However, as 1 + ( k + 1 ) x + kx < sup > 2 </ sup > ≥ 1 + ( k + 1 ) x ( since kx < sup > 2 </ sup > ≥ 0 ), it follows that ( 1 + x )< sup > k + 1 </ sup > ≥ 1 + ( k + 1 ) x, which means the statement is true for r = k + 1 as required.

However the ConScript Unicode Registry has defined the to U + E0FF range of the Unicode " Private Use Area " for Cirth.

However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.

However, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to k + n.

However, 2 + ions ( Be < sup > 2 +</ sup >) or even 1 + ( Li < sup >+</ sup >) show some polarizing power because their sizes are so small ( e. g., LiI is ionic but has some covalent bonding present ).

However, at least the late Soviet version КР580ВМ80А was able to work with a single + 5 V power source, the + 12 V pin being connected to + 5 V and the − 5 V pin to ground.

However this method is possible only if the array slot A + 1 exists but is not being otherwise used.

However, as a result of conservative fiscal policies and a sound financial system, in 2010 the country credit rating improved slightly to BB + and was kept at that level in 2011.

However, many languages use mixtures of bases, and other features, for instance 79 in French is soixante dix-neuf ( 60 + 10 + 9 ) and in Welsh is pedwar ar bymtheg a thrigain ( 4 +( 5 + 10 )+( 3 × 20 )) or ( somewhat archaic ) pedwar ugain namyn un ( 4 × 20 − 1 ).

However, it can formulate individual instances of divisibility ; for example, it proves " for all x, there exists y: ( y + y

However, this theory needs to be generalized in ( 2 + 1 ) or ( 3 + 1 ) dimensions although, in principle, the field equations are amenable to such generalization as shown with the inclusion of a one-graviton process and yielding the correct Newtonian limit in d dimensions if a dilaton is included.

However, for convenience we will stick to the idea that information can be classified according to Table 1.

However, neither of these two cities is on the desired July 1 to June 30 fiscal year.

However, in the actual assessment of the cutting force by instrumental methods for any thickness of coating a number of spurious effects occur which must be taken into account and which make the measured value larger than the true cutting force indicated by eqn. ( 1 ).

However, readers who accept Freud's findings and believe that he has solved completely the mystery of dreams, should ponder over the following words in his Interpretation Of Dreams, Chapter 1::

However, Ancient Egyptian is highly divergent from Proto-Afroasiatic ( Trombetti 1905: 1 – 2 ), and considerable time must have elapsed in between them.

However, very small amounts of steel, ( an alloy of iron and around 1 % carbon ), was always a byproduct of the bloomery process.

However, according to Josephus, in Antiquities, Book 7, Chapter 1, Joab had forgiven Abner for the death of his brother, Asahel, the reason being that Abner had slain Asahel honorably in combat after he had first warned Asahel and had no other choice but to kill him out of self defense.

* However, a larger 35ml measure is increasingly used ( and in particular is standard in Northern Ireland ), which contains 1. 4 units of alcohol.

However, if this pixel uses premultiplied alpha, all of the RGB values ( 0, 1, 0 ) are multiplied by 0. 5 and then the alpha is appended to the end to yield ( 0, 0. 5, 0, 0. 5 ).

(€ 19 million as a group ) However, in 2008 – 09 season saw the decrease of gate and TV income, co-currently with finished 6th in Serie A, which saw Roma made a net loss of € 1, 894, 330.

However 1. 4 billion people still live without clean drinking water and 2. 6 billion of the world ’ s population lack access to proper sanitation.

However, recent changes to the train timetables have been a disservice to Accrington, increasing the journey time to Preston ( a vital link to London or Scotland ) by up to 1. 5 hours.

However, the film's ambitious scope and its extensive effects work forced Campbell, Raimi and producer Rob Tapert to put up $ 1 million of their collective salaries to shoot a new ending and not film a scene where a possessed woman pushes down some giant pillars.

