Abstract In analogy with the Manin–Mumford conjecture for algebraic curves, one may ask how a metric graph under Abel–Jacobi embedding intersects torsion points of its Jacobian. We show that number is finite graphs genus ${g\geq 2}$, which are biconnected and have edge lengths “sufficiently irrational” in precise sense. Under these assumptions, bounded by $3g-3$. Next, we study bounds on image ...

In the previous article [3], the author investigated Diophantine equations of the form (∗) X − f(x)Y 2 = 1 and found that the set of the polynomial solutions of (∗) can be described in terms of the theory of twists and that of generalized Jacobian varieties. On the other hand, there are several articles ([1], [7]) which relate the solutions of (∗) with certain torsion points on the Jacobian var...

conclusions these findings emphasize the potential clinical benefits of therapeutic procedures such as cardiac resynchronization therapy (crt) or apex-sparing volume-reduction surgery in dcm. a better definition of the role and implications of reverse apical torsion in dcm and its importance and effectiveness in making therapeutic decisions like crt implantation requires further studies. case p...

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

torsion of the gallbladder is a relatively rare surgical disease which mimics acute cholecystitis' symptoms that usually would not be respondable to medical therapies. the torsion would mostly be diagnosed intra-operatively. cholecystectomy is the treatment of choice. in general in our centre, general surgery department, imam reza hospital, mashhad, iran, since 1986 over 14000 cholecystect...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...

Fix a prime number . Graphs of isogenies of degree a power of are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse graphs of so-called l-isogenies, resolving that, in arbitrary dimension, their structure is similar, but not identical, to the “volcanoes” occurri...