# Our Schemes

Climate change, Environmental contaminants and Reproductive Health. Velocity is the time derivative of position.

## Lista dei programmi ai quali afferiscono i progetti ENEA

Judaism has had a long history in Europe and has coexisted with the other religions for centuries, despite periods of persecution or genocide by European rulers. Islam too has had a long history in Europe, with Spain and Portugal at one time having a Muslim majority. The first official language of each of the 28 Member Countries has the status of an official language of the European Union. In total there are 24, with Irish , Bulgarian and Romanian gaining official language status on 1 January , when the last two countries joined the European Union, and Croatian becoming official in The EU faces challenges in its demographic future.

Most concerns center around several related issues: After hitting a historical low of 1. The largest increases over this period were observed in Bulgaria from 1. The increasing fertility rate has also been accompanied by an upward trend in the natural increase of the population which is due to the moderate increase of the crude birth rate that reached The increase was observed in all member countries except Germany.

The EU crude death rate remained stable at 9. The EU faces a potential future dominated by an ever-increasing population of retired citizens, without enough younger workers to fund via taxes retirement programs or other state welfare agendas.

A low fertility rate, without supplement from immigration, also suggests a declining overall EU population, [26] which further suggests economic contraction or even a possible economic crisis. In , a breakdown of the population by citizenship showed that there were Over the last 50 years, life expectancy at birth in the EU27 has increased by around 10 years for both women and men, to reach The life expectancy at birth rose in all Member States, with the largest increases for both women and men recorded in Estonia and Slovenia.

The table figures below are in thousands. There is no precise or universally accepted definition of the terms "ethnic group" or "nationality". In the context of European ethnography in particular, the terms ethnic group , people without nation state , nationality , national minority , ethnic minority , linguistic community , linguistic group and linguistic minority are used as mostly synonymous, although preference may vary in usage with respect to the situation specific to the individual countries of Europe.

The rest are various smaller ethnic groups include Hungary c. On current trends European populations will become more ethnically diverse, with the possibility that today's majority ethnic groups will no longer comprise a numerical majority in some countries.

The number of foreign-born which includes those who have naturalised or are dual nationals was A total of 8. The next biggest group was from Africa Romanians living in another EU Member State and Turkish citizens made up the biggest groups of non-nationals living in the EU in The third largest group was Moroccans 1. Live Births outside marriage: From Wikipedia, the free encyclopedia.

Immigration to Europe and Emigration from Europe. Religion in the European Union. Languages of the European Union. This is the right-hand rule. For arbitrary choices of spatial orientation that is, allowing for left-handed as well as right-handed coordinate systems the cross product of two vectors is a pseudovector instead of a vector see below.

The scalar triple product also called the box product or mixed triple product is not really a new operator, but a way of applying the other two multiplication operators to three vectors. The scalar triple product is sometimes denoted by a b c and defined as:. It has three primary uses. First, the absolute value of the box product is the volume of the parallelepiped which has edges that are defined by the three vectors. Second, the scalar triple product is zero if and only if the three vectors are linearly dependent , which can be easily proved by considering that in order for the three vectors to not make a volume, they must all lie in the same plane.

Third, the box product is positive if and only if the three vectors a , b and c are right-handed. In components with respect to a right-handed orthonormal basis , if the three vectors are thought of as rows or columns, but in the same order , the scalar triple product is simply the determinant of the 3-by-3 matrix having the three vectors as rows.

The scalar triple product is linear in all three entries and anti-symmetric in the following sense:. However, a vector can be expressed in terms of any number of different bases that are not necessarily aligned with each other, and still remain the same vector. In the e basis, a vector a is expressed, by definition, as.

The values of p , q , r , and u , v , w relate to the unit vectors in such a way that the resulting vector sum is exactly the same physical vector a in both cases.

It is common to encounter vectors known in terms of different bases for example, one basis fixed to the Earth and a second basis fixed to a moving vehicle. In such a case it is necessary to develop a method to convert between bases so the basic vector operations such as addition and subtraction can be performed. One way to express u , v , w in terms of p , q , r is to use column matrices along with a direction cosine matrix containing the information that relates the two bases.

Such an expression can be formed by substitution of the above equations to form. This matrix equation relates the scalar components of a in the n basis u , v , and w with those in the e basis p , q , and r. Each matrix element c jk is the direction cosine relating n j to e k.

