Polynomial growth of sumsets in abelian semigroups

Let S be an abelian semigroup, and A a finite subset of S. The sumset hA consists of all sums of h elements of A, with repetitions allowed. Let |hA| denote the cardinality of hA. Elementary lattice point arguments are used to prove that an arbitrary abelian semigroup has polynomial growth, that is, there exists a polynomial p(t) such that |hA| = p(h) for all sufficiently large h. Lattice point counting is also used to prove that sumsets of the form h_1A_1 + >... + h_rA_r have multivariate polynomial growth.Comment: 8 pages. LaTex. To appear in Journal de Theorie des Nombres de Bordeau

Binary linear forms over finite sets of integers

Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y and g(x,y)=u_2x+v_2y with integral coefficients, there exist arbitrarily large finite sets of integers A and B such that |f(A)| > |g(A)| and |f(B)| < |g(B)|.Comment: 20 page

Simulation Studies of Nanomagnet-Based Architecture

We report a simulation study on interacting ensembles of Co nanomagnets that can perform basic logic operations and propagate logic signals, where the state variable is the magnetization direction. Dipole field coupling between individual nanomagnets drives the logic functionality of the ensemble and coordinated arrangements of the nanomagnets allow for the logic signal to propagate in a predictable way. Problems with the integrity of the logic signal arising from instabilities in the constituent magnetizations are solved by introducing a biaxial anisotropy term to the Gibbs magnetic free energy of each nanomagnet. The enhanced stability allows for more complex components of a logic architecture capable of random combinatorial logic, including horizontal wires, vertical wires, junctions, fanout nodes, and a novel universal logic gate. Our simulations define the focus of scaling trends in nanomagnet-based logic and provide estimates of the energy dissipation and time per nanomagnet reversal

Quantum chaos in one dimension?

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.Comment: 7 pages, 10 figures, minor correction, references extende

Deriving feasible deployment alternatives for parallel and distributed simulation systems

Cataloged from PDF version of article.Parallel and distributed simulations (PADS) realize the distributed execution of a simulation system over multiple physical resources. To realize the execution of PADS, different simulation infrastructures such as HLA, DIS and TENA have been defined. Recently, the Distributed Simulation Engineering and Execution Process (DSEEP) that supports the mapping of the simulations on the infrastructures has been defined. An important recommended task in DSEEP is the evaluation of the performance of the simulation systems at the design phase. In general, the performance of a simulation is largely influenced by the allocation of member applications to the resources. Usually, the deployment of the applications to the resources can be done in many different ways. DSEEP does not provide a concrete approach for evaluating the deployment alternatives. Moreover, current approaches that can be used for realizing various DSEEP activities do not yet provide adequate support for this purpose. We provide a concrete approach for deriving feasible deployment alternatives based on the simulation system and the available resources. In the approach, first the simulation components and the resources are designed. The design is used to define alternative execution configurations, and based on the design and the execution configuration; a feasible deployment alternative can be algorithmically derived. Tool support is developed for the simulation design, the execution configuration definition and the automatic generation of feasible deployment alternatives. The approach has been applied within a large-scale industrial case study for simulating Electronic Warfare systems. © 2013 ACM

Mixed-metal pillared layer clays and their pillaring precursors

Mixed-metal pillared layer clays (Fe,Al-PILCs and Cr,Al-PILCs) of various compositions and the pillaring precursors have been prepared and characterised with a combination of chemical and instrumental methods. Chemical analysis data, IR, (57)Mossbauer and Al-27 NMR spectroscopic measurements on the precipitated pillaring precursors and comparison of redox behaviour [temperature-programmed reduction (TPR) results and Fe-57 Mossbauer measurements on the heat-treated and the reduced samples] of the ion-exchanged and Al-pillared and mixed-metal pillared clays revealed that isomorphous substitution of Al for Fe or Cr did not occur in either the tetrahedral or the octahedral positions. Heat treatment, however, resulted in mixed-metal pillared clays which were active in both acid- catalysed and redox transformations

(n,m)-fold covers of spheres

A well-known consequence of the Borsuk-Ulam theorem is that if the d-dimensional sphere Sd is covered with less than d + 2 open sets, then there is a set containing a pair of antipodal points. In this paper we provide lower and upper bounds on the minimum number of open sets, not containing a pair of antipodal points, needed to cover the d-dimensional sphere n times, with the additional property that the northern hemisphere is covered m > n times. We prove that if the open northern hemisphere is to be covered m times, then at least ⌈(d − 1)/2⌉ + n + m and at most d + n + m sets are needed. For the case of n = 1 and d ≥ 2, this number is equal to d + 2 if m ≤ ⌊d/2⌋ + 1 and equal to ⌊(d − 1)/2⌋ + 2 + m if m > ⌊d/2⌋ + 1. If the closed northern hemisphere is to be covered m times, then d + 2m − 1 sets are needed; this number is also sufficient. We also present results on a related problem of independent interest. We prove that if Sd is covered n times with open sets not containing a pair of antipodal points, then there exists a point that is covered at least ⌈d/2⌉ + n times. Furthermore, we show that there are covers in which no point is covered more than n + d times. © 2015, Pleiades Publishing, Ltd

Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.Comment: RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Let