text: Requiring only an elementary knowledge of ordinary differential equations, this concise text is dedicated to helping engineering students solve problems in their field involving partial differential equations. Recently, the Lie symmetry analysis has been widely applied in different areas of mathematics, mechanics, physics, and applied sciences. Sometimes, it is difficult to estimate the shear stress accurately with this method by its complex shape. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Partial differential equations are introduced and solved using Fourier integral methods under a variety of boundary conditions. 5 0 obj In the paper “Applications of Group Theoretical Methods to Non-Newtonian Fluid Flow Models: Survey of Results,” T. Aziz and F. M. Mahomed offered a comprehensive survey of the studies which deal with flow models of non-Newtonian fluids using the Lie group method and conditional symmetries. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Ordinary Differential Equations with Applications Carmen Chicone Springer. Background of Study . We tried to focus on material that either advances the state-of-the-art of experimental, numerical, and theoretical methodologies or extends the bounds of existing methodologies to new contributions in mechanical sciences. A partial derivative represents the rate of change of a function (a physical quantity in engineering analysis) with respect to … Differential equations have wide applications in various engineering and science disciplines. At present, there exist several theoretical and experimental problems in engineering which are still unsolved. Differential Equations. stream And it is more reasonable to use this frequency equation to analyze vibration and measure modulus. A partial differential equation is an equation that involves partial derivatives. In the paper “Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity,” A. R. Ali and M. A. Kamel presented a mathematical model of an electric field sensor based on the whispering gallery mode (WGM). We'll explore their applications in different engineering fields. To Jenny, for giving me the gift of time. PDEs are used to formulate problem involving function of several variable and are either solved by … It is a transcendental equation with two unambiguous physical meaning parameters which can be defined as the ratio of rotary mass moment of inertia and the ratio of the mass, respectively. As a result, the accuracy of the proposed mesh-based scheme has been proven to be comparable to that of the polygon-based scheme, which is commonly adopted in straightforward implementation. In general, modeling of the variation of a physical quantity, such as temperature,pressure,displacement,velocity,stress,strain,current,voltage,or concentrationofapollutant,withthechangeoftimeorlocation,orbothwould result in differential equations. Partial Differentiation. However, there is one important difference. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. Application of First Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering San Jose State University San Jose, California, USA ME 130 Applied Engineering Analysis. The chapter makes the classification about the classical and the generalized solutions. 2 SOLUTION OF WAVE EQUATION. A differential algebraic equation (DAE) is a differential equation comprising differential and algebraic terms, given in … Keywords: Differential equations, Applications, Partial differential equation, Heat equation. Preface This book is based on a two-semester course in ordinary diﬀerential equa-tions that I have taught to graduate students for two decades at the Uni-versity of Missouri. The error sources in the proposed implementation are sourced from (1) the surface area vector of the staircase body shape and (2) the approximated shear stress. If the shear stress is appropriately evaluated, the fluid force can be accurately obtained by summing over the mesh faces, because the surface area vector components converge with increasing grid density while the surface area does not. Access Free Application Of Ordinary Differential Equation In Mechanical Engineering methods of their solving, and some applications to physics, engineering and economics. The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. READ PAPER. Linear Homogeneous Systems of Differential Equations with Constant Coefficients Method of Eigenvalues In general, modeling reported the transient squeezing flow in a channel in existence of magnetic field and chemical reaction. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. They found that flow field, temperature, and chemical reaction profiles are significantly influenced by magnetic parameter, heat generation/absorption parameter, and chemical parameter. Differential equations arising in mechanics, physics, engineering, biological sciences, economics, and other fields of sciences are classified as either linear or nonlinear and formulated as initial and/or boundary value problems. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This chapter presents the applications to partial differential equations. These are second-order differential equations, categorized according to the highest order derivative. 1 INTRODUCTION . Differential equations have wide applications in various engineering and science disciplines. The finite element method (FEM) (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. These are second-order differential equations, categorized according to the highest order derivative. In the case of the ordinary differential equation Lu = 0 with constant coefficients, every solution is the classical solution. 37 Full PDFs related to this paper. Roles of melting parameter , CuO–H2O volume fraction , Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. This course is specially designed to help you understand the concepts you need help in. Equation In Mechanical Engineering the differential equation defines a relationship between the two. This method has been developed by employing a novel mesh-face integration method and an extrapolation method for evaluating pressure and shear stresses at the mesh faces, such as the first-order, ghost-cell, or ghost-fluid methods. endstream Applications of differential equations in engineering … The laboratory component of the course emphasizes engineering applications in mechanical vibrations, control systems, robotics, fluid dynamics, material … Fourier Series. Such models are described by several constitutive relations as opposed to one, and as a result they have found wide range of applications in many areas of engineering and sciences, such as mechanical engineering, for example, in solid mechanics; aerospace engineering, for example, in aerodynamics; geophysical/astrophysical phenomena, for example, in weather-forecasting and space-exploration; and biomedical and health sciences, for example, in infectious disease control. Differential equations arising in mechanics, physics, engineering, biological sciences, economics, and other fields of sciences may be classified into either linear or nonlinear formulated as initial or boundary value problems. Common adaptive mesh approaches involve complex adaptive operations but this method was developed as an adaptive mesh method which is free from complex adaptive operations. Int by Substitution. applications of partial differential equations in mechanical engineering The aim when designing a controller, There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. In mathematics a Partial Differential Equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives (A special Case are ordinary differential equations. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Partial diﬀerential equations in modelling and control of manufacturing systems R.A. van den Berg SE 420379 Master’s Thesis Supervisor: Prof.dr.ir. Application of Partial Differential Equation in Engineering. New exact solutions to linear and nonlinear equations are included. A short summary of this paper. Then, the problem comes down to finding a finite set of parameters that define … Laplace Transforms. Obtained results have been validated by several examples. Simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. Ordinary Differential Equations (ODEs) An ordinary differential equation is an equation that contains one or several derivatives of an unknown function, which we usually call y(x) (or sometimes y(t) if the independent variable is time t). have studied a finite element mesh-partitioning strategy based on the direct transcription method to solve the optimal control problem with error estimation on noncollocation point. In the paper “A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems,” Z.-W. Cao et al. Offered by The Hong Kong University of Science and Technology. Differential equation denotes the relationship between a function and its derivatives, with some set of formulas. Due to vast range of application the investigations on this special issue were still scant. The focus of the course is the concepts and techniques … In order to fill this gap, researchers were invited to contribute original research and review articles. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. They employed Finite Element Model (FEM). <> Both theoretical and applied viewpoints have obtained great attention from many different natural sciences. For nonlinear problems, it is mostly difficult to obtain closed-form solutions. 1.INTRODUCTION The Differential equations have wide applications in various engineering and science disciplines. Over the last hundred years, many techniques have been developed for the solution of ordinary Application of First Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering San Jose State University San Jose, California, USA ME 130 Applied Engineering Analysis. We also look at simple electric circuit problems. 478 endobj We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. This Live course will cover all the concepts of Ordinary Differential Equations of 1st Order under the Engineering Mathematics syllabus. 3 0 obj examined the impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer by means of CVFEM. reported new numerical approach to solve convection-dominated diffusion problems. Both basic theory and applications are taught. Finally we look at the application of differential equations in Modern and Nuclear physics. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. addressed the derivation of the frequency equation of flexural vibrating cantilever beam considering the bending moment generated by an additional mass at the free end of beam, not just the shear force. Applications of Partial Differential Equations in Science and Engineering Edited by José Luis Galán-García , Gabriel Aguilera-Venegas , María Á Galán-García Volume 78, Issue 9, Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. [You may see the derivative with respect to time represented by a dot.For example, ⋅ (“ s dot”) denotes the first derivative of s with respect to t, and (“ s double dot”) denotes the second derivative of s with respect tot.The dot notation is used only for derivatives with respect to time.]. The applied electric field can be obtained by calculating these shifts. INVENTIONOF DIFFERENTIAL EQUATION: • In mathematics, the history of differential equations traces the development of "differential equations" from calculus, which itself was independently invented by English physicist Isaac Newton and German mathematician Gottfried Leibniz. In the paper “Level-of-Service Based Hierarchical Feedback Control Method of Network-Wide Pedestrian Flow,” Z. Zhang et al. An examination of the forces on a spring-mass system results in a differential equation of the form $mx″+bx′+kx=f(t), \nonumber$ where mm represents the mass, bb is the coefficient of the damping force, $$k$$ is the spring constant, and $$f(t)$$ represents any net external forces on the system. Partial differential equations are introduced and solved using Fourier integral methods under a variety of boundary conditions. In addition, we have addressed the computational costs. A brief version of the nonclassical symmetry method for partial differential equations is also included and the present survey provides a platform for researchers to apply this method to tackle nonlinear problems of Fluid Mechanics. • Partial Differential Equations A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to … Alvaro Suárez. A stochastic partial differential equation (SPDE) is an equation that generalizes SDEs to include space-time noise processes, with applications in quantum field theory and statistical mechanics. The shear stress is adequately evaluated by the second-order finite differencing scheme with the ghost-cell or ghost-fluid method. Nusselt number detracts with rise of Ha. 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# In what generality does the following statement hold: A fibration is acyclic if and only if all fibres are contractible fibrant objects.

This may not be precise enough for MO, but I'll give it a go.

Let $M$ be a symmetric closed monoidal model category with unit $u\in Ob(M)$. We define the vertices of an object $A$ to be points $x\in \operatorname{Hom}_M(u,A)$. We define the fibre of $f:B\to A$ over a vertex of $x$ of $A$ to be the pullback of $f$ by the map $x:u\to A$ classifying $x$.

It can be shown in the category of simplicial sets with the cartesian monoidal structure (and unit $\Delta^0$) that a Kan fibration is acyclic if and only if all of its fibres are contractible (I'm pretty sure that a similar statement holds for CGWH spaces in the Quillen model structure). However, the proof uses specific properties of the category of simplicial sets to prove this fact. Is there some general additional structure on $M$ that we would need to prove this statement in more generality?

Edit: It's at least clear that we must require the monoidal unit to be trivially fibrant.

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In which general situation do you want to apply this result? – Martin Brandenburg Sep 14 '10 at 6:29
Or you could just ask: in a model category when is the following true of some class $S$ of objects? A fibration $X\to Y$ must be a weak equivalence if for every $s\in S$ the resulting morphism $s\times_Y X\to s$ is a weak equivalence. In this form it has nothing to do with monoidal structure or with $s$ being equivalent to the final object. – Tom Goodwillie Sep 14 '10 at 13:36

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## Friday, September 28, 2007

### Laugh a little

SMS laughs

Knock! Knock!
Who is it?
Misbah…
Misbah who?
Mis bah 5 runs!

Misbah thought he was sending the ball into no man’s land. Little did he know that there is a Mallu in every corner of the world.

PS: Misbah played very well and thanks to him we won both matches.

## Thursday, September 27, 2007

### Celebrations!!!!!

Hey ppl!!!! Quo Vadis is 1 today!!!!!!!

When I started blogging I called this page Quo Vadis because I wasn't too sure where this blog would go. But over the past one year you have seen it and have been a part of it and have helped it grow to what it is today.
Thank you.

Now for the rest of the post.....

# 100 (number)

100 (one hundred) (the Roman numeral is C for centum) is the natural number following 99 and preceding 101.

 100one hundred 100thone hundredth $2^2 \cdot 5^2$ 1, 2, 4, 5, 10,20, 25, 50, 100 C Roman numeral (Unicode) C, c hecto-/hect- (from Greek) centi- (from Latin) 1100100 144 84 64 ק (Kuf)

## In mathematics

One hundred is the square of 10 (in scientific notation it is written as 102). The standard SI prefix for a hundred is "hecto-".

One hundred is the basis of percentages (literally "per hundred"), with 100% being a full amount.

It is the sum of the first nine prime numbers, as well as the sum of two prime numbers (47 + 53), and the sum of the cubes of the first four integers (100 = 13 + 23 + 33 + 43). Also, 26 + 62 = 100, thus 100 is a Leyland number.

One hundred is also an 18-gonal number. It is divisible

by the number of primes below it, 25 in this case. But it can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. However, it can be expressed as a sum of some of its divisors, making it a semiperfect number.

100 is a Harshad number in base 10, and also in base 4, and in that base it is a self-descriptive number.

## In science

### Astronomy

The Messier object M100, a magnitude 10.5 spiral galaxy in the constellation Coma Berenices.

The New General Catalogue object NGC 100, a magnitude 13.3 spiral galaxy in the constellation Pisces.

The Saros number of the solar eclipse series which began on 264 May 13 and ended on 1526 June 10 with a duration of 1262.1 years and 71 solar eclipses. Further, the number of the lunar eclipse series which began on 403 November 15 and ended on 1864 April 22 with a duration of 1460.4

years, and 82 lunar eclipses.

## In other fields

One hundred is also:

Pssst!: This post is No. 100, FYKI.

## Wednesday, September 26, 2007

### Watch this space for more...

Puzzled?

 One-Day Internationals 99 not out Player Runs Balls 4s 6s SR Team Opposition Ground Match Date Scorecard BA Edgar 99* 136 6 1 72.79 New Zealand v India Auckland 14-Feb-81 ODI # 116 DM Jones 99* 77 4 3 128.57 Australia v Sri Lanka Adelaide 28-Jan-85 ODI # 299 RB Richardson 99* 141 11 1 70.21 West Indies v Pakistan Sharjah 15-Nov-85 ODI # 339 A Flower 99* 111 7 2 89.18 Zimbabwe v Australia Harare 24-Oct-99 ODI # 1521 ADR Campbell 99* 124 8 0 79.83 Zimbabwe v New Zealand Bulawayo 1-Oct-00 ODI # 1629 RR Sarwan 99* 104 8 0 95.19 West Indies v India Ahmedabad 15-Nov-02 ODI # 1896 BJ Hodge 99* 86 7 1 115.11 Australia v New Zealand Melbourne 4-Feb-07 ODI # 2501 Test matches 99 not out Player Runs Mins Balls 4s 6s Team Opposition Ground Match Date Scorecard G Boycott 99* 337 285 8 0 England v Australia Perth 14-Dec-79 Test # 864 SR Waugh 99* 288 183 12 0 Australia v England Perth 3-Feb-95 Test # 1287 AJ Tudor 99* 182 119 21 0 England v New Zealand Birmingham 1-Jul-99 Test # 1455 SM Pollock 99* 252 170 9 2 South Africa v Sri Lanka Centurion 15-Nov-02 Test # 1626 AJ Hall 99* 126 87 15 2 South Africa v England Leeds 21-Aug-03 Test # 1656 To get out in the nineties must be really tough, just ask Sachin Tendulkar. But to stay unbeaten on 99, it must be a rare kind of experience.

PS: Quo Vadis 99* in 364 days

## Wednesday, September 19, 2007

### Man in the mirror, refreshed

(This is a partly recycled post. I have done some ^C & ^V to an earlier post that you may like to read)

"I'm starting with the man in the mirror, I'm asking him to change his ways, and no message could have been any clearer, if you want to make the world a better place take a look at yourself and make that change..."

- Micheal Jackson

Very powerful words with a deep meaning, how often we have heard the world is bad etc etc. Not a day will pass until we hear some one complaining about the poor infrastructure, bad roads, cleanliness, pollution, corruption and many of the ills that plague the world around. I think its time to wave a red flag and say STOP right there! It is your right to express you opinion (even blog! ; ) ) about something that concerns you, but what have you done about it the problem?

How many times have we seen well educated, well mannered people with high social standing complaining in public fora about the civic problems plaguing us and the next moment do not have the slightest remorse in throwing a recently used paper cup on the road. Just today we saw that the recently concluded local body elections having such ridiculously low voter turnout. The same middle class that will not hesitate to condone, criticize the politicians will just sit on their backsides , twiddling their thumbs watching a tear jerker soap on the tv on their day off and just ignore the future of the city. Then tell me what bloody right do these people have to complain?

This post was inspired by a hoarding that D showed me the other day that had the following words (incidentally the ad was for a tech firm)

Need I say any more?????

## Friday, September 14, 2007

### Tagged Ver. 2.0

Chriz tagged me because he liked these questions. And as the world is round my tag has returned to me.

Just a word of caution, you wont learn much about me from these questions (yes, I have been truthful)

1. Pick out a scar you have, and explain how you got it.
The scar on my nose, It started off as a simple mosquito bite but constant itching and a little scratching made it permanent.

2. What does your phone look like?
Last time I saw it, it still looked like a phone.

A Sony Ericcson W810i to be precise.

3. What is on the walls of your bedroom?

Paint!!! (I'm partly colour blind, so don't ask me what colour.)

4. What is your current desktop picture?

5. Do you believe in gay marriage?

Are you crazy? It will work only where men and women don’t know how normal marriages last. Yet another silly invention of the west.

If man did evolve from apes, ever seen one male ape doing another?

6. What do you want more than anything right now?

Actually, I’m stretched out watching a good T20 match and also blogging. Can’t ask for more.

7 . What time were you born?

6 AM and there was light!!!!!

8. Are your parents still together?

YES.

9. Last person who made you cry?

The joy of my life.

10. What is your favorite perfume / cologne?

Cuba. But I’m allergic to sprays so I tend to prefer ethnic roll-ons.

11. What kind of hair/eye color do you like in the opposite sex?

Any natural colour.

12. What are you listening to?

Some junk on TV.

13. Do you get scared of the dark?

No.

14. Do you like pain killers?

Nope. They are just a necessary evil.

15. Are you too shy to ask someone out?

Sometimes…... (Those were the good old days, too late now)

16. If you could eat anything right now, what would it be?.

Having too much hotel food lately, so as of now, I’d rather starve.

Ref Q. 9

18. Who was the last person who made you smile?

Who am I tagging?

That's a little secret.

## Thursday, September 06, 2007

### My blog is rated PG!!!!

Hey,

Saw this blog rating on Anju's blog and was curious enough to rate mine and guess what?

Mingle2 - Minneapolis Singles

This rating was determined based on the presence of the following words:

• kill (2x)
• hell (1x)
So all you kids out there, better keep your parents around when you read my blog.

