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# Math Help - Base 5 Division

1. ## Base 5 Division

I am stuck on a base five division problem.

I have to divide 4 base five into 134 base five.

I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

Thanks

What do you mean by "dividing by base 5". Base 5 means there are only 4 possibly used digits : 0, 1, 2, 3 and 4. So you can get 32, 44, 10, but you cannot get 5, nor can you get 77 or 19. See what I mean ? You don't divide a number by a base, this is totally different sort of stuff.

So, do you mean that you want to divide 134 by 4, knowing you are only working on base 5 ? Or do you want to convert 4 and 134 (they are in base 10 then) into base 5 ?

3. I don't have to covert the number (they're already in base ten). I have to divide 4 base five by 134 base five. Is there a "pencil icon" so that I can write it out?

4. Originally Posted by albinuta
I don't have to covert the number (they're already in base ten). I have to divide 4 base five by 134 base five. Is there a "pencil icon" so that I can write it out?
Uhm ... what do you mean ? You say they are already in base 10, but then you say they are in base 5. What base are they in, and what base should they be in ?

5. the question reads: 4five divided 134five

I know that if I times 2 by 4 it gives me 8 and the eight converted to base five is 1 with a remainder of three which leaves me with the 4 of the 134. I don't know what to do with that 4. If I multiply the 4 by 1 it gives me just a 4 and that cant be coverted into base five. But the 4 can be multiplied by 1 which would give me 4.

Would my final answer be 21five?

Is there a writing tool so that I can write out the actual problem? I don't see a pencil icon anywhere.

6. Originally Posted by albinuta
I know that if I times 2 by 4 it gives me 8 and the eight converted to base five is 1 with a remainder of three [...]
I think you are confusing bases with modular arithmetic.

Bases : 8 (base 10) converted to base 5 gives 13 (the first numbers in base 5 are : 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31 ...)
Modular arithmetic : $8 \equiv 3$ (mod 5) (which means that the remainder of the division of 8 by 5 is 3)

To write out the actual problem, you can either try to use LaTeX symbols (painful to write), or you can open Paint and roughly scribble your problem, then upload and paste the image on a new comment ?

7. Originally Posted by albinuta
I am stuck on a base five division problem.

I have to divide 4 base five into 134 base five.

I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

Thanks
i don't know if this what you mean. 4(base5) / 134(base5) = 0.0211402114...(base5)

8. ## 4(base5) / 134(base5) ?

Originally Posted by albinuta
I am stuck on a base five division problem.

I have to divide 4 base five into 134 base five.

I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

Thanks
i don't know if this what you mean. 4(base5) / 134(base5) = 0.0211402114...(base5)

9. You could try the basis representation theorem, that all numbers, say, of base 5, can be written like this: $a_0 + a_15^1 + a_25^2 + \cdot\cdot\cdot + a_n5^n$
and numbers of base 4 can be written like this: $a_0 + a_14^1 + a_24^2 + \cdot\cdot\cdot + a_n4^n$

see where you can get from there...

Hope I helped!


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# A glimps of Inverse Problems

November 15, 2012
By

(This article was originally published at Statisfaction » Statistics, and syndicated at StatsBlogs.)

Hi folks !

Last Tuesday a seminar on Bayesian procedure for inverse problems took place at CREST. We had time for two presentations of young researchers Bartek Knapik and Kolyan Ray. Both presentations deal with the problem of observing a noisy version of a linear transform of the parameter of interest

$Y_i = K\mu + \frac{1}{\sqrt{n}} Z$
where $K$ is a linear operator and $Z$ a Gaussian white noise.  Both presentations considered asymptotic properties of the posterior distribution (Their papers can be found on arxiv, here for Bartek’s, and here for Kolyan’s). There is a wide literature on asymptotic properties of the posterior distribution in direc models. When looking at the concentration of $f$ toward a true distribution $f_0$  given the data, with respect to some distance $d(.,.)$,  well known problem is to derive concentration rates, that is the rate $\epsilon_n$ such that

$\pi(d(f,f_0) > \epsilon_n | X^n) \to 0.$

For inverse problems, the usual methods as introduced by Ghosal, Ghosh and van der Vaart (2000) usually fails, and thus results in this settings are in general difficult to obtain.

Bartek presented some very refined results in the conjugate case. He manages to get some results on the concentration rates of the posterior distribution, on Bayesian Credible Sets and Bernstein – Von Mises theorems – that states that the posterior is asymptotically Gaussian – when estimating a linear functional of the parameter of interest. Kolyan got some general conditions on the prior to achieve concentration rate, and prove that these techniques leads to optimal concentration rates for classical models.

