Ductal

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Firstly, a Fraudulent Misrepresentation is one that is made knowingly by the Representor that it was false or if it was made without belief in its fact or made recklessly without concerning whether or not it is true or false. For instance estate agent A told the potential consumers that the tenure of a landed property they are considering is freehold when it is really one with a ninety nine-yr leasehold! A is responsible of constructing a fraudulent misrepresentation if he is aware of that the tenure is the truth is a ninety nine-yr leasehold instead of it being freehold or he didn't consider that the tenure of the house was freehold or he had made the assertion with out caring whether or not the tenure of the topic property is in fact freehold.

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Notice that the application must be submitted by the appointed Key Government Officer (KEO) such as the CEO, COO, or MD. Once the KEO has submitted the mandatory paperwork and assuming all documents are in order, an email notification shall be sent stating that the applying is permitted. No hardcopy of the license might be issued. A delicate-copy could be downloaded and printed by logging into the CEA website. It takes roughly four-6 weeks to course of an utility.

In geometry, collinearity is a property of a set of points, specifically, the property of lying on a single line. A set of points with this property is said to be collinear (often misspelled as colinear). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row". In statistics, collinearity refers to an exact or approximate linear relationship between two explanatory variables, multicollinearity extends the concept to more than two explanatory variables, and lateral collinearity expands the concept still further.

Points on a line

In most geometries a line is a primitive (undefined) object type. A model for the geometry supplies an interpretation of what points, lines and other object types are. This abstract point of view requires a richer vocabulary to describe its concepts than does Euclidean geometry. Thus, in spherical geometry, where lines are represented in the standard model by great circles of a sphere, sets of collinear points lie on the same great circle. Such points do not lie on a "straight line" in the Euclidean sense, and are not thought of as being in a row. Of course, if the geometry is Euclidean, then collinear points lie on a straight line.

Linear maps (or linear functions), as geometric maps, preserve the collinearity property (that is, they map collinear point sets to collinear point sets), which is another way to say that they map lines to lines. In projective geometry such mappings are called homographies and are a special type of collineation.

Examples in Euclidean geometry

Triangles

In any triangle the following sets of points are collinear:

• The orthocenter, the circumcenter, the centroid, the Exeter point, the de Longchamps point, and the center of the nine-point circle are collinear, all falling on a line called the Euler line.

• The de Longchamps point also has other collinearities.

• Any vertex, the tangency of the opposite side with an excircle, and the Nagel point are collinear in a line called a splitter of the triangle.

• The midpoint of any side, the point that is equidistant from it along the triangle in either direction (so these two points bisect the perimeter), and the center of the Spieker circle are collinear in a line called a cleaver of the triangle. (The Spieker circle is the incircle of the medial triangle, and its center is the center of mass of the perimeter of the triangle.)

• Any vertex, the tangency of the opposite side with the incircle, and the Gergonne point are collinear.

• From any point on the circumcircle of a triangle, the nearest points on each of the three extended sides of the triangle are collinear in the Simson line of the point on the circumcircle.

Quadrilaterals

• In a convex quadrilateral ABCD whose opposite sides intersect at E and F, the midpoints of AC, BD, and EF are collinear and the line through them is called the Newton line (sometimes known as the Newton-Gauss line). If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line.

• In a convex quadrilateral, the quasiorthocenter H, the "area centroid" G, and the quasicircumcenter O are collinear in this order, and HG = 2GO. (See Quadrilateral#Remarkable points and lines in a convex quadrilateral.)

• Other collinearities of a tangential quadrilateral are given in Tangential quadrilateral#Collinearities and concurrencies.

• In a cyclic quadrilateral, the circumcenter, the vertex centroid (the intersection of the two bimedians), and the anticenter are collinear.

• In a cyclic quadrilateral, the area centroid, the vertex centroid, and the intersection of the diagonals are collinear.

• In a tangential trapezoid, the tangencies of the incircle with the two bases and collinear with the incenter.

• In a tangential trapezoid, the midpoints of the legs are collinear with the incenter.

Hexagons

• Pascal's theorem (also known as the Hexagrammum Mysticum Theorem) states that if an arbitrary six points are chosen on a conic section (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon. The converse is also true: the Braikenridge–Maclaurin theorem states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line, then the six vertices of the hexagon lie on a conic, which may be degenerate as in Pappus's hexagon theorem.

Conic sections

• By Monge's theorem, for any three circles in a plane, none of which is inside one of the others, the three intersection points of the three pairs of lines, each externally tangent to two of the circles, are collinear.

• In an ellipse, the center, the two foci, and the two vertices with the smallest radius of curvature are collinear, and the center and the two vertices with the greatest radius of curvature are collinear.

• In a hyperbola, the center, the two foci, and the two vertices are collinear.

Cones

• The center of mass of a conic solid of uniform density lies one-quarter of the way from the center of the base to the vertex, on the straight line joining the two.

Tetrahedrons

• The centroid of a tetrahedron is the midpoint between its Monge point and circumcenter. These points define the Euler line of the tetrahedron that is analogous to the Euler line of a triangle. The center of the tetrahedron's twelve-point sphere also lies on the Euler line.

