Imox

We prove several Paley--Wiener-type theorems related to the spherical transform on the Gelfand pair $\big(H_n\rtimes U(n),U(n)\big)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in ${\mathbb R}^2$, we prove that spherical transforms of $ U(n)$--invariant functions and distributions with compact support in $H_n$ admit unique entire extensions to ${\mathbb C}^2$, and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations. - Imox

This paper studies automatic structures for subsemigroups of Baumslag--Solitar semigroups (that is, semigroups presented by $\ < x,y \mid (yx^m, x^ny)\ >$, where $m$ and $n$ are natural numbers). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if $m \gt n$, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If $m \lt n$, all of its finitely generated subsemigroups are left-automatic. If $m = n$, there exist finitely generated subsemigroups that are not automatic. An appendix discusses the implications of these results for the theory of Malcev presentations. (A Malcev presentation is a special type of presentation for semigroups embeddable into groups.) - Imox

We extend the study by Ornstein and Weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a certain class of mixing processes. Further, an estimator for entropy based on recurrence times is proposed for which large deviation behavior is proved for stationary and ergodic sources satisfying similar mixing conditions. - Imox

Mathematical model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the nonzero vorticity. Generalized advection-diffusion-reaction equation is derived for arbitrary number components in the flux. The fluxes in the layers are objects for matching requirements on the boundaries between the layers. - Imox

A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration and equilibrium of the particle are similar to the Segr\'e-Silberberg effect in our numerical simulations. Surprisingly, two lateral equilibrium positions are observed corresponding to the releasing positions of the biconcave particle. The upper equilibrium positions significantly decrease with the growth of the Reynolds number, whereas the lower ones are almost insensitive to the Reynolds number. Interestingly, the regular wave accompanied by nonuniform rotation is exhibited in the lateral movement of the biconcave particle. It can be attributed to that the biconcave shape in various postures interacts with the parabolic velocity distribution of the Poiseuille flow. A set of contours illustrate the dynamic flow field when the biconcave particle has successive postures in a rotating... - Imox

In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper. - Imox

A challenge for nuclear physics is to measure masses of exotic nuclei up to the limits of nuclear existence which are characterized by low production cross sections and short half-lives. The large acceptance Collector Ring (CR) at FAIR tuned in the isochronous ion-optical mode offers unique possibilities for measuring short-lived and very exotic nuclides. However, in a ring designed for maximal acceptance, many factors limit the resolution. One point is a limit in time resolution inversely proportional to the transverse emittance. But most of the time aberrations can be corrected and others become small for large number of turns. We show the relations of the time correction to the corresponding transverse focusing and that the main correction for large emittance corresponds directly to the chromaticity correction for transverse focusing of the beam. With the help of Monte-Carlo simulations for the full acceptance we demonstrate how to correct the revolution times so that in principle... - Imox

This paper presents the integral(or differential) form of G-BSDEs, gives some kind of apriori estimates of their solutions, and under a very strong condition, proves the G-martingale representation theorem, and the existence and uniqueness theorem of G-BSDEs. - Imox

We prove a Poincare-Alexander-Lefschetz duality theorem for rational torus-equivariant cohomology and rational homology manifolds. We allow non-compact and non-orientable spaces. We use this to deduce certain short exact sequences in equivariant cohomology, originally due to Duflot in the differentiable case, from similar, but more general short exact sequences in equivariant homology. A crucial role is played by the Cohen-Macaulayness of relative equivariant cohomology modules arising from the orbit filtration. - Imox

The counter rotating-wave term (CRT) effects from the system-bath coherence on the dynamics of quantum correlation of two qubits in two independent baths and a common bath are systematically investigated. The hierarchy approach is extended to solve the relevant spin boson models with the Lorentzian spectrum, the exact dynamics for the quantum entanglement and quantum discord (QD) are evaluated, and the comparisons with previous ones under the rotating-wave approximation are performed. For the two independent baths, beyond the weak system-bath coupling, the CRT essentially changes the evolution of both entanglement and QD. With the increase of the coupling, the revival of the entanglement is suppressed dramatically and finally disappears, and the QD becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the CRT, but the QD shows quite different behaviors, if initiated from the correlated Bell states. In the non-Markovian regime, the QD is almost not... - Imox

We establish an achievable rate region for discrete memoryless interference relay channels that consist of two source-destination pairs and one or more relays. We develop an achievable scheme combining Han-Kobayashi and noisy network coding schemes. We apply our achievability to two cases. First, we characterize the capacity region of a class of discrete memoryless interference relay channels. This class naturally generalizes the injective deterministic discrete memoryless interference channel by El Gamal and Costa and the deterministic discrete memoryless relay channel with orthogonal receiver components by Kim. Moreover, for the Gaussian interference relay channel with orthogonal receiver components, we show that our scheme achieves a better sum rate than that of noisy network coding. - Imox

