text:
## abstracts for 2017-18 seminars

(The seminar webpage is here.)

Sam Grushevsky (Stony Brook University)

September 29, 2017

Geometry of compactified moduli of cubic threefolds

Starting from considering the GIT compactification of the moduli of cubic threefolds, the “wonderful” compactification, which is smooth with normal crossing boundary, is constructed by an explicit sequence of blowups. We show that there exists a family of intermediate jacobians over the wonderful compactification. We compute the cohomology of the wonderful compactification by comparing it to the symplectic resolution. Based on joint works with Casalaina-Martin, Hulek, Laza

Felix Janda (University of Michigan)

October 6, 2017

Genus two curves on quintic threefolds

Virtual (Gromov-Witten) counts of maps from algebraic curves to quintic 3-folds in projective space have been of significant interest for mathematicians and physicists since the early 90s. While there are (very inefficient) algorithms for computing any specific Gromov-Witten invariant, explicit formulae are only known in genus zero and one. On the other hand, physicists have explicit conjectural formulas up to genus 51.

I will discuss a new approach to the Gromov-Witten theory of the quintic (using logarithmic geometry) which yields an explicit formula in genus two that agrees with the physicists’ conjecture.

This is based on joint works in progress with Q. Chen, S. Guo and Y. Ruan.

Remy van Dobben de Bruyn (Columbia)

October 20, 2017

Dominating varieties by liftable ones

Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

Jason Lo (Cal State Northridge)

October 27, 2017

The effect of Fourier-Mukai transforms on slope stability on elliptic fibrations

Slope stability is a type of stability for coherent sheaves on smooth projective varieties. On a variety where the derived category of coherent sheaves admits a non-trivial autoequivalence, it is natural to ask how slope stability `transforms’ to a different stability under the autoequivalence. This question also has implications for understanding the symmetries within various counting invariants. In this talk, we will give an answer to the above question for elliptic surfaces and threefolds under a Fourier-Mukai transform.

Daniel Litt (Columbia University)

December 1, 2017

Galois actions on fundamental groups

Let X be a variety over a field k, and let x be a k-rational point of X. Then the absolute Galois group of k acts on the etale fundamental group of X. If k is an arithmetically interesting field (i.e. a number field, a p-adic field, or a finite field), then this action reveals a great deal about the geometry of X; if X is a variety with an interesting fundamental group, this action reveals a great deal about the arithmetic of k.

This talk will discuss (1) joint work with Alexander Betts about the structure of Galois actions on fundamental groups, (2) how to describe invariants of these actions in terms of more geometric invariants of X, and (3) applications of this work to classical algebraic geometry, and, if time permits, arithmetic.

Pablo Solis (Stanford)

January 19, 2018

Hunting Vector Bundles on $\mathbf{P}^1 \times \mathbf{P}^1$

Motivated by Boij-Soderberg theory, Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbf{P}^1 \times \mathbf{P}^1$ with natural cohomology and prescribed Euler characteristic. I’ll give some background on Boij-Soderberg theory, explain what natural cohomology means and prove the conjecture in “most” cases.

Izzet Coskun (University of Illinois at Chicago)

January 26, 2018

The geometry of moduli spaces of sheaves on surfaces

In this talk, I will discuss recent results concerning the Brill-Noether Theory of higher rank bundles on rational surfaces and stable cohomology of moduli spaces of sheaves. In joint work with Jack Huizenga, we characterize when the cohomology of a general stable sheaf on a Hirzebruch surface is determined by its Euler characteristic. We use these results to classify moduli spaces where the general bundle is globally generated. If time permits, I will discuss joint work with Matthew Woolf on the stable cohomology of moduli spaces on rational surfaces.

Katrina Honigs (Utah)

February 2, 2018

Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic

There are many results characterizing when derived categories of two complex surfaces are equivalent, including theorems of Bridgeland and Maciocia showing that derived equivalent Enriques or bielliptic surfaces must be isomorphic. The proofs of these theorems strongly use Torelli theorems and lattice-theoretic methods which are not available in positive characteristic. In this talk I will discuss how to prove these results over algebraically closed fields of positive characteristic (excluding some low characteristic cases). This work is joint with M. Lieblich and S. Tirabassi.

Junliang Shen (ETH)

February 9, 2018

K3 categories, cubic 4-folds, and the Beauville-Voisin conjecture

We discuss recent progress on the connection between 0-cycles of holomorphic symplectic varieties and structures of K3 categories. We propose that there exists a sheaf/cycle correspondence for any K3 category, which controls the geometry of algebraically coisotropic subvarieties of certain holomorphic symplectic varieties. Two concrete cases will be illustrated in details:
(1) the derived category of a K3 surface (joint with Qizheng Yin and Xiaolei Zhao),
(2) Kuznetsov category of a cubic 4-fold (joint with Qizheng Yin).
If time permits, we will also discuss the connection to rational curves in cubic 4-folds.

Michael Viscardi (Berkeley)

February 16, 2018

Quantum cohomology and 3D mirror symmetry

Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric Knizhnik-Zamolodchikov (KZ)-type connection of the Langlands dual group of G. These symplectic resolutions are expected to be symplectic duals of Nakajima quiver varieties, so that our result is an analogue of (part of) the work of Maulik and Okounkov in the symplectic dual setting.

Roya Beheshti (Washington U. St. Louis)

February 23, 2018

Moduli spaces of rational curves on hypersurfaces

I will talk about the geometry of moduli spaces of rational curves on Fano hypersurfaces and discuss some results concerning their dimension and birational geometry.

Yongbin Ruan (Michigan)

March 9, 2018

The structure of higher genus Gromov-Witten invariants of quintic 3-fold

The computation of higher genus Gromov-Witten invariants of quintic 3–fold (or compact Calabi-Yau manifold in general) has been a focal point of research of geometric and physics for more than twenty years. A series of deep conjectures have been proposed via mirror symmetry for the specific solutions as well as structures of its generating functions. Building on our initial success for a proof of genus two conjecture formula of BCOV, we present a proof of two conjectures regarding the structure of the theory. The first one is Yamaguchi-Yau’s conjecture that its generating function is a polynomial of five generators and the other one is the famous holomorphic anomaly equation which governs the dependence on four out of five generators. This is a joint work with Shuai Guo and Felix Janda.

Andrei Calderaru (Wisconsin)

April 13, 2018

Computing a categorical Gromov-Witten invariant

In his 2005 paper “The Gromov-Witten potential associated to a TCFT” Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.

In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.

Daniel Halpern-Leistner (Cornell)

April 20, 2018

What is wall-crossing?

I will discuss recent progress in understanding geometric invariant theory from an “intrinsic” perspective. This leads to a conceptually clean meta-principle for how to study the birational geometry of moduli spaces as well as a universal wall-crossing formula for the integrals of tautological K-theory classes on these moduli spaces. I will apply this perspective to the example of Bridgeland semistable complexes on an algebraic surface. The result is a relatively straightforward construction of K-theoretic Donaldson invariants, along with wall-crossing formulas for these invariants which are new-ish (conjecturally equivalent to Mochizuki’s cohomological wall crossing formulas in the context where both are defined).

Sean Howe (Stanford)

April 27, 2018

Motivic random variables and random matrices

As first shown by Katz-Sarnak, the zero spacing of L-functions of smooth plane curves over finite fields approximate the infinite random matrix statistics observed experimentally for the zero spacing of the Riemann-Zeta function (arbitrarily well by first taking the size of the finite field to infinity, and then the degree of the curve to infinity). The key geometric inputs are a computation of the image of the monodromy representation and Deligne’s purity theorem, which ensures that only the zeroth cohomology group of irreducible local systems will contribute asymptotically to the statistics. In this talk, we explain how higher order terms (i.e. the lower weight part of cohomology) can be computed starting from a simple heuristic for the number of points on a random smooth plane curve.

Isabel Vogt (MIT)

May 4, 2018, 3-4 pm

Interpolation problems for curves in projective space

In this talk we will discuss the following question: When does there exist a curve of degree $d$ and genus $g$ passing through $n$ general points in $\mathbb{P}^r$?

Eric Larson (MIT)

May 4, 2018, 4:30-5:30 pm

The Maximal Rank Conjecture

We find the Hilbert function of a general curve of genus $g$, embedded in $\mathbb{P}^r$ via a general linear series of degree $d$. Note that Isabel Vogt’s talk earlier this afternoon is a pre-requisite for this talk.

Dori Bejleri (Brown)

May 18, 2018, 3-4 pm

Stable pair compactifications of the moduli space of degree one del Pezzo surfaces via elliptic fibrations

A degree one del Pezzo surface is the blowup of $\mathbb{P}^2$ at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs $(X,D)$ is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher.

Francois Greer (Stony Brook)

May 18, 2018, 4:30-5:30 pm

Elliptic fibrations in the presence of singularities

The Gromov-Witten generating series for an elliptic fibration is expected to have modular properties by mirror symmetry. When the homology class in the base is irreducible and the total space is smooth, we obtain a classical modular form for the full modular group. If the base class is reducible, we expect the series to be quasi-modular. If the fibration does not admit a section, then the modular form has higher level. Both of these relaxations are related to the presence of singularities in the geometry.

Soren Galatius (Stanford)

May 25, 2018, 3-4 pm, Room TBA

$M_g$, $M_g^{trop}$, GRT, and Kontsevich’s complex of graphs

I will report on recent joint work with Melody Chan and Sam Payne on the cohomology of $M_g$ in degree $4g-6$. It is known that the rational cohomology vanishes above this degree. We prove that the rational cohomology in this degree is non-trivial for all $g \geq 7$ and that its dimension grows faster than $1.324^g +$ constant, making it asymptotically larger than the entire tautological ring and disproving a recent conjecture of Church-Farb-Putman and an older conjecture of Kontsevich. Our proof relates the weight filtration on compactly supported cohomology of $M_g$ with the moduli space of tropical curves and with the cohomology of Kontsevich’s graph complex. We then use a theorem of Willwacher to construct an injection of the Grothendieck-Teichmüller Lie algebra into $H^{2g}_c(M_g)$.

Tathagata Basak (Iowa State University)

May 25, 2018, 4:30-5:30 pm

A complex ball quotient and the monster

We shall talk about an arithmetic lattice M in $PU(13,1)$ acting on the the unit ball B in thirteen dimensional complex vector space. Let X be the space obtained by removing the hypersurfaces in B that have nontrivial stabilizer in M and then quotienting the rest by M. The fundamental group G of the ball quotient X is a complex hyperbolic analog of the braid group. We shall state a conjecture that relates this fundamental group G and the monster simple group and describe our results (joint with D. Allcock) towards this conjecture.

The discrete group M is related to the Leech lattice and has generators and relations analogous to Weyl groups. Time permitting, we shall give a second example in $PU(9,1)$ related to the Barnes-Wall lattice for which there is a similar story.

This entry was posted in seminars. Bookmark the permalink.


text:
# Finding Profit or Loss – Basic Concept, Formulas, Tricks, Examples | Profit and Loss Problems with Solutions PDF

Profit and loss are one we see in our daily life when we go shopping. It is to determine the price of goods or products in the market and understand how profitable or lost a business is. As we discussed in the previous topics, a product has cost price and selling price. There are some important terms for finding profit or loss they are cost price, selling price, list price, fixed price, margin, etc.

We can find the profit or loss of a product with the help of the formula using cost price and selling price. Build your self-confidence by solving the questions given in the below section. If you solve those questions you can be sure about solving any type of question on finding loss or profit.

Do Refer:

### Basic Concepts of Profit or Loss

Profit: The price gained by selling a good or profit with more than its cost price is known as profit.
Loss: The price the seller obtained after selling the goods with less than the cost price is known as loss.
Selling Price: The amount for the product which is sold by the seller is known as the selling price. It is denoted by S.P.
Cost Price: The amount paid for the raw material and product to purchase is known as the cost price. It is denoted by C.P.

## Profit and Loss Formula

• When the selling price is greater than the cost price then
Profit = selling price – cost price
• When the selling price is less than the cost price
Loss = cost price – selling price
• Percentage Profit(%) = Profit/Cost Price × 100
• Percentage Loss(%) = Loss/Cost Price × 100

### Profit and Loss Questions with Solutions

The students of 5th grade can make their preparation easy by practicing the question and answers on finding profit or loss. This will help you to score good marks in the exams.

Example 1.
If Riya buys paddy at Rs. 287 per kg and she sells it at Rs. 300 per kg she makes a profit or loss?
Solution:
She sells at ( selling price ) = Rs. 300
Here selling price is greater than cost price
So, profit = selling price – cost price
300 – 287 = 13
Profit = Rs. 13
Thus the profit is Rs. 13

Example 2.
Rao buys carrots from the former for Rs. 180 and for cleaning purposes he spent Rs. 20 and for packing he sent Rs. 20 and he sold it for Rs. 200. Find that he have a profit or loss?
Solution:
Given,
Rao buys carrots from the former = Rs. 180
Rao used for cleaning purposes = Rs. 20
He spent for packing purposes = Rs. 20
Total money he spent to buy a carrots = 180 + 20 + 20 = 220
He sold for = 200
Here selling price is less than the cost price
Loss = cp – sp
220 – 200 = 20
Loss = 20
Therefore Rao has a loss of Rs. 20

Example 3.
If Sita buys a bar of gold at $840 per gram and she sells it at$984 per gram she makes a profit or loss?
Solution:
Given,
Sita buy a gold = $840 She sells it =$984
Here selling price is greater than the cost price.
Profit = sp – cp
$984 –$840 = $144 Profit =$144
Therefore Sita has a profit of $144. Example 4. If Milky buys a cycle for$28000 and she sold at $25000 she makes a profit or loss? Solution: Given, Milky buy a cycle =$28000
She sold = $25000 Here selling price is less than the cost price Loss = cp – sp 28000 – 25000 = 3000 Loss =$3000
Thus Milky makes a loss of $3000 on cycle. Example 5. Roman buy a ticket at a cost of$68 and he sold it for $72 that he makes a profit or loss? Solution: Given, Roman buy a ticket at a cost =$68
Roman sold a ticket at a cost = $72 Here selling price is greater than the cost price So, profit = sp – cp 72 – 68 = 4 Profit = 4 Thus Roman makes a profit of$4.

Points to Remember:

• For Loss, the C.P should be more than the S.P.
• For Profit, the C.P should be less than the S.P.
• The percentage value for profit and loss is calculated in terms of C.P.

### FAQs on Profit Loss Formula

1. What is the profit and loss percentage formula?

The formula for profit percentage is P% = profit/C.P × 100
The formula for loss percentage is L% = loss/C.P × 100

2. What is the Selling Price Formula?

Selling Price = Cost Price + Profit

3. What is Profit Loss Formula?

The formula which is used to find the profit loss is
Profit = Selling Price – Cost price
Loss = Cost Price – Selling Price

Scroll to Top

format: plain


text:
HRSCumulativeMultiplier¶

Bases: qiskit.circuit.library.arithmetic.multipliers.multiplier.Multiplier

A multiplication circuit to store product of two input registers out-of-place.

Circuit uses the approach from [1]. As an example, a multiplier circuit that performs a non-modular multiplication on two 3-qubit sized registers with the default adder is as follows (where Adder denotes the CDKMRippleCarryAdder):

  a_0: ────■─────────────────────────
│
a_1: ────┼─────────■───────────────
│         │
a_2: ────┼─────────┼─────────■─────
┌───┴────┐┌───┴────┐┌───┴────┐
b_0: ┤0       ├┤0       ├┤0       ├
│        ││        ││        │
b_1: ┤1       ├┤1       ├┤1       ├
│        ││        ││        │
b_2: ┤2       ├┤2       ├┤2       ├
│        ││        ││        │
out_0: ┤3       ├┤        ├┤        ├
│        ││        ││        │
out_1: ┤4       ├┤3       ├┤        ├
out_2: ┤5       ├┤4       ├┤3       ├
│        ││        ││        │
out_3: ┤6       ├┤5       ├┤4       ├
│        ││        ││        │
out_4: ┤        ├┤6       ├┤5       ├
│        ││        ││        │
out_5: ┤        ├┤        ├┤6       ├
│        ││        ││        │
aux_0: ┤7       ├┤7       ├┤7       ├
└────────┘└────────┘└────────┘

Multiplication in this circuit is implemented in a classical approach by performing a series of shifted additions using one of the input registers while the qubits from the other input register act as control qubits for the adders.

References:

[1] Häner et al., Optimizing Quantum Circuits for Arithmetic, 2018. arXiv:1805.12445

Parameters
• num_state_qubits (int) – The number of qubits in either input register for state $$|a\rangle$$ or $$|b\rangle$$. The two input registers must have the same number of qubits.

• num_result_qubits (Optional[int]) – The number of result qubits to limit the output to. If number of result qubits is $$n$$, multiplication modulo $$2^n$$ is performed to limit the output to the specified number of qubits. Default value is 2 * num_state_qubits to represent any possible result from the multiplication of the two inputs.

• adder (Optional[QuantumCircuit]) – Half adder circuit to be used for performing multiplication. The CDKMRippleCarryAdder is used as default if no adder is provided.

• name (str) – The name of the circuit object.

Raises

NotImplementedError – If num_result_qubits is not default and a custom adder is provided.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

Return type

List[AncillaQubit]

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{‘gate_name’: {(qubits, params): schedule}}

Return type

dict

clbits

Returns a list of classical bits in the order that the registers were added.

Return type

List[Clbit]

data

Return the circuit data (instructions and context).

Returns

a list-like object containing the tuples for the circuit’s data.

Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.

Return type

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

Return type

Union[ParameterExpression, float]

instances = 9

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Return type

dict

num_ancillas

Return the number of ancilla qubits.

Return type

int

num_clbits

Return number of classical bits.

Return type

int

num_parameters

Convenience function to get the number of parameter objects in the circuit.

Return type

int

num_qubits

Return number of qubits.

Return type

int

num_result_qubits

The number of result qubits to limit the output to.

Return type

int

Returns

The number of result qubits.

num_state_qubits

The number of state qubits, i.e. the number of bits in each input register.

Return type

int

Returns

The number of state qubits.

parameters

Convenience function to get the parameters defined in the parameter table.

Return type

ParameterView

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.

Return type

List[Qubit]


text:
Testing for cointegration and building a VEC model

I have 3 variables which are all stationary at 2nd order difference. I want to check for cointegration using the piece of code below. If I run pairwise cointegration analysis then I get these results:

VARselect(f1[2:3], lag.max=10)$selection ## optimal no of lags to be 7 coint=ca.jo(f1[2:3], ecdet="none", type="trace", K=7, spec="longrun") summary(coint) ## indicates cointegrating relationship Values of teststatistic and critical values of test: test 10pct 5pct 1pct r <= 1 | 29.23 6.50 8.18 11.65 r = 0 | 75.18 15.66 17.95 23.52  This means that there is no cointegrating relationship between them. If I do this for other variables, f1[3:4] and f1[c(2,4)] then I get one cointegrating relationship. VARselect is used to choose the optimal lag. For all the variables together: VARselect(f1[2:4], lag.max=10)$selection
AIC(n)  HQ(n)  SC(n) FPE(n)
5      5      5      4

coint=ca.jo(f1[2:4], ecdet="none", type="trace", K=5, spec="longrun")
summary(coint)
Values of test statistic and critical values of test:
test 10pct  5pct  1pct
r <= 2 |  0.08  6.50  8.18 11.65
r <= 1 | 14.24 15.66 17.95 23.52
r = 0  | 39.67 28.71 31.52 37.22

1. Do I need to take in all variable while running a VECM?
2. Is VARselect the right way to choose the lag to be specified in ca.jo?

This would mean that there is cointegration between the variables and I need to run a VECM. But how do I know how many cointegrating relationships are there. As far as i have seen $r=2$ will be specified while doing a vecm

3. Is $r=2$ the correct way to specify a VECM?

cajools(coint)
cajorls(coint, r = 2) # or use this

Is this procedure that I am following a correct way to model?

Update 1:

1. For 1. I think it is up to us to determine what kind of relationship we would like to examine and then set up a model!
2. Ya its a iterative VAR to choose the right lag length.
3. Not clear: so the highest rank I can not reject would be 2 for the 3 variable case?

Update 2: Regarding 3. I was asking for the f1[2:4] where I produced the statistics. According to me there is only 1 cointegrating relationship. So $r=1$ in fitting a VECM.

Update 3:

1. As my variables becomes stationary at 2nd order of difference, can I perform a Johansen co-integration which works at I(1)? Or do I have to feed in the first difference of my variables in order to perform Johansen co-integration.
2. Also since using VARselect the optimal lag turned out to be 4. So I have to take lag=3 while running a cointegration model.
• What type of data is this? Having I(2) series is not very common, especially three of them. How did you conclude this? – hejseb May 20 '16 at 16:32
• This is time series data with 24 obs. i used adf test and after 2nd diff they would become stationary. – Chirayu Chamoli May 20 '16 at 16:46

You seem to be doing pairwise analysis when you in fact have three variables. This way you may miss cointegrating relationships that are not pairwise but involve more variables. The standard way in modelling of cointegrated variables is to use all the variables you have if they are integrated of the same order.

1. Yes, include all three variables in VAR modelling and cointegration testing.
2. Yes, it is an acceptable method. You can find it used, e.g., in Pfaff (2008), p. 149 or in the vignette of "vars" package in R, p. 17.
3. Johansen procedure as implemented in function ca.jo will help you find the number of cointegrating vectors. Take the output of ca.jo, start with $r=0$ and see if you can reject the null hypothesis of $r=0$ using the test statistic and the critical values reported in the output. If you reject, move to $r=1$ and upwards until you cannot reject. The first rank that you cannot reject is the number of cointegrating vectors. If you can reject all of them, all of your series appear to be stationary.
In general, any modern time series textbook should include a section on cointegration testing using Johansen procedure; just follow it.

Update (for the updated OP)

1. Neglecting cointegration relationships beyond pairwise ones may lead to omitted variable bias -- because you would be omitting error correction terms associated with the neglected cointegrating vectors.
2. Cannot understand the question, sorry.
3. If the variables are truly integrated, you cannot have $r=m$ for $m$ being the number of time series in the system. In a three-variable case, $r=2$ is the highest rank; $r=3$ already implies the variables are not integrated to begin with.

References

• Pfaff, Bernhard. Analysis of integrated and cointegrated time series with R. Springer Science & Business Media, 2008.
• Pfaff, Bernhard. "VAR, SVAR and SVEC models: Implementation within R package vars." Journal of Statistical Software 27.4 (2008): 1-32.
• If you are updating your post with new material, it is best to include a clearly marked new section or ask a separate new question. Because the initial answer addresses the original post and should be judged in relation to it. – Richard Hardy May 20 '16 at 16:55
• Ok i have italicized my edits. – Chirayu Chamoli May 20 '16 at 17:00
• Italics does not seem quite sufficient. Normally you would add a separate section called Update and list your new questions there. This is what is usually done. – Richard Hardy May 20 '16 at 17:05
• Yeah I have added an update section. – Chirayu Chamoli May 20 '16 at 17:09
• Hahah I have read time series but it was a long time back! And cant Thank you enough for this. – Chirayu Chamoli May 20 '16 at 17:14


text:
# A company that makes thing-a-ma-bobs has a start up cost of $44055. It costs the company$1.97 to make each thing-a-ma-bob. The company charges $5.31 for each thing-a-ma-bob. Let x denote the number of thing-a-ma-bobs produced. Write the cost function for this company. C(x) = Write the revenue function for this company. R(x) = What is the minumum number of thing-a-ma-bobs that the company must produce and sell to make a profit? # A company that makes thing-a-ma-bobs has a start up cost of$44055. It costs the company $1.97 to make each thing-a-ma-bob. The company charges$5.31 for each thing-a-ma-bob. Let x denote the number of thing-a-ma-bobs produced. Write the cost function for this company. C(x) = Write the revenue function for this company. R(x) = What is the minumum number of thing-a-ma-bobs that the company must produce and sell to make a profit?

Question
Analysis
A company that makes thing-a-ma-bobs has a start up cost of $44055. It costs the company$1.97 to make each thing-a-ma-bob. The company charges $5.31 for each thing-a-ma-bob. Let x denote the number of thing-a-ma-bobs produced. Write the cost function for this company. C(x) = Write the revenue function for this company. R(x) = What is the minumum number of thing-a-ma-bobs that the company must produce and sell to make a profit? ## Answers (1) 2021-01-20 The cost would be the start up cost plus the cost to make xx thing-a-ma-bobs. C(x)=44055+1.97xC(x)=44055+1.97x The revenue is how much the company makes per x thing-a-ma-bobs sold. R(x)=5.31xR(x)=5.31x In order to make a profit, total revenue has to exceed total cost. R(x)>C(x)R(x)>C(x) 5.31x>44055+1.97x5.31x>44055+1.97x 3.34x>440553.34x>44055 x>13190.1x>13190.1 Because you can only sell an integer number of thing-a-ma-bobs, the company must sell at least 1319113191 thing-a-ma-bobs. ### Relevant Questions asked 2021-04-20 (1 pt) A new software company wants to start selling DVDs withtheir product. The manager notices that when the price for a DVD is19 dollars, the company sells 140 units per week. When the price is28 dollars, the number of DVDs sold decreases to 90 units per week.Answer the following questions: A. Assume that the demand curve is linear. Find the demand, q, as afunction of price, p. Answer: q= B. Write the revenue function, as a function of price. Answer:R(p)= C. Find the price that maximizes revenue. Hint: you may sketch thegraph of the revenue function. Round your answer to the closestdollar. Answer: D. Find the maximum revenue. Answer: asked 2021-03-11 Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p $$200 53.00$$ $$250 52.50$$ $$300 52.00$$ $$35051.50$$ (a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. $$R=$$ Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost, $$C= 35N + 900$$, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month $$p=$$ (d) Is Pa linear function of N2 e. Explain how you would find breakeven. What does breakeven represent? asked 2021-05-12 4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs. a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy? b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives? asked 2021-02-14 Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts$180 per foot across the river and $100 per foot along theland. (a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x. (b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P. asked 2021-05-16 Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P. A. Let y=f(x) be the equation of C. Find f(x). B. Find the slope at P of the tangent to C. C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P? D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx. E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D. Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P. asked 2021-05-05 The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $$\displaystyle\mu={1.5}$$ and $$\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$$. (a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability. (b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$. (c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring. (d) What point has the property that only 10% of the soil samples have bulk density this high orhigher? (e) What is the moment generating function for X? asked 2021-04-07 Ok, If a bobsled makes a run down an ice track starting at 150m vertical distance up the hill and there is no friction, what isthe velocity at the bottom of the hill? I know that the initial velocity here is 0 because it isstarting from rest. And this problem deal with theconservation of energy. But, I don't know where to go fromhere. asked 2020-12-06 A gambling book recommends the following "winning strategy" for the game of roulette. It recommends that a gambler bet$1 onred. If red appears (which has probablity 18/38), then the gamblershould take her $1 profit and quit. If the gambler loses this bet (which has probablity 20/38 of occurring), she should make additional$1 bets on red on each of the next two spins of the roulette wheel and then quite. Let X denote the gambler's winnings when she quites.
(a) Find P{X > 0}.
(b) Are you concinved that the strategy is indeed a "winning" strategy? Explain your answer.
(c) Find E[X].
The cost in dollars to produce x youth baseball caps is C(x) = 4.3x + 75. The revenue in dollars from sales of x caps is $$\displaystyle{R}{\left({x}\right)}={25}{x}$$.
(a) Write and simplify a function P that gives profit in terms of x.
(b) Find the profit if 50 caps are produced and sold.
$$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}$$
$$\displaystyle{p}=$$
$$\displaystyle{R}=$$
(c) On the basis of the tables in this exercise and using cost, $$\displaystyle{C}={35}{N}+{900}$$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
$$\displaystyle{P}=$$


text:
# Lambert W function: limits and inverse relation

I'm looking for a specific limit of a function containing The lambert W function.

for the most simplified case, my function looks as follows:

$y=W(-rxe^x)$

this is the plot of the function for $r=0.1$:

As you can see from the figure, $y\rightarrow -\infty$ somewhere $x\approx1.1$.

I would like to find this limit.

When I Inverse the function using mathematica, I get a solution (which I think is only one branch) of the form:

$x=W(-\frac{1}{r} y e^y)$

The mathematica plot of that function looks as follows:

As you can see from the figure, when $y\rightarrow\infty$, then $x\rightarrow0$.

This does not coincide with the previous result.

Can anyone please, reference, direct or explain how to solve the following problems:

1. Finding the inverse function of $y(x)=W(-rxe^x)$, i.e, $x(y)$.

2. Find the value of $x$ in which $y(x)=W(-rxe^x)$ converges to, in the limit of $y(x)\rightarrow -\infty$.

1) The branch point $x_b$ of LambertW is at $x_b=-\frac{1}{e}$. So your limit point $x_l$ is the solution of $-\frac{1}{e}= -rxe^x$, and therefore $$x_l(r) = W\left(\frac{1}{re}\right)$$

$$x_l(0.1) = W\left(\frac{1}{0.1e}\right)=W\left(\frac{10}{e}\right) = 1.156868396615\dots$$

The limit is not $-\infty$ but $$\lim_{x\to x_l^{-}}y(x) = -1$$ For $x > x_l$ the function values $y(x)$ are complex.

