Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

Cyclical games with prohibitions

We consider a certain combinatorial game on a digraph for two cases of the price function. For one case the game in question extends the cyclical game studied in Ehrenfeucht and Mycielski (1979) and Gurvitch, Karzanov and Khachiyan (1988) which, in its turn, is a generalization of the well-known problem of finding a minimum mean cycle in an edge-weighted digraph. We prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies.This work was partially supported by Chaire municipale, Mairie de Grenoble.     

土壤环境中铅的化学

论述了环境中铅的背景值、来源、污染、质量标准、化学循环以及环境中铅的烷基化，为铅污染治理提供理论依据。     

Thermodynamic investigation of zirconium diselenite

Summary On the basis of calorimetric research of selenium dioxide, zirconium dioxide and zirconium diselenite dissolution reactions in the hydrofluoric acid solution under 298 K a standard enthalpy of Zr(SeO₃)₂ formation reaction from ZrO₂ and SeO₂ and a standard enthalpy of zirconium diselenite formation have been obtained. The value of enthalpy has been equal to -58.1±3.43 kJ mol^-1 in ZrO_2(solid)+2SeO_2(solid) Zr(SeO₃)_2(solid) reaction. The standard enthalpy of zirconium diselenite formation is equal to H_f,298⁰Zr(SeO₃)_2(solid)= -1603.2±3.8 kJ mol^-1. The H_f,298⁰ Zr(SeO₃)_2(solid) value has been determined for the first time.     

Organomineral sorbents based on clinoptilolite-containing tuffs

The anion-exchange properties of a new organomineral sorbent obtained by modification of clinoptilolite-containing tuffs by polyhexamethyleneguanidine have been studied after different periods of storage (time after synthesis) and numbers of sorption-regeneration cycles. The sorbent can be used as a cation- and an anion-exchanger simultaneously. Selectivity coefficients (exchange constants) for F^–, SO₄ ^2–, and HPO₄ ^2– ionsvs. Cl^– ions on modified clinoptilolite-containing tuffs have been determined. The modification improves the mechanical properties of clinoptilolite tuffs.For part 1, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1554–1556, September, 1994.     

Enhanced visible light photocatalytic activity of CeO2@Zn0.5Cd0.5S by facile Ce(IV)/Ce(III) cycle

In this study, CeO₂@Zn_0.5Cd_0.5S heterostructure (Ce@ZCS) is synthesized via a simple two-step hydrothermal method. The effect of CeO₂ loading on the visible-light photoactivity of Zn_0.5Cd_0.5S is mainly investigated. It is found that Ce@ZCS shows a 1.9 times activity as high as ZCS for the MB degradation. The improved activity mainly results from the significant enhanced charge separation by CeO₂, in which the electron transfer is obviously promoted by the facile Ce(IV)/Ce(III) cycle. The excited electrons of ZCS is easy to transfer to CeO₂, thus obviously increasing the charge separation of ZCS. The accepted electrons by CeO₂ may easily be captured by the adsorbed O₂ to form O₂⁻, and then O₂⁻ could combine with H⁺/H₂O to form HO₂, and OH. Finally, O₂⁻, h⁺ and OH are confirmed as the major oxidative species in photocatalytic reaction for Ce@ZCS, and a possible photocatalytic mechanism is proposed. The cheap, efficient Ce@ZCS photocatalyst could be applied for practical waste water treatment.     

Effects of glucose,glutamine, and malate on the metabolism of spodoptera frugiperda clone 9 (sf9) cells

