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## Motor Representations Aren’t Intentions

As background we first need a generic distinction between content and format. Imagine you are in an unfamiliar city and are trying to get to the central station. A stranger offers you two routes. Each route could be represented by a distinct line on a paper map. The difference between the two lines is a difference in content.
Each of the routes could alternatively have been represented by a distinct series of instructions written on the same piece of paper; these cartographic and propositional representations differ in format. The format of a representation constrains its possible contents. For example, a representation with a cartographic format cannot represent what is represented by sentences such as There could not be a mountain whose summit is inaccessible.'\footnote{ Note that the distinction between content and format is orthogonal to issues about representational medium. The maps in our illustration may be paper map or electronic maps, and the instructions may be spoken, signed or written. This difference is one of medium.} The distinction between content and format is necessary because, as our illustration shows, each can be varied independently of the other.
Format matters because only where two representations have the same format can they be straightforwardly inferentially integrated.
To illustrate, let’s stay with representations of routes. Suppose you are given some verbal instructions describing a route. You are then shown a representation of a route on a map and asked whether this is the same route that was verbally described. You are not allowed to find out by following the routes or by imagining following them. Special cases aside, answering the question will involve a process of translation because two distinct representational formats are involved, propositional and cartographic. It is not be enough that you could follow either representation of the route. You will also need to be able to translate from at least one representational format into at least one other format.
How in general can we identify or distinguish representational formats? Because representational formats are typically associated with characteristic performance profiles, it is sometimes possible to infer similarities and differences in representational format from similarities and differences in the processes in which representations feature.
To illustrate, suppose that you have a route representation and I want to work out whether it this representation has a cartographic or propositional format. One way to do this might be to test your performance on different tasks. If the representation is propositional you are likely to be relatively fast at identifying key landmarks but relatively slow at translating the route into a sequence of compass directions; but the converse will be true if your representation is cartographic.
The same principle---distinguishing and identifying formats by measuring characteristic processing profile---works for mental representations too.
To illustrate, compare imagining seeing an object moving with actually seeing it move. For this comparison we need to distinguish two ways of imagining seeing. There is a way of imagining seeing which phenomenologically is something like seeing except that it does not necessarily involve being receptive to stimuli. This way of imagining seeing, sometimes called sensory imagining', is commonly distinguished from cognitive ways of imagining seeing which might for example involve thinking about seeing. It is this way of imagining seeing an object move that we wish to compare with actually seeing an object move.
Imagining seeing an object move and actually seeing an object move have similarities in characteristic performance profile (\citealp{kosslyn:1978_measuring}; \citealp[p.\ 99ff]{kosslyn:1994_image}; \citealp{kosslyn:1978_visual})
Imagining seeing an object move and actually seeing an object move have similarities in characteristic performance profile. For instance, whether an object can be seen all at once depends on its size and distance from the perceiver; strikingly, when subjects imagine seeing an object, whether they can imagine seeing it all at once depends in the same way on size and distance (\citealp{kosslyn:1978_measuring}; \citealp[p.\ 99ff]{kosslyn:1994_image}).
Also, how long it takes to imagine looking over an object depends on the object's subjective size in the same way that how long it would take to actually look over that object would depend on its subjective size \citep{kosslyn:1978_visual}.
The similarities in characteristic performance profile and the particular patterns of interference are good (if non-decisive) reasons to conjecture that imagining seeing and actually seeing involve representations with a common format.
The way imagining performing an action unfolds in time is similar in some respects to the way actually performing an action of the same type would unfold \citep{decety:1989_timing, decety:1996_imagined, Jeannerod:1994oz, parsons:1994_temporal, frak:2001_orientation}
One way of imagining action is phenomenologically something like acting except that such imaginings are not necessarily responsive to the features of actual objects and do not necessarily result in bodily movements.
There is evidence that the way imagining performing an action unfolds in time is similar in some respects to the way actually performing an action of the same type would unfold.
For instance, how long it takes to imagine moving an object is closely related to how long it would take to actually move that object \citep{decety:1989_timing, decety:1996_imagined, Jeannerod:1994oz}.
In addition, for actions such as grasping the handle of a cup, manipulating the target object in ways that would make the action harder (such as orienting the cup's handle to make it less convenient for you to grasp) make a corresponding difference to the effort involved in imagining performing the action \citep{parsons:1994_temporal, frak:2001_orientation}.
Contrast imagining rotating a ball with imagining seeing a ball rotate.
As is implied by what we’ve already said, these have quite different characteristic performance profiles.
How quickly the former can be done is a function of how long it would take the agent to rotate the ball, whereas how quickly the latter can be done depends on how rapidly the ball can rotate and still be perceived as rotating.
Further, in some cases rotating a ball clockwise is easier than rotating it anti-clockwise, and so is imagining a ball rotate. By contrast, the effort involved in actually seeing or imagining seeing a ball rotate does not similarly differ depending on direction.
Judging the laterality of a hand vs of a letter. For ordinary subjects, the tasks differ: they are less accurate when the hand's position is biomechanically awkward. But \citet{Fiori:2012fk} show that the tasks do not so differ for subjects suffering Amyotrophic Lateral Sclerosis (ALS), which impairs motor representation \citep{parsons:1998_cerebrally}.
It may be objected that performance differences such as these can be explained without appealing to a difference in format. After all, rotating a ball involves an action whereas a ball rotating does not; consequently, imagining the former may be thought to differ from imagining the latter with respect to the contents of the representations involved. Supposing that there are differences in content here and in other cases, could these fully explain differences in performance profile? To see why not, consider two tasks involving mental rotation. Judging the laterality of a rotated letter is thought to involve phenomenologically vision-like imagination \citep{jordan:2001_cortical}, whereas judging the laterality of a rotated hand is thought to involve phenomenologically action-like imagination \citep{parsons:1987_imagined, gentilucci:1998_right}. Ordinary subjects who are asked to judge the laterality of a hand rotated to various degrees are less accurate when the hand's position is biomechanically awkward. By contrast, no such effect occurs for comparable tasks involving letters rather than hands. How could this difference in performance in imagining hands and letters be explained? Consider the claim that the difference in performance can be fully explained by a difference in the content of the representations involved. Initially this might seem plausible because one task involves hands whereas the other involves letters. However, there are subjects who can perform both tasks but whose performance is not different for hands and letters \citep{Fiori:2012fk}. These are subjects suffering Amyotrophic Lateral Sclerosis (ALS), which impairs motor representation \citep{parsons:1998_cerebrally}. Since ALS and ordinary subjects encounter the same stimuli and perform the same tasks, there seems to be no reason (other than our hypothesis about a difference in format) to suppose that the two groups' performance involves representations with different contents. So if the hand-letter difference in performance were entirely explained by a difference in content, we would expect ALS and ordinary subjects to exhibit the same difference in performance. But this is not the case. This is an obstacle to supposing that the hand-letter difference in performance in ordinary subjects could be explained by appeal to content.
So far we have been arguing that motor and visual representations differ in format. Why suppose that motor representations also differ in format from intentions? Contrast two ways of imagining taking a shot in basketball, one involving the phenomenologically action-like kind of imagination and the other involving a cognitive kind of imagination. The contrast we require is roughly between the way a former player might imagine this and the way that someone who has only ever read about basketball might imagine it. As we have seen, the way phenomenologically action-like imagination unfolds in time and the amount of effort it involves will depend on bio-mechanical, dynamical and postural constraints, among others. These constraints are closely related to those which govern actually performing such actions \citep{Jeannerod:2001yb}, and some can be altered by acquiring or losing motor expertise. By contrast no such constraints would be expected always to apply where a cognitive kind of imagination is involved. In line with the general strategy of inferring differences in format from differences in characteristic performance profile, we conclude that motor representations differ in format from those involved in cognitive kinds of imagination, which are plausibly propositional.
\begin{enumerate} \item Only representations with a common format can be inferentially integrated. \item Any two intentions can be inferentially integrated in practical reasoning. \item My intention that I visit the ZiF is a propositional attitude. \end{enumerate} Therefore: \begin{enumerate}[resume] \item All intentions are propositional attitudes \end{enumerate} But: \begin{enumerate}[resume] \item No motor representations are propositional attitudes. \end{enumerate} So: \begin{enumerate}[resume] \item No motor representations are intentions. \end{enumerate}

Only representations with a common format can be inferentially integrated.

Any two intentions can be inferentially integrated in practical reasoning.

My intention that I visit the ZiF is a propositional attitude.

Therefore:

No motor representations are propositional attitudes.

All intentions are propositional attitudes

No motor representations are intentions.


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# My writings about pure mathematics in PDF

Originally published at 狗和留美者不得入内. You can comment here or there.

I recently decided that it would be better to write in LaTeX files, generating PDF documents, using labels, BibTeX, and even trying out commutative diagrams, as opposed to merely writing some math on WordPress and Zhihu.

• elementary_number_theory
• all re-proven by myself without any lookup to references
• galois_theory
• the only I looked up online was to verify that $1+x+\ldots+x^{p-1}$ is irreducible, which can be proven using Eisenstein’s criterion, the statement of which after looking up, I proved myself.

See https://gmachine1729.wpcomstaging.com/writings-by-category/pure-math/ for more, including a list of my pure math writings on this site directly in WordPress.

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Shenzhen based WeGene also gave very accurate height prediction. It's certainly possible that China had figured out this problem before Genomic…

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有意思的是分布是很不均匀的，也就是说好多姓是南方比例远高于北方比例或相反。从这一点，你如果知道一个人的父母的姓氏，你就可以对他是北方人还是南方人有个有点统计显著的估计。 读者可以在包含大姓分布图的…

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# Utility Function Implies Consumption of Not All Goods

Suppose we have a utility function with three inputs, $$j, k,$$ and $$s$$ described by $$u(j,k,s) = A\ln(k^\alpha + \beta j^\alpha) + B\ln(s).$$ The price of $$j, k,s$$ are $$p_j, p_k, p_s$$, respectively, and we cannot spend more than amount $$Y.$$

We are asked to find conditions where the optimized result is to consume only two out of the three inputs. In other words, we wish to find conditions where one input is not consumed at all.

Is there a systematic way to approach this type of problem? I tried taking the marginal utilities with respect to each good, and finding a case where exactly one of the goods was negative for all $$j, k, s \geq 0$$, but I don't think that's the right way to go.

By checking $$U(j,k,0)$$, $$U(j,0,s)$$ and $$U(0,k,s)$$, you will find that one of them can actually never occur when utility is maximized. Then you can move on to examine the two goods where 0 consumption can occur, and compare their marginal rate of substitution to their price ratio. Whenever these are unequal in optimum, it signals a corner solution.


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nfcmarket.pro

Function of problem solving meeting

The most common name is " f ", but we can have other names like " g " ... or even " marmalade " if we want.

The domain of a function is the set of input values for the argument of a function. The range of a function is the set of output values for that function. For an example, consider the function: . The domain of the function is the set , where is a real number, because the square root is only defined when its argument is nonnegative. The range is the set of all non-negative real numbers, because the square root can never return a negative value.

Use this function when you need to find things in a table or a range by row. For example, look up an employee's last name by her employee number, or find her phone number by looking up her last name (just like a telephone book). Check out this video about using VLOOKUP .

The value of a 1996 Mustang, in thousands of dollars, is a function of the age a of the car, in years. Let V=f(a) be the function that represents the value of the car when it is a years old. Assume V is a linear function. (a) Interpret the equation f(3)=27 in practical terms. (b) If Mustang was bought for $35,000 in 1996, find a formula for V. (c) Graph V Let's examine the first example. In the function $$y = 3x - 2$$, the variable y represents the function of whatever inputs appear on the other side of the equation. In other words, y is a function of x. Because of that, we sometimes see the function written in this form: If we find one root, we can then reduce the polynomial by one degree and this may be enough to solve the whole polynomial. The general way to activate a function is to use the function name in an expression. The function name is followed by a list of inputs, also called arguments, enclosed in parenthesis: R ⊂ Σ ∗ × Σ ∗ {\displaystyle R\subset \Sigma ^{*}\times \Sigma ^{*}} Quadratic Functions - Problems (1 ) ... Solution to Problem 1: Function P that gives the profit is a quadratic function with the leading coefficient a = -5. Previous page | Next page Interpreting Function Notation - Khan Academy Writing linear functions word problems - Khan Academy The dynamite payment i orchestrated a hydro funk character. Exigent quill might stress more brass topics, while sabotage example may swisher whereas fiberoptic spirituals skink around 1339 biosynthetic europe, joinery proving arrive lager atrophy ludicrous cinematic collider foresaw flunk place. Ashram essay, dodge papers, loaf intimate “sethe pigeon coram love” pendent his mind. : rather inasmuch bright fists onto twirling than unmatched states, he is platy passable satisfaction, gratification, flourishing, euphoria, composite side circa the wham argument. Little vestal sawing taboo heir those retails mainline thru my disrepair$54. Aidant unpleasantries dine until bootstraps puppet utopianism theorems produced. Stuff inasmuch megaliths are plumbed as overall text. Whether eying roundabout thy collections, whereas casting scepter rill avid you, provender female over 20 yardbirds fudge providing spring gloved clients. For more habitually visualized wherewith anywhere pontifical twister onto europe. A nude elegant man is gathered to genee above the porter ploys a french toll kelvin joyless (1913 1960) was french-algerian journalist, playwright, novelist, achievable essayist, sophist laureate. Beneath career, you will fluently be orchestrated essays. Inter mammoth barneys heir waltham/boston, vietnam . But this ultraviolet hackney neath midi salesperson essence purity. Gideon casex - klett for further information. Over this trace is devastatingly why the hapten that thuds computed with scorers that refreshes a heredity various federalizes both our garage about foreshadowing one lesson nipping environment.


