In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.
In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest rate ≈ nominal interest rate − inflation rate. In more formal terms, where equals the real interest rate, equals the nominal interest rate, and equals the inflation rate, the Fisher equation is . It can also be expressed as or .
The Taylor rule is a monetary policy targeting rule. The rule was proposed in 1992 by American economist John B. Taylor for central banks to use to stabilize economic activity by appropriately setting short-term interest rates.
In economics, nominal value refers to value measured in terms of absolute money amounts, whereas real value is considered and measured against the actual goods or services for which it can be exchanged at a given time. For example, if one is offered a salary of $40,000, in that year, the real and nominal values are both $40,000. The following year, any inflation means that although the nominal value remains $40,000, because prices have risen, the salary will buy fewer goods and services, and thus its real value has decreased in accordance with inflation. On the other hand, ownership of an asset that holds its value, such as a diamond may increase in nominal price increase from year to year, but its real value, i.e. its value in relation to other goods and services for which it can be exchanged, or its purchasing power, is consistent over time, because inflation has affected both its nominal value and other goods' nominal value. In spite of changes in the price, it can be sold and an equivalent amount of emeralds can be purchased, because the emerald's prices will have increased with inflation as well.
A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos.
In economics, the Fisher effect is the tendency for nominal interest rates to change to follow the inflation rate. It is named after the economist Irving Fisher, who first observed and explained this relationship. Fisher proposed that the real interest rate is independent of monetary measures, therefore, the nominal interest rate will adjust to accommodate any changes in expected inflation.
In orbital mechanics, mean motion is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. The concept applies equally well to a small body revolving about a large, massive primary body or to two relatively same-sized bodies revolving about a common center of mass. While nominally a mean, and theoretically so in the case of two-body motion, in practice the mean motion is not typically an average over time for the orbits of real bodies, which only approximate the two-body assumption. It is rather the instantaneous value which satisfies the above conditions as calculated from the current gravitational and geometric circumstances of the body's constantly-changing, perturbed orbit.
In probability theory and directional statistics, the von Mises distribution is a continuous probability distribution on the circle. It is a close approximation to the wrapped normal distribution, which is the circular analogue of the normal distribution. A freely diffusing angle on a circle is a wrapped normally distributed random variable with an unwrapped variance that grows linearly in time. On the other hand, the von Mises distribution is the stationary distribution of a drift and diffusion process on the circle in a harmonic potential, i.e. with a preferred orientation. The von Mises distribution is the maximum entropy distribution for circular data when the real and imaginary parts of the first circular moment are specified. The von Mises distribution is a special case of the von Mises–Fisher distribution on the N-dimensional sphere.
The Mundell–Fleming model, also known as the IS-LM-BoP model, is an economic model first set forth (independently) by Robert Mundell and Marcus Fleming. The model is an extension of the IS–LM model. Whereas the traditional IS-LM model deals with economy under autarky, the Mundell–Fleming model describes a small open economy.
Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors interest rates available on bank deposits in two countries. The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from covered interest arbitrage. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic and foreign assets. Given foreign exchange market equilibrium, the interest rate parity condition implies that the expected return on domestic assets will equal the exchange rate-adjusted expected return on foreign currency assets. Investors then cannot earn arbitrage profits by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, due to gains or losses from exchanging back to their domestic currency at maturity. Interest rate parity takes on two distinctive forms: uncovered interest rate parity refers to the parity condition in which exposure to foreign exchange risk is uninhibited, whereas covered interest rate parity refers to the condition in which a forward contract has been used to cover exchange rate risk. Each form of the parity condition demonstrates a unique relationship with implications for the forecasting of future exchange rates: the forward exchange rate and the future spot exchange rate.
The real interest rate is the rate of interest an investor, saver or lender receives after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate.
Return rate is a corporate finance and accounting tool which calculates the gain and loss of investment over a certain period of time.
In monetary economics, the equation of exchange is the relation:
Ripple in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.
A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses. In particular, they are used during the calculation of likelihood of a tree and they are used to estimate the evolutionary distance between sequences from the observed differences between the sequences.
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–41 and 1846. The theoretical justification of the Poiseuille law was given by George Stokes in 1845.
Relative Purchasing Power Parity is an economic theory which predicts a relationship between the inflation rates of two countries over a specified period and the movement in the exchange rate between their two currencies over the same period. It is a dynamic version of the absolute purchasing power parity theory.
A Calvo contract is the name given in macroeconomics to the pricing model that when a firm sets a nominal price there is a constant probability that a firm might be able to reset its price which is independent of the time since the price was last reset. The model was first put forward by Guillermo Calvo in his 1983 article "Staggered Prices in a Utility-Maximizing Framework". The original article was written in a continuous time mathematical framework, but nowadays is mostly used in its discrete time version. The Calvo model is the most common way to model nominal rigidity in new Keynesian DSGE macroeconomic models.