By referring collectively to e 1 , e 2 , e 3 as the e basis and to n 1 , n 2 , n 3 as the n basis, the matrix containing all the c jk is known as the " transformation matrix from e to n ", or the " rotation matrix from e to n " because it can be imagined as the "rotation" of a vector from one basis to another , or the " direction cosine matrix from e to n " [13] because it contains direction cosines.

The properties of a rotation matrix are such that its inverse is equal to its transpose. This means that the "rotation matrix from e to n " is the transpose of "rotation matrix from n to e ". The properties of a direction cosine matrix, C are [14]:. The advantage of this method is that a direction cosine matrix can usually be obtained independently by using Euler angles or a quaternion to relate the two vector bases, so the basis conversions can be performed directly, without having to work out all the dot products described above.

By applying several matrix multiplications in succession, any vector can be expressed in any basis so long as the set of direction cosines is known relating the successive bases. With the exception of the cross and triple products, the above formulae generalise to two dimensions and higher dimensions.

For example, addition generalises to two dimensions as. The cross product does not readily generalise to other dimensions, though the closely related exterior product does, whose result is a bivector.

In two dimensions this is simply a pseudoscalar. A seven-dimensional cross product is similar to the cross product in that its result is a vector orthogonal to the two arguments; there is however no natural way of selecting one of the possible such products. In abstract vector spaces, the length of the arrow depends on a dimensionless scale. Thus there is typically consistency in scale among quantities of the same dimension, but otherwise scale ratios may vary; for example, if "1 newton" and "5 m" are both represented with an arrow of 2 cm, the scales are 1 m: Equal length of vectors of different dimension has no particular significance unless there is some proportionality constant inherent in the system that the diagram represents.

Often in areas of physics and mathematics, a vector evolves in time, meaning that it depends on a time parameter t. For instance, if r represents the position vector of a particle, then r t gives a parametric representation of the trajectory of the particle. Vector-valued functions can be differentiated and integrated by differentiating or integrating the components of the vector, and many of the familiar rules from calculus continue to hold for the derivative and integral of vector-valued functions.

The length of this vector gives the straight-line distance from x to y. Displacement has the dimensions of length. The velocity v of a point or particle is a vector, its length gives the speed. For constant velocity the position at time t will be.

Velocity is the time derivative of position. Acceleration a of a point is vector which is the time derivative of velocity. Work is the dot product of force and displacement. A vector may also be defined as a directional derivative: Therefore, any directional derivative can be identified with a corresponding vector, and any vector can be identified with a corresponding directional derivative.

A vector can therefore be defined precisely as. An alternative characterization of Euclidean vectors, especially in physics, describes them as lists of quantities which behave in a certain way under a coordinate transformation.

A contravariant vector is required to have components that "transform opposite to the basis" under changes of basis. The vector itself does not change when the basis is transformed; instead, the components of the vector make a change that cancels the change in the basis.

In other words, if the reference axes and the basis derived from it were rotated in one direction, the component representation of the vector would rotate in the opposite way to generate the same final vector.

Similarly, if the reference axes were stretched in one direction, the components of the vector would reduce in an exactly compensating way. This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities. For example, if v consists of the x , y , and z -components of velocity , then v is a contravariant vector: On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract vector , but this vector would not be contravariant, since rotating the box does not change the box's length, width, and height.

Examples of contravariant vectors include displacement , velocity , electric field , momentum , force , and acceleration. In the language of differential geometry , the requirement that the components of a vector transform according to the same matrix of the coordinate transition is equivalent to defining a contravariant vector to be a tensor of contravariant rank one.

Alternatively, a contravariant vector is defined to be a tangent vector , and the rules for transforming a contravariant vector follow from the chain rule. Some vectors transform like contravariant vectors, except that when they are reflected through a mirror, they flip and gain a minus sign. A transformation that switches right-handedness to left-handedness and vice versa like a mirror does is said to change the orientation of space.

A vector which gains a minus sign when the orientation of space changes is called a pseudovector or an axial vector. Ordinary vectors are sometimes called true vectors or polar vectors to distinguish them from pseudovectors.

Pseudovectors occur most frequently as the cross product of two ordinary vectors. One example of a pseudovector is angular velocity. Driving in a car , and looking forward, each of the wheels has an angular velocity vector pointing to the left. If the world is reflected in a mirror which switches the left and right side of the car, the reflection of this angular velocity vector points to the right, but the actual angular velocity vector of the wheel still points to the left, corresponding to the minus sign.

Other examples of pseudovectors include magnetic field , torque , or more generally any cross product of two true vectors. This distinction between vectors and pseudovectors is often ignored, but it becomes important in studying symmetry properties. From Wikipedia, the free encyclopedia. Redirected from Vector geometric. This article is about the vectors mainly used in physics and engineering to represent directed quantities. For mathematical vectors in general, see Vector mathematics and physics.

For other uses, see Vector disambiguation. Affine space , which distinguishes between vectors and points Array data structure or Vector Computer Science Banach space Clifford algebra Complex number Coordinate system Covariance and contravariance of vectors Four-vector , a non-Euclidean vector in Minkowski space i. For historical development of the word vector , see "vector n. Oxford English Dictionary 3rd ed.

We have not found a replacement. There are a couple of websites that have photo essays on doing 'micro-surgery' on them, but it's very difficult, time consuming with sketchy results. Probably the most practical way to address the issue with the balance pot is to 'jumper' across it. It can either be left in place or removed once jumpered. The same 'fix' can be utilized on the 'Headphone' level pot, then simply use the main volume of the pre-amp to control the headphone level like EVERY other unit does.

Would match up well with any power amp and is very "utilitarian". Loaded with "real world" features. Again, with the exception of the 'bypassed balance control', the unit works well and sounds great! Cosmetically the only issue really worth mentioning is that the top, metal cover has scratches from someone sitting a unit with no feet on it and moving it around. Kenwood C2 Features include: MC carts require an extra head-amp and this amplifier has one built in - Built-in Low and Subsonic Filters to eliminate excess rumble from sources such as turntables.

It's simply hard to beat for specs, features and performance. That is also evidenced by the fact that it was current in Kenwood's lineup, as their upper end pre, for almost half a decade.

Again, we have completely gone through the unit cleaning all contacts, pots, switches and controls. All functions again, with the exception of the 'Balance' control' test as original.

Unit looks and sounds great! Comes with original owners manual and includes our 90 day limited warranty. While it has been cleaned and lubed, it will not 'lock in' so consider there's no 'Hi-Filter' on this one yes, the circuitry still functions, but was not practical for use to source a replacement switch on this unit with the other two issues.

Also, as the 'Balance' and 'Headphone Level' are 'non-functional', we inserted hole plugs where the knobs would be the pots are still there if anyone wants to attempt a repair in the future. GREAT sounding as well. Kenwood C-1 Features include: Perfect for basic control of system. Amp designed using Huge Power Supply Transformer and super quality expensive filter caps.

This amplifier is in both great electronic and physical shape. Following restoration procedures, we burned it in, in the shop at continuous high volume for 8 hours straight and it functioned flawlessly. Technician's note; "this amp was final evolution of the DH's. Idle AC current draw. Super quiet operation and build quality. We run it's little brother in our main demo system and have for years. This circuit configuration results in excellent front-end headroom and a simple, straightforward connection to the remainder of the circuitry.

The cascade stage is connected to an emitter-follower and current mirror configuration that amplifies the current level about ten times, necessary to drive the biasing string and final output stage driver emitter followers. Thermal runaway is a phenomenon whereby a transistor heats up as it conducts more current, which causes it to get hotter, and conduct more current, and so on, until the device self-destructs.

Conversion to Mono Mode is accomplished by driving the negative input feedback point of the right channel with the output of the left channel. This causes the right channel to mirror exactly the output of the left channel, but degrees out of phase. This creates twice the voltage swing to be available across the two red output binding posts.

This simple method of bridging the amplifier involving only one resistor eliminates the costly and sonically degrading invertors circuitry used in other amplifiers.

We wouldn't recommend constant 2 ohm load personally for very many amps Sensitivity for 10 5 watts 8 Ohms: Full thermal Speaker Protection: Measures 1 7 " wide x 1 2. Amp has been cleaned inside and out. All input level pots cleaned for static free performance. Internals inspected, transformer secondary's tested and our technician has completely Certified this amp. All functions have been tested and pass with flying colors! Super quality all around. All 5 inputs and all 5 outputs tested and both side produces clean and even sine waves!

Following restoration procedures, we burned it in, in the shop at continuous high volume for 4 hours straight and it functioned flawlessly. On our test bench, each of this particular unit's Lots of punch and headroom.

Your AV series II has arrived set up in this configuration. This allows for linking of multiple amplifiers. Overall amp in great cosmetic condition, with only minor wear to the top cover.

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