Algebra

Collinearity of points whose coordinates are given

In coordinate geometry, in n-dimensional space a set of three or more distinct points are collinear if and only if, for every subset of three points X = (x₁, x₂, ... , x_n), Y = (y₁, y₂, ... , y_n), and Z = (z₁, z₂, ... , z_n), the matrix

${\begin{bmatrix}1&x_{1}&x_{2}&\dots &x_{n}\\1&y_{1}&y_{2}&\dots &y_{n}\\1&z_{1}&z_{2}&\dots &z_{n}\end{bmatrix}}$

has rank less than 3. In particular, for three points in the plane (n = 2), the above matrix is square and the points are collinear if and only if its determinant is zero; since that 3 × 3 determinant is plus or minus twice the area of a triangle with those three points as vertices, this is equivalent to the statement that the three points are collinear if and only if the triangle with those points as vertices has zero area.

Collinearity of points whose pairwise distances are given

A set of at least three distinct points is called straight, meaning all the points are collinear, if and only if, for every three points A, B, and C, the following determinant of a Cayley–Menger determinant is zero (with d(AB) meaning the distance between A and B, etc.):

$\det {\begin{bmatrix}0&d(AB)^{2}&d(AC)^{2}&1\\d(AB)^{2}&0&d(BC)^{2}&1\\d(AC)^{2}&d(BC)^{2}&0&1\\1&1&1&0\end{bmatrix}}=0.$

This determinant is, by Heron's formula, equal to −16 times the square of the area of a triangle with side lengths d(AB), d(BC), and d(AC); so checking if this determinant equals zero is equivalent to checking whether the triangle with vertices A, B, and C has zero area (so the vertices are collinear).

Equivalently, a set of at least three distinct points are collinear if and only if, for every three points A, B, and C with d(AC) greater than or equal to each of d(AB) and d(BC), the triangle inequality d(AC) ≤ d(AB) + d(BC) holds with equality.

Number theory

Two numbers m and n are not coprime—that is, they share a common factor other than 1—if and only if for a rectangle plotted on a square lattice with vertices at (0, 0), (m, 0), (m, n), and (0, n), at least one interior point is collinear with (0, 0) and (m, n).

Concurrency (plane dual)

In various plane geometries the notion of interchanging the roles of "points" and "lines" while preserving the relationship between them is called plane duality. Given a set of collinear points, by plane duality we obtain a set of lines all of which meet at a common point. The property that this set of lines has (meeting at a common point) is called concurrency, and the lines are said to be concurrent lines. Thus, concurrency is the plane dual notion to collinearity.

Collinearity graph

Given a partial geometry P, where two points determine at most one line, a collinearity graph of P is a graph whose vertices are the points of P, where two vertices are adjacent if and only if they determine a line in P.

Usage in statistics and econometrics

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In statistics, collinearity refers to a linear relationship between two explanatory variables. Two variables are perfectly collinear if there is an exact linear relationship between the two, so the correlation between them is equal to 1 or −1. That is, $X_{1}$ and $X_{2}$ are perfectly collinear if there exist parameters $\lambda _{0}$ and $\lambda _{1}$ such that, for all observations i, we have

$X_{2i}=\lambda _{0}+\lambda _{1}X_{1i}.$

This means that if the various observations (X_1i, X_2i ) are plotted in the (X₁, X₂) plane, these points are collinear in the sense defined earlier in this article.

Perfect multicollinearity refers to a situation in which k (k ≥ 2) explanatory variables in a multiple regression model are perfectly linearly related, according to

$X_{ki}=\lambda _{0}+\lambda _{1}X_{1i}+\lambda _{2}X_{2i}+\dots +\lambda _{k-1}X_{(k-1),i}$

for all observations i. In practice, we rarely face perfect multicollinearity in a data set. More commonly, the issue of multicollinearity arises when there is a "strong linear relationship" among two or more independent variables, meaning that

$X_{ki}=\lambda _{0}+\lambda _{1}X_{1i}+\lambda _{2}X_{2i}+\dots +\lambda _{k-1}X_{(k-1),i}+\varepsilon _{i}$

where the variance of $\varepsilon _{i}$ is relatively small.

The concept of lateral collinearity expands on this traditional view, and refers to collinearity between explanatory and criteria (i.e., explained) variables.

Usage in other areas

Antenna arrays

An antenna mast with four colinear directional arrays.

In telecommunications, a collinear (or co-linear) antenna array is an array of dipole antennas mounted in such a manner that the corresponding elements of each antenna are parallel and aligned, that is they are located along a common line or axis.

Photography

The collinearity equations are a set of two equations, used in photogrammetry and remote sensing to relate coordinates in an image (sensor) plane (in two dimensions) to object coordinates (in three dimensions). In the photography setting, the equations are derived by considering the central projection of a point of the object through the optical centre of the camera to the image in the image (sensor) plane. The three points, object point, image point and optical centre, are always collinear. Another way to say this is that the line segments joining the object points with their image points are all concurrent at the optical centre.

See also

• Pappus's hexagon theorem
• No-three-in-line problem
• Incidence (geometry)#Collinearity

Notes

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References

• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010