Linear Versus Quadratic Estimators in Linearized Models

In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria for an ordering linear and quadratic estimators.     

“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).     

A Joint Limit Theorem on the Complex Plane for General Dirichlet Series

We prove a joint two-dimensional limit theorem in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series.     

Test for the existence of finite-dimensional Chebyshev subspaces in Lϕ spaces

Vilnius University. Translated from Lietuvos Matematikos Rinkinys (Litovskii Matematicheskii Sbornik), Vol. 30, No. 1, pp. 44–55, January–March, 1990.     

Über eine bemerkenswerte Klasse von Hyperflächen

Ohne Zusammenfassung     

Ultrasonically tunable filter for ψ-rays

A new type of an ultra-narrow frequency transmission filter for ψ-rays is presented. The principle of its operation is based on the Mössbauer-sideband-spectroscopy [1–3]: A resonant absorber onto a thin piezo-electric polymer foil vibrates piston like at an ultrasonic frequency ω. At certain definite amplitudes the zero-order-sideband, i.e. the transition energy ω₀, is fully transmitted without any resonant absorption, whereas simultanously sidebands displaced by energies ±hhΩ from ω₀ are resonantly absorbed. Using several absorbers of this type in series having different frequencies a broadband filter for ψ-rays with a well defined transmission-profile can be designed. Symmetrically, on both sides of the central transmission window there exist resonant absorption bands. The energy width of these different bands is only limited by the possible ultrasonic frequencies and can be adjusted from 10^?o to 10^?5 eV. First experimental results using such an assembly of absorbers are presented. The limit of the efficiency of the filter, caused by non-resonant scattering is discussed.     

Voltammetric determination of nitrate,perchlorate and iodide at a hanging electrolyte drop electrode

The use of a hanging electrolyte drop electrode is examined for the determination of nitrate, perchlorate and iodide. A three-electrode system was used with a polarographic analyzer. Crystal violet dicarbollylcobaltate(III) electrolyte in the nitrobenzene phase and magnesium sulphate in the aqueous phase with a Pb/PbSO₄ reference electrode made it possible to increase the viable potential range. For nitrate, the peak current/concentration relation was linear over the range 0–5 × 10^?5 M, and nitrate in potable water was easily determined.