Riemann Hypothesis

The real part (red) and imaginary part (blue) of the Riemann zeta-function along the critical line Re(s) = 1/2. You can see the first non-trivial zeros at Im(s) = ±14.135, ±21.022 and ±25.011.


The Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics. It has been an open question for almost 150 years, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs.

The Riemann hypothesis (RH) is a conjecture about the distribution of the zeros of the Riemann zeta-function ζ(s). The Riemann zeta-function is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, s = −4, s = −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:

The real part of any non-trivial zero of the Riemann zeta function is ½.

Thus the non-trivial zeros should lie on the so-called critical line, ½ + it, where t is a real number and i is the imaginary unit. The Riemann zeta-function along the critical line is sometimes studied in terms of the Z-function, whose real zeros correspond to the zeros of the zeta-function on the critical line.

The Riemann hypothesis is one of the most important open problems of contemporary mathematics, mainly because a large number of deep and important other results have been proven under the condition that it holds. Most mathematicians believe the Riemann hypothesis to be true. (J. E. Littlewood and Atle Selberg have been reported as skeptical. Selberg's skepticism, if any, waned from his young days. In a 1989 paper, he suggested that an analogue should hold for a much wider class of functions, the Selberg class.) A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof.



A value graph of zeta, that is, Re(zeta) vs. Im(zeta), along the critical line s = it + 1/2, with t running from 0 to 34.

Double Pendulum

In horology, a double pendulum is a system of two simple pendulums on a common mounting which move in anti-phase.

In mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior. The motion of a double pendulum is governed by a set of coupled ordinary differential equations. Above a certain energy its motion is chaotic.



The double pendulum undergoes chaotic motion, and shows a sensitive dependence on initial conditions. The image to the right shows the amount of elapsed time before the pendulum "flips over", as a function of initial conditions.

BSDF

The definition of the BSDF (Bidirectional scattering distribution function) is not well standardized. The term was probably introduced in 1991 by Paul Heckbert. Most often it is used to name the general mathematical function which describes the way in which the light is scattered by a surface. However in practice this phenomenon is usually split into the reflected and transmitted components, which are then treated separately as BRDF (Bidirectional reflectance distribution function) and BTDF (Bidirectional transmittance distribution function).



* BSDF is a superset and the generalization of the BRDF and BTDF. The concept behind all BxDF functions could be described as a black box with the inputs being any two angles, one for incoming (incident) ray and the second one for the outgoing (reflected or transmitted) ray at a given point of the surface. The output of this black box is the value defining the ratio between the incoming and the outgoing light energy for the given couple of angles. The content of the black box may be a mathematical formula which more or less accurately tries to model and approximate the actual surface behavior or an algorithm which produces the output based on discrete samples of measured data. This implies that the function is 4 (+1) dimensional (4 values for 2 3D angles + 1 optional for wave length of the light), which means that it cannot be simply represented by 2D and not even by a 3D graph. Each 2D or 3D graph, sometimes seen in the literature, shows only a slice of the function.

* Some tend to use the term BSDF simply as a category name covering the whole family of BxDF functions.

* The term BSDF is sometimes used in a slightly different context, for the function describing the amount of the scatter (not scattered light), scatter being simply a function of the incident light angle. An example to illustrate this context: for perfectly lambertian surface the BSDF(angle)=const. This approach is used for instance to verify the output quality by the manufacturers of the glossy surfaces.

* Another recent usage of the term BSDF can be seen in some 3D packages, when vendors use it as a 'smart' category to encompass the simple well known cg algorithms like Phong, Blinn etc.

BDRF

The bidirectional reflectance distribution function (BRDF) is a 4-dimensional function that defines how light is reflected at an opaque surface. The function takes an incoming light direction, and outgoing direction, both defined with respect to the surface normal, and returns the ratio of reflected radiance exiting along to the irradiance incident on the surface from direction. Physically based BRDFs have additional restrictions, including Helmholtz reciprocity, and energy conservation. The BRDF has units sr-1, with steradians (sr) being a unit of solid angle.

The BRDF is a fundamental radiometric concept, and accordingly is used in computer graphics for photorealistic rendering of synthetic scenes, as well as in computer vision for many inverse problems such as object recognition.

Piri Reis (1465 – 1554)

Key to the Piri Reis' Map

Piri Reis (full name Hadji Muhiddin Piri Ibn Hadji Mehmed) (about 1465 – 1554 or 1555) was an Ottoman-Turkish admiral and cartographer born between 1465 and 1470 in Gallipoli on the Aegean coast of Turkey.

