On some equations in prime rings

The main purpose of this paper is to prove the following result. Let R be a prime ring of characteristic different from two and let T : R → R be an additive mapping satisfying the relation T(x ³) = T(x)x ² − xT(x)x + x ² T(x) for all x ∈ R. In this case T is of the form 4T(x) = qx + xq, where q is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.     

Semiovals contained in the union of three concurrent lines

Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG(2,p) and PG(2,p²), p an odd prime, is given. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 491–501, 2007     

Computational experience with known variable metric updates

Variable metric methods from the Broyden family are well known and commonly used for unconstrained minimization. These methods have good theoretical and practical convergence properties which depend on a selection of free parameters. We demonstrate, using extensive computational experiments, the influence of both the Biggs stabilization parameter and Oren scaling parameter on 12 individual variable metric updates, two of which are new. This paper focuses on a class of variable metric updates belonging to the so-called preconvex part of the Broyden family. These methods outperform the more familiar BFGS method. We also experimentally demonstrate the efficiency of the controlled scaling strategy for problems of sufficient size and sparsity.     

Quaternionic operators with finite matrix trace

In this paper we consider bounded liner operators in quaternionic Hilbert space, having finite and invariant matrix trace. We prove that any such operator is selfadjoint. Besides, we prove that dual space of the real normed space of all such operators is isomorphic to the Banach space of all selfadjoint operators.This research was supported by Science Fund of Serbia, through the Mathematical Faculty of Belgrade.     

Spectroscopy of neutron deficient 65Ge

Excited states of ⁶⁵Ge were populated via the ¹²C + ⁵⁸Ni (261 MeV) reaction using the NORDBALL detector array equipped with charged-particle and neutron detector systems for reaction channel separation. On the basis of γγ-coincidence relations and angular distribution ratios a significantly extended level scheme was constructed up to E _x = 9 MeV and J ^π = (33/2^?). The low-energy states of the nucleus are discussed in the framework of the interacting boson-fermion model.     

Characterization of microwave plasma generated in inhomogeneous magnetic field

The paper is devoted to the investigation of the electron cyclotron resonance (ECR) discharge in the decreasing magnetic field in the pressure range from 0.02 Pa to 90 Pa and the absorbed microwave power from 50 W to 400 W. For a discharge characterization we used the floating potentialU _fl and the saturated ion current densityi _sat ⁺ . The influence of the substrate holder presence on the plasma microparameters was studied. It was shown that for the substrate holder located near ECR at pressures below 0.3 Pa mainly the magnitude ofU _fl strongly depends on the pressurep, the absorbed microwave powerP _a, and the position of the substrate holder with respect to ECR. The values ofU _fl in the plasma in which the substrate holder is inserted strongly differ from those in the plasma without the substrate holder.U _fl of low pressuresp<0.05 Pa achieves high positive values of about +50 V and this results in sputtering of chamber walls.     

Productive Coreflective Classes in Top

If sequential cardinals do not exist then every topological space is generated from a converging sequence by using finite products, disjoint sums and quotients. The author acknowledges the support of the grants MSM 0021620839 and GAČR 201/06/0933 of Czech Republic.     

Uncertainty of chemical oxygen demand determination in wastewater samples

 The measurement uncertainty of the result of chemical oxygen demand determination in wastewater was evaluated. The major sources of uncertainty of the result of measurement were identified as the purity of reagents, volumetric operations, gravimetric operations, bias, and the repeatability of the method. Identification and evaluation of uncertainty sources was followed by combined uncertainty calculations. The combined uncertainty was compared to the experimentally determined variation and good agreement was found, indicating that the major uncertainty sources had been identified. The results show that the major sources of uncertainty arose from repeatability at high concentration level and volumetric steps at low concentration level, thus revealing the target operations for reducing the measurement uncertainty of this determination. Received: 5 August 2002 Accepted: 5 November 2002 Acknowledgements This research was supported by the Ministry of Education, Science and Sport of the Republic of Slovenia (Project Z2–3530). Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to A. Drolc     

“Naturadeus”, a metaphor of the Perfect Diamond

In this essay, the author outlines his re-construction of Spinoza’s ontological monism by re-presenting the system of Ethica, ordine geometrico demonstrata, in an “intuitive” model of the Perfect Diamond, called NATURADEUS. So, for example, ordo et connexio idearum et rerum, is presented to the inner eye in the forms of two parallel structures, of rays and of facets within the NATURADEUS, respectively. The conceptual background of the proposed model is mostly analytic, the author essays to develop some ideas of Jonathan Bennett’s Spinoza’s metaphysics (especially “transattributive mode identity”), with strong emphasis on ethical issues of ontological monism or pantheism. This essay is written as a dialogue between master Bruno and his student John (physically absent at the moment). More philosophical dialogues of this kind can be found on the author’s web page and in his book Four Seasons (in Slovenian, 2002).     

Approximation of the Lerch Zeta-Function

We consider uniform in parameters approximations of the Lerch zeta-function by Dirichlet polynomials. It allows us to obtain uniform in parameters bounds in the critical strip.