As S approaches T the square will be outside C and therefore both Af and Af must cross C an odd number of times as S varies from zero to T.

A technique called bootstrapping the simulation model is used, which bootstraps initial data points using a pseudorandom number generator to schedule an initial set of pending events, which schedule additional events, and with time, the distribution of event times approaches its steady state — the bootstrapping behavior is overwhelmed by steady-state behavior.

The need to support more writing systems for different languages, including the CJK family of East Asian scripts, required support for a far larger number of characters and demanded a systematic approach to character encoding rather than the previous ad hoc approaches.

Where the canal is not at sea level a number of approaches have been adopted.

In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article.

" In that interview he also mentioned a course he has twice given at Indiana University, in which he took a " skeptical look at a number of highly-touted AI projects and overall approaches.

The launching of Sputnik in 1957 at the height of the cold war gave rise to a number of intellectually competitive approaches to disciplinary knowledge, such as BSCS biology PSSC physics, led by university professors such as Jerome Bruner and Jerrold Zacharias.

Indeed, a number of studies dispute the reality of this statistical distinction or its increasing occurrence, or both, either arguing the reliable record is too short to detect such a distinction, finding no distinction or trend using other statistical approaches, or that other types should be distinguished, such as standard and extreme El Niños.

A controversial claim of the frequentist approach is that in the " long run ," as the number of trials approaches infinity, the relative frequency will converge exactly to the true probability:

A number of astronomers and observatories have attempted and are attempting to detect such evidence, mostly through the SETI organization, although other approaches, such as

There are about 300 franchise systems and the number of franchised outlets approaches 2000.

In particular, the limit is taken as the complex number z approaches z < sub > 0 </ sub >, and must have the same value for any sequence of complex values for z that approach z < sub > 0 </ sub > on the complex plane.

For a " well-behaved " set X, the Hausdorff dimension is the unique number d such that N ( r ) grows as 1 / r < sup > d </ sup > as r approaches zero.

As the number of blogs approaches the number of possible producers ( humans ), saturation occurs, growth declines, and the number of blogs eventually stabilizes.

NASA, ESA and other space agencies have been engaging in research into these topics for several years, and have accumulated a number of theoretical approaches.

There are any number of approaches to teaching literacy ; each is shaped by its informing assumptions about what literacy is and how it is best learned by students.

Specification of the parameters of the linear predictor is a wide topic and a large number of other approaches have been proposed.

There are a number of surgical approaches to the removal of the thymus gland: transsternal ( through the sternum, or breast bone ), transcervical ( through a small neck incision ), and transthoracic ( through one or both sides of the chest ).

In response to these questions, modern scholars have adopted a number of different approaches.

Today it is usually used to refer to mainstream economics, although it has also been used as an umbrella term encompassing a number of other schools of thought, notably excluding institutional economics, various historical schools of economics, and Marxian economics, in addition to various other heterodox approaches to economics.

Both these approaches apply to other areas of mathematics beyond analysis, including number theory, algebra and topology.

As the number of degrees of freedom becomes arbitrarily large, a system approaches continuity ; examples include a string or the surface of a body of water.

The prime number theorem then states that the limit of the quotient of the two functions π ( x ) and x / ln ( x ) as x approaches infinity is 1, which is expressed by the formula

Additionally, the Lombards would have known of the weakness of Byzantine Italy, which had endured a number of problems after being retaken from the Goths.

A number of harmful and undesired ( adverse ) effects have been observed, including lowered life expectancy, extrapyramidal effects on motor control – including akathisia ( an inability to sit still ), trembling, and muscle weakness – weight gain, decrease in brain volume ( although this is being debated, since schizophrenia, which is often treated with antipsychotics, also causes a shrinkage of brain volume ), enlarged breasts ( gynecomastia ) in men and milk discharge in men and women ( galactorrhea due to hyperprolactinaemia ), lowered white blood cell count ( agranulocytosis ), involuntary repetitive body movements ( tardive dyskinesia ), diabetes, sexual dysfunction, a return of psychosis requiring increasing the dosage due to cells producing more neurochemicals to compensate for the drugs ( tardive psychosis ), and a potential for permanent chemical dependence leading to psychosis worse than before treatment began, if the drug dosage is ever lowered or stopped ( tardive dysphrenia ).