However, despite those efforts, the presence of the Armed Forces on the border regions of the Brazilian Amazon continues to be sparse and disperse, given the fact that the Army has just 28 border detachments in that area, a total of 1, 600 soldiers, or 1 men for every of borders.

However, it's not injective in both variables simultaneously, because ( for example ) f ( 2, 4 ) = f ( 1, 2 ).

However, peaches contain more sucrose ( 6. 66 %) than they do fructose ( 0. 93 %) or glucose ( 1. 47 %).

However, in a 2005 poll by British film magazine Empire, Braveheart was # 1 on their list of " The Top 10 Worst Best Pictures ".

However, Wolfram points out that at the time " Clovis got no farther than the Seine ; only after several more years did the Franks succeed in occupying the rest of the Gallo-Roman buffer state north of the Loire.

However, as Andronikos ' rule went on, the Emperor became increasingly paranoid and violent – in September 1185, Andronikos ordered the execution of all prisoners, exiles and their families for collusion with the invaders – and the Byzantine Empire descended into a terror state.

However, passage of a bill by the state assembly alone does not change the law and the state senate and governor had not yet endorsed the bill.

However, with his campaigns in India exhausting the state treasury, and with his troops stretched thin throughout Central Asia, Ahmad Shah lacked sufficient resources to check the advance of Qing forces.

However the cementation process was not abandoned and as late as the early 19th century there are descriptions of solid state cementation in a domed furnace at around 900 – 950 ° C and lasting up to 10 hours.

However, a series of reforms were undertaken in the 1990s, which resulted in the consolidation of the banking sector and in the privatization of all state banks.

However, in private, many British officials agreed with the interpretation of the Zionists that a state would be established when a Jewish majority was achieved.

However, other sources state that Herennius died with his father.

However, in 1931, gambling was legalized throughout the state of Nevada, along with Las Vegas and Reno.

However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the stoichiometry of the reaction as Guldberg and Waage had proposed ( see, for example, nucleophilic aliphatic substitution by S < sub > N </ sub > 1 or reaction of hydrogen and bromine to form hydrogen bromide ).

However, the observational evidence began to support the idea that the universe evolved from a hot dense state.

However, references to " condensed " state can be traced to earlier sources.

However, in October 2004, the Cuban government announced an end to this policy: from November US dollars would no longer be legal tender in Cuba, but would instead be exchanged for convertible pesos ( since April 2005 at the exchange rate of $ 1. 08 ) with a 10 % tax payable to the state on the exchange of US dollars cash — though not on other forms of exchange.

( However, it should be noted that those organizations are heavily monitored by the state.

However, today the church officially state it is a " matter to be decided solely by the prescribed processes of civil law.

However, the study made no attempt to ascertain the occurrence of the disease in other parts of the state, or elsewhere in the country.

However, since the lawsuit was filed in a state California court, the lawsuit was tossed out because only federal courts have jurisdiction over intellectual property issues.

However, the toad gained a foothold in the state after an accidental release by an importer at Miami International Airport in 1957, and deliberate releases by animal dealers in 1963 and 1964 established the toad in other parts of Florida.

However, a lawyer discovered that the injunction was only enforceable in the state of Pennsylvania.

However, similar to the stabilizability condition above, if a state cannot be observed it might still be detectable.

All other forms of intrastate conflict, such as rebellion, are not accounted for because, in theoretical terms, Clausewitz could not account for warfare before the state ( However, near the end of his life, Clausewitz grew increasingly aware of the importance of non-state military actors.

However, when the research team synthesized element 98, they could not think of a good analogy for dysprosium, and instead named the element californium in honor of the state in which it was synthesized.

However December 16 is only the date on which the state celebrates the event, while the actual day on which the independence of Bahrain was declared was August 15, 1971 ( see Bahrain Independence Day )

However, in general, the state is viewed as a positive location for corporate tax purposes because favorable laws of incorporation allow companies to minimize the corporate expenditures ( achieved through legal standardization of corporate legal processes ), creating a nucleus in Delaware with operating companies often in other states.