Month: August 2019

Program Theory

We begin with a very simple model of computation. A computer has a memory, and we can
observe its contents, or state. Our input to a computation is to provide an initial state, or prestate.
After a time, the output from the computation is the final state, or poststate. Although the memory
contents may physically be a string of bits, we can consider it to be a string of any items; we only
need to group the bits and view them through a code. A state σ (sigma) may, for example, be
given by
σ = –2; 15; “A”; 3.14
The indexes of the items in a state are usually called “addresses”. The bunch of possible states is
called the state space. For example, the state space might be
int; (0,..20); char; rat
If the memory is in state σ , then the items in memory are σ0 , σ1 , σ2 , and so on. Instead of
using addresses, we find it much more convenient to refer to items in memory by distinct names
such as i , n , c , and x . Names that are used to refer to items in the state are called state variables.
We must always say what the state variables are and what their domains are, but we do not bother to
say which address a state variable corresponds to. Formally, there is a function address to say
where each state variable is. For example,
x = σaddress “x”
A state is then an assignment of values to state variables.
Our example state space in the previous paragraph is infinite, and this is unrealistic; any physical
memory is finite. We allow this deviation from reality as a simplification; the theory of integers is
simpler than the theory of integers modulo 232 , and the theory of rational numbers is much
simpler than the theory of 32-bit floating-point numbers. In the design of any theory we must
decide which aspects of the world to consider and which to leave to other theories. We are free to
develop and use more complicated theories when necessary, but we will have difficulties enough
without considering the finite limitations of a physical memory.

Classical and Art Music

Popular music is, by denition, music that appeals to many people. You don’t have to know anything
about music to like a pop tune – it’s “catchy”. Art music is a catch-all term for any music that
is enjoyed by a smaller crowd. This can include the more challenging types of jazz and rock music,
as well as Classical. Most people agree that the appreciation of art music requires some study,
careful listening, or other extra eort. But it can be harder to agree on what exactly belongs in this
category. This is at least partly because popular tastes do change. For example, most operas were
written to be popular, middle-class entertainments, and artists such as Liszt and Paganini enjoyed
rock-star-like fame and popularity in their day. Today, however, nineteenth century operas are no
longer considered popular entertainment, and popular works that could technically be considered
opera – except for the fact that they are written in popular musical styles – are instead grouped with
musicals. As another example, ragtime50 was wildly popular during Scott Joplin’s51 lifetime. It
later fell out of favor and was known only to some jazz connoisseurs. Then in the 1970’s it became
popular again.
Classical music is a confusing term with more than one meaning. In the visual arts, the
term classical refers to ancient Greece and Rome. In the 1700’s, Western Europeans became very
interested in the ancient classical style, which was imitated by many artists, sculptors, and architects.
Art historians call that period the neoclassical (“new classical”). Unfortunately, nobody really
knows what the music of ancient times sounded like. So instead of being inuenced by the sound
of ancient Greek music, eighteenth-century composers were inuenced by the ideals of classical art.
The music of Mozart, Haydn, and the early works of Beethoven are in this style, which we call
classical rather than neoclassical, because the original classical music of ancient Greece and Rome
is lost. (And actually, it probably would sound very exotic and Non-Western to us if we could listen
to it!)

What is Meter?

The meter of a piece of music is the arrangment of its rhythms in a repetitive pattern of strong and
weak beats. This does not necessarily mean that the rhythms themselves are repetitive, but they
do strongly suggest a repeated pattern of pulses. It is on these pulses, the beat of
the music, that you tap your foot, clap your hands, dance, etc.
Some music does not have a meter. Ancient music, such as Gregorian chants; new music, such
as some experimental twentieth-century art music; and Non-Western music, such as some native
American ute music, may not have a strong, repetitive pattern of beats. Other types of music,
such as traditional Western African drumming, may have very complex meters that can be dificult
for the beginner to identify.
But most Western music has simple, repetitive patterns of beats. This makes meter
a very useful way to organize the music. Common notation, for example, divides
the written music into small groups of beats called measures, or bars. The lines
dividing each measure from the next help the musician reading the music to keep track of the rhythms.

