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Allinson, A.R. (2006). The War Diary of the Emperor Frederick III - 1870 - 1871. Home Farm Books. ISBN 1-4067-9995-5.
Hough, Richard (1996). Victoria and Albert. New York: St. Martin's Griffin. ISBN 0-312-30385-8.
= Kersal Moor =
Kersal Moor is one of the many fluvioglacial ridges that formed along the Irwell Valley during the melting of the glaciers at the end of the last ice age. Typically for this type of landform, the subsoil is composed of sand mixed with coarse gravel. The 19th century botanist Richard Buxton described this as "Mr. E.W. Binney's drift deposit no.2 ... a deposit of sharp forest sand, parted with layers of gravel composed of Azoic, Palaeozoic and Triassic rocks, well rounded, parted with layers of fine sand, and having every appearance of a regular deposit by water." This deposit is overlaid with a thin topsoil supporting a range of mosses, heathers, grasses, ferns, common broom, gorse and some trees, which are predominantly oak with some rowan, cherry and other broadleaved species. The land to the south is elevated, rising to a high point towards the south west. From this elevated position there are views across Manchester to the Derbyshire hills in the south, to the Pennines in the north east and across the Irwell Valley and Salford in the west. The land falls away to the north, ending with two drumlin-shaped hills on the northern edge, which were probably formed by sediment from the meltwater of the receding glaciers, in a process known as sedimentary fluting. The moor is criss-crossed with footpaths, many of which cut through to the sand and gravel below. Singleton Brook, to the north of the moor, denotes the boundary between Salford and Prestwich.
The Broughton Archers, and the bowmen good
The largest of a series of Chartist meetings was held on the moor on 24 September 1838. The meeting, which was planned as a show of strength and to elect delegates for the Chartist national convention, attracted speakers from all over the country and a massive crowd, which was estimated at 30,000 by the Manchester Guardian and 300,000 by the Morning Advertiser.
Enraged by this, and by accusations of fraudulently passing off foreign moths as British, Cribb gave up collecting and left the rest of the specimens with his landlady as security for a debt. Here the stories from Manchester University and The Australian Museum, Victoria differ as to whether it was Cribb's pub landlady or the landlady of his lodgings, but either way the result was the same. The debt was not paid on time and when Cribb went back for the moths, which he had already sold to another collector, his landlady had burnt them. Subsequent efforts by other collectors to find more of the moths were unsuccessful, and the three specimens left in existence are thought to be the only representatives of an extinct species.
Healey I advised to go to his brother at Bolton, and get some money, and keep out of sight entirely, until something further was known. His best way would be to avoid Manchester, and go over Kersal moor and Agecroft bridge; and as I had a relation in that quarter who wished to see me, I would keep him company as far as Agecroft.
In strange confusion thro ' the hazy skies;
Kersal Moor
Oft have I roved you craggy steeps,
... Oh lay me down in moorland ground,
=== Early Jurchen shamanism ===
=== Healing rituals ===
ᠮᠠᠨᠵᡠᠰᠠᡳ
== Diversity of practices ==
At least into the eighteenth century, shamanism served to strengthen Manchu ethnic identity by forming "the spiritual core of Manchu life." The Qing emperors also used shamanism to shape Manchu identity. In an edict dated 17 April 1727 in which he opposed Jesuit attempts to convert Chinese and Manchus to Catholicism, the Yongzheng Emperor (r. 1722 – 1735) singled out Manchu converts for criticism. To the emperor, the "Lord of Heaven" — the Jesuit name for God in Chinese — was none other than the Heaven the Chinese and Manchus already worshipped. To convince Manchu nobles that they should use existing Manchu rituals for worshipping Heaven, he explained that, "In the empire we have a temple for honoring Heaven and sacrificing to Him. We Manchus have Tiao Tchin. The first day of every year we burn incense and paper to honor Heaven. We Manchus have our own particular rites for honoring Heaven." In this edict, which we know through a French translation by court Jesuit Antoine Gaubil, Tiao Tchin refers to Tiao Shen (跳神, literally "spirit-jumping"), the Chinese name of the Manchu shamanic ceremony.