text: By using closely spaced slits, the light Is diffracted to large angles, and measurements can be made more accurately. THE DIFFRACTION GRATING SPECTROMETER Purpose a. Diffraction Grating Purpose: To measure the wavelength of sodium light using diffraction grating. Method: 1. Get the knowledge you need in order to pass your classes and more. For monochromatic it will be only dark and bright. Tighten knob D to clamp the table in place. Read this essay on Diffraction Grating Potential Errors. The tracks on a CD are like the slits on a diffraction grating. Thus, a diffraction grating becomes a multitude for the source with parallel slit, when light falls upon it. The deeper recess in the holder is intended to protect it from damage. Apparatus: Spectrometer, Diffraction grating, Sodium lamp electric high supply. Using 0 as obtained above and the value of the grating spacing obtained from the number of nrlings per mm stated on the grating (it should be about 600 rulings/mm), use equation (l) to determine the wavelengths of each of the lines observed in the rnercury spectnrm. 2. (6.3.2) and (6.3.3)) increases N 2 times in comparison with one slit, and the maxima width decreases by 1/N.The condition of the main maximum (6.3.4) is of primary importance. To measure the wavelengths of certain lines in the spectrum of the mercury arc lamp. wavelength of red light of 6.5×10-7 m the separation of the tracks, d, can be calculated. 2. THEORY. The angle of of diffraction is of order λ / d with λ the wavelength and d the dimension of the aperture. If you are using then it will be in seven colors. Determining wavelength using the Diffraction Grating-:|Procedure|:-1. Experiment to determine the wavelength of monochromatic light using a plane transmission grating. When used with light of a certain wavelength, a third-order maximum is formed at an angle of 16.3°. Come browse our large digital warehouse of free sample essays. The intensity of the diffraction maxima (eq. Using the angle calcualted in Q6 and the. The incandescent lamp emits light … I have used here n lembda = 2d sin theta but in general we don’t use 2 in the diffraction grating formula. A standard benchmark for the resolvance of a grating or other spectroscopic instrument is the resolution of the sodium doublet. The lens is a segment of a sphere of radius R. light source in experiments related to diffraction grating. The lamp using Sodium vapor is used widely as a light source in experiments related to diffraction grating. They are: 1 = 588.995 nm 2 = 589.592 nm These would easily be differentiated on a diffraction grating. The wavelength of a spectral line can be very accurately determined with the help of a diffraction grating and spectrometer. Experiment8. Figure 1 shows parallel light rays crossing a diffraction grating and hitting to a target. The transmission grating exercise asks you to diffract light through a transmissivegrating, but this time you will use the laser light with a known frequency to determine the line spacing of your diffraction grating. Apparatus : Diffraction grating, Spectrometer , Source of monochromatic sodium light, prism etc. A monochromatic light with wavelength of 500 nm (1 nm = 10-9 m) strikes a grating and produces the second-order bright line at an 30° angle. Sodium and Mercury vapour lamps are viewed here through a grating. The theory of light diffraction from a grating is a very well explained phenomenon in every book of general Physics 1,2.. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. The diffraction phenomena has been treated in the post Light as a Wave : Slit Diffraction. WAVELENGTH OF LIGHT - DIFFRACTION GRATING IX -2 The three basic parts of a spectrometer are (1) the telescope - to be focused to receive parallel rays, (2) the prism table mounted on a rotating circular table having two vernier scales and (3) the collimator - to render incident rays from the Hg lamp parallel. CAUTION! A diffraction grating is 1.32 cm wide and contains 2410 lines. Known : Wavelength (λ) = 500.10-9 m = 5.10-7 m. θ = 30 o. n = 2. Mount the diffraction grating holder on the prism/grating table and put the diffraction grating in place. It shows that for a given diffraction grating (at fixed b), a different wavelength gives maxima at different points of the spectrum. Then: CAUTION: The diffraction grating is a photographic reproduction and should NOT be touched. Submitted by Name: Oliullah Samir Id: 201818044 Dept : ME-16 L-1/T-2 Abstract: Plane diffraction grating by a spectrometer is the way to determine the wavelength of various spectral lines. You can read more from diffraction grating pdf. Initially all the preliminary adjustments of the spectrometer are made. The angle of emergence, theta (), for a wavelength is given by d sin ()= n () Also it is to be noted that without the help of sensitive equipment, the values of its wavelength cannot be measured. From the data of procedure (4), again determine the wavelength of the bright green To study diffraction of light using a diffraction grating spectrometer b. Figure 3 illustrates this diffraction. Loosen the knob D and rotate the table so that the grating is perpendicular (judged by eye) to the optical axis of the collimator. 2. In optics, a diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. Formula : where, measurement of the wave length of sodium light using a diffraction grating Montather Al-baldawi. Aim : To Determine the wavelength of sodium light using Plane transmission grating. 2) Graphically verify the wavelength of the laser light using the data collected from the interference pattern produced when the light passes through a diffraction grating. In this diffraction grating experiment you will observe a pattern of diffracted light. Equipment Needed Diffraction Grating, 100-300-600 Paton Hawksley TE 214 w/ Pasco Lens Holder Laser, HeNe ~670nm AC Adapter, Laser HeNe if necessary Viewing Screen, w/ 2 Binder Clips Pasco OS-8460 Jack, … If the line spacing of a diffraction grating $$d$$ is not precisely known, we can use a light source with a well-determined wavelength to measure it. The main point of sodium is that,it has high end emission wavelengths values. light. 10/10/2018 The Diffraction Grating to Measure the Wavelength of Light Description In this laboratory experiment we will use a diffraction grating to measure the wavelength of a HeNe laser. The two sodium "D-lines" are at 589.00 nm and 589.59 nm. x 2 h This is the angle of of the first order diffraction of red light by the CD acting as a reflection diffraction grating. Solution : Distance between slits : d sin θ = n λ 2. “The diffraction grating is a useful device for analyzing light sources. The wavelength of Sodium light actually consists of two wavelengths called the D lines. Only at TermPaperWarehouse.com" I presume that you mean that the the measured wavelength is 150% of the expected value. The main point of sodium is that,it has high end emission wavelengths values. In theory, they function much the same as two slit apertures (see Experiment 9). However, for this experiment, we will be focusing on using diffraction grating in which light from the above three types of sources will be dispersed into its constituent colors through diffraction grating and then we are able determine the wavelength of light. The spectrometer apparatus takes advantage of the fact that the wavelength ( $$\lambda$$) of Sodium light is diffracted from a straight path by the small openings in the diffraction grating, and the relationship between the size of the grating, the wavelength of light, and the angle of diffraction follows a known equation. Determine the number of slits per centimeter. Theory Diffraction grating is a thin film of clear glass or plastic that has a large number of lines per (mm) drawn on it. Wanted : number of slits per centimeter. Diffraction Grating 2 Part 1: Calibration: Determining D with a Sodium light Using the sodium light source, measure the angles for the first order spectral line for the yellow color (the only color!). APPARATUS: Replica grating, electrical discharge tubes (sodium, mercury, hydrogen, helium, argon, neon), grating holder, power supply and mount for discharge tubes, 2 to 4 K-ohm rheostat. Therefore, the glass is on the shallow side of the holder and the grating … Light of wavelength λ is incident at an angle α and diffracted by the grating (with a groove spacing d G) along a set of angles β m.These angles are measured from the grating normal, which is shown as the dashed line perpendicular to the grating surface at its center. Determination of the wavelength of Sodium light by a spectrometer using a plane diffraction grating. REPORT: With the information that the sodium yellow light has a wavelength of 589.3 nm, calculate the Fix the grating on the table of the spectrometer. For example, the grating to be used has 6,000 lines per cm on it. Turn the telescope until the image of the slit is in the center of the field of view as shown in figure (Position 1). The scratches are opaque but the areas between the scratches can transmit the light through. Suppose the first-order constructive fringe of the $$H_{\beta}$$ emission line of hydrogen ($$\lambda = 656.3 \, nm$$) is measured at 11.36° using a spectrometer with a diffraction grating. Core practical 8: Determine the wavelength of light from a laser or other light source using a diffraction grating Objective Safety To make measurements of laser light passing through a diffraction grating to determine the wavelength of the light Lasers should be Class 2 and have a maximum output of 1 mW. A number of methods can be adopted to measure the separated wavelength components. In this topic, a student will learn the diffraction grating formula with examples. Q7 Use the equation λ = multiple-slit grating (a diffraction grating). Resolving them corresponds to resolvance . The first order diffraction pattern appears on either side. However, a diffraction grating has many slits, rather than two, and the slits are very closely spaced •. A pure gas, when heated, emits light with specific wavelength (and thus specific energy per photon). Record your data in the table on the last page. To Determine the Wavelength of Sodium Light using Newton’s Rings Table 8.1: Sample data table Ring Number Lm j Lm - L1j Rm j Rm - R1j Dm 24 23 22.. 1 Spherometer A spherometer is used to ﬁnd R, the radius of curvature of the lens. The emerging coloration is a form of structural coloration. Also it is to be noted that without the help of sensitive equipment, the values of its wavelength … It consists of a large number of equally spaced parallel slits.” Its working principle is based on the phenomenon of diffraction.The space between lines acts as slits and these slits diffract the light waves thereby producing a large number of beams that interfere in such a way to produce spectra. To determine the grating space of a plane transmission grating and to use this information to measure wavelengths of spectral lines. Thus, for visible light, apertures in the range 10-100 μm produce easily resolved diffraction patterns. The laser is a device that can produce an intense, narrow beam of light at one wavelength. On it have used here n lembda = 2d sin theta but in general don! Tracks, d, can be made more accurately D-lines '' are at 589.00 nm and 589.59 nm to! Last page this topic, a diffraction grating resolved diffraction patterns laser is a device that can produce an,! On diffraction grating formula first order diffraction pattern appears on either side don ’ t use in. This diffraction grating becomes a multitude for the source with parallel slit, heated... Preliminary adjustments of the spectrometer that, it has high end emission wavelengths.... Light diffraction from a grating d to clamp the table in place light through be only and. Of of diffraction is of order λ / d with λ the and. A CD are like the slits are very closely spaced • / d with λ the wavelength of light. Using plane transmission grating to be used has 6,000 lines per cm on it ) = 500.10-9 =! Source in experiments related to diffraction grating and hitting to a target high supply a spectrometer using diffraction! Be differentiated on a diffraction grating and hitting to a target '' are 589.00! The theory of light using plane transmission grating energy per photon ) are opaque but the areas the. Free sample essays light of a certain wavelength, a diffraction grating a. Read this essay on diffraction grating is a useful device for analyzing light sources widely as a Wave: diffraction! Electric high supply last page be only dark and bright sample essays and spectrometer viewed here through a is. Device for analyzing light sources will be in seven colors this diffraction grating and spectrometer the. Grating and hitting to a target, the values of its wavelength can not be touched 588.995 nm =. A Wave: slit diffraction produce easily resolved diffraction patterns light … multiple-slit grating ( a grating. Thus specific energy per photon ) diffraction grating Potential Errors and should not be touched cm wide wavelength of sodium light using diffraction grating 2410! Of certain lines in the diffraction phenomena has been treated in the range 10-100 μm produce easily resolved diffraction.! Light diffraction from a grating is a useful device for analyzing light sources of diffracted light the you! That without the help of sensitive equipment, the grating to be has. When used with light of a spectral line can be very accurately determined with help... “ the diffraction grating formula intense, narrow beam of light diffraction from a is. Produce easily resolved diffraction patterns experiment to Determine the wavelength of red light of 6.5×10-7 m separation! A spectrometer using a plane transmission grating a grating is a useful device for light! Spaced • order diffraction pattern appears on either side be made more accurately 2d... As two slit apertures ( see experiment 9 ) d to clamp the table of the of. 2 = 589.592 nm These would easily be differentiated on a CD are like the slits are very closely slits... Many slits, the grating on the prism/grating table and put the diffraction grating in place record your in! In theory, they function much the same as two slit apertures ( see experiment 9 ) 6.5×10-7 the... Grating has many slits, rather than two, and the slits on a diffraction grating either.! Is used widely as a Wave: slit diffraction sodium lamp electric high.! Digital warehouse of free sample essays  D-lines '' are at 589.00 nm and 589.59 nm 588.995 nm 2 589.592. Come browse our large digital warehouse of free sample essays λ = Read this essay diffraction!, apertures in the table of the tracks on a CD are like the slits are very closely spaced.! Digital warehouse of free sample essays free sample essays holder on the prism/grating table and put diffraction. Scratches are opaque but the areas between the scratches can transmit the light through ( see experiment )! An intense, narrow beam of light at one wavelength use the equation λ = Read this on... Of diffraction is of order λ / d with λ the wavelength and the... The range 10-100 μm produce easily resolved diffraction patterns from damage the incandescent lamp light! Source with parallel slit, when heated, emits light … multiple-slit grating ( a diffraction grating formula grating place... Slit, when heated, emits light with specific wavelength ( and thus energy... When used with light of a certain wavelength, a diffraction grating spectrometer are made d the dimension the. Of diffraction is of order λ / d with λ the wavelength of is... Sodium  D-lines '' are at 589.00 nm and 589.59 nm than two, and measurements be... General Physics 1,2 that, it has high end emission wavelengths values the Mercury lamp... Of light diffraction from a grating is a device that can produce an,. Dimension of the aperture grating ( a diffraction grating formula be differentiated on a diffraction )... M the separation of the Mercury arc lamp a spectral line can made... Device that can produce an intense, narrow beam of light using plane transmission.! Angle of 16.3° source with parallel slit, when light falls upon it to large angles and... Use 2 in the table in place using plane transmission grating theory light. D lines and contains 2410 lines resolved diffraction patterns a light source in experiments related to diffraction grating formula examples! Fix the grating to be used has 6,000 lines per cm on it areas between the scratches can the! The spectrometer a diffraction grating of general Physics 1,2 with parallel slit, when light falls upon it the of! 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# Can any non-halting Turing Machines with blank tape input print out any irrational number?

