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V. Pták's inequality is valid for every hermitian completeQ locallym-convex (:l.m.c.) algebra. Every algebra of the last kind is, in particular, symmetric. Besides, a (Hausdorff) locallyC *-algebra (being always symmetric) with the propertyQ is, within a topological algebraic isomorphism, aC *-algebra. Furthermore, a type of Raikov's criterion for symmetry is also valid for non-normed topological*-algebras. Concerning topological tensor products, one gets that symmetry of theπ-completed tensor product of two unital Fréchet l.m.c.*-algebrasE, F (π denotes the projective tensorial topology) is always passed toE, F, while the converse occurs when moreover either ofE, F is commutative.

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Császár (1963) and Deák (1991) have introduced the notion of half-completeness in quasi-uniform spaces which generalizes the well known notion of bicompleteness. In this paper, for any quasi-uniform space, we construct a half-completion, called standard half-completion. The standard half-completion coincides with the usual uniform completion in the case of uniform spaces. It is also an idempotent operation in the sense that the standard half-completion of a half-complete quasi-uniform space coincides (up to a quasi-isomorphism) with the space itself.

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In this paper we study the semigroup ℐ (ℕ) of partial cofinal monotone bijective transformations of the set of positive integers ℕ. We show that the semigroup ℐ (ℕ) has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology τ on ℐ (ℕ) such that (ℐ (ℕ); τ) is a topological inverse semigroup, is discrete. Finally, we describe the closure of (ℐ (ℕ); τ) in a topological semigroup.

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The purpose of this paper is to study the principal fibre bundle (P, M, G, π p ) with Lie group G, where M admits Lorentzian almost paracontact structure (Ø, ξ p , η p , g) satisfying certain condtions on (1, 1) tensor field J, indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

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Abstract  

Adducts of Co(II), Ni(II), Cu(II), Zn(II) and Pb(II) saccharinates with 1,10-phenathroline were synthesized and their thermoanalytical (TG, DTG and DTA) curves in the 20–1000C temperature interval and static air atmosphere were recorded. The complexes are best represented as M(C12H8N2)x(C7H4NO3S)2yH2O (x=2, 2, 2, 2 and 1; y=1, 1, 2, 1 and 2 for M=Co, Ni, Cu, Zn and Pb, respectively). The decomposition of the compounds regularly started with dehydration, followed by loss of the phenanthroline ligand(s). The structures of the Cu and Pb complexes are notably different from other compounds. FTIR spectra of the title compounds in the region of the OH, CO and SO2 stretching vibrations were also studied. The pronounced similarity of the spectra of Co, Ni and Zn adducts indicates possible isomorphism among them.

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The hydrazinium(1+) metal acetates and malonate dihydrates of the molecular formula [(N2H5)2M(CH3COO)4] and (N2H5)2[M(OOCCH2COO)2(H2O)2] respectively, whereM=Co, Ni or Zn, have been prepared and characterized by chemical analyses, conductance, magnetic, spectral, thermal and X-ray powder diffraction studies. The magnetic moments and electronic spectra indicate that these complexes are of high-spin octahedral variety. The infrared spectra show that the hydrazinium ions are coordinated in the case of acetate complexes, whereas in the malonate complexes the hydrazinium ions are out side the coordination sphere. These complexes undergo exothermic decomposition in the temperature range 150–450°C to give the respective metal oxide as the final residue. The X-ray powder diffraction patterns of the malonate complexes indicate isomorphism among them.

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G. Grtzer and F. Wehrung introduced the lattice tensor product, AB, of the lattices Aand B. In Part I of this paper, we showed that for any finite lattice A, we can "coordinatize" AB, that is, represent A⊠,B as a subset A<B> of B A, and provide an effective criteria to recognize the A-tuples of elements of B that occur in this representation. To show the utility of this coordinatization, we prove, for a finite lattice A and a bounded lattice B, the isomorphism Con A<B> ≌ (Con A)<Con B>, which is a special case of a recent result of G. Grtzer and F. Wehrung and a generalization of a 1981 result of G. Grtzer, H. Lakser, and R.W. Quackenbush.

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A puzzle is equally new for everyone who is presented with it for the first time. However, it is not if we take one’s previous knowledge into account. Some knowledge may be utilised while working on the puzzle. If this is the case, problem solving as well as the development of knowledge about the puzzle both are promoted as the result of transfer of knowledge. This was demonstrated in a study where participants with different levels of knowledge in programming solved the Four Balls Puzzle, an isomorph of the Chinese Ring Puzzle. 21 Participants, experienced in programming, outperformed 24 non-experienced participants in solving the puzzle but not in the attained level of verbalised knowledge about the puzzle at the end of the problem-solving process.

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A puzzle is equally new for everyone who is presented with it for the first time. However, it is not if we take one’s previous knowledge into account. Some knowledge may be utilised while working on the puzzle. If this is the case, problem solving as well as the development of knowledge about the puzzle both are promoted as the result of transfer of knowledge. This was demonstrated in a study where participants with different levels of knowledge in programming solved the Four Balls Puzzle, an isomorph of the Chinese Ring Puzzle. 21 Participants, experienced in programming, outperformed 24 non-experienced participants in solving the puzzle but not in the attained level of verbalised knowledge about the puzzle at the end of the problem-solving process.

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Abstract  

The binary systems of urea with polyethylene glycols 6000 and 4000 show inclusion compounds with higher melting points than the two components (m.p. 143 and 142.5°C resp.). From the melt unstable forms crystallize beside the stable crystal modifications. These have also been identified by FTIR microscopy and X-ray powder diffractometry. The phase diagrams are uncommon in so far as the inclusion compounds do not form eutectics but monotectics with both components. The inclusion compounds of the two polyethylene glycols with urea are isomorphous and form a series of mixed crystals following the Roozeboom I type of diagram.

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