Shirokogoroff's and Eliade's views of shamanism were both centered on individuals and on the role of shamans in small groups. Shirokogoroff, for instance, considered eighteenth-century Qing shamanism too formalized to be authentic. Historians of northeast Asia have criticized Eliade's and Shirokogoroff's interpretations because they neglect the political roles of shamans and shamanism's relation with the state. Eliade's claim that shamanism is by essence archaic, individualistic, and socially transgressive led him and his followers to neglect historical contexts in which shamanism fulfilled political functions or served the needs of the state, as it did under the Qing.
The exponent is usually shown as a superscript to the right of the base. Some common exponents have their own names: the exponent 2 (or 2nd power) is called the square of b (b2) or b squared; the exponent 3 (or 3rd power) is called the cube of b (b3) or b cubed. The exponent − 1 of b, or 1 / b, is called the reciprocal of b.
= 10a + b, necessary to manipulate powers of 10. In the 9th century, the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī used the terms mal for a square and kahb for a cube, which later Islamic mathematicians represented in mathematical notation as m and k, respectively, by the 15th century, as seen in the work of Abū al-Hasan ibn Alī al-Qalasādī.
= 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 =
<formula>
The following identity holds for an arbitrary integer n and nonzero b:
and more generally for any nonzero b and any nonnegative integer n,
=== Identities and properties ===
6, but 23
<formula>
In the base ten (decimal) number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 103
The positive powers of 2 are important in computer science because there are 2n possible values for an n-bit binary register.
Any power of one is always one:
2.
<formula>
= − 1, the definition of bu / v when b is negative and v is even must use the imaginary unit i, as described more fully in the section § Powers of complex numbers.
The identities and properties shown above for integer exponents are true for positive real numbers with non-integer exponents as well. However the identity
<formula>
=== The exponential function ===
Since exp (1) is equal to e and exp (x) satisfies this exponential identity, it immediately follows that exp (x) coincides with the repeated-multiplication definition of ex for integer x, and it also follows that rational powers denote (positive) roots as usual, so exp (x) coincides with the ex definitions in the previous section for all real x by continuity.
for each real number x.
The rational exponent method cannot be used for negative values of b because it relies on continuity. The function f (r) =
= x1 + iy1, z2 =
The solutions to the equation ez =
More simply: eiπ
Before the invention of complex numbers, cosine and sine were defined geometrically. The above formula reduces the complicated formulas for trigonometric functions of a sum into the simple exponentiation formula
=== Complex exponents with positive real bases ===
<formula>
Complex powers of positive reals are defined via ex as in section Complex exponents with positive real bases above. These are continuous functions.
The powers of negative real numbers are not always defined and are discontinuous even where defined. In fact, they are only defined when the exponent is a rational number with the denominator being an odd integer. When dealing with complex numbers the complex number operation is normally used instead.
If z is an integer, then the value of wz is independent of the choice of log w, and it agrees with the earlier definition of exponentiation with an integer exponent.
A complex number w such that wn
In order to compute the complex power wz, write w in polar form:
This final formula allows complex powers to be computed easily from decompositions of the base into polar form and the exponent into Cartesian form. It is shown here both in polar form and in Cartesian form (via Euler's identity).
<formula>
<formula>
<formula>
<formula>
If the operation also has two-sided inverses and is associative, then the magma is a group. The inverse of x can be denoted by x − 1 and follows all the usual rules for exponents.
=== Over sets ===
= V for each i, the resulting direct sum can be written in exponential notation as V ⊕ N, or simply VN with the understanding that the direct sum is the default. We can again replace the set 1 with a cardinal number n to get Vn, although without choosing a specific standard set with cardinality n, this is defined only up to isomorphism. Taking V to be the field R of real numbers (thought of as a vector space over itself) and n to be some natural number, we get the vector space that is most commonly studied in linear algebra, the real vector space Rn.
In a Cartesian closed category, the exponential operation can be used to raise an arbitrary object to the power of another object. This generalizes the Cartesian product in the category of sets. If 0 is an initial object in a Cartesian closed category, then the exponential object 00 is isomorphic to any terminal object 1.
== Repeated exponentiation ==
= 1 at x =
More recent authors interpret the situation above in different ways:
Most programming language with a power function are implemented using the IEEE pow function and therefore evaluate 00 as 1. The later C and C + + standards describe this as the normative behaviour. The Java standard mandates this behavior. The .NET Framework method System.Math.Pow also treats 00 as 1.
Matlab, Python, Magma, GAP, singular, PARI / GP and the Google and iPhone calculators evaluate 00 as 1.
