Palladium(II) Complexes with the Mixed‐Donor Ligand CH3S‐(CH2)3‐PPh2 Crystal Structures of [PdCl2{CH3S‐(CH2)3‐PPh2}n](n = 1, 2)

The phosphorus‐sulfur ligand 1‐(methylthio)‐3‐(diphenylphosphino)‐propane (S‐P3) has been synthesized and characterized by ¹H NMR and ¹³C NMR. Reactions of S‐P3 with [PdCl₂(PhCN)₂] afforded the complexes [PdCl₂(S‐P3)] ( I ) and [PdCl₂(S‐P3)₂] ( II ), in which S‐P3 acts as a bidentate and monodentate ligand, respectively. Compound I crystallizes in monoclinic space group P2₁/n (No. 14) with cell dimensions: a = 8.589(3), b = 15.051(3), c = 17.100(3)Å, β = 102.91(2)°, V = 2154.7(9)ų, Z = 4. Likewise, compound II crystallizes in monoclinic space group P2₁/n (No. 14) with a = 9.993(5), b = 8.613(4), c = 18.721(5)Å, β = 90.18(3)°, V = 1611.3(12)ų, Z = 2. Compound II has a trans square planar configuration with only the P‐site of the ligand bonded to the palladium atom.     

On the origin of residual dipolar couplings from denatured proteins

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.     

On the interpretation of residual dipolar couplings as reporters of molecular dynamics

The analysis of residual dipolar couplings from an ensemble of conformations to extract molecular dynamics is intricate. The very mechanism that is necessary to perturb overall molecular tumbling to generate nonvanishing residual dipolar couplings gives rise to convoluted data. The measured values are essentially weighted averages over conformations. However, the weights are not simply the populations of conformations. Consequently, the observed order parameter is not exactly the true measure of motion. In the case of paramagnetic alignment, the apparent order parameter is expected to depend on the number of torsions that separate the locus of interest from the paramagnetic site. In the case of alignment due to steric obstruction, the uneven selection of conformations by their differing Saupe order matrices leads to a bias in the residual dipolar couplings-probed molecular dynamics.     

A multilayer coated fiber-based substrate suitable for printed functionality

A recyclable multilayer coated fiber-based substrate combining sufficient barrier and printability properties for printed functional devices was developed using reel-to-reel techniques. The substrate consists of a mineral pigment layer coated on top of a barrier latex layer. The pigment layer allows controlled absorption of ink solvents. By adjusting the thickness and porosity of the top coating the printability can be tuned for various functional inks. As a proof of concept a hygroscopic insulator field effect transistor (HIFET) was successfully printed on the multilayer-coated paper.     

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.     

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting theta(sol)+theta(C)=pi/4, where theta(C) is the Cabibbo angle, theta(atm)+theta(CKM)(23)=pi/4 and theta(MNS)(13) approximately theta(CKM)(13) approximately O(lambda(3)), in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.     

Notes on the complexity of sorting in abstract machines

The complexity of sorting with pointer machines and successor-predecessor random access machines is studied. The size of the problem is defined as the length of the problem string. A linear time algorithm is achieved for sorting by pointer machines. For successor-predecessor random access machines linear time is sufficient in a special case.     

NP-completeness of the hamming salesman problem

It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.     

Different aspects of the monotonicity of a function

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare.     

A generalization of the role expectation conflict theory with a methodological analysis

Gross’, Mason's and McEachern's role conflict theory with two incompatible role expectations is generalized by letting the number of incompatible role expectations increase. It is proved that the generalized theory is consistent and that its four axioms are independent. Three methodological results are proven. They show that the generalized theory is, in principle, testable from the point of view of three different well‐defined testing situations. Finally, it is shown that the original theory is a special case of the generalization.