Optimal design and operation of bioreactors for insect cell culture is facilitated by functional relations providing quantitative information on cellular metabolite consumption kinetics, as well as on the specific cell growth rates (μ_G). Initial specific consumption rates of glucose, malate, and oxygen, and associated changes in μ_G, were measured forSpodoptera frugiperda clone 9 (Sf9) cells grown in batch suspension culture in medium containing 7–35 mM glucose, 0–16 mM malate, and 4–16 mM glutamine. The initial specific glucose consumption rate (q _G ) could be described by a modified Michaelis-Menten equation treating malate as a “competitive” inhibitorK ₁ = 6.5 mM) and glutamine as a “noncompetitive” inhibitorK _I = 14 mM) ofq _G , with aK _m of 7.1 mM for glucose. All three carbon sources were found to increase μ_G in a saturable manner, and a modified Monod equation was employed to describe this relationship (μ_Gmax = 0.047 h^-1). The initial specific oxygen consumption rate (q_O2) in Sf9 cells could be related to μ_G by the maintenance energy model, and it was calculated that, under typical culture conditions, about 15–20% of the cellular energy demand comes from functions not related to growth. Fitted parameters in mathematical expression for μg: K₄, Monod constant for glucose (mM); K₅, modified Monod constant for malate (mM); K₆, Monod constant for glutamine (mM); m_o2, specific consumption rate of oxygen by the cells under zero-growth conditions (nmol/cell/h); q_F, initial specific fumarate production rate (nmol/cell/ h);q _G , initial specific glucose consumption rate (nmol/cell/h); q_Gmax, maximum initial specific glucose consumption rate (nmol/cell/h);q _M , initial specific malate consumption rate (nmol/cell/h); q_o2, initial specific oxygen consumption rate (nmol/cell/h); Y_o2, cell yield on oxygen (cells/nmol); μ, initial specific cell growth rate (h^-1); μ_g, initial specific cell growth rate (h^-1); μG_max, maximum initial specific cell growth rate (h^-1).     

The circular chemistry conceptual framework: A way forward to sustainability in industry 4.0

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Molecular structure and conformation of 2,3-dichloro-1-propene as determined by gas-phase electron diffraction

The molecular structure and conformation of 2,3-dichloro-1-propene have been determined by gas-phase electron diffraction at nozzle temperatures of 24, 90 and 273°C. The molecules exist as a mixture of two conformers with the chlorine atoms anti (torsion angle ∠φ = 0°) or gauche (∠φ = 109°) to each other and with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ was found to be 0.55 (0.08), 0.49 (0.08) and 0.41 (0.10) at 24, 90 and 273°, respectively. These values correspond to an energy difference with estimated standard deviation ΔE° = E°_g-E°_a = 0.7 ± 0.3 kcal mol^?1 and an entropy difference ΔS° = S°_g-S°_a = 0.6 ± 0.9 cal mol^?1 K^?1. Some of the diffraction results, together with spectroscopic observations, permit the evaluation of an approximate torsional potential function of the form 2V = V₁ (1 - cos φ) + V₂ (1 - cos 2φ) + V₃ (1 - cos 3φ); the results are V₁ = 4.4 ± 0.5, V₂ = ?2.9 ± 0.5 and V₃ = 4.8 ± 0.2, all in kcal mol^?1. The results at 24°C for the distance (r_a) and angle (∠_α) parameters, with estimated uncertainties of 2σ, are: r(C_sp²-H) = 1.098(0.020)Å, r(C_sp³-H) = 1.103(0.020)Å, r(CC) = 1.334(0.009)Å, r(C-C) = 1.504(0.013)Å, r(C_sp²-Cl) = 1.752(0.021)Å, r(C_sp³-Cl) = 1.776(0.020)Å, ∠C-CC = 127.6(1.1)°, ∠C_sp³-C_sp²-Cl = 110.2(1.0), ∠C_sp²-C_sp³-Cl = 113.1(1.2)°, ∠H-C_sp³-H = 109.5° (assumed), ∠CC-H = 120.0° (assumed) and ∠φ = 108.9(3.4)°.     

Fast-cycle trace analysis of dioxin in flue gas. Monitoring of the incineration of dioxin-containing waste from seveso

The fast trace analysis method used to monitor 2,3,7,8-TCDD in stack gas during the incineration of the waste from Seveso is described. The sampling of volatile organic compounds from flue gases, distributed between all three aggregation states, is based on a micromethod developed for the trace analysis of water using a specially dimensioned adsorptive charcoal filter (1.5 mg charcoal). In conjunction with subsequent GC/MS measurements the rapid “fast cycle trace analysis” ensured specific 2,3,7,8-TCDD detection down to 100 pg per m³ flue gas in cycle times of about 1–2 hours.