text:
# Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe

@article{Murphy2008StrongLO,
title={Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe},
author={Michael T. Murphy and Victor V. Flambaum and S{\'e}bastien Muller and Christian Henkel},
journal={Science},
year={2008},
volume={320},
pages={1611 - 1613}
}
• Published 18 June 2008
• Physics
• Science
The Standard Model of particle physics assumes that the so-called fundamental constants are universal and unchanging. Absorption lines arising in molecular clouds along quasar sightlines offer a precise test for variations in the proton-to-electron mass ratio, μ, over cosmological time and distance scales. The inversion transitions of ammonia are particularly sensitive to μ as compared to molecular rotational transitions. Comparing the available ammonia spectra observed toward the quasar B0218…
135 Citations
Does the proton-to-electron mass ratio vary on cosmological scales?
We report a strong constraint on the variation of the proton-to-electron mass ratio on a cosmological time scale from the analysis of molecular absorption lines in a quasar spectrum. A possible
A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe
• Physics
Science
• 2013
An improved limit on the possible timevariation of the proton-to-electron mass ratio is set by comparing the frequencies of methanol transitions observed in a galaxy at a look-back time of 7 billion years with those measured in the laboratory, consistent with no variation over cosmic time.
New Limit on Space-Time Variations in the Proton-to-Electron Mass Ratio from Analysis of Quasar J110325-264515 Spectra
Astrophysical tests of current values for dimensionless constants known on Earth, such as the fine-structure constant, α, and proton-to-electron mass ratio, μ = mp/me, are communicated using data
Constraint on a varying proton-to-electron mass ratio from molecular hydrogen absorption towards quasar SDSS J123714.60+064759.5
• Physics
• 2015
Molecular hydrogen transitions in the sub-damped Lyman alpha absorber at redshift z = 2.69, toward the background quasar SDSS J123714.60+064759.5, were analyzed in order to search for a possible
Keck Telescope Constraint on Cosmological Variation of the Proton-to-Electron Mass Ratio
• Physics
• 2010
Molecular transitions recently discovered at redshift z(abs) = 2.059 towards the bright background quasar J2123-0050 are analysed to limit cosmological variation in the proton-to-electron mass ratio,
New constraint on cosmological variation of the proton-to-electron mass ratio from Q0528−250
• Physics
• 2011
Molecular hydrogen transitions in quasar spectra can be used to constrain variation in the proton-to-electron mass ratio, μ ≡ mp/me, at high redshifts (z 2). We present here an analysis of a new
AN OBSERVATIONAL DETERMINATION OF THE PROTON TO ELECTRON MASS RATIO IN THE EARLY UNIVERSE
• Physics
Proceedings of the International Astronomical Union
• 2009
In an effort to resolve the discrepancy between two measurements of the fundamental constant μ, the proton to electron mass ratio, at early times in the universe we reanalyze the same data used in
Potential microwave probes of the proton-to-electron mass ratio at very high redshifts
• Physics
• 2014
Recently a stringent constraint on the change in the proton-to-electron mass ratio at a redshift of 0.89 has been established using theoretical predictions and radio observations of the methanol
Constraint on a varying proton-electron mass ratio 1.5 billion years after the big bang.
• Physics
Physical review letters
• 2015
A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10% of the age of the Universe today, is analyzed to put a constraint on a varying proton-electron mass ratio, μ, yielding a limit on the relative deviation from the current laboratory value.

## References

SHOWING 1-10 OF 48 REFERENCES
The kinetic temperature of a molecular cloud at redshift 0.7: ammonia in the gravitational lens B0218+357
Context. Little is known about the structure of the interstellar medium and the nature of individual clouds in galaxies at intermediate redshifts. The gravitational lens toward PKS 1830–211 offers
Astronomical constraints on the cosmic evolution of the fine structure constant and possible quantum dimensions.
• Physics
Physical review letters
• 2000
Measurements of absorption by the 21 cm hyperfine transition of neutral hydrogen toward radio sources at substantial look-back times are presented to set limits on the evolution of the fine structure constant.
Constraining variations in the fine-structure constant, quark masses and the strong interaction
• Physics
• 2003
We present evidence for variations in the fine-structure constant from Keck/HIRES spectra of 143 quasar absorption systems over the redshift range 0.2 1.8). Our most robust estimate is a weighted
Indication of a cosmological variation of the proton-electron mass ratio based on laboratory measurement and reanalysis of H2 spectra.
• Physics
Physical review letters
• 2006
A new set of sensitivity coefficients K(i) is derived for all lines in the H2 spectrum, representing the dependence of their transition wavelengths on a possible variation of the proton-electron mass ratio mu, indicating that mu could have decreased in the past 12 Gyr.
Limit on the cosmological variation of mp/me from the inversion spectrum of ammonia.
• Physics
Physical review letters
• 2007
We obtain the limit on the space-time variation of the ratio of the proton mass to the electron mass, mu=m(p)/m(e), based on comparison of quasar absorption spectra of NH3 with CO, HCO+ and HCN
A new constraint on the time dependence of the proton-to-electron mass ratio - Analysis of the Q 0347-383 and Q 0405-443 spectra
• Physics
• 2005
A new limit on the possible cosmological variation of the proton-to-electron mass ratio $\mu=m_{\rm p}/m_{\rm e}$ is estimated by measuring wavelengths of H 2 lines of Lyman and Werner bands from two
Probing the cosmological variation of the fine - structure constant: Results based on VLT - UVES sample
• Physics
• 2004
Development of fundamental physics relies on the constancy of various fundamental quantities such as the fine- structure constant. Detecting or constraining the possible time variations of these
Redshifted formaldehyde from the gravitational lens B0218+357
• Physics
• 2007
Context. Little is known about individual molecular clouds at high redshifts. The gravitational lens toward B0218+357 offers the unique possibility to study cool moderately dense gas with high
Neutral hydrogen 21 centimeter absorption at Z = 0.6847 toward the 'smallest Einstein ring'
• Physics
• 1993
We detect neutral hydrogen 21 cm absorption toward the smallest Einstein ring, 0218+357, at a redshift of 0.6847. The implied H I column density is N(H I)=4×10 18 (T s /f) cm −2 , where T s is the
Formaldehyde Absorption at z=0.685 toward the
• Physics
• 1996
We report VLA observations of absorption in the 211 → 212 transition of formaldehyde (H2CO) at a redshift of 0.68466 toward the Einstein ring gravitational lens system B0218+357. We observe the H2CO


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# How do you combine  (–2x^4 – 3x^2) – (–9x^2 + 4x – 4) ?

Apr 29, 2015

You can only "combine" terms where the $x$ components are raised to the same exponent.
In this case only the $- 3 {x}^{2}$ and the $- 9 {x}^{2}$ can be combined

$\left(- 2 {x}^{4} - 3 {x}^{2}\right) - \left(- 9 {x}^{2} + 4 x - 4\right)$

$= - 2 {x}^{4} - 3 {x}^{2} + 9 {x}^{2} - 4 x + 4$

$= 2 {x}^{4} + 6 {x}^{2} - 4 x + 4$

This could be simplified, but I assume that is not part of your question.

format: plain


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Connect with us

# CBD Hemp Prices are Slipping as US is Producing 8X Over Demand, is a Price Crash Imminent?

Published

on

• Farmers have overplanted their crops, amounting to about 180 million pounds.
• Prices for hemp will likely crash for about 18 months, starting in October.

The legalization of hemp with the Farm Bill last year was important for the CBD industry. However, a massive number of farmers have leapt to the challenge of getting involved at the ground level of hemp’s legalization. Anyone presently farming hemp may need to worry about exactly what their future will hold, as a recent article popped up on Yahoo Finance that explained an overabundance of hemp has entered the market.

As a reasonable estimate on the US market’s use of CBD, the public could potentially consume 22.5 million pounds of 10% CBD Hemp annually. However, the present amount of hemp being grown is about 180 million pounds, exceeding the needs of the public by eight times over.

To explain the dire situation, a little math is necessary. The numbers appear to be rough estimates, based on the assumption that half of the US residents (327 million people) consumed a total of 10mg CBD per day, which would add up to 596,775 kg yearly, which is still fairly high.

Presently, based on data from HempBenchmarks.com, hemp farming has 400,0000 acres allotted for permitted land. If 30% of the allotted acreage was planted, that would amount to 120,000 acres. If each acre creates 1,500 pounds (which is a conservative estimate), then the acres would ultimately yield 180 million pounds of biomass. Considering that lb. essentially amounts to 0.026 kg of isolate, the total isolate yielded from 180 million pounds of biomass would amount to 4.7 million kg of isolate.

To keep up with the processing necessary to extract that much isolate, the industry would need to have a capacity that can process 500,000 pounds every day for a whole year. As a result, by having far too much raw material, the price would have to drop, which is incredibly worrisome for hemp farms.

While the average price is $3.94 right now, the current purchases may drop down to$2.30 before harvest season, which is due to early harvests. Still, it looks like the price will reach a bad level by October 1st but remember – this isn’t the first time that these kinds of problems have happened in the hemp and cannabis industry.

It actually happened in Washington and Oregon, starting with sudden legalization. When the demand immediately increases, prices spike when the supply becomes limited. To meet the demands, the farms raise capital and increase production, but none of the other farms know exactly how much other farmers are creating. As soon as the harvest occurs, the price ended up dropping, and farms end up losing business.

Realistically, if the history in the market shows any indication of what’s to come, it is likely that the price crash will only last for about a year and a half. However, in these specific states, the crash lasts for more like three years. The only reason that stabilization of prices takes as long as it does is due to the fact that it takes a couple of years to grow enough to dig out of the hole that they ended up in.

Brands with distribution primarily have the power in the market, but the next change that the market needs to prepare for is the wholesale input prices will crash.


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# [CEA] Extending the halo mass resolution of $N$-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.

Date added: Wed, 16 Oct 13


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# Does Michio Kaku agree with Lawrence Krauss' concept of nothingness?

## Main Question or Discussion Point

Michio Kaku and Lawrence Krauss are both well-renowned physicists who propose that the universe (or universes) was generated out of nothing.

Krauss, in his book "A Universe from Nothing" argued that the universe was probably created by a primordial "nothingness" with no space and time and composed by quantum fields and vacua of virtual particles and fluctuations. But, of course, this is not a true nothingness, so he also considers the possibility that everything was created somehow from truly nothingness (with no space, time, energy, vacua, quantum laws, or any kind of physical or even mathematical or logical laws).

However, although Kaku and Krauss have worked together and Kaku also wrote a book where he proposed that everything originated from nothingness, I have not seen any single comment from Kaku mentioning Krauss' book.

So, basically my question is, does Kaku also considers that the universe (or universes) could have been originated by true nothingness (as Krauss does)?

Creation is before time. There is no way to conclude anything about $t\leq 0$. In order to gain information, there must exist something which requires a positive time. Hence the proposed answer has to be pure speculation and belongs into the field of faith and philosophy. Whether or not they share an opinion on something which cannot be decided is meaningless.


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# How to Work Out Meters Squared?

A meter square is calculated by multiplying the length of a square and its width. This will give out a total area of an enclosed square. These measurements are derived at by measuring the length of a square and also its width.
Working out square meters (also known as area of a shape) is dependent on shapes of objects. To calculate the square meters/ area of a circle, multiply the radius squared by Pi. To calculate the area of a square or rectangle, multiply its length by its width.
To work out a square metre, multiply the length and width of that area in metres, its symbol is m2. It is derived from the SI base unit of metre, which is defined as the length travelled by light in absolute vacuum during a time interval of 1/299,792,458 of the second.
Working out square meters (also known as area of a shape) is dependent on shapes of objects. To calculate the square meters/ area of a circle, multiply the radius squared by Pi.To calculate the area of a square or rectangle multiply its length by its width.
To work out metres squared of a given area, you need the measurements for the area that you want to measure. For a rectangle, you need the length and width, while for a circle you need the radius. Apply a formula that is used for the given area. For a list of the formulae, visit: http://www.ask.com/wiki/Area
To work out square metres simply get the length and the width. Simply multiply them together to get the square metres. This formula is used for rectangular shapes.
To work out a square metre, you need to find the value of the length and the width. After getting these values, you can now multiply them together to get the answer. Example: Length is = 10, Width is = 10. 10x10=100. The square metre value is 100.
To work out metres squared, you should first measure the length and width of your figure. When measured, multiply them together and you will get the answer for metres squared.
Finding out how many square meters something is requires a formula that is fairly simple. You would determine the length of your area multiply it by the width. Your result will be your square meters.
Q&A Related to "How to Work Out Meters Squared?"
 A square meter is a section of area whose length and width both measure out to one meter long. This is the basic unit of area in the metric system. http://answers.ask.com/Reference/Other/what_is_a_s...
 1. Multiply the length by the width to calculate the area in square meters. For example, if a field measures 120 by 80 meters, its area is 120 * 80 = 9,600 square meters. 2. Multiply http://www.ehow.com/how_7385587_convert-square-met...
 1. Measure the length and width of the area or object you're calculating square meters for. Make your measurements in meters if possible. 2. Convert the measurements to meters, if http://www.wikihow.com/Calculate-Square-Meters
 100 square meters is an amount of surface area. The area can have any shape. To give you an idea of its size, any of the following has an area of 100 square meters: a square, 10 meters http://wiki.answers.com/Q/What_is_a_100_square_met...
Top Related Searches
Explore this Topic
To work out the square meter normally involves multiplying the length of a regular polygon with four sides and angles by its width. The square metre is an international ...
One square metre is equal to 100 cm x 100 cm or 1 m x 1m. To calculate areas in square metres, measure the width and the length in metres and multiply the two ...
To work out a square meter ,simply use this formula: Length (L) multiplied by Width (W). Once you multiply the length by the width you will have the square meters ...