Let $k$ be a field of characteristic different from 2 and $F_n=k(!(t_1,\dotsc, t_n)!)$ a Laurent series field in $n\ge 2$ variables over $k$. We study the Pythagoras number $p(F_n)$ and the $u$-invariant $u(F_n)$ (in the sense of Elman--Lam) of the field $F_n$. We prove an equality which relates $p(F_2)$ (resp. $u(F_2)$) to the Pythagoras numbers (resp. the $u$-invariants) of the rational function fields $k'(t)$ for all finite extensions $k'$ of $k$. This enables us to get the exact value of $p(k(!(t_1,\,t_2)!))$ when $k$ is a number field. In particular, we obtain $p(\mathbb{Q}(!(t_1,\,t_2)!))=5$. The formula for the $u$-invariant implies the finiteness of $u(k(!(t_1,\,t_2)!))$ for any finitely generated extension $k$ of $\mathbb{R}$. In general, we show that $p(F_n)\le p(F_{n-1}(t))$ and $u(F_n)\le u(F_{n-1}(t))$. This leads us to a proof of the equality $p(\mathbb{R}(!(t_1,\,t_2,\,t_3)!))=4$. We also make two conjectures for general $n$ based on our specific results. - Imox

A total dominating set in a graph is a set of vertices such that every vertex of the graph has a neighbor in the set. We introduce and study graphs that admit non-negative real weights associated to their vertices so that a set of vertices is a total dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We show that these graphs, which we call total domishold graphs, form a non-hereditary class of graphs properly containing the classes of threshold graphs and the complements of domishold graphs. We present a polynomial time recognition algorithm of total domishold graphs, and obtain partial results towards a characterization of graphs in which the above property holds in a hereditary sense. Our characterization in the case of split graphs is obtained by studying a new family of hypergraphs, defined similarly as the Sperner hypergraphs, which might be of independent interest. - Imox

The aim of this paper is to classify indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on compete intersection Calabi-Yau (CICY) threefolds and prove the existence of some of them. New geometric properties of the curves corresponding to rank 2 ACM bundles (by Serre correspondence) are obtained. These follow from minimal free resolutions of curves in suitably chosen fourfolds (containing Calabi-Yau threefolds as hypersurfaces). Also the existence of an indecomposable vector bundle of higher rank on a CICY threefold of type (2,4) is proved. - Imox

We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest-neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models as... - Imox

We consider the power series expansion of Lame function in the Weierstrass's form and its integral forms applying three term recurrence formula by Choun. And we investigate how Lame functions behaves as independent variable $\xi= sn^2(z,\rho)$ goes to $\infty $ asymptotically for the cases of infinite series and polynomials. We show how to transform power series expansion of Lame function to an integral formalism mathematically in an elegant way for cases of infinite series and polynomial. And we show that integral form of Lame function involves $_2F_1$ function in itself analytically. - Imox

Previous measurements with a single trapped proton or antiproton detected spin resonance from the increased scatter of frequency measurements caused by many spin flips. Here individual spin transitions and states are detected instead. This suggests the possibility to eventually use quantum jump spectroscopy to measure the proton and antiproton magnetic moments much more precisely. - Imox

New measurements using radio and plasma-wave instruments in interplanetary space have shown that nanometer-scale dust, or nanodust, is a significant contributor to the total mass in interplanetary space. Better measurements of nanodust will allow us to determine where it comes from and the extent to which it interacts with the solar wind. When one of these nanodust grains impacts a spacecraft, it creates an expanding plasma cloud, which perturbs the photoelectron currents. This leads to a voltage pulse between the spacecraft body and the antenna. Nanodust has a high charge/mass ratio, and therefore can be accelerated by the interplanetary magnetic field to speeds up to the speed of the solar wind: significantly faster than the Keplerian orbital speeds of heavier dust. The amplitude of the signal induced by a dust grain grows much more strongly with speed than with mass of the dust particle. As a result, nanodust can produce a strong signal, despite their low mass. The WAVES... - Imox

Assume that a finite almost simple group with simple socle isomorphic to an exceptional group of Lie type possesses a solvable Hall subgroup. Then there exist four conjugates of the subgroup such that their intersection is trivial. - Imox

The fundamental "two-fluid" model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions in three space dimensions for the Euler-Maxwell system. Our construction applies equally well to other plasma models such as the Euler-Poisson system for two-fluids and a relativistic Euler-Maxwell system for two fluids. Our solutions appear to be the first nontrivial global smooth solutions in all of these models. - Imox

In this paper we prove that the shape optimization problem $$\min\left\{\lambda_k(\Omega):\ \Omega\subset\R^d,\ \Omega\ \hbox{open},\ P(\Omega)=1,\ |\Omega|<+\infty\right\},$$ has a solution for any $k\in\N$ and dimension $d$. Moreover, every solution is a bounded connected open set with boundary which is $C^{1,\alpha}$ outside a closed set of Hausdorff dimension $d-8$. Our results are more general and apply to spectral functionals of the form $f(\lambda_{k_1}(\Omega),\dots,\lambda_{k_p}(\Omega))$, for increasing functions $f$ satisfying some suitable bi-Lipschitz type condition. - Imox

