Weakly representable atom structures that are not strongly representable,with an application to first order logic

Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

论假设检验中的两类错误

蔡越江．论假设检验中的两类错误．本文从假设检验的两个例子谈起,指出备择假设也是影响接区域的。接着论述了假设检验中的两类错误之间的关系。最后讨论如何同时控制两类错误。     

Single-Crystal Growth and Classification of EuAlF5 and Solid Solutions M(II)1−xEuxAlF5 (M=Ca, Sr, Ba) within the Structural Family of Tetragonal M(II)M(III)F5 Compounds

The compound EuAlF₅, as well as the solid solutions Ca_0.19(1)Eu_0.81(1)AlF₅, Sr_0.15(1)Eu_0.85(1)AlF₅, Sr_0.55(1)Eu_0.45(1)AlF₅, Sr_0.77(1)Eu_0.23(1)AlF₅, and Ba_0.62(1)Eu_0.38(1)AlF₅, crystallize in colorless tetragonal columns. These have been prepared by solid state reactions at 900°C, starting from mixtures of the binary fluorides. According to Vegard's rule the solid solution Sr_1−xEu_xAlF₅ shows a linear dependence of the crystal volume on the molar ratio Eu/Sr. All crystal structures have been refined from single-crystal diffractometer data. EuAlF₅ and the M_1−xEu_xAlF₅ (M=Ca, Sr) compounds obtained are isotypic with β-SrAlF₅. They crystallize in a superstructure in space group I4₁/a (no. 88) with 64 formula units and lattice parameters a≈19.9 Å, c≈14.3 Å. The structure is characterized by chains of trans-corner-sharing [AlF_4/2F_2/1] and branched [AlF_5/1F_1/2] octahedra forming a channel structure. Inside the channels isolated ordered dimeric units [AlF_4/1F_2/2]₂ are located. The divalent metal atoms show coordination numbers 8 and 9; they connect the [AlF₆] octahedra into a three-dimensional structure. Ba_0.62(1)Eu_0.38(1)AlF₅ is isotypic with the corresponding Sr compound Ba_0.43(1)Sr_0.57(1)AlF₅, and it crystallizes with 16 formula units and lattice parameters a=14.3860(7) Å, c=7.2778(3) Å in space group I4/m (no. 87). The network structure is identical with that of EuAlF₅. Instead of the dimeric units, infinite chains [AlF_4/1F_2/2]_∞ of trans-corner-sharing [AlF₆] octahedra extending along the c- axis are located inside the channels. The bridging fluorine atoms of this chain show large anisotropic displacement parameters, but no superstructure reflections have been observed for this compound.     

Sorption and Desorption of Inclusion Compound Guests Different Types of Inclusion Compounds

The guests present in inclusion compounds participate in bonding with the hosts. The conditions for the sorption and desorption of the guests are decisive for the properties of the inclusion compounds. They are surveyed for many types of inclusion compounds. This revised version was published online in August 2006 with corrections to the Cover Date.     

水泥浆体中氯盐阳离子种类对游离氯离子浓度的影响

研究了不同阳离子氯盐作用下, 水泥净浆中游离氯离子浓度和结合氯离子浓度的变化, 并通过X射线衍射技术和电镜扫描分析技术观察其微观状态. 结果表明: 掺氯化钠的试件中游离氯离子浓度更高, 钙离子对氯离子的结合能力更强; 氯化钙比氯化钠更易与水泥熟料发生反应, 生成水化产物Friendel复盐和C-S-H凝胶; 掺氯化钙的试块表面晶体更为细密且结构多样.     

Stability of axially compressed cylindrical shells made of reinforced materials with specific fiber orientation within each layer

A technique for stability analysis of anisotropic cylindrical shells is developed. It permits us to examine the cases of reinforcement where the elastic axes of layers do not coincide with the coordinate axes of the shell. The solution is obtained using the mixed equations of the Donnell-Mushtari-Vlasov theory of shells. The deflection and force functions are approximated by trigonometric series. Single-layer and multilayer cylindrical shells with fiber orientation of two types are analyzed for stability. It is revealed that when layers are few, failure to incorporate the direction of fibers in layers into the design model results in highly inaccurate values of critical loads __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 80–88, March 2006.     

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

Effects of Vocal Training and Phonatory Task on Voice Onset Time

OBJECTIVES/HYPOTHESIS: The purpose of this study was to examine the temporal-acoustic differences between trained singers and nonsingers during speech and singing tasks. METHODS: Thirty male participants were separated into two groups of 15 according to level of vocal training (ie, trained or untrained). The participants spoke and sang carrier phrases containing English voiced and voiceless bilabial stops, and voice onset time (VOT) was measured for the stop consonant productions. RESULTS: Mixed analyses of variance revealed a significant main effect between speech and singing for /p/ and /b/, with VOT durations longer during speech than singing for /p/, and the opposite true for /b/. Furthermore, a significant phonatory task by vocal training interaction was observed for /p/ productions. CONCLUSIONS: The results indicated that the type of phonatory task influences VOT and that these influences are most obvious in trained singers secondary to the articulatory and phonatory adjustments learned during vocal training.     

Arithmetic Interpretability Types of Varieties and Some Additive Problems with Primes

We deal with varieties with one basic operation f(x₁,...,x_n) and one defining identity f(x₁,..., x_n) = f(x_π(1),...,x_π(n)), where π is a permutation whose cyclic set consists of distinct primes p₁,...,p_r, with the sum p₁+...+p_r = n. Their interpretability types, together with the greatest element 1 in a lattice ^int, are said to be arithmetic. It is proved that the arithmetic types constitute a distributive lattice _ar, which is dual to a lattice Sub _fΠ of finite subsets of the set Π of all primes. It is shown that for n ⩾ 2, the poset _ar( _n) of arithmetic types defined by permutations in _n, for n fixed, is a lattice iff n = 2, 3, 4, 6, 8, 9, 11. __________ Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005.