2) The inverse of $y(x) = W(-rxe^x)$ is indeed $$x(y) = W\left(-\frac{ye^y}{r}\right)$$ and with Maple I get limit(LambertW(-1/r*y*exp(y)), y=-infinity) = 0.

But note that $x(-1) = x_l,$ so there is no inconsistency to $y(x_l) = -1.$

• you are correct, this function has many branches, and it does not diverge at $x_l$ but rather the $W_0$ branch meet that $W_{-1}$ branch. – jarhead Feb 13 '18 at 16:21


text:
# 2.3 Staggered holes

 Page 1 / 1

#### Failure due to staggered holes

When a member has staggered bolt holes, a different approach to finding ${A}_{e}$ for the fracture limit state is taken. This is because the effective net area ( $t$ x ${w}_{n}$ ) is different as the line of fracture changes due to the stagger in the holes. The test for the yielding limit state remainsunchanged (the gross area is still the same).

#### Failure lines

The net width now must account for the change in direction of the line of fracture. First, look at different ways a tension memberwith staggered holes can fracture. These pictures depict the different lines of failure. When analyzing a member like this,it is important to find all the lines of failure and then determine which line of failure is the weakest cross section.That cross section will be taken as the net width, ${w}_{n}$ .

#### Net width

In order to find the net width, first the variables $s$ and $g$ must be known. They are shown in .

${w}_{n}={w}_{g}-N{\phi }_{d}+\frac{s^{2}}{4g}$

#### Where:

• ${w}_{n}$ = net width
• ${w}_{g}$ = gross width
• ${\phi }_{d}={\phi }_{b}+\frac{1}{16}+\frac{1}{16}$ where: ${\phi }_{b}$ = diameter of the bolt
• $N$ = number of bolts in cross section
• $s$ = longitudinal center-to-center spacing of any two consecutive holes, in.
• $g$ = transverse center-to-center spacing between fastener gage lines, in.
• The term $\frac{s^{2}}{4g}$ is added for every non-straight segment

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!


text:
Presentation is loading. Please wait.

# Alternation Alternation: generalizes non-determinism, where each state is either “existential” or “universal”: Old: existential states New: universal states.

## Presentation on theme: "Alternation Alternation: generalizes non-determinism, where each state is either “existential” or “universal”: Old: existential states New: universal states."— Presentation transcript:

Alternation Alternation: generalizes non-determinism, where each state is either “existential” or “universal”: Old: existential states New: universal states Existential state is accepting iff any of its child states is accepting (OR) Universal state is accepting iff all of its child states are accepting (AND) Alternating computation is a “tree”. Final states are accepting Non-final states are rejecting Computation accepts iff initial state is accepting Note: in non-determinism, all states are existential       

Alternation Theorem: a k-state alternating finite automaton can be converted into an equivalent 2 k -state non-deterministic FA. Proof idea: a generalized powerset construction. Theorem: a k-state alternating finite automaton can be converted into an equivalent 2 2 k -state deterministic FA. Proof: two composed powerset constructions. Def: alternating Turing machine is an alternating FA with an unbounded read/write tape. Theorem: alternation does not increase the language recognition power of Turing machine. Proof: by simulation.

Alternating Complexity Classes Def: ATIME(t(n))={L | L is decidable within time O(t(n)) by some alternating TM} Def: ASPACE(s(n))={L | L decidable within space O(s(n)) by some alternating TM} Def: AP =  ATIME(n k )  k>1 AP  alternating polynomial time Def: APSPACE =  ASPACE(n k )  k>1 APSPACE  alternating polynomial space Properties!

Alternating Complexity Classes Def: AEXPTIME =  ATIME(2 n k )  k>1 AEXPTIME  alternating exponential time Def: AEXPSPACE =  ASPACE(2 n k )  k>1 AEXPSPACE  alternating exponential space Def: AL = ALOGSPACE = ASPACE(log n) AL  alternating logarithmic space Note: AP, ASPACE, AL are model-independent

Alternating Space/Time Relationships Theorem: P  NP  AP Open: NP = AP ? Open: P = AP ? Corollary: P=AP  P=NP Theorem: ATIME(f(n))  DSPACE(f(n))  ATIME(f 2 (n)) Theorem: PSPACE  NPSPACE  APSPACE Theorem: ASPACE(f(n))  DTIME(c f(n) ) Theorem: AL = P Theorem: AP = PSPACE Theorem: APSPACE = EXPTIME Theorem: AEXPTIME = EXPSPACE  

Quantified Boolean Formula Problem Def: Given a fully quantified Boolean formula, where each variable is quantified existentially or universally, does it evaluate to “true”? Example: Is “  x  y  z (x  z)  y” true? Also known as quantified satisfiability (QSAT) Satisfiability (one  only) is a special case of QBF Theorem: QBF is PSPACE-complete. Proof idea: combination of [Cook] and [Savitch]. Theorem: QBF  TIME(2 n ) Proof: recursively evaluate all possibilities. Theorem: QBF  DSPACE(n) Proof: reuse space during exhaustive evaluations. Theorem: QBF  ATIME(n) Proof: use alternation to guess and verify formula.

QBF and Two-Player Games SAT solutions can be succinctly (polynomially) specified. It is not known how to succinctly specify QBF solutions. QBF naturally models winning strategies for two-player games:  a move for player A  moves for player B  a move for player A  moves for player B  a move for player A... player A has a winning move!   

QBF and Two-Player Games Theorem: Generalized Checkers is EXPTIME-complete. Theorem: Generalized Chess is EXPTIME-complete. Theorem: Generalized Go is EXPTIME-complete. Theorem: Generalized Othello is PSPACE-complete.

Idea: bound the number of “existential” / “universal” states Old: unbounded existential / universal states New: at most i existential / universal alternations Def: a  i -alternating TM has at most i runs of quantified steps, starting with existential Def: a  i -alternating TM has at most i runs of quantified steps, starting with universal Note:  i - and  i - alternation-bounded TMs are similar to unbounded alternating TMs        The Polynomial Hierarchy i=1 i=2 i=3 i=4 i=5  5 -alternating

Def:  i TIME(t(n))={L | L is decidable within time O(t(n)) by some  i -alternating TM} Def:  i SPACE(s(n))={L | L is decidable within space O(s(n)) by some  i -alternating TM} Def:  i TIME(t(n))={L | L is decidable within time O(t(n)) by some  i -alternating TM} Def:  i SPACE(s(n))={L | L is decidable within space O(s(n)) by some  i -alternating TM} Def:  i P =   i TIME(n k )  k>1 Def:  i P =   i TIME(n k )  k>1      The Polynomial Hierarchy

Def:  PH =   i P  i>1 Def:  PH =   i P  i>1 Theorem:  PH =  PH Def: The Polynomial Hierarchy PH =  PH  Languages accpted by polynomial time, unbounded-alternations TMs Theorem:  0 P=  0 P= P Theorem:  1 P=NP,  1 P= co-NP Theorem:  i P   i+1 P,  i P   i+1 P Theorem:  i P   i+1 P,  i P   i+1 P      The Polynomial Hierarchy

Theorem:  i P  PSPACE Theorem:  i P  PSPACE Theorem: PH  PSPACE Open: PH  PSPACE  Open:  0 P=  1 P  P=NP  Open:  0 P=  1 P  P=co-NP  Open:  1 P=  1 P  NP=co-NP  Open:  k P   k+1 P for any k ? Open:  k P   k+1 P for any k ? Open:  k P   k P for any k ? Theorem: PH = languages expressible by 2 nd -order logic      The Polynomial Hierarchy Infinite number of “P=NP”–type open problems!

Open: Is the polynomial hierarchy infinite ? Theorem: If any two successive levels conicide (  k P   k+1 P or  k P   k P for some k) then the entire polynomial hierarchy collapses to that level (i.e., PH =  k P =  k P). Corollary: If P = NP then the entire polynomial hierarchy collapses completely (i.e., PH = P = NP). Theorem: P=NP  P=PH Corollary: To show P ≠ NP, it suffices to show P ≠ PH. Theorem: There exist oracles that separate  k P ≠  k+1 P. Theorem: PH contains almost all well-known complexity classes in PSPACE, including P, NP, co-NP, BPP, RP, etc. The Polynomial Hierarchy

… … … … … … … … … … PSPACE-complete QBF The Extended Chomsky Hierarchy Reloaded Context-free ww R PanbncnPanbncn NP Recognizable Not Recognizable HH Decidable Presburger arithmetic NP-complete SAT Not finitely describable  ** EXPTIME EXPTIME-complete Go EXPSPACE-complete =RE  Context sensitive LBA EXPSPACE PSPACE Dense infinite time & space complexity hierarchies … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … Regular a* … … … … … … … … … … … … … … … Turing degrees Other infinite complexity & descriptive hierarchies … … … … … Det. CF a n b n … … … … … Finite {a,b} … … … … … PH

Probabilistic Turing Machines Idea: allow randomness / coin-flips during computation Old: nondeterministic states New: random states changes via coin-flips Each coin-flip state has two successor states Def: Probability of branch B is Pr[B] = 2 -k where k is the # of coin-flips along B. Def: Probability that M accepts w is sum of the probabilities of all accepting branches. Def: Probability that M rejects w is 1 – (probability that M accepts w). Def: Probability that M accepts L with probability  if: w  L  probability(M accepts w)  1-  w  L  probability(M rejects w)  1- 

Probabilistic Turing Machines Def: BPP is the class of languages accepted by probabilistic polynomial time TMs with error  =1/3. Note: BPP Bounded-error Probabilistic Polynomial time Theorem: any error threshold 0<  can be substituted. Proof idea: run the probabilistic TM multiple times and take the majority of the outputs. Theorem [Rabin, 1980]: Primality testing is in BPP. Theorem [Agrawal et al., 2002]: Primality testing is in P. Note: BPP is one of the largest practical classes of problems that can be solved effectively. Theorem: BPP is closed under complement (BPP=co-BPP). Open: BPP  NP ? Open: NP  BPP ?

