Some results on embeddings of algebras, after de Bruijn and McKenzie

In 1957, N.G. de Bruijn showed that the symmetric group Sym(Ω) on an infinite set Ω contains a free subgroup on 2^card(Ω) generators, and proved a more general statement, a sample consequence of which is that for any group A of cardinality card(Ω), the group Sym(Ω) contains a coproduct of 2^card(Ω) copies of A, not only in the variety of all groups, but in any variety of groups to which A belongs. His key lemma is here generalized to an arbitrary variety of algebras V, and formulated as a statement about functors Set V. From this one easily obtains analogs of the results stated above with “group” and Sym(Ω) replaced by “monoid” and the monoid Self(Ω) of endomaps of Ω, by “associative K-algebra” and the K-algebra End_K (V) of endomorphisms of a K-vector-space V with basis Ω, and by “lattice” and the lattice Equiv(Ω) of equivalence relations on Ω. It is also shown, extending another result from de Bruijn's 1957 paper, that each of Sym(Ω), Self(Ω) and End_K(V) contains a coproduct of 2^card(Ω) copies of itself.That paper also gave an example of a group of cardinality 2^card(Ω) that was not embeddable in Sym(Ω), and R. McKenzie subsequently established a large class of such examples. Those results are shown here to be instances of a general property of the lattice of solution sets in Sym(Ω) of sets of equations with constants in Sym(Ω). Again, similar results - this time of varying strengths - are obtained for Self(Ω), End_K(V), and Equiv(Ω), and also for the monoid Rel(Ω) of binary relations on Ω.Many open questions and areas for further investigation are noted.     

Holographic recording of fast events on a CCD camera

We report on holographic recording of nanosecond events on a conventional CCD camera. Three frames of an air-discharge event, with resolution of 5.9 ns and frame interval of 12 ns, are recorded in a single CCD frame. Each individual frame is reconstructed by digital filtering of the CCD frame, since successively recorded holograms are centered at different carrier frequencies in the spatial frequency domain.     

Boundary stabilization of structural acoustic interactions with interface on a Reissner–Mindlin plate

Boundary stabilization of a structural acoustic model comprised of a wave and a Reissner–Mindlin plate is addressed. Both the components of the dynamics are subject to localized nonlinear boundary damping: the acoustic dissipative feedback is restricted to the flexible boundary and only a portion of the rigid wall; the plate is damped only on a segment of its edge.Derivation of stabilization/observability inequalities for a coupled system requires weighted energy multipliers dependent on the geometry of the domain, and special microlocal trace estimates for the Reissner–Mindlin plate. The behavior of the energy at infinity can be quantified by a solution to an explicitly constructed nonlinear ODE. The nonlinearities in the feedbacks may include sub- and superlinear growth at infinity, in which case the decay scheme presents a trade-off between the regularity of trajectories and attainable uniform dissipation rates of the finite energy.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Secure Polar Coding for the Primitive Relay Wiretap Channel

With the emergence of wireless networks, cooperation for secrecy is recognized as an attractive way to establish secure communications. Departing from cryptographic techniques, secrecy can be provided by exploiting the wireless channel characteristics; that is, some error-correcting codes besides reliability have been shown to achieve information-theoretic security. In this paper, we propose a polar-coding-based technique for the primitive relay wiretap channel and show that this technique is suitable to provide information-theoretic security. Specifically, we integrate at the relay an additional functionality, which allows it to smartly decide whether it will cooperate or not based on the decoding detector result. In the case of cooperation, the relay operates in a decode-and-forward mode and assists the communication by transmitting a complementary message to the destination in order to correctly decode the initial source’s message. Otherwise, the communication is completed with direct transmission from source to the destination. Finally, we first prove that the proposed encoding scheme achieves weak secrecy, then, in order to overcome the obstacle of misaligned bits, we implement a double-chaining construction, which achieves strong secrecy.     

Semisimple Modules for Finite Groups of Lie Type

Let k be an algebraically closed field of characteristic p >0, and let G be a connected, reductive algebraic group overk. In [8] and [11], conditions on the dimension of rationalG modules were seen to imply semisimplicity of these modules.In [8], certain of these conditions were extended to cover thefinite groups of Lie type. In this paper, we extend some ofthe results of [11] to cover these finite Lie type groups. Themain such extension is the following result.     

Electron-Impact Induced Molecular Fluoresence Spectroscopy

Abstract

By the bombardment of gaseous molecules with monoenergetic electrons the molecules can be electronically excited and/or fragmented, depending upon the energy supplied by the electrons. Any fragments which may be produced also have the possibility of being produced in electronically (as well as vibrationally and rotationally) excited states. The electronically excited molecules and fragments both possess the possibility of radiative decay (fluorescence). The measurement of this fluorescence as a function of both electron energy and photon wavelength is termed “electron-impact induced fluorescence spectroscopy.” A plot of fluorescence intensity as a function of the electron energy at a given photon wavelength is generally referred to as an “excitation function,” which is exactly analogous to the excitation spectrum which can be obtained in conventional (optically excited) fluorescence spectrometry. A plot of the fluorescence intensity as a function of photon wavelength at a given electron energy is termed the “fluorescence spectrum.” A three dimensional plot of the fluorescence intensity as a function of both the photon wavelength and the electron energy may also be constructed, and is referred to as an “excitation contour plot.”     

CO2 hydrogenation to formic acid on Ni(110)

Hydrogen (H) in the subsurface of transition-metal surfaces exhibits unique reactivity for heterogeneously catalyzed hydrogenation reactions. Here, we explore the potential of subsurface H for hydrogenating carbon dioxide (CO₂) on Ni(110). The energetics of surface and subsurface H reacting with surface CO₂ to form formate, carboxyl, and formic acid on Ni(110) is systematically studied using self-consistent, spin-polarized, periodic density functional theory (DFT-GGA-PW91) calculations. We show that on Ni(110), CO₂ can be hydrogenated to formate by surface H. However, further hydrogenation of formate to formic acid by surface H is hindered by a larger activation energy barrier. The relative energetics of hydrogenation barriers is reversed for the carboxyl-mediated route to formic acid. We suggest that the energetics of subsurface H emerging to the surface is suitable for providing the extra energy needed to overcome the barrier to formate hydrogenation. CO₂ hydrogenation to formic acid could take place on Ni(110) when subsurface H is available to react with CO₂. Additional electronic-structure based dynamic calculations would be needed to elucidate the detailed reaction paths for these transformations.     

The first pulsar discovered by FAST

<正>To assist with the commissioning [1] of the Five-hundredmeter Aperture Spherical radio Telescope (FAST), we performed a pulsar search, with the primary goal of developing and testing the pulsar data acquisition and processing pipelines. We tested and used three pipelines, two (P1 and P2 hereafter) searched for the periodic signature of pulsars     

Generalized Bosbach states: part I

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics.