Geometric classification of warped products isometrically immersed into Sasakian space forms

The main objective of this paper is to study the warped product pointwise semi‐slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi‐slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi‐slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established.     

Eine neue Schnellmethode zur makro- und mikrochemischen Bestimmung des Wismuts

Ohne Zusammenfassung     

Inequivalent frame-spun knots with the same complement

Partially supported by a Northeastern University Junior Research Fellowship     

The time required to focus on a cued signal frequency

How quickly can a listener focus on a single tonal cue that indicates the frequency of an upcoming signal? Initial measurements were made with frequency uncertainty (signal frequency varies randomly from trial to trial) and with certainty (same frequency on all trials). Measured by a yes-no procedure, thresholds for 40- and 20-ms signals presented in continuous broadband noise at 50 dB SPL were higher in uncertainty than in certainty; the difference decreased monotonically from 5 dB at frequencies below 500 Hz to under 3 dB above about 2500 Hz. This decrease in the detrimental effect from uncertainty, which comes about with increasing signal frequency, may result from preferential attention to higher frequencies. In a second experiment, frequency again varied randomly, but each trial now began with a cue at the signal frequency. The critical variable was the delay from cue onset to signal onset. A delay of 352 ms eliminated the detrimental effect of frequency uncertainty at all frequencies. At the shortest delays of 52 and 82 ms the detrimental effect was reduced primarily at lower frequencies. Our analysis suggests that shifting focus to a cued frequency region, under optimal stimulus conditions, requires less than 52 ms.     

4f–3d exchange coupling in Gd/X/Co (X=Pt, Cr) multilayers

We have studied the interlayer exchange coupling between Gd and Co through Pt and Cr spacers in a series of multilayers. Magnetization curves have been analyzed with a model, taking into account bilinear and biquadratic interlayer exchange couplings between Gd and Co. The interlayer exchange coupling constants have been determined as a function of the Pt or Cr spacer layer thickness.     

Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence

If is a complex hyperplane arrangement, with complement , we show that the Chen ranks of are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the cohomology ring , viewed as a module over the exterior algebra on :

   for

where is a field of characteristic 0. The Chen ranks conjecture asserts that, for sufficiently large, , where is the number of -dimensional components of the projective resonance variety . Our earlier work on the resolution of over and the above equality yield a proof of the conjecture for graphic arrangements. Using results on the geometry of and a localization argument, we establish the inequality

   for

for arbitrary . Finally, we show that there is a polynomial of degree equal to the dimension of , such that , for all .

     

Thermal behaviour of some Al(III)-Mg(II) polynuclear coordination compounds with polycarboxylic acid anions as ligands,precursors of aluminates

A TG, DTG and DTA study of three polynuclear coordination compounds,containing Al(III)-Mg(II), namely (NH₄)₄[Al₂Mg(C₄O₅H₄)₄(OH)₄]?2H₂O,(NH₄)₄[MgAl₂(C₄H₄O₆)₄(OH)₄]?3H₂Oand (NH₄)₂[Al₂Mg(C₆O₇H₁₁)₅(OH)₅]?3H₂O,has been reported together with the associated thermal decomposition mechanismrationalized in terms of intermediate products. As decomposition end-product,magnesium-aluminum spinel is obtained. The values of MgAl₂O₄mean crystallite size depend on the anionic ligand contained by the precursorcompound, varying in the order: malate (143 Å) ligand contained by theprecursor compound, varying in the order: malate (143 Å)     

Borel-Carathéodory and Fan Type Inequalities for Hilbert Space Bicontractions

This paper deals with some operator versions of the classical Borel–Carathéodory and Ky Fan theorems for analytic functions of complex variable. Our results refer to the functional calculus with analytic functions on the unit bidisk induced by strict bicontractions on a complex Hilbert space.