= [− ∞, + ∞], endowed with the product topology ), which will contain the points at which the function f has a limit.
= + ∞, when 0 ≤ x < 1.
On the other hand, when n is an integer, the power xn is already meaningful for all values of x, including negative ones. This may make the definition 0n =
4
= 216 =
264 232 24
Placing an integer superscript after the name or symbol of a function, as if the function were being raised to a power, commonly refers to repeated function composition rather than repeated multiplication. Thus, f 3 (x) may mean f (f ( f ( x) ) ); in particular, f − 1 (x) usually denotes the inverse function of f. Iterated functions are of interest in the study of fractals and dynamical systems. Babbage was the first to study the problem of finding a functional square root f 1 / 2 (x).
x ↑ y: Algol, Commodore BASIC
Citing the trust relationship between the federal government and the tribes, the Court held that removal treaties could only be enforced against the tribes by the federal government, not private parties (whether through self-help or through the courts). In other words, the federal government retained the discretion not to enforce such treaties. At the same time, the Court held that enrolled treaties are conclusively valid, and refused to consider the plaintiffs claim that the Treaty of Buffalo Creek (1838) was fraudulent.
Oliver Phelps and Nathaniel Gorham acquired the right of pre-emption to the lands at issue in Fellows v. Blacksmith from Massachusetts in 1788 as part of the Phelps and Gorham Purchase. However, Phelps and Gorham only consummated the right of pre-emption for a tract east of the Genesee River in 1788. Phelps and Gorham defaulted on their payments to Massachusetts in 1790, causing the pre-emption rights to return to the state. Massachusetts then conveyed the pre-emption rights to Samuel Ogden on behalf of Robert Morris on May 12, 1791. Morris retained the pre-emptive right to the Morris Reserve for himself, but sold the pre-emptive right to the lands in question to the Holland Land Company on July 20, 1793 (the Holland Purchase).
The suit was originally brought by John Blacksmith in 1846. Represented by lawyer John H. Martindale, Blacksmith sued Joseph Fellows and Robert Kendle, agents of the Land Company, for the torts of assault and battery and trespass, quare clausum fregit, with the sawmill as the locus in quo. Blacksmith's wife and Ely S. Parker (Blacksmith's successor as sachem of the Wolf Clan), together the administrators of Blacksmith's estate, succeeded Blacksmith as plaintiffs.
U.S. Supreme Court oral argument
The situation of [blacks] was altogether unlike that of the Indian race. The latter. .. were situated in territories to which the white race claimed the ultimate right of dominion. But that claim was acknowledged to be subject to the right of the Indians to occupy it as long as they thought proper, and neither the English nor colonial Governments claimed or exercised any dominion over the tribe or nation by whom it was occupied, nor claimed the right to the possession of the territory, until the tribe or nation consented to cede it.
The Court observed:
Because its aforementioned holdings required affirmance, the Court did not reach the alternate ground for decision of the trial court that the appraisal and the payments were conditions precedent.
that it shall be the duty of the district attorneys respectively of the several counties in this state in which any lands belonging to any Indian tribe shall be situated, (among other things) to make complaint of all intrusions upon Indian lands, forbidden by the act; and from time to time to make inquiries whether any persons other than Indians are settled upon such lands, and to cause them to be removed in the manner therein prescribed.
That June, Judge Jewett granted Tracy's motion to quash, without costs. The court held that only the district attorney could bring such an action to enforce the statute:
=== Seneca land claims ===
Guitar Hero is a music rhythm video game developed by Harmonix and published by RedOctane for the PlayStation 2 video game console. It is the first entry in the Guitar Hero series. Guitar Hero was released on November 8, 2005 in North America, April 7, 2006 in Europe and June 15, 2006 in Australia. The game's development was a result of collaboration between RedOctane and Harmonix to bring a Guitar Freaks-like game to America.