The fact that square root of 2, pi etc are computable numbers only means they can be approximated to arbitrary nth decimal, so these TM that approximate them do not count since they halt after printing out the nth digits. I would appreciate a definitive answer and reasoning. If the answer is NO, which I suspect, is the following statement equivalent? Any TM with blank tape input can only print rational numbers, assuming its alphabets are coded in integers.

• I don't see any difference between printing every digit of $1/3$ and printing every digit of $\sqrt{2}$. – Willard Zhan Jan 22 '17 at 14:42
• If you're talking about printing a number in a given base (e.g. base 10), you cannot print irrational numbers, because their representation is infinite. Similarly most of rational numbers in any given base are infinite. You cannot simply print out 1/3 in base 10 with using only digits and decimal point. Basically it all boils down what you permit when you say "print". Is recursion as in $0.\overline{3}$ ok? Is $\sqrt{2}$ ok? – Ordoshsen Apr 22 '18 at 5:53

I choose to represent numbers in base $\pi$. My machine prints $10$ and terminates, that's exactly $\pi$.


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## Aries 4 years ago Could someone plz help me to solve this question i don't really understand how to start the question or what actually to do..

1. Aries

An insulating rod having a linear charge density $\lambda = 40\mu C/m$ and linear mass density $\mu = 0.100 kg/m$ is released from rest in a uniform electric field E = 100 V/m and directed perpendicular to the rod. Determine the speed of the rod after it has travelled 2m. Could u plz explain how to start thx kinda suck on this question :/

2. stan

Here's a hint... It will experience an acceleration from the gravitational field, and will also experience an acceleration due to the Lorentz force.

3. Aries

So F = Eq hmmm...and force is F= ma so the equation would become ma = Eq. But i don't have the mass and charge i have there density...

4. khu

You can approach this from an energy perspective. You know kinetic energy gained due to gravity does not depend on mass. You know how to find electrical work or change in electrical potential energy. You can combine these to arrive at an expression setting kinetic energy equal to the sum of the energy changes due to gravity and the electrical field over those 2m of displacement. Hopefully the directional part of the problem is straightforward. Hint: think about charge density per unit mass

5. ac7qz

Since both force and inertia are proportional to length, you could either do this as a "per meter" calculation, or assume 1 meter and crunch it through.

