Fresnel integral

Fresnel integrals, S(x) and C(x), are two transcendental functions named after Augustin-Jean Fresnel that are used in optics, which are closely related to the error function (erf). They arise in the description of far field Fresnel diffraction phenomena, and are defined through the following integral representations:

The simultaneous parametric plot of S(x) and C(x) is the Euler spiral (also known as the Cornu spiral or clothoid). Recently, they have been used in the design of highways and other engineering projects.

Definition

The Fresnel integrals admit the following power series expansions that converge for all x:

Some authors, including Abramowitz and Stegun, (eqs 7.3.1 – 7.3.2) use for the argument of the integrals defining S(x) and C(x). To get these functions, multiply the above integrals by and multiply the argument x by .

Euler spiral

The Euler spiral, also known as Cornu spiral or clothoid, is the curve generated by a parametric plot of S(t) against C(t). The Cornu spiral was created by Marie Alfred Cornu as a nomogram for diffraction computations in science and engineering.

SX

SX, Sx, or sx may refer to:S

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IBM System z9

IBM System z9 is a line of IBM mainframe computers. The first models were available on September 16, 2005. The System z9 also marks the end of the previously used eServer zSeries naming convention. It was also the last mainframe computer that NASA ever used.

Background

System z9 is a mainframe using the z/Architecture, previously known as ESAME. z/Architecture is a 64-bit architecture which replaces the previous 31-bit-addressing/32-bit-data ESA/390 architecture while remaining completely compatible with it as well as the older 24-bit-addressing/32-bit-data System/360 architecture. The primary advantage of this arrangement is that intensive applications like DB2 are no longer bounded by 31-bit memory restrictions while older applications can run without modifications.

Name change

With the announcement of the System z9 Business Class server, IBM has renamed the System z9 109 as the System z9 Enterprise Class server. IBM documentation abbreviates them as the z9 BC and z9 EC, respectively.

Securities Act of 1933

The United States Congress enacted the Securities Act of 1933 (the 1933 Act, the Securities Act, the Truth in Securities Act, the Federal Securities Act, or the '33 Act, Title I of Pub. L. 73-22, 48 Stat. 74, enacted May 27, 1933, codified at 15 U.S.C. § 77a et seq.), in the aftermath of the stock market crash of 1929 and during the ensuing Great Depression. Legislated pursuant to the interstate commerce clause of the Constitution, it requires that any offer or sale of securities using the means and instrumentalities of interstate commerce be registered with the SEC pursuant to the 1933 Act, unless an exemption from registration exists under the law. "Means and instrumentalities of interstate commerce" is extremely broad, and it is virtually impossible to avoid the operation of this statute by attempting to offer or sell a security without using an "instrumentality" of interstate commerce. Any use of a telephone, for example, or the mails, would probably be enough to subject the transaction to the statute.

Regulation S-X

Regulation S-X is a prescribed regulation that lays out the specific format and content of financial reports. It is cited as 17 C.F.R. Part 210; the name of the part is "Form and Content of and Requirements for Financial Statements, Securities Act of 1933, Securities Exchange Act of 1934, Public Utility Holding Company Act of 1935, Investment Company Act of 1940, Investment Advisers Act of 1940, and Energy Policy and Conservation Act of 1975".

Regulation S-X and the Financial Reporting Releases (Staff Accounting Bulletins) set forth the form and content of and requirements for financial statements required to be filed as a part of (a) registration statements under the Securities Act of 1933 and (b) registration statements under section 12, annual or other reports under sections 13 and 15(d) and proxy and information statements under section 14 of the Securities Exchange Act of 1934; except as otherwise specifically provided in the forms.

Regulation S-X is seen less frequently but equally validly for (c) registration statements, annual reports and shareholder reports filed under the Public Utility Holding Company Act of 1935 and likewise for (d) the Investment Company Act of 1940.