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# A simple and fast algorithm for computing exponentials of power series

@article{Bostan2009ASA,
title={A simple and fast algorithm for computing exponentials of power series},
author={Alin Bostan and {\'E}ric Schost},
journal={ArXiv},
year={2009},
volume={abs/1301.5804}
}
• Published 1 June 2009
• Computer Science
• ArXiv

## Figures from this paper

Fast algorithms for elementary operations on complex power series
Abstract It is shown that the inversion of a complex-valued power series can be realised asymptotically with complexity of 5/4 multiplications (if we compare the upper bounds). It is shown that the
Homotopy techniques for multiplication modulo triangular sets
• Mathematics, Computer Science
J. Symb. Comput.
• 2011
Homotopy techniques for multiplication modulo triangular sets ( Spine
• Computer Science, Mathematics
• 2009
This thesis obtains a quasi-linear time complexity for substantial families of examples, for which no such result was known before, and proposes an algorithm that relies on homotopy and fast evaluation-interpolation techniques.
Complete Fast Analytical Solution of the Optimal Odd Single-Phase Multilevel Problem
• Computer Science, Mathematics
IEEE Transactions on Industrial Electronics
• 2010
A new general modulation strategy for ML inverters is introduced, which takes an analytic form and is very fast, with a complexity of only O(n log2 n) arithmetic operations, where n is the number of controlled harmonics.
Counting Matrices that are Squares
On the math-fun mailing list (7 May 2013), Neil Sloane asked to calculate the number of $n \times n$ matrices with entries in $\{0,1\}$ which are squares of other such matrices. In this paper we
Single-phase optimal Odd PWM problem
• Computer Science
2008 34th Annual Conference of IEEE Industrial Electronics
• 2008
An exact and fast algorithm with the complexity of only O(n log2 n) arithmetic operations is introduced for computation of optimal switching angles of a odd PWM waveform for generating general odd symmetric waveforms.

## References

SHOWING 1-10 OF 14 REFERENCES
The truncated fourier transform and applications
A truncated version of the classical Fast Fourier Transform that has the nice property of eliminating the "jumps" in the complexity at powers of two and gains a logarithmic factor with respect to the best previously known algorithms.
Fast Algorithms for Manipulating Formal Power Series
• Mathematics
JACM
• 1978
This paper shows that the composition and reversion problems are equivalent (up to constant factors), and gives algorithms which require only order (n log n) ~/2 operations in many cases of practical importance.
Modern computer algebra
This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
Modern Computer Algebra
• Computer Science
• 1998
This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
Relax, but Don't be Too Lazy
This paper surveys several classical and new zealous algorithms for manipulating formal power series, including algorithms for multiplication, division, resolution of differential equations, composition and reversion, and gives various relaxed algorithms for these operations.
Removing redundancy in high-precision
• Newton iteration,
• 2004
REMOVING REDUNDANCY IN HIGH-PRECISION NEWTON ITERATION
This paper presents new algorithms for several high-precision operations in the power series ring C[[x]]. Compared to computing n coefficients of a product in C[[x]], computing n coefficients of a


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COMPREHENSIVE CAPITAL BUDGETING PROJECT
A comprehensive capital budgeting project will be due at the end of this module.
Assignment: You are interested in proposing a new venture to the management of your company. Pertinent financial information is given below.
BALANCE SHEET

Cash 2,000,000
Accounts Receivable 28,000,000
Net Fixed Assets 133,000,000
Inventories 42,000,000
Total Assets 205,000,000

Accounts Payable and Accruals 18,000,000
Long-Term Debt 60,000,000
Notes Payable 40,000,000
Preferred Stock 10,000,000
Common Equity 77,000,000
Total Claims 205,000,000

Last year's sales were $225,000,000. • The company has 60,000 bonds with a 30-year life outstanding, with 15 years until maturity. The bonds carry a 10 percent semi-annual coupon, and are currently selling for$874.78.
• You also have 100,000 shares of $100 par, 9% dividend perpetual preferred stock outstanding. The current market price is$90.00. Any new issues of preferred stock would incur a 3.33% per share flotation cost.
• The company has 10 million shares of common stock outstanding with a current price of $14.00 per share. The stock exhibits a constant growth rate of 10 percent. The last dividend (D0) was$.80. New stock could be sold with flotation costs of 15 percent.
• The risk-free rate is currently 6 percent, and the rate of return on the stock market as a whole is 14 percent. Your stock's beta is 1.22.
• Stockholders require a risk premium of 5 percent above the return on the firms bonds.
• The firm expects to have additional retained earnings of $10 million in the coming year, and expects depreciation expenses of$35 million.
• Your firm does not use notes payable for long-term financing.
• The firm considers its current market value capital structure to be optimal, and wishes to maintain that structure. (Hint: Examine the market value of the firm's capital structure, rather than its book value when determining the weights in the WACC calculations.)
• The firm's management requires a 2% adjustment to the cost of capital for risky projects.
• Your firm's federal state marginal tax rate is 40%.
• The firm has the following investment opportunities currently available in addition to the venture that you are proposing:
Project Cost IRR
A 10,000,000 20%
B 20,000,000 18%
C 15,000,000 14%
D 30,000,000 12%
E 25,000,000 10%
Your venture would consist of a new product introduction (You should label your venture as Project I, for \introduction.). You estimate that your product will have a six-year life span, and the equipment used to manufacture the project falls into the MACRS 5-year class. Your venture would require a capital investment of $15,000,000 in equipment, plus$2,000,000 in installation costs. The venture would also require an initial investment in accounts receivable and inventories of $4,000,000. At the end of the six-year life span of the venture, you estimate that the equipment could be sold at a$4,000,000 salvage value.
Your venture, which management considers risky, would increase fixed costs by a constant $1,000,000 per year, while the variable costs of the venture would equal 30 percent of revenues. You are projecting that revenues generated by the project would equal$5,000,000 in year 1, $10,000,000 in year 2,$14,000,000 in year 3, $16,000,000 in year 4,$12,000,000 in year 5, and \$8,000,000 in year 6.
The following list of steps provides a structure that you should use in analyzing your new venture.
Note: Carry all final calculations to two decimal places.
Phase 1
1. Find the costs of the individual capital components (12 points): a. Long-term debt b. Preferred stock c. Retained earnings (avg. Of CAPM, DCF, & bond yield risk premium approaches) d. New common stock
2. Determine the target percentages (weights) for the optimal capital structure. (Carry weights to four decimal places. For example: 0.2973 or 29.73%) (3 points)
3. Compute the retained earnings break point. (3 points)
4. Draw the MCC schedule, including depreciation-generated funds in the schedule. (7 points)
Phase 2
5. Compute the Year 0 investment for Project I. (3 points)
6. Compute the annual operating cash flows for years 1-6 of the project. (12 points)
7. Compute the non-operating (end-of-project) cash flows at the end of year 6. (3 points)
8. Draw a timeline that summarizes all of the cash flows for your venture. (3 points)
Note: You may complete #5-8 in an Excel spreadsheet or calculate these manually.
Phase 3
9. Compute the IRR and payback period for Project I. (10 points)
10. Draw the IOS schedule, including Project I along with Projects A-E. (4 points)
11. Determine your firm's corporate cost of capital. (5 points)
12. Compute the discounted payback and NPV for Project I at the risk-adjusted cost of capital for project I. (10 points)
13. Indicate which projects should be accepted, and why. (10 points)
14. Would your answer be different if the project I was determined to be of average risk? Explain. (5 points)
Phase 4
15. Summarize your findings and recommendations in a brief (1-2 page) memo to the President of the firm. (10 points)
16. Conclude the project with your reflections on what you have learned from this course and how it has affected your view of your own job and career.


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# zbMATH — the first resource for mathematics

## Roe, Philip L.

Compute Distance To:
 Author ID: roe.philip-l Published as: Roe, P.; Roe, P. L.; Roe, Philip; Roe, Philip L.
 Documents Indexed: 77 Publications since 1968, including 1 Book
all top 5

#### Co-Authors

 25 single-authored 6 Arora, Mohit 4 van Leer, Bram 3 Deconinck, Heline 3 Gombosi, Tamas I. 3 Hittinger, Jeffrey A. F. 3 Karni, Smadar 3 Paillère, Henri 3 Powell, Kenneth Grant 2 Carette, J.-C. 2 Deconinck, Herman 2 Linde, Timur J. 2 Lowrie, Robert B. 2 Mazaheri, Karim 2 Myong, Rho-Shin 2 Nishikawa, Hiroaki 2 Pike, John 2 Starinshak, David P. 2 Struijs, R. 1 Abgrall, Rémi 1 Baines, Mike J. 1 Balsara, Dinshaw S. 1 Barlow, Andrew J. 1 Barsukow, Wasilij 1 Brown, Shawn L. 1 Clarke, John F. 1 De Zeeuw, Darren L. 1 Dezeeuw, D. L. 1 Einfeldt, Bernd 1 Fidkowski, Krzysztof J. 1 Groth, Clinton P. T. 1 Hohm, Jonathan 1 Hubbard, Matthew E. 1 Ismail, Farzad 1 Jones, J. G. 1 Klingenberg, Christian 1 Lee, Wen-Tzong 1 Linda, Timur 1 Moore, Kayran C. 1 Morton, Bill 1 Morton, Keith William 1 Müller, Jens-Dominik 1 Munz, Claus-Dieter 1 Pike, James 1 Quirk, James J. 1 Rad, Mani 1 Rumsey, Christopher L. 1 Sidilkover, David 1 Simmonds, L. G. 1 Sjogreen, Bjorn 1 Tai, Chang-Hsien 1 Toro, Eleuterio F. 1 Tóth, Gyula I. 1 Zaide, Daniel W.
all top 5

#### Serials

 15 Journal of Computational Physics 6 Computers and Fluids 5 International Journal for Numerical Methods in Fluids 4 Journal of Scientific Computing 3 SIAM Journal on Scientific Computing 2 Numerical Methods for Partial Differential Equations 1 AIAA Journal 1 Ingenieur-Archiv 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 SIAM Journal on Numerical Analysis 1 SIAM Journal on Scientific and Statistical Computing 1 Communications in Applied Numerical Methods 1 Computational Mechanics 1 SIAM Journal on Applied Mathematics 1 International Journal of Computational Fluid Dynamics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Communications in Computational Physics 1 The College Mathematics Journal
all top 5

#### Fields

 60 Fluid mechanics (76-XX) 32 Numerical analysis (65-XX) 22 Partial differential equations (35-XX) 2 History and biography (01-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

69 Publications have been cited 2,991 times in 2,305 Documents Cited by Year
Approximate Riemann solvers, parameter vectors, and difference schemes. Zbl 0474.65066
Roe, P. L.
1981
On Godunov-type methods near low densities. Zbl 0709.76102
Einfeldt, B.; Munz, C. D.; Roe, P. L.; Sjögreen, B.
1991
Characteristic-based schemes for the Euler equations. Zbl 0624.76093
Roe, P. L.
1986
A solution-adaptive upwind scheme for ideal magnetohydrodynamics. Zbl 0952.76045
Powell, Kenneth G.; Roe, Philip L.; Linde, Timur J.; Gombosi, Tamas I.; De Zeeuw, Darren L.
1999
Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks. Zbl 1280.76015
2009
High-order fluctuation schemes on triangular meshes. Zbl 1068.65133
Abgrall, R.; Roe, P. L.
2003
Notes on the eigensystem of magnetohydrodynamics. Zbl 0845.35092
Roe, P. L.; Balsara, D. S.
1996
A multidimensional generalization of Roe’s flux difference splitter for the Euler equations. Zbl 0790.76054
Deconinck, H.; Roe, P. L.; Struijs, R.
1993
Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. Zbl 0587.76126
Roe, Philip L.
1986
Optimum positive linear schemes for advection in two and three dimensions. Zbl 0765.65093
Roe, P. L.; Sidilkover, D.
1992
On postshock oscillations due to shock capturing schemes in unsteady flows. Zbl 0869.76050
Arora, Mohit; Roe, Philip L.
1997
Some contributions to the modelling of discontinuous flows. Zbl 0665.76072
Roe, Philip L.
1985
Approximate Riemann solvers, parameter vectors, and difference schemes. (Reprint). Zbl 0890.65094
Roe, P. L.
1997
Upwind differencing schemes for hyperbolic conservation laws with source terms. Zbl 0626.65086
Roe, P. L.
1987
Fluctuations and signals - A framework for numerical evolution problems. Zbl 0569.76072
Roe, P. L.
1982
A well-behaved TVD limiter for high-resolution calculations of unsteady flow. Zbl 0878.76045
Arora, Mohit; Roe, Philip L.
1997
Efficient construction and utilisation of approximate Riemann solutions. Zbl 0558.76001
Roe, P. L.; Pike, J.
1984
Vorticity-preserving Lax-Wendroff-type schemes for the system wave equation. Zbl 0994.35011
Morton, K. W.; Roe, P. L.
2001
Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws. Zbl 0771.76048
Deconinck, H.; Paillère, H.; Struijs, R.; Roe, P. L.
1993
An upwind scheme for magnetohydrodynamics. Zbl 0900.76344
Powell, K. G.; Roe, P. L.; Myong, R. S.; Gombosi, T.; de Zeeuw, D.
1995
Compact high-resolution algorithms for time-dependent advection on unstructured grids. Zbl 0985.76064
Hubbard, M. E.; Roe, P. L.
2000
Algorithms for advection and shock problems. Zbl 0482.76008
Roe, P. L.; Baines, M. J.
1982
A cell centred Lagrangian Godunov scheme for shock hydrodynamics. Zbl 1431.76006
Barlow, A. J.; Roe, P. L.
2011
An entropy adjoint approach to mesh refinement. Zbl 1213.65142
Fidkowski, Krzysztof J.; Roe, Philip L.
2010
Numerical computation of two-dimensional unsteady detonation waves in high energy solids. Zbl 0770.76040
Clarke, J. F.; Karni, S.; Quirk, J. J.; Roe, P. L.; Simmonds, L. G.; Toro, E. F.
1993
Sonic flux formulae. Zbl 0747.65073
Roe, P. L.
1992
A frontal approach for internal node generation in Delaunay triangulations. Zbl 0780.76064
Müller, J.-D.; Roe, P. L.; Deconinck, H.
1993
A multidimensional flux function with applications to the Euler and Navier-Stokes equations. Zbl 0767.76039
Rumsey, Christopher L.; van Leer, Bram; Roe, Philip L.
1993
Accelerated convergence of Jameson’s finite-volume Euler scheme using van der Houwen integrators. Zbl 0571.76003
Pike, J.; Roe, P. L.
1985
Divergence- and curl-preserving prolongation and restriction formulas. Zbl 1143.65322
Tóth, G.; Roe, P. L.
2002
Design of optimally smoothing multistage schemes for the Euler equations. Zbl 0758.76043
van Leer, Bram; Lee, Wen-Tzong; Roe, Philip L.; Powell, Kenneth G.; Tai, Chang-Hsien
1992
Multidimensional upwinding: Its relation to finite elements. Zbl 0840.76032
Carette, J.-C.; Deconinck, H.; Paillère, H.; Roe, P. L.
1995
Characteristic-based schemes for dispersive waves. I: The method of characteristics for smooth solutions. Zbl 0787.65066
Roe, Philip L.; Arora, Mohit
1993
Upwind schemes using various formulations of the Euler equations. Zbl 0609.76075
Roe, P. L.
1985
Linear bicharacteristic schemes without dissipation. Zbl 0915.65106
Roe, Philip
1998
Discontinuous solutions to hyperbolic systems under operator splitting. Zbl 0741.65077
Roe, P. L.
1991
Space-time methods for hyperbolic conservation laws. Zbl 0947.76055
Lowrie, Robert B.; Roe, Philip L.; van Leer, Bram
1998
A basis for upwind differencing of the two-dimensional unsteady Euler equations. Zbl 0607.76074
Roe, P. L.
1986
Third-order active-flux scheme for advection diffusion: hyperbolic diffusion, boundary condition, and Newton solver. Zbl 1390.76499
Nishikawa, Hiroaki; Roe, Philip L.
2016
On Godunov-type schemes for magnetohydrodynamics. I: A model system. Zbl 0917.76053
Myong, R. S.; Roe, P. L.
1998
A new level set model for multimaterial flows. Zbl 1349.76647
Starinshak, David P.; Karni, Smadar; Roe, Philip L.
2014
Is discontinuous reconstruction really a good idea? Zbl 1381.65073
Roe, Philip
2017
Multidimensional upwinding. Zbl 1368.65168
Roe, P.
2017
Computational fluid dynamics – retrospective and prospective. Zbl 1184.76811
Roe, P. L.
2005
The active flux scheme on Cartesian grids and its low Mach number limit. Zbl 1442.65190
Barsukow, Wasilij; Hohm, Jonathan; Klingenberg, Christian; Roe, Philip L.
2019
A simple explanation of superconvergence for discontinuous Galerkin solutions to $$u_t+u_x=0$$. Zbl 1388.65105
Roe, Philip
2017
Adaptive grid generation by minimizing residuals. Zbl 1048.76049
Roe, Philip; Nishikawa, Hiroaki
2002
Remote boundary conditions for unsteady multidimensional aerodynamic computations. Zbl 0665.76058
Roe, P. L.
1989
A new level-set model for the representation of non-smooth geometries. Zbl 1307.65113
Starinshak, David P.; Karni, Smadar; Roe, Philip L.
2014
An Euler code that can compute potential flow. Zbl 1052.65556
1999
Numerical wave propagation and steady-state solutions: Soft wall and outer boundary conditions. Zbl 0894.76044
Mazaheri, K.; Roe, P. L.
1997
Toward Godunov-type methods for hyperbolic conservation laws with stiff relaxation. Zbl 1036.76041
Roe, Philip L.; Hittinger, Jeffrey A. F.
2001
On uniformly accurate upwinding for hyperbolic systems with relaxation. Zbl 1052.65527
Hittinger, Jeffrey; Roe, Philip
1999
Preserving vorticity in finite-volume schemes. Zbl 1052.65536
Roe, Philip; Morton, Bill
1999
On multidimensional positively conservative high-resolution schemes. Zbl 0939.76069
Linde, Timur; Roe, Philip L.
1998
Compounded of many simples. Reflections on the role of model problems in CFD. Zbl 0954.76081
Roe, Philip
1998
Issues and strategies for hyperbolic problems with stiff source terms. Zbl 0958.76076
Arora, M.; Roe, P. L.
1998
On a mistaken notion of “proper upwinding”. Zbl 0938.76092
Linda, Timur; Roe, Philip
1998
Gaussian-based moment-method closures for the solutions of the Boltzmann equation. Zbl 0930.76064
Groth, Clinton P. T.; Gombosi, Tamas I.; Roe, Philip L.; Brown, Shawn L.
1996
A fresh look at viscous conservation laws via equivalent relaxation systems. Zbl 0900.65262
Arora, Mohit; Roe, Philip L.
1996
On oscillations due to shock capturing in unsteady flows. Zbl 0861.76046
Arora, Mohit; Roe, Philip L.
1995
Mathematical problems associated with computing flow of real gases. Zbl 0810.76034
Roe, P. L.
1994
On the numerical solution of conservation laws by minimizing residuals. Zbl 0809.76077
Lowrie, R. B.; Roe, P. L.
1994
The best shape for a tin can. Zbl 1266.49029
Roe, P. L.
1993
Multidimensional upwinding: Its relation to finite elements. Zbl 0879.76047
Carette, J. C.; Deconinck, H.; Paillère, H.; Roe, P. L.
1993
Waves in discrete fluids. Zbl 0820.76070
Roe, P. L.
1993
Numerical modelling of shockwaves and other discontinuities. Zbl 0562.76057
Roe, P. L.
1982
Numerical methods in aeronautical fluid dynamics. (Proceedings of a Conference held at the University of Reading, March 30 - April 1, 1981). Zbl 0546.00036
Roe, P. L. (ed.)
1982
A method for designing lifting configurations for high supersonic speeds using axisymmetric flow fields. Zbl 0172.53002
Jones, J. G.; Moore, K. C.; Pike, J.; Roe, P. L.
1968
