Ernests Fogels was a Latvian mathematician who specialized in number theory. Fogels discovered new proofs of the Gauss-Dirichlet formula on the number of classes of positively definite quadratic forms and of the de la Vallée-Poussin formula for the asymptotic location of prime numbers in an arithmetic progression. Fogels was born on 12 October 1910 in Lidzibas, Saldus, Latvia, he discovered his interests in mathematics. In 1928 E. Fogels entered the Faculty of Natural Sciences of University of Latvia. After graduating in 1933, he was invited in 1935 to join this university to lecture in algebra and number theory and did research on Diophantine equations. At the end of 1938 he went to University of Cambridge, England to work under the supervision of Albert E. Ingham to help improving the estimate of the difference between two consecutive primes. World war II broke out after Fogels had returned to Latvia in 1939. In 1940, E. Fogels was appointed associate professor at University of Latvia. In 1947 he defended his PhD thesis on the sequences of asymptotically uniformly distributed numbers and went to work at the newly formed Institute of Physics and Mathematics of the Academy of Sciences of the Latvian SSR as a research fellow.
In 1950 he started working at the Riga Pedagogical Institute where he had no time for research. In 1961 he became a research fellow at the Radioastrophysical Observatory of the Academy of Sciences of the Latvian SSR, his research focused on the density of zeros of different zeta-functions, on the distribution of primes in arithmetical progressions, on various algebraic fields and on binary and ternary quadratic forms. Fogels retired in 1966 but continued his scientific work with research on the Hecke's L-functions, prime ideals and the Riemann hypothesis until his death on 22 February 1985 in Latvia. L Reizins, E Riekstins, E K Fogels, Latvijskij Matematičeskij Ežegodnik, No. 30, 3-8. "Ernests Fogels biography". Www-history.mcs.st-and.ac.uk. Retrieved 2019-01-12. Ernests Fogels at zbMATH
In business, amortization refers to spreading payments over multiple periods. The term is used for two separate processes: amortization of loans and amortization of assets. In the latter case it refers to allocating the cost of an intangible asset over a period of time. In lending, amortization is the distribution of loan repayments into multiple cash flow installments, as determined by an amortization schedule. Unlike other repayment models, each repayment installment consists of both interest. Amortization is chiefly used in sinking funds. Payments are divided into equal amounts for the duration of the loan, making it the simplest repayment model. A greater amount of the payment is applied to interest at the beginning of the amortization schedule, while more money is applied to principal at the end, it is known as EMI or Equated Monthly Installment. P = A ⋅ 1 − n r or, equivalently, A = P ⋅ r n n − 1 where: P is the principal amount borrowed, A is the periodic amortization payment, r is the periodic interest rate divided by 100, n is the total number of payments.
Negative amortization occurs. The remaining interest owed is added to the outstanding loan balance, making it larger than the original loan amount. If the repayment model for a loan is "fully amortized" the last payment pays off all remaining principal and interest on the loan. If the repayment model on a loan is not amortized the last payment due may be a large balloon payment of all remaining principal and interest. If the borrower lacks the funds or assets to make that payment, or adequate credit to refinance the balance into a new loan, the borrower may end up in default. In accounting, amortization refers to expensing the acquisition cost minus the residual value of intangible assets in a systematic manner over their estimated "useful economic lives" so as to reflect their consumption and obsolescence, or other decline in value as a result of use or the passage of time. Depreciation is a corresponding concept for tangible assets. Methodologies for allocating amortization to each accounting period are the same as these for depreciation.
However, many intangible assets such as goodwill or certain brands may be deemed to have an indefinite useful life and are therefore not subject to amortization. While theoretically amortization is used to account for the decreasing value of an intangible asset over its useful life, in practice many companies will amortize what would otherwise be one-time expenses through listing them as a capital expense on the cash flow statement and paying off the cost through amortization, having the effect of improving the company's net income in the fiscal year or quarter of the expense. Amortization is recorded in the financial statements of an entity as a reduction in the carrying value of the intangible asset in the balance sheet and as an expense in the income statement. Under International Financial Reporting Standards, guidance on accounting for the amortization of intangible assets is contained in IAS 38. Under United States accepted accounting principles, the primary guidance is contained in FAS 142