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We study the properties of gluon plasma subjected to a weak acceleration using first-principle numerical Monte Carlo simulations. We use the Luttinger (Tolman-Ehrenfest) correspondence between temperature gradient and gravitational field to impose acceleration in imaginary time formalism. Under acceleration, the system resides in global thermal equilibrium. Our results indicate that even the weakest acceleration up to $a \simeq 27$ MeV drastically softens the deconfinement phase transition, converting the first-order phase transition of a static system to a soft crossover for accelerating gluons. The accelerating environment can be relevant to the first moments of the early Universe and the initial glasma regime of relativistic heavy ion collisions. In particular, our results imply that the acceleration, if present, may also inhibit the detection of the thermodynamic phase transition from quark-gluon plasma to the hadronic phase., Comment: 8 pages, 5 figures

The action of the rotation group $SO(3)$ on systems of $n$ points in the $3$-dimensional Euclidean space $\mathbf{R}^3$ induces naturally an action of $SO(3)$ on $\mathbf{R}^{3n}$. In the present paper we consider the following question: do there exist $3$ polynomial functions $f_1$, $f_2$, $f_3$ on $\mathbf{R}^{3n}$ such that the intersection of the set of common zeros of $f_1$, $f_2$, and $f_3$ with each orbit of $SO(3)$ in $R^{3n}$ is nonempty and finite? Questions of this kind arise when one is interested in relative motions of a given set of $n$ points, i.e., when one wants to exclude the local motions of the system of points as a rigid body. An example is the problem of deciding whether a given polyhedron is non-trivially flexible. We prove that such functions do exist. To get a necessary system of equations $f_1=0$, $f_2=0$, $f_3=0$, we show how starting by choice of a hypersurface in $\mathbf{CP}^{n-1}$ containing no conics, no lines, and no real points one can find such a system., Comment: 14 pages

Based on an eddy-permitting ocean circulation model, the eddy kinetic energy (EKE) sources are studied in the Sea of Okhotsk. An analysis of the spatial distribution of the EKE showed that intense mesoscale variability occurs along the western boundary of the Sea of Okhotsk, where the East-Sakhalin Current extends. It was found a pronounced seasonally varying EKE with its maximal magnitudes in winter, and its minimal magnitudes in summer. An analysis of the EKE sources and the energy conversions showed that time-varying (turbulent) wind stress is a main contribution to mesoscale variability along the western boundary of the Sea of Okhotsk. The contribution of baroclinic instability to the generation of mesoscale variability predominates over that of barotropic instability along the western boundary of the Sea of Okhotsk. To demonstrate the mechanism of baroclinic instability, the circulation was considered along the western boundary of the Sea of Okhotsk from January to April 2005. An analysis of hydrological conditions showed outcropping isopycnals and being strong vertical shear of the along-shore velocity from January to May 2005. In April, mesoscale eddies are observed along the western boundary of the Sea of Okhotsk. It was established that seasonal variability of turbulent wind stress and the baroclinic instability of the East-Sakhalin Current are major reasons of mesoscale variability along the western boundary of the Sea of Okhotsk., Comment: 17 pages, 11 figures

Let $k$ be a field with a real valuation $\nu$ and $R$ a $k$-algebra. We show that there exist a $k$-algebra $K$ and a real valuation $\mu$ on $K$ extending $\nu$ such that any real ring valuation of $R$ is induced by $\mu$ via some homomorphism from $R$ to $K$; $K$ can be chosen to be a field. Then we study the case when $\nu$ is trivial and $R$ a complete local Noetherian ring with the residue field $k$. Let $K$ be the ring $\bar{k}[[t^\R]]$ of Hahn series with its natural valuation $\mu$; $\bar{k}$ is an algebraic closure of $k$. Despite $K$ is not universal in the strong sense defined above, it has the following weak universality property: for any local valuation $v$ and a finite set of elements $x_1,...,x_n$ of $R$ there exists a homomorphism $f\colon R\to K$ such that $v(x_i)=\mu(f(x_i))$, $i=1,...,n$. If $R=k[[x_1,...,x_n]]/I$ for an ideal $I$, this property implies that every point of the local tropical variety of $I$ lifts to a $K$-point of $R$. Similarly, if $R=k[x_1,...,x_n]/I$ is a finitely generated algebra over $k$, lifting points in the tropical variety of $I$ can be interpreted as the weak universality property of the field $\bar{k}((t^\R))$ of Hahn series., Comment: 13 pages

Let a finite group G act linearly on a finite dimensional vector space V over an algebraically closed field k of characteristic p>2. Assume that the quotient V/G is an isolated singularity. In the case when p does not divide the order of G, isolated singularities V/G are completely classified and their classification reduces to Zassenhaus-Vincent-Wolf classification of isolated quotient singularities over the field of complex numbers. In the present paper we show that if dimension of V is 3, then also in the modular case (p divides the order of G) classification of isolated quotient singularities reduces to Zassenhaus-Vincent-Wolf classification. Some remarks on modular quotient singularities in other dimensions and in even characteristic are also given., Comment: v2: some references added, minor improvements; 14 pages

In this paper we review the classification of isolated quotient singularities over the field of complex numbers due to H. Zassenhaus, G. Vincent, and G. A. Wolf. As an application we describe Gorenstein isolated quotient singularities over C, generalizing a result of K. Kurano and S. Nishi., Comment: 27 pages