Probabilistic Turing Machines Theorem: BPP  PH Theorem: P=NP  BPP=P Theorem: NP  BPP  PH  BPP Note: the former is unlikely, since this would imply efficient randomized algorithms for many NP-hard problems. Def: A pseudorandom number generator (PRNG) is an algorithm for generating number sequences that approximates the properties of random numbers. Theorem: The existance of strong PRNGs implies that P=BPP. “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.” John von Neumann

… … … … … … … … … … PSPACE-complete QBF The Extended Chomsky Hierarchy Reloaded Context-free ww R PanbncnPanbncn NP Recognizable Not Recognizable HH Decidable Presburger arithmetic NP-complete SAT Not finitely describable  ** EXPTIME EXPTIME-complete Go EXPSPACE-complete =RE  Context sensitive LBA EXPSPACE PSPACE Dense infinite time & space complexity hierarchies … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … Regular a* … … … … … … … … … … … … … … … Turing degrees Other infinite complexity & descriptive hierarchies … … … … … Det. CF a n b n … … … … … Finite {a,b} … … … … … PH BPP

Blueberry Muffin Turing Machines L(M) = {w | w  *, w=w R }

Download ppt "Alternation Alternation: generalizes non-determinism, where each state is either “existential” or “universal”: Old: existential states New: universal states."

Similar presentations

Ads by Google


text:
# What is 45/67 as a decimal?

## Solution and how to convert 45 / 67 into a decimal

45 / 67 = 0.672

Converting 45/67 to 0.672 starts with defining whether or not the number should be represented by a fraction, decimal, or even a percentage. Both are used to handle numbers less than one or between whole numbers, known as integers. In certain scenarios, fractions would make more sense. Ex: baking, meal prep, time discussion, etc. While decimals bring clarity to others including test grades, sale prices, and contract numbers. So let’s dive into how and why you can convert 45/67 into a decimal.

## 45/67 is 45 divided by 67

The first step in converting fractions is understanding the equation. A quick trick to convert fractions mentally is recognizing that the equation is already set for us. All we have to do is think back to the classroom and leverage long division. Fractions have two parts: Numerators and Denominators. This creates an equation. We must divide 45 into 67 to find out how many whole parts it will have plus representing the remainder in decimal form. Here's how our equation is set up:

### Numerator: 45

• Numerators are the top number of the fraction which represent the parts of the equation. Overall, 45 is a big number which means you'll have a significant number of parts to your equation. The bad news is that it's an odd number which makes it harder to covert in your head. Large two-digit conversions are tough. Especially without a calculator. Now let's explore X, the denominator.

### Denominator: 67

• Denominators are located at the bottom of the fraction, representing the total number of parts. 67 is a large number which means you should probably use a calculator. But the bad news is that odd numbers are tougher to simplify. Unfortunately and odd denominator is difficult to simplify unless it's divisible by 3, 5 or 7. Ultimately, don't be afraid of double-digit denominators. Now let's dive into how we convert into decimal format.

## Converting 45/67 to 0.672

### Step 1: Set your long division bracket: denominator / numerator

$$\require{enclose} 67 \enclose{longdiv}{ 45 }$$

To solve, we will use left-to-right long division. This is the same method we all learned in school when dividing any number against itself and we will use the same process for number conversion as well.

### Step 2: Extend your division problem

$$\require{enclose} 00. \\ 67 \enclose{longdiv}{ 45.0 }$$

We've hit our first challenge. 45 cannot be divided into 67! So we will have to extend our division problem. Add a decimal point to 45, your numerator, and add an additional zero. Now 67 will be able to divide into 450.

### Step 3: Solve for how many whole groups you can divide 67 into 450

$$\require{enclose} 00.6 \\ 67 \enclose{longdiv}{ 45.0 }$$

Now that we've extended the equation, we can divide 67 into 450 and return our first potential solution! Multiply this number by 67, the denominator to get the first part of your answer!

### Step 4: Subtract the remainder

$$\require{enclose} 00.6 \\ 67 \enclose{longdiv}{ 45.0 } \\ \underline{ 402 \phantom{00} } \\ 48 \phantom{0}$$

If you hit a remainder of zero, the equation is done and you have your decimal conversion. If there is a remainder, extend 67 again and pull down the zero

### Step 5: Repeat step 4 until you have no remainder or reach a decimal point you feel comfortable stopping. Then round to the nearest digit.

Sometimes you won't reach a remainder of zero. Rounding to the nearest digit is perfectly acceptable.

### Why should you convert between fractions, decimals, and percentages?

Converting between fractions and decimals is a necessity. Remember, fractions and decimals are both representations of whole numbers to determine more specific parts of a number. This is also true for percentages. It’s common for students to hate learning about decimals and fractions because it is tedious. But each represent values in everyday life! Here are just a few ways we use 45/67, 0.672 or 67% in our daily world:

### When you should convert 45/67 into a decimal

Tax - Taxes are also in decimal form. Example. \$0.06 on every dollar spent. This is also represented in percentages.

### When to convert 0.672 to 45/67 as a fraction

Meal Prep - Body builders need to count macro calories. One of the ways of doing this is measuring every piece of food consumed. This is through halves and quarters in order to keep it consistent.

### Practice Decimal Conversion with your Classroom

• If 45/67 = 0.672 what would it be as a percentage?
• What is 1 + 45/67 in decimal form?
• What is 1 - 45/67 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 0.672 + 1/2?


text:
5 Postcript added that summarizes present knowledge
4 Fixed the URL to Lipton's weblog.

On Dick Lipton's weblog, I posted a brief essay on demi-exponential functions, which I repeat here:

To expand upon Ken's remarks regarding demi-exponential functions (which is a fine name for them!), the analytic structure of these functions derives from the Lambert $W$ function, which is the subject of a classic article On the Lambert W Function (1996) by Corless, Gonnet, Hare, Jeffrey, and Knuth (yes, one somehow knew that Donald Knuth's name would arise in connection to such an interesting function ... to date this article has received more than 1600 references).

The connection arises via the following construction. Suppose that a demi-exponential function $d$ satisfies $d \circ d \circ \dots \circ d \circ z = \gamma \beta^z$, where $d$ is composed $k$ times. We say that $k$ is the order of the demi-function, $\gamma$ is the gain and $\beta$ is the base. It is easy to show that the fixed points of $d$ are given explicitly in terms of the $n$-th branch of the Lambert function as $z_f = -W_n(-\gamma \ln \beta)/\ln \beta$. Then by a series expansion about these fixed points (optionally augmented by a Pade resummation) it is straightforward to construct the demi-exponential functions both formally and numerically.

Provided the demi-exponential base and gain satisfy $\gamma \le 1/(e \ln \beta)$, such that the fixed points associated to the $n=-1$ branch of the $W$-function are real and positive, this construction yields smooth demi-exponential functions that pleasingly accord with our intuition of what demi-exponential functions should'' look like.

Counter-intuitively though, whenever the specified gain and base are sufficiently large that $\gamma > 1/(e \ln \beta)$, then the demi-exponential function has no real-valued fixed points, but rather develops jump-type singularities. In particular, the seemingly reasonable parameters $\beta=e$ and $\gamma=1$ have no smooth demi-exponential function associated to them (at least, that's the numerical evidence).

Perhaps this is one reason that demi-exponential functions have a reputation for being difficult to construct ... it is indeed very difficult to construct smooth functions for ranges of parameters such that no function has the desired smoothness!

It might be feasible (AFAICT) to write an article \emph{On On demi-exponential functions associated to the Lambert W Function}Function, and to include these functions in standard numerical packages (SciPy, MATLAB, Mathematica, etc.).

Some tough challenges would have to be met, however. Especially, there is at present no known integral representation of the demi-exponential functions (known to me, anyway), and yet such a representation would be very useful (perhaps even essential) in rigorously proving the analytical structures that the numerical Pade approximants show us so clearly.

Here's what these functions look like:

Mathematica script here (PDF).

On Scott Aaronson's Dick Lipton's weblog, I have posted numerical examples of half-exponential a brief essay on demi-exponential functions, which were numerically computed by high-order Padé approximant techniques.

The specific compositional equation solved I repeat here:

To expand upon Ken's remarks regarding demi-exponential functions (which is $f_\beta\circ f_\beta = \beta\ \text{exp}$, so that $\beta$ may be regarded as a half-exponential gain parameter.

The Padé approximants paint fine name for them!), the following picture analytic structure of these functions derives from the Lambert $f_\beta(z)$:

(1) YesW$function,$f_\beta(z)$which is analytic in$z$and$\beta$.the subject of a classic article On the Lambert W Function (2) No1996) by Corless,$f_\beta(z)$is not Gonnet, Hare, Jeffrey, and Knuth (yes, one somehow knew that Donald Knuth's name would arise in connection to such an entire interesting function ; it ... to date this article has a real-axis branch cut for$-\infty < z < -1/2$. (3) On received more than 1600 references). The connection arises via the following construction. Suppose that a demi-exponential function$-1/2 < z$real axis with d$ satisfies $\beta$ real, d \circ d \circ \dots \circ d \circ z = \gamma \beta^z$, where$f_\beta(z)$d$ is smooth iff composed $0 < \beta \le 1/e$k$times. For We say that$\beta > 1/e$k$ is the order of the demi-function, $\gamma$ is the function gain and $f_\beta(z)$ exhibits discrete jumps (see graph above) that are accompanied by \beta$is the well-known Gibbs phenomenon (that base. It is , numerical overshoot); these are associated easy to show that the well-known branch cut fixed points of$d$are given explicitly in terms of the Lambert function$W_{-1}(-\beta)$. Perhaps surprisingly, n$-th branch of the compositional relation Lambert function as $f_\beta\circ f_\beta z_f = -W_n(-\gamma \beta\ ln \text{exp}$ is satisfied even beta)/\ln \beta$. Then by a series expansion about these "jump" solutions. It thus appears that the conventional gain choice$\beta = 1$, which has often appeared in the mathematical literature fixed points (and also here on MathOverflowoptionally augmented by a Pade resummation) it is unfortunate from an analytic point of view; smaller values of straightforward to construct the demi-exponential functions both formally and numerically. Provided the demi-exponential base and gain satisfy$\beta \gamma \le 1/e$yield the smooth "half-exponential" behavior 1/(e \ln \beta)$, such that is most natural for information-theory purposes.

