(4) A topological spaces X is minimal CH if and only if for each x∈X and each open CH-filterbase μ,if {x}=∩U∈μU=∩U∈μclU, then μ is a neighborhood base of x.

Secondly, we introduce the neighborhood semantics, give the frame conditions of the character axioms and rules of EK1 - EK3, prove the frame soundness of EK1 - EK3 with respect to the frame conditions, respectively.

IMPENDING-EARTHQUAKE MODULATION EFFECTS ON M_L≥4.0 EVENTS OCCURRED IN YUNNAN AREA AND ITS NEIGHBORHOOD BY THE VIBRATION OF THE ATMOSPHERIC FIELD IN SOUTHWEST CHINA

Like the truncations of the Taylor expansion, the truncations of a chromatic expansion at t = t0 of an analytic function f(t) approximate f(t) locally, in a neighborhood of t0.

It is available for the case that the sign of f(x) changes frequently or the derivative f'(x) does not exist in the neighborhood of the root, while the Newton method is hard to work.

One allows the appearance of eight limit cycles in the neighborhood of infinity, which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.

Neighborhood union of independent sets and hamiltonicity of claw-free graphs

Let G be a graph, for any u∈V(G), let N(u) denote the neighborhood of u and d(u)=|N(u)| be the degree of u.

In this article it is pointed out that the semi-empirical van der Waals' equation of state for gases is particularly unsatisfactory in the neighborhood of the critical point, as indicated by the fact that the experimental values of the critical ratio (?) seldom agree with the theoretical constant value 8/3. It is also noted that this τ value may serve as a satisfactory measure (at least to a first approximation) of the deviation of the law of corresponding states when applied to gases at high densities....

In this article it is pointed out that the semi-empirical van der Waals' equation of state for gases is particularly unsatisfactory in the neighborhood of the critical point, as indicated by the fact that the experimental values of the critical ratio (?) seldom agree with the theoretical constant value 8/3. It is also noted that this τ value may serve as a satisfactory measure (at least to a first approximation) of the deviation of the law of corresponding states when applied to gases at high densities. We have therefore proposed in this communication a rather straightforward modification of the van der Waals' equation which leads to an empirical three-constant equation of state for gases involving this τ value as an adjustable parameter and thus requiring only critical data for the determination of the three constants. This equation is made to fit the p-V-T data at the critical point, but reduces itself to the simpler forms of the van der Waals' equation and the ideal gas equation for lower values of gas densities. Numerical calculations made for gases of widely different τ values show that this rather simple equation of state is fairly satisfactory even at high densities. The plausibility of using the τ value as an adjustable parameter both for the equation of state and for the law of corresponding states is also briefly discussed.

本文指出任何僅含兩個常數的氣態方程,在臨界點附近的缺點是特別顯著的。同時也指出,對應態定律應用到高密度氣體的偏差,可以相當滿意地用臨界係數(?)來衡量。因此我們建議將van der Waals方程,修改爲三常數的經驗方程,它的優點是這三個常數可以直接從氣體的臨界點數據計算出來;而且實例計算(包括極性很強和τ值很大的甲醇)說明它在相當大的温度和密度範圍內可以適用。將這個經驗式,寫成對比方程顯然含有臨界係數τ,就離開臨界點不太遠的氣體來說,這個函數關係可以相當满意地用本文方程總結出來。

By heat treatment study, extraction experiments and powder photography, the differential thermal effects occuring below 250°of three amorphous sulfides of antimony are inter- preted in this paper. At about 220°, all the three amorphous sulfides produce crystalline Sb_2S_3. In the neighborhood of 160°, the pentasulfide and tetrasulfide segregate into easily extractable sulfur and amorphous Sb_2S_3. The latter change has been identifid in the main with the following reaction: 1/xS_x→1/8S_8+~3 kcal. On...

By heat treatment study, extraction experiments and powder photography, the differential thermal effects occuring below 250°of three amorphous sulfides of antimony are inter- preted in this paper. At about 220°, all the three amorphous sulfides produce crystalline Sb_2S_3. In the neighborhood of 160°, the pentasulfide and tetrasulfide segregate into easily extractable sulfur and amorphous Sb_2S_3. The latter change has been identifid in the main with the following reaction: 1/xS_x→1/8S_8+~3 kcal. On the basis of the above identification, the pentasulfide and tetrasulfide prepared from Na_3SbS_4·9H_2O are probably complex systems of [Sb_2S_3+S_μ+S_λ] and of [Sb_2S_3+S_μ] respectively. The fact that a synthetic sample containing 91% amorphous Sb_2S_3 and 9% Sμ gives essentially the same differential thermal diagram as the pentasulfide and tetrasulfide strongly supports the proposed model. According to Currie, Bunsen's pentasulfide contains no easily extractable sulfur. However, Bunsen's pentasulfide may not be a chemical individual either, inasmuch as it produces easily extractable sulfur at about 160°. In the light of the proposed theory, Bunsen's pentasulfide is probably a complex system of [Sb_2S_3+2S_μ]. The differential thermal diagram of the pentasulfide is probably a pertinent reference to its quality.

We have made three pyrex floats of the bulb-rod stream-line type, modified from that used in the Trail laboratories. These floats possess cach a thick-walled bulb 6.5 mm in diameter, with an upper rod 3.5 mm long and a lower rod 8 mm long, each rod being 2.5 mm in diameter and forming an angle of 60° at the end. With baths having temperature fluctuations within ±0.0005°, the velocity-temperature relationship has been determiued in the neighborhood of their flotation temperatures. It is found that the temperature...

We have made three pyrex floats of the bulb-rod stream-line type, modified from that used in the Trail laboratories. These floats possess cach a thick-walled bulb 6.5 mm in diameter, with an upper rod 3.5 mm long and a lower rod 8 mm long, each rod being 2.5 mm in diameter and forming an angle of 60° at the end. With baths having temperature fluctuations within ±0.0005°, the velocity-temperature relationship has been determiued in the neighborhood of their flotation temperatures. It is found that the temperature iuterval in which such a relationship is linear is much more extensive when the flotation temperature of the float is lower. Correspondingly, the velocity interval is only slightly larger. The results are as follows:Float Flotation Temperature Velocity intervalNo. temperature, ℃ interval, ℃ mm/sec1 28.86 ±0.08 ±0.192 24.17 ±0.12 ±0.203 17.79 ±0.26 ±0.22So it is advcntageous to use floats with lower flotation temperatures. With Aoat No. 2 we have determined the deuterium contents of two samples of heavy water.Besides, we have measured the effect of pressure on the flotation temperatures of these floats. Float No. 1 has been studied in more detail with the result that the relationship between the flotation temperature and the pressure is linear in the investigated pressure range of 48 cm Hg in the neighborhood of one atmosphere.