I only knew little about inverse problems but both talks were very accessible and I will surely get more involved in this field !

Please comment on the article here: Statisfaction » Statistics

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## Mirror-extended standard model with spontaneously broken left-right symmetry

#### by Alexander Kaganovich

##### at Particles and Fields Seminar

Mon, 20 Dec 2021, 14:00
Sacta-Rashi Building for Physics (54), room 207

#### Abstract

A left-right symmetric extension of the standard electroweak model (SM) with a doubled particle content is proposed. Mirror copy have the same $SU(2)\times U(1)$ gauge structure and parameters as SM; the mirror fermion counter-partners have opposite chiralities. The model contains neither additional dynamical degrees of freedom, nor additional interactions. A Two Measures Theory is used that allows one to obtain MESM in Minkowski space only if we start with an accurate account of gravity and only at the end go to the limit of Minkowski space. Spontaneous breaking of left-right symmetry and the "wrong" sign in the mass terms of the Higgs fields potentials arise due to the initial conditions imposed on the inflaton in the $\alpha$-attractor inflationary model. MESM allows choosing the universal Yukawa coupling constant $y$ in the underlying Lagrangian for all generations of charged leptons and up-quarks. As an example, with $y\approx10^{-3}$, it is shown that a set of additional dimensionless parameters in width range less than 0.5 is sufficient to obtain the masses of all known charged leptons and up-quarks. In this sense, MESM bypasses the problem of the fermion mass hierarchy. With this choice of parameters, MESM predicts that vacuum expectation value for the mirror Higgs field is $10^{14} GeV$ and masses of mirror particles are in the range $10^{8}GeV - 10^{14}GeV$. There is only gravitational interaction between particles of the SM and mirror sectors. Hence, mirror particles can constitute dark matter.

Created on 13-12-2021 by Palti, Eran (palti)
Updaded on 13-12-2021 by Palti, Eran (palti)


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# Black Hole Mass Scaling Relations for Early-type Galaxies. I. M BH–M *, sph and M BH–M *,gal

@article{Sahu2019BlackHM,
title={Black Hole Mass Scaling Relations for Early-type Galaxies. I. M BH–M *, sph and M BH–M *,gal},
author={Nandini Sahu and Alister W. Graham and Benjamin Lee Davis},
journal={The Astrophysical Journal},
year={2019}
}
• Published 12 March 2019
• Physics
• The Astrophysical Journal
Analyzing a sample of 84 early-type galaxies with directly-measured super-massive black hole masses---nearly doubling the sample size of such galaxies with multi-component decompositions---a symmetric linear regression on the reduced (merger-free) sample of 76 galaxies reveals $M_{BH}\propto M_{*,sph}^{1.27\pm 0.07}$ with a total scatter of $\Delta_{rms}=$ 0.52 dex in the $\log(M_{BH})$ direction. However, and importantly, we discover that the ES/S0-type galaxies with disks are offset from the…
The Black Hole Mass–Color Relations for Early- and Late-type Galaxies: Red and Blue Sequences
• Physics
The Astrophysical Journal
• 2020
[Abridged] Tight correlations between supermassive black hole (SMBH) mass ($M_{\rm BH}$) and the properties of the host galaxy have useful implications for our understanding of the growth of SMBHs
The Black Hole–Bulge Mass Relation Including Dwarf Galaxies Hosting Active Galactic Nuclei
• Physics
The Astrophysical Journal
• 2019
We present a new relationship between central black hole (BH) mass and host galaxy stellar bulge mass extending to the lowest BH masses known in dwarf galaxies ($M_{\rm BH} \lesssim 10^{5} Revealing Hidden Substructures in the M BH–σ Diagram, and Refining the Bend in the L–σ Relation • Physics The Astrophysical Journal • 2019 Using 145 early- and late-type galaxies (ETGs and LTGs) with directly-measured super-massive black hole masses,$M_{BH}\$, we build upon our previous discoveries that: (i) LTGs, most of which have
Defining the (Black Hole)–Spheroid Connection with the Discovery of Morphology-dependent Substructure in the M BH–n sph and M BH–R e,sph Diagrams: New Tests for Advanced Theories and Realistic Simulations
• Physics
• 2020
For 123 local galaxies with directly-measured black hole masses (MBH), we provide the host spheroid’s Sérsic index (nsph), effective half-light radius (Re,sph), and effective surface brightness (μe),
Probing black hole accretion tracks, scaling relations, and radiative efficiencies from stacked X-ray active galactic nuclei
• Physics
• 2019
The masses of supermassive black holes at the centres of local galaxies appear to be tightly correlated with the mass and velocity dispersions of their galactic hosts. However, the local M_bh–M_star
Central X-Ray Point Sources Found to Be Abundant in Low-mass, Late-type Galaxies Predicted to Contain an Intermediate-mass Black Hole
• Physics
The Astrophysical Journal
• 2021
Building upon three late-type galaxies in the Virgo cluster with both a predicted black hole mass of less than ∼105 M ⊙ and a centrally located X-ray point source, we reveal 11 more such galaxies,
Constraining black hole-galaxy scaling relations from the large-scale clustering of Active Galactic Nuclei and implied mean radiative efficiency
• Physics
• 2019
A supermassive black hole has been found at the centre of nearly every galaxy observed with sufficient sensitivity. The masses of these black holes are observed to increase with either the total mass
Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering
• Physics
• 2019
The masses of supermassive black holes are observed to increase with either the total mass or the mean (random) velocity of the stars in their host galaxies. The origin of these correlations remains
Coevolution of black hole accretion and star formation in galaxies up to z = 3.5
• Physics
Astronomy & Astrophysics
• 2020
Aims. We study the coevolution between the black hole accretion rate (BHAR) and the star formation rate (SFR) in different phases of galaxy life: main-sequence star-forming galaxies, quiescent
No Significant Evolution of Relations between Black Hole Mass and Galaxy Total Stellar Mass Up to z ∼ 2.5
• Physics
The Astrophysical Journal
• 2020
We investigate the cosmic evolution of the ratio between black hole mass (MBH) and host galaxy total stellar mass (Mstellar) out to z~2.5 for a sample of 100 X-ray-selected moderate-luminosity,

