Formalization of Complex Vectors in Higher-Order Logic

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting this analysis within the sound core of a theorem prover: HOL Light. Our definition of complex vector builds upon the definitions of complex numbers and real vectors. This extension allows us to extensively benefit from the already verified theorems based on complex analysis and real vector analysis. To show the practical usefulness of our library we adopt it to formalize electromagnetic fields and to prove the law of reflection for the planar waves.Comment: 15 pages, 1 figur

Minimax estimation with thresholding and its application to wavelet analysis

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James-Stein estimator is such an estimator, having a property called minimaxity. However, the estimator considers only one reduced model, namely the origin. Hence it reduces no coefficient estimator to zero or every coefficient estimator to zero. In many applications including wavelet analysis, what should be more desirable is to reduce to zero only the estimators smaller than a threshold, called thresholding in this paper. Is it possible to construct this kind of estimators which are minimax? In this paper, we construct such minimax estimators which perform thresholding. We apply our recommended estimator to the wavelet analysis and show that it performs the best among the well-known estimators aiming simultaneously at estimation and model selection. Some of our estimators are also shown to be asymptotically optimal.Comment: Published at http://dx.doi.org/10.1214/009053604000000977 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Synthesis of polyethers of hexafluorobenzene and hexafluoropentanediol

Two new polyethers, poly /hexafluoropentamethylene tetrafluoro-p-phenylene ether/ and a completely hydroxyl-terminated polyether, is prepared by reactions of hexafluorobenzene with hexafluoropentanediol. The polyethers can be prepared as low molecular weight oils, as intermediate molecular weight waxes, or as high molecular weight elastomers

Quantum transport in semiconductor quantum dot superlattices: electron-phonon resonances and polaron effects

Electron transport in periodic quantum dot arrays in the presence of interactions with phonons was investigated using the formalism of nonequilibrium Green's functions. The self-consistent Born approximation was used to model the self-energies. Its validity was checked by comparison with the results obtained by direct diagonalization of the Hamiltonian of interacting electrons and longitudinal optical phonons. The nature of charge transport at electron -- phonon resonances was investigated in detail and contributions from scattering and coherent tunnelling to the current were identified. It was found that at larger values of the structure period the main peak in the current -- field characteristics exhibits a doublet structure which was shown to be a transport signature of polaron effects. At smaller values of the period, electron -- phonon resonances cause multiple peaks in the characteristics. A phenomenological model for treatment of nonuniformities of a realistic quantum dot ensemble was also introduced to estimate the influence of nonuniformities on current -- field characteristics

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Life raft stabilizer

An improved life raft stabilizer for reducing rocking and substantially precluding capsizing is discussed. The stabilizer may be removably attached to the raft and is defined by flexible side walls which extend a considerable depth downwardly to one another in the water. The side walls, in conjunction with the floor of the raft, form a ballast enclosure. A weight is placed in the bottom of the enclosure and water port means are provided in the walls. Placement of the stabilizer in the water allows the weighted bottom to sink, producing submerged deployment thereof and permitting water to enter the enclosure through the port means, thus forming a ballast for the raft

Stable, inflatable life raft for high seas rescue operations

Raft is easily deployed and highly maneuverable in water. It has false bottom of water ballast containers attached to underside, making it exceptionally stable platform from which swimmers can operate. Raft is attachable to external moorings

Zapotec Language Activism And Talking Dictionaries

Online dictionaries have become a key tool for some indigenous communities to promote and preserve their languages, often in collaboration with linguists. They can provide a pathway for crossing the digital divide and for establishing a first-ever presence on the internet. Many questions around digital lexicography have been explored, although primarily in relation to large and well-resourced languages. Lexical projects on small and under-resourced languages can provide an opportunity to examine these questions from a different perspective and to raise new questions (Mosel, 2011). In this paper, linguists, technical experts, and Zapotec language activists, who have worked together in Mexico and the United States to create a multimedia platform to showcase and preserve lexical, cultural, and environmental knowledge, share their experience and insight in creating trilingual online Talking Dictionaries in several Zapotec languages. These dictionaries sit opposite from big data mining and illustrate the value of dictionary projects based on small corpora, including having the flexibility to make design decisions to maximize community impact and elevate the status of marginalized languages

Experimental observation of Frohlich superconductivity in high magnetic fields

Resistivity and irreversible magnetisation data taken within the high-magnetic-field CDWx phase of the quasi-two-dimensional organic metal alpha-(BEDT-TTF)2KHg(SCN)4 are shown to be consistent with a field-induced inhomogeneous superconducting phase. In-plane skin-depth measurements show that the resistive transition on entering the CDWx phase is both isotropic and representative of the bulk.Comment: ten pages, four figure