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| [[File:Borromean Seifert surface.png|thumb|A Seifert surface bounded by a set of [[Borromean rings]].]]
| | While almost everyone encounters bouts of anxious moments once in a while, it does not necessarily mean you suffer from an anxiety disorder. 5 A 2004 study by Tache et al suggests a shared signalling pathway for generalized anxiety disorder and IBS-D through corticotropin signalling factor and related ligands: might each condition escalate the other. Don't fill your body up with refined sugars and unhealthy food, a diet that is balanced and nutritional is what you require. Once you have a list of 10 items prioritize these in order of your preference, the best one first. As a result, treating the anxiety with medication or therapy may alleviate the insomnia as well. <br><br>WHY DO YOU IGNORE WARNING SIGNS & HINTS WHICH YOU MUST KNOW BY HEART ALREADY. And these therapy consequences are not dangerous by any means, you're just loosing fat, not loosing electrolytes. Reassure each child by repeating often that parents will return at the end of the day. This disorder often seen in adolescence period but not guaranteed it can occur at any time. People who suffer from depression cannot lead a normal life and maintaining relationships for them is not practically possible. <br><br>A certain humming sound or a continuous sound can make the person lose his balance. Considering medication can make adverse reactions, various most people with anxiety disorder are afraid to take them owing to anxieties about brief and long phrase facet outcomes. The Valerian root in the tea decreased my anxiety like nothing I had ever found. Perhaps you find it hard to believe that water can have that much of an effect on how you feel and your state of mind. And don’t forget to watch what you eat, quit smoking, and quit drinking so much coffee. <br><br>Although there is no evidence that any particular diet can cure anxiety, some studies suggest that eating and avoiding particular types of foods may help decrease the number as well as the severity of attacks. Nothing contributes more to anxiety like “what if” statements, when in reality we have to concentrate on “what is”. Connect with others with similar health concerns and issues. ) God - even before I found a drug that helped me control my anxiety, I would feel myself starting to have an attack and I would begin to pray. Your breathing was rapid and ineffective, making you feel anxious. <br><br>If this is too soon into the No Contact Rule stage, it's better for you to stand your ground and stay on the rule with your ex girlfriend or boyfriend. Anxiety, Panic Attacks, Depression are all inter-related. The first step to anxiety hypnosis is finding a quiet place of ease where you are comfortable and feel safe. Benzodiazepines (such as Xanax, Klonopin, Ativan, and Valium) will work well for both panic attacks and anxiety attacks, but you are more likely to run into problems with habituation (i. Rich Presta here urges all those suffering from anxiety or panic attack (and even those feigning ignorance about their inherent problem) to realize the TRUTH that has led to this complex condition.<br><br>If you liked this article and you would like to get more info pertaining to natural cures for anxiety - [http://www.stress-lavoro-correlato.info/ please click the up coming document] - nicely visit our web-site. |
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| In [[mathematics]], a '''Seifert surface''' (named after [[Germany|German]] [[mathematician]] [[Herbert Seifert]]<ref>{{Cite journal |first=H. |last=Seifert |title={{lang|de|Über das Geschlecht von Knoten}} |journal=[[Mathematische Annalen|Math. Annalen]] |volume=110 |issue=1 |pages=571–592 |year=1934 |doi=10.1007/BF01448044 }} {{de icon}}</ref><ref>{{Cite journal |first=Jarke J. |last=van Wijk | author1-link = Jack van Wijk |first2=Arjeh M. |last2=Cohen |title=Visualization of Seifert Surfaces |journal=IEEE Trans. on Visualization and Computer Graphics |volume=12 |issue=4 |pages=485–496 |year=2006 |doi=10.1109/TVCG.2006.83 }}</ref>) is a [[surface]] whose [[boundary of a manifold|boundary]] is a given [[knot (mathematics)|knot]] or [[link (knot theory)|link]].
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| Such surfaces can be used to study the properties of the associated knot or link. For example, many [[knot invariants]] are most easily calculated using a Seifert surface. Seifert surfaces are also interesting in their own right, and the subject of considerable research.
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| Specifically, let ''L'' be a [[tame knot|tame]] [[oriented]] knot or link in [[Euclidean space|Euclidean 3-space]] (or in the [[3-sphere]]). A Seifert surface is a [[compact space|compact]], [[connected space|connected]], [[oriented]] [[surface]] ''S'' embedded in 3-space whose boundary is ''L'' such that the orientation on ''L'' is just the induced orientation from ''S'', and every connected component of ''S'' has non-empty boundary.