## References

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The Most Precise Extra-Galactic Black-Hole Mass Measurement
I use archival data to measure the mass of the central black hole in NGC 4526, M = (4.70 +- 0.14) X 10^8 Msun. This 3% error bar is the most precise for an extra-galactic black hole and is close to
Gravitational wave research using pulsar timing arrays
• Physics
• 2017
A pulsar timing array (PTA) refers to a program of regular, high-precision timing observations of a widely distributed array of millisecond pulsars. Here we review the status of the three primary PTA
2007a, in American Astronomical Society
• Meeting Abstracts,
• 2007
Elliptical Galaxies With Nuclear Disks of Stars: Black Hole Search and Stellar Populations, HST Proposal
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1987b, in Structure and Dynamics of Elliptical Galaxies, ed
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Spectroscopy of the Rapidly Rotating Nuclear Disk in the Virgo s0 NGC4526, HST Proposal
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PASA, 33, e062, doi: 10.1017/pasa.2016.60 Ciotti, L
• A&A,
• 2016


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## Results (9 matches)

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 13 19
6422.2.a.f $$1$$ $$51.280$$ $$\Q$$ None $$1$$ $$0$$ $$-2$$ $$-4$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots$$
6422.2.a.h $$1$$ $$51.280$$ $$\Q$$ None $$1$$ $$1$$ $$0$$ $$1$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$$
6422.2.a.i $$1$$ $$51.280$$ $$\Q$$ None $$1$$ $$2$$ $$3$$ $$0$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+2q^{3}+q^{4}+3q^{5}+2q^{6}+q^{8}+\cdots$$
6422.2.a.j $$1$$ $$51.280$$ $$\Q$$ None $$1$$ $$3$$ $$3$$ $$-3$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-3q^{7}+\cdots$$
6422.2.a.s $$3$$ $$51.280$$ $$\Q(\zeta_{18})^+$$ None $$3$$ $$-3$$ $$-3$$ $$6$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+q^{4}+\cdots$$
6422.2.a.x $$3$$ $$51.280$$ 3.3.1129.1 None $$3$$ $$0$$ $$-2$$ $$-3$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$$
6422.2.a.y $$3$$ $$51.280$$ 3.3.1129.1 None $$3$$ $$0$$ $$0$$ $$4$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
6422.2.a.bd $$6$$ $$51.280$$ 6.6.316645497.1 None $$6$$ $$2$$ $$2$$ $$1$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$$
6422.2.a.bq $$15$$ $$51.280$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None $$15$$ $$0$$ $$1$$ $$18$$ $$-$$ $$+$$ $$+$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{10}q^{5}+\beta _{1}q^{6}+\cdots$$