Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

Rare earth transition metal sulfides, LnMS3

Ternary rare earth transition metal sulfides LnMS3 with Ln = La, Nd, and Gd, and M = V and Cr; as well as Ln = La and M = Mn, Fe, Co, and Ni have been prepared and characterized. The vanadium and chromium sulfides crystallize in a monoclinic layer structure isotypic with LaCrS3, while the other LnMS3 sulfides crystallize in a hexagonal structure. Chemical shifts of the metal K-absorption edge and XPS binding energies of core levels indicate that the transition metal is trivalent in the V and Cr sulfides, while it is divalent in the Mn, Fe, Co, and Ni sulfides. Electrical and magnetic properties of the sulfides are discussed in terms of their structures and the electronic configurations of the transition metal ions.

2,6-Lutidine-N-oxide complexes of rare-earth bromides

2,6-Lutidine-N-oxide (LNO) complexes of rare-earth bromides of the composition $$MBr_3 .(LNO)_{4_{ - n} } .nH_2 O$$ wheren = l for M = La, Pr, Nd, Sm, Gd, Ho, Er; andn = 0 for M = Y have been prepared and characterised by analyses, conductance and infrared data. Infrared spectra of the complexes indicate that the coordination of ligand to the metal ion takes place through the oxygen of the ligand, and the water molecule in the complexes present is coordinated to the metal. A coordination number of seven has been suggested to all the rare-earth metal ions.

Topochemically controlled hydrogen reduction of scheelite-related rare-earth metal molybdates

Scheelite-related -Ln2Mo3O12(Ln = La, Pr, Nd, Sm, Gd, Tb, or Dy) oxides are reduced by hydrogen at 780–870 K yielding molybdenum (IV) oxides of formula Ln2Mo3O9. The latter crystallize in a tetragonal scheelite (ABO4) type structure where one third of the A sites and a quarter of the anion sites are vacant: Ln2/3(cat)1/3MoO3(an). The reaction Ln2Mo3O12+ 3H2 Ln2Mo3O9(an)3+ 3H2O may be regarded as topochemically controlled, since both the parent and the product phases have scheelite-related structures. Infrared spectra and electrical and magnetic properties of these metastable defect scheelite phases are reported.

Structure and Bonding in N-Methylacetamide Complexes of Alkali and Alkaline Earth Metals

A detailed crystallographic investigation of N-methylacetamide complexes of Li, Na, K, Mg and Ca has been made in view of its importance in the coordination chemistry and biochemistry of alkali and alkaline earth metals. The metal ions bind to the amide oxygen causing an increase in the carbonyl distance and a proportionate decrease in the central C-N bond distance. The decrease in the central C-N distance is accompanied by an increase in the distance of the adjacent C-C bond and a decrease in the adjacent C-N bond distance. The metal ion generally deviates from the direction of the lone pair of the carbonyl oxygen and also from the plane of the peptide, the out-of-plane deviation varying with the ionic potential of the cation. The metal-oxygen distance in alkali and alkaline earth metal complexes of a given coordination number also varies with the ionic potential of the cation, as does the strength of binding of the cations to the amide. The amide molecules are essentially planar in these complexes, as expected from the increased bond order of the central C-N bond. The NH bonds of the amide are generally hydrogen bonded to anions. The structures of the amide complexes are compared with those of other oxygen donor complexes of alkali and alkaline earth metals. The structural study described here also provides a basis for the interpretation of results from spectroscopic and theoretical investigations of the interaction of alkali and alkaline earth metal cations with amides.

Thermal decomposition of rare-earth trioxalatocobaltates

The thermal decomposition of rare-earth trioxalatocobaltates LnCo(C2O4)3 · x H2O, where Ln = La, Pr, Nd, has been studied in flowing atmospheres of air/oxygen, argon/ nitrogen, carbon dioxide and a vacuum. The compounds decompose through three major steps, viz. dehydration, decomposition of the oxalate to an intermediate carbonate, which further decomposes to yield rare-earth cobaltite as the final product. The formation of the final product is influenced by the surrounding gas atmosphere. Studies on the thermal decomposition of photodecomposed lanthanum trioxalatocobaltate and a mechanical mixture of lanthanum oxalate and cobalt oxalate in 1 : 2 molar ratio reveal that the decomposition behaviour of the two samples is different. The drawbacks of the decomposition scheme proposed earlier have been pointed out, and logical schemes based on results obtained by TG, DTA, DTG, supplemented by various physico-chemical techniques such as gas and chemical analyses, IR and mass spectroscopy, surface area and magnetic susceptibility measurements and X-ray powder diffraction methods, have been proposed for the decomposition in air of rare-earth trioxalatocobaltates as well as for the photoreduced lanthanum salt and a mechanical mixture of lanthanum and cobalt oxalates.

Lanthanide coordination in dimethyl sulphoxide and antipyrine complexes of rare earth nitrates

Abstract is not available.

A versatile and flexible digital pulse programmer for pulsed nuclear magnetic resonance

A versatile and flexible digital pulse programmer for two-pulse, three-pulse, saturation burst and Carr-Purcell sequences is described. Independently variable controls for pulse widths (0.2 mu s to 100 mu s), delay between pulses (0.2 mu s to 100 s) and for number of pulses (1 to 99) for the saturation burst and for the Carr-Purcell sequence, are brought to the front panel. The programmer can be used for one-shot experiments as well as for repetitive experiments.

Preparation, IR and nuclear magnetic resonance studies on the rare-earth perchlorate complexes of 3-methylpyridine-1-oxide

THE COMPLEXES of pyridine-l-oxide and 2- and 4-substituted pyridine-l-oxides have been investigated previously[l]. The complexes of 3-substituted pyfidine-l-oxides, however, have received little attention. The rare-earth complexes of pyridine-Ioxide[l, 2], 4-methylpyridine- l-oxide [1] and 2,6- dimethylpyfidine-l-oxide[3,4] have been reported earlier. The present paper deals with the isolation and characterisation of 3-methylpyridine-l-oxide (3-Picoline-N-oxide, 3-PicNO) complexes with rare-earth perchlorates.

Itinerant electron ferromagnetism in Sr2+-, Ca2+-, and Ba2+-doped rare-earth orthocobaltites (Ln3+1�xM2+xCoO3)

Electronic and magnetic properties of Ln1�xSrxCoO3 (Ln = Pr, Nd, Sm, Eu, and Gd) systems show that above a critical value of x, the d electrons become itinerant while the materials become ferromagnetic at low temperatures. The ferromagnetic component increases with increase in x and decrease in temperature. The Curie temperature increases with x and decreases with decrease in the size of the rare-earth ion. Incorporation of Ba2+ in LaCoO3 favors itinerant electron ferromagnetism relative to Sr2+ while Ca2+ is less favorable than Sr2+.

An innovative clustering technique for unsupervized learning in the context of remotely sensed earth resources data analysis

A new clustering technique, based on the concept of immediato neighbourhood, with a novel capability to self-learn the number of clusters expected in the unsupervized environment, has been developed. The method compares favourably with other clustering schemes based on distance measures, both in terms of conceptual innovations and computational economy. Test implementation of the scheme using C-l flight line training sample data in a simulated unsupervized mode has brought out the efficacy of the technique. The technique can easily be implemented as a front end to established pattern classification systems with supervized learning capabilities to derive unified learning systems capable of operating in both supervized and unsupervized environments. This makes the technique an attractive proposition in the context of remotely sensed earth resources data analysis wherein it is essential to have such a unified learning system capability.

An absolute digital positioning numerical control system

A module containing all the functional components required for a digital absolute positioning process of one axis of a machine tool has been designed and constructed. Circuit realization makes use of integrated circuit elements.

3-Picoline-N-oxide complexes of rare-earth bromides

3-Picoline-N-oxide (3-PicNO) complexes of rare-earth bromides of the formulaMBr3(3-PicNO)8–n·nH2O wheren=0 forM=La, Pr, Nd, Sm Tb or Y andn=2 forM=Ho or Yb have been prepared. Infrared and proton NMR studies indicate that the coordination of the ligand is through oxygen. Conductance data in acetonitrile suggest that two bromide ions are coordinated to the metal ion. Proton NMR studies suggest a bicapped dodecahedral arrangement of the ligands around the metal ion in solution for Pr(III), Nd(III) and Tb(III) complexes.