Canonical State/Signal Shift Realizations of Passive Continuous Time Behaviors

This work is devoted to the construction of canonical passive and conservative state/signal shift realizations of arbitrary passive continuous time behaviors. By definition, a passive future continuous time behavior is a maximal nonnegative right-shift invariant subspace of the Kreĭn space L²([0,￥);W){L^2([0,\infty);\mathcal W)}, where W{\mathcal W} is a Kreĭn space, and the inner product in L²([0,￥);W){L^2([0,\infty);\mathcal W)} is the one inherited from W{\mathcal W}. A state/signal system S = (V;X,W){\Sigma=(V;\mathcal X,\mathcal W)}, with a Hilbert state space X{\mathcal X} and a Kreĭn signal space W{\mathcal W}, is a dynamical system whose classical trajectories (x, w) on [0, ∞) satisfy x ? C¹([0,￥);X){x\in C^1([0,\infty);\mathcal X)}, w ? C([0,￥);W){w \in C([0,\infty);\mathcal W)}, and

Parseval frame wavelets with -dilations

We study Parseval frame wavelets in with matrix dilations of the form , where A is an arbitrary expanding n×n matrix with integer coefficients, such that |detA|=2. We show that each A-MRA admits either Parseval frame wavelets, or Parseval frame bi-wavelets. The minimal number of generators for a Parseval frame associated with an A-MRA (i.e. 1 or 2) is determined in terms of a scaling function. All Parseval frame (bi)wavelets associated with A-MRA's are described. We then introduce new classes of filter induced wavelets and bi-wavelets. It is proved that these new classes strictly contain the classes of all A-MRA Parseval frame wavelets and bi-wavelets, respectively. Finally, we demonstrate a method of constructing all filter induced Parseval frame (bi)wavelets from generalized low-pass filters.     

J-inner matrix functions, interpolation and inverse problems for canonical systems, V: The inverse input scattering problem for Wiener class and rational p×q input scattering matrices

The general formulas developed in the fourth paper in this series are applied to solve the inverse input scattering problem for canonical integral systems in the special cases that the input scattering matrix is ap×q matrix valued function in the Wiener class (and the associated pairs are homogeneous). These formulas are then further specialized to the rational case. Whenp=q, these formulas are connected to the earlier results of Alpay-Gohberg and Gohberg-Kaashoek-Sakhnovich, who studied inverse problems for a related system of differential equations.This research was partially supported by a Minerva Foundation grant that is acknowledged with thanks.     

New bifunctional N-thiophosphorylated thiourea and 2,5-dithiobiurea derivatives. Crystal structures of R[C(S)NHP(S)(OiPr)2]2 (R = –N(Ph)CH2CH2N(Ph)– and –NHNH–)

A new bifunctional N-thiophosphorylated thiourea and 2,5-dithiobiurea of the common formula R[C(S)NHP(S)(OiPr)₂]₂ [R = –N(Ph)CH₂CH₂N(Ph)– (H₂L^a); –NHNH– (H₂L^b)] have been synthesized and characterized by IR, ¹H, ³¹P spectroscopy and the single crystal X-ray diffraction method. The structure of the latter compound in CDCl₃ and acetone-d₆ solutions has been discussed in comparison with the monofunctional thiosemicarbazide PhNHNHC(S)NHP(S)(OiPr)₂ (HL^c).     

Determination of the Rb atomic number density in dense rubidium vapors by absorption measurements of Rb2 triplet bands

A simple and accurate way of determining atom number densities in dense rubidium vapors is presented. The method relies on the experimental finding that the reduced absorption coefficients of the Rb triplet satellite bands between 740 nm and 750 nm and the triplet diffuse band between 600 nm and 610 nm are not temperature dependent in the range between 600 K and 800 K. Therefore, the absolute values of the reduced absorption coefficients of these molecular bands can provide accurate information about atomic number density of the vapor. The rubidium absorption spectrum was measured by spatially resolved white-light absorption in overheated rubidium vapor generated in a heat pipe oven. The absolute values for the reduced absorption coefficients of the triplet bands were determined at lower vapor densities, by using an accurate expression for the reduced absorption coefficient in the quasistatic wing of the Rb D1 line, and measured triplet satellite bands to the resonance wing optical depth ratio. These triplet satellite band data were used to calibrate in absolute scale the reduced absorption coefficients of the triplet diffuse band at higher temperatures. The obtained values for the reduced absorption coefficient of these Rb molecular features can be used for accurate determination of rubidium atomic number densities in the range from about 5 × 10¹⁶ cm^− 3 to 1 × 10¹⁸ cm^− 3.     