A piece is assigned a time signature that tells
the performer how many beats to expect in each measure, and what type of note should get one beat. (For more on reading time signatures, please see Time Signature.)
Conducting25 also depends on the meter of the piece; conductors use dierent conducting patterns
for the dierent meters. These patterns emphasize the dierences between the stronger and weaker
beats to help the performers keep track of where they are in the music.
But the conducting patterns depend only on the pattern of strong and weak beats. In other
words, they only depend on “how many beats there are in a measure”, not “what type of note gets a
beat”. So even though the time signature is often called the “meter” of a piece, one can talk about
meter without worrying about the time signature or even being able to read music.

Marine insurance

Marine insurance covers the loss or damage of ships, cargo, terminals, and any transport by which the property is transferred, acquired, or held between the points of origin and the final destination.

What are the types of marine insurance?

Marine insurance protects from business losses incurred during water transport operations. While policies vary, there are four standard types: hull, cargo, freight revenue, and negligence.

What is covered under ocean marine insurance?

To protect your goods while they are at seaand in transit, you need Ocean Marine Insurance. This is a specialty insurance that covers legal liability for negligence, damages, and loss of revenue to cargo and ships, and anything else to do with marine transport.

How is marine insurance calculated?

Cargo insurance is calculated on a rate of X per $100. For example if you have a shipment valued at $15,000 USD and the rate is .25 per $100, you take $15,000 / $100 = 150 X .25 = $37.50 in total premium due.

What are the advantages of marine insurance?

As such, marine insurance provides a comprehensive coverage and compensates businesses against any possible loss suffered in the transit of goods. Marine insurance thus, helps in maintaining the financial stability of companies and reduces their risk. These are the advantages of a marine insurance policy.

How much does marine insurance cost?

The general rule of thumb when it comes to calculating average boat insurance prices is that you’ll pay about 1.5% of the value of yourboat in annual rates. To insure a boat worth around $20,000, it would cost you only about $300 per year to have it fully insured.

Why do we need marine insurance?

It is particularly important for removals firms to ensure they are covered by adequate marine insurance when shipping their customers goods so that they can provide reassurance to their customers in the event of any accidents or damage.

Pet Insurance

Pet insurance pays, partly or in total, for veterinary treatment of the insured person’s ill or injured pet. Some policies will pay out when the pet dies, or if the pet is lost or stolen.

Is it worth it to have pet insurance?

In our exercise, a Healthy Paws plan was the only one that paid more than it cost. But if his owner continues to cover cancer treatments, all three plans may be worth it. Last year routine vet care cost cat owners just $196 and dog owners only $235, according to the American Pet Products Association.

How does the pet insurance work?

Pet insurance is a way to save on veterinary costs when your pet gets sick or is injured. Most pet health insurance plans are paid on a monthly schedule and cost a few hundred dollars a year. After you pay the vet, you can file a claim with your insurer to be reimbursed.

Why do you need pet insurance?

Pet insuranceis a safety net to help protect you against unexpected costs related to your pet. The most obvious reason to have insurance on your cat or dog is to cover veterinary bills. However, it can seem like an unnecessary expense.

What does pet insurance actually cover?

What does Pet Insurance cover? Pet Insurance covers essential medical costs in an emergency. Depending on the plan you choose, it can also help pay for treatment when your pet is ill, plus routine pet healthcare like teeth cleaning and worming.

Does Pet Insurance pay the vet directly?

Pet cover can help with vet bills. … By using direct-to-vet payments a pet owner only pays the excess out of pocket, which is certainly preferably for any large vet bills. Find out which pet insurance companies will pay direct and learn about vets’ willingness to accept direct payments.

House Insurance

There is no such place like home in the entire Universe. After all, it is a place where you and your loved ones can rejoice, weave thousands of memories that last for a lifetime. While we put our life’s savings into buying or constructing a home but we rarely realize that our home needs a protection in the form of insurance too. By investing in a good home insurance policy, also referred as home owners insurance, you can protect your home from threats. Situations like burglary, fire, earthquake or destruction of house due to riots are quite common in India.

