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The paper presents the results of a study investigating a possible influence of the viewpoint (perfective vs. imperfective) and lexical (telic vs. atelic) aspect of Polish verbs on the countability of eventive nominalizations (substantiva verbalia) derived from these verbs. Polish substantiva verbalia preserve many properties of the base verbs, including the eventive meaning and aspectual morphology. Native speakers of Polish rated the acceptability of nominalizations in count and mass contexts. An effect of both viewpoint and lexical aspect was found in mass contexts, where aspectually delimited (perfective, accomplishment) nominalizations were less acceptable than non-delimited (imperfective, state) nominalizations. In count contexts, only an effect of the lexical aspect was clearly present, with accomplishment nominalizations being more acceptable than state nominalizations. The nominalizations were overall rated as more natural in mass than count constructions, regardless of the aspect. The results indicate that aspect plays a role in establishing the countability of a word, but it does not fully determine it.

In this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced. Finally, one-dimensional signal propagation in such electromagnetic media is considered. The proposed FDTD method is derived based on a discrete approximation of the Grünwald–Letnikov definition of the fractional derivative and evaluated in a code. The stability condition is derived for the proposed FDTD method based on a numerical-dispersion relation. The obtained numerical results are compared with the outcomes of reference frequency-domain simulations, proving the accuracy of the proposed approach. However, high spatial resolution is required in order to obtain accurate results. The developed FDTD method is, unfortunately, computation and memory demanding when compared to the ordinary FDTD algorithm.

The number meaning of grammatically plural nouns is to some extent context sensitive. In negative sentences, plural nouns typically receive an inclusive reading referring to any number of individuals (one or many). This contrasts with their more frequent exclusive reading referring to a group of two or more individuals. The present study investigated whether a plural noun in a negative sentence is treated as inclusive immediately when it is encountered or whether this interpretation is delayed. In an experiment using a technique based on a numerical variant of the Stroop effect (Berent et al. in J Mem Lang 53:342-358, 2005. 10.1016/j.jml.2005.05.002; Patson and Warren in J Exp Psychol Learn Mem Cogn 36(3):782-789, 2010. 10.1037/a0018783), participants counted visually presented singular and plural Polish nouns embedded in either affirmative or negative sentences. The nouns were displayed once or as two copies. Plural nouns were easier to count when they were repeated twice on the screen than when only one copy was displayed. For singular nouns this pattern was reversed and the effect was weaker. Crucially, no difference was found for plural nouns appearing in affirmative and negative sentences. This indicated that an inclusive ("one or more") reading of plural nouns in the scope of sentential negation was not immediate. The results are in line with past research suggesting that the semantic processing of a negative sentence may proceed in two phases (Fischler et al. in Psychophysiology 20(4):400-409, 1983. 10.1111/j.1469-8986.1983.tb00920.x; Kaup et al. in J Pragmat 38:1033-1050, 2006. 10.1016/j.pragma.2005.09.012; Lüdtke et al. in J Cogn Neurosci 20(8):1355--1370, 2008. 10.1162/jocn.2008.20093; Spychalska in Proceedings of the 2011 ESSLLI student session, 2011).

We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localization-dependent seismic properties manifested by deviations from Gutenberg–Richter law.

In this article we consider singular Sturm-Liouville problems whose right-hand side is a function of bounded Jordan variation. We present necessary and sufficient conditions for all solutions to be of bounded Jordan variation.

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited applicability in the circuit theory. Out of the most popular approaches considered in this paper, only the Grünwald–Letnikov and Marchaud definitions (which are actually equivalent) satisfy the semigroup property and are naturally representable in the phasor domain. The generalization of this concept, i.e., the two-sided fractional Ortigueira–Machado derivative, satisfies the semigroup property, but its phasor representation is less natural. Other ideas (including the Riemann–Liouville and Caputo derivatives—with a finite or an infinite base point) seem to have limited applicability.

We study the finitely dimensional approximations of the elliptic problem $$displaylines{ (Lu)(x,y) + varphi(lambda,(x,y),u(x,y) ) = 0 quad hbox{for } (x,y)inOmegacr u(x,y) = 0 quad hbox{for } (x,y)inpartialOmega, }$$ defined for a smooth bounded domain $Omega$ on a plane. The approximations are derived from Bernstein polynomials on a triangle or on a rectangle containing $Omega$. We deal with approximations of global bifurcation branches of nontrivial solutions as well as certain existence facts.

A global bifurcation theorem for the following nonlinear Sturm–Liouville problem is given Moreover we give various versions of existence theorems for boundary value problems The main idea of these proofs is studying properties of an unbounded connected subset of the set of all nontrivial solutions of the nonlinear spectral problem , associated with the boundary value problem , in such a way that .

We comprehensively review several general methods and analytical tools used for causality evaluation of photonic materials. Our objective is to call to mind and then formulate, on a mathematically rigorous basis, a set of theorems which can answer the question whether a considered material model is causal or not. For this purpose, a set of various distributional theorems presented in literature is collected as the distributional version of the Titchmarsh theorem, allowing for evaluation of causality in complicated electromagnetic