### On my desktop!

Found this remarkable poster on the net.

Really awesome way to explain persistence on the job.

## Wednesday, September 05, 2007

### Pop that bubbly!!!!!!!!

I'm still celebrating a famous victory of the Indian cricket team at the oval. After a superb team effort built on a fabulous opening partnership from the superb partnership firm Tendulkar and Ganguly, the icing on the cake was laid by one young spark.

Take a bow Robin Uthappa!!!! You deserve all the applause.

## Saturday, September 01, 2007

### Teacher??????????

I remember being taught “matha, pitha, guru, deivam” or “mother, father, teacher, god” way back in school during my earliest Tamil classes.

The order of priority may vary and I’m sure is an intensely personal issue, but the fact that parents and teacher are elevated above the Almighty shows the roles and responsibilities they have.

However we have seen incidents that were probably going on for so long but now have been brought to the public eye by our innumerable media houses, incidents like beating, abuse, molestation, rape and other unspeakable abuses the children endure under the hands of teachers. Too often we see teachers committing crimes that deserve the strictest possible form of punishment and often getting away with it easily.

Yesterday we saw a teacher in a girl’s school trapped in a sting operation by a Hindi news channel. Her crime (yes, it was a woman), drugging her students and making pornographic movies with them, later on using these movies to threaten them into prostitution.

I was so revolted by the news and for a while I did not know how to react. My heart goes out to all those kids who have to endure all these abuses during the best part of their lives; they will surely be scarred for life.

But as I condemn such teachers, I wonder what are the parents doing? It is all very good to go around torching jeeps and stoning buses and making a general nuisance of themselves just to show their fury at the teacher, who incidentally has just been suspended and is in police custody.

So many questions cloud my mind:

• Why are the parents reacting and not being proactive to ensure that such crimes never occur? They may not know that a pervert teaches their kids but surely there will be some tell tale signs.

• Are not the parents the first line of defense for any child? Don’t children confide their fears and worries with their parents anymore?

• How can parents of these victims be so oblivious to such things till they see it on the news?

• When a baby cries, I have seen with amazement that the mother knows whether it is for milk or a change of nappy without a single word being spoken. Yet when these children go to school and endure so many scars, can not the parents see the un-cried tears in the eyes?

• Is there a break down in the parent child communication?

• Do parents have time actually for their children?

I remember even while in college my mother used to take active interest in what happened at class, often irritating “grown up” me. But this was something that she used to do from my kindergarten. Though the quantity and quality of the information decreased over the years it still was an open channel of communication for which today I’m intensely grateful for. I know without doubt that if I would have had one bad day in school over the years, my mother would have known, either by my words or by my actions. Even today she has not lost her skills but chooses to stay in the back ground till she is asked.

Thank you mum.


text:
Towards Procedurally Generated Stories via Free Monads

Strongly inspired by Dave Laing's fantastic series Cofun with cofree comonads. This post and the next are mostly rehashes of (superior) blog posts of his, but there is novel material to be covered soon.

I am eternally torn between a dichotomy I like to call "finish shit vs. solve cool problems." Finishing shit requires a lot of polish around the boring corners of a project, after all the cool stuff has been solved -- and there's always another cool problem waiting to be solved.

In particular, this dichotomy has recently manifested itself as "I should make an RPG vs. I already know how to make RPGs, it'd be fun creatively but gee that sounds like a lot of tedium and wouldn't teach me much in the end, except for maybe the value of hard work."

Then I realized making an RPG doesn't need to be tedious and boring. I'll just teach a computer how to generate an RPG. Goldmine genius idea. I don't know how to make a procedurally generated RPG, but really, how hard could it be?

This post is the first of many on just how hard it can be.

The Motivation

People have been making roguelikes for decades. While roguelikes are spectacularly cool, they're not really RPGs in the more common sense of the word. There's no narrative to a roguelike, you just adventure around and kill shit.

The RPG that inspired me to make an RPG was Earthbound, which is known for its quirky atmosphere and for managing to pull of some sort of weird-humorous-plot-mixed-with-lovecraftian-horror juxtaposition. Earthbound feels like it might have been made on drugs, but somehow manages to still be a fantastic experience.

This is the kind of thing I want to generate. Lots of games have tried to generate interesting worlds and plots, but, at least when I was in the games industry, the state of the art was prefabricating modules and stitching them together. Sure, it's hard to generate solid plots, but I don't think its intractable.

I think the problem might have been this: this problem is fundamentally functional; any imperative approach is going to be a Bad time.

Maybe. Lots of this is vaporware still, but it feels right, and I have a plausible path to actually executing on it.

The Idea

Enough run-around. Are you ready to hear my revolutionary idea to generate procedural RPGs with coherent and interesting stories?

1. Build a datastructure representing a story.
2. Turn this datastructure into a game.

Amazing, right?

Okay, not that amazing, but here's the rub. Instead of building this datastructure by hand, we'll write a domain specific language (DSL) which will generate the datastructure for us. And then if we then embed this language into Haskell, we'll lift all of the expressiveness of Haskell into our DSL. If we limit the DSL to a few number of primitive operations, and implement all of the interesting pieces as combinators on top, it will be easy to abstract over, and more importantly, to interpret.

This interpretation step is, unsurprisingly, where the "magic" happens.

Separating the structure of what we want to do (which is what the DSL provides us) from how we do it means we can do different things with the same data. For example, given a basic plot skeleton, we can run over it, and with the help of a random number generator, determine a theme. Then, given the theme and the plot skeleton, build necessary locations to help advance the plot from one scene to the next. Then, with all of this, we can build intermediate landscapes to stitch the locations together. And so on and so forth.

There are lots of potential failure modes here, but the approach seems feasible.

The Pieces

So I went through a bunch of games whose stories I adore, and I attempted to deconstruct them into their primitive operations. A simplified datastructure of what I came up with is provided here:

type Story = [StoryPrim]

data StoryPrim = Change Character ChangeType
| Interrupt Story Story

data ChangeType = Introduce
| Die
| Leave
| Arrive Location
| Kill Character
| Learn ChangeResult

data ChangeResult = ChangeResult Character ChangeType

which is to say, a Story is a list of StoryPrims, which is either a change in character state, or one Story being interrupted by another (eg. if someone's murder attempt is foiled by an unexpected arrival.)

This isn't comprehensive enough to generate entire stories, but it's definitely good enough to motivate the remainder of this post.

Let's take a little break and talk some math.

Free monads are one of the neatest things I've learned about recently. The definition (in Haskell) of a free monad over a functor f is this:

data Free f a = Pure a
| Bind (f (Free f a))

Which can be thought of a recursive datastructure which bottoms out with a Pure or recurses with an Bind. The definition was hard for me to work my head around, so let's give it a concrete functor and see what pops out:

data Free [] a = Pure a
| Bind [Free [] a]

If we squint, this is actually just a tree where Bind is a n-ary branch, and Pure is a value at a leaf. So a tree is just a special case of the free monad. That's kinda hot, if you're as into this stuff as much as I am.

But what's more hot is that given any instance Functor f, Free f forms a monad:

instance Functor f => Monad (Free f) where
return a = Pure a
Pure a >>= f = f a
Bind m >>= f = Bind (fmap (>>= f) m)

It's probably the dumbest Monad instance imaginable, but hey, it adheres to the monad laws, and that's really all we ask for. The laws are satisfied only in a very trivial sense, in that all we've done here is encode the rules of return and (>>=) into our datastructure which is to say, we haven't done any processing yet. We'll return to this in a moment.

It's called "free" for exactly this reason of trivially satisfying the laws -- given any functor f we can get an (admittedly stupid) monad over f for free.

Because our free monad is just a datastructure in the exact shape of a computation we would want to carry out over its contents, it's easy to write an interpreter for it. Or several.

See where I'm going with this?

Here's the kicker: Free monads turn out to be the abstraction behind DSLs because they encode the structure of a computation, without imposing an interpretation over it.

But remember, getting a free monad requires having a functor. If we can find a means of encoding our Story grammar above as a functor, we can lift it into a DSL via Free.

The Command Functor

So we need a means of getting a Functor instance for our Story type described above. But how?

Let's start playing madlibs with what we know.

type Story a = Free StoryF a

data StoryF a = -- ???

Looking at the definition of Free specialized over our functor StoryF once again hints us in the right direction:

data Story a = Pure a
| Bind (StoryF (Story a))

The polymorphic variable of our StoryF functor is only ever going to be a Story a, which is to say a pure a or a bind computing more of the final value.

So our polymorphic type variable is the type of the continuing computation. Because Pure from Free takes care of how computations terminate, our functor should always have a continuing computation. Voila:

data StoryF a = Change Character ChangeType (ChangeResult -> a)
| Interrupt (Story ()) (Story ()) a

contrasting this against our old StoryPrim, we've just added a new product involving a to all each of our sum terms. Again, a should be considered to be the type of the continuing computation.

But what's this funny ChangeResult -> a thing? Well, recall that we wanted a Change to return a ChangeResult indicating what changed, which is to say this result should be a parameter to the rest of the computation -- thus our function type1.