If $X$ is an algebraic variety with at worst canonical singularities and $S$ is a $\Q$-Cartier hypersurface in $X$, the canonical threshold of the pair $(X,S)$ is the supremum of $c\in\R$ such that the pair $(X,cS)$ is canonical. We show that the set of all possible canonical thresholds of the pairs $(X,S)$, where $X$ is a germ of smooth 3-dimensional variety, satisfies the ascending chain condition. We also deduce a formula for the canonical threshold of $(\C^3,S)$, where S is a Brieskorn singularity., Comment: Dedicated to the memory of my advisor Vasilii Alekseevich Iskovskikh. 14 pages; v3: minor corrections

The low-lying spectra of $^8$He and $^{10}$He nuclei were studied in the $^3$H($^6$He,$p$)$^8$He and $^3$H($^8$He,$p$)$^{10}$He transfer reactions. The $0^+$ ground state (g.s.) of $^8$He and excited states, $2^+$ at $3.6-3.9$ MeV and $(1^+)$ at $5.3-5.5$ MeV, were populated with cross sections of 200, 100-250, and 90-125 $\mu$b/sr, respectively. Some evidence for $^8$He state at about 7.5 MeV is obtained. We discuss a possible nature of the near-threshold anomaly above 2.14 MeV in $^8$He and relate it to the population of a $1^-$ continuum (soft dipole excitation) with peak value at about 3 MeV. The lowest energy group of events in the $^{10}$He spectrum was observed at $\sim 3$ MeV with a cross section of $\sim 140$ $\mu$b/sr. We argue that this result is possibly consistent with the previously reported observation of $^{10}$He, in that case providing a new g.s. position for $^{10}$He at about 3 MeV., Comment: 18 pages, 8 figures, submitted to Phys. Lett. B

The dual complex can be associated to any resolution of singularities whose exceptional set is a divisor with simple normal crossings. It generalizes to higher dimensions the notion of the dual graph of a resolution of surface singularity. The homotopy type of the dual complex does not depend on the choice of a resolution and thus can be considered as an invariant of singularity. In this preprint we show that the dual complex is homotopy trivial for resolutions of 3-dimensional terminal singularities and for resolutions of Brieskorn singularities. We also review our earlier results on resolutions of rational and hypersurface singularities., Comment: 18 pages; to appear as a preprint of the Max-Planck-Institut, Bonn

The spectrum of $^9$He was studied by means of the $^8$He($d$,$p$)$^9$He reaction at a lab energy of 25 MeV/n and small center of mass (c.m.) angles. Energy and angular correlations were obtained for the $^9$He decay products by complete kinematical reconstruction. The data do not show narrow states at $\sim $1.3 and $\sim $2.4 MeV reported before for $^9$He. The lowest resonant state of $^9$He is found at about 2 MeV with a width of $\sim $2 MeV and is identified as $1/2^-$. The observed angular correlation pattern is uniquely explained by the interference of the $1/2^-$ resonance with a virtual state $1/2^+$ (limit on the scattering length is obtained as $a > -20$ fm), and with the $5/2^+$ resonance at energy $\geq 4.2$ MeV., Comment: 5 pages, 4 figures, 2 tables

It is well known that the exceptional set in a resolution of a rational surface singularity is a tree of rational curves. We generalize the combinatoric part of this statement to higher dimensions and show that the highest cohomologies of the dual complex associated to a resolution of an isolated rational singularity vanish. We also prove that the dual complex associated to a resolution of an isolated hypersurface singularity is simply connected. As a consequence, we show that the dual complex associated to a resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy type of a point., Comment: 10 pages, the structure of the paper has been slightly revised and a mistake in the proof of degeneration of spectral sequence in Lemma 2.3 (Lemma 2.4 of the published version of the paper) has been corrected

The dual complex associated to a resolution of singularities generalizes the notion of a resolution graph of a surface singularity to any dimension. We show that homotopy type of the dual complex is an invariant of an isolated singularity., Comment: 5 pages

Let $(X,o)$ be a germ of a 3-dimensional terminal singularity of index $m\geq 2$. If $(X,o)$ has type cAx/4, cD/3-3, cD/2-2, or cE/2, then assume that the standard equation of $X$ in $\mathbb{C}^4/\mathbb{Z}_m$ is non-degenerate with respect to its Newton diagram. Let $\pi\colon Y\to X$ be a resolution. We show that there are not more than 2 non-rational divisors $E_i$, $i=1,2$, on $Y$ such that $\pi(E_i)=o$ and discrepancy $a(E_i,X)\leq 1$. When such divisors exist, we describe them as exceptional divisors of certain blowups of $X$ and study their birational type., Comment: 17 pages, LaTeX2e

Let $(X,o)$ be a 3-dimensional terminal singularity of type $cD$ or $cE$ defined in $\mathbb{C}^4$ by an equation non-degenerate with respect to its Newton diagram. We show that there is not more than 1 non-rational divisor $E$ over $(X,o)$ with discrepancy $a(E,X)=1$. We also describe all blowups $\sigma$ of $(X,o)$ such that $E=\Exc(\sigma)$ is non-rational and $a(E,X)=1$., Comment: 15 pages