93,511 research outputs found

### Linear relations with conjugates of a Salem number

In this paper we consider linear relations with conjugates of a Salem number
$\alpha$. We show that every such a relation arises from a linear relation
between conjugates of the corresponding totally real algebraic integer
$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem number
with a nontrivial relation between its conjugates is $8$, whereas the smallest
length of a nontrivial linear relation between the conjugates of a Salem number
is $6$.Comment: v1, 12 page

### Natural PDE's of Linear Fractional Weingarten surfaces in Euclidean Space

We prove that the natural principal parameters on a given Weingarten surface
are also natural principal parameters for the parallel surfaces of the given
one. As a consequence of this result we obtain that the natural PDE of any
Weingarten surface is the natural PDE of its parallel surfaces. We show that
the linear fractional Weingarten surfaces are exactly the surfaces satisfying a
linear relation between their three curvatures. Our main result is
classification of the natural PDE's of Weingarten surfaces with linear relation
between their curvatures.Comment: 16 page

### The distribution of supermassive black holes in the nuclei of nearby galaxies

The growth of supermassive black holes by merging and accretion in
hierarchical models of galaxy formation is studied by means of Monte Carlo
simulations. A tight linear relation between masses of black holes and masses
of bulges arises if if the mass accreted by supermassive black holes scales
linearly with the mass forming stars and if the redshift evolution of mass
accretion tracks closely that of star formation. Differences in redshift
evolution between black hole accretion and star formation introduce
considerable scatter in this relation. A non-linear relation between black hole
accretion and star formation results in a non-linear relation between masses of
remnant black holes and masses of bulges. The relation of black hole mass to
bulge luminosity obseved in nearby galaxies and its scatter are reproduced
reasonably well by models in which black hole accretion and star formation are
linearly related but do not track each other in redshift. This suggests that a
common mechanism determines the efficiency for black hole accretion and the
efficiency for star formation, especially for bright bulges.Comment: 6 pages, 3 figures, submitted to MNRA

### A family of linearizable recurrences with the Laurent property

We consider a family of non-linear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced recently by Lam and Pylyavskyy. Furthermore, each member of this family is shown to be linearizable in two different ways, in the sense that its iterates satisfy both a linear relation with constant coefficients and a linear relation with periodic coefficients. Associated monodromy matrices and first integrals are constructed, and the connection with the dressing chain for SchrÃ¶dinger operators is also explained

### A New Relation between post and pre-optimal measurement states

When an optimal measurement is made on a qubit and what we call an Unbiased
Mixture of the resulting ensembles is taken, then the post measurement density
matrix is shown to be related to the pre-measurement density matrix through a
simple and linear relation. It is shown that such a relation holds only when
the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is
also shown explicitly that non-orthogonal measurements fail to give such a
linear relation no matter how the ensembles are mixed. The result has been
proved to be true for arbitrary quantum mechanical systems of finite
dimensional Hilbert spaces. The result is true irrespective of whether the
initial state is pure or mixed.Comment: 4 pages in REVTE

### On the Estimation of the Linear Relation when the Error Variances are known

The present article considers the problem of consistent estimation in measurement error models. A linear relation with not necessarily normally distributed measurement errors is considered. Three possible estimators which are constructed as different combinations of the estimators arising from direct and inverse regression are considered. The efficiency properties of these three estimators are derived and analyzed. The effect of non-normally distributed measurement errors is analyzed. A Monte-Carlo experiment is conducted to study the performance of these estimators in finite samples and the effect of a non-normal distribution of the measurement errors

### Scaling of the Strain Hardening Modulus of Glassy Polymers with the Flow Stress

In a recent letter, Govaert et al. examined the relationship between strain
hardening modulus $G_r$ and flow stress $\sigma_{flow}$ for five different
glassy polymers. In each case, results for $G_r$ at different strain rates or
different temperatures were linearly related to the flow stress. They suggested
that this linear relation was inconsistent with simulations. Data from previous
publications and new results are presented to show that simulations also yield
a linear relation between modulus and flow stress. Possible explanations for
the change in the ratio of modulus to flow stress with temperature and strain
rate are discussed.Comment: 8 pages, 2 figures: clarified arguments on linear proportionality.
Accepted for publication in J. Poly. Sci Part B - Polym. Phy

### On a generalization of restricted sum formula for multiple zeta values and finite multiple zeta values

We prove a new linear relation for multiple zeta values. This is a natural
generalization of the restricted sum formula proved by Eie, Liaw and Ong. We
also present an analogous result for finite multiple zeta values

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