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| Note that any compact, connected, oriented surface with nonempty boundary in [[Euclidean 3-space]] is the Seifert surface associated to its boundary link. A single knot or link can have many different inequivalent Seifert surfaces. A Seifert surface must be [[oriented]]. It is possible to associate unoriented (and not necessarily orientable) surfaces to knots as well.
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| ==Examples==
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| [[File:Hopf_band_wikipedia.png|150px|right|thumb|A Seifert surface for the [[Hopf link]]. This is an annulus, not a Möbius strip. It has two half-twists and is thus orientable.]]
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| The standard [[Möbius strip]] has the [[unknot]] for a boundary but is not considered to be a Seifert surface for the unknot because it is not orientable. | |
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| The "checkerboard" coloring of the usual minimal crossing projection of the [[trefoil knot]] gives a Mobius strip with three half twists. As with the previous example, this is not a Seifert surface as it is not orientable. Applying Seifert's algorithm to this diagram, as expected, does produce a Seifert surface; in this case, it is a punctured torus of genus ''g=1'', and the Seifert matrix is
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| :<math>V = \begin{pmatrix}1 & -1 \\ 0 & 1\end{pmatrix}.</math>
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| ==Existence and Seifert matrix==
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| It is a [[theorem]] that any link always has an associated Seifert surface. This theorem was first published by [[Felix Frankl|Frankl]] and [[Lev Pontryagin|Pontrjagin]] in 1930.<ref>{{Cite journal |first=F. |last=Frankl |first2=L. |last2=Pontrjagin |year=1930 |title={{lang|de|Ein Knotensatz mit Anwendung auf die Dimensionstheorie}} |journal=Math. Annalen |volume=102 |issue=1 |pages=785–789 |doi=10.1007/BF01782377 }} {{de icon}}</ref> A different proof was published in 1934 by [[Herbert Seifert]] and relies on what is now called the [[Seifert algorithm]]. The [[algorithm]] produces a Seifert surface <math>S</math>, given a projection of the knot or link in question.
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| Suppose that link has ''m'' components (''m''=1 for a knot), the diagram has ''d'' crossing points, and resolving the crossings (preserving the orientation of the knot) yields ''f'' circles. Then the surface <math>S</math> is constructed from ''f'' disjoint disks by attaching ''d'' bands. The homology group <math>H_1(S)</math> is free abelian on ''2g'' generators, where
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| :''g'' = (2 + ''d'' − ''f'' − ''m'')/2
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| is the [[Genus (mathematics)|genus]] of <math>S</math>. The [[intersection form]] ''Q'' on <math>H_1(S)</math> is [[skew-symmetric]], and there is a basis of ''2g'' cycles
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| :''a<sub>1</sub>,a<sub>2</sub>,...,a<sub>2g</sub>''
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| with
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| :''Q=(Q(a<sub>i</sub>,a<sub>j</sub>))''
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| the direct sum of ''g'' copies of
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| :<math>\begin{pmatrix} 0 & -1 \\ 1 & 0\end{pmatrix}</math>.
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| The ''2g''<math>\times</math>''2g'' integer '''Seifert matrix'''
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| :''V=(v(i,j))'' has
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| <math>v(i,j)</math> the [[linking number]] in [[Euclidean 3-space]] (or in the [[3-sphere]]) of ''a<sub>i</sub>'' and the pushoff of ''a<sub>j</sub>'' out of the surface, with
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| :<math>V-V</math>''<sup>*</sup>''<math>=Q</math>
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| where ''V<sup>*</sup>=(v(j,i))'' the transpose matrix. Every integer ''2g''<math>\times</math>''2g'' matrix <math>V</math> with <math>V-V</math><sup>*</sup><math>=Q</math> arises as the Seifert matrix of a knot with genus ''g'' Seifert surface.
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| The [[Alexander polynomial]] is computed from the Seifert matrix by <math>A(t)=det(V-tV</math><sup>*</sup>), which is a polynomial in the indeterminate <math>t</math> of degree <math> \leq 2g</math>. The Alexander polynomial is independent of the choice of Seifert surface <math>S</math>, and is an invariant of the knot or link.
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| The [[signature of a knot]] is the [[Symmetric bilinear form#Signature and Sylvester's law of inertia|signature]] of the symmetric Seifert matrix <math>V+V^\top</math>. It is again an invariant of the knot or link.
