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This property can be understood in terms of the continued fraction representation for the golden ratio:

The Fibonacci numbers occur as the ratio of successive convergents of the continued fraction for φ , and the matrix formed from successive convergents of any continued fraction has a determinant of +1 or −1. The matrix representation gives the following closed-form expression for the Fibonacci numbers:

Taking the determinant of both sides of this equation yields Cassini's identity ,

Moreover, since A n A m = A n + m for any square matrix A , the following identities can be derived (they are obtained from two different coefficients of the matrix product, and one may easily deduce the second one from the first one by changing n into n + 1 ),

In particular, with m = n ,

These last two identities provide a way to compute Fibonacci numbers Clearance Wholesale Price Mens Cotton Pocket Square Silver Stencil by VIDA VIDA Comfortable Online Cheap Sale 100% Guaranteed Where Can You Find Enjoy hbQ68322L
in O (log( n )) arithmetic operations and in time O ( M ( n )log( n )) , where M ( n ) is the time for the multiplication of two numbers of n digits. This matches the time for computing the n th Fibonacci number from the closed-form matrix formula, but with fewer redundant steps if one avoids recomputing an already computed Fibonacci number (recursion with Rondeur Perlee Doublée Chain earring Anissa Kermiche Buy Cheap For Sale Buy Cheap Perfect Clearance Recommend Authentic dhd5y
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The question may arise whether a positive integer x is a Fibonacci number. This is true if and only if one or both of 5 x 2 + 4 {\displaystyle 5x^{2}+4} or 5 x 2 4 {\displaystyle 5x^{2}-4} is a Womens Km500600151 Sunglasses Black 51 Karen Millen Looking For Clearance The Cheapest Recommend For Sale LVCpOE7Qdi
. [29] This is because Binet's formula above can be rearranged to give

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Methodology Procedures

Projects covered include state-owned and private projects in the Infrastructure, Electric Power, Oil Gas (excluding upstream), Water and Waste, and Mining sectors.

Where applicable, a project is considered as such until the end of construction and ramp-up to full capacity (with the exception of mining projects, where the date of commissioning signifies the end of the project). Projects must have a:

a) Start date b) Estimate for completion c) Initial investment estimate

For state-owned projects, initial information about the start date and estimates for completion and investment are taken from original signed contracts, along with addendums and annexes.

If original contracts cannot be obtained, information is taken from public documents, presentations, news articles from BNamericas archives, and external sources.

In cases where contracts are subject to approval by legislators, the start date is the date of the law or legislative approval.

In the case of private projects, information is taken from public sources, such as stock exchange filings, annual reports, company presentations, third party research and press releases.

In judging the timing of investment decisions for private projects, great care was taken to differentiate between large projects receiving environmental approval and proceeding directly to construction, and smaller projects where the investment decision hinges on securing financing.

Best care is taken to ensure that recorded data is correct at the time of entry and that each entry is backed with a relevant source.

The greatest care possible was taken to ensure consistency of information in order make a like-for-like comparison in project costs. Insofar as the figures rely on disclosure by the organization or company responsible, the figures can be considered to be conservative in nature.

No attempt was made to adjust figures for inflation during the course of research or for consideration of the time value of money.

In the case of state-owned projects, validation is carried out where possible with either a member of the consortium, EPC contractor, a relevant state agency or advisors to either party.

Projects costs are measured in US dollars. Where project costs are measured in a local currency, amounts are converted to US dollars at the date of the relevant announcement, signature or report.

The severity of deviation from original estimates is defined according to set criteria.

Changes in scope beyond the start date are not accounted for.

Where guidance is non-specific as to dates for completion, the following is used. Project to be completed by 2018 = December 31, 2017 Project to be completed in 2018 = December 31, 2018

­
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Abu A. Hamour, MBBS, MSc, FRCP(Edin), FRCP,

ABSTRACT: Pyogenic liver abscesses are relatively uncommon but potentially life-threatening. Most infections that lead to an abscess are associated with underlying biliary disease, or are due to hematogenous spread from a variety of nonbiliary sites. Although most infections are polymicrobial, monomicrobialabscesses do occur. These exceedingly rare monomicrobial infections typically occur in immunocompromised individuals or in the presence of periodontal disease. A recent case involved a solitary pyogenic liver abscess due toin an immunocompetent 44-year-old woman with no underlying risk factors. Despite the cryptogenic nature of the abscess, the patient was treated successfully with percutaneous drainage and antibiotics.

Clinicians should consider the possibility of pyogenic liver abscess when patients present with fever, right upper quadrant pain, and shortness of breath.

Formation of a pyogenic liver abscess (PLA) is potentially life-threatening, with an estimated incidence rate of 2.3 cases per 100 000 patients.[ Charm Bracelet Sails of Reflections II by VIDA VIDA Outlet Shopping Online fm2hg4NvQh
] Despite recent advances in the investigation and management of such abscesses, the mortality rate still ranges from 2% to 12%.[ Cheap Best Sale Fashionable Cheap Online whale inflatable toy chain bag Blue Mary Katrantzou Discount Real Deals egdN08
] Amebic liver abscess is the most common form of liver abscess worldwide, whereas PLA is the most common form in North America,[ 5 ] and is usually the result of polymicrobial infection.[ 6 ] It is believed that the introduction of pyogenic bacteria to the liver most often occurs during an intra-abdominal infection, particularly one involving biliary tract pathology.[ Thick silver bangle Pearls Before Swine Outlet Visit New Discount Codes Clearance Store Buy Cheap For Nice 2018 Newest Cheap Online Buy Cheap Best Prices N2mpNrU
] Less often, bacteria spread by way of the portal vein or hematogenously during systemic infection,[ Outlet Where Can You Find Mens GordonBowtieQ7027 Bomber Hat Gelb Dark Yellow 1508 One Size Suit Buy Sale Online l0NGj
] with periodontal disease being recognized increasingly as a source of pathogens in this setting.[ Statement Clutch HummingBird in Turquoise by VIDA VIDA Shopping Online Clearance Amazon Footaction Clearance Low Price Fee Shipping Best For Sale Quality jfaHs
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Although monomicrobial infections are rare, they do occur. A recent case involved Fusobacterium nucleatum , a nonmotile, gram-negative, anaerobic bacterium that normally inhabits the oropharynx and is a significant contributor to the formation of periodontal plaques.[ 10 ] Anaerobic bacteria have long been known to play a part in PLA formation, with one case series identifying anaerobes in up to 45% of cases.[ 11 ] Typically, systemic F. nucleatum infections occur in immunocompromised individuals or are of odontogenic origin.[ Clearance Brand New Unisex Womens Straw Hat Yosuzi Footlocker Finishline Very Cheap Online Order Discount Clearance Store qbgNOjk
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Case data A 44-year-old woman presented to the emergency room with a 6-day history of fever, chills, rigor, vomiting, headache, and shortness of breath. She had diffuse abdominal pain that had become localized to the right upper quadrant, and had progressed to being sharp and steady in nature and worse with inspiration. Her surgical history included a total hysterectomy that had been complicated by an Escherichia coli bacteremia and sepsis secondary to a surgical site infection. Her medical history included chronic gastroesophageal reflux disease, which was controlled with esomeprazole. Her dental history was unremarkable.

© 2018 Unidad Editorial Revistas, S.L.U. Todos los derechos reservados.
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