Coverage under My Home Insurance Policy

Loss or damage to building: We will indemnify you in respect of the accidental loss or damage to building based on the plan selected by you.

Sum insured options for Flat/Apartment

Reinstatement Value Basis

Indemnity Basis

Emergency expense cover: Expenses incurred towards emergency purchase of food, clothing, medicines and similar daily essentials up to Rs. 20,000 will be covered in case a claim is admissible under the Building section of the policy

Loss of or damage to curios, works of art and paintings whilst stored or lying in your Building : We will indemnify you in respect of the accidental loss or damage to curios, works of art and paintings” whilst stored or lying in your building.

Home owner can enjoy peace of mind by giving their residence and its belongings the protection it deserves. HDFC ERGO Home Insurance provides a host of benefits, and you get a cover that secures your home for upto 5 years.

You need not break into a sweat when your house gets broken into. Secure your home from losses due to theft, larceny and burglary.

Don’t let the forces of nature wreak havoc on your dream home. Protect it from flood, storm, earthquake, and more.

Motor Insurance

Car insurance is essential if you own a car. It can be difficult to choose a car insurer. But if you buy a policy from Bharti AXA you can seek assistance over a call by calling at their toll-free car insurance customer care number. For smooth purchase and claim, it is important that the insurance company that you choose offers you seamless customer service and smooth payment services.

Bharti Axa Car Insurance offers its customers cashless repair services in more than 3000 garages network workshops across India. Their customer service team is also available on call to offer your assistance at the time of need. Looking at the insurer’s claim settlement ratio of 98.27% it is likely that you claim will be settled timely.

Talking about post-sale services offered by TATA AIG, the insurer is quite particular on this part and try to ensure prompt and satisfactory service. The most sought-after online services one could ask for include- buying the policy, renewing the policy, register a claim or a complaint; ask for the premium calculation etc. But are you aware of the fact that you can even initiate Tata AIG Policy download online? If not, then let us tell you that downloading your policy document is easy.

Hope such an incident doesn’t happen with anyone. If your current car insurance policy was a comprehensive one, then you will get reimbursement for the theft, based on the Insured Declared Value of your car. And you would need to buy a new car insurance policy for your new car. Once you receive the claim amount you can cancel your current car insurance policy.

Surely, car theft is a nightmare for anyone, especially if you haven’t bought a car insurance policy. Having an adequate car insurance policy would ease your financial burden that comes along with car theft.  

Black Holes

According to Newton’s theory of gravity, the escape velocity v from a distance r from the center of gravity of a heavy object with mass m, is described by

1 2v2 = Gm r

. (1.1)

What happens if a body with a large mass m is compressed so much that the escape velocity from its surface would exceed that of light, or, v > c? Are there bodies with a mass m and radius R such that 2Gm Rc2 ≥1 ? (1.2) This question was asked as early as 1783 by John Mitchell. The situation was investigated further by Pierre Simon de Laplace in 1796. Do rays of light fall back towards the surface of such an object? One would expect that even light cannot escape to infinity. Later, it was suspected that, due to the wave nature of light, it might be able to escape anyway. Now, we know that such simple considerations are misleading. To understand what happens with such extremely heavy objects, one has to consider Einstein’s theory of relativity, both Special Relativity and General Relativity, the theory that describes the gravitational field when velocities are generated comparable to that of light. Soon after Albert Einstein formulated this beautiful theory, it was realized that his equations have solutions in closed form. One naturally first tries to find solutions with maximal symmetry, being the radially symmetric case. Much later, also more general solutions, having less symmetry, were discovered. These solutions, however, showed some features that, at first, were difficult to comprehend. There appeared to be singularities that could not possibly be accepted as physical realities, until it was realized that at least some of these singularities were due only to appearances. Upon closer examination, it was discovered what their true physical nature is. It turned out that, at least in principle, a space traveller could go all the way in such a “thing” but never return. Indeed, also light would not emerge out of the central region of these solutions. It was John Archibald Wheeler who dubbed these strange objects “black holes”. Einstein was not pleased. Like many at first, he believed that these peculiar features were due to bad, or at least incomplete, physical understanding. Surely, he thought, those crazy black holes would go away. Today, however, his equations are much better understood. We not only accept the existence of black holes, we also understand how they can actually form under various circumstances.

Time Dialation

In classical Newtonian physics, the concepts of space and time are absolute. Space is composed of three orthogonal dimensions, and time is represented as a fourth dimension, perpendicular to each of the spatial axes. Both space and time are free to be discussed independent of the other. Einstein demonstrated that space and time are, in reality, dependent and inseparable by assuming the velocity of light is constant. He accomplished this through a thought experiment, where an illumination source at the center of a moving boxcar emits a pulse of light towards the front and towards the rear of the boxcar. Observers on the train see the two pulses of light hit the front and the rear walls of the box her one hits the front. This indeed demonstrated that time, i.e. the simultaneity of two events, had to be placed in the context of space, i.e. the reference frame of the observer. In kinetic physics, we can use a Cartesian frame (x, t) to describe the motion of a particle moving along one dimension, where the horizontal axis designates position and the vertical axis designates time. To describe the motion of that particle in the other two spatial dimensions, thus completely representing the particle’s motion in time, an additional two sets of Cartesian frames (y, t) and (z, t) must be constructed. Because the three frames cannot be tied together physically, i.e. 4 mutually orthogonal axes (three spatial and 1 time) cannot be represented as a single entity, they must be bound together with an external constraint. In order to derive the Lorentz transformation between the coordinates xyzt of a system S and the coordinates x′y′z′t′ of another system S’ which is moving with velocity v relative to S, we need add the constrain x2 + y2 + z2 = c2t2 in S and the constrain x′2 + y′2 + z′2 = c2t′2 in S’ for describing the wave-front of the light emitted from the common origin which two systems coincide at t = t′ = 0. In order to eliminate the need for a constraint, a three-dimensional space-time (3-D S-T) frame can be constructed in similar fashion to a polar coordinate frame. In a polar coordinate frame, the coordinates consist of a pole length r and the angle φ between the pole and the polar axis. Both the radial coordinate r and the polar axis are in terms of length. In a 3-D S-T frame, time is represented by distances, thus embedding it into space. This is accomplished by taking the units of time and multiplying them by the speed of an appropriat

Schrodinger wave equation

6.1 Derivation of the Schr¨odinger Wave Equation

6.1.1 The Time Dependent Schr¨odinger Wave Equation

In the discussion of the particle in an infinite potential well, it was observed that the wave function of a particle of fixed energy E could most naturally be written as a linear combination of wave functions of the form

Ψ(x,t) = Aei(kx−ωt) (6.1)

representing a wave travelling in the positive x direction, and a corresponding wave travelling in the opposite direction, so giving rise to a standing wave, this being necessary in order to satisfy the boundary conditions. This corresponds intuitively to our classical notion of a particle bouncing back and forth between the walls of the potential well, which suggests that we adopt the wave function above as being the appropriate wave function

Chapter 6 The Schr¨odinger Wave Equation 43

for a free particle of momentum p = !k and energy E = !ω. With this in mind, we can then note that ∂2Ψ ∂x2 =−k2Ψ (6.2) which can be written, using E = p2/2m = !2k2/2m:

!2 2m

∂2Ψ ∂x2

= p2 2m

Ψ. (6.3)


∂Ψ ∂t

=−iωΨ (6.4)

which can be written, using E = !ω: i!∂Ψ ∂t

= !ωψ = EΨ. (6.5)

We now generalize this to the situation in which there is both a kinetic energy and a potential energy present, then E = p2/2m+V(x) so that EΨ = p2 2m Ψ+V(x)Ψ (6.6) where Ψ is now the wave function of a particle moving in the presence of a potential V(x). But if we assume that the results Eq. (6.3) and Eq. (6.5) still apply in this case then we have − !2 2m ∂2ψ ∂x2 +V(x)Ψ = i!∂ψ ∂t (6.7) which is the famous time dependent Schr¨odinger wave equation.

Curiously enough, to answer this question requires ‘extracting’ the time dependence from the time dependent Schr¨odinger equation. To see how this is done, and its consequences, we will turn our attention to the closely related time independent version of this equation.