Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Scheme of squares: Part II. Systems formalism for sinusoidal perturbations

We extend here the formalism developed in Part I (for the potentiostatic response) to the admittance analysis of the scheme of squares. The results are applicable, as before, to several configurations of the electrode such as the rotating disk or the planar. All that one has to do is “to plug in” the appropriate matrices relating the interfacial concentrations to the fluxes.

A modified least squares algorithm to treat associations in liquid alloys

The associated model for binary systems has been modified to include volume effects and excess entropy arising from preferential interactions between the associate and the free atoms or between the free atoms. Equations for thermodynamic mixing functions have been derived. An optimization procedure using a modified conjugate gradient method has been used to evaluate the enthalpy and entropy interaction energies, the free energy of dissociation of the complex, its temperature dependance and the size of the associate. An expression for the concentration—concentration structure factor [Scc (0)] has been deduced from the modified associated solution model. The analysis has been applied to the thermodynamic mixing functions of liquid Ga-Te alloys at 1120 K, believed to contain Ga2Te3 associates. It is observed that the modified associated solution model incorporating volume effects and terms for the temperature dependance of interaction energies, describes the thermodynamic properties of Ga-Te system satisfactorily.

Parameter estimation in water-distribution systems by least squares

The weighted-least-squares method using sensitivity-analysis technique is proposed for the estimation of parameters in water-distribution systems. The parameters considered are the Hazen-Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted-least-squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water-distribution system in India.

Self-assembled molecular squares containing metal-based donor: synthesis and application in the sensing of nitro-aromatics

Self-assemblies between a linear Pt-based donor and ferrocene- chelated metallic acceptors produced novel heterometallic squares 4 and 5, which show fluorescence quenching upon the addition of nitro-aromatics.

Self-Assembly of Manganese(I)-Based Molecular Squares: Synthesis and Spectroscopic and Structural Characterization

Syntheses of manganese(I)-based molecular squares have been accomplished in facile one-pot reaction conditions at room temperature. Self-assembly of eight components has resulted in the formation of M4L4-type metallacyclophanes [Mn(CO)(3)Br(mu-L)(4) (1-3) using pentacarbonylbromomanganese as metal precursor and rigid azine ligands such as pyrazine, 4,4'-bipyridine, and trans-1,2-bis(4pyridyl)ethylene, respectively, as bridging ligands. The metallacyclophanes have been characterized on the basis of IR, NMR, and UV-vis spectroscopic techniques and single-crystal X-ray diffraction methods.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Wireless Network-Coded Bidirectional Relaying Using Latin Squares for M-PSK Modulation

The design of modulation schemes for the physical layer network-coded two-way relaying scenario is considered with a protocol which employs two phases: multiple access (MA) phase and broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of MA interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, that this relationship can be used to get the network coding maps satisfying the exclusive law. The channel fade states for which the minimum distance of the effective constellation at the relay become zero are referred to as the singular fade states. For M - PSK modulation (M any power of 2), it is shown that there are (M-2/4 - M/2 + 1) M singular fade states. Also, it is shown that the constraints which the network coding maps should satisfy so that the harmful effects of the singular fade states are removed, can be viewed equivalently as partially filled Latin Squares (PFLS). The problem of finding all the required maps is reduced to finding a small set of maps for M - PSK constellations (any power of 2), obtained by the completion of PFLS. Even though the completability of M x M PFLS using M symbols is an open problem, specific cases where such a completion is always possible are identified and explicit construction procedures are provided. Having obtained the network coding maps, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map chosen in a particular region. It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for M = 4-PSK signal set by Koike-Akino et al., when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by Koike-Akino et al.

Probabilistic least squares approach to ordinal regression

This paper proposes a novel approach to solve the ordinal regression problem using Gaussian processes. The proposed approach, probabilistic least squares ordinal regression (PLSOR), obtains the probability distribution over ordinal labels using a particular likelihood function. It performs model selection (hyperparameter optimization) using the leave-one-out cross-validation (LOO-CV) technique. PLSOR has conceptual simplicity and ease of implementation of least squares approach. Unlike the existing Gaussian process ordinal regression (GPOR) approaches, PLSOR does not use any approximation techniques for inference. We compare the proposed approach with the state-of-the-art GPOR approaches on some synthetic and benchmark data sets. Experimental results show the competitiveness of the proposed approach.