The discovery of differential cryptanalysis is generally attributed to Eli Biham and Adi Shamir in the late 1980s, who published a number of attacks against various block ciphers and hash functions, including a theoretical weakness in the Data Encryption Standard ( DES ).

The Knights happen to have a weakness in that a number of words, when spoken to them, has the same effect on them as their saying, " Ni " has on others.

Shoghi Effendi's reason was due to his belief in the weakness of the existing Bahá ' í institutions — there were a very limited number of national spiritual assemblies and local spiritual assemblies.

Tarquinius, believing Rome's military weakness lay in its lack of horsemen, doubled the number of the equites.

Spotting this weakness, Grouchy, who had been reinforced by Bordesoulle's division, energetically launched his three divisions against the Coalition squares, dispersing a number of them, with these men disorderly fleeing to take refuge in the Étoges forest.

To overcome these weakness a number of design objectives were created ; Harness the full potential of the StrongARM CPU, support multiple processors, add support for PCI expansion, offer the best possible graphics, run existing RISC OS applications and to provide enhanced RISC OS functionality.

On Fire reached number 7 in the UK Indie Chart, and met with much critical acclaim in the United Kingdom, but was less well received by the US music press, who cited Wareham's ' vocal limitations ' as a weakness.

He said: No, you will be many in number, but you will be scum, like the scum of a flash-flood, without any weight, since fear will be removed from the hearts of your enemies, and weakness ( wahn ) will be placed in your hearts.

It is characterised by a number of relatively nonspecific symptoms, such as abdominal pain and weakness, but under certain circumstances, these may progress to Addisonian crisis, a severe illness which may include very low blood pressure and coma.

One such is instant noodles, where an early 2005 increase in the Thai " Mama Noodles Index " ( the number of the popular Mama-brand instant noodles sold in that country ) was seen as a sign of weakness after about ten years of stability.

Because polio survivors have already lost a considerable number of motor neurons, further age-related loss of neurons may contribute substantially to new muscle weakness.

Some growth in international wealth and the number of high net worth individuals can be attributed to the weakness of the US dollar, as stated in the report.

Increasing span lengths increases the usable unencumbered floorspace in buildings ; diminishing the number of joints leads to lower maintenance costs over the design life of a building, since joints are the major focus of weakness in concrete buildings.

Sensing Cesare's weakness, the dispossessed lords of the Romagna offered to submit to the Republic of Venice in exchange for aid in regaining their dominions ; the Venetian Senate accepted and had taken possession of Rimini, Faenza and a number of other cities by the end of 1503.

The French model spread into Iberia in the second half of the century, where the most powerful nobles in Castile built a number of similar tall keeps, such as that at Peñafiel, taking advantage of the weakness of the Castilian Crown during the period.

Due to a demonstrated weakness to head-on fighter attacks, the number of machine guns in the forward dorsal turrets was doubled to four.

This service was discontinued in September 2008, due to escalating fuel prices and the expectation of a drop in the number of passengers due to the weakness of the dollar at the time.

A key weakness was the limited number of modern Krupp and du Bange guns.

Lamb, who would go on to play a total of 201 international matches for England ( 79 Tests, 122 One-Day Internationals ), was regarded as a fine player of fast bowling, but like a large number of South African-born batsmen he had a comparative weakness against spin, and his final average of 36 in Tests from over 4, 500 runs did not do justice to his ability.

German forces were fighting in Poland and lacked sufficient strength to mount an offensive, while for a number of reasons, the Allies did not exploit this weakness to go on the offensive themselves on this front.

One weakness of PBKDF2 is that while its number of iterations can be adjusted to make it take an arbitrarily large amount of computing time, it can be implemented with a small circuit and very little RAM, which makes brute-force attacks using ASICs or GPUs relatively cheap.

After a number of tests, he was diagnosed with a rare condition called myasthenia gravis, an autoimmune disorder with hallmark symptoms of muscle weakness and fatigue.