5,372 research outputs found

### Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3)
nonlinear $\sigma$--model are constructed. We calculate the corresponding
contribution to the spin--spin correlation function, and compare with
predictions from the spectral density scaling hypothesis. The resulting
approximation to the spin--spin correlation function agrees well with that
computed in renormalized (asymptotically free) perturbation theory in the
expected energy range. Further we observe simple lower and upper bounds for the
sum of the absolute square of the form factors which may be of use for analytic
estimates.Comment: 14 pages, 3 figures, late

### Structure functions of the 2d O(n) non-linear sigma models

We investigate structure functions in the 2-dimensional (asymptotically free)
non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap
program. In particular the exact small (Bjorken) x behavior is derived.
Structure functions in the special case of the n=3 model are accurately
computed over the whole x range for $-q^2/M^2<10^5$, and some moments are
compared with results from renormalized perturbation theory. Some results
concerning the structure functions in the 1/n approximation are also presented.Comment: 57 pages, 5 figures, 3 table

### Illusionism's discontent

Frankish positions his view, illusionism about qualia (a.k.a. eliminativist physicalism), in opposition to what he calls radical realism (dualism and neutral monism) and conservative realism (a.k.a. non-eliminativist physicalism). Against radical realism, he upholds physicalism. But he goes along with key premises of the Gap Arguments for radical realism, namely, 1) that epistemic/explanatory gaps exist between the physical and the phenomenal, and 2) that every truth should be perspicuously explicable from the fundamental truth about the world; and he concludes that because physicalism is true, there could be no phenomenal truths, and no qualia. I think he is wrong to accept 2); and even if he was right to accept it, the more plausible response would be not to deny the existence of qualia but to deny physicalism. In either case, denying the existence of qualia is the wrong answer. I present a physicalist realist alterative that refutes premise 2 of the Gap Argument; I also make a general case against the scientism that accompanies Frankishâs metaphysics

### An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

We present an exact two-particle solution of the Currie-Hill equations of
Predictive Relativistic Mechanics in $1 + 1$ dimensional Minkowski space. The
instantaneous accelerations are given in terms of elementary functions
depending on the relative particle position and velocities. The general
solution of the equations of motion is given and by studying the global phase
space of this system it is shown that this is a subspace of the full kinematic
phase space.Comment: 13 pages, LaTeX. arXiv admin note: text overlap with arXiv:1402.699

### The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution

Lattice artifacts in the 2d O(n) non-linear sigma-model are expected to be of
the form O(a^2), and hence it was (when first observed) disturbing that some
quantities in the O(3) model with various actions show parametrically stronger
cutoff dependence, apparently O(a), up to very large correlation lengths. In a
previous letter we described the solution to this puzzle. Based on the
conventional framework of Symanzik's effective action, we showed that there are
logarithmic corrections to the O(a^2) artifacts which are especially large,
(ln(a))^3, for n=3 and that such artifacts are consistent with the data. In
this paper we supply the technical details of this computation. Results of
Monte Carlo simulations using various lattice actions for O(3) and O(4) are
also presented.Comment: 62 pages, 15 figures, published version with references adde

### Effective potential from zero-momentum potential

We obtain the centre-of-mass frame effective potential from the zero-momentum
potential in Ruijsenaars-Schneider type 1-dimensional relativistic mechanics
using classical inverse scattering methods.Comment: 24 pages, 10 figure

### Capital allocation in financial institutions: the Euler method

Capital allocation is used for many purposes in financial institutions and for this purpose several methods are known. The aim of this paper is to review possible methods (we present six of them) and to help financial companies to choose between the methods. There are some properties that an allocation method should satisfy: full allocation, core compatibility, riskless allocation, symmetry and suitability for performance measurement (compatibility with Return on Risk Adjusted Capital calculation). If we think about practical application we should also consider simplicity of the methods. First we examine the methods from the point of view if they are satisfying core compatibility. We test this with simulation where we add to the existing literature that we test core compatibility with different assumptions on returns: on normal and t-distributed returns and also on returns generated from a copula. We find that if we measure risk by a coherent risk measure, the Expected Shortfall there are two methods satisfying core compatibility: the Euler method (that always fulfills the criteria) and cost gap method (obeys it around in about 99%). As Euler method is very easy to calculate even for many players while cost gap method becomes very complicated as the number of the players increases we examine further the properties of Euler method. We find that it fulfills all the above given criteria but symmetry and as aforementioned it is also very easy to calculate. Therefore we believe that the method might be suggested for practical applications.Capital Allocation, Coherent Measures of Risk, Core, Simulation

### On the Sum of Dilations of a Set

We show that for any relatively prime integers $1\leq p<q$ and for any finite
$A \subset \mathbb{Z}$ one has $$|p \cdot A + q \cdot A | \geq (p + q) |A| -
(pq)^{(p+q-3)(p+q) + 1}.$

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