He is primarily known today for his maps and charts collected in his Kitab-ı Bahriye (Book of Navigation), a book which contains detailed information on navigation as well as extremely accurate charts describing the important ports and cities of the Mediterranean Sea. He gained fame as a cartographer when a small part of his first world map (prepared in 1513) was discovered in 1929 at Topkapı Palace in Istanbul. The most surprising aspect was the presence of the Americas on an Ottoman map, making it the first Turkish map ever drawn of the Americas -- although not the first ever, which was drawn by pilot and cartographer Juan de la Cosa in 1500 and is conserved in the naval museum (Museo Naval) in Madrid.



The most striking characteristic of the first world map (1513) of Piri Reis, however, is the level of accuracy in positioning the continents (particularly the relation between Africa and South America) which was unparalleled for its time. Even maps drawn decades later did not have such accurate positioning and proportions; a quality which can be observed in other maps of Piri Reis in his Kitab-ı Bahriye (Book of Navigation). Piri Reis' map is centered in the Sahara at the Tropic of Cancer latitude, and some believe it's also the oldest surviving map of Antarctica[citation needed], despite being drawn more than 3 centuries before the official discovery of that continent.

In 1528 Piri Reis drew a second world map, of which a small fragment showing Greenland and North America from Labrador and Newfoundland in the north to Florida, Cuba and parts of Central America in the south still survives.

8b/10b

Original paper by Franaszek and Widmer

In telecommunications, 8b/10b is a line code that maps 8-bit symbols to 10-bit symbols to achieve DC-balance and bounded disparity, and yet provide enough state changes to allow reasonable clock recovery. This means that the difference between the count of 1s and 0s in a string of at least 20 bits is no more than 2, and that there are not more than five 1s or 0s in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal.

The code was described in 1983 by Al Widmer and Peter Franaszek in the IBM Journal of Research and Development. IBM was issued a patent for the scheme the following year. IBM's patent notwithstanding, the method, implementation and goals are very similar to Group Code Recording (GCR) used on floppy disks in some computers during late 1970s/early 80s.

Technologies that use 8b/10b

Now that the IBM patent has expired, the scheme has become even more popular and is the default DC-free line code for new standards.

Among the areas in which 8B/10B encoding finds application are

* PCI Express
* IEEE 1394b
* Serial ATA
* SAS
* Fibre Channel
* SSA
* Gigabit Ethernet (except for the twisted pair based 1000Base-T)
* InfiniBand
* XAUI
* Serial RapidIO
* DVI and HDMI (Transition Minimized Differential Signaling)
* DVB Asynchronous Serial Interface (ASI)
* HyperTransport

Anti-satellite

Anti-satellite weapons (ASATs) are space weapons designed to destroy satellites for strategic military purposes. Currently, only the USA, the former USSR and the People's Republic of China are known to have developed these weapons, with India claiming the technical capability to develop such weapons. On January 11, 2007, China destroyed an old orbiting weather satellite, the world's first test since the 1980s.



USA-193 was an American spy satellite, which was launched on 14 December 2006 by a Delta II rocket, from Vandenberg Air Force Base. It was reported about a month after launch that the satellite had failed. In January 2008, it was reported that the satellite was decaying from orbit at a rate of 1,640 feet (500 m) per day. On 14 February 2008, it was reported that the US Navy had been instructed to fire an SM-3 ABM weapon at it, to act as an anti-satellite weapon.

This mission is different from "normal" ASAT operations in that the target vehicle is at a much lower altitude than would normally be the case. However, some analysts believes this is a coincidental, convenient reason for a passive response to the Chinese ASAT test carried out on January 11, 2007.

According to news media, the primary reason for destroying the satellite is the large amount of the highly toxic fuel hydrazine contained on board, which could pose environmental and health risks should any significant amount survive the reentry.

On Febuary 20, 2008, it was announced that the launch was carried out successfully and an explosion was observed consistent with the destruction of the hydrazine fuel tank.

WINDS

WINDS / Kizuna

WINDS (Wideband InterNetworking engineering test and Demonstration Satellite, also known as Kizuna), is a Japanese communication satellite. Launch was originally scheduled for 2007. The launch date was eventually set for 15 February 2008, however a problem detected in a second stage manoeuvring thruster delayed it to 23 February. Lift-off occurred at 08:55 GMT on 23 February, and the satellite separated from the carrier rocket, into a Geosynchronous transfer orbit at 09:23, launched by an H-IIA carrier rocket from the Tanegashima Space Centre. It will be used to relay the internet to Japanese homes and businesses, through Ka-Band signals. It will also develop technologies to be utilised by future Japanese communication spacecraft. It is part of Japan's i-Space programme, and is to be operated by JAXA and NICT.