StoryF is what's known as our command functor, because as we will see, its constructors will eventually act as commands in our DSL.

But wait! Not so fast. We haven't yet provided a Functor instance for StoryF. It's trivial, but we present it here for completeness:

instance Functor StoryF where
fmap f (Change c ct k)    = Change c ct (f . k)
fmap f (Interrupt s s' k) = Interrupt s s' (f k)

And so StoryF is now a Functor, which means that Free StoryF is a Monad, which means that we can use do notation inside of it! We're most of the way to our DSL!

All that's left is to lift our StoryF data constructors into Story constructors. The details of this are a little messy, but luckily liftF from the free package does most of the manual labor for us.

change :: Character -> ChangeType -> Story ChangeResult
change c ct = liftF $Change c ct id interrupt :: Story () -> Story () -> Story () interrupt s s' = liftF$ Interrupt s s' ()

and that's it! Short of some helpful combinators, we're done! We can now write basic stories in Haskell using do notation!

myStory :: Story Int
myStory = do
let mandalf = Character "Mandalf the Wizard"
orcLord = Character "Orclord Lord of the Orcs"
orcBaby = Character "Orclord's Child"

return 5

die :: Character -> Story ChangeResult
die who = change who Die

kill :: Character -> Character -> Story ChangeResult
kill who whom = change who (Kill whom) <* die whom

As far as stories go, one about a child learning of its father's death is probably not going to win any feel-good-novella-of-the-year, but the example serves to showcase several things:

• We can build abstractions with standard Haskell combinators (eg. killing someone implies that they die.)
• The fact that this typechecks shows that our language is expressive enough for characters to learn of the arbitrary actions of one another (including learning that they've learned something.) Furthermore, knowledge is first-class and can be passed around the story however we see fit.
• Like all monads, our DSL can describe things that happen while returning potentially unrelated data. The 5 above is meaningless, but allows us to interleave story descriptions with arbitrary computations.

This seems like a good place to stop for today -- we've covered a lot of ground. Next time we'll discuss how we can use cofree comonads (I am not kidding here) to build an interpreter for our DSL.

1. If this isn't immediately evident to you, make sure you understand how do desugaring works.


text:
## CVAR

 Global C-script variable Inputs(0) Parameters(1) p1 Default p1=0, Text1 Variable Text2 Select from Components/Blocks/Cscript&Expression Function In the CVAR block you define a global variable which is declared in all C-scripts defined by all the CSCRIPT blocks. In the C-Script block you can define C code to create your own blocks. The C code is interpreted, so no external compiler is required.Inside the C-script block local variables are declared. Global variables are defined in the block CVAR. Special Example of a simple adder:In a CVAR block the global variable iGlobal is defined at text1. Its initial value is defined as parameter p1The value defined in the block CVAR is declared global in the entire scope of each C-script.Defined in the CVAR block: (int iGlobal=42;)Text1 = iGlobalp1 = 42Defined in the Cscript block:int iCount;int y;main()  {  iCount=1;  //the value of the global value is added to y  y=a+iCount+iGlobal;  //the value of the local varaiable iCount is passed to the global variable iGlobal  iGlobal=iCount;  return(y);  }The value of the local variable iCount is finally passed into the global variable iGlobal fro mthe CVAR block. The output of the CVAR block is equal to the value of the global variable.Since ANSI C is case-sensitive, lowercase variables and uppercase variables are not equal, so a<>A and iCount<>icount.See the tutorial on the C-Script for more details on the syntax of the C-script.


text:
1. Home
2. Article Catalog
3. Forecasting steel and iron ore prices using Fbprophet Python library

ARTICLE

Forecasting steel and iron ore prices using Fbprophet Python library

Tamara Thorne
Raksina Samasiri

# Introduction

China’s steel market has been very volatile in the past several years. It is inherently difficult to forecast commodities prices, particularly in the post-pandemic environment but in the case of steel and iron ore (the main material used in steel production), this task is even harder for a few reasons.

Firstly, China’s government has embarked on a de-carbonization journey which resulted in steel production cuts and capacity replacements, particularly in the highly polluted industrial areas of Tangshan. Since January 2021, there have been many announcements from the government and official media confirming China’s plans to become carbon neutral by 2060. Some of the announced measures were addressed directly at the steel industry which has already undergone major transformations including mergers and acquisitions and other structural adjustments like shutting down outdated capacities and plans to introduce green technology like hydrogen and carbon capturing.

Secondly, China has been struggling with some structural challenges in the property market. A combination of zero-covid rules, a slowdown in real estate, and environmental production cuts have been hurting steel demand for the better part of last year. However, last month China’s government announced 16 measures to revive the housing market. The measures among other things aim to provide financial support for viable construction developments, resume stalled projects and help mortgage holders. Although the new property policies do a lot to address the problem, they may not help solve the main issue of the little trust China’s buyers have in real-estate developers.

Thirdly, protectionists policies in various countries across the world are becoming a more prominent feature of the governments’ economic plans. This results in high tariffs imposed on steel products from China. Lastly, the tragic events in Ukraine do not only cost lives in the region and energy crisis in Europe but also threaten economic stability in the rest of the world by reshaping supply chains and causing a major supply crisis.

All the above must be considered in qualitative price forecasting as these developments define fundamentals. One might argue that in such an environment qualitative approach should be the only way. However, on the other hand, predicting the outcome of these uncertainties is extremely difficult and time series forecasting could still be useful in certain circumstances.

## Prerequisite

To run the code in this article, any of the below can be used

• The CodeBook application inside the Eikon Desktop/Refinitiv Workspace
• The code is available in the CodeBook application (Example folder)
• The codeBook is a feature that provides you with a cloud-hosted development environment for Python scripting, and supports bespoke workflow design. With CodeBook, we are redefining how you access, evaluate and build on the breadth and depth of our data. Whether you are a professional developer, occasional coder or have no coding skills, CodeBook offers the capabilities for you to design your own data models or access Python applications built by your colleagues – the possibilities are endless. Available in Refinitiv Workspace and Eikon, CodeBook also gives you access to our APIs and platform services in a single interface so you can be even more efficient. With our data, you can build analytics, applications and other use cases that are critical for your daily workflow needs.
the Jupyter notebook file is located in /__Examples__/06. Commodities Research/ (screenshot below)
• Or your own local Python Environment with
• Required Python libraries and their version:
• eikon==1.1.14
• fbprophet==0.7.1
• statsmodels==0.11.0
• numpy==1.22.4
• pandas==1.3.5
• datetime==4.3
• plotly==5.4.0
• Jupyter Lab or Jupyter Notebook application is installed and ready to use

# Hypothesis

It has been written a lot on the topic of time series forecasting. The purpose of this article is to describe the process used in our model which employs fbprophet Python library (Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data. Prophet is robust to missing data and shifts in the trend, and typically handles outliers well.) to forecast the price (of HRC steel prices in China and iron ore 62% Fe content CFR China prices, in this article)

There are multiple reasons why the Fbprophet Python library could be a good fit for our forecast modeling:

1. It works well with stationary time series where non-linear trends follow some type of seasonality (weekly, yearly, daily).
2. Fbprophet requires several cycles of such seasonality to be observed in the historical time series
3. Fbprophet is relatively robust with shifts in data trends and deals well with outliers.

# Step-by-Step Process

ek.set_app_key('DEFAULT_CODE_BOOK_APP_KEY')
sd = datetime.date(day = 1, month = 1, year = 2018).strftime('%d-%m-%Y')
ed = datetime.date.today().strftime('%d-%m-%Y')
a_interval = 'daily'

ric_names = ['SH-CCN-IRNOR62','SH-WUH-3HRCOIL']
rics = {}

def get_timeseries(ric):
print(f'Getting timeseries data of {ric}')
df = ek.get_timeseries(ric, start_date = sd, interval = a_interval)
df.columns.values[0] = 'Value'
df['Date'] = pd.to_datetime(df.index)
df['Price'] = df['Value']
rics[ric] = df

for ric in ric_names:
get_timeseries(ric)

# Prep Data
ric_prep = {}
def prep_data(ric):
this_ric = rics[ric]
this_ric['Price'] = this_ric['Price'].apply(lambda x:float(x)) # Price values as float
this_ric = this_ric.resample('D').mean() # resample for daily
this_ric['Date_Day'] = this_ric.index
this_ric['Date_Day'] = this_ric['Date_Day'].dt.strftime('%Y-%m-%d').copy() # changing Date format

holidays = this_ric[this_ric['Price'].isin([np.nan])] # saving holidays and weekends for further predictions in prophet
holidays = holidays.Date_Day.tolist()
holidays_df = pd.DataFrame({'holiday' : 'weekend', 'ds' : pd.to_datetime(holidays)})

this_ric['Price'] = this_ric['Price'].fillna(method='ffill') # replacing gaps in values
this_ric = this_ric.reset_index(drop=True)

ric_prep[ric] = this_ric
return holidays_df

for ric in rics:
holidays_df = prep_data(ric)

Secondly, we perform Augmented Dickey-Fuller Test (ADF) to check whether our data is stationary/non-stationary. Using the diff() function will allow us to calculate the first-order difference in the selected time series with a predefined shift period. The shift period is defined as a parameter period. We then test the resulting row of data for stationarity/non-stationarity and print the test statistics as per the method below.

