $1$, or do I ought to parameterize the given curve and then treat it like a line integral?

• It's not clear what $C=[i,1]$ means. How are you getting from $i$ to $1$? – Adrian Keister Apr 25 '18 at 19:49
• How do you define $\log z$? – José Carlos Santos Apr 25 '18 at 19:49
• C is the line segment from i to 1 and Logz is the complex logarithm. – Jevaut Apr 25 '18 at 19:54
• @Andrew Tzevas: In that case, since your path never crosses a pole and is analytic on a domain containing the path, I think you could simply compute the antiderivative and use the fundamental theorem for line integrals. – Adrian Keister Apr 25 '18 at 20:00
• $z = \mathrm{i} + \left(1 -\mathrm{i}\right)t$. – Felix Marin Apr 25 '18 at 22:25


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## Calculus 10th Edition

Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis. (-x)$y^{2}$=-10 x$y^{2}$=10 Equations are not equivalent, so not symmetric to y-axis. Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis. x$(-y)^{2}$=-10 x$y^{2}$=-10 Equations are equivalent, so function is symmetric to x-axis. Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin. (-x)$(-y)^{2}$=-10 x$y^{2}$=10 Equations are not equivalent, so not symmetric to origin.


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Home > Standard Error > Relationship Between Standard Error And 95 Confidence Interval

# Relationship Between Standard Error And 95 Confidence Interval

## Contents

Recall from the section on the sampling distribution of the mean that the mean of the sampling distribution is μ and the standard error of the mean is For the present Said shortly, tolerance intervals refer to the distribution inside the population, whereas confidence intervals refer to a degree of certainty regarding an estimation. American Statistician. All such quantities have uncertainty due to sampling variation, and for all such estimates a standard error can be calculated to indicate the degree of uncertainty.In many publications a ± sign navigate here

range" (which is something that is closer to a tolerance interval). –whuber♦ May 9 '15 at 13:18 That's not how I understood the question : it seemed to me Confidence interval for a proportion In a survey of 120 people operated on for appendicitis 37 were men. Making Sense of ResultsLearning from StakeholdersIntroductionChapter 1 – Stakeholder engagementChapter 2 – Reasons for engaging stakeholdersChapter 3 – Identifying appropriate stakeholdersChapter 4 – Understanding engagement methodsChapter 5 – Using engagement methods, This is expressed in the standard deviation. http://www.healthknowledge.org.uk/e-learning/statistical-methods/practitioners/standard-error-confidence-intervals

## Standard Error And 95 Confidence Limits Worked Example

Table 2: Probabilities of multiples of standard deviation for a normal distribution Number of standard deviations (z) Probability of getting an observation at least as far from the mean (two sided There is much confusion over the interpretation of the probability attached to confidence intervals. Scenario 2.

For a sample of size n, the t distribution will have n-1 degrees of freedom. Standard error of a proportion or a percentage Just as we can calculate a standard error associated with a mean so we can also calculate a standard error associated with a We usually collect data in order to generalise from them and so use the sample mean as an estimate of the mean for the whole population. Convert Standard Error To Standard Deviation To understand it, we have to resort to the concept of repeated sampling.

The mean age was 33.88 years. Calculate Confidence Interval From Standard Error In R To compute the 95% confidence interval, start by computing the mean and standard error: M = (2 + 3 + 5 + 6 + 9)/5 = 5. σM = = 1.118. The ages in that sample were 23, 27, 28, 29, 31, 31, 32, 33, 34, 38, 40, 40, 48, 53, 54, and 55. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1255808/ Note that this does not mean that we would expect, with 95% probability, that the mean from another sample is in this interval.

However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and Error Intervals Bitesize If we take the mean plus or minus three times its standard error, the interval would be 86.41 to 89.59. The standard error for the percentage of male patients with appendicitis is given by: In this case this is 0.0446 or 4.46%. Standard error of mean versus standard deviation In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation or the mean with the standard error.