The active flux scheme on Cartesian grids and its low Mach number limit. Zbl 1442.65190
Barsukow, Wasilij; Hohm, Jonathan; Klingenberg, Christian; Roe, Philip L.
2019
Is discontinuous reconstruction really a good idea? Zbl 1381.65073
Roe, Philip
2017
Multidimensional upwinding. Zbl 1368.65168
Roe, P.
2017
A simple explanation of superconvergence for discontinuous Galerkin solutions to $$u_t+u_x=0$$. Zbl 1388.65105
Roe, Philip
2017
Third-order active-flux scheme for advection diffusion: hyperbolic diffusion, boundary condition, and Newton solver. Zbl 1390.76499
Nishikawa, Hiroaki; Roe, Philip L.
2016
A new level set model for multimaterial flows. Zbl 1349.76647
Starinshak, David P.; Karni, Smadar; Roe, Philip L.
2014
A new level-set model for the representation of non-smooth geometries. Zbl 1307.65113
Starinshak, David P.; Karni, Smadar; Roe, Philip L.
2014
A cell centred Lagrangian Godunov scheme for shock hydrodynamics. Zbl 1431.76006
Barlow, A. J.; Roe, P. L.
2011
An entropy adjoint approach to mesh refinement. Zbl 1213.65142
Fidkowski, Krzysztof J.; Roe, Philip L.
2010
Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks. Zbl 1280.76015
2009
Computational fluid dynamics – retrospective and prospective. Zbl 1184.76811
Roe, P. L.
2005
High-order fluctuation schemes on triangular meshes. Zbl 1068.65133
Abgrall, R.; Roe, P. L.
2003
Divergence- and curl-preserving prolongation and restriction formulas. Zbl 1143.65322
Tóth, G.; Roe, P. L.
2002
Adaptive grid generation by minimizing residuals. Zbl 1048.76049
Roe, Philip; Nishikawa, Hiroaki
2002
Vorticity-preserving Lax-Wendroff-type schemes for the system wave equation. Zbl 0994.35011
Morton, K. W.; Roe, P. L.
2001
Toward Godunov-type methods for hyperbolic conservation laws with stiff relaxation. Zbl 1036.76041
Roe, Philip L.; Hittinger, Jeffrey A. F.
2001
Compact high-resolution algorithms for time-dependent advection on unstructured grids. Zbl 0985.76064
Hubbard, M. E.; Roe, P. L.
2000
A solution-adaptive upwind scheme for ideal magnetohydrodynamics. Zbl 0952.76045
Powell, Kenneth G.; Roe, Philip L.; Linde, Timur J.; Gombosi, Tamas I.; De Zeeuw, Darren L.
1999
An Euler code that can compute potential flow. Zbl 1052.65556
1999
On uniformly accurate upwinding for hyperbolic systems with relaxation. Zbl 1052.65527
Hittinger, Jeffrey; Roe, Philip
1999
Preserving vorticity in finite-volume schemes. Zbl 1052.65536
Roe, Philip; Morton, Bill
1999
Linear bicharacteristic schemes without dissipation. Zbl 0915.65106
Roe, Philip
1998
Space-time methods for hyperbolic conservation laws. Zbl 0947.76055
Lowrie, Robert B.; Roe, Philip L.; van Leer, Bram
1998
On Godunov-type schemes for magnetohydrodynamics. I: A model system. Zbl 0917.76053
Myong, R. S.; Roe, P. L.
1998
On multidimensional positively conservative high-resolution schemes. Zbl 0939.76069
Linde, Timur; Roe, Philip L.
1998
Compounded of many simples. Reflections on the role of model problems in CFD. Zbl 0954.76081
Roe, Philip
1998
Issues and strategies for hyperbolic problems with stiff source terms. Zbl 0958.76076
Arora, M.; Roe, P. L.
1998
On a mistaken notion of “proper upwinding”. Zbl 0938.76092
Linda, Timur; Roe, Philip
1998
On postshock oscillations due to shock capturing schemes in unsteady flows. Zbl 0869.76050
Arora, Mohit; Roe, Philip L.
1997
Approximate Riemann solvers, parameter vectors, and difference schemes. (Reprint). Zbl 0890.65094
Roe, P. L.
1997
A well-behaved TVD limiter for high-resolution calculations of unsteady flow. Zbl 0878.76045
Arora, Mohit; Roe, Philip L.
1997
Numerical wave propagation and steady-state solutions: Soft wall and outer boundary conditions. Zbl 0894.76044
Mazaheri, K.; Roe, P. L.
1997
Notes on the eigensystem of magnetohydrodynamics. Zbl 0845.35092
Roe, P. L.; Balsara, D. S.
1996
Gaussian-based moment-method closures for the solutions of the Boltzmann equation. Zbl 0930.76064
Groth, Clinton P. T.; Gombosi, Tamas I.; Roe, Philip L.; Brown, Shawn L.
1996
A fresh look at viscous conservation laws via equivalent relaxation systems. Zbl 0900.65262
Arora, Mohit; Roe, Philip L.
1996
An upwind scheme for magnetohydrodynamics. Zbl 0900.76344
Powell, K. G.; Roe, P. L.; Myong, R. S.; Gombosi, T.; de Zeeuw, D.
1995
Multidimensional upwinding: Its relation to finite elements. Zbl 0840.76032
Carette, J.-C.; Deconinck, H.; Paillère, H.; Roe, P. L.
1995
On oscillations due to shock capturing in unsteady flows. Zbl 0861.76046
Arora, Mohit; Roe, Philip L.
1995
Mathematical problems associated with computing flow of real gases. Zbl 0810.76034
Roe, P. L.
1994
On the numerical solution of conservation laws by minimizing residuals. Zbl 0809.76077
Lowrie, R. B.; Roe, P. L.
1994
A multidimensional generalization of Roe’s flux difference splitter for the Euler equations. Zbl 0790.76054
Deconinck, H.; Roe, P. L.; Struijs, R.
1993
Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws. Zbl 0771.76048
Deconinck, H.; Paillère, H.; Struijs, R.; Roe, P. L.
1993
Numerical computation of two-dimensional unsteady detonation waves in high energy solids. Zbl 0770.76040
Clarke, J. F.; Karni, S.; Quirk, J. J.; Roe, P. L.; Simmonds, L. G.; Toro, E. F.
1993
A frontal approach for internal node generation in Delaunay triangulations. Zbl 0780.76064
Müller, J.-D.; Roe, P. L.; Deconinck, H.
1993
A multidimensional flux function with applications to the Euler and Navier-Stokes equations. Zbl 0767.76039
Rumsey, Christopher L.; van Leer, Bram; Roe, Philip L.
1993
Characteristic-based schemes for dispersive waves. I: The method of characteristics for smooth solutions. Zbl 0787.65066
Roe, Philip L.; Arora, Mohit
1993
The best shape for a tin can. Zbl 1266.49029
Roe, P. L.
1993
Multidimensional upwinding: Its relation to finite elements. Zbl 0879.76047
Carette, J. C.; Deconinck, H.; Paillère, H.; Roe, P. L.
1993
Waves in discrete fluids. Zbl 0820.76070
Roe, P. L.
1993
Optimum positive linear schemes for advection in two and three dimensions. Zbl 0765.65093
Roe, P. L.; Sidilkover, D.
1992
Sonic flux formulae. Zbl 0747.65073
Roe, P. L.
1992
Design of optimally smoothing multistage schemes for the Euler equations. Zbl 0758.76043
van Leer, Bram; Lee, Wen-Tzong; Roe, Philip L.; Powell, Kenneth G.; Tai, Chang-Hsien
1992
On Godunov-type methods near low densities. Zbl 0709.76102
Einfeldt, B.; Munz, C. D.; Roe, P. L.; Sjögreen, B.
1991
Discontinuous solutions to hyperbolic systems under operator splitting. Zbl 0741.65077
Roe, P. L.
1991
Remote boundary conditions for unsteady multidimensional aerodynamic computations. Zbl 0665.76058
Roe, P. L.
1989
Upwind differencing schemes for hyperbolic conservation laws with source terms. Zbl 0626.65086
Roe, P. L.
1987
Characteristic-based schemes for the Euler equations. Zbl 0624.76093
Roe, P. L.
1986
Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. Zbl 0587.76126
Roe, Philip L.
1986
A basis for upwind differencing of the two-dimensional unsteady Euler equations. Zbl 0607.76074
Roe, P. L.
1986
Some contributions to the modelling of discontinuous flows. Zbl 0665.76072
Roe, Philip L.
1985
Accelerated convergence of Jameson’s finite-volume Euler scheme using van der Houwen integrators. Zbl 0571.76003
Pike, J.; Roe, P. L.
1985
Upwind schemes using various formulations of the Euler equations. Zbl 0609.76075
Roe, P. L.
1985
Efficient construction and utilisation of approximate Riemann solutions. Zbl 0558.76001
Roe, P. L.; Pike, J.
1984
Fluctuations and signals - A framework for numerical evolution problems. Zbl 0569.76072
Roe, P. L.
1982
Algorithms for advection and shock problems. Zbl 0482.76008
Roe, P. L.; Baines, M. J.
1982
Numerical modelling of shockwaves and other discontinuities. Zbl 0562.76057
Roe, P. L.
1982
Numerical methods in aeronautical fluid dynamics. (Proceedings of a Conference held at the University of Reading, March 30 - April 1, 1981). Zbl 0546.00036
Roe, P. L. (ed.)
1982
Approximate Riemann solvers, parameter vectors, and difference schemes. Zbl 0474.65066
Roe, P. L.
1981
A method for designing lifting configurations for high supersonic speeds using axisymmetric flow fields. Zbl 0172.53002
Jones, J. G.; Moore, K. C.; Pike, J.; Roe, P. L.
1968
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#### Cited by 3,372 Authors

