


Title

Complex Numbers





Abstract 
A complex number is a number which can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where i2 = −1. In this expression, a is called the real part and b the imaginary part of the complex number. Complex numbers extend the idea of the onedimensional number line to the twodimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a+bi can be identified with the point (a, b). A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with only real numbers. Complex numbers are used in many scientific fields, including engineering, electromagnetism, quantum physics, and applied mathematics, such as chaos theory. Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them \"fictitious\", during his attempts to find solutions to cubic equations in the 16th century. (Source: Wikipedia) 


Title

Translation





Abstract 
Eukaryotic translation (animation). Eukaryotic translation is the process by which messenger RNA is translated into proteins in eukaryotes. It consists of initiation, elongation and termination ^{[1]} Initiation of translation usually involves the interaction of certain key proteins with a special tag bound to the 5'end of an mRNA molecule, the 5' cap. The protein factors bind the small ribosomal subunit (also referred to as the 40S subunit), and these initiation factors hold the ... 


Title

Sleep Apnea





Abstract 
Sleep apnea is a sleep disorder characterized by pauses in breathing during sleep. Each episode, called an apnea (Greek: ἄπνοια (ápnoia), from α (a), privative, πνέειν (pnéein), to breathe), lasts long enough so that one or more breaths are missed, and such episodes occur repeatedly throughout sleep. The standard definition of any apneic event includes a minimum 10 second interval between breaths, with either a neurological arousal (a 3second or greater shift in EEG frequency, measured at C3, C4, O1, or O2), a blood oxygen desaturation of 34% or greater, or both arousal and desaturation. Sleep apnea is diagnosed with an overnight sleep test called a polysomnogram, or a "Sleep Study" which is often conducted by a pulmonologist.
Clinically significant levels of sleep apnea are defined as five or more episodes per hour of any type of apnea (from the polysomnogram). There are three distinct forms of sleep apnea: central, obstructive, and complex (i.e., a combination of central and obstructive) constituting 0.4%, 84% and 15% of cases respectively.[1] Breathing is interrupted by the lack of respiratory effort in central sleep apnea; in obstructive sleep... 


Title

Lugosi teaches math  Absolute convergence2





Abstract 
Béla Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  Absolute convergence2





Abstract 
Béla Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  Absolute convergence1





Abstract 
Béla Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  uniform convergance2





Abstract 
BÃ©la Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  polynomial approximatio...





Abstract 
BÃ©la Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  polynomial approximatio...





Abstract 
BÃ©la Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. 


Title

Lugosi teaches math  Many Vs Infinite 1





Abstract 
Béla Lugosi teaches teaches advanced mathematical concepts. This is rare footage of Lugosi in his last on screen contibution in what is consdered by many a low point in his career and what is considered by some inspirational. This educational series was left unfinised due to Lugosi's death in 1958. The series was an attempt to show undergraduate students that math is not scary. Lugosi's hidden love for mathematics is illuminated by his animated teaching style 

