Grid oscillators

Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequencylocking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.     

Grid oscillators

Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequencylocking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.     

Freudenthal–Weil theorem for pro-Lie groups

An analog of the Freudenthal–Weil theorem holds for the discontinuous homomorphisms of a connected pro-Lie group into a compact group if and only if the radical of the pro-Lie group is amenable.     

Quasirepresentations of amenable groups: Results, errors, and hopes

In the paper, the structure of continuous Banach space quasirepresentations of amenable topological groups (which are not necessarily locally compact) is discussed, together with the corresponding results, errors, ways to reveal and correct some of the errors, and related hopes.     

磁性晶体二级相变理论与镧系金属的磁结构

本文讨论了Ландау二级相变理论中的稳定性条件,阐明了Лифшиц提出的对称改变限制条件是不必要的,从而可以讨论过去认为无法讨论的镧系金属镝(Dy)等在Neél点的二级相变,解释了镧系金属镝等在Neél点以下螺旋磁结构的螺距与温度成线性关系。同时,利用空间羣表示论和热力势极小条件,建立了一个讨论磁结构的新方法,用这方法分析了镧系金属的磁结构,所得的结果与中子衍射实验相符合。     

Complex bifurcations in a periodically forced normal form

The effect of a periodic forcing on the normal form of a two-dimensional dynamical system, in which both roots of the characteristic equation can vanish simultaneously, is analyzed. In the space spanned by the system's parameters, the onset of nonperiodic behavior and subharmonic behavior are determined analytically using standard perturbation theory. Moreover it is shown that complex behavior can already appear in the immediate vicinity of singular points. An example of physico-chemical system amenable to the normal form is also constructed.     

Amenability of crossed products ofC*-algebras

It is shown that the class of amenable (resp. strongly amenable)C*-algebras is closed under the process of taking crossed products with discrete amenable groups. Under certain circumstances, amenability is also preserved under taking a crossed product with an amenable semigroup of linear endomorphisms. These facts are used to show that certain simpleC*-algebras studied by J. Cuntz are amenable but not strongly amenable (thus answering a question of B. E. Johnson), yet are stably isomorphic to strongly amenable algebras.Partially supported by NSF     

A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction (MISDC) algorithm designed to advance the conservation equations in time at scales associated with advective transport. The fast and nontrivial interactions of electrons with the electric field are treated implicitly using a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is developed. Within the MISDC framework, this enables a close and stable coupling of diffusion, reactions and dielectric relaxation terms with advective transport and is shown to exhibit second-order convergence in space and time. The algorithm is then applied to a series of steady and unsteady problems to demonstrate its capability and stability. Although developed in a one-dimensional case, the algorithmic ingredients are carefully designed to be amenable to multi-dimensional applications.     

Formulation of few-body equations without partial waves

A formalism is developed whereby the two-body Lippmann-Schwinger equation may be solved in momentum space without partial-wave decomposition. The integral equation derived is two-dimensional and so is amenable to direct numerical solution. Because the technique uses the well-known helicity formalism, the matrices involved can be further reduced by taking advantage of symmetries common in nuclear and atomic systems (parity conservation, particle symmetry). An example is shown for nucleon-nucleon scattering, and the results are compared to those obtained from the usual partial-wave method.     

Effect test spaces and effect algebras

The concept of an effect test space, which is equivalent to a D-test space of Dvurečenskij and Pulmannová, is introduced. Connections between effect test space. (E-test space, for short) morphisms, and event-morphisms as well as between algebraic E-test spaces and effect algebras, are studied. Bimorphisms and E-test space tensor products are considered. It is shown that any E-test space admits a unique (up to an isomorphism) universal group and that this group, considered as a test group, determines the E-test space uniquely (up to an isomorphism).     

Comparison Theory and Smooth Minimal C*-Dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar’s Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff’s uncountable family of II₁ factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras. This research was supported in part by an NSERC Discovery Grant.     

Classification of Minimal Actions of a Compact Kac Algebra with Amenable Dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II₁. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.     

Silicon molecules in space and in the laboratory

Despite the highly non-volatile nature of Si, silicon bearing molecules are a significant trace constituent of the gas associated with late-type stars and star forming regions, representing nearly 10% of the molecular species that have been identified in space. The early astronomical detection of SiO and its remarkable maser emission stimulated laboratory studies of other small silicon species that were crucial to the astronomical identifications. Although the pace of this laboratory work until recently has been slow, the application of Fourier transform microwave spectroscopy to supersonic molecular beams has overcome many experimental difficulties, yielding the detection of more than 20 new silicon chains and rings of astronomical interest during the past three years. Three of these, the rhomboidal ring Sic3 and the isovalent linear molecules SiCN and SiNC, have now been found in space, and with dedicated searches other recently discovered silicon molecules may soon be found. A number of exotic silicon molecules of astronomical and chemical interest should be amenable to laboratory detection with present techniques.     

Comments on the paper: “Active representations of space groups based on the simple cubic lattice” by H. Kunert and M. Suffczyński

It is pointed out that there are several errors and omissions in the above paper. In particular, an incorrect formula is given to determine if the unit representation of a space group is contained in the totally symmetrized cube of a space group irreducible representation.     

Spectral Triples of Holonomy Loops

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of Lie-groups composed of copies of the gauge group. A spectral triple over the space of connections is obtained by factoring out the diffeomorphism group. The triple consist of equivalence classes of loops acting on a hilbert space of sections in an infinite dimensional Clifford bundle. We find that the Dirac operator acting on this hilbert space does not fully comply with the axioms of a spectral triple.     

Uniform Existence of the Integrated Density of States on Metric Cayley Graphs

Given an arbitrary, finitely generated, amenable group we consider ergodic Schrödinger operators on a metric Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states (IDS) as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions. In this context, the present work generalises the hitherto known uniform IDS approximation results for operators on the d-dimensional metric lattice to a very large class of geometries.     

Semisimplicial Unital Groups

If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G ⁺ onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semisimplicial unital group G as the Banach dual space of a finite dimensional order-unit space that contains G as an additive subgroup. In terms of this representation, we formulate necessary and sufficient conditions for G to be archimedean.     

The conformal factor in the SAS Einstein-Maxwell field equations and a central extension of a formal loop group

We consider a relation between the conformal factor in the stationary axisymmetric (SAS) Einstein-Maxwell field equations and a central extension of a formal loop group which is described by a group 2-cocycle on the formal loop group. The corresponding 2-cocycle on the Lie algebra of the formal loop group is the one which describes an affine Lie algebra. As a result, we see that the space of formal solutions with conformal factors is a homogeneous space of a central extension of the Hauser group.     

On the Problem of the Amenability of the Gauge Group

Let G be one of the local gauge groups C(X, U(n)),C (X, U(n)), C(X, SU(n)) or C (X, SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz. the relative weak topology of C(X, M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology.