Ergodicity for Singular-Degenerate Stochastic Porous Media Equations

The long time behaviour of solutions to generalized stochastic porous media equations on bounded intervals with zero Dirichlet boundary conditions is studied. We focus on a degenerate form of nonlinearity arising in self-organized criticality. Based on the so-called lower bound technique, the existence and uniqueness of an invariant measure is proved.

Brama zamku „Golesz” w Krajowicach w świetle badań archeologicznych i prac zabezpieczająco-restauratorskich prowadzonych w latach 2010–2019

The subject of the article is a gate of the medieval and modern period castle “Golesz” in the former Sandomierz land. First of all, there is a description of the gate as the only element of the castle that survived on the surface in a degenerate form and was described in this form at the turn of the 19th and 20th centuries. Later, the results of archaeological research and conservation work carried out in 2010–2019 have been presented. A gate system (12×10 m) was recognized, with a thickened section housing two small rooms on the right, a 4-meter-wide passageway in the centre and an outer wall with a buttress on the left. The exposed walls were secured and left in the form of a permanent ruin. Both stages of work at the site have been thoroughly documented on the basis of 3D laser scanning technologies.

Weak solutions for generalized p-Laplacian systems via Young measures

We prove the existence of weak solutions to a generalized p-Laplacian systems in degenerate form. The techniques of Young measure for elliptic systems are used to prove the existence result.

Continuous space-time transformations

We prove that every continuous map acting on the four-dimensional Minkowski space and preserving light cones in one direction only is either a Poincaré similarity, that is, a product of a Lorentz transformation and a dilation, or it is of a very special degenerate form.

Extreme events of Markov chains

The extremal behaviour of a Markov chain is typically characterised by its tail chain. For asymptotically dependent Markov chains, existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the extreme tail region, and, for asymptotically independent chains, recent results fail to cover well-known asymptotically independent processes, such as Markov processes with a Gaussian copula between consecutive values. We use more sophisticated limiting mechanisms that cover a broader class of asymptotically independent processes than current methods, including an extension of the canonical Heffernan‒Tawn normalisation scheme, and reveal features which existing methods reduce to a degenerate form associated with nonextreme states.

From words and sentences to interjections: The anatomy of exclamations in Peirce and Wittgenstein

Interjections are exclamatory signs fostering a realistic conception of the perils and uncertainties of human experience. Natural interjections are reactionary signs in degenerate pre-signs (preverbs or prenouns), unconnected to other syntactic forms of grammar. The simplicity of natural interjections are distinguished from the more complex occasional interjections, expressed in full pseudo-sentences with grammatical constructions. The prehistory of the natural interjections are first the simple cries of babies, and second the artificial construction of pidgin (creolization) of mixed languages. In interjections, literal language becomes transformed into figurative and metaphorical “language,” that is intermedial speech with vocalization and gestures. Peirce’s “syntax” (Charles Sanders Peirce 1839–1914) argues for the pragmatic interjections in the exclamations of spontaneous cries and shouts. In the framework of Peirce’s logical categories, interjections represent first of secondness. The degenerate form analyzes the vague or indeterminate meaning through pictures of diagrams. Wittgenstein’s social “grammar” (Ludwig Wittgenstein 1889–1951) of language-games is subject to cultural forms of life. Wittgenstein disagrees on accepting the “nonsensical” or meaningless interjections, but in his later writings he will agree to giving the interjections fuzzy meanings.

Opera for Sale: Folksong, Sentimentality and the Market

The Lautenlied from Korngold's Die tote Stadt and the Schlummerlied from Schreker's Die Schatzgräber flaunt their ‘folksong’ style in ways that are clearly similar. Contemporary criticism reveals the significance of this stylization. Folksong symbolized genuineness, but also, in its supposedly degenerate form, emotional manipulation of the masses. Both topics informed critics' reaction to diese two arias. Alongside analysis of the many recordings of Korngold's aria up to 1933, the article suggests how folksong characterization contributed to the opera's plot.