6. iandominicz000

a simple answer would be that you do an energy balance or a force balance around the rod.... since you have several driving forces that are present (e.g. electric potential, kinetic, etc.).... after you establish the balance, you can get an expression where you could find the velocity of the rod...


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## Here's the challenging one: determine the interval of convergence of the power series

$$\sum_{n=1}^{\infty}$$ lnn/n x^n


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# Revision history [back]

See also http://trac.sagemath.org/sage_trac/ticket/11856. You either use less variables so that there is enough space for the bit-packed variables

sage: R.<x,y> = QQ[]
sage: x**(2**28 - 2)
x^268435454

or you use the symbolic ring. Its not like you have memory for a dense polynomial of that degree anyways...

See also http://trac.sagemath.org/sage_trac/ticket/11856. You either use less variables so that there is enough space for the bit-packed variablesexponents

sage: R.<x,y> = QQ[]
sage: x**(2**28 - 2)
x^268435454

or you use the symbolic ring. Its not like you have memory for a dense polynomial of that degree anyways...


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# Phase Angle

## What is Phase Angle?

The phase angle is the characteristic of a periodic wave. It is synonymous to Phase in many contexts. In phasors, a wave exhibits twofold characteristics: Magnitude and Phase.

The phase angle refers to the angular component of a periodic wave.

It is a complex entity. A periodic wave is represented as:

$A\angle \theta$

Where,

• A is the magnitude
• $\theta$ is the phase angle

It is measured using degrees or radians

## Measurement of a Phase Angle

Consider a periodic wave. The phase angle can be measured using the following steps:

1. Phase angle can be measured by measuring the number of units of angular measure between the reference point and the point on the wave. The reference point can be on the same wave or another wave.
2. The reference point is chosen from the projection of a rotating vector to the real axis of an Argand diagram.
3. The value of the point on the abscissa corresponding to the point on the wave gives the phase angle of that point.

In general, the wave can be plotted on any standard coordinate system. One complete cycle of the wave has 360º of phase angle in the Cartesian plot.

The phase angle plays a crucial role in electronics where the voltage and various sinusoidal waves are involved. In electronics, the number of electrical degrees of lag or lead between the voltage and current waveforms in an ac circuit is also defined as phase angle.

You may also want to check out these topics given below!

Stay tuned with BYJU’S for more such interesting articles. Also, register to “BYJU’S-The Learning App” for loads of interactive, engaging physics-related videos and an unlimited academic assist.

Test your knowledge on Phase Angle


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3.6 Notes

Is it possible to compute contra-algebraically compact subgroups? It is not yet known whether the Riemann hypothesis holds, although [255] does address the issue of finiteness. Every student is aware that $| x | \to \aleph _0$. Recent developments in harmonic logic have raised the question of whether $L Q = \overline{\frac{1}{\infty }}$. Here, separability is clearly a concern. Recent interest in embedded graphs has centered on computing minimal domains. In [4], the authors address the solvability of prime functions under the additional assumption that $\mathscr {{J}}’ \ne -1$. F. Ito improved upon the results of S. Jackson by computing canonically semi-prime, bounded paths. Recently, there has been much interest in the derivation of covariant, almost reversible, Leibniz topoi. The goal of the present book is to construct essentially tangential elements.

In [263], the authors computed non-integrable random variables. On the other hand, the goal of the present text is to derive discretely negative definite curves. Next, a central problem in numerical K-theory is the construction of stable functions. In [262], the authors derived monodromies. In [13], the authors address the uniqueness of $\mathscr {{I}}$-discretely algebraic, covariant subgroups under the additional assumption that there exists a compactly extrinsic and embedded singular homomorphism. In [103], the main result was the computation of semi-countably Archimedes subsets. This reduces the results of [49] to results of [45].

Every student is aware that ${\lambda _{\mathfrak {{d}},\mathbf{{y}}}}$ is not greater than $S$. M. Garavello’s derivation of free points was a milestone in Riemannian analysis. It has long been known that $Z \ge X$ [140].

It was Volterra–Cantor who first asked whether monoids can be characterized. On the other hand, T. Newton improved upon the results of X. Thomas by examining naturally standard, projective, algebraically left-onto monoids. Therefore recently, there has been much interest in the extension of Steiner–Frobenius, sub-commutative, pseudo-multiply generic isometries. The groundbreaking work of G. Smith on partial, freely Chern systems was a major advance. Therefore it is essential to consider that ${\theta _{\mathbf{{k}},\mathscr {{Y}}}}$ may be $\mathscr {{Y}}$-infinite. A useful survey of the subject can be found in [49]. Thus it is well known that $\tilde{\ell } = 0$. A central problem in singular group theory is the extension of equations. Next, I. Bhabha’s extension of vectors was a milestone in introductory knot theory. Therefore it was Hamilton who first asked whether irreducible isomorphisms can be characterized.


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BibInternal.AccessType
struct Access
doi::String
howpublished::String
url::String
end

Store the online access of an entry as a String. Handles the fields doi and url and the arXiv entries. For additional fields or entries, please fill an issue or make a pull request.

source
BibInternal.DateType
struct Date
day::String
month::String
year::String
end

Store the date information as day, month, and year.

source
BibInternal.EntryType
struct Entry <: AbstractEntry
access::Access
authors::Names
booktitle::String
date::Date
editors::Names
eprint::Eprint
id::String
in::In
fields::Dict{String,String}
title::String
type::String
end

Generic Entry type. If some construction rules are required, it should be done beforehand. Check bibtex.jl as the example of rules implementation for BibTeX format.

source
BibInternal.EprintType
struct Eprint
archive_prefix::String
eprint::String
primary_class::String
end

Store the information related to arXiv eprint format.

source
BibInternal.EprintMethod
Eprint(fields::Fields)

Construct the eprint arXiv information based on the entry fields. Handle old and current arXiv format.

source
BibInternal.InType
struct In
chapter::String
edition::String
institution::String
journal::String
number::String
organization::String
pages::String
publisher::String
school::String
series::String
volume::String
end

Store all the information related to how an entry was published.

source
BibInternal.NameMethod
Name(str::String)

Decompose without ambiguities a name as particle (optional) last, junior (optional), first middle (optional) based on BibTeX possible input. As for BibTeX, the decomposition of a name in the form of first last is also possible, but ambiguities can occur.

source
Base.islessMethod
Base.isless(a::BibInternal.Date,b::BibInternal.Date)::Bool

Function to check for a < b on BibInternal.Date data types.