## Calculate Confidence Interval From Standard Error In R

These assumptions may be approximately met when the population from which samples are taken is normally distributed, or when the sample size is sufficiently large to rely on the Central Limit http://stats.stackexchange.com/questions/151541/confidence-intervals-vs-standard-deviation In other words, the student wishes to estimate the true mean boiling temperature of the liquid using the results of his measurements. Standard Error And 95 Confidence Limits Worked Example National Library of Medicine 8600 Rockville Pike, Bethesda MD, 20894 USA Policies and Guidelines | Contact 7.7.7.2 Obtaining standard errors from confidence intervals and P values: absolute (difference) measures If a Error Interval Maths Confidence Intervals for Unknown Mean and Unknown Standard Deviation In most practical research, the standard deviation for the population of interest is not known.

The standard error is also used to calculate P values in many circumstances.The principle of a sampling distribution applies to other quantities that we may estimate from a sample, such as check over here The question conflates the 95% of sample and 95% of sample means, and that should be addressed. –Penguin_Knight May 9 '15 at 15:15 Ah, I understand your comments now. This section considers how precise these estimates may be. Repeating the sampling procedure as for the Cherry Blossom runners, take 20,000 samples of size n=16 from the age at first marriage population. Standard Error Of Measurement Confidence Interval

However, to explain how confidence intervals are constructed, we are going to work backwards and begin by assuming characteristics of the population. The standard deviation of the age for the 16 runners is 10.23. This common mean would be expected to lie very close to the mean of the population. http://wapgw.org/standard-error/relationship-between-standard-error-of-the-mean-and-confidence-interval.php The mean of all possible sample means is equal to the population mean.

Sampling from a distribution with a large standard deviation The first data set consists of the ages of 9,732 women who completed the 2012 Cherry Blossom run, a 10-mile race held Difference Between Standard Error And Standard Deviation Standard error of a proportion or a percentage Just as we can calculate a standard error associated with a mean so we can also calculate a standard error associated with a To take another example, the mean diastolic blood pressure of printers was found to be 88 mmHg and the standard deviation 4.5 mmHg.

## Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample.

The variation depends on the variation of the population and the size of the sample. For each sample, the mean age of the 16 runners in the sample can be calculated. df 0.95 0.99 2 4.303 9.925 3 3.182 5.841 4 2.776 4.604 5 2.571 4.032 8 2.306 3.355 10 2.228 3.169 20 2.086 2.845 50 2.009 2.678 100 1.984 2.626 You Standard Error Excel For some more definitions and examples, see the confidence interval index in Valerie J.

All journals should follow this practice.NotesCompeting interests: None declared.References1. Assumptions and usage Further information: Confidence interval If its sampling distribution is normally distributed, the sample mean, its standard error, and the quantiles of the normal distribution can be used to A natural way to describe the variation of these sample means around the true population mean is the standard deviation of the distribution of the sample means. weblink HomeAboutThe TeamThe AuthorsContact UsExternal LinksTerms and ConditionsWebsite DisclaimerPublic Health TextbookResearch Methods1a - Epidemiology1b - Statistical Methods1c - Health Care Evaluation and Health Needs Assessment1d - Qualitative MethodsDisease Causation and Diagnostic2a -

If p represents one percentage, 100-p represents the other. If σ is known, the standard error is calculated using the formula σ x ¯   = σ n {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt {n}}}} where σ is the Often, this parameter is the population mean , which is estimated through the sample mean . This observation is greater than 3.89 and so falls in the 5% of observations beyond the 95% probability limits.

The sampling distribution of the mean for N=9.


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## définition - Valence (chemistry)

voir la définition de Wikipedia

Wikipedia

# Valence (chemistry)

In chemistry, valence, also known as valency or valence number, is the number of valence bonds[1] a given atom has formed, or can form, with one or more other atoms. For most elements the number of bonds can vary. The IUPAC definition limits valence to the maximum number of univalent atoms that may combine with the atom, that is the maximum number of valence bonds that is possible for the given element.[2]

The valence of an element depends on the number of valence electrons that may be involved in the forming of valence bonds. A univalent (monovalent) atom, ion or group has a valence of one and thus can form one covalent bond. A divalent molecular entity has a valence of two and can form two sigma bonds to two different atoms or one sigma bond plus one pi bond to a single atom.[3] Alkyl groups and hydroxyl ions are univalent examples; oxo ligands are divalent.

