Measuring the Student Group Capacity for Obtaining Geometric Information in the van Hiele Developmental Thought Process：A Fuzzy Approach

1　 IntroductionThe van Hiele level theory of geometric reasoning[1,5,9] describes the ways of studentreasoning inEuclidean geometry.The ontogeny of thiscognitive activity of mental developmentis characterised byfive hierarchical and qualitatively differe…     

Periodic,almost periodic and chaotic motions of forced self-sustained oscillators

Steady motions of the Van der Pol oscillator and an oscillator with hysteresis are studied numerically in this paper. Some features of periodic, almost periodic and chaotic motions of forced self-sustained oscillators are investigated. This paper has been presented at the ICTAM XVI Lyngby.     

Response statistic of strongly non-linear oscillator to combined deterministic and random excitation

The principal resonance of a van der Pol-Duffing oscillator to the combined excitation of a deterministic harmonic component and a random component has been investigated. By introducing a new expansion parameter , the method of multiple scales is adapted for the strongly non-linear system. Then the method of multiple scales is used to determine the equations of modulation of response amplitude and phase. The behavior and the stability of steady-state response are studied by means of qualitative analysis. The effects of damping, detuning, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the non-trivial steady-state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady-state solutions. Random jump may be observed under some conditions. The results obtained in the paper are adapted for a strongly non-linear oscillator that complement previous results in the literature for the weakly non-linear case.     

Solubility and thermodynamic function of a new anticancer drug ibrutinib in 2-(2-ethoxyethoxy)ethanol + water mixtures at different temperatures

Ibrutinib is a recently approved anticancer drug recommended for the treatment of mantle cell lymphoma and chronic lymphocytic leukemia. It has been reported as practically insoluble in water and hence it is available in the market at higher doses. Poor solubility of ibrutinib limits its development to oral solid dosage forms only. In this work, the solubilities of ibrutinib were measured in various 2-(2-ethoxyethoxy)ethanol (Carbitol) + water mixtures at T = (298.15 to 323.15) and p = 0.1 MPa. The solubility of ibrutinib was measured using an isothermal method. The thermodynamics function of ibrutinib was also studied. The measured solubilities of ibrutinib were correlated and fitted with Van’t Hoff, the modified Apelblat and Yalkowsky models. The results of curve fitting of all three models showed good correlation of experimental solubilities of ibrutinib with calculated ones. The mole fraction solubility of ibrutinib was observed highest in pure 2-(2-ethoxyethoxy)ethanol (2.67 · 10⁻² at T = 298.15 K) and lowest in pure water (1.43 · 10⁻⁷ at T = 298.15 K) at T = (298.15 to 323.15) K. Thermodynamics data of ibrutinib showed an endothermic, spontaneous and an entropy-driven dissolution behavior of ibrutinib in all 2-(2-ethoxyethoxy)ethanol + water mixtures. Based on these results, ibrutinib has been considered as practically insoluble in water and freely soluble in 2-(2-ethoxyethoxy)ethanol. Therefore, 2-(2-ethoxyethoxy)ethanol could be used as a physiologically compatible cosolvent for solubilization and stabilization of ibrutinib in an aqueous media. The solubility data of this work could be extremely useful in preformulation studies and formulation development of ibrutinib.     

Increase in Axial Compressibility in a Spinning Van der Waals Gas

We investigated the adiabatic compression along the axial direction of a spinning Van der Waals gas by applying theoretical analysis and molecular dynamics (MD) simulations. Based on the analytical results, the rotation-induced compressibility increase effect is significant in a Van der Waals gas, while the attraction term in the Van der Waals equation of states (EOS) contributes significantly to the compressibility increase in a spinning system. We conducted MD simulations to the axial compression of a spinning gas, whose state is far from the ideal gas state, and further demonstrated that the rotation-induced compressibility increase effect in a dense state is robust, implying that such a phenomenon can be detected in experiments under high-energy-density conditions.     