=== Modes and other features ===
According to Rob Kay, the game's Lead Designer, the idea of Guitar Hero was directly inspired by Konami's Guitar Freaks arcade game, where the player used a guitar-shaped controller to interact with the game. At the time, GuitarFreaks had not seen much exposure in North America. RedOctane was making dance pads for games like Dance Dance Revolution for home consoles and also operated an online video rental service similar to Netflix. RedOctane's Kai and Charles Huang recognized the popularity of GuitarFreaks in Japan through their rental service, and planned to create guitar controllers to bring the game to North America. The Huangs raised $ 1.75 million for the effort, despite being turned down by some investors who "thought [the idea] was too weird". Greg Fischbach, one of the founders of Acclaim Entertainment, noted, regretfully several years later, they had passed on Guitar Hero, questioning "Who's going to buy a peripheral like that?" The Huangs approached Harmonix, who had previously made music video games such as Frequency, Amplitude and Karaoke Revolution about making a guitar-based video game for those controllers. With a budget of about one million dollars (which Kay noted was "pretty tiny for a video game"), the two companies worked together to develop Guitar Hero. Kay noted that "No one had any notions about it being a massive success; we all just thought it would be fun to do." Harmonix's president Alex Rigopulos also claims that former Microsoft vice-president of game publishing Ed Fries indirectly influenced the game's creation, who had previously told Harmonix when they were pitching Frequency to Microsoft that no music-rhythm game would succeed without custom hardware for it, prompting Rigopulos to investigate the Guitar Hero opportunity when it arose.
Steffen Peters (born September 18, 1964) is a German-born equestrian who competes for the United States in dressage. He has participated in three Olympic Games, winning a bronze medal at the 1996 Summer Olympics. Peters has been successful in numerous other international competitions, including winning team bronze at the 2006 World Equestrian Games, two individual bronze medals at the 2010 World Equestrian Games and individual and team gold at the 2011 Pan Am Games. The horse upon which he won many of his titles, Ravel, was retired in 2012, and Peters is currently working with a new international competition horse, Legolas.
Peters'show record before the 1992 Summer Olympics made him a hopeful to compete for the US team. However, his citizenship papers were not processed in time to compete in the Olympic trials, and so he did not compete in Barcelona. Peters won his first Olympic medal when he rode with the US dressage team to a bronze medal at the 1996 Summer Olympics in Atlanta, together with Robert Dover, Michelle Gibson and Guenter Seidel. Peters, riding Floriano, was an alternate for the US team at the 2004 Summer Olympics, and did not compete. In 2006, with an aging Floriano, Peters and the US team won bronze at the 2006 World Equestrian Games. Soon after, he began riding TC Ravel, who would become his most successful horse. Despite being gelded while in quarantine after his shipment from the Netherlands and suffering an injury in 2007 that prevented training, Ravel carried Peters to a qualification for the 2008 Summer Olympics. In individual dressage competition at the Games, Peters placed fourth, riding Ravel. The US team finished fourth at the 2008 Games, but was disqualified after team member Courtney King's horse tested positive for felbinac, a banned substance. In 2009, Peters and Ravel had the highest scores in all three portions of the prestigious German Aachen World Equestrian Festival Grand Prix competition, leading them to be the first American pair to be named the Aachen Grand Prix Champions.
Gardner Lake State Park is a small 9.75-acre (3.95 ha) Connecticut state park located on the south portion of the lake and provides access for fishing, swimming, and boating on the lake. Added to the state park list in 2001, it expected to be open around 2002 and serves as one of the few public inland swimming areas ighyt dog poopn the New London County area.
== Service history ==
=== Second patrol ===
== Summary of raiding history ==
Three group 3 elements occur naturally, scandium, yttrium, and either lanthanum or lutetium. Lanthanum continues the trend started by two lighter members in general chemical behavior, while lutetium behaves more similarly to yttrium. This is in accordance with the trend for period 6 transition metals to behave more similarly to their upper periodic table neighbors. This trend is seen from hafnium, which is almost identical chemically to zirconium, to mercury, which is quite distant chemically from cadmium, but still shares with it almost equal atomic size and other similar properties. They all are silvery-white metals under standard conditions. The fourth element, either actinium or lawrencium, has only radioactive isotopes. Actinium, which occurs only in trace amounts, continues the trend in chemical behavior for metals that form tripositive ions with a noble gas configuration; synthetic lawrencium is calculated and partially shown to be more similar to lutetium and yttrium. So far, no experiments have been conducted to synthesize any element that could be the next group 3 element. Unbiunium (Ubu), which could be considered a group 3 element if preceded by lanthanum and actinium, might be synthesized in the near future, it being only three spaces away from the current heaviest element known, ununoctium.