JAXA claim that WINDS will be able to provide 155 Mb/s download speed to home users with 45-centimetre diameter satellite dishes, whilst providing industrial users, via 5-metre diameter dishes, with 1.2 Gb/s speeds.

WINDS has a launch mass of 4,850 kg, reducing to around 2,750 kg when in orbit. The spacecraft is 8 m x 3 m x 2 m in size, and its solar panels have a span of 21.5 metres. It has three-axis stabilisation, and a design life expectancy of five years.

KIZUNA will lead to ultra-high speed international Internet-based communications. The technology takes advantage of the fact that satellite communications are far-reaching, multicasting, and disaster-resistant. It will enable high-speed, large-volume data transmission, allowing ultra-fast domestic and international Internet-based communications, in particular between Japan and its neighboring countries in the Asia-Pacific region.
Ultra-fast satellite-based Internet-based communications will remove the so-called digital divide by providing high-speed Internet service in areas where the terrestrial communications infrastructure is poor. Among other uses, this will make possible great advances in telemedicine, which will bring high-quality medical treatment to remote areas, and in distance education, connecting students and teachers separated by great distances.

Project Constellation

NASA Project Constellation

Project Constellation is a NASA program to create a new generation of spacecraft for human spaceflight, consisting primarily of the Ares I and Ares V launch vehicles, the Orion crew capsule, the Earth Departure Stage and the Altair lunar lander. These spacecraft will be capable of performing a variety of missions, from Space Station resupply to lunar landings.

Most of the Constellation hardware is based on systems originally developed for the Space Shuttle, although Orion's two-part crew and service module system is heavily influenced by the earlier Apollo Spacecraft, and it uses engines derived from the Saturn V and Delta IV rockets. Proposed Constellation missions may employ both Earth Orbit Rendezvous and Lunar Orbit Rendezvous techniques.

Constellation Program

NASA has formed the Constellation Program to achieve the objectives of maintaining American presence in low Earth orbit, returning to the Moon for purposes of establishing an outpost, and laying the foundation to explore Mars and beyond in the first half of the 21st century. The Constellation Program's heritage rests on the successes and lessons learned from NASA’s previous human spaceflight programs: Mercury, Gemini, Apollo, Space Shuttle and the International Space Station (ISS).

Spacecraft

Orion will consist of two main parts, a Crew Module (CM) similar to the Apollo Command Module capable of holding four to six crew members, and a cylindrical Service Module (SM) containing the primary propulsion systems and consumable supplies. The Orion CM will be reusable for up to 10 flights, allowing NASA to construct a fleet of Orion CMs.

Current plans call for the phased introduction of Orion variants tailored for specific missions. The Block I Orion will be employed for ISS crew rotation and resupply and other Earth orbit missions, while the Block II and III variants will be designed for deep-space exploration.

Launch vehicles

As currently envisioned, the Orion spacecraft will be launched into a low earth orbit using the proposed Ares I rocket (the "Stick"). Formerly referred to as the Crew Launch Vehicle (CLV), the Ares I consists of a single Solid Rocket Booster (SRB) derived from the boosters used in the Space Shuttle system, connected at its upper end by an interstage support assembly to a new liquid-fueled second stage powered by an uprated Apollo-era J-2X rocket engine. The Orion spacecraft would be lifted into orbit atop this "stack", while a larger launch vehicle (the proposed Ares V) would be used to launch the heavier Earth Departure Stage and Altair.

In January 2007, NASA announced that a different launch vehicle design, the Ares IV, was actively under consideration for the program. If chosen, the Ares IV might replace both the Ares I and the Ares V launch vehicles for some Constellation launches at later dates, or all of them altogether.

Lockheed YF-12

National Museum of USAF Lockheed YF-12

The Lockheed YF-12 was an American prototype interceptor aircraft, which the United States Air Force evaluated as a development of the CIA's highly-secret A-12 OXCART that also spawned the now-famous SR-71 Blackbird.

Design and development

The United States Air Force (USAF) YF-12 program was a development of the Lockheed A-12 OXCART spy plane designed for the CIA and first flown 26 April 1962, the first YF-12A flew on 7 August 1963. The existence of the aircraft was not officially revealed until 29 February 1964. Lockheed was able to interest the Air Force in the project after the United States Air Force had been forced to cancel the XF-108 Rapier, a Mach 3-capable interceptor intended to replace the F-106 Delta Dart in service. It was pointed out that an aircraft based on the A-12 would provide a less costly alternative to the XF-108, since much of the design and development work on the YF-12 had already been done and paid for. In 1960, the USAF agreed to take the 11th through 13th slots on the A-12 production line and have them completed in the YF-12A interceptor configuration.