When I have a little more material (and time) available, I will post as a MathOverflow question/exercise the problems fixed points associated to the $n=-1$ branch of (1) proving the above assertions rigorously, and (2) providing numerical algorithms for computing $f_\beta(z)$ efficiently W$-function are real and to arbitrary accuracypositive, for all (complex) values this construction yields smooth demi-exponential functions that pleasingly accord with our intuition of$\beta$what demi-exponential functions should'' look like. Counter-intuitively though, whenever the specified gain and base are sufficiently large that$z$. In \gamma > 1/(e \ln \beta)$, then the interimdemi-exponential function has no real-valued fixed points, my algorithms for constructing high-order Padé approximants to $f_\beta(z)$ are herebut rather develops jump-type singularities. In summaryparticular, the strikingly simple (and numerically robust) analytic structure of the Padé approximants provides seemingly reasonable evidence that the above picture of the analytic structure of parameters $f_\beta(z)$ is likely \beta=e$and$\gamma=1$have no smooth demi-exponential function associated to confirmed by future more rigorous investigationsthem (at least, that's the numerical evidence). It therefore appears Perhaps this is one reason that —with considerable further mathematical work—$f_\beta(z)\$ may eventually take its place as a fully-qualified member of the pantheon of special demi-exponential functions have a reputation for being difficult to construct ... if it is indeed very difficult to construct smooth functions for no other reason, than ranges of parameters such that this no function has the desired smoothness!

It might be feasible (AFAICT) to write an article \emph{On demi-exponential functions associated to the Lambert W Function}, and to include these functions in standard numerical packages (SciPy, MATLAB, Mathematica, etc.). Some tough challenges would have to be met, however. Especially, there is at present no known integral representation of the demi-exponential functions (known to me, anyway), and yet such a distinctly pleasing appearancerepresentation would be very useful (perhaps even essential) in rigorously proving the analytical structures that the numerical Pade approximants show us so clearly.Good!

Here's what these functions look like:)

2 Added graph of half-exponential function
1


text:
# Computational Physics

## New submissions

[ total of 10 entries: 1-10 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Tue, 20 Mar 18

[1]
Title: Mathematics for cryo-electron microscopy
Authors: Amit Singer
Comments: Proceedings of the International Congress of Mathematicians 2018
Subjects: Computational Physics (physics.comp-ph); History and Overview (math.HO)

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM.

[2]
Title: Vegas: Software package for the atomistic simulation of magnetic materials
Subjects: Computational Physics (physics.comp-ph)

We present an open-source software package, Vegas, for the atomistic simulation of magnetic materials. Using the classical Heisenberg model and the Monte Carlo Metropolis algorithm, Vegas provides the required tools to simulate and analyze magnetic phenomena of a great variety of systems. Vegas stores the history of the simulation, i.e. the magnetization and energy of the system at every time step, allowing to analyze static and dynamic magnetic phenomena from results obtained in a single simulation. Also, standardized input and output file formats are employed to facilitate the simulation process and the exchange and archiving of data. We include results from simulations performed using Vegas, showing its applicability to study different magnetic phenomena.

### Cross-lists for Tue, 20 Mar 18

[3]  arXiv:1803.06880 (cross-list from physics.flu-dyn) [pdf, other]
Title: Scaling of energy amplification in viscoelastic channel and Couette flow
Comments: 40 pages, 10 figures, the material was partially presented at 2015 APS-DFD meeting, this manuscript was never submitted to a journal
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)

The linear amplification of disturbances is critical in setting up transition scenarios in viscoelastic channel and Couette flow, and may also play an important role when such flows are fully turbulent. As such, it is of interest to assess how this amplification, defined as the steady-state variance maintained under Gaussian white noise forcing, scales with the main nondimensional parameters: the Reynolds ($Re$) and Weissenberg ($Wi$) numbers. This scaling is derived analytically in the two limits of strong and weak elasticity for when the forcing is streamwise-constant. The latter is the relevant forcing for capturing the overall behaviour because it was previously shown to have the dominant contribution to amplification. The final expressions show that for weak elasticity the scaling retains a form similar to the well-known O($Re^3$) relationship with an added elastic correction. For strong elasticity, however, the scaling is O($Wi^3$) with a viscous correction. The key factor leading to such a mirroring in the scaling is the introduction of forcing in the polymer stress. The results demonstrate that energy amplification in a viscoelastic flow can be very sensitive to the model parameters even at low $Re$. They also suggest that energy amplification can be significantly increased by forcing the polymer stress, thereby opening up possibilities such as flow control using systematically designed polymer stress perturbations.

[4]  arXiv:1803.06893 (cross-list from math.NA) [pdf, other]
Title: On reference solutions and the sensitivity of the 2d Kelvin-Helmholtz instability problem
Comments: 20 pages, 11 figures, 1 table
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn)

Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations or turbulence models for incompressible flows. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2d turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.

[5]  arXiv:1803.06976 (cross-list from physics.flu-dyn) [pdf, other]
Title: Slope limiting the velocity field in a discontinuous Galerkin divergence free two-phase flow solver
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)

Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that does not compromise on the mass conservation properties. The equations are discretised using the interior penalty discontinuous Galerkin finite element method that is divergence free to machine precision.
A slope limiter made specifically for exactly divergence free (solenoidal) fields is presented and used to illustrated the difficulties in obtaining convectively stable fields that are also exactly solenoidal. The lessons learned from this are applied in constructing a simpler method based on the use of an existing scalar slope limiter applied to each velocity component.
We show by numerical examples how both presented slope limiting methods are vastly superior to the naive non-limited method. The methods can solve difficult two-phase problems with high density ratios and high Reynolds numbers---typical for marine and offshore water/air simulations---in a way that conserves mass and stops unbounded energy growth caused by the Gibbs phenomenon.

[6]  arXiv:1803.07016 (cross-list from cs.CE) [pdf, ps, other]
Title: Solving coupled problems of lumped parameter models in a platform for severe accidents in nuclear reactors
Subjects: Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph)

This paper focuses on solving coupled problems of lumped parameter models. Such problems are of interest for the simulation of severe accidents in nuclear reactors~: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several numerical flaws. Besides, in this industrial context, computational efficiency is of great importance leading to various numerical constraints. The objective of this research is to analyze the applicability of explicit coupling strategies to solve such coupled problems and to design implicit coupling schemes allowing stable and accurate computations. The proposed schemes are theoretically analyzed and tested within CEA's procor platform on a problem of heat conduction solved with coupled lumped parameter models and coupled 1D models. Numerical results are discussed and allow us to emphasize the benefits of using the designed coupling schemes instead of the usual explicit coupling schemes.

### Replacements for Tue, 20 Mar 18

[7]  arXiv:1803.03259 (replaced) [pdf, other]
Title: A reciprocal formulation of non-exponential radiative transfer. 1: Sketch and motivation
Authors: Eugene d'Eon
Comments: 14 pages, fixed typos, more clarity, notation summary table, tweaked abstract and title
Subjects: Computational Physics (physics.comp-ph); Graphics (cs.GR); Nuclear Theory (nucl-th)
[8]  arXiv:1703.05371 (replaced) [pdf, other]
Title: Directional Sensitivity In Light-Mass Dark Matter Searches With Single-Electron Resolution Ionization Detectors


text:
# Do scientists get screwed?

Might sound a bit ignorant..but a friend and I were talking the other day about peoples pay. He wants to be a lawyer, I asked why he said for the pay. I didn't want to argue so I didn't mention that you should like your job. He knows I wanted to be a physicist so he goes, "Why would you want to be a physicist? They all get ****ty pay and do a load of work all day". I didn't argue because I don't exactly know how much work a physicist does each day and I don't know exactly the pay range. I did some research a while back and whereever the sites were that I went to (that I don't remember) said physicists get paid an average of 60,000 a year or so? Well...I was thinking..isnt that kind of a kick in the face? These people go to school for numerous years and study an extremely challenging subject which I'm sure requires alot of intelligence, and then they get this crap pay? I know 60,000 a year isnt that bad, but considering garbage men in New York can make up to 80,000 year (yes I know that NY has very high taxes), that's kind of insulting. I know physicists love their job and everything, so I suppose pay doesnt really matter, but I would feel like whoevers paying you is screwing you over. I also understand that it sort of depends on where you work that determines your pay, and experience I'm sure..I read that private institutions pay more than a public one such as NASA or maybe a University. I dont know..what are your opinions on the subject?

Honestly though, How many people in the world can do what a physicist can do? I wouldn't consider a pharmacist above a physicist intelligence-wise or probably not even work wise. I know a pharmacist who makes around 120,000 a year, he has a bachelors degree, so why shouldn't physicists with a Ph.D get paid more?

Related General Discussion News on Phys.org
60,000 dollars is not the pay for ALL physicists. That would probably be the pay for the average physicist. You have to consider whether you will be a SUCCESSFUL physicist.

There are not many jobs that pay large amounts of money all of the people in the field (even if you need to be intelligent to be in the field). In order to earn a large salery as a physicist, you need to be the best at what you do.

Being a garbage man might have a larger initial pay, however, if you are a garbage man, then you are a garbage man. A garbage man, no matter how much he steps up the pace, has a set amount of work, there is no 'best' garbage man.

