29,701 research outputs found

### State Transitions in Ultracompact Neutron Star LMXBs: towards the Low Luminosity Limit

Luminosity of X-ray spectral state transitions in black hole and neutron star
X-ray binaries can put constraint on the critical mass accretion rate between
accretion regimes. Previous studies indicate that the hard-to-soft spectral
state transitions in some ultracompact neutron star LMXBs have the lowest
luminosity. With X-ray monitoring observations in the past decade, we were able
to identify state transitions towards the lowest luminosity limit in 4U
0614+091, 2S 0918-549 and 4U 1246-588. By analysing corresponding X-ray pointed
observations with the Swift/XRT and the RXTE/PCA, we found no hysteresis of
state transitions in these sources, and determined the critical mass accretion
rate in the range of 0.002 - 0.04 $\dot{\rm M}_{\rm Edd}$ and 0.003 - 0.05
$\dot{\rm M}_{\rm Edd}$ for the hard-to-soft and the soft-to-hard transition,
respectively, by assuming a neutron star mass of 1.4 solar masses. This range
is comparable to the lowest transition luminosity measured in black hole X-ray
binaries, indicating the critical mass accretion rate is not affected by the
nature of the surface of the compact stars. Our result does not support the
Advection-Dominated Accretion Flow (ADAF) model which predicts that the
critical mass accretion rate in neutron star systems is an order of magnitude
lower if same viscosity parameters are taken. The low transition luminosity and
insignificant hysteresis in these ultracompact X-ray binaries provide further
evidence that the transition luminosity is likely related to the mass in the
disc.Comment: 12 pages, 4 figures, to appear in MNRA

### Tame Automorphisms Fixing a Variable of Free Associative Algebras of Rank Three

We study automorphisms of the free associative algebra K over a field
K which fix the variable z. We describe the structure of the group of z-tame
automorphisms and derive algorithms which recognize z-tame automorphisms and
z-tame coordinates

### Coordinates and Automorphisms of Polynomial and Free Associative Algebras of Rank Three

We study z-automorphisms of the polynomial algebra K[x,y,z] and the free
associative algebra K over a field K, i.e., automorphisms which fix the
variable z. We survey some recent results on such automorphisms and on the
corresponding coordinates. For K we include also results about the
structure of the z-tame automorphisms and algorithms which recognize z-tame
automorphisms and z-tame coordinates

### Embeddings of curves in the plane

In this paper, we contribute toward a classification of two-variable
polynomials by classifying (up to an automorphism of $C^2$) polynomials whose
Newton polygon is either a triangle or a line segment. Our classification has
several applications to the study of embeddings of algebraic curves in the
plane. In particular, we show that for any $k \ge 2$, there is an irreducible
curve with one place at infinity, which has at least $k$ inequivalent
embeddings in $C^2$. Also, upon combining our method with a well-known theorem
of Zaidenberg and Lin, we show that one can decide "almost" just by inspection
whether or not a polynomial fiber is an irreducible simply connected curve.Comment: 11 page

### The strong Anick conjecture is true

Recently Umirbaev has proved the long-standing Anick conjecture, that is,
there exist wild automorphisms of the free associative algebra K over a
field K of characteristic 0. In particular, the well-known Anick automorphism
is wild. In this article we obtain a stronger result (the Strong Anick
Conjecture that implies the Anick Conjecture). Namely, we prove that there
exist wild coordinates of K. In particular, the two nontrivial
coordinates in the Anick automorphism are both wild. We establish a similar
result for several large classes of automorphisms of K. We also find a
large new class of wild automorphisms of K which is not covered by the
results of Umirbaev. Finally, we study the lifting problem for automorphisms
and coordinates of polynomial algebras, free metabelian algebras and free
associative algebras and obtain some interesting new results.Comment: 25 pages, corrected typos and acknowledgement

### Polynomial Retracts and the Jacobian Conjecture

Let $K[x, y]$ be the polynomial algebra in two variables over a field $K$ of
characteristic $0$. A subalgebra $R$ of $K[x, y]$ is called a retract if there
is an idempotent homomorphism (a {\it retraction}, or {\it projection})
$\varphi: K[x, y] \to K[x, y]$ such that $\varphi(K[x, y]) = R$. The presence
of other, equivalent, definitions of retracts provides several different
methods of studying them, and brings together ideas from combinatorial algebra,
homological algebra, and algebraic geometry. In this paper, we characterize all
the retracts of $K[x, y]$ up to an automorphism, and give several applications
of this characterization, in particular, to the well-known Jacobian conjecture.
Notably, we prove that if a polynomial mapping $\varphi$ of $K[x,y]$ has
invertible Jacobian matrix {\it and } fixes a non-constant polynomial, then
$\varphi$ is an automorphism

### Instantons on General Noncommutative R^4

We study the U(1) and U(2) instanton solutions of gauge theory on general
noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results
for the projection operators. In some cases we computed numerically the
instanton charge and found that it is an integer, independent of the
noncommutative parameters $\theta_{1,2}$.Comment: 14 pages, LaTeX; deleted some confusing statements in the U(1)
1-instanton case, added ref

- â€¦