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| ==Genus of a knot==
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| Seifert surfaces are not at all unique: a Seifert surface ''S'' of genus ''g'' and Seifert matrix ''V'' can be modified by a [[surgery theory|surgery]], to be replaced by a Seifert surface ''S''' of genus ''g+1'' and Seifert matrix
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| :''V'=V''<math>
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| \oplus \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}</math>.
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| The '''genus''' of a knot ''K'' is the [[knot invariant]] defined by the minimal [[genus (mathematics)|genus]] ''g'' of a Seifert surface for ''K''.
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| For instance:
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| * An [[unknot]]—which is, by definition, the boundary of a [[disk (mathematics)|disc]]—has genus zero. Moreover, the unknot is the ''only'' knot with genus zero.
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| * The [[trefoil knot]] has genus one, as does the [[Figure-eight knot (mathematics)|figure-eight knot]].
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| * The genus of a (''p'',''q'')-[[torus knot]] is (''p'' − 1)(''q'' − 1)/2
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| * The degree of the [[Alexander polynomial]] is a lower bound on twice the genus of the knot.
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| A fundamental property of the genus is that it is additive with respect to the [[knot sum]]:
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| :<math>g(K_1 \# K_2) = g(K_1) + g(K_2)</math>
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| ==See also==
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| *[[Crosscap number]]
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| *[[Arf invariant of a knot]]
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| ==References ==
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| {{Reflist}}
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| ==External links==
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| *The [http://www.win.tue.nl/~vanwijk/seifertview/ SeifertView programme] of [[Jack van Wijk]] visualizes the Seifert surfaces of knots constructed using Seifert's algorithm.
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| {{Knot theory|state=collapsed}}
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| [[Category:Geometric topology]]
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| [[Category:Knot theory]]
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| [[Category:Surfaces]]
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While almost everyone encounters bouts of anxious moments once in a while, it does not necessarily mean you suffer from an anxiety disorder. 5 A 2004 study by Tache et al suggests a shared signalling pathway for generalized anxiety disorder and IBS-D through corticotropin signalling factor and related ligands: might each condition escalate the other. Don't fill your body up with refined sugars and unhealthy food, a diet that is balanced and nutritional is what you require. Once you have a list of 10 items prioritize these in order of your preference, the best one first. As a result, treating the anxiety with medication or therapy may alleviate the insomnia as well.
WHY DO YOU IGNORE WARNING SIGNS & HINTS WHICH YOU MUST KNOW BY HEART ALREADY. And these therapy consequences are not dangerous by any means, you're just loosing fat, not loosing electrolytes. Reassure each child by repeating often that parents will return at the end of the day. This disorder often seen in adolescence period but not guaranteed it can occur at any time. People who suffer from depression cannot lead a normal life and maintaining relationships for them is not practically possible.
A certain humming sound or a continuous sound can make the person lose his balance. Considering medication can make adverse reactions, various most people with anxiety disorder are afraid to take them owing to anxieties about brief and long phrase facet outcomes. The Valerian root in the tea decreased my anxiety like nothing I had ever found. Perhaps you find it hard to believe that water can have that much of an effect on how you feel and your state of mind. And don’t forget to watch what you eat, quit smoking, and quit drinking so much coffee.
Although there is no evidence that any particular diet can cure anxiety, some studies suggest that eating and avoiding particular types of foods may help decrease the number as well as the severity of attacks. Nothing contributes more to anxiety like “what if” statements, when in reality we have to concentrate on “what is”. Connect with others with similar health concerns and issues. ) God - even before I found a drug that helped me control my anxiety, I would feel myself starting to have an attack and I would begin to pray. Your breathing was rapid and ineffective, making you feel anxious.
If this is too soon into the No Contact Rule stage, it's better for you to stand your ground and stay on the rule with your ex girlfriend or boyfriend. Anxiety, Panic Attacks, Depression are all inter-related. The first step to anxiety hypnosis is finding a quiet place of ease where you are comfortable and feel safe. Benzodiazepines (such as Xanax, Klonopin, Ativan, and Valium) will work well for both panic attacks and anxiety attacks, but you are more likely to run into problems with habituation (i. Rich Presta here urges all those suffering from anxiety or panic attack (and even those feigning ignorance about their inherent problem) to realize the TRUTH that has led to this complex condition.
If you liked this article and you would like to get more info pertaining to natural cures for anxiety - please click the up coming document - nicely visit our web-site.