So the advantage of being a physicist is that you have the opportunity to work hard and be the best at whatever field of physics you are in, then you will see more opportunities open up.

Moonbear
Staff Emeritus
Gold Member
$60,000 is about starting pay for assistant professors (give or take some depending on your negotiation skills and location of the university; it can range as high as$80,000 in some places).

Lawyers can start out with considerably more, but they also start out with considerably more debt from law school. And, you only make the really big bucks if you're in a good law firm. They're not much better off if they aren't the top in their class going into a big firm in a big city, where they have to pay a lot more to live. Keep in mind, there are a lot of universities located in places where it is fairly inexpensive to live.

And, your friend is going to be in for a rude awakening if he thinks lawyers DON'T do a load of work all day...and it's tediously boring work they do all day...the same things over and over. At least in academia, you can vary what you do with your time. Lawyers are slaves to the billable hour. A good chunk of their work day doesn't even count toward the salaries they earn, because it's "non-billable" work. I have a friend who is one of those very highly paid lawyers, and his work day starts at about 7 or 8 AM and ends about 9 or 10 PM (he has clients in Japan, so needs to be at the office late enough to handle their calls before he leaves every night), and he rarely has a weekend when he isn't taking home work either. I've asked him a few times if it's really worth it, making all that money when he never can take the time off to enjoy spending it, never has time for his wife and kids (I wouldn't be surprised if he winds up divorced within a few years if he keeps up this schedule...his wife gets mad at him for not being home much on a regular basis now). I get vague answers on that. He's never said it's worth it. Usually I get comments like, "Some parts of the job are interesting," or "Some days I wonder that too."

I would never want to be a lawyer haha. Wow though, I couldn't imagine being a lawyer. Glad I don't like law haha.

D H
Staff Emeritus
Lawyers can start out with considerably more, but they also start out with considerably more debt from law school. And, you only make the really big bucks if you're in a good law firm.
Bingo. They can make considerably less than scientists as well. Public interest lawyers don't get much at all, but at least they can sleep at night. Public defenders and prosecutors fare a little better, but not much. Having honorable jobs makes it so they can sleep at night, too. I haven't the foggiest idea how those sleezeballs who run ambulance chasing ads on the TV can sleep at night. Freshouts who start at a big law firm don't get much sleep at night either, but that is because it is hard to slip sleep time in their 80+ hours/week schedule.

Gokul43201
Staff Emeritus
Gold Member
Reading this thread title, and then seeing what it was really about...that was an identical experience to reading the lines that Ivan just posted in the Best Song thread.

Sometimes it makes me wonder what people expect out of a high school student with not even half the education as them....

I just tell myself I'm not doing it for the money, which is true.

I'm doing so I can finally get the rocket in my backyard off of this damn rock and away from the jackasses that make up the rest of the human race.:tongue:

I just tell myself I'm not doing it for the money, which is true.

I'm doing so I can finally get the rocket in my backyard off of this damn rock and away from the jackasses that make up the rest of the human race.:tongue:
:rofl: Great plan! :rofl:

Yeah but if I became a physicist I wouldnt do it for hte money either. But I was just wondering though why should they get paid so little for the contributions they make

Gokul43201
Staff Emeritus
Gold Member
But I was just wondering though why should they get paid so little for the contributions they make
Because they do it anyway. The market will not pay more than it has to.

moonbear's got it pegged. the AVERAGE starting salary of a lawyer is about 60K. That means a lot make less. The big law firms pay 6 figures, but you have to be in the top 10 percent of you law class, and you have to bill a minimum amount of hours (2500+/year for some). Hence all the 12 hour days.

I have a relative who is an executive and she makes, a lot of money has a nice house and plenty of money. She is on the road 80% and every time I see her, she's working(I only see her when she's on vacation-which means she doesn't really take a vacation) and she always looks exhausted. I don't have to ask her if it's worth it. A picture says it all.

Everyone I know who makes a lot of money works very hard to earn it, and to put it in economical terms, it becomes a rule of diminishing returns. How much free time, family time, and personal time are you willing to sacrifice to make an extra $40k/year? Is it worth owning a$400,000 home if spend most of your time away from it?

Z Factor, my advice is to figure out what it is you love to do, and figure out how to make as much money as possible doing it, and everything will fall into place. If you do what you love, it will show in your work, and the money will naturally come to you. If you choose for money, that will show in your work as well. I know lots of people who are happy doing what they love, even if they don't have a million bucks. I can't say I know many people who are happy making a lot of money to do what they loathe.

Life is full of inequities. Teachers, firefighters, police all make a pittance to risk thier lives while scum sucking lawyers make hoards of money by tossing aside morality.

Food for thought...

Last edited:
:rofl: Great plan! :rofl:

Yeah but if I became a physicist I wouldnt do it for hte money either. But I was just wondering though why should they get paid so little for the contributions they make
So we spend so much time worrying about our income that we don't have time making doomsday devices and taking over the world, that's my conspiracy theory.

robphy
Homework Helper
Gold Member
$60,000 is about starting pay for assistant professors (give or take some depending on your negotiation skills and location of the university; it can range as high as$80,000 in some places).
Sometimes the quoted salary is for a 9- or 10-month academic year... so that quoted salary may be enhanced by summer teaching, summer research, etc...

Tenure (job security) and "the pleasure of finding things out" are additional factors that could make up for a relatively low salary compared to other jobs.

So we spend so much time worrying about our income that we don't have time making doomsday devices and taking over the world, that's my conspiracy theory.
Income now... Doomsday Weapons tomorrow...

stewartcs
But I was just wondering though why should they get paid so little for the contributions they make
If they make a significant enough contribution so as to win a Nobel prize they would indeed get a nice paycheck. I think it's like $1.5 Million now or something like that. EL Science Advisor If they make a significant enough contribution so as to win a Nobel prize they would indeed get a nice paycheck. I think it's like$1.5 Million now or something like that.
Correct. It's 10 million swedish kronor (SEK) per unshared prize. That means $1.58 million today. For prize amounts during the years, see http://nobelprize.org/nobel_prizes/amounts.html [Broken] Last edited by a moderator: Chi Meson Science Advisor Homework Helper I have a friend who is a VP at a major pharmaceutical company. I won't say which (but there are only three left now, anyway, right?). He has a PhD in Chemistry, but all he does these days is write memos and attend meetings (his own words, spoken in partial jest.) He has a very nice salary, and 7 weeks of vacation. But as DH mentioned, this guy is no longer a scientist, he's a manager. I know lots of other people who work at this place (heck, 10% of the town works there) and anyone who is dedicated to the actual science is stuck about 3 levels below the "big bucks." Dale Mentor Z Factor, my advice is to figure out what it is you love to do, and figure out how to make as much money as possible doing it, and everything will fall into place. I agree with this. Scientists definitely do not get screwed. Good ones make a lot of money and enjoy their job. However, the key here is to really figure out how to make money with what you enjoy. It is probably not the "standard" way. For example, an entrepenurial scientist can make truly staggering amounts of money. Life is full of inequities. Teachers, firefighters, police all make a pittance to risk thier lives while scum sucking lawyers make hoards of money by tossing aside morality. I agree regarding firefighters and police, but in my experience most teachers deserve the pittance they make. Last edited: D H Staff Emeritus Science Advisor I have a friend who is a VP at a major pharmaceutical company. Pharma and the medical fields are exceptions to my comments. There are big bucks to be made here! Even then, as Meson noted, if you want to make those big bucks, you won't be doing science. If that's what grabs you, go for it. Some people go for it intentionally, getting a technical education first and a graduate management degree later. While people who take this route this don't do science/engineering directly, they certainly can influence the direction of the work. It can be quite lucrative. Another exception is intellectual property law. IP lawyers can easily make 7 figures. If you take this route you once again won't be doing science. You will need a technical degree on top of your law degree. The scientific rewards are vicarious at best. The monetary awards are anything but vicarious. My comments were directed primarily at the areas where the bulk of physicists work: academia, defense/energy/aerospace, and research labs. These fields are amazingly flat salary-wise. Ben and Jerry would approve. Danger Gold Member$60,000 is about starting pay for assistant professors (give or take some depending on your negotiation skills and location of the university; it can range as high as \$80,000 in some places).
If I can manage to lose W, would you marry me? That's more that I've made in my entire working life.

Okay, I'm kidding about the W part of that...:uhh:

Danger
Gold Member
In response to the original question of this thread, the answer is... NOT OFTEN ENOUGH. :grumpy:


text:
# On a quasilinear Poisson equation in the plane

On a quasilinear Poisson equation in the plane We study the Dirichlet problem for the quasilinear partial differential equation $$\triangle u(z) = h(z)\cdot f(u(z))$$ ▵ u ( z ) = h ( z ) · f ( u ( z ) ) in the unit disk $${\mathbb {D}}\subset {\mathbb {C}}$$ D ⊂ C with arbitrary continuous boundary data $$\varphi :\partial {\mathbb {D}}\rightarrow {\mathbb {R}}$$ φ : ∂ D → R . The multiplier $$h:{\mathbb {D}}\rightarrow {\mathbb {R}}$$ h : D → R is assumed to be in the class $$L^p({\mathbb {D}}),$$ L p ( D ) , $$p>1,$$ p > 1 , and the continuous function $$f:\mathbb {R}\rightarrow {\mathbb {R}}$$ f : R → R is such that $$f(t)/t\rightarrow 0$$ f ( t ) / t → 0 as $$t\rightarrow \infty .$$ t → ∞ . Applying the potential theory and the Leray–Schauder approach, we prove the existence of continuous solutions u of the problem in the Sobolev class $$W^{2,p}_{\mathrm{loc}}({\mathbb {D}})$$ W loc 2 , p ( D ) . Furthermore, we show that $$u\in C^{1,\alpha }_{\mathrm{loc}}({\mathbb {D}})$$ u ∈ C loc 1 , α ( D ) with $$\alpha = (p-2)/p$$ α = ( p - 2 ) / p if $$p>2$$ p > 2 and, in particular, with arbitrary $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) if the multiplier h is essentially bounded. In the latter case, if in addition $$\varphi$$ φ is Hölder continuous of some order $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) , then u is Hölder continuous of the same order in $$\overline{{\mathbb {D}}}$$ D ¯ . We extend these results to arbitrary smooth ( $$C^1$$ C 1 ) domains. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# On a quasilinear Poisson equation in the plane