The main changes involved modifying the aircraft's nose to accommodate the Hughes AN/ASG-18 fire-control radar originally developed for the XF-108, and the addition of a second cockpit for a crewmember to operate the fire control radar. The nose modifications changed the aircraft's aerodynamics enough to require ventral fins to be mounted under the fuselage and engine nacelles to maintain stability. Finally, bays previously used to house the A-12's reconnaissance equipment were converted to carry four Hughes AIM-47A (GAR-9) missiles.

SPECIFICATIONS:

Span: 55 ft. 7 in.
Length: 101 ft.
Height: 18 ft. 6 in.
Weight: 127,000 lbs. loaded
Armament: Three Hughes AIM-47A missiles
Engines: Two Pratt & Whitney J58s of 32,000 lbs. thrust each with afterburner
Crew: Two

PERFORMANCE:
Maximum speed: Mach 3+
Range: 2,000+ miles
Service ceiling: Above 80,000 ft.

Ghost In The Shell SAC: SSS

Kôkaku kidôtai: Stand Alone Complex Solid State Society

Production I.G. GITS SAC SSS

Manga GITS SAC SSS

Ghost in the Shell: S.A.C. Solid State Society (S.A.C. Solid State Society, Kōkaku Kidōtai: Solid State Society) is the 2006 anime film based on the Ghost in the Shell: Stand Alone Complex series, which is based on Masamune Shirow's manga Ghost in the Shell. It was produced by Production I.G, who announced the film at the 2006 Tokyo Anime Fair, and was directed by Kenji Kamiyama.

In order to provide theatrical quality, the film premiered on the Japanese satellite PPV platform SKY PerfecTV! Perfect Choice ch160, on September 1, 2006. It also aired in Japan on the anime satellite TV network Animax starting May 27, 2007. The film was also released on DVD in Japan on November 24, 2006 and was released in the U.S. by Bandai Entertainment and Manga Entertainment, in a normal and limited edition on July 3, 2007. It was announced at Anime Expo 2006 that Solid State Society is not scheduled to be the final iteration of the Stand Alone Complex series.

A.D. 2034. It has been two years since Motoko Kusanagi left Section 9. Togusa is now the new leader of the team, that has considerably increased its appointed personnel. The expanded new Section 9 confronts a rash of complicated incidents, and investigations reveal that an ultra-wizard hacker named the Puppeteer is behind the entire series of events.

In the midst of all, Batou, who was stalking the case on a separate track, encounters Motoko. She goes away after saying, "Stay away from the Solid State Society." Batou is left with a doubt in his mind. Could Motoko be the the Puppeteer?

The series of intriguing incidents that Section 9 faces gradually link together almost artistically. Who is the Puppeteer? What will happen to Batou's relationship with Motoko? What is the full truth behind this carefully planned perfect crime? And what will the outcome be? Mysteries surround the Solid State Society...

i386

Intel Museum

i386 at CPU-Info

The Intel386 is a microprocessor which has been used as the central processing unit (CPU) of many personal computers since 1986. During its design phase the processor was code-named simply "P3", the third-generation processor in the x86 line, but is normally referred to as either i386 or just 386. The 80386 operated at about 5 million instructions per second (MIPS) to 11.4 MIPS for the 33 MHz model. It was the first x86 processor to have a 32-bit architecture, with a basic programming model that has remained virtually unchanged for over twenty years and remains completely backward compatible. Successively newer implementations of this same architecture have become literally several hundred times faster than the original i386 chip during these years.

Designed and manufactured by Intel, the i386 processor was taped-out in October of 1985. Intel decided against producing the chip before that date, as the cost of production would have been uneconomical. Full-function chips were first delivered to customers in 1986. Motherboards for 386-based computer systems were highly elaborate and expensive to produce, but were rationalized upon the 386's mainstream adoption. The first personal computer to make use of the 386 was designed and manufactured by Compaq, and Andy Grove, Intel's CEO at the time, made the decision to single-source the processor, a decision that was ultimately crucial to both the processor's and Intel's success in the market.

The range of processors compatible with the 80386 is often collectively termed x86 or the i386 architecture; today, Intel prefers the name IA-32 however.

In May 2006 Intel announced that production of the 386 would cease at the end of September 2007. Although it had long been obsolete as a personal computer CPU, Intel, and others, had continued to manufacture the chip for embedded systems, including aerospace.