A “sodium trap” based on benzo-15-crown-5 with an exocyclic N-(thiophosphoryl)thiourea moiety

For N-(thio)phosphorylthioureas of the common formula RC(S)NHP(X)(OiPr)₂HL^I (R = N-(4′-aminobenzo-15-crown-5), X = S), HL^II (R = N-(4′-aminobenzo-15-crown-5), X = O), HL^III (R = PhNH, X = S), HL^IV (R = PhNH, X = O), and (N,N′-bis-[C(S)NHP(S)(OiPr)₂]₂-1,10-diaza-18-crown-6) H₂L^V, salts LiL^I,III,IV, NaL^I–IV, KL^I–IVM₂L^V (M = Li⁺, Na⁺, K⁺), Ba(L^I,III,IV)₂, and BaL^V have been synthesized and investigated. Compounds NaL^I,II quantitatively drop out as a deposit in ethanol medium, allowing the separation of Na⁺ and K⁺ cations. This effect is not displayed for the other compounds. The crystal structures of HL^III and the solvate of the composition [K(Me₂CO)L^III] have been investigated by X-ray crystallography.     

Numerical Kekulé structures of fullerenes and partitioning of pi-electrons to pentagonal and hexagonal rings

We calculated the partitioning of pi-electrons within individual pentagonal and hexagonal rings of fullerenes for a collection of fullerenes from C20 to C72 by constructing their Kekulé valence structures and averaging the pi-electron content of individual rings over all Kekulé valence structures. The resulting information is collected in Table 2, which when combined with the Schlegel diagram of fullerenes (illustrated in Figure 7) uniquely characterizes each of the 19 fullerenes considered. The results are interpreted as the basic information on the distributions (variation) of the local (ring) pi-electron density.     

Influence of the Homopolar Dihydrogen Bonding CH⋅⋅⋅HC on Coordination Geometry: Experimental and Theoretical Studies

The reaction of the N‐thiophosphorylated thiourea (HOCH₂)(Me)₂CNHC(S)NHP(S)(OiPr)₂ (HL), deprotonated by the thiophosphorylamide group, with NiCl₂ leads to green needles of the pseudotetrahedral complex [Ni(L‐1,5‐S,S′)₂] ? 0.5 (n‐C₆H₁₄) or pale green blocks of the trans square‐planar complex trans‐[Ni(L‐1,5‐S,S′)₂]. The former complex is stabilized by homopolar dihydrogen C?H???H?C interactions formed by n‐hexane solvent molecules with the [Ni(L‐1,5‐S,S′)₂] unit. Furthermore, the dispersion‐dominated C?H??? H?C interactions are, together with other noncovalent interactions (C?H???N, C?H???Ni, C?H???S), responsible for pseudotetrahedral coordination around the Ni^II center in [Ni(L ‐1,5‐S,S′)₂] ? 0.5 (n‐C₆H₁₄).     

Hydrazine selective dual signaling chemodosimetric probe in physiological conditions and its application in live cells

A rhodamine–cyanobenzene conjugate, (E)-4-((2-(3′,6′-bis(diethylamino)-3-oxospiro[isoindoline-1,9′-xanthene]-2-yl)ethylimino)methyl)benzonitrile (1), which structure has been elucidated by single crystal X-ray diffraction, was synthesized for selective fluorescent “turn-on” and colorimetric recognition of hydrazine at physiological pH 7.4. It was established that 1 detects hydrazine up to 58 nM. The probe is useful for the detection of intracellular hydrazine in the human breast cancer cells MCF-7 using a fluorescence microscope. Spirolactam ring opening of 1, followed by its hydrolysis, was established as a probable mechanism for the selective sensing of hydrazine.