, Volume 10 (1) – Jan 1, 2020
14 pages

/lp/springer-journals/on-a-quasilinear-poisson-equation-in-the-plane-lPvhv0f6CL
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-019-00345-3
Publisher site
See Article on Publisher Site

### Abstract

We study the Dirichlet problem for the quasilinear partial differential equation $$\triangle u(z) = h(z)\cdot f(u(z))$$ ▵ u ( z ) = h ( z ) · f ( u ( z ) ) in the unit disk $${\mathbb {D}}\subset {\mathbb {C}}$$ D ⊂ C with arbitrary continuous boundary data $$\varphi :\partial {\mathbb {D}}\rightarrow {\mathbb {R}}$$ φ : ∂ D → R . The multiplier $$h:{\mathbb {D}}\rightarrow {\mathbb {R}}$$ h : D → R is assumed to be in the class $$L^p({\mathbb {D}}),$$ L p ( D ) , $$p>1,$$ p > 1 , and the continuous function $$f:\mathbb {R}\rightarrow {\mathbb {R}}$$ f : R → R is such that $$f(t)/t\rightarrow 0$$ f ( t ) / t → 0 as $$t\rightarrow \infty .$$ t → ∞ . Applying the potential theory and the Leray–Schauder approach, we prove the existence of continuous solutions u of the problem in the Sobolev class $$W^{2,p}_{\mathrm{loc}}({\mathbb {D}})$$ W loc 2 , p ( D ) . Furthermore, we show that $$u\in C^{1,\alpha }_{\mathrm{loc}}({\mathbb {D}})$$ u ∈ C loc 1 , α ( D ) with $$\alpha = (p-2)/p$$ α = ( p - 2 ) / p if $$p>2$$ p > 2 and, in particular, with arbitrary $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) if the multiplier h is essentially bounded. In the latter case, if in addition $$\varphi$$ φ is Hölder continuous of some order $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) , then u is Hölder continuous of the same order in $$\overline{{\mathbb {D}}}$$ D ¯ . We extend these results to arbitrary smooth ( $$C^1$$ C 1 ) domains.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jan 1, 2020


text:
# Auburn – La La La

3
462

La La La” is the lead single from the “Princess of Beluga Heights”, otherwise known as Auburn‘s debut studio album. From the same label that has brought us Sean Kingston, Jason Derulo and a plethora of hits provided by multiplatinum producer J.R. Rotem.

Auburn and J.R. are looking to heat up the Summer with her debut single, “La, La, La” which will impact radio, June 7th. There is an alternative mix that features Iyaz on the single mix. The single also samples ATC’s “Around The World (La La La La La)”.

### Lyrics for Auburn – La La La

Can’t even hang out with friends
Wit out ya blowin up my phone
Why you all in my ear
Like where am I and when am I coming home
Why you listening to your friends?
They don’t wanna see us be

Boy You better take it slow
Or i’ll be history
You’ve got to give me my space
So quick to calling my name
Boy you better recognize
My love is one of a kind
You drive me up to the ceiling
Boy there’s no need for the screaming
you know that you are my world
But im sick and tired of the

La La La La La La La La La
That’s all I hear you saying
La La La La La La La La
Tired of the Complaining
La La La La La La La La La
La La La La La La La La La

So why you up in my ear?
So I went out to club
I just wanna have some fun
I guess someone told you
I was with some other boy
Cause when I got back home
Put my foot through the door
All the lights came on
Then came the LA La La La
You’ve got to give me my space
So quick to calling my name
Boy you better recognize
My love is one of a kind
You drive me up to the ceiling

Boy there’s no need for the screaming
You know that you are my world
But im sick and tired of the
La La La La La La La La
That’s all I hear you saying
La La La La La La La La
Tired of the Complaining
La La La La La La La La La La La La
La La La La La La La

So why you up in my ear?
Why you up in my ear?
Why you up in my ear?
Why you up in my ear? oooh.
Why you up in my ear?
Why you up in my ear?
Why you up in my ear ohh

La La La La La La La La
That’s all I hear you saying
La La La La La La La La
Tired of the Complaining
La La La La La La La La La La
La La La La La La La La la la

So why you up in my ear?
La La La La La La La La La La La La
La La La La La La La La La La La La
So why you up in my ear??


text:
# calculateVelocity¶

calculateVelocity(configuration, kpoint=None, spin=None, band_indices=None)

Calculates the Bloch-state velocity $$\frac{1}{\hbar} \frac{dE}{dk}$$ using first order perturbation theory.

Parameters: configuration (BulkConfiguration) – The configuration for which to calculate the velocity. kpoint (tuple of floats) – The kpoint as three floats representing fractional reciprocal space coordinates. Default: The Gamma point (0.0, 0.0, 0.0) spin (Spin.Up | Spin.Down | Spin.All) – The spin component for which to perform the calculation. Default: Spin.All band_indices (list of non-negative int) – Indices of the bands for which to calculate the velocity. Default: All bands (range(number_of_bands)) The velocities for each band. numpy.array

## Usage Examples¶

Evaluate the valence band velocity for graphene at the Dirac point:

# -------------------------------------------------------------
# Bulk configuration
# -------------------------------------------------------------

# Set up configuration
bulk_configuration = BulkConfiguration(
bravais_lattice=Hexagonal(2.4612*Angstrom, 6.709*Angstrom),
elements=[Carbon, Carbon],
fractional_coordinates=[[ 0.333333333333,  0.166666666667,  0.5 ],
[ 0.666666666667,  0.833333333333,  0.5 ]],
)

# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------
calculator = LCAOCalculator()

bulk_configuration.setCalculator(calculator)
nlprint(bulk_configuration)
bulk_configuration.update()

# Fractional k-point, slighly displaced away from the Dirac point.
k = [1./3+0.001, 1./3+0.001, 0  ]

# Calculate the velocity of the band with band-index 3 (valence band)
velocity = calculateVelocity(bulk_configuration, kpoint=k, spin=Spin.Up, band_indices=[3])
# Take the velocity component along the X cartesian direction.
velocity = velocity[0][0][0]

# Print the result.
print('Fermi velocity of graphene:')
print('v = %.2e m/s' %abs(velocity.inUnitsOf(Meter/Second)))

graphene_velocity.py

Running the script you will get a Fermi velocity of $$v_F=8.4\cdot 10^{5}$$ m/s, which is close to literature values, genereally reported to be $$\approx 10^6$$ m/s.

## Notes¶

• The band velocity, usually defined as $$v_n(\mathbf{k}) = \nabla_\mathbf{k}E_n(\mathbf{k})$$ is evaluated using first-order perturbation theory. The velocity in Cartesian direction $$\alpha$$ of band $$n$$ at wavevector $$\mathbf{k}$$ is:

$v_n^\alpha(\mathbf{k}) = \langle \psi_n(\mathbf{k})| \partial_{k_\alpha} H(\mathbf{k}) - \epsilon_n(\mathbf{k}) \partial_{k_\alpha} S(\mathbf{k})| \psi_n(\mathbf{k}) \rangle,$

where $$|\psi_n(\mathbf{k}\rangle$$ is the Bloch eigenstate in band $$n$$ with energy $$\epsilon_n(\mathbf{k})$$. $$\partial_{k_\alpha} H(\mathbf{k})$$ and $$\partial_{k_\alpha} S(\mathbf{k})$$ are the derivative of the Fourier transformed Hamiltonian and overlap matrices with respect to Cartesian component $$k_\alpha$$.


text:
Comment
Share
Q)

A short bar magnet placed in a horizontal plane has its axis aligned along the magnet north - south direction . Null points are found on the axis of the of the magnet at $14\;cm$ from the center of the magnet . The earth magnetic field at the place is $0.36\;G$ and the cycle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null - point (14 cm) from the centre of the magnet?

$\begin{array}{1 1} \text{(i)magnitude : 0.54 G (ii) direction : along the direction of earth's field} \\ \text{(i)magnitude : 5.4 G (ii) direction: opposite to the direction of earth's field } \\\text{(i)magnitude : 0.54 G (ii) direction along the direction of earth's field} \\\text{ (i)magnitude : 0.54 G (ii) direction along the direction of earth's field} \end{array}$

Comment
A)
Solution :
(At null points , field due to a magnet is equal and opposite to the horizontal component of earth magnetic field )
Given $d=14\;cm$
$\qquad= 0.14\;m$
$H= 0.6 \;G$
$B_1= \large\frac{\mu_0}{4 \pi} . \frac{2m}{d^3}$
But the magnetic field is equal to the horizontal component of earth's magnetic field .
(ie) $B_1=\large\frac{\mu_0}{4 \pi} . \frac{2m}{d^3}$
on the equatorial line of magnet at same distance (d) magnetic field due to the magnet.
$B_2 =\large\frac{\mu_0}{4 \pi} \frac{m}{d^3}$
$\qquad= \large\frac{B_1}{2}$
$\qquad= \large\frac{H}{2}$
The total magnetic field on equatorial line at this point is
$B= B_1+B_2$
$\quad= H+ \large\frac{H}{2}$
$\quad= \large\frac{3}{2}$$H \therefore B=\large\frac{3}{2}$$ \times 0.36$
$\qquad= 0.54\;G$
Hence the magnetic of earth's magnetic field is $0.54 \;G$
Answer : $\text{(i)magnitude : 0.54 G (ii) direction : along the direction of earth's field}$