Over the last century, the concept of valence evolved into a range of approaches for describing the chemical bond, including Lewis structures (1916), valence bond theory (1927), molecular orbitals (1928), valence shell electron pair repulsion theory (1958) and all the advanced methods of quantum chemistry.

 In cyclohexanonoxime (image left), the nitrogen atom has three valence bonds and therefore a valence of three.

## History

The etymology of the word "valence" traces back to 1425, meaning "extract, preparation," from Latin valentia "strength, capacity," and the chemical meaning referring to the "combining power of an element" is recorded from 1884, from German Valenz.[4]

William Higgins' combinations of ultimate particles (1789)

In 1789, William Higgins published views on what he called combinations of "ultimate" particles, which foreshadowed the concept of valency bonds.[5] If, for example, according to Higgins, the force between the ultimate particle of oxygen and the ultimate particle of nitrogen were 6, then the strength of the force would be divided accordingly, and likewise for the other combinations of ultimate particles (see illustration).

The exact inception, however, of the theory of chemical valencies can be traced to an 1852 paper by Edward Frankland, in which he combined the older theories of free radicals and “type theory” with thoughts on chemical affinity to show that certain elements have the tendency to combine with other elements to form compounds containing 3, i.e. in the three atom groups (e.g., NO3, NH3, NI3, etc.) or 5, i.e. in the five atom groups (e.g., NO5, NH4O, PO5, etc.), equivalents of the attached elements. It is in this manner, according to Frankland, that their affinities are best satisfied. Following these examples and postulates, Frankland declares how obvious it is that:[6]

 “ A tendency or law prevails (here), and that, no matter what the characters of the uniting atoms may be, the combining power of the attracting element, if I may be allowed the term, is always satisfied by the same number of these atoms. ”

This “combining power” was afterwards called quantivalence or valency (and valence by American chemists).[5]

### Covalence

The concept of covalence was developed in the middle of the nineteenth century in an attempt to rationalize the formulae of different chemical compounds. In 1919, Irving Langmuir, borrowed the term to explain Gilbert N. Lewis's cubical atom model by stating that "the number of pairs of electrons which any given atom shares with the adjacent atoms is called the covalence of that atom." The prefix co- means "together", so that a co-valent bond means that the atoms share valence. Hence, if an atom, for example, had a +1 valence, meaning it has one valence electron beyond the complete shell, and another a −1 valence, meaning it requires one electron to complete its outer shell (missing an electron) , then a bond between these two atoms would result because they would be complementing or sharing their out of balance valence tendencies. Subsequent to this, it is now more common to speak of covalent bonds rather than "valence", which has fallen out of use in higher level work with the advances in the theory of chemical bonding, but is still widely used in elementary studies where it provides a heuristic introduction to the subject.

## Common valences

For elements in the main groups of the periodic table, the valence can vary between one to seven, but usually these elements form a number of valence bonds between one and four. The number of bonds formed by a given element was originally thought to be a fixed chemical property. In fact, in most cases this is not true. For example, phosphorus often has a valence of three, but can also have other valences.

Nevertheless, many elements have a common valence related to their position in the periodic table, following the octet rule. Elements in the main groups 1 (alkali metals) and 17 (halogens) commonly have a valence of 1; elements in groups 2 (alkaline earth metals) and 16 (chalcogens) valence 2; elements in groups 13 (boron group) and 15 (nitrogen group) valence 3; elements in group 14 (carbon group) valence 4.

## Valence versus oxidation state

Because of the ambiguity of the term valence,[3] nowadays other notations are used in practice. Beside the system of oxidation numbers as used in Stock nomenclature for coordination compounds,[7] and the lambda notation, as used in the IUPAC nomenclature of inorganic chemistry,[8] "oxidation state" is a more clear indication of the electronic state of atoms in a molecule.

