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Charulata - The Criterion Collection
Bollywood family drama directed by Satyajit Ray. Set in Calcutta at the end of the 19th century when India was under British rule, the film follows Charulata (Madhabi Mukherjee), the intelligent and childless wife of politically active publisher Bhupati (Shailen Mukherjee).Aware of his wife's ever-growing boredom due to his own absence, Bhupati asks his younger cousin Amal (Soumitra Chatterjee) to stay in their house and encourage his wife's literary ambitions.As Amal and Charulata get to know one another a relationship grows between the pair, but will either go beyond their loyalty to Bhupati and act upon it?
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Summertime - The Criterion Collection
Director David Lean's first colour film starring Katharine Hepburn.American spinster Jane Hudson (Hepburn) has finally saved enough money to take the trip of a lifetime, and she hopes that Venice will bring a spark of magic into her life.Overwhelmed by the beauty of her surroundings, she soon finds her holiday becoming even more special when she is swept off her feet by charming antiques dealer Renato de Rossi (Rossano Brazzi).Could this be the romance she has waited her whole life for?
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Funny Girl - The Criterion Collection
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Funny Girl - The Criterion Collection
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Which criterion is it, the root criterion or the quotient criterion?
It is the root criterion. This criterion states that if the limit of the absolute value of the terms of a series to the power of 1/n is less than 1, then the series converges. This criterion is used to test the convergence of series with non-negative terms.
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What are the Abel's convergence criterion and the Leibniz criterion?
Abel's convergence criterion states that if a series ∑an converges and the sequence {bn} is bounded and monotonically decreasing, then the series ∑anbn also converges. This criterion is useful for determining the convergence of a series when the terms can be factored into two separate sequences. The Leibniz criterion is a test for the convergence of alternating series. It states that if the terms of an alternating series satisfy the conditions of being monotonically decreasing and approaching zero, then the series converges. This criterion is particularly useful for determining the convergence of series with alternating signs.
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What is the difference between the quotient criterion and the difference criterion?
The quotient criterion and the difference criterion are both used to test for convergence or divergence of a series. The quotient criterion involves taking the limit of the ratio of consecutive terms in the series, and if the limit is less than 1, the series converges. The difference criterion involves taking the limit of the difference between consecutive terms in the series, and if the limit is 0, the series converges. In essence, the quotient criterion focuses on the ratio of consecutive terms, while the difference criterion focuses on the difference between consecutive terms.
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What is the sterilization criterion?
The sterilization criterion refers to the standard that must be met in order to ensure that a sterilization process has been successful in eliminating all forms of microbial life, including bacteria, viruses, and fungi. This criterion typically involves achieving a certain level of microbial reduction, often measured by a logarithmic reduction factor (e.g. a 6-log reduction for sterilization). Meeting the sterilization criterion is crucial in various industries such as healthcare, pharmaceuticals, and food processing to prevent the spread of infections and ensure product safety.
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Magnificent Obsession - The Criterion Collection
Rock Hudson and Jane Wyman star in this romantic drama directed by Douglas Sirk.Doctors attending an accident in which Bob Merrick (Hudson), a spoilt rich man, has crashed his speedboat through negligence are thus unable to save the life of local physician Dr. Phillips. Phillips was a kind, giving man who selflessly saved many lives and bettered the lot of many locals.Learning this, Merrick is inspired to take up Phillips' good work in atonement but his initial efforts are clumsy and do more harm than good.As he commits to becoming a doctor, he finds himself falling in love with Dr. Phillips' widow Helen (Wyman). Barbara Rush and Otto Kruger also star.
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24 Frames - The Criterion Collection
Experimental film by Iranian director Abbas Kiarostami.Consisting of 24 short films, the work aims to bridge the gap between Kiarostami's two favoured art forms, film and photography, as he looks at what happens before and after a photograph is taken.
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The Uninvited - The Criterion Collection
Ray Milland and Ruth Hussey star in this 1940s gothic ghost story directed by Lewis Allen.Brother and sister Roderick and Pamela Fitzgerald (Milland and Hussey) are nearing the end of their seaside holiday in Cornwall when they happen across a beautiful, seemingly deserted Georgian clifftop mansion while running after their dog.The Fitzgeralds meet the unforthcoming owner (Donald Crisp) and soon agree to purchase the house for a surprisingly small sum of money - but it is only later that the building's unsavoury past emerges to terrify them.
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Love Affair - The Criterion Collection
Leo McCarey directs this romantic drama starring Irene Dunne and Charles Boyer.When French artist and notorious womaniser Michel Marnet (Boyer) has a chance encounter with American singer Terry McKay (Dunne) while on a ship crossing the Atlantic, he worries that his past reputation will prove daunting for Terry, of whom he grows terribly fond.As they disembark, they arrange to meet in six months after which time Michel aims to have his life and career in better shape.Can their love conquer whatever is thrown their way?
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What is the exclusion criterion?
The exclusion criterion is a predefined set of conditions or characteristics that are used to determine which individuals or subjects should be excluded from a study or analysis. These criteria are established to ensure that the study results are not influenced by certain factors that could skew the findings or introduce bias. By applying exclusion criteria, researchers can maintain the integrity and validity of their study results.
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What is the Leibniz criterion?
The Leibniz criterion is a test used to determine the convergence of an alternating series. It states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges. In other words, if the terms of the series eventually become smaller and smaller, the series will converge. This criterion is named after the German mathematician and philosopher Gottfried Wilhelm Leibniz.
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Is it a mistake to apply the majorant criterion here instead of the minorant criterion?
Yes, it would be a mistake to apply the majorant criterion instead of the minorant criterion in this case. The majorant criterion is used to show convergence, while the minorant criterion is used to show divergence. Since we are trying to show divergence in this case, the minorant criterion would be the appropriate choice. Using the majorant criterion would not provide the necessary information to prove divergence.
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What is the monotonicity criterion 2?
Monotonicity criterion 2 states that if a change in the value of an input variable leads to a change in the value of an output variable in the same direction, then the partial derivative of the output variable with respect to the input variable is non-negative. In other words, if an increase in the input variable results in an increase in the output variable, then the partial derivative is positive. This criterion is used to determine the relationship between input and output variables in mathematical models and functions.
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