Formally definition

Formally means without speech or comment.
Formally means here that the proof requires conver- gence of any simple integral to the exchange of integra- tion order by the Fubinis theorem [4].
Formally means that we ignore the mathematical niceties of verifying that we can differentiate the function v by differentiating the terms in the infinite series. D D Referring back to our original initial/boundary value problem in (2.5), we see that the function v defined in (2.14) satisfies everything except the initial condition v.x; 0/ g.x/ f .x/ us .x/: However, we have yet to determine the coefficients bn. Using the series definition for v in (2.14), the initial condition becomes 1X g.x/ D v.x; 0/ D bn sinnD1n xL ; for 0 x L: (2.15)LEquation (2.15) will be recognized as the Fourier sine expansion for the initial tem- perature g. According to Section 12.3, and in particular equation (3.7), the values of bn are given by20bn D L Zg.x/ sin n xL dx: (2.16)Substituting these values into (2.14) gives a complete solution to the homoge-neous initial/boundary value problem in (2.5). As indicated previously, the functionD Cu.x; t/ us .x/ v.x; t/ satisfies the original initial/boundary value problem in equations (2.1), (2.2), and (2.3). DEXAMPLE 2.17 ◆ Suppose a rod of length 1 meter (100cm) is originally at 0ÆC. Starting at time t 0, one end is kept at the constant temperature of 100ÆC, while the other is kept at 0ÆC. Find the temperature distribution in the rod as a function of time and position.Assume that the thermal diffusivity of the rod is k D 1 cm2=sec.DIf we use the meter as the unit of length, then k 0:0001 m2/sec. The temper- ature in the rod, u.x; t/, must solve the initial/boundary value problemut .x; t/ D 0:0001 ux x.x; t/; for t > 0 and 0 < x < 1,u.0; t/ D 0 and u.1; t/ D 100; for t > 0,u.x; 0/ D 0; for 0 x 1.(2.18)

Examples of Formally in a sentence

  • Formally, the statutory responsibility of Controller is assigned to the Board of Management.

  • Formally opened the quarantine facilities at San Andres Sports Complex, P.

  • Formally advertise the bid in a newspaper of general circulation for at least seven full days between the date of the advertisement and the date of the public bid opening.

  • Supportive Work Environment 1115 Workplace Violence: Prevention and Response (Formally Workplace Abuse and Harassment) The policy outlines the process for reporting and investigating workplace violence allegations.

  • Formally identical or formally different treatment shall be considered to be less favourable if it modifies the conditions of competition in favour of services or service suppliers of a Party compared to like services or service suppliers of the other Party.

  • Formally identical or formally different treatment shall be considered to be less favourable if it modifies the conditions of competition in favour of services or service suppliers of the Party compared to like services or service suppliers of any other Party.

  • Formally identical or formally different treatment shall be considered to be less favourable if it modifies the conditions of competition in favour of services or service suppliers of the Party compared to like services or service suppliers of the other Party.

  • SECNAV Formally Names USS Tripoli,” Navy News Service, June 2, 2014.

  • Formally listed in the State or Tribal register of historic places of the SHPO (designated under section 101(b)(1)(B) of the NHPA) or the THPO (designated under section 101(d)(1)(C) of the NHPA).

  • Formally, we have thatp lim ؈= p lim Øˆ× ‡ Cov (Odmjt, Opjt—fi) = p lim Øˆ× ‡ bsa‹V (Opjt—fi)bsa‹ = Cov (Odmjt, Opjt—fi) c 0V (Opjt—fi)The bias is due to changes in switching consumers as a response to price changes, and is therefore related to ç×.


More Definitions of Formally

Formally means that in order to stay within the limits of applicability of perturbation theory we have to cut off the sum in Eq. (26) at a certain value of n = n∗.

Related to Formally

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  • Preschool means a program licensed to offer early childhood services, which follows a preschool curriculum and course of study designed primarily to enhance the educational development of the children enrolled and which serves no child for more than three hours per day.

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