The "oxidation state" of an atom in a molecule gives the number of valence electrons it has gained or lost.[9] In contrast to the valency number, the oxidation state can be positive (for an electropositive atom) or negative (for an electronegative atom).

Elements in a high oxidation state can have a valence larger than four. For example, in perchlorates, chlorine has seven valence bonds and ruthenium, in the +8 oxidation state in ruthenium(VIII) tetroxide, has even eight valence bonds.

## "Maximum number of bonds" definition

The International Union of Pure and Applied Chemistry (IUPAC) has made several attempts to arrive at an unambiguous definition of valence. The current version, adopted in 1994,[10]:

The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an atom of the element under consideration, or with a fragment, or for which an atom of this element can be substituted.[2]

Hydrogen and chlorine were originally used as examples of univalent atoms, because of their nature to form only one single bond. Hydrogen has only one valence electron and can form only one bond with an atom that has an incomplete outer shell. Chlorine has seven valence electrons and can form only one bond with an atom that donates a valence electron to complete chlorine's outer shell. However, chlorine can also have oxidation states from +1 to +7 and can form more than one bond by donating valence electrons.

Although hydrogen has only one valence electron, it can form bonds with more than one atom in hypervalent bonds. In the bifluoride ion ([HF2]), for example, it forms a three-center four-electron bond with two fluoride atoms: $[\ F \frac{\quad}{\quad} H\ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}\!H \frac{\quad}{\quad} F\ ]$

Another example is the Three-center two-electron bond in diborane (B2H6).

## Examples

(valencies according to the number of valence bonds definition and conform oxidation states)

COMPOUND FORMULA VALENCE OXIDATION STATE
Hydrogen chloride HCl H=1   Cl=1 H=+1   Cl=−1
Chlorine Cl2 Cl=1   Cl=1 Cl=+1   Cl=−1
Perchlorate * HClO4 H=1   Cl=7   O=2 H=+1   Cl=+7   O=−2
Sodium hydride NaH Na=1   H=1 Na=+1   H=−1
Ferrous oxide ** FeO Fe=2   O=2 Fe=+2   O=−2
Ferric oxide ** Fe2O3 Fe=3   O=2 Fe=+3   O=−2

* The univalent perchlorate ion (ClO4) has valence 1.
** Iron oxide appears in a crystal structure, so no typical molecule can be identified.
In ferrous oxide, Fe has oxidation number II, in ferric oxide, oxidation number III.

## Maximum valences of the elements

Maximum valences for the elements are based on the data from list of oxidation states of the elements.

Maximum valences of the elements
Group → 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
↓ Period
1 1
H
2
He
2 3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
3 11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
4 19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
28
Ni
29
Cu
30
Zn
31
Ga
32
Ge
33
As
34
Se
35
Br
36
Kr
5 37
Rb
38
Sr
39
Y
40
Zr
41
Nb
42
Mo
43
Tc
44
Ru
45
Rh
46
Pd
47
Ag
48
Cd
49
In
50
Sn
51
Sb
52
Te
53
I
54
Xe
6 55
Cs
56
Ba
*
72
Hf
73
Ta
74
W
75
Re
76
Os
77
Ir
78
Pt
79
Au
80
Hg
81
Tl
82
Pb
83
Bi
84
Po
85
At
86
Rn
7 87
Fr
88
Ra
**
104
Rf
105
Db
106
Sg
107
Bh
108
Hs
109
Mt
110
Ds
111
Rg
112
Cn
113
Uut
114
Fl
115
Uup
116
Lv
117
Uus
118
Uuo

* Lanthanides  57
La
58
Ce
59
Pr
60
Nd
61
Pm
62
Sm
63
Eu
64
Gd
65
Tb
66
Dy
67
Ho
68
Er
69
Tm
70
Yb
71
Lu
** Actinides  89
Ac
90
Th
91
Pa
92
U
93
Np
94
Pu
95
Am
96
Cm
97
Bk
98
Cf
99
Es
100
Fm
101
Md
102
No
103
Lr
Maximum valences are based on the List of oxidation states of the elements

