Amalgamation,interpolation and epimorphisms in algebraic logic

In his landmark paper on amalgamation published in Algebra Universalis in 1971, Don Pigozzi posed some open questions in connection with amalgamation of subclasses of cylindric algebras. Some of these questions were originally raised by Comer, Daigneault, Johnson, McKenzie and others. In this paper we give answers to all these as well as a number of other related questions. Most of the solutions were found by the authors of this paper. However, a few were contributed by others who will of course be given due credit at the appropriate points. This paper is dedicated to Don Pigozzi on his retirement. Presented by R. W. Quackenbush. The first author’s research was supported by the Hungarian National Foundation for Scientific Research grants no T30314 and T23234. The second author’s research was supported by the Hungarian National Foundation for Scientific Reserach OKTA grant no T30314. All the new results in this article were announced by Judit Madarász in the Workshop on Abstract Algebraic Logic, held in Centre de Recerca Matematica Bellaterra, Spain July 1–5, 1997. Received December 15, 2002; accepted in final form January 3, 2006.     

Star‐Shaped Polyaromatic Ethers Coordinated to Redox‐Active Cyclopentadienyliron Moieties

This communication is focused on the controlled design of star‐shaped aromatic ethers with pendent cyclopentadienyliron moieties. A trimetallic core was prepared, which was then reacted with a number of oligomeric ether complexes to give star‐shaped polymers with six, nine, twelve and fifteen pendent cationic cyclopentadienyliron moieties. Cyclic voltammetric studies showed reduction of the iron centers between –0.99 and –1.41 V. Thermogravimetric analysis showed that loss of the metallic moieties occurred between 225 and 284°C.     

Novel method for preparation of poly(benzoxazinone‐imide)

A novel method was developed to prepare poly(benzoxazinone‐imide) by the dealcoholization of poly(amide‐imide), having pendent ethoxycarbonyl groups, which was prepared from poly(amide acid). The poly(amide acid) was prepared from the reaction of pyromellitic dianhydride and 4,4′‐diamino‐6‐ethoxycarbonyl benzanilide. The curing behavior of the poly(amide acid) was monitored by DSC, which indicated the presence of two broad endotherms, one with maximum at 153 °C due to imide‐ring formation and the other with maximum at 359 °C due to benzoxazinone‐ring formation. The poly(amide acid) was thermally treated at 300 °C/1 h to get poly(amide‐imide) with pendent ester groups, then at 350 °C/2 h to convert into poly(benzoxazinone‐imide) by dealcoholization. Viscoelastic measurements of the poly(amide‐imide) showed that the storage modulus dropped at about 280 °C with glass‐transition temperature (T_g ) at about 340 °C. The storage modulus of poly(benzoxazinone‐imide), however, was almost constant up to 400 °C and no T_g was detected below 400 °C. Also, the tensile modulus and tensile strength of the poly(benzoxazinone‐imide) was much higher than that of the poly(amide‐imide). The 5% decomposition of poly(benzoxazinone‐imide) film was at 535 °C, which reflects its excellent thermal stability. Also, poly(benzoxazinone‐imide) showed more hydrolytic stability against alkali in comparison to polyimides. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1647–1655, 2000     

Exploiting the subharmonic parametric resonances of a buckled beam for vibratory energy harvesting

The potential of harvesting vibratory energy via a bistable beam subjected to subharmonic parametric excitations is investigated. The vibrating structure is a buckled beam with two stable equilibria separated by a potential barrier. The beam is subjected to a superposition of a static axial load beyond its buckling load and a harmonic axial excitation whose frequency is around twice the frequency of the buckled beam’s first vibration mode. A macro-fiber composite patch is attached to one side of the beam to convert the strain energy resulting from the beam’s oscillation into electricity. The study considers two regimes of excitations: an amplitude sweep and a frequency sweep. In the first regime, the amplitude of excitation is quasi-statically varied while the excitation frequency is tuned at twice the natural frequency of the first vibration mode. In the second regime, the excitation frequency is swept forward and backward around the subharmonic resonant frequency while the amplitude of excitation is kept constant. A theoretical model which governs the electromechanical coupling of the transverse vibrations of the beam and the output voltage is used to monitor the response as the excitation parameters are changed. An experimental setup is also built and a series of tests is performed to validate the theoretical findings. It is shown that, depending on the amplitude and frequency of excitation, the harvester can perform small-amplitude periodic intra-well motion, intra- and inter-well chaotic motions, as well as periodic inter-well motions. Experimental results also show that, as compared to the classical linear resonance, utilizing the sub-harmonic resonance of a bistable energy harvesters can result in a broadband frequency response.     

