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1.
The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes
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Prof. Biao Wu Dr. Shaoguang Li Prof. Yibo Lei Prof. Huaiming Hu Dr. Nader de Sousa Amadeu Prof. Dr. Christoph Janiak Dr. Jennifer S. Mathieson Dr. De‐Liang Long Prof. Leroy Cronin Prof. Xiao‐Juan Yang 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(6):2588-2593
By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A2L3 complexes (A represents anion, here orthophosphate PO43?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes. 相似文献
2.
This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal‐sharing” or “per‐unit‐quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced. 相似文献
3.
Jane Cullum 《Advances in Computational Mathematics》1996,6(1):1-24
We study the convergence of the GMRES/FOM and QMR/BiCG methods for solving nonsymmetric systems of equationsAx=b. We prove, in exact arithmetic, that any type of residual norm convergence obtained using BiCG can also be obtained using FOM but on a different system of equations. We consider practical comparisons of these procedures when they are applied to the same matrices. We use a unitary invariance shared by both methods, to construct test matrices where we can vary the nonnormality of the test matrix by variations in simplified eigenvector matrices. We used these test problems in two sets of numerical experiments. The first set of experiments was designed to study effects of increasing nonnormality on the convergence of GMRES and QMR. The second set of experiments was designed to track effects of the eigenvalue distribution on the convergence of QMR. In these tests the GMRES residual norms decreased significantly more rapidly than the QMR residual norms but without corresponding decreases in the error norms. Furthermore, as the nonnormality ofA was increased, the GMRES residual norms decreased more rapidly. This led to premature termination of the GMRES procedure on highly nonnormal problems. On the nonnormal test problems the QMR residual norms exhibited less sensitivity to changes in the nonnormality. The convergence of either type of procedure, as measured by the error norms, was delayed by the presence of large or small outliers and affected by the type of eigenvalues, real or complex, in the eigenvalue distribution ofA. For GMRES this effect can be seen only in the error norm plots.In honor of the 70th birthday of Ted RivlinThis work was supported by NSF grant GER-9450081. 相似文献
4.
Andrew D. Abell Bruce M. Clark Kathryn B. Morris Jane M. Taylor 《Journal of mass spectrometry : JMS》1993,28(1):27-29
Positive-ion fast atom bombardment mass spectra of 13 keto acid and keto ester phosphoranes were examined. All compounds gave a protonated molecular ion and characteristic peaks at m/z 303, 279, 262 and 201. 相似文献
5.
6.
We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents).
For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini
derivative of f.
Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002 相似文献
7.
E. Todd Brown Karen Karp Joseph M. Petrosko Jane Jones Gloria Beswick Carrie Howe Kathy Zwanzig 《School science and mathematics》2007,107(3):102-116
This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands. 相似文献
8.
The interaction of ethoxycarbonyl isothiocyanate with semicarbazides or thiosemicarbazides produces 1-ethoxycarbonyl-2-thiobiureas or bithioureas, respectively. The former are cyclisable to 2-ethoxycarbonamido-5-hydroxy-l,3,4-thiadiazole in acid, or to 2(H)-carbamoyl-3-hydroxy-5-alkylthio-1,2,4-triazoles, and thence to 3-hydroxy-5-mercapto-1,2,4-triazole in alkaline media. The ring-closure of the 1-ethoxycarbonylbithioureas proceeds similarly affording, under the influence of acids, 5-amino (or mercapto)-2-ethoxycarbonamido-1,3,4-thiadiazoles. The action of alkali produces compounds derived from 3-hydroxy-5-mercapto-1,2,4-triazole; the isolation, in a selected example, of the 2(H)-phenylthiocarbamoyl-derivative, elucidates the course of this reaction. Hydrazinolysis of 1-ethoxycarbonylbithiourea yields 4-amino-3-hydrazino-5-mercapto-1,2,4-triazole. 相似文献
9.
We have carried out an ab initio self-consistent-field molecular orbital study of the structures and relative bond strengths of some monoamine derivatives of cubane, azacubane, and 1,3-diazacubane. Our focus has been on the effect of the NH2 group on the strengths of the endocyclic strained bonds in these molecules, and, in particular, on the conformation dependence of this effect. Our results show a consistent bond-weakening observed in one [and only one] C-C or C-N bond adjacent to the site of NH2 substitution. We find that the particular bond that is weakened is in all cases essentially coplanar with the C-NH2 bond and the position of the most negative electrostatic potential of the amine nitrogen. This direction-specific bond-weakening is viewed as an example of the anomeric effect. 相似文献
10.
The synthesis of four new oxo‐centered Fe clusters ( 1 a – c , 2 ) of the form [FeIII3(μ3‐O)(CH2=CHCOO)6] with acrylate as the bridging ligand gives rise to potentially intrinsically chiral oxo‐centered {M3} trimers that show a tendency to spontaneously resolve upon crystallization. For instance, 1 a , [FeIII3(μ3‐O)(CH2=CHCOO)6‐(H2O)3]+, crystallizes in the chiral space group P31 as a chloride salt. Crystallization of 1 b , [Fe3(μ3‐O)(C2H3CO2)6(H2O)3]NO3?4.5H2O, from aqueous solution followed by recrystallization from acetonitrile also gives rise to spontaneous resolution to yield the homochiral salt [Fe3(μ3‐O)(C2H3CO2)6‐(H2O)3]NO3?CH3CN of 1 c (space group P212121). Furthermore, the reaction of 1 a with hexamolybdate in acetonitrile gives the helical coordination polymer {[(Fe3(μ3‐O)L6(H2O))(MoO4)‐(Fe3(μ3‐O)L6(H2O)2)]?2CH3CN?H2O}∞ 2 (L: H2C?CHCOO), which crystallizes in the space group P21. The nature of the ligand geometry allows the formation of atropisomers in both the discrete ( 1 a – c ) and linked {Fe3} clusters ( 2 ), which is described along with a magnetic analysis of 1 a and 2 . 相似文献