Vibrations of double-nanotube systems with mislocation via a newly developed van der Waals model

This study deals with transverse vibrations of two adjacent-parallel-mislocated single-walled carbon nanotubes (SWCNTs) under various end conditions. These tubes interact with each other and their surrounding medium through the intertube van der Waals (vdW) forces, and existing bonds between their atoms and those of the elastic medium. The elastic energy of such forces due to the deflections of nanotubes is appropriately modeled by defining a vdW force density function. In the previous works, vdW forces between two identical tubes were idealized by a uniform form of this function. The newly introduced function enables us to investigate the influences of both intertube free distance and longitudinal mislocation on the natural transverse frequencies of the nanosystem which consists of two dissimilar tubes. Such crucial issues have not been addressed yet, even for simply supported tubes. Using nonlocal Timoshenko and higher-order beam theories as well as Hamilton's principle, the strong form of the equations of motion is established. Seeking for an explicit solution to these integro-partial differential equations is a very problematic task. Thereby, an energy-based method in conjunction with an efficient meshfree method is proposed and the nonlocal frequencies of the elastically embedded nanosystem are determined. For simply supported nanosystems, the predicted first five frequencies of the proposed model are checked with those of assumed mode method, and a reasonably good agreement is achieved. Through various studies, the roles of the tube's length ratio, intertube free space, mislocation, small-scale effect, slenderness ratio, radius of SWCNTs, and elastic constants of the elastic matrix on the natural frequencies of the nanosystem with various end conditions are explained. The limitations of the nonlocal Timoshenko beam theory are also addressed. This work can be considered as a vital step towards better realizing of a more complex system that consists of vertically aligned SWCNTs of various lengths.     

以范德瓦耳斯气体为工质的3种热机循环效率

利用热力学的普遍理论推导了范德瓦尔斯气体热力学函数的表达式,再求出绝热过程和3种等值过程中功和热量的表达式.在此基础上,研究了斯特林循环、奥拓循环和狄塞尔循环的功和效率,并计算和分析了3种循环效率随各种参量变化的关系.     

Rubber elasticity and network structure

By defining stretching-invariant subunits of deformation in terms of the van der Waals model it is shown that the density of these subsystems can be smaller than the density of the cross-links. This is observed in short-chain networks with rigid cross-linkages, where due to the broad chain length distribution, very short and therefore stiff network chains appear. It is in any case possible to relate the modulus to the weight fraction of the cross-linking agent if the production of chemical cross-limits per agent molecule is properly defined. The stress-strain behavior of the rubbers can then be fully described within the total range of strains embracing also the upturn at largest elongation.Moreover, on the use of a thermodynamics of swelling of van der Waals networks, a set of swelling experiments drawn from literature can be described: the key assumption is that configurational exclusion effects within the swollen short-chain network must be accounted for. In the case of swelling with flexible molecules there is a need for further empirical modification of the thermodynamical formalism indicating that the configurational abilities within these swollen networks seem also to depend on the relative ratio of the network chain length related to the length of the linear solvent molecules.Dedicated to Prof. Dr. R. Kosfeld on the occasion of his 60th birthday.     

Asymptotic analysis of a perturbation problem

An asymptotic expansion is constructed for the solution of the initial-value problem

when t is restricted to the interval [0,T/ε], where T is any given number. Our analysis is mathematically rigorous; that is, we show that the difference between the true solution u(t,x;ε) and the Nth partial sum of the asymptotic series is bounded by ε^N+1 multiplied by a constant depending on T but not on x and t.     

取代芳烃水中溶解度的测定与估算

本文应用线性溶剂化能相关法回归分析了多种有机有机物的溶解度与范德华体积、Ｌｅｗｉｓ酸性及Ｌｅｗｉｓ碱性之间的相关性，结果表明，溶解度与范德华体积、Ｌｅｗｉｓ酸性及碱性之间呈良好的相关性，用这种方法估算的溶解度值与测定吻合得较好。