Moment (mathematics)

In mathematics, a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points. If the points represent mass, then the zeroth moment is the total mass, the first moment divided by the total mass is the center of mass, and the second moment is the rotational inertia. If the points represent probability density, then the zeroth moment is the total probability (i.e. one), the first moment is the mean, the second central moment is the variance, the third moment is the skewness, and the fourth moment (with normalization and shift) is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.

For a bounded distribution of mass or probability, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution.

Significance of the moments

The n-th moment of a real-valued continuous function f(x) of a real variable about a value c is

It is possible to define moments for random variables in a more general fashion than moments for real values—see moments in metric spaces. The moment of a function, without further explanation, usually refers to the above expression with c = 0.

Moment (film)

Moment (Serbian: Трен, translit. Tren) is a 1978 Yugoslav war film directed by Stole Janković. It was entered into the 11th Moscow International Film Festival where Bata Živojinović won the award for Best Actor.

Cast

References

External links

Moment (physics)

In physics, moment is a combination of a physical quantity and a distance. Moments are usually defined with respect to a fixed reference point or axis; they deal with physical quantities as measured at some distance from that reference point or axis. For example, a moment of force is the product of a force and its distance from an axis, which causes rotation about that axis. In principle, any physical quantity can be combined with a distance to produce a moment; commonly used quantities include forces, masses, and electric charge distributions.

Elaboration

In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, multiplied by some physical quantity such as the force, charge, etc. at that point:

where is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity is not concentrated solely at a single point, the moment is the integral of that quantity's density over space:

Greeks (finance)

In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities,risk measures or hedge parameters.

Use of the Greeks

The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.

The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.

Lotna

Lotna is a Polish war film released in 1959 and directed by Andrzej Wajda.

Overview

This highly symbolic movie is both the director's tribute to the long and glorious history of the Polish cavalry, as well as a more ambiguous portrait of the passing of an era. Wajda was the son of a Polish Cavalry officer who was murdered by the Soviets during the Katyn massacre.

The horse Lotna represents the entire Romantic tradition in culture, a tradition that had a huge influence in the course of Polish history and the formation of Polish literature. Lotna is Wajda's meditation on the historical breaking point that was 1939, as well as a reflection on the ending of an entire era for literature and culture in Poland and in Europe as a whole. Writing of the film, Wajda states that it "held great hopes for him, perhaps more than any other." Sadly, Wajda came to think of Lotna "a failure as a film."

The film remains highly controversial, as Wajda includes a mythical scene in which Polish horsemen suicidally charge a unit of German tanks, an event that never actually happened.

Speed (Montgomery Gentry song)

"Speed" is a song written by Jeffrey Steele and Chris Wallin, and recorded by American country music duo Montgomery Gentry. It was released in December 2002 as the second single from their album My Town. The title from the cover of this single borrows its font from Speed Racer.

"She Couldn't Change Me" was included as a B-side.

Music video

The music video was directed by Trey Fanjoy. A young man trades his old truck for a car with speed as his truck just brings back memories of his ex-lover. He buys the car, then he drives the car really fast, but as he keeps seeing the memory of his ex-lover on the road, he jumps out of the car, and then he heads out running into the field. The duo is performing the song in the middle of a two-lane road at a night time setting.

Chart positions

"Speed" debuted at #57 on the U.S. Billboard Hot Country Songs for the week of December 28, 2002.

Year-end charts

References

External links