Maximum valences of chemical elements

Zero      One       Two       Three     Four      Five      Six       Seven     Eight     Unknown

black=Solid (at standard conditions: 0 °C and 1 atm):

## References

1. ^ Note: A valence bond (or bonding equivalent) is a covalent or ionic bond, formed by the interaction of two bonding electrons.
2. ^ a b IUPAC Gold Book definition: valence
3. ^ a b The Free Dictionary: valence
4. ^ Valence - Online Etymology Dictionary.
5. ^ a b Partington, J.R. (1989). A Short History of Chemistry. Dover Publications, Inc. ISBN 0-486-65977-1.
6. ^ Frankland, E. (1852). Phil. Trans., vol. cxlii, 417.
7. ^ IUPAC, Gold Book definition: oxidation number
8. ^ IUPAC, Gold Book definition: lambda
9. ^ IUPAC Gold Book definition: oxidation state
10. ^ Pure Appl. Chem. 66: 1175 (1994).

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# Estimating P-values from simulations

You might need: Calculator

## Problem

An employee at an aquarium monitors how much their sea otters eat. The amount of food a particular otter eats daily is approximately normally distributed with a mean of 17 pounds and a standard deviation of 1 pound. They suspected this otter was not eating enough, so they took a random sample n, equals, 10 days and observed a sample mean of x, with, \bar, on top, equals, 16, point, 5 pounds of food per day.
To see how likely a sample like this was to occur by random chance alone, the employee performed a simulation. They simulated 40 samples of n, equals, 10 values from a normal population with a mean of 17 pounds and a standard deviation of 1 pound. They recorded the mean of the values in each sample. Here are the sample means from their 40 samples:
They want to test H, start subscript, 0, end subscript, colon, mu, equals, 17, start text, space, l, b, s, end text vs. H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 17, start text, space, l, b, s, end text where mu is the true mean amount of food per day.
Based on these simulated results, what is the approximate p-value of the test?
Note: The sample result was x, with, \bar, on top, equals, 16, point, 5, start text, space, l, b, s, end text.


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# How are reflexive verbs used?

Sep 5, 2017

A reflexive verb is a verb which is used in a structure where the object (possibly implied) is identical to the subject.

#### Explanation:

Note that a reflexive verb is always transitive (with a subject and an object), although (especially in English) the object may be implied.

Here is an example:
$\textcolor{w h i t e}{\text{XXXX}}$The acrobat balanced on a high wire.
or (with the object may explicit)
$\textcolor{w h i t e}{\text{XXXX}}$The acrobat balanced himself on a high wire.

Sep 5, 2017

A reflexive "verb" is really a verb used with a reflexive pronoun. It "reflects" the action from the subject to the direct object.

#### Explanation:

We use a reflexive pronoun after a transitive verb (see Clauses, Sentences and Phrases) when the direct object is the same as the subject of the verb:

I am teaching myself to play the piano.
Be careful with that knife. You might cut yourself .

These are the verbs most often found with reflexive pronouns:
cut
dry
enjoy
hurt
introduce
kill
prepare
see or saw
teach

https://learnenglish.britishcouncil.org/en/english-grammar/verbs/reflexive-and-ergative-verbs


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Economics » Perfect Competition » How Perfectly Competitive Firms Make Output Decisions

# Determining the Highest Profit by Comparing Total Revenue and Total Cost

## Determining the Highest Profit by Comparing Total Revenue and Total Cost

A perfectly competitive firm can sell as large a quantity as it wishes, as long as it accepts the prevailing market price. Total revenue is going to increase as the firm sells more, depending on the price of the product and the number of units sold. If you increase the number of units sold at a given price, then total revenue will increase. If the price of the product increases for every unit sold, then total revenue also increases. As an example of how a perfectly competitive firm decides what quantity to produce, consider the case of a small farmer who produces raspberries and sells them frozen for $4 per pack. Sales of one pack of raspberries will bring in$4, two packs will be $8, three packs will be$12, and so on. If, for example, the price of frozen raspberries doubles to $8 per pack, then sales of one pack of raspberries will be$8, two packs will be $16, three packs will be$24, and so on.

