System identification based on distribution theory and wavelet transform

A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.     

Mathematical background for a method on quotient signal decomposition

The blind source separation problem is discussed in this article. Focusing on the assumption of independency of the sources in the time-frequency domain, we present a mathematical formulation for the estimation problem of the number of sources. The proposed method uses the quotient of complex valued time-frequency information of only two observed signals to detect the number of sources. No fewer number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. We propose algorithms with feedback and give numerical simulations to show the method works well even for noisy case.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

Theory of ferromagnetism in Ca(1-x)La(x)B(6)

Novel ferromagnetism in Ca(1-x)La(x)B(6) is studied in terms of the Ginzburg-Landau theory for excitonic-order parameters, taking into account symmetry of the wave functions. We found that the minima of the free energy break both inversion and time-reversal symmetries, while the product of these two remains preserved. This explains various novelties of the ferromagnetism and predicts a number of magnetic properties, including the magnetoelectric effect, which can be tested experimentally.     

Hole transport in polymers of (N-ethylcarbazol-3-yl) methyl acrylate and methacrylate

(N-Ethylcarbazol-3-yl)methyl acrylate and methacrylate were polymerized anionically and radically. Anionically-polymerized polyacrylate using ethylmagnesium chloride-benzalacetophenone as catalyst is an isotactic rich polymer with 85% isotactic dyad. All polymers except anionically polymerized polymethacrylate showed good film forming property. Hole drift mobilities measured by the time-of-flight method at room temperature and at 5 × 10⁵ V/cm are in the following order: isotactic polyacrylate (1.0 × 10^-5 cm²/V s) > atactic polyacrylate (1.8 × 10^-6 cm²/V s) > atactic polymethacrylate (1.2 × 10^-6 cm²/V s) at 5 × 10⁵ V/cm. These results are discussed in terms of the hopping model between localized sites.     

Surface properties of styrene–ethylene oxide block copolymers

Hydrophobic–hydrophilic block copolymers were prepared by “living” anionic polymerization. They consist of polystyrene and poly(ethylene oxide) blocks, and are soluble in water. Their interfacial properties were investigated, employing aqueous solutions. The block copolymers lowered the surface tension of water in analogy with the low molecular weight surfactants such as sodium lauryl sulfate and heptaethylene oxide n-dodecyl ether. Their aqueous solutions exhibited solubilization properties differing from those of polyethylene glycol. Therefore, it is thought that the polystyrene blocks produce solubilization phenomena. In samples of the same styrene content, the precipitation temperature of a high molecular weight copolymer in water was lower than that of a low molecular weight copolymer at the same concentration in the same solvent. The surface tension and precipitation temperature of aqueous solutions seem to be influenced by molecular weight and composition.     

Gapless spin liquid behavior in two-dimensional solid 3He

Direct demagnetization has been made for two-dimensional solid 3He in both the paramagnetic and the antiferromagnetic phases. The lowest temperature is about 10 microK, judging from the observed magnetization for the paramagnetic solid 3He. The magnetization of the antiferromagnetic solid 3He shows a gradual increase to about 10 microK for the 4/7 phase adsorbed on both one layer of 4He and two layers of HD preplated graphite. This strongly suggests that the triangular antiferromagnet with the higher order multiple exchange has a quantum spin liquid ground state with nearly zero or extremely small spin gap less than 10 microK.     

Selective solvation effects in phase separation in aqueous mixtures

Selective solvation can be crucial in phase separation in polar binary mixtures (water–oil) with a small amount of hydrophilic ions or hydrophobic particles. They are preferentially attracted to one of the solvent components, leading to a number of intriguing effects coupled to phase separation. For example, if cations and anions interact differently with the two components, an electric double layer emerges at a liquid–liquid interface. The main aim of this paper is to show that a strongly hydrophilic (hydrophobic) solute induces precipitation of water-rich (oil-rich) domains above a critical solute density n_p outside the solvent coexistence curve.     

Synthesis of mono- and 1,3-diaminocalix[4]arenes via Ullmann-type amination and amidation of 1,3-bistriflate esters of calix[4]arenes

Practical methods are described for the preparation of monoamines 4 and 1,3-diamines 5, bearing one or two amino group(s) instead of the hydroxy group(s) at the 28-position or at both the 26- and 28-positions of p-tert-butylcalix[4]arene (1a) and p-tert-butylthiacalix[4]arene (1b), via the Ullmann-type amination or amidation. Thus, the copper-catalyzed or mediated amination of the 1,3-bistriflate ester (2a) of 1a with benzylamine affords either mono(benzylamino) triflate 7a or 1,3-bis(benzylamine) 8 in a high yield, depending on the reaction conditions. On the other hand, the 1,3-bistriflate ester (2b) of 1b resists disubstitution and produces, under stoichiometric conditions, mono(benzylamino) triflate 7b. The disubstitution of 2b is achieved by amidation with tosylamide, giving 1,3-bis(tosylamide) 17b. The hydrogenolysis of the benzylamino moiety of 7a, followed by the hydrolysis of the Tf moiety, affords monoamine 4a, while the hydrogenolysis of 8 affords 1,3-diamine 5a. The amino moiety of 7b can be deprotected under acidic conditions to give, after hydrolysis, monoamine 4b. The hydrolysis of 17b affords 1,3-diamine 5b. The overall yields of compounds 4a, 4b, 5a, and 5b are 72%, 45%, 78%, and 24%, respectively, based on commercially available compounds 1 and are much higher than the ones previously reported in the literature.