Quiver App Free Download
Angelines Mulready
quiver(X,Y,U,V) plots arrows with directional components U and V at the Cartesian coordinates specified by X and Y. For example, the first arrow originates from the point X(1) and Y(1), extends horizontally according to U(1), and extends vertically according to V(1). By default, the quiver function scales the arrow lengths so that they do not overlap.
When scale is a positive number, the quiver function automatically adjusts the lengths of arrows so they do not overlap, then stretches them by a factor of scale. For example, a scale of 2 doubles the length of arrows, and a scale of 0.5 halves the length of arrows.
quiver(___,LineSpec) sets the line style, marker, and color. Markers appear at the points specified by X and Y. If you specify a marker using LineSpec, then quiver does not display arrowheads. To specify a marker and display arrowheads, set the Marker property instead.
quiver(___,Name,Value) specifies quiver properties using one or more name-value pair arguments. For a list of properties, see Quiver Properties. Specify name-value pair arguments after all other input arguments. Name-value pair arguments apply to all of the arrows in the quiver plot.
Create a quiver plot of the subset you selected. The vectors X and Y represent the location of the base of each arrow, and U and V represent the directional components of each arrow. By default, the quiver function shortens the arrows so they do not overlap. Call axis equal to use equal data unit lengths along each axis. This makes the arrows point in the correct direction.
Display the gradient vectors as a quiver plot. Then, display contour lines in the same axes. Adjust the display so that the gradient vectors appear perpendicular to the contour lines by calling axis equal.
Arrow scaling factor, specified as a positive number or 'off'. By default, the quiver function automatically scales the arrows so they do not overlap. The quiver function applies the scaling factor after it automatically scales the arrows.
Specifying scale is the same as setting the AutoScaleFactor property of the quiver object. For example, specifying scale as 2 doubles the length of the arrows. Specifying scale as 0.5 halves the length of the arrows.
To disable automatic scaling, specify scale as 'off' or 0. When you specify either of these values, the AutoScale property of the quiver object is set to 'off' and the length of the arrow is determined entirely by U and V.
There is a trend, for some people, to study representations of quivers. The setting of the problem is undoubtedly natural, but representations of quivers are present in the literature for already >40 years.
Are there any connections of this trend with other Maths? For, it seems like it is a self-contained topic and basically I wonder why people study quivers so much -- in a sense everything becomes clear after the initial results of Gabriel and the old result of Yuri Drozd about wild/tame dichotomy, and these things ought to become boring.
The first applications are of course inside representation theory and ring theory, because Gabriel's Theorem states, that if you have a property of a finite dimensional algebra over an algebraically closed field that can be detected in the module category, then it suffices to look at path algebras of quivers (with relations). For example for proving that an algebra is wild, it suffices to find a subquiver (with relations) that is known to be wild; and there are several lists of such quivers. This is useful in representation theory of Lie algebras and finite groups.
So whatever motivation you have to be interested in representations of finite dimensional algebras immediately carries over to quivers and their algebras, plus the obvious plus that it becomes extraordinarily easy to build up examples.
A classical example is the Kronecker-Wierstrass classification of the indecomposable representations of the quiver $\bullet\rightrightarrows\bullet$ , motivated by the conjugation classification of certain systems of ODEs. There is another example, from control theory, in Gabriel-Roiter's book. I am pretty sure these two examples are real, in that the non-representation-theoretic problem came before the representationists took over.
Similarly, the whole cluster explosion of the last 10 years should be a nice example of representation theory of quivers and friends and the methods involved in it helping understand (and solve, in many cases) problems exterior to the theory. Of course, here the source of the problems is also of representation-theoretic nature ---Lie theory--- but in a rather palpable sense this is a quite different part of the theory.
As was mentioned above, many moduli spaces have a quiver description; one of the most famousexample is given by Nakajima quiver varieties, which are defined for any quiver (and they serve as the main example of symplectic complex varieties which are resolutions of an affine variety), but when the quiver is the affine quiver of ADE type, they describe moduli spaces of torsion free sheaves on the quotients $\mathbb C^2/\Gamma$ where $\Gamma$ is a finite subgroupof $SL(2)$ (these are also known as ALE spaces). These moduli spaces are very important in many places in mathematics and physics (gauge theory) and quiver description is very useful when you want to tackle some explicit problems related to them.
The formation of quiver algebras is useful in ring theory in attempts to construct examples/counter-examples. One can often classify when a quiver algebra has some property in terms of some intrinsic property of the quiver itself, and then finding counter-examples boils down to forming a quiver with a certain easy-to-see property.
In the framework of Algebraic Geometry there is the equivalence (introduced by Bondal, Kapranov, and Hille) between the category of homogeneous bundles $E$ on any Hermitian symmetric variety $X=G/P$ of ADE-type and the category of representations of a certain quiver $\mathcalQ_X$ with relations.
Since I believe Victor did some work in semigroup theory, these examples may be interesting to him. If $S$ is a finite monoid such that each maximal subgroup is abelian and the structure matrix of each regular $\mathcal J$-class contains only $1$s (i.e. products of $\mathcal J$-equivalent idempotents are idempotents) then for any field $\Bbbk$ the monoid algebra $\Bbbk M$ is basic and so is the quotient of the path algebra of its quiver modulo an admissible ideal. See my paper Quivers of monoids with basic algebras with Margolis for how to compute this quiver. Thus one can really use quiver theory to understand your semigroup's representation theory.
For instance, the quiver of a 2x2 rectangular band with adjoined identity consists of two vertices $1,2$ and an edge $x\colon 1\to 2$ and an edge $y\colon 2\to 1$. The admissible ideal is generated by the relation $xy=0$. Thus a representation of a $2\times 2$ rectangular band amounts to taking to vector spaces $V,W$ and linear maps $A\colon V\to W$ and $B\colon W\to V$ such that $AB=0$. One can also prove this directly.
If you like categories, viewed as an algebraic structure, then the path algebra is just the "category algebra" of the free category on the quiver. Incidence algebras are category algebras of posets and so one can view all of this as studying representation theory of category algebras modulo relations.
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Replacement quiver bracket for Barnett Lightweight Quiver (item 6840). Installs on crossbows with a bottom picatinny accessory rail. Single screw installation (included) Mounts quiver perpendicular beneath the front end of the crossbow. Compatible only with crossbows having bottom picatinny accessory rail.
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