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.     

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.     

The peak algebra and the descent algebras of types B and D

We show the existence of a unital subalgebra of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that is the image of the descent algebra of type B under the map to the descent algebra of type A which forgets the signs, and also the image of the descent algebra of type D. The algebra contains a two-sided ideal which is defined in terms of interior peaks. This object was introduced in previous work by Nyman (2003); we find that it is the image of certain ideals of the descent algebras of types B and D. We derive an exact sequence of the form . We obtain this and many other properties of the peak algebra and its peak ideal by first establishing analogous results for signed permutations and then forgetting the signs. In particular, we construct two new commutative semisimple subalgebras of the descent algebra (of dimensions and by grouping permutations according to their number of peaks or interior peaks. We discuss the Hopf algebraic structures that exist on the direct sums of the spaces and over and explain the connection with previous work of Stembridge (1997); we also obtain new properties of his descents-to-peaks map and construct a type B analog.