Physical layer network coding for two-way relaying with QAM and latin squares

In the design of modulation schemes for the physical layer network-coded two way relaying scenario with two phases (Multiple access (MA) Phase and Broadcast (BC) Phase), it was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference and all these network coding maps should satisfy a requirement called the exclusive law. In [11] the case in which the end nodes use M-PSK signal sets is extensively studied using Latin Squares. This paper deals with the case in which the end nodes use square M-QAM signal sets. In a fading scenario, for certain channel conditions, termed singular fade states, the MA phase performance is greatly reduced. We show that the square QAM signal sets lead to lesser number of singular fade states compared to PSK signal sets. Because of this, the complexity at the relay is enormously reduced. Moreover lesser number of overhead bits are required in the BC phase. We find the number of singular fade states for PAM and QAM signal sets used at the end nodes. The fade state γejθ = 1 is a singular fade state for M-QAM for all values of M and it is shown that certain block circulant Latin Squares remove this singular fade state. Simulation results are presented to show that QAM signal set perform better than PSK.

Wireless bidirectional relaying and Latin squares

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) Phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA Phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. Using the structural properties of the Latin Squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps for M-PSK constellations. This is achieved using the notions of isotopic and transposed Latin Squares. Furthermore, the channel conditions for which the bit-wise XOR will perform well is analytically obtained which holds for all values of M (for M any power of 2). We illustrate these results for the case where both the end users use QPSK constellation.

Self-Assembled Pd(II) Metallocycles Using an Ambidentate Donor and the Study of Square-Triangle Equilibria

The self-assembly reaction of a cis-blocked 90° square planar metal acceptor with a symmetrical linear flexible linker is expected to yield a [4 + 4] self-assembled square, a [3 + 3] assembled triangle, or a mixture of these.However, if the ligand is a nonsymmetrical ambidentate, it is expected to form a complex mixture comprising several linkage isomeric squares and triangles as a result of different connectivities of the ambidentate linker. We report instead that the reaction of a 90° acceptor cis-(dppf)Pd(OTf)2 [where dppf ) 1,1′-bis(diphenylphosphino)- ferrocene] with an equimolar amount of the ambidentate unsymmetrical ligand Na-isonicotinate unexpectedly yields a mixture of symmetrical triangles and squares in the solution. An analogous reaction using cis-(tmen)Pd(NO3)2 instead of cis-(dppf)Pd(OTf)2 also produced a mixture of symmetrical triangles and squares in the solution. In both cases the square was isolated as the sole product in the solid state, which was characterized by a single crystal structure analysis. The equilibrium between the triangle and the square in the solution is governed by the enthalpic and entropic contributions. The former parameter favors the formation of the square due to less strain in the structure whereas the latter one favors the formation of triangles due to the formation of more triangles from the same number of starting linkers. The effects of temperature and concentration on the equilibria have been studied by NMR techniques. This represents the first report on the study of square-triangle equilibria obtained using a nonsymmetric ambidentate linker. Detail NMR spectroscopy along with the ESI-mass spectrometry unambiguously identified the components in the mixture while the X-ray structure analysis determined the solid-state structure.

Steady state optimization of an ammonia reactor

A hybrid simulation technique for identification and steady state optimization of a tubular reactor used in ammonia synthesis is presented. The parameter identification program finds the catalyst activity factor and certain heat transfer coefficients that minimize the sum of squares of deviation from simulated and actual temperature measurements obtained from an operating plant. The optimization program finds the values of three flows to the reactor to maximize the ammonia yield using the estimated parameter values. Powell's direct method of optimization is used in both cases. The results obtained here are compared with the plant data.

x-ray studies on crystalline complexes involving amino-acids and peptides .10. head-to-tail sequences in the crystal-structure of l-lysine acetate

l-Lysine acetate crystallises in the monoclinic space group P21 with a = 5.411 (1), b = 7.562(1), c= l2.635(2) Å and β = 91.7(1). The crystal structure was solved by direct methods and refined to an R value of 0.049 using the full matrix least squares method. The conformation and the aggregation of lysine molecules in the structure are similar to those found in the crystal structure of l-lysine l-aspartate. A conspicuous similarity between the crystal structures of l-arginine acetate and l-lysine acetate is that in both cases the strongly basic side chain, although having the largest pK value, interacts with the weakly acidic acetate group leaving the α-amino and the α-carboxylate groups to take part in head-to-tail sequences. These structures thus indicate that electrostatic effects are strongly modulated by other factors so as to give rise to head-to-tail sequences which have earlier been shown to be an almost universal feature of amino acid aggregation in the solid state.

Assignment of fundamental vibrations of. ,N'-dimethylthiourea,

The infrared spectra of symmetric N,N′-dimethylthiourea (s-DMTU) and its N-deuterated (s-DMTU-d2) species have been measured. The fundamental frequencies have been assigned by comparison with the assignments in structurally related molecules and the infrared band shifts on N-deuteration, S-methylation, available Raman data and with the aid of theoretical band assignments from normal coordinate treatments for s-DMTU-d0 and -d2. A force field is derived for s-DMTU by transferring the force constants chiefly from N-methylthiourea and the subsequent refinement of the force constants by a least squares procedure.