Fractal Geometry

Hmm,...what a beautiful topic???
till mr.ikhsan said to Lia, "i deal with this title and i'll guide it!" without think a second, ogh,.!

it's different when i show mine,..
vector differentiation of square form !
mr. ikhsan ask me to explain--again and again--before deal, need long argument and sweat to fight it. finally, he said okey,..and you'll be guided by mrs. erni !

fiuhhh,..Alhamdulillah,..!
i hav headache again and again when looked for the title for my colloquium class.

ok,.today i'll share u some about fractals, check it out!

Fractals

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.

Roots of mathematical interest on fractals can be traced back to the late 19th Century, the term however was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.

A fractal often has the following features:

* It has a fine structure at arbitrarily small scales.
* It is too irregular to be easily described in traditional Euclidean geometric language.
* It is self-similar (at least approximately or stochastically).
* It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
* It has a simple and recursive definition.

Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms).
Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, even various vegetables (cauliflower and broccoli).
However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.

Generating fractals

Four common techniques for generating fractals are:

* Escape-time fractals – (also known as "orbits" fractals) These are defined by a formula or recurrence relation at each point in a space (such as the complex plane). Examples of this type are the Mandelbrot set, Julia set, the Burning Ship fractal, the Nova fractal and the Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escape-time formulae also give rise to a fractal form when points (or pixel data) are passed through this field repeatedly.

* Iterated function systems – These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Highway dragon curve, T-Square, Menger sponge, are some examples of such fractals.

* Random fractals – Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters.

* Strange attractors – Generated by iteration of a map or the solution of a system of initial-value differential equations that exhibit chaos.

In Nature

Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range.
Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels.
Coastlines may be loosely considered fractal in nature.

Hmm,...i think it's hard to prove in math formula.
ok,..that's all for this shine monday,.many thanks to wikipedia !

see ya,..^o^ !

Accounting Basic Info

Hi guys,..how hav u been?!
today i wanna share u some basic info of accounting.
hopefully useful !

Accountancy
or accounting is the art of communicating financial information about a business entity to users such as shareholders and managers. The communication is generally in the form of financial statements that show in money terms that show the economic resources under the control of management.

Etymology
The English term accountant is derived from accomptant, which was pronounced by dropping the 'p' and over time further changed in pronunciation and spelling. Accomptant was derived from the French compter, itself originating from the Latin computare. From the word accountant the term accountancy is derived.

Types of accounting
* Financial accounting is "a major branch of accounting involving the collection, recording and extraction of financial information, and the summary of it in the form of a periodic profit and loss account, a balance sheet and a cash flow statement in accordance with legal, professional, and capital market requirements".
* Management accounting is another branch of accounting performed within an organization to provide information only accessible to its decision-makers.
* Open-book accounting is an accounting principle that aims to improve accounting transparency of organizations.
* Tax accounting is the accounting needed to comply with jurisdictional tax regulations.
* Accounting scholarship is the academic discipline which studies the theory of accountancy.

The related, but separate financial audit comprises internal audit and external audit. External audit—carried out by independent auditors—examines the financial statements and accounting records in order to express an opinion as to the truth and fairness and adherence to Generally Accepted Accounting Principles (GAAP). Commonly used GAAP include the US Financial Accounting Standards Board (FASB), which issues FASB Pronouncements including Statements of Accounting Standards, and the International Accounting Standards Board (IASB), which issues International Financial Reporting Standards (IFRS). Many other countries have instituted local standards resulting in a local country GAAP. Internal audit aims at providing information for management usage, and is typically carried out by employees.

Accounting scandals
The year 2001 witnessed a series of financial information frauds involving Enron Corporation, auditing firm Arthur Andersen, the telecommunications company WorldCom, Qwest and Sunbeam, among other well-known corporations. These problems highlighted the need to review the effectiveness of accounting standards, auditing regulations and corporate governance principles. In some cases, management manipulated the figures shown in financial reports to indicate a better economic performance. In others, tax and regulatory incentives encouraged over-leveraging of companies and decisions to bear extraordinary and unjustified risk.

The Enron scandal deeply influenced the development of new regulations to improve the reliability of financial reporting, and increased public awareness about the importance of having accounting standards that show the financial reality of companies and the objectivity and independence of auditing firms.

In addition to being the largest bankruptcy reorganization in American history, the Enron scandal undoubtedly is the biggest audit failure.The scandal caused the dissolution of Arthur Andersen, which at the time was one of the five largest accounting firms in the world.It involved a financial scandal of Enron Corporation and their auditors Arthur Andersen, which was revealed in late 2001. After a series of revelations involving irregular accounting procedures conducted throughout the 1990s, Enron filed for Chapter 11 bankruptcy protection in December 2001

One consequence of these events was the passage of Sarbanes-Oxley Act in 2002, as a result of the first admissions of fraudulent behavior made by Enron. The act significantly raises criminal penalties for securities fraud, for destroying, altering or fabricating records in federal investigations or any scheme or attempt to defraud shareholders.

Hmm....that's all for now, many thanks to wikipedia.

ok,.see ya!