So far, no experiments were conducted to synthesize any element that could be the next group 3 element; if lutetium and lawrencium are considered to be group 3 elements, then the next element in the group should be element 153, unpenttrium (Upt). However, after element 120, filling electronic configurations stops obeying Aufbau principle. According to the principle, unpenttrium should have an electronic configuration of [Uuo] 8s25g186f147d1 and filling the 5g-subshell should be stopped at element 138. However, the 7d-orbitals are calculated to start being filled on element 137, while the 5g-subshell closes only at element 144, after filling of 7d-subshell begins. Therefore, it is hard to calculate which element should be the next group 3 element. Calculations suggest that unpentpentium (Upp, element 155) could also be the next group 3 element. If lanthanum and actinium are considered group 3 elements, then element 121, unbiunium (Ubu), should be the fifth group 3 element. The element is calculated have electronic configuration of [Uuo] 8s28p1 / 21, which is not associated with transition metals, without having a partially filled d-subshell. No experiments have been performed to create unpenttrium, unbiunium or any element that could be considered the next group 3 element; however, unbiunium is the element with the lowest atomic number that has not been tried to be created and thus has chances to be, while unpenttrium, unpentpentium or any other element considered if preceded by lawrencium is very unlikely to be created due to drip instabilities that imply that the periodic table ends soon after the island of stability at unbihexium.
Most of the chemistry has been observed only for the first three members of the group; chemical properties of both actinium and especially lawrencium are not well-characterized. The remaining elements of the group (scandium, yttrium, lutetium) are reactive metals with high melting points (1541°C, 1526°C, 1652°C respectively). They are usually oxidized to the + 3 oxidation state, even through scandium, yttrium and lanthanum can form lower oxidation states. The reactivity of the elements, especially yttrium, is not always obvious due to the formation of a stable oxide layer, which prevents further reactions. Scandium (III) oxide, yttrium (III) oxide, lanthanum (III) oxide and lutetium (III) oxide are white high-temperature-melting solids. Yttrium (III) oxide and lutetium (III) oxide exhibit weak basic character, but scandium (III) oxide is amphoteric. Lanthanum (III) oxide is strongly basic.
It is disputed whether lutetium and lawrencium should be included in group 3, rather than lanthanum and actinium. Other d-block groups are composed of four transition metals, and group 3 is sometimes considered to follow suit. Scandium and yttrium are always classified as group 3 elements, but it is controversial which elements should follow them in group 3, lanthanum and actinium or lutetium and lawrencium. Scerri has proposed a resolution to this debate on the basis of moving to a 32-column table and consideration of which option results in a continuous sequence of atomic number increase. He thereby finds that group 3 should consist of Sc, Y, Lu, Lr. The current IUPAC definition of the term "lanthanoid" includes fifteen elements including both lanthanum and lutetium, and that of "transition element" applies to lanthanum and actinium, as well as lutetium but not lawrencium, since it does not correctly follow the Aufbau principle. Normally, the 103rd electron would enter the d-subshell, but quantum mechanical research has found that the configuration is actually [Rn] 7s25f147p1 due to relativistic effects. IUPAC thus has not recommended a specific format for the in-line-f-block periodic table, leaving the dispute open.
Scandium, yttrium, and lutetium tend to occur together with other lanthanides (except promethium) tend to occur together in the Earth's crust, and are often harder to extract from their ores. The abundance of elements in Earth's crust for group 3 is quite low — all the elements in the group are uncommon, the most abundant being yttrium with abundance of approximately 30 parts per million (ppm); the abundance of scandium is 16 ppm, while that of lutetium is about 0.5 ppm. For comparison, the abundance of copper is 50 ppm, that of chromium is 160 ppm, and that of molybdenum is 1.5 ppm.
Sc2O3 + 3 HF → 2 ScF3 + 3 H2O
Group 3 elements are generally hard metals with low aqueous solubility, and have low availability to the biosphere. No group 3 element has any documented biological role in living organisms. The radioactivity of the actinides generally makes them highly toxic to living cells, causing radiation poisoning.
The dates of the moves are not known exactly. The Wichita move from the Arkansas to the Red occurred at some time between 1768 and 1772. The Osages occupied the former Pawnee-Wichita hunting grounds on the Arkansas in 1774, indicating that the Pawnees had left by then; in 1777, a Spanish report indicated that they were in Nebraska.
At times, the entire Kitkehahki band abandoned the Republican and moved to the Platte. Generally, this took place in times of war, when the bands sought protection in numbers. Movement between the Republican and the Platte probably occurred continually until about 1825.