Math question Let A be a matrix such that A^2 = I where I is the ide.pdf

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Math question Let A be a matrix such that A^2 = I where I is the identity matrix, Show that e^At = cosh(t)I + sinh(t) A. (Hint: use identities cos h(t) = cos(it) and sinh(t) = -isin(it) and the power series expansion of cosh(t) and sinh(t)). Solution cosht = cos (it) sinht = -isinit Hence coshtI + sinhtA = cos(it)I -isin(it) A = cos it (A2) - i sin (it) A = A(cosit-sin itA) = eAt.

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Measuring treatment outcomes as Solution The following is an extract from a journal I came across the other day: Optimizing treatment outcomes with disease-modifying therapies involves several factors: Initiating the appropriate treatment at the appropriate time. Most MS specialists advocate for early intervention, although differences of opinion exist within the MS community: Hawkins, 2012 vs. Amato, 2012 Pittock et al., 2006 vs. Frohman et al., 2006 The following image of the natural history of MS indicates the significant amount of MRI activity that occurs in the pre-clinical phase and early relapsing-remitting MS, the gradual decrease in inflammatory attacks (relapses) over time, and the increasing MRI burden of disease that occurs along with a decrease in brain volume. This schematic supports the role of DMTs early in the disease course. CMS_ms.natural.history (.png) Explaining to patients and family members about the purpose of disease-modifying therapies in MS management (Rio et al., 2005) Setting realistic expectations for the treatment; unrealistic expectations are a common reason why patients discontinue their medication (Mohr et al., 1996). Instructing patients on proper use of a medication, particularly injection techniques and rotation regimens to minimize skin reactions with injectable medications (Saunders et al., 2010; Webb, 2008). Monitoring for side effects and providing management strategies; inadequate management of side effects is another key reason why people discontinue their medication (Webb, 2008). Identifying a sub-optimal response (Cohen et al., 2004; Waubant, 2012) Treating sub-optimal responders Increasing from a lower dose to a higher dose IFN beta medication (Durelli et al., 2002; Panitch et al., 2002; Schwid & Panitch, 2007) in the absence of neutralizing antibodies. Switching from an IFN beta medication to glatiramer acetate or vice versa (Freedman et al., 2009; Caon, 2009) Switching from an injectable to fingolimod (Marriott & O.

Measuring treatment outcomes asSolutionThe following is an ext.pdf

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MC#4: Which of the following statements is most CORRECT? a. In a typical LBO, bondholders do well but shareholders see their value decline. b. Firms are forbidden by law to sell any assets during the first five years following a leverage buyout. c. LBOs are never backed by private equity firms. d. LBOs typically use a lot of debt. e. Leveraged buyouts (LBOs) occur when a firm issues equity and uses the proceeds to take a firm public Solution Which of the following statements is most CORRECT? e. LBOs typically use a lot of debt. LBOs typically use a lot of debt. to buy company.

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Math Analysis question: Please determine compactness and connectedness of the following set in R: Please briefly explain why. Solution by a known theorem ,A subspace of a real line is connected if and only if it is an interval. therefore A is connected in extended real line. By Heine-Borel theorem, Every closed and bounded subspace of real line is compact, therefore A is compact in exteneded real line. if R =(-inf,inf) open interval then A is not subset of R. both are not happen.

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Materials questions: The intersections of which two lines in a phase diagram are related to the cooling curves generated from different compositions? The solvus and the liquidus The solidus and liquidus The solidus and the solvus Solution The intersection of two lines an a phase diagram related to cooloing curves generated from differnet composition is the solidus and the Liquidus. For a cooling curve we start with liquid and then allow it to cool slowly until all the liquid has been converted to solid.

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Match the term with the letter corresponding to the definition in the list below. There are more definitions than terms. Terms ____ Contra Account ____ Carrying Value ____ Deferral Adjustment ____ Closing Journal Entry ____ Net Loss ____ Adjusted Trial Balance ____ Temporary Account ____ Accrual Adjustment Definitions A. When revenue minus expenses is a negative number. B. Adds new values into the balance sheet and income statement accounts. C. Also known as balance sheet accounts. D. Entries made to update existing accounts and record new events. E. The level of profit prior to considering income tax. F. Lists the balances of all accounts to check that revenues equal expenses. G. The amount at which an asset or liability is reported in the financial statements. H. An account that is paired with another account to reduce its book value. I. Lists the balances of all temporary and permanent accounts to check that debits equal credits. J. A journal entry that transfers net income or loss to the retained earnings account. K. Converts some of an asset\'s or liability\'s book value into an expense or revenue. L. An account that must have a zero balance after Closing entries have been made. M. Lists the balances of all permanent accounts to check that debits equal credits. Solution A. When revenue minus expenses is a negative number - NET LOSS Net profit = Revenue - Expense > 0 So, Revenue - Expense < 0 means a Net Loss. B. Adds new values into the balance sheet and income statement accounts - ACCRUAL ADJUSTMENT F. Lists the balances of all accounts to check that revenues equal expenses - TEMPORARY ACCOUNT Also known as Income Statement account G. The amount at which an asset or liability is reported in the financial statements - CARRYING VALUE H. An account that is paired with another account to reduce its book value - CONTRA ACCOUNT For example: Sales returns is a contra-account that reduces sales revenue, or depreciation is a contra-asset account that reduces fixed asset. I. Lists the balances of all temporary and permanent accounts to check that debits equal credits - ADJUSTED TRIAL BALANCE J. A journal entry that transfers net income or loss to the retained earnings account - CLOSING JOURNAL ENTRY K. Converts some of an asset\'s or liability\'s book value into an expense or revenue - DEFERRAL ADJUSTMENT.

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