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51.
52.
In Baak et al. (J Math Anal Appl 314(1):150–161, 2006) the authors considered the functional equation where \(d,\ell \in \mathbb {N}\), \(1<\ell <d/2\) and \(r\in \mathbb {Q}{\setminus }\{0\}\). The authors determined all odd solutions \(f:X\rightarrow Y\) for vector spaces X, Y over \(\mathbb {Q}\). In Oubbi (Can Math Bull 60:173–183, 2017) the author considered the same equation but now for arbitrary real \(r\not =0\) and real vector spaces X, Y. Generalizing similar results from (J Math Anal Appl 314(1):150–161, 2006) he additionally investigates certain stability questions for the equation above, but as for that equation itself for odd approximate solutions only. The present paper deals with the general solution of the equation and the corresponding stability inequality. In particular it is shown that under certain circumstances non-odd solutions of the equation exist.
相似文献
$$\begin{aligned} r f\left( \frac{1}{r}\,\sum _{j=1}^{d}x_j\right)+ & {} \sum _{i(j)\in \{0,1\} \atop \sum _{1\le j\le d} i(j)=\ell }r f\left( \frac{1}{r}\,\sum _{j=1}^d (-1)^{i(j)}x_j\right) \\= & {} \left( {d-1\atopwithdelims ()\ell }-{d-1\atopwithdelims ()\ell -1} +1\right) \sum _{j=1}^{d} f(x_j) \end{aligned}$$
53.
Adriano Almeida Gonçalves Siqueira Rodrigo Nicoletti Nicklas Norrick Kátia Lucchesi Cavalca Helio Fiori de Castro Jens Bauer Fadi Dohnal 《Journal of sound and vibration》2012,331(10):2220-2232
Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or super-critical speeds. 相似文献
54.
55.
A full-phase measurement of low-energy femtosecond UV pulses is presented. The method relies on phase retrieval of measured sonogram traces and is greatly simplified by a two-dimensional shaper-assisted cross correlation setup. As all required pulses are generated by the pulse shaper, the method is free of external references and additional tunable filter setups. 相似文献
56.
We consider a stochastic control problem over an infinite horizon where the state process is influenced by an unobservable
environment process. In particular, the Hidden-Markov-model and the Bayesian model are included. This model under partial
information is transformed into an equivalent one with complete information by using the well-known filter technique. In particular,
the optimal controls and the value functions of the original and the transformed problem are the same. An explicit representation
of the filter process which is a piecewise-deterministic process, is also given. Then we propose two solution techniques for
the transformed model. First, a generalized verification technique (with a generalized Hamilton–Jacobi–Bellman equation) is
formulated where the strict differentiability of the value function is weaken to local Lipschitz continuity. Second, we present
a discrete-time Markovian decision model by which we are able to compute an optimal control of our given problem. In this
context we are also able to state a general existence result for optimal controls. The power of both solution techniques is
finally demonstrated for a parallel queueing model with unknown service rates. In particular, the filter process is discussed
in detail, the value function is explicitly computed and the optimal control is completely characterized in the symmetric
case. 相似文献
57.
Jochen Münchenberg Jens R. Goerlich Axel K. Fischer Peter G. Jones Reinhard Schmutzler 《无机化学与普通化学杂志》1996,622(2):348-354
Synthesis, Structure, and some Reactions of N-(N′,N′,N″,N″-tetramethyl)guanidinyl-substituted Phosphoryl Compounds The tetramethylguanidinyl-substituted phosphoryl compounds 1 – 10 were prepared in the reaction of the appropriate chlorophosphoryl compounds with either N′,N′,N″,N″-tetramethylguanidine (HTMG) or N-trimethylsilyl-(N′,N′,N″,N″-tetramethyl)guanidine (TMSTMG). With methyl iodide 1 reacted with N-alkylation to give the ammonium salt 11. 1 reacted with BF3 · Et2O at both imino nitrogen atoms with formation of the bis-BF3-adduct 12 . The X-ray structure determination of phenylphosphonic acid-bis(N′,N′,N″,N″-tetramethylguanidinide) 3 shows shortened PN-bonds and widened PNC-angles, consistent with the partial double bond character of the PN-bond. 相似文献
58.
The molecular and vibrational structure of the title compound (C4-HSL) was studied by experimental and theoretical methods. The infrared (IR) absorption spectrum was measured in the solid state and in CCl4 suspension. The observed absorption bands were compared with transitions obtained with B3LYP/cc-pVTZ density functional theory (DFT) calculations. Two stable molecular conformations were predicted, corresponding to an endo- and an exo-conformer with similar energies. Intermolecular amide–amide hydrogen bonding in the crystal state was approximated by a simple cluster model, leading to excellent agreement with the observed solid state IR spectrum. Due to the low solubility of C4-HSL in common solvents for IR spectroscopy, such as CS2 and CCl4, a liquid solution spectrum of pure, monomeric C4-HSL was not obtained. However, absorbance peaks observed in oversaturated CCl4 solution could be assigned to distinct contributions from suspended micro-crystalline aggregates and dissolved monomeric species. The key vibrational bands of the monomeric form of C4-HSL are reported here for the first time: 3425 cm?1 [ν(N–H)], 1784 cm?1 [ν(CO), lactone], 1688 cm?1 [amide I], and 1494 cm?1 [amide II] (CCl4). 相似文献
59.
Daniel Göbke Yuriy Romanyshyn Sébastien Guimond Jacobus Marinus Sturm Dr. Helmut Kuhlenbeck Dr. Jens Döbler Dr. Ulrike Reinhardt Maria Veronica Ganduglia‐Pirovano Dr. Joachim Sauer Prof. Dr. Hans‐Joachim Freund Prof. Dr. 《Angewandte Chemie (International ed. in English)》2009,48(20):3695-3698
Hydroxy‐mediated methoxy formation or stabilization is probably an important process in many methanol adsorption systems. Hydrogen atoms originating from the scission of the methanol O? H bond react with the substrate and form water. This process may result 1) in the production of additional surface defects as reactive centers for methoxy formation and 2) in the stabilization of methoxy groups by suppression of methanol formation.
60.
Men Y Rieger J Roth SV Gehrke R Kong X 《Langmuir : the ACS journal of surfaces and colloids》2006,22(20):8285-8288
A polymer dispersion consisting of soft latex spheres with a diameter of 135 nm was used to produce a crystalline film with face-centered cubic (fcc) packing of the spheres. Different from conventional small-molecule and hard-sphere colloidal crystals, the crystalline latex film in the present case is soft (i.e., easily deformable). The structural evolution of this soft colloidal latex film under stretching was investigated by in-situ synchrotron ultra-small-angle X-ray scattering. The film exhibits polycrystalline scattering behavior corresponding to fcc structure. Stretching results not only in a large deformation of the crystallographic structure but also in considerable nonaffine deformation at high draw ratios. The unexpected nonaffine deformation was attributed to slippage between rows of particles and crystalline grain boundaries. The crystalline structure remains intact even at high deformation, suggesting that directional anisotropic colloidal crystallites can be easily produced. 相似文献