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.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Identification of parameters in unconfined aquifers

A method is presented for identification of parameters in unconfined aquifers from pumping tests, based on the optimisation of the objective function using the least squares approach. Four parameters are to be evaluated, namely: The hydraulic conductivity in the radial and the vertical directions, the storage coefficient and the specific yield. The sensitivity analysis technique is used for solving the optimisation problem. Besides eliminating the subjectivity involved in the graphical procedure, the method takes into account the field data at all time intervals without classifying them into small and large time intervals and does not use the approximation that the ratio of the storage coefficient to the specific yield tends to zero. Two illustrative examples are presented and it is found that the parameter estimates from the computational and graphical procedures differ fairly significantly.

Synthesis and structure of mixed ligand isonitroso-β-ketoiminenickel(II) complexes. Crystal structure of (1-ethoxycarbonyl-2-npropylimino-1-propanoneoximato) (1-methoxycarbonyl-2-imino-1-propanoneoximato)nickel(II)

Mixed ligand complexes of the type Ni(R-AB)(AC') and Ni(R-AC)(AB') where AB/AC denote N-bonded isonitroso- [3-ketoimino ligands, AB'/AC' denote the corresponding Obonded ligands and R = Me, Et, n-Pr are synthesised and characterised. The complexes are neutral with square planar geometry around nickel(II). The bonding isomerism of the isonitroso group is discussed on the basis of i.r. and 1H n.m.r. studies. The crystal structure of the title complex, Ni(n-Pr-IEAI)(IMAI') has been determined from diffractometer data by Patterson and Fourier methods and refined by least squares to R = 0.088 for 2209 observed reflections. Unit cell constants are: a = 11.945(2), b = 22.436(7), c = 13.248(5) ~, [3 = 95.13(2) ~ The space group is P2Jc with Z = 8. Niekel(II) has a square planar coordination of two imine nitrogens, an isonitroso-nitrogen (from n-Pr-IEAI) and another isonitrosooxygen (from IMAI').

Structure of 2-(2,6-dimethoxyphenyl)-2,5- dimethylbicyclo[3.2.1]octane-6,8-dione

C18H2204, orthorhombic, P212~21, a = 7.343 (4), b = 11.251 (4), c = 19.357 (4)A, Z = 4, Dr, ' = 1.20, D e = 1.254 g cm -3, F(000) = 648, p(MoKa) = 0.94 cm -~. X-ray intensity data were collected on a Nonius CAD-4 diffractometer and the structure was solved by direct methods. Full-matrix least-squares refinement gave R = 0.052 (R w = 0.045) for 1053 observed reflections. The stereochemical configuration at C(2) has been shown to be 2-exo-methyl-2-endo-(2,6-dimethoxyphenyl), i.e. (3) in contrast to the structure (2) assigned earlier based on its ~H NMR data.

Structure and Conformation of an Antidepressant Drug, Nitroxazepine Hydrochloride Monohydrate

CIsH20N3Oa+.C1-.H2 O, M r = 395, orthorhombic, Pn21a, a = 7.710 (4), b = 11.455 (3), c -- 21.199 (3)/k, Z = 4, V = 1872.4/k 3, D m = 1.38, D C = 1.403 g cm -3, F(000) = 832, g(Cu Kct) = 20.94 cm -l. Intensities for 1641 reflections were measured on a Nonius CAD-4 diffractometer; of these, 1470 were significant. The structure was solved by direct methods and refined to an R index of 0.045 using a blockdiagonal least-squares procedure. The angle between the least-squares planes through the benzene rings is 125.0 (5) ° and the side chain is folded similarly to one of the independent molecules of imipramine hydrochloride.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

MAS NMR as a probe for investigating the distribution of Si---O---Si angles in lithium silicate glasses

Magic-angle-spinning NMR has been used to study Si---O---Si bond-angle distributions associated with various structural elements, Qn, present in lithium silicate glasses of different compositions. It is shown that glasses contain a plurality of structural elements with a broad distribution of Si---O---Si bond angles, and that the width of the distribution is characteristic of a particular Qn species

Ternary metal complexes of anionic and neutral pyridoxine (vitamin B6) with 2,2'-bipyridine. Syntheses and x-ray structures of (pyridoxinato)bis(2,2'-bipyridyl)cobalt(III) perchlorate and chloro(2,2'-bipyridyl)(pyridoxine)copper(II) perchlorate hydrate

Ternary metal complexes involving vitamin B6 with formulas [CO",(PN-H)](anCdI [OC)'(bpy)(PN)Cl]C10(.bpHy 0 = 2,2'-bipyridine, PN = neutral pyridoxine, PN-H = anionic pyridoxine) have been prepared for the first time and characterized by means of magnetic and spectroscopic measurements. The crystal structures of the compounds have also been determined. [CO(PN-H)](CcryIsOta,l)lize s in the space group P2,/c with a = 18.900 (3) A, b = 8.764 (1) A, c = 20.041 (2) A,p = 116.05 (l)', and Z = 4 and [Cu(bpy)(PN)C1]C104-H20in the space group Pi with a = 12.136 (5) A, b = 13.283 (4) A,c = 7.195 (2) A, a = 96.91 (Z)', 0 = 91.25 (3)', y = 71.63 (3)', and Z = 2. The structures were solved by the heavy-atom method and refined by least-squares techniques to R values of 0.080 and 0.042 for 3401 and 2094 independent reflections, respectively. Both structures consist of monomeric units. The geometry around Co(II1) is octahedral and around Cu(I1) is distorted square pyramidal. In [CO(PN-H)]t(wCo IoxOy~ge)n~s ,fro m phenolic and 4-(hydroxymethyl) groups of PN-H and two nitrogens from each of two bpy's form the coordination sphere. In [Cu(bpy)(PN)C1]C104.H20o ne PN and one bpy, with the same donor sites, act as bidentate chelates in the basal plane, with a chloride ion occupying the apical position. In both structures PN and PN-H exist in the tautomeric form wherein pyridine N is protonated and phenolic 0 is deprotonated. However, a novel feature of the cobalt compound is that PN-H is anionic due to the deprotonation of the 4-(hydroxymethyl) group. The packing in both structures is governed by hydrogen bonds, and in the copper compound partial stacking of bpy's at a distance of -3.55 also adds to the stability of the system. Infrared, NMR, and ligand field spectroscopic results and magnetic measurements are interpreted in light of the structures.