Given a permutation $\sg = \sg_1 \ldots \sg_n$ in the symmetric group $S_n$, we say that $\sg_i$ matches the marked mesh pattern $MMP(a,b,c,d)$ in $\sg$ if there are at least $a$ points to the right of $\sg_i$ in $\sg$ which are greater than $\sg_i$, at least $b$ points to the left of $\sg_i$ in $\sg$ which are greater than $\sg_i$, at least $c$ points to the left of $\sg_i$ in $\sg$ which are smaller than $\sg_i$, and at least $d$ points to the right of $\sg_i$ in $\sg$ which are smaller than $\sg_i$. This paper is continuation of the systematic study of the distribution of quadrant marked mesh patterns in 132-avoiding permutations started in \cite{kitremtie} and \cite{kitremtieII} where we studied the distribution of the number of matches of $MMP(a,b,c,d)$ in 132-avoiding permutations where at most two elements of of $a,b,c,d$ are greater than zero and the remaining elements are zero. In this paper, we study the distribution of the number of matches of $MMP(a,b,c,d)$ in 132-avoiding... - Imox

Large scale simulations and analytical theory have been combined to obtain the non-equilibrium velocity distribution, $f(v)$, of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions which are independent of volume fraction and collision processes. Consequently, a one-particle model can capture all the essential features of $f(v)$. We have solved the one particle model analytically in the limit of strong damping, where we find a divergence of $f(v)$ for small argument, a $1/v$-decay for intermediate and a Gaussian decay for the largest velocities. Many particle simulations and solution of the one-particle model agree for all values of the damping. - Imox

In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y_2SiO_5 crystals. The homogeneous line width was measured to be about 3 MHz, which is essentially limited by the excited state lifetime. Based on the line width measurements, the oscillator strength, absorption cross section and saturation intensity were calculated to be about 9*10^-7, 5*10^-19 m^2 and 1*10^7 W/m^2, respectively. One projection of the difference in permanent dipole moment, Delt_miu_Ce, between the ground and excited states of the Ce ion was measured as 6.3 * 10^-30 C*m, which is about 26 times as large as that of Pr ions. The measurements done on Ce ions indicate that... - Imox

It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail in [S. S. Ray et al., Phys. Rev. E 84, 016301 (2011)], and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution. In this work, we propose a way to remove this resonance by filtering a wavelet representation of the Galerkin-truncated equations. A method previously developed with a complex-valued wavelet frame is applied and expanded to embrace the use of real-valued orthogonal wavelet basis, which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space. We also apply the complex-valued wavelet based method to the 2D Euler equation problem, showing that it is able to filter the resonances in this case... - Imox

We have proved in this paper that the Lindel\" of hypothesis generates essential contraction of distances between consecutive odd-order zeros of the function $Z'(t)$. This paper is the translation of the paper \cite{11} into the English except part 8 that we added in order to point out the I. M. Vinogradov' scepticism on possibilities of the method of trigonometric sums. - Imox

This paper is concerned with fixed-point free $\s^1$-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a dominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, there are at most finitely many distinct smooth (resp. topological) 4-manifolds which support a fixed-point free smooth (resp. locally linear) $\s^1$-action and realize the given group as the fundamental group. A similar statement holds for the number of equivalence classes of fixed-point free $\s^1$-actions under some further conditions on the fundamental group. The connection between the classification of the $\s^1$-manifolds and the fundamental group is given by a certain decomposition, called {\it fiber-sum decomposition}, of the $\s^1$-manifolds. More concretely, each fiber-sum decomposition naturally gives rise to a Z-splitting of the fundamental group. There are two... - Imox

We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3. - Imox

We give sufficient conditions for two Cantor sets of the line to be nested for a positive set of translation parameters. This problem is a toy model of the parameter selection for nonuniformly hyperbolic attractors of the plane. In natural such models, we show that this condition is optimal. - Imox

We study the chiral two-matrix model with polynomial potential functions $V$ and $W$, which was introduced by Akemann, Damgaard, Osborn and Splittorff. We show that the squared singular values of each of the individual matrices in this model form a determinantal point process with correlation kernel determined by a matrix-valued Riemann-Hilbert problem. The size of the Riemann-Hilbert matrix depends on the degree of the potential function $W$ (or $V$ respectively). In this way we obtain the chiral analogue of a result of Kuijlaars-McLaughlin for the non-chiral two-matrix model. The Gaussian case corresponds to $V,W$ being linear. For the case where $W(y)=y^2/2+\alpha y$ is quadratic, we derive the large $n$-asymptotics of the Riemann-Hilbert problem by means of the Deift-Zhou steepest descent method. This proves universality in this case. An important ingredient in the analysis is a third-order differential equation. Finally we show that if also $V(x)=x$ is linear, then a... - Imox