ASACUSA MUSASHI: New progress with intense ultra slow antiproton beam

Our group “ASACUSA MUSASHI” has established an efficient way for accumulating antiprotons and extracting them as intense ultra-slow mono-energetic beams at the CERN-AD facility. This novel beam opens new frontiers for investigating a variety of physics. For realizing H? spectroscopy and the test for charge-parity-time symmetry, we have also developed the cusp trap, a combination of an anti-Helmholz superconducting coil and a multi-ring electrode trap, for trapping both antiprotons and positrons and then synthesizing antihydrogens. Recently, the cusp trap was practically used to accumulate antiprotons. The last piece for synthesizing antihydrogens in the cusp trap is the positron accumulator. We have developed a compact system to effectively accumulate positrons based on N₂ gas-buffer scheme with a specially designed high precision cylindrical multi-ring electrode trap. The recent progress of the developing work is an important milestone for upcoming antihydrogen science of ASACUSA MUSASHI.     

Conformational stability, r 0 structural parameters, barriers to internal rotation, ab initio calculations, and vibrational assignment for 2,2-difluoroethanol

The infrared spectra (4,000–30 cm^?1) of the gas and solid and the Raman spectrum of liquid 2,2-difluoroethanol as well as variable temperature infrared spectra of krypton/xenon solutions have been recorded. From all these data, two (Gg and Tg) out of the five possible stable conformers have been confidently identified. The order of the stabilities has been predicted to be Gg > Tg > Gt > Gg′ > Tt by utilizing ab initio MP2 (full) and DFT (B3LYP method) calculations, where the first indicator (capital letter) is in reference to rotation around the C–C bond (G = gauche or T = trans) and the second one (small letter) refers to the orientation of the hydroxyl group. The percentage of the minor conformer Tg, at ambient temperature, is estimated to be (16 ± 3%). The optimized geometries, fundamental frequencies, infrared intensities, Raman activities, and depolarization values as well as centrifugal distortion constants have been obtained from ab initio and density functional theory calculations by utilizing a variety of basis sets as well as those with diffuse functions. By utilizing the previously reported microwave rotational constants for two isotopomers of the Gg conformer combined with ab initio MP2(full)/6-311+G(d,p) predicted structural values, adjusted r ₀ parameters have been obtained. The determined heavy atom distances (Å) for the Gg conformer are: C₁–C₂ = 1.510(3), C₂–F₄ = 1.371(3), C₂–F₅ = 1.362(3), C₁–O₃ = 1.412(3) Å and angles ∠O₃C₁C₂ = 111.0(5), ∠F₄C₂C₁ = 108.8(5), ∠F₅C₂C₁ = 109.8(5), τF₄C₂C₁O₃ = 63.5(5), τF₅C₂C₁O₃ = 179.1(5)°. Barriers of internal rotation have been obtained and vibrational assignments for the Gg and Tg conformers are given. The five predicted centrifugal distortion constants compared to the experimental values are in reasonable agreement except for ?_K, which appears to be in error. The results are discussed and the structural parameters compared to the corresponding ones for 2-fluoroethanol and 2,2,2-trifluoroethanol where those for the latter molecule have been redetermined. The currently determined heavy atom parameters are quite different from the earlier assumed values, which led to poor values of the six adjusted parameters.     

METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.     

A novel design approach for the epitaxial layer for 4H-SiC and 6H-SiC power bipolar devices

The paper evaluates the optimal design of the low-doped base region inside power diodes and other bipolar devices. It is demonstrated theoretically that a low-doped base region of P⁺N⁻N⁺ diodes can provide a high breakdown voltage and an optimal on-resistance . A simple, accurate and CPU timesaving approach is presented to extract an optimal value for the base region width, W_B, and its doping concentration, N_D. The paper details an analytical relation between W_B and N_D, and gives a method for quantifying the trade-off between their values for a given breakdown voltage and for obtaining the minimal on-resistance. Analytical results are confronted with experimental results for 4H-SiC- and 6H-SiC-based diodes.     

Efficient construction of the hexacyclic ring core of palau'amine: the pKa concept for proceeding with unfavorable equilibrium reactions

Palau''amine has received a great deal of attention as an attractive synthetic target due to its intriguing molecular architecture and significant immunosuppressive activity, and we achieved its total synthesis in 2015. However, the synthesized palau''amine has not been readily applicable to the mechanistic study of immunosuppressive activity, because it requires 45 longest linear steps from a commercially available compound. Here, we report the short-step construction of the ABCDEF hexacyclic ring core of palau''amine. The construction of the CDE tricyclic ring core in a single step is achieved by our pK_a concept for proceeding with unfavorable equilibrium reactions, and a palau''amine analog without the aminomethyl and chloride groups is synthesized in 20 longest linear steps from the same starting material. The palau''amine analog is confirmed to retain the immunosuppressive activity. The present synthetic approach for a palau''amine analog has the potential for use in the development of palau''amine probes for mechanistic elucidation.

A palau''amine analog (2) was synthesized from 2-cyclopentenone in 20 steps. The construction of the CDE tricyclic ring core in a single step is achieved by our pK_a concept for proceeding with the unfavorable equilibrium reactions.     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.