# Augmented Dickey-Fuller Test
diff = vals.diff(periods=1).dropna()
print('====> p-value:',test[1])
print('Critical values:',test[4])
if test[0] > test[4]['5%']:
print(f'{ric} non stationary')
else:
print(f'{ric} stationary! The row of first differences is stationary and the initial row is an integrated row of the first order')

for ric in ric_prep:

The output is as below

====> p-value: 0.0
Critical values: {'1%': -3.433926456232207, '5%': -2.863119805756803, '10%': -2.5676110344808043}
SH-CCN-IRNOR62 stationary! The row of first differences is stationary and the initial row is an integrated row of the first order
====> p-value: 3.821856158152293e-15
Critical values: {'1%': -3.4339580289794225, '5%': -2.8631337437669275, '10%': -2.567618456010139}
SH-WUH-3HRCOIL stationary! The row of first differences is stationary and the initial row is an integrated row of the first order

After performing the stationarity check, we need to define the model’s characteristics and “tune it” so to speak. We define the prediction period as a period of 30 days (this could be increased). We then create ds (date as DateTime) and y (values that we are going to predict) columns. We will then convert the Price column into a log value. In statistical analysis, logging helps to convert multiplicative relationships between datapoints into additive relationships, and converts exponential (compound growth) trends into linear trends. Therefore, by taking logarithms of values which are multiplicatively related we can explain their behaviour with a linear model.

We are taking data (except for the last 30 values) for training our model in order to compare the actual values in our time series with the 30 values predicted by the model

ric_train = ric[:-period]

We create the model, using the fit method, and get the prognosis. It is worth mentioning that Fbprophet is a very flexible and easy-to-train model. Very often the quality of the forecast depends on the time series' characteristics as well as the model’s parameters that can be defined (and tuned) depending on our knowledge about the time series and multiple rounds of testing. These parameters include:

• Interval_width: the width of the uncertainty intervals
• N_changepoints: changepoints are the DateTime points where the time series have sudden changes in the trajectory (there is a full list of changepoints in prophet which are accessible using ch_points = pr_model.changepoints)
• Changepoints_prior_scale: helps adjust the strength of the trend. It is possible to increase the value of changepoints_prior_scale to make the trend more flexible
• Changepoints_range: the range of historical data points (starting from the first observation) within which the changepoints in trend will be assessed
• Yearly, weekly and daily seasonality: self-explanatory parameters that we can set as true or false for our time series
• Holidays: we can create a custom holiday list by creating a data frame with two columns ds and holiday

For predictions, we need to create a data frame with ds (DateTime) containing the dates for which we want to create a forecast. We are using make_future_dataframe() where we specify prediction dates. We then combine actual data and our forecast data into one table. It is useful to have a look at MAE (mean absolute error) which helps in understanding how precise the model’s predictions are.

Lastly, we perform the prediction of all available data points within our time series as per the below steps:

# Test Prediction
ric_plot = {}
for ric_name in ric_prep:
print(f'run Test {ric_name} Predict...')
period = 30
ric = ric_prep[ric_name]
ric = pd.DataFrame({'ds' : ric.Date_Day, 'y' : ric.Price})
ric['y'] = np.log(ric['y'])
ric = ric.reset_index(drop=True)

ric_train = ric[:-period]
pr_model = Prophet(interval_width=0.95, # The width of the uncertainty intervals (by default 80%) can be set using the parameter interval_width
n_changepoints=40,
changepoint_prior_scale=0.08,
changepoint_range=0.09,
yearly_seasonality=True,
weekly_seasonality=False,
daily_seasonality=False,
holidays=holidays_df)
pr_model.fit(ric_train)

future = pr_model.make_future_dataframe(periods = period, freq = 'D') # df for date +30 forecast days
forecast = pr_model.predict(future)

forecast['ds'] = forecast['ds'].dt.strftime('%Y-%m-%d').copy()
cmp_df = forecast.set_index('ds')[['yhat_lower','yhat_upper','yhat']].join(ric.set_index('ds')).copy() #df compare
cmp_df['MAE'] = cmp_df['y'] - cmp_df['yhat'] # mean absolute error (on average the models error)
print('MAE', np.mean(abs(cmp_df[-period:]['MAE'])))

# Prediction
print(f'run {ric_name} Predict...')

ric = ric_prep[ric_name]
ric = pd.DataFrame({'ds':ric.Date_Day,'y':ric.Price})
pr_model = Prophet(interval_width=0.95, # The width of the uncertainty intervals (by default 80%) can be set using the parameter interval_width
n_changepoints=40, # 25 by default
changepoint_prior_scale=0.08, # 0.05 by default
changepoint_range=0.09,   # 0.8 by default
yearly_seasonality=True,
weekly_seasonality=False,
daily_seasonality=False,
holidays=holidays_df)

ric['y'] = np.log(ric['y'])
ric = ric.reset_index(drop=True)
pr_model.fit(ric)
future = pr_model.make_future_dataframe(periods = period, freq = 'D')
forecast = pr_model.predict(future)

ric['y'] = np.exp(ric['y']) #converting back into numerical values
forecast['yhat_lower'] = np.exp(forecast['yhat_lower'])
forecast['yhat_upper'] = np.exp(forecast['yhat_upper'])
forecast['yhat'] = np.exp(forecast['yhat'])

forecast['ds'] = forecast['ds'].dt.strftime('%Y-%m-%d').copy() #creating a table with actual data and predictions
prophet_ric = pd.DataFrame({'Date':forecast.ds,'Price':forecast.yhat})
prophet_ric = prophet_ric.tail(period).copy()

ric = ric.rename(columns={'ds':'Date','y':'Price'}) #renaming back our columns as date and price
ric = pd.concat([ric, prophet_ric])
ric = ric.reset_index(drop=True)
ric_plot[ric_name] = ric
print(f'done {ric_name} Predict...')

Example output of one of the instrument

As a final step, we are plotting our data and predictions using the Plotly Python library

# Plot
for ric_name in ric_plot:
if ric_name == 'SH-CCN-IRNOR62':
color = 'cyan'
title_text = 'SteelHome 62% CFR China & forecast'
yaxis_title = 'Price USD'
elif ric_name == 'SH-WUH-3HRCOIL':
color = 'crimson'
title_text = 'SteelHome HRC Wuhan & forecast'
yaxis_title = 'Price CNY'
else:
color = ''
title_text = ''
yaxis_title = ''

ric = ric_plot[ric_name]
fig = go.Figure()
start_pred = ric.head(1).reset_index(drop = True).loc[0, 'Date']
fig.update_layout(title_text=title_text, yaxis_title=yaxis_title)
fig.show()

print('Finish')

# Conclusion

This article demonstrates how the Fbprophet Python Library can be used in price forecast modeling using an example of Hot Rolled Coil (HRC) steel price in China and iron ore 62% Fe content CFR China. The prices’ historical data and predictions are plotted as a graph with Plotly Python library as a visualisation to help with analysing price trends and a potential direction the prices may take in the short-term future.

# References

For further details, please check out the following resources:

For any questions related to the Eikon Data API, please use the Developers Community Q&A Forum.


text:
Opuscula Math. 36, no. 4 (2016), 489-498
http://dx.doi.org/10.7494/OpMath.2016.36.4.489

Opuscula Mathematica

Uniform approximation by polynomials with integer coefficients

Artur Lipnicki

Abstract. Let $$r$$, $$n$$ be positive integers with $$n\ge 6r$$. Let $$P$$ be a polynomial of degree at most $$n$$ on $$[0,1]$$ with real coefficients, such that $$P^{(k)}(0)/k!$$ and $$P^{(k)}(1)/k!$$ are integers for $$k=0,\dots,r-1$$. It is proved that there is a polynomial $$Q$$ of degree at most $$n$$ with integer coefficients such that $$|P(x)-Q(x)|\le C_1C_2^r r^{2r+1/2}n^{-2r}$$ for $$x\in[0,1]$$, where $$C_1$$, $$C_2$$ are some numerical constants. The result is the best possible up to the constants.

Keywords: approximation by polynomials with integer coefficients, lattice, covering radius.

Mathematics Subject Classification: 41A10, 52C07.

Full text (pdf)

Artur Lipnicki, Uniform approximation by polynomials with integer coefficients, Opuscula Math. 36, no. 4 (2016), 489-498, http://dx.doi.org/10.7494/OpMath.2016.36.4.489

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text:
Question:

#### What if I've chosen the wrong course?

(Last edited: Tuesday, 1 March 2016, 4:48 PM)


text:
## FANDOM

1,168 Pages

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of sides is

$\frac{r}{R}= \frac{\cot(\frac{180}{n})}{\csc(\frac{180}{n})}= \cos(\frac{180}{n})$

The total length of the spiral for an n-gon with side length is therefore $J= \frac{s}{2[1-\cos(\frac{180}{n})]}$

Consider the solid region obtained by filling in subsequent triangles which the spiral encloses. The area of this region, illustrated above for n-gons of side length , is $A= \frac{s^2}{4}\cot(\frac{180}{n})$

The shaded triangular polygonal spiral is a rep-4-tile.