Total revenue and total costs for the raspberry farm, broken down into fixed and variable costs, are shown in the table below and also appear in this figure. The horizontal axis shows the quantity of frozen raspberries produced in packs; the vertical axis shows both total revenue and total costs, measured in dollars. The total cost curve intersects with the vertical axis at a value that shows the level of fixed costs, and then slopes upward. All these cost curves follow the same characteristics as the curves covered in the Cost and Industry Structure tutorial.

Total Cost and Total Revenue at the Raspberry Farm

Total revenue for a perfectly competitive firm is a straight line sloping up. The slope is equal to the price of the good. Total cost also slopes up, but with some curvature. At higher levels of output, total cost begins to slope upward more steeply because of diminishing marginal returns. The maximum profit will occur at the quantity where the gap of total revenue over total cost is largest.

Total Cost and Total Revenue at the Raspberry Farm

Quantity
(Q)
Total Cost
(TC)
Fixed Cost
(FC)
Variable Cost
(VC)
Total Revenue
(TR)
Profit
0$62$62$0−$62
10$90$62$28$40−$50 20$110$62$48$80−$30
30$126$62$64$120−$6 40$144$62$82$160$16
50$166$62$104$200$34 60$192$62$130$240$48
70$224$62$162$280$56 80$264$62$202$320$56
90$324$62$262$360$36 100$404$62$342$400−$4

Based on its total revenue and total cost curves, a perfectly competitive firm like the raspberry farm can calculate the quantity of output that will provide the highest level of profit. At any given quantity, total revenue minus total cost will equal profit. One way to determine the most profitable quantity to produce is to see at what quantity total revenue exceeds total cost by the largest amount. On this figure, the vertical gap between total revenue and total cost represents either profit (if total revenues are greater that total costs at a certain quantity) or losses (if total costs are greater that total revenues at a certain quantity). In this example, total costs will exceed total revenues at output levels from 0 to 40, and so over this range of output, the firm will be making losses. At output levels from 50 to 80, total revenues exceed total costs, so the firm is earning profits. But then at an output of 90 or 100, total costs again exceed total revenues and the firm is making losses. Total profits appear in the final column of the table above. The highest total profits in the table, as in the figure that is based on the table values, occur at an output of 70–80, when profits will be \$56.

A higher price would mean that total revenue would be higher for every quantity sold. A lower price would mean that total revenue would be lower for every quantity sold. What happens if the price drops low enough so that the total revenue line is completely below the total cost curve; that is, at every level of output, total costs are higher than total revenues? In this instance, the best the firm can do is to suffer losses. But a profit-maximizing firm will prefer the quantity of output where total revenues come closest to total costs and thus where the losses are smallest.

(Later we will see that sometimes it will make sense for the firm to shutdown, rather than stay in operation producing output.)


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# Why does helium balloon goes high up in the sky ater immediately releasing it? whereas if any other gas is filled inside the balloon, it does not do so

Nov 19, 2016

For the same reason that a boat floats on water, or oil floats on vinegar. There is a net buoyant force upwards.

#### Explanation:

You could have filled the balloon with dihydrogen gas, which would have half the mass of a helium-filled balloon of equivalent size. If the volume of air displaced by the balloon has more mass than the mass of gas inside the balloon, PLUS the mass of the balloon itself, then the balloon will float inasmuch there is a net buoyant force.

This goes back to old Archimedes' principle:

$\text{Any object, wholly or partially immersed in a fluid,}$
$\text{is buoyed up by a force equal to the weight of the fluid}$ $\text{displaced by the object.}$

So here's a chemistry question to go with the physics. Why should a helium filled balloon or dirigible be preferred to a hydrogen-filled balloon given that the mass of the hydrogen is HALF that of the helium? Note also that since the dihydrogen molecule is LARGER than the helium atom, we would need a less specialized membrane with which to construct the balloon.