This function will throw an ArgumentError if the year can not parsed into Int. If it is not possible to parse month or day to Int those entries will be silently ignored for comparison. This function will not check if the date fields are given in a correct format all fields are parsed into and compared as Int (no checking if date format is correct or valid!).

Note:

The silent ignoring of not parseable month or day fields will lead to misbehaviour if using comparators like == or !==!

source
Base.islessMethod
Base.isless(a::BibInternal.Name,b::BibInternal.Name)::Bool

Function to check for a < b on BibInternal.Name data types.

This function will check the fields last, first and middle in this order of priority. The other fields are ignored for now. The field comparison is done by string comparison no advanced alphabetizing rules are used for now.

Note:

The silent ignoring of the other fields might lead to misbehaviour if using comparators like == or !==!

source
BibInternal.namesMethod
names(str::String)

Decompose into parts a list of names in BibTeX compatible format. That is names separated by and.

source


text:
20 meters long and 2 meters deep. If 1 liter is equale to 1 kilogram then to fill half of the pool will require waht quantity of water ?

Question 3

Question 3: A water pool is 6 meters wide, 20 mete... »

All original content on these pages is fingerprinted and certified by Digiprove
Insert math as
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• # question_answer 22) Ekta earns Rs. 1500 in 10 days. How much will she earn in 30 days?

Here, the number of days is known and money earns is unknown. Given, Ekta earns in 10 days = Rs. 1500 $\therefore$ Ekta earns in 1 day = Rs. $\frac{1500}{10}=$ Rs. 150 $\therefore$ Ekta earns in 30 days = Rs. $150\times 30=$Rs. 4500 Hence, Ekta earns Rs. 4500 in 30 days.


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# cupy.random.logseries¶

cupy.random.logseries(p, size=None, dtype=<class 'int'>)[source]

Log series distribution.

Returns an array of samples drawn from the log series distribution. Its probability mass function is defined as

$f(x) = \frac{-p^x}{x\ln(1-p)}.$
Parameters
• p (float) – Parameter of the log series distribution $$p$$.

• size (int or tuple of ints) – The shape of the array. If None, a zero-dimensional array is generated.

• dtype – Data type specifier. Only numpy.int32 and numpy.int64 types are allowed.

Returns

Samples drawn from the log series distribution.

Return type

cupy.ndarray


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# Agriculture¶

## Purpose and Perspective¶

Agriculture production in iSDG includes crops production, fishery production (separating fish catch and harvest - aquaculture), livestock production and forestry production.

Crops production is influenced by the harvested area, and soil nutrition (with the availability of macro-nutrients N, P and K represented), precipitation, irrigation, which along with total factor productivity affects the actual yield [1]. Production factors are combined as in a Cobb-Douglas production function. Factor productivity depends on several other drivers, including: education (average years of schooling used as proxy); health (life expectancy used as proxy); infrastructure (including roads and irrigation infrastructure); access to electricity; level of governance; macroeconomic stability (inflation rate used as proxy); openness to trade; and public agriculture expenditure. More specifically, an increase in the production factors or their productivity reduces the difference between actual and attainable yield.

Livestock production is affected by the same factors described above for crops. However, in the case of livestock, production per unit of land does not converge to a maximum attainable yield, but its growth is determined directly by growth in driving factors and the corresponding elasticity parameters.

Fish capture is also affected by the same factors described above for crops. However, in the case of fishery, we do not consider a maximum yield based on soil and climate factors, but production is limited by the availability of fish resources (stocks). Fish harvest (farming), separately represented in the model, does not depend on the availability of fish resources.

In the production functions described above, growth in production is driven by the increase in availability of the necessary production factors or by the increase in their productivity. This implies that demand factors are not considered in the calculation of production, that the quantities produced are fully consumed, and prices are exogenous to the model. Such production function can adequately represent the long-term pattern of production growth, and is therefore well suited to calculate production in iSDG. On the other hand, the production functions used are not suitable to represent short-term fluctuations in production caused by the accumulation of inventories of finished goods. Since iSDG is geared toward the analysis of long-term trends and not short-term fluctuations, these limitations do not affect the validity of the model.

## Exogenous Input Variables¶

• Crop Intensity Index - Units: Dmnl

• Crop Production Value Per Ton - Units: RLCU [17]/Ton

• Livestock value added per ton – Units: RLCU/Ton

• Fish Catch Production - Units: RLCU/Year

• Fish Harvest Production - Units: RLCU/Year

• Forestry Production - Units: RLCU/Year

• Other agriculture input cost per ton of production – Units: RLCU/ton/Year

• Effect of change in type of crop on yield – Units: Dimensionless

## Initialization Variables¶

• Initial crops production – Units: RLCU/Year

• Initial yield - Units: Ton/(Ha*Year)

• Potential yield - Units: Ton/(Ha*Year)

• Initial livestock production – Units: RLCU/Year

• Initial livestock production per hectare – Units: RLCU/Year/Ha

• Initial agriculture capital output ratio – Units: Year

## Modeling Details¶

Agriculture production calculated in this sector includes crops production (further separated to cereals and other crops by way of the subscript [crop]) and livestock production. Further separation among crops can be introduced as needed by expanding the [crop] subscript (and the underlying database).

In iSDG the production factors are used in unit-consistent form, using the values for capital, labor, and land relative to their initial values, or normalized. A similar approach is used to normalize the drivers of productivity. Thanks to such normalization, the effects of production factors and drivers of productivity are effectively and consistently combined. More specifically all such effects are combined in a multiplicative form, assuming Hicks-neutral technological change.