 33 Abgrall, Rémi 31 Dumbser, Michael 31 Shu, Chi-Wang 28 Glaister, Paul 26 Farhat, Charbel H. 24 Garcia-Navarro, Pilar 23 Ricchiuto, Mario 23 Toro, Eleuterio F. 21 Balsara, Dinshaw S. 20 Deconinck, Herman 19 Castro, Manuel J. 19 Gassner, Gregor J. 18 Murillo, Javier 18 Nishikawa, Hiroaki 18 Winters, Andrew R. 17 Parés Madroñal, Carlos 17 Roe, Philip L. 16 Jameson, Antony 15 Yan, Chao 14 Benkhaldoun, Fayssal 14 Capdeville, Guy 14 Guardone, Alberto 13 Darmofal, David L. 13 Fidkowski, Krzysztof J. 13 Giannakoglou, Kyriakos C. 13 Mishra, Siddhartha 13 Ollivier-Gooch, Carl F. 13 Vázquez-Cendón, María Elena 12 Adams, Nikolaus A. 12 Carpenter, Mark H. 12 Kuzmin, Dmitri 12 Persson, Per-Olof 11 Gaitonde, Datta V. 11 Groth, Clinton P. T. 11 Hubbard, Matthew E. 11 Karni, Smadar 11 Ren, Yuxin 11 Seaïd, Mohammed 10 Egorov, I. V. 10 Hérard, Jean-Marc 10 Luo, Hong 10 Mavriplis, Dimitri J. 10 Wang, Zhijian 10 Yee, Helen C. 9 Fujii, Kozo 9 Gallouët, Thierry 9 Goncalves, Eric 9 Ismail, Farzad 9 Munz, Claus-Dieter 9 Napolitano, Michele 9 Nogueira, Xesús 9 Nonomura, Taku 9 Parsani, Matteo 9 Tadmor, Eitan 8 Berthon, Christophe 8 De Palma, Pietro 8 Elmahi, Imad 8 Gallardo, José M. 8 Kim, Chongam 8 Kitamura, Keiichi 8 Lerat, Alain 8 LeVeque, Randall J. 8 Löhner, Rainald 8 Nkonga, Boniface 8 Papadimitriou, Dimitrios I. 8 Pascazio, Giuseppe 8 Saurel, Richard 8 Shu, Chang 8 Tóth, Gábor Zsolt 8 Turkel, Eli L. 7 Colominas, Ignasi 7 Del Rey Fernández, David C. 7 Delis, Argiris I. 7 Edwards, Michael G. 7 Ghidaglia, Jean-Michel 7 Gombosi, Tamas I. 7 Guinot, Vincent 7 Hicken, Jason E. 7 Jiwari, Ram 7 Klingenberg, Christian 7 Koobus, Bruno 7 Kurganov, Alexander 7 Lanteri, Stéphane 7 Liu, Gui-Rong 7 Lukáčová-Medvid’ová, Mária 7 Peraire, Jaime 7 Shyue, Keh-Ming 7 Sjogreen, Bjorn 7 Svärd, Magnus 7 Trepanier, Jean-Yves 7 Unnikrishnan, Sanil 7 Xu, Kun 6 Bonfiglioli, Aldo 6 Camarero, Ricardo 6 Castro-Díaz, Manuel Jesús 6 Chacón Rebollo, Tomás 6 Chen, Shusheng 6 Chizari, Hossain 6 Christlieb, Andrew J. 6 Dadone, Andrea ...and 3,272 more Authors
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text:
# Abstract:

Maps $f$ defined on the interior of the standard non-negative cone $K$ in ${\mathbb{R}}^N$ which are both homogeneous of degree $1$ and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson's part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least one eigenvector in $K-\{0\}$. In the case where the cycle time $\chi(f)$ of the original map does not exist, such eigenvectors must lie in $\partial{K}-\{0\}$.


text:
# partition theory: meet the COP

Recall that $(a;q)_0:=1,\,(a;q)_n=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^{n-1})$ and $(a;q)_{\infty}=(1-a)(1-aq)(1-aq^2)\cdots$. Let's introduce the following (generalized) concept.

A colored overpartition (COP) is a partition where the last occurrence of each distinct number may receive any one of $c$ colors. The number of such partitions of $n$ we denote by $\overline{p}_c(n)$. For example, the $8$ COP partitions of $n=3$ with $c=2$ colors are: $$3,\, \overline{3}, \, 2+1, \, \overline{2}+1, \, 2+\overline{1}, \, \overline{2}+\overline{1}, \, 1+1+1, \, 1+1+\overline{1}.$$ Note. In the literature, (i) ordinary partitions $p(n)=\overline{p}_1(n)$; (ii) overpartitions $\overline{p}(n)=\overline{p}_2(n)$.

Question. Does this generating function hold true? $$\sum_{n\geq0}\overline{p}_c(n)q^n=\frac{((1-c)q;q)_{\infty}}{(q;q)_{\infty}}.$$

• Just a typographical suggestion, $COP$ uses mathemarics spacing for what is an acronym, so looks wrong. I think the small-caps \textsc{COP}, italic \textit{COP} or just plain COP would look better. – J.J. Green Mar 7 '17 at 12:46
• @J.J.Green: Thanks, I edited as such. How about now? – T. Amdeberhan Mar 7 '17 at 12:52
• Google search returned only 6 hits regarding "colored overpartition". One of them is your paper arxiv.org/abs/1207.4045 where this question goes under Theorem 12.1. This shows that you already have a proof. – Nemo Mar 7 '17 at 13:31
• @Nemo: No, I don't have a proof. In the preprint you saw it should read "conjectures" instead of "theorem". Sorry, it appeared misleading. – T. Amdeberhan Mar 7 '17 at 13:33
• For overpartitions overlined parts form a partition into distinct parts and the non-overlined parts form an ordinary partition, therefore the generating function is $\prod_{n=1}^\infty\frac{1+q^n}{1-q^n}$. In analogy with this well known case, for $\textrm{COP}$ with $c$ colors, the non-overlined parts form an ordinary partition and the overlined parts form a partition into distinct parts such that each part can take one of $c-1$ colors. So it is not surprising that generating function is $\prod_{n=1}^\infty\frac{1+(c-1)q^n}{1-q^n}$. – Nemo Mar 7 '17 at 14:33

Rather than coloring the last occurrence of each distinct number, we can equivalently for each part $i$ color all the $i$'s with the same color. Thus $$\sum_{n\geq 0}\bar{p}_c(n)q^n = \prod_{i\geq 1}(1+c(q^i+q^{2i}+q^{3i}+\cdots))$$ $$= \prod_{i\geq 1}\frac{1+(c-1)q^i}{1-q^i}.$$


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# Welcome!

I am a 2nd-year PhD student in Machine Learning at Imperial College London, supervised by Yingzhen Li. I obtained my MPhil degree in Machine Learning and Machine Intelligence from the University of Cambridge in 2020, supervised by José Miguel Hernández-Lobato. Before that, I graduated with a BSc (Hons) in Mathematics and Statistics from McMaster University.

During my PhD, I will mainly study uncertainty estimation, Bayesian deep learning and approximate inference. In general, I am also interested in probabilistic graphical model design, meta learning, causality and explainable AI. I aim to develop reliable algorithms with improved generalization, robustness and interpretability.

# Publication

• Andrew Campbell*, Wenlong Chen*, Vincent Stimper*, Jose Miguel Hernandez-Lobato, Yichuan Zhang. A Gradient Based Strategy for Hamiltonian Monte Carlo Hyperparameter Optimization. ICML 2021 [pdf]

*equal contribution


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# The kinetic energy 𝐾 of a particle moving along a circle or radius 𝑅 depends on the distance covered 𝑠 as 𝐾 = 𝑎 𝑠 2 . The force acting on the particle is

Question : The kinetic energy 𝐾 of a particle moving along a circle or radius 𝑅 depends on the distance covered 𝑠 as 𝐾 = 𝑎 𝑠 2 . The force acting on the particle is

(A) 2 𝑎 𝑠 𝑅

(B) $2as\left[ \dfrac{1+s^{2}}{R^{2}}\right] ^{\dfrac{1}{2}}$

(C) 2 𝑎 s

(D) $\dfrac{2as^{2}}{R}$


text:
# 3) Propose a synthesis.

###### Question:

3) Propose a synthesis.

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text:
# It's a bit hazy

Calculus Level 5

What is the probability an Eisenstein integer is visible from the origin (that is, a line from the origin to the integer does not intersect any other Eisenstein integers)?

Note: An Eisenstein integer is a complex number of the form $$a+b\omega$$ where $$\displaystyle \omega = \frac{-1+i\sqrt{3}}{2}$$ and $$a,b \in \mathbb{Z}$$. For example, $$1, \omega$$ and $$3+2\omega$$ are all Eisenstein integers.

×


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# If 3 and 8 are the lengths of two sides of a triangular

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If 3 and 8 are the lengths of two sides of a triangular  [#permalink]

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Updated on: 31 Jul 2012, 10:26
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If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI

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Regards, S

Originally posted by saurya_s on 10 Oct 2005, 06:34.
Last edited by Bunuel on 31 Jul 2012, 10:26, edited 1 time in total.
Edited the question and added the OA.
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Posts: 52149
Re: If 3 and 8 are the lengths of two sides of a triangular  [#permalink]

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31 Jul 2012, 10:34
5
3
shreya717 wrote:
Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?

I don't quite understand what you mean by the red part above. Anyway:

If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, $$(8-3)<x<(8+3)$$ --> $$5<x<11$$. Hence 5 and 11 cannot be the length of the third side, while 8 can be.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
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Re: PS Sides of a triangle  [#permalink]

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10 Oct 2005, 06:42
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saurya_s wrote:
15. If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ?I only
(B) ?II only
(C) I and ?I only
(D) II and ?II only
(E) I, ??, and ???

Plz explain.
Thanks

the rest side x must satisfy : 8-3<x< 8+3 <==> 5<x<11
B.
##### General Discussion
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10 Oct 2005, 06:44
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the sum of the two sides must be greater than the third side. 3+8 =11
the difference of the two sides mut be less than the third side. 8-3=5

therefore the third side is between 5 and 11. Only B fulfills this.
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10 Oct 2005, 08:21
Since the new side has to be less than the sum of the other two sides

Choosing 5 -
3, 8 is not possible as 3+5 leads to 8 - so the other side will have to be less than 8 (but we know it is 8). So 5 is not a correct side.

Choosing 8 -
3, 8, 8 is still valid - (isosceles triangle if I still remember how to spell those) as the sum of any two is still bigger than the other side.

So Choice B.
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Re: If 3 and 8 are the lengths of two sides of a triangular  [#permalink]

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31 Jul 2012, 10:19
Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?
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Re: If 3 and 8 are the lengths of two sides of a triangular  [#permalink]

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