Community content is available under CC-BY-SA unless otherwise noted.


text:
## Saturday, July 5, 2014

### generalizaton of the Hartle-Hawking no boundary proposal and the Perfect Cosmological Principle

Excerpts from The Revolution of Matter

Writing the Euclidean Hamiltonian as a function of a scalar field and allowing the total energy of Euclidean space to be zero, where the dynamical variables momentum and energy are dimensionless in $\mathbb{R}^4$, and accordingly any wave equation is a purely mathematical object.

$$\mathcal{H}_E (\phi) =\mathbb{T} (\phi) -\mathbb{U} (\phi) =0$$

Here $\mathbb{U} (\phi)$  is the geometric potential for the entire universe of  $\mathbb {R^4} (\phi)$, and since  $\mathbb { R^{1,3}}$ is a subspace of  $\mathbb{R}^4$ any global change in $\mathbb{U} (\phi)$  causes a global change in $\mathbb {R^{1,3}}$. Under the premise that no physical matter existed before the Big Bang at $\mathbb{U}_i$, then matter is absent in  $\mathbb {R^{1,3}}$ and the dynamical variables T, V are zero,

$$\mathcal{H}_M(\mathbb{R}^{1,3})=T+V -G =0$$

$$T=V=G=0$$

Therefore initially $\mathbb {R^{1,3}}$ is as flat as $\mathbb{R}^4$ . Since  $\mathcal{H}_E (\phi)$ = 0, this implies -and most importantly - there is no center or boundaries to  $\mathbb{U}$, for as the momentum and energy tends to zero so the Heisenberg uncertainties in position and time also tend to infinity,

And this is the key idea, applying the Heisenberg uncertainties to the Euclidean and Minkowskian spaces as a whole states the total uncertainty in space and time tends to infinity,

$$X_i\simeq X_i\pm \text{\delta X}_i\simeq X_i\pm \infty$$

So the boundary to any point is at infinity, which is a restatement of the Hartle-Hawking no boundary proposal. Yet adding the maximal uncertainty to the boundary itself,

$$X_i\simeq X_{\max }\pm \text{\delta X}_{\max }$$

implies the boundary simultaneously coincides with every other point within this model universe and has the remarkable result that every point within the potential behaves as a boundary of the potential.

In effect, at $\mathbb{U}_i$ where starting from a homogeneous and isotropic $\mathbb{R}^4$ and then applying the Heisenberg Uncertainty principle to $\mathcal{H}_E$ as $\mathbb{R}^4$ evolves smoothly under the Wick Transformation into $\mathbb {R^{1,3}}$  to the $\mathcal{H}_M$ results in every point in $\mathbb {R^{1,3}}$ being bounded and adjacent to every other point in $\mathbb {R^{1,3}}$ , therefore at the Big Bang every point in $\mathbb {R^{1,3}}$  is homogeneous and isotropically identical to every other point which is of course the Perfect Cosmological Principle.

The maximal uncertainty in the position of the boundary also places each point $x_i$ at infinity, this contradiction is resolved by noting the statistical nature of Heisenberg's Uncertainty principle, it follows that any particles reflecting off the boundary do so with a statistical expectation and therefore the boundary has a probability of position - the boundary is simultaneously at infinity and every point within the potential.

This is a generalization of the Hartle-Hawking no boundary proposal, strictly speaking the uncertainty in the boundary has it everywhere as opposed to placing the boundary at infinity, accordingly I call this the generalized Hartle-Hawking no boundary proposal (gHH).

Hartle-Hawking proposal $X_i\to \infty$
generalized Hartle-Hawking proposal $X_i \to (0,\infty)$

This has three important ideas
1: A universe with zero total energy which is necessary for evolving a universe out of nothing,
2: each point in spacetime is in contact with every other point, which leads to the Perfect Cosmological Principle,
3: the Hartle-Hawking proposal of the universe where having no beginning which removes the problem of a primal cause for the universe.

In succeeding posts to this blog I'm intending to discuss other features of my paper The Revolution of Matter.


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# Tag Info

1

In the example circuit, R1 has virtually no effect on the speed of the flashing, since it is so much lower in value than R2. Therefore, if you replace R1 with the ALS, changing the light level will not change the speed of the flashing. And you can't put the ALS where R2 is, since the circuit relies on current flowing both ways through R2, but the ALS won't ...

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A nice guide for abbreviations used in electronics you can find here Includes some of the appendix A of ANSI/IEEE Std. 991-1986 which is the standard

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If you use level-triggered flip-flops (without a two-phase, non-overlapping clock) then all of the flip-flops will be transparent at the same time. The input to the first flip-flop will propagate all of the way to the output of the last flip-flop whenever the clock input is asserted. By the way, I think it is better to call a level-sensitive storage element ...

3

A linear circuit obeys the principles of proportionality and superposition. A linear circuit is an ideal approximation of a real-world physical circuit. All physical circuits have some non-linearity. Linear analysis is useful when the real-world non-linearity is small enough that you get answers that are close enough to your required accuracy. Ideal ...

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For very quick solutions (and under legal issues) I would suggest to use COTS hardware like programmable ISM Band wireless transceiver modules, which you can easily program using, e.g., C. eZ430-RF2500 AT86RF230 etc. You have just to wire the button and the LED to the boards, write a small program and that's it. All the interesting high frequency stuff ...

2

A lot depends on whether you are doing a commercial PCB to be manufactured and sold, or a few one-off boards for your own use. If the former, then a ground plan is more important to keep radiated emissions down to meet FCC (Part 15, unintentional radiators), CE and other regulations, although I've seen plenty of commercial products with one or two-sided ...

0

Short answer: No, you can't use a resistor to reduce the voltage seen by the switch in your circuit. It's the voltage difference across the component's terminals that matters, not the voltage at the component. In your circuit, when the switch is closed the voltage across it is (close to) zero: When the switch is opened, it will see the full voltage of ...

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Idealy you should always use a ground plane. But for different kind of reason it is not always possible or suitable: 1 and 2 layer(s) PCB: For 1 layer, I think the reason is quite obvious. You can fill the unrouted PCB with copper to GND but that's not a real ground plane. For two layers, you don't always have enough space for routing on one layer and a ...

1

First, you need to make sure that your assumptions are valid. For example, if your circuit is connected to two pieces of equipment powered by switch mode supplies, there will be a common-mode high frequency current flowing between those units. The current will flow through your device, generating "noise" voltages on the impedances of the traces in your ...

1

The first op amp sets up a reference at Vcc/2 for single supply operation. The resistors on the input limit current to the body and set up a body reference at or near the common mode voltage on the electrodes (using big noisy resistors). The instrumentation amp takes the differential signal, provides a gain of 5, and spits it out as a single-ended output, ...

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I=Vs/(R1+(R2∗Rl)/(R2+Rl)) is correct. VRL=I∗Rl is the wrong part. VRL=I*Req; Req=RL||R2=RLR2/(RL+R2);

0

You are right about open circuit, the wires are disconnected. In case of short circuit as well as closed circuit, the wires ARE connected but the difference is that in case of short circuit, the resistance between the connection is extremely low so very high current flows as per ohm's law, whereas in case of close circuit, the connection offers considerable ...

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Your equation for I is correct. The next step is Vo=I*(R2||RL)

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It looks like you're implementing a relatively straightforward ripple-carry adder. It looks like it would probably work, though the wiring is a bit of a rat's nest. An alternative approach also using five DIPs, but without such a rat's nest, would be to use four 74HC153 chips and a quad XOR. The 74HC153 chip contains two four-input multiplexers with ...

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If R$_L$ wasn't present the voltage output would just be: - $V_{S}\times\dfrac{R_2}{R_1 + R_2}$ So, adjust R2 mathematically to account for R$_L$ being in parallel with it. Can you take it from here?

1

You can probably use smaller resistor values, or none at all, with the LEDs. Most CMOS gates, operated at 5 V, will not be able to supply 20 mA anyway so there is little risk of damaging the LEDs. However, it is essential that you add a pulldown resistor on the right side of each switch (the side connected to the gates). Otherwise your gate inputs will be ...

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The admittance of this circuit can be written as : Y = $\dfrac{1}{sL} + \dfrac{1}{R + \dfrac{1}{sC}}\ = \dfrac{CLs^2 + CRs + 1}{Ls(CRs + 1)}$. Substituting $s = j\omega$, multiplying the denominator by its complex cojugated and simplifying into real and imaginary parts gives us: $\dfrac{R}{\frac{1}{C^2 \omega^2} + R^2} + ... 1 Multi-layer boards and huge ground planes are your enemies. Your friends are a powerful iron and this strategy: crush, melt, or otherwise break the connector so you can extract each pin individually (if all pins are on the perimeter, preferably snip them free of the plastic body) heat the pin, not the pad, just enough so it can be wiggled free with a ... 4 Usually, there is one pin that is making it hard to remove. That is usually the ground pin, and it will be attached to the ground plane. The ground plane will try to suck away the heat as fast as you can apply it. This is where you need a high wattage iron, so you can get it hot quickly. On a good day, you can remove the solder, then wiggle each pin ... 3 If you've already removed some of the solder, but find the pin is still stuck in the hole. What I've found helps is adding a little extra solder back onto the pin to make sure you get a nice reflow up through the hole and then I use a solder sucker instead of a braid. Also, you might check for any kind of glue under the part. Circuit parts that are ... 9 Add more solder. Use tin-lead solder or special low-temperature solder (ChipQuik). If you can make a solder blob over all five pins you can just lift the jack out. The solder is easy to clean up with braid afterwards. 2 Logic level converter: - This one works with two Vcc levels from 0.8V to 3.6V. 1 You can also use a bi-directional voltage-level translation device. Here are some from ti, analog and maxim. 2 The$s$-domain or frequency domain is not really what is special. It is the Laplace transform that is special. With appropriate assumptions, Laplace transform gives an equivalence between functions in the time domain and those in the frequency domain. Laplace transform is useful because it interchanges the operations of differentiation and ... 1 You could use a RC delay circuit. A simple one is made out of a resistor and a capacitor. For example, charge the capacitor, attached to ground, through a pull-up resistor R1. Then discharge through another resistor R2 and the "long-press" reset button to the ground. The trick is to calculate the values of C, R1 and R2 to make the timings right, so that ... 3 Your question makes little sense. You haven't even specified the type of transistor. For bipolar transistors, it is current, not charge (electrons or holes), that turn on the transistor. A small charge thru the base will allow a larger charge to flow thru the collector, but this is a one-time thing and wouldn't make the transistor be "on", whatever that ... 0 You can calculate the number of electrons required to turn on a discrete MOSFET from the gate charge datasheet numbers. It is not a small number. For example, looking at figure 10 of the 2N7002 datasheet we can see that 0.8nC is about enough. The charge of an electron is$1.6\times 10^{-19}$C, so it takes ~$4 \times 10^9electrons. If you're ... 0 Use a microcontroller that receives the button signal and drives the reset and on/off lines accordingly. Even the tiny PIC 10F200 can do this job easily. It comes in a SOT-23 6-pin package, with one input line and 3 I/O lines. You'll even have a extra I/O line left over. The first thing the micro needs to do is debounce the button. This creates a ... 1 Well, to consider your basic question: what is the minimum number of full adders required? You have initially twelve partial products (bits), while your result has six. Each fully utilized full adder will remove one partial product (bit) and therefore you need exactly12 - 6 = 6 full adders. Then, given that you do not use half adders, there may in practice ... 2 It could also be, more specifically, a norator. I've never used this symbol before, but I saw it in a paper that mentions a nullor equivalent circuit. _Dependent Current Source_ _Independent Current Source_ _____Norator_____ 2 A 60W incandescant light bulb requires 500 mA @ 120 V to light it up to full brightness. You can easily pass 10 mA through it — enough to operate a control module like Lightwave — without causing it to light up at all. This is why such modules are often specified to work only with incandescant (resistive) loads. CFLs and LED bulbs will often ... 0 There are a few misconceptions in your question, and it might help you understand things if we clear those up. For a) and b), replace "there is" with "there may be". The way you have defined an "open circuit" means that there is effectively an open circuit between any two points in a circuit that are not connected together by an ideal wire. When there is not ... 1 simulate this circuit – Schematic created using CircuitLab 0 I may be wrong since I did not study this in English, but I see a major difference between b) and c). From a very practical point of view, a closed circuit is good, a short circuit is very bad ! Short circuit is for instance connecting a wire directly between the poles of a battery or power supply. Whereas a closed circuit is just a "normal" load between ... 1 For (a,b,c) that's more or less correct. In general, there doesn't have to be a voltage/current just because there is a short/open, there just can't be any voltage in a perfect short and there can't be any current in a perfect open. Another way to re-word these two terms is that a short circuit has 0 resistance (R=0), and an open circuit has infinite ... 1 Yes. The component that does this is called a transformer. However, keep in mind that transformers are subject to the law of conservation of energy. This means that power in must equal power out. Electrical power is the product of current and voltage:  P = IV  If power in and power out are equal, then:  \begin{align} P_{in} &= P_{out} \\ I_{in} ... 1 The law of Energy Conservation say that energy must be conserved; the Law of Entropy says there will be some loss. So, if you want a 3333:1 gain in current, you need to see at least a 3333:1 loss in voltage. So, if the input is 10V, the output will be less than 3 mV. In general, passive conversion of current or voltage of an AC signal is done with a ... 1 The formula is derived by practical experiences and not from mathematical 1st principles. It is unprovable other than by being practical and thinking what a diode detector has to achieve. Firstly, the formula states that RC has to be equal to or greater than\dfrac{1}{\omega_c}\$. If the RC time constant were too short there would be significant levels ... 1 I have tried it too, it's due to Q4 connected to Q3, instead connect the emitter of Q3 to the base of Q4. Download the Falstad Java simulator and import this, it will make a simulated circuit showing how it works. (http://www.falstad.com/circuit/) Falstad Code:$ 1 5.0E-6 78.57719942274176 85 5.0 50 R 368 128 368 80 0 0 40.0 9.0 0.0 0.0 0.5 r 368 128 368 ...

0

Yes, R1, R2 & R3 are parallel to each other & hence, resultant resistance is 5 ohms. While finding equivalent resistance between any two points, imagine that you're travelling from one point to the other. Let's consider here that we're travelling from A to B. One end of R2 is short-circuited to A & other end is short-circuited to B. Same is the ...

4

simulate this circuit – Schematic created using CircuitLab Try redrawing the circuit with the 'A' connections in a bar at the top and the 'B' connections in a bar at the bottom (or use left/right). They've deliberately made it confusing. If you're redrawing, here's a set of guidelines that Olin wrote up: Rules and guidelines for drawing ...

0

Yes, you should consider that the initial current is V/2R, as inductors behave as short circuits in the steady state. However, without doing any calculations, there are many things that tell me your answer is incorrect: The dimension for your current is Voltage/Inductance, which is wrong, should be voltage/resistance. The dimension of your exponent is ...

0

Although the electron velocity is very low, which is propagated almost instantaneously is the electric field. This causes the effect that all the electrons in the wire to start moving simultaneously (almost).

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An analogy Imagine pressing 1 cm ball-bearings into a 10 m long horizontal pipe (1.1cm internal diameter) which is full of identical ball-bearings. You take 1s to slowly press one new bearing into your end of the pipe That 1 cm ball bearing travelled at 0.01 m/s As you press a new ball-bearing in at your end, another ball bearing gets pushed out the far ...

0

Maybe this analogy will help. Imagine you and a friend are holding two ends of a very long rope, and you're holding it tight, without any slack. If you pull on the rope, your friend will feel you pull almost instantly. The rope hardly has to move, and could move quite slowly. Similarly, an electron from a battery doesn't have to move very fast or far for ...

0

Imagine one electron drifting slowly from the negative pole of your battery into the wire. At nearly the same moment, an electron from the beginning of the wire drifts to a bit further on in the wire, replacing an electron that is (at nearly the same moment) drifting yet further ..... and at the end of the chain an electron from the end of the wire drifts ...

2

IF the system is linear, then you are right, it can be characterized solely from its impulse response. It can be thought of as convolving the input by the impulse response. Often the impulse response is difficult to meaure. One way around this is to measure the step response, which is usually easier, then differentiate that. That may have a lot of noise, ...

1

As @Andy aka said, cost is a big issue. There's no reason to use a part that is more expensive or takes up more space than a better alternative. One other thing to consider is EMC. Remember capacitors store energy in the form of electric fields and inductors store energy in the form of magnetic fields. Therefore, if you have a circuit that emits a great ...

2

If you want to block dc but let frequencies above 20 Hz through largely unaffected (as in a simple audio amplifier), the time constant of your circuit will need to be about 0.01. Additionally, if you want an input impedance of at least 1 kohm (ball-park for audio) you will find that the inductive or capacitive Reactance at 20 Hz needs to be also 1 kohm: - ...

0

For an electronic switch you can use the circuit below : simulate this circuit – Schematic created using CircuitLab R5/R6 create a voltage divider that keeps M2 gate at about 9.5-10v (if the 24v can be much lower you can use a zener instead of the divider). R4 is a pull down resistor keeping the source grounded when there is no 12v supply, ...

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# Math Help - Mathematical Modelling through ODE

1. ## Mathematical Modelling through ODE

Please help to solve the following :

"Cigarette consumption in a country increased from 50 per capita in 1900 AD to 3600 per capita in 1960 AD. Assuming that the growth in consumption follows a logistic law with a limiting consumption of 4000 per capita, estimate the consumption per capita in 1950."

Thanks in advance.

2. If $\displaystyle P = P(t)$ is the population who smoke at any year with a carrying capacity (limiting population) of $\displaystyle K$, then the logistic model is

$\displaystyle \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right)$

a separable DE.

Solve the DE, then use the two points you have been given to solve for $\displaystyle r$ and your integration constant.


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# Tag Info

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We don't.${}{}{}{}{}{}{}{}{}{}$

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We don't ever know, in the information theory sense, that a crypto algorithm wont fail suddenly. If we ever knew that, we'd quit using it. However, it has been shown that crypto algorithm failing has a strong tendency to fail according to a two step process: Most crypto algorithms fail quickly in the initial analysis phase, as we apply a pile of known ...

