Unitary invariants of spectral measures with the CGS-property

A «CGS-property» for the spectral measures is introduced and the classical results of determining complete systems of unitary invariants for self-adjoint and bounded normal operators on separable Hilbert spaces are extended to the class of spectral measures with this property. As a consequence, the above mentioned results are extended to unbounded normal operators on separable Hilbert spaces. Moreover, three different kinds of multiplicity are defined and it is shown that for the measures with the «CGS-property» they all coincide. In the last section some analogues of the multiplicity functions defined by Stone [14] are related to the total multiplicity.     

The regioselectivity of the formation of 2-pyrazolylthiazoles and their precursors from the reaction of 2-hydrazinothiazoles with 4,4,4-trifluoro-1-hetaryl-1,3-butanediones

Reaction of 2-hydrazinothiazoles 1 with 1-thienyl- and 1-furyl-1,3-butanediones 2a,b in methanol in the presence of hydrochloric acid mainly leads to a mixture of pyrazoles 3 and pyrazolines 4 or pyrazoles 3 and 5 in strong acidic conditions. Isomeric hydrazones 6 and pyrazolines 4 were formed and isolated in these reactions in the absence of hydrochloric acid. It has been shown that the regioselectivity in the reaction of diketones 2 with hydrazine 1 is governed by both the concentration of acid and the nature of substituents in the 1,3-diketones 2. Cyclization of hydrazones 6 is shown to occur under milder conditions than dehydration for pyrazolines 4. The new heterocyclic compounds were prepared and fully characterized by NMR spectra and by X-ray analysis for 3c.     

HDDR过程中三元和多元Nd-Fe-B合金磁畴结构的MFM研究

用磁力显微镜研究了三元Nd-Fe-B合金在HDDR过程的不同阶段(铸态、不充分吸氢歧化、充分吸氢歧化和脱氢再复合)的破畴结构。在铸态样品表面清楚地观察到了易磁化轴互相垂直的柱状晶表面的两类磁畴图型。当样品不充分吸氢歧化和充分吸氢歧化时，破畴结构明显发生变化，反映了Nd-Fe-B的分解产物NdH2，α-Fe和Fe2B及其微晶结构的变化。脱氢再复合后形成的微晶的磁畴结构则表明样品保留了铸态样品柱状晶的构型。此外，还对比研究了多元Nd-Fe-B合金在HDDR过程中的磁畴结构，并根据微磁结构分析，指出过量的Ga元素添加可抑制Nd2(Fe，M)14B相的吸氢歧化，从而导致相应HDDR粘结磁体性能降低。     

Titanates de cuivre substitués à structure bixbyite: Les composés Cu1−xTi1−xFe2xO3 (0.15 ≤ x ≤ 0.33)

A new bixbyite family, Cu_1?xTi_1?xFe_2xO₃ (0.15 ≤ x ≤ 0.33) has been synthesized and characterized. The unit cell is cubic: a ～ 9.40Å. The X-ray powder diffraction study shows up an isotypism with the (Fe, Mn)₂O₃ compounds. There is a disordered distribution of Cu^II, Ti^IV, and Fe^III over the two cyrstallographic sites: P_I and P_II. P_II is highly distorted (two long MO distances) by the Jahn-Teller effect of Cu^II. The bixbyite structure is described in terms of polyhedra arrangement, as a particular case of the CM₂O₃ family. The cation packing is discussed in relation with the existence of the bixbyite structure for the Cu_1?xTi_1?xFe_2xO₃ compounds. The electrical properties (σ ～ 10^?5(Ω cm)^?1 for x = 0.286 at room temperature) show an electron conduction with probably a hopping mechanism.     

Etude des equilibres solide-liquide des systems MIPO3Sm(PO3)3 (MI = Li,Na, Ag)

The M^IPO₃Sm(PO₃)₃(M^I = Li, Na, Ag) systems were studied. Differential thermal analysis and X-ray diffraction were used to investigate the liquidus and solidus relations. Three compounds LiSm(PO₃)₄, NaSm(PO₃)₄, and AgSm(PO₃)₄ were obtained which melt incongruently at 1248, 1143, and 1078 K, respectively. These compounds are isomorphous with their homologs LiLn(PO₃)₄, NaLn(PO₃)₄, AgLn(PO₃)₄ (Ln = Ce, La, Nd). They belong to the monoclinic system. The LiSm(PO₃)₄ unit cell parameters refined by least squares method are a = 16.43(3) Å, b = 7.16(1) Å, c = 9.65(3) Å, β = 125,9°(1), with the space group $\text{C2}\text{c}$ and Z = 4. NaSm(PO₃)₄ and AgSm(PO₃)₄ are isotypic; they cristallize in the $\text{P2}{}_1\text{c}$ space group, Z = 4; their unit cell parameters are, respectively, a = 12.18(1) Å, b = 13.05(1) Å, c = 7.25(5) Å, β = 126,53°(4), $\text{a = 12.25(1)}\text{A}\text{?}$, b = 13.06(1) Å, c = 7.201(9) Å, β = 126,57°(7). The ir spectra of the last two compounds indicate that these phosphates are chain phosphates.     

AlSiP3, a compound with a novel wurtzite-pyrite intergrowth structure

AlSiP₃ is formed by heating aluminum and silicon powder with red phosphorus and adding small amounts of iodine or AlCl₃. Small, black crystals with metallic lustre grow at 1200°K. The compound crystallizes in the orthorhombic space group Pmnb (No. 62) with a = 987.2 pm, b = 586.1 pm, c = 608.8 pm and four formula units. In the structure isolated P atoms as well as P₂ pairs are present (PP = 218.2 pm). Silicon is tetrahedrally bonded (SiP = 224.2 ? 228.2 pm) whereas aluminum has octahedral coordination (AlP = 244.2 – 260.8 pm). The structure can be described as an intergrowth structure of wurtzite and pyrite type.     

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

Revision of the decay data of166–170Re,including new isomers167m,169mRe

The neutron-deficient rhenium isotopes^166–170Re were investigated using reactions of³²S with monoisotopic¹⁴¹Pr targets. Gamma-rays following the-decays of^166–169Re were measured for the first time. Four new-rays with energies of 4.70,4.83, 4.87, and 5.02 MeV were detected in addition to the known 5.50, 5.26, and 5.06 MeV-rays. Alpha-decaying isomer pairs were discovered in¹⁶⁷Re and¹⁶⁹Re. The measured half-lives are 2.3(2)s for¹⁶⁶Re, 3.4(4)s and 6.2(5)s for¹⁶⁷Re, 4.4(1)s for¹⁶⁸Re, 8.1(5)s and 16.3(8)s for¹⁶⁹Re, and 9.2(2)s for¹⁷⁰Re. The nuclear structure is discussed in terms of single-particle states.This work has been funded by the German Federal Minister for Research and Technology (BMFT) under contract number 06GÖ105     

Investigation of the fusion reaction27Al+236U→263105 at excitation energies of 57 MeV and 65 MeV

The neutron-deficient isotopes^257,258105 were produced in the reaction²⁷Al+²³⁶u in 6n and 5n evaporation channels, respectively. The evaporation residues emerging from the target were separated in-flight from the projectiles and from products of different nuclear reactions by the electrostatic separator VASSILISSA [1]. The isotopes were then implanted into position-sensitive silicon detectors and identified using the --correlation method. The measured production cross-section is (5n)=(0.45±0.20)nb atE _P =154 MeV and (6n)=(0.075±0.055) nb atE _P =163 MeV. These cross-sections are compared with data measured for the same isotopes in the more symmetrical reaction⁵⁰Ti+²⁰⁹Bi.