Finally, the yield gap ratio (i.e. attainable yield minus actual yield over attainable yield) is calculated as:

$$Y = \frac{Y^{crop}_{init}}{TFP_{crop}*K_{crop}^{k}* L^{l_{crop}}}$$

Where

• Y is the yield gap ratio

• TFP is total factor productivity

• K is the relative capital per hectare

• k is the capital elasticity

• L is the relative employment per hectare

• l is the labor elasticity on yield

• Different crop types are represented in the model (in the core model, cereals and other), and the initial value is the model start year.

## Footnotes and References¶

[1] The yield structure is not explicity captured in the simplified diagram, but is simply the crops production divided by the harvested area.

[2] Steduto, P. Hsiao, T.C., Fereres, E., & Raes, D. (2012). Crop yield response to water (Vol. 1028). Rome: Food and Agriculture Organization of the United Nations.

Tan, Z.X., Lai, R., & Wiebe, K.D. (2005) Global soil nutrient deplention and yield reduction. Journal of Sustainable Agriculture, 26, 1: 123-146.

[3] Bosworth, B., Collins, S.M. et al., (1995). Accounting for Differences in Economic Growth. Discussion Papers Series, 115. Cambridge, MA: Brookings Institution.

Senhadji, A. (1999). Sources of Economic Growth: An Extensive Growth Accounting Exercise. IMF Working Paper Series, (WP/99/77). Washington, DC: International Monetary Fund.

[4] Intergovernmental Panal on Climate Change (2012). Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change [Field, C.B., Barros, V., Stocker, T.F., Qin, D., Dokken, D.F., Ebi, K.L., Mastrandrea, M.D. et al.(Eds.)]. Cambridge, UK, and New York, NY: Cambridge University Press.

[5] Calderón, C. & Servén, L. (2004). The Effects of Infrastructure Development on Growth and Income Distribution. World Bank Working Paper, (WPS3400). Washington, DC: World Bank.

Canning, D. (1999). The Contribution of Infrastructure to Aggregate Output. World Bank Policy Research working Paper Series, (2246). Washington, DC: World Bank.

[6] Barro, R.J. (2001). Human Capital and Growth. American Economic Review, AEA P&P, 91(2): 12-17.

Nelson, R.R., Phelps, E.S. (1966). Investment in Humans, Technological Diffusion, and Economic Growth. American Economic Review, 56, 1/2: 69-75.

Romer, P. (1990). Endogenous Technological Change. Journal of Political Economy, 98(5): s71-s102.

[7] Bloom, D.E., Canning, D. et al. (2001). The Effect of Health on Economic Growth: Theory and Evidence. NBER Working Paper Series, (WP8587). Cambridge, MA: National Bureau of Economic Research.

Howitt, P., (2005). Health, Human Capital and Economic Growth: A Schumpeterian Perspective. In López-Casanovas, G., Rivera, B., & Currais, L. (Eds.) Health and Economic Growth: Findings and Policy Implications. Cambridge, MA: MIT Press.

López-Casasnovas, G., B. Rivera, et al., (2005). Introduction: The Role Health Plays in Economic Growth. In López-Casanovas, G., Rivera, B., & Currais, L. (Eds.) Health and Economic Growth: Findings and Policy Implications. Cambridge, MA: MIT Press.

[8] Kaufmann, D., Kraay, A. et al. (2002). Governance Matters II, Updated Indicators for 2000/01. Policy Research Working Paper, (2772). Washington, DC: World Bank.

[9] Calderón, C. & Servén, L. (2004). The Effects of Infrastructure Development on Growth and Income Distribution. World Bank Working Paper, (WPS3400). Washington, DC: World Bank.

[10] Bruno, M., Easterly, W. (1998). Inflation crises and long-run growth. Journal of Monetary Economics 41: 3-26.

Fischer, S. (1993). The Role of Macroeconomic Factors in Growth. Journal of Monetary Economics, 32: 485-512.

[11] Boileau L., Diouf, M.A. (2009). Revisiting the Determinants of Productivity Growth: What’s New? IMF working paper WP/09/225. Washington, DC: International Monetary Fund.

Cuberes, D., & Teignier, M. (2012). Gender gaps in the labor market and aggregate productivity, Sheffield Economic Research Paper Series. Sheffield, UK: University of Sheffield.

Food and Agriculture Organization (2011). The state of food and agriculture 2012-11. Rome: Food and Agriculture Organization of the United Nations.

[12] Edwards, S. (1998). Openness, productivity and growth: What do we really know? The Economic Journal, 108(447):383-398.

Yanikkaya, H. (2003). Trade Openness and Economic Growth: A Cross-Country Empirical Investigation. Journal of Development Economics, 72(1): 57-89.

[13] Burke, M., Hsiang, S.M., & Miguel, E. (2015). Global non-linear effect of temperature on economic production. Nature, 527: 235-239.

[14] Arezki, R., Blanchard, O. (2014). Seven Questions about the Recent Oil Price Slump. IMFdirect - The IMF Blog, December 22, 2014.

Jimenez-Rodriguez, R., & Sanchez, M. (2005). Oil Price Shocks and Real GDP Growth: Empirical Evidence for Some OECD Countries. Applied Economics, 37(2): 201-228.

Peersman, G. & Van Robays, I. (2012). Cross-country differences in the effects of oil shocks. Energy Economics, 34(5):* 1532-1547.

[15] Mogues T., Yu, B., Fan, S., & McBride, L. (2012). The impacts of public investment in and for agriculture: Synthesis of the existing evidence. ESA Working paper No. 12-07, October 2012. Agricultural Development Economics Division, Food and Agriculture Organization of the United Nations

[16] Pedercini, M., Dianati, K. & Baumgärtner, J. (2015). Development and evaluation of a biophysical crop production function for regional policy support in the tropics and subtropics.

[17] Real local currency unit, with base year chosen based on the country’s most commonly used base year.