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CBC does not perform authentication This property makes it less suitable for places where authentication is required, basically any transport protocol. TLS uses CBC, but by default performs authentication over the plain text instead of the ciphertext, which opened up a host of attacks. CBC can be used here, but it is error prone and may require an ...

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yyyyyyy's answer is the correct short version. There is only a single cryptographic algorithm that is mathematically proven secure: the one-time pad. It's hardly ever used because it's impractical: the key size is as large as the data to protect. You can prove that any algorithm that is secure against an adversary with infinite computational power is ...

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I restrict to hash functions $H$ with an output of some fixed size $n\ge1$ bit(s), accepting as input some strings, including all $n$-bit strings; MD5 (resp. SHA-1, SHA-256) is an example of such function for $n=128$ (resp. $n=160$, $n=256$). Whether there exists a solution to $H(x)=x$ depends on the particular hash function. If $H$ is a random function (as ...

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The simple answer is nobody can prove that an algorithm won't break in a given period of time. The achievable goal is to increase the probability that no effective attack will be developed without warning. There are a couple of characteristics that indicate a particular cipher may remain secure and if degraded will do so 'gracefully'. 1. Time. Time is the ...

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Contrary to your assumption, this is done, and it is secure: For instance, the hash functions SHA-224 and SHA-384 are basically the same algorithms as SHA-256 and SHA-512! The only differences are in the initial values for the Merkle-Damgård construction used internally and, of course, in that only the first $224$ or $384$ bits of the resulting hash are ...

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What choice did they have? F1 is a bitwise function with three inputs and one output. There are $2^8 = 256$ such functions. Only 70 of them are "unbiased" (i.e. have as many 0 and 1 outputs in their image). If you further require that each input, as well as the order of inputs, matters for the output, you are left with only 36. However, those 36 are all ...

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There are several scenarios where you wouldn’t want to use AES in CBC mode. In CBC mode, each block is dependent on a previous one. As @fgrieu nicely hinted at in his comment, using CBC means that if you have a large, encrypted file and you only want to update/change/modify a tiny fraction of it, you would have to follow the decrypt-modify-encrypt path each ...

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XSalsa20 uses the same cryptographic core as Salsa20 and comes with a security proof that it's secure if Salsa20 is secure. It doesn't use the core of ChaCha and thus has worse diffusion. The way XSalsa20 works is that it hashes its 256 bit key and the first 128 bits of the nonce using HSalsa down to a 256 bit key and then uses that key together with the ...

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"In software" means programming the cipher on a multifunctional processor or smart chip. The normal instruction set is used to build the algorithm, and not available operations have to be emulated. "In hardware" means building the cipher in real hardware, like on a Field-programmable gate array (FPGA) or Application-specific integrated circuit (ASIC). ...

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GF$(2^8)$ or $\mathbb F_{2^8}$ can also be viewed as the vector space $\mathbb F_2^8$ of $8$-bit vectors (or bytes) over GF$(2)$ or $\mathbb F_2$. Suppose $\{\beta_0, \beta_1, \cdots, \beta_7\}$ is a basis of $\mathbb F_2^8$ over $\mathbb F_2$, that is, the sum $$a_0\beta_0 \oplus a_1\beta_1 \oplus \cdots \oplus a_7\beta_7, ~ a_i \in \mathbb F_2$$ equals ...

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Your doubts are absolutely valid. Disguising the algorithm is not a valid argument for security. It also contradicts to Kerckhoffs Law. It (the algorithm) should not require secrecy, and it should not be a problem if it falls into enemy hands; Designing cryptographic algorithms (ciphers, hashfunctions, ...) is a long and complicated process. In ...

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First, it's not said that AES is unbreakable, merely that none of the currently known attacks reduce the computational cost to a point where it's feasible. The current best attack on AES-128 takes 2^126.1 operations, if we had a computer (or cluster) several million times more efficient than any current computer and could operate at the thermodynamic ...

5

The pseudocode has a serious issue: changing the value of nonce2 in an otherwise valid cryptogram is not detected, and results in invalid deciphered plaintext. That would be fixed by encrypt(password, string): nonce1 := generate_random_nonce() nonce2 := generate_random_nonce() key := derive_key(nonce1, password) encrypted := nonce2 || cipher(nonce2, ...

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There are attacks on both blockciphers and hash functions that can exploit symmetry in the round functions. For example, completely identical round functions can permit Slide Attacks on Hash Functions, and rotational symmetries of the round function can permit rotational cryptanalysis. The round constant addition or 'iota' step of the Keccak Hash Function ...

5

Most standard-use iterative hash functions (including SHA-512) are build in a way that these types of operation are not possible (without breaking the hash function). They work generally in this way: The message is split in same-size blocks (usually with some padding at the end to fill the last block): $pad(M) = M_0 || M_1 || M_2 ... || M_n$. There is ...

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The sum of PRPs is a secure PRF. That paper gives as a security bound for a sum of two independent PRPs $q^3/2^{2n-1}$, where $q$ is the number of queries and $n$ the block size (i.e. 128 for AES). That means that your construction, correctly used, is more secure than a single PRP, for which the bound is $q^2/2^n$. If you wanted to give an adversary an ...

4

No, this is safe. In fact, if you show a way of distinguish the stream $AES_{k_1}(C) \oplus AES_{k_2}(C)$ from a random stream with fewer than $2^{64}$ outputs, you have just demonstrated a way of distinguishing AES from a random permutation. Here is how this works: suppose we are given Oracle assess to a permutation $P$, which might be $AES_{k_1}$ for ...

4

Since you encrypt just a single letter, there are $26^2$ combinations of $p$ and $c$ where $c=E(p)$. This is because there are $26$ possible shift keys in the key space, an therefore each $p$ can be mapped to one of $26$ letters in the code space. Now, assuming that the key is distributed uniformly in the key space, each of those combinations of $(p,c)$ has ...

4

Yes, it would be more secure if they were used correctly. But as it would require a substantially different algorithm, you really would not be talking about DES anymore. Brute forcing usually scales exponentially with the size of the key. However, if the algorithm is substantially altered then it is required to analyze the algorithm again. Note that AES is ...

4

Where did SHAKE128 and SHAKE256 originate from? They follow from the general properties of the sponge construction. A sponge function can generate an arbitrary length of output. The submission of Keccak to the SHA-3 competition proposed a single "XOF" (extendable-output function) with a user defined length, which would have been essentially SHAKE-288. ...

4

Compared to fixed rotations, data-dependent rotations improve resistance to differential and linear cryptanalysis. A fixed rotation has no effect (beyond helping with diffusion) in the probability of a (xor-)differential characteristic, whereas a data-dependent rotation also introduces differences in the rotation amounts, which brings probabilities down. ...

4

You are essentially asserting that if $k \equiv 1 \pmod N$, then $a^k \equiv a \pmod N$. This is false in general. The correct assertion is the following: $a^k \equiv a^\ell \pmod N$ if $k\equiv \ell \pmod{\phi(N)}$. In more general group-theoretic terms, if $a$ is an element of order $n$ in a group $G$, then $a^k = a^\ell$ if and only if $k \equiv \ell ... 4 Does the value of the key array(T) have to be in this range [0-255] if yes could you please specify why? Yes. RC4 operates on bytes. There are 256 possible values for an 8 bit (1 byte) number, that range from 0 to 255. RC4 treats the key as an array of bytes, so every entry in the key array is by definition in the range 0 to 255. Why did they use ... 3 The key you wrote down contains a mixed alphabetic and digit symbols because it is written in its hexadecimal representation: i.e. using symbols from 0 to 9 and from A to F. More on this topic on Wikipedia page. You can easily convert hexadecimal to decimal using software as python, sage, Pari/GP and many others. An online converter could be found here: ... 3 The correction question you should ask about why various operations in RC4 (or, for that matter, any other cipher) are there would be "if I were to remove that, what would the impact be? Would this weaken the cipher in some way?" At your current state of knowledge, that may be a rather imponderable question, but it is still the correct one. I can try to ... 3 Here's an approach that corrects some errors: Alice has a bitstring S that is indistinguishable from random that she wants Trent to know. (Perhaps it's actually a ciphertext that only Bob knows how to decrypt). Alice generates 5 fresh new random bit-strings pM, pN, pP, pQ, and pR just as long as the original random bitstring S. For each bit of S, Alice ... 3 It depends on what you think of as an alternative. If you think of the scheme where you do not use$M$as a modulus, but the keys a picked as: $$k \leftarrow \{1, \ldots, M-1\}$$ Encryption: $$C = d + k$$ Decryption: $$d = C - k$$ Then the scheme is insecure. One way to see this is to note that we have$C \geq d\$. So the ciphertext communicates the ...

3

A Vigenère cypher can be unbreakable if, and only if: the key is random, the key is at least as long as the message being encrypted the key is used only once. In that case a Vigenère cypher is mathematically equivalent to a One Time Pad, and the same mathematical proof of unbreakability applies. You proposal is closer to being unbreakable than standard ...

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