Order of integration

Order of integration, denoted I(d), is a summary statistic for a time series. It reports the minimum number of differences required to obtain a covariance stationary series.

Integration of order zero

A time series is integrated of order 0 if it admits a moving average representation with

where is the possibly infinite vector of moving average weights (coefficients or parameters). This implies that the autocovariance is decaying to 0 sufficiently quickly. This is a necessary, but not sufficient condition for a stationary process. Therefore, all stationary processes are I(0), but not all I(0) processes are stationary.

Integration of order d

A time series is integrated of order d if

is integrated of order 0, where is the lag operator and is the first difference, i.e.

In other words, a process is integrated to order d if taking repeated differences d times yields a stationary process.

Constructing an integrated series

An I(d) process can be constructed by summing an I(d − 1) process:

I1

I1, i1, or I-1 may refer to :

Dam

A dam is a barrier that impounds water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for such activities as irrigation, human consumption, industrial use, aquaculture, and navigability. Hydropower is often used in conjunction with dams to generate electricity. A dam can also be used to collect water or for storage of water which can be evenly distributed between locations. Dams generally serve the primary purpose of retaining water, while other structures such as floodgates or levees (also known as dikes) are used to manage or prevent water flow into specific land regions.

The word dam can be traced back to Middle English, and before that, from Middle Dutch, as seen in the names of many old cities.

History

Ancient dams

Early dam building took place in Mesopotamia and the Middle East. Dams were used to control the water level, for Mesopotamia's weather affected the Tigris and Euphrates rivers, and could be quite unpredictable.

The earliest known dam is the Jawa Dam in Jordan, 100 kilometres (62 mi) northeast of the capital Amman. This gravity dam featured an originally 9-metre-high (30 ft) and 1 m-wide (3.3 ft) stone wall, supported by a 50 m-wide (160 ft) earth rampart. The structure is dated to 3000 BC.

Damè

Damè is a town and arrondissement in the Atlantique Department of southern Benin. It is an administrative division under the jurisdiction of the commune of Toffo. According to the population census conducted by the Institut National de la Statistique Benin on February 15, 2002, the arrondissement had a total population of 11,034.

References

Coordinates: 6°51′00″N 2°05′00″E / 6.8500°N 2.0833°E / 6.8500; 2.0833

Dam methylase

Dam methylase, an abbreviation for Deoxyadenosine methylase, is an enzyme that adds a methyl group to the adenine of the sequence 5'-GATC-3' in newly synthesized DNA. Immediately after DNA synthesis, the daughter strand remains unmethylated for a short time. The 2015 Nobel Prize in Chemistry was awarded to Paul Modrich for his work on DNA mismatch repair.

Role in mismatch repair of DNA

When DNA polymerase makes an error resulting in a mismatched base-pair or a small insertion or deletion during DNA synthesis, the cell will repair the DNA by a pathway called mismatch repair. However, the cell must be able to differentiate between the template strand and the newly synthesized strand. In bacteria, DNA strands are methylated by Dam methylase, and therefore, immediately after replication, the DNA will be hemimethylated. A repair enzyme, MutS, binds to mismatches in DNA and recruits MutL, which subsequently activates the endonuclease MutH. MutH binds hemimethylated GATC sites and when activated will selectively cleave the unmethylated daughter strand, allowing helicase and exonucleases to excise the nascent strand in the region surrounding the mismatch. The strand is then re-synthesized by DNA polymerase III.

Aspic

Aspic is a dish in which ingredients are set into a gelatin made from a meat stock or consommé. Non-savory dishes, often made with commercial gelatin mixes without stock or consommé, are usually called gelatin salads.

When cooled, stock that is made from meat congeals because of the natural gelatin found in the meat. The stock can be clarified with egg whites, and then filled and flavored just before the aspic sets. Almost any type of food can be set into aspics. Most common are meat pieces, fruits, or vegetables. Aspics are usually served on cold plates so that the gel will not melt before being eaten. A meat jelly that includes cream is called a chaud-froid.

Nearly any type of meat can be used to make the gelatin: pork, beef, veal, chicken, turkey, or fish. The aspic may need additional gelatin in order to set properly. Veal stock provides a great deal of gelatin; in making stock, veal is often included with other meat for that reason. Fish consommés usually have too little natural gelatin, so the fish stock may be double-cooked or supplemented. Since fish gelatin melts at a lower temperature than gelatins of other meats, fish aspic is more delicate and melts more readily in the mouth.

Advanced Space Propulsion Investigation Committee

Advanced Space Propulsion Investigation Committee (ASPIC) was a research group of specialists, including Y.Minami, and T.Musha, which was organized under the Japan Society for Aeronautical and Space Sciences in 1994. The purpose of which was to study all kinds of non-chemical space propulsion systems instead of the conventional rocket for the use of space missions to the nearby Earth, the Moon, and the outer solar system, including plasma propulsion, laser propulsion, nuclear propulsion, solar sail and field propulsion systems which utilize a strain on space, zero-point energy in a vacuum, electro-gravitic effect, non-Newtonian gravitic effect predicted from the Einstein Theory of Gravity, and the terrestrial magnetism. The research report was published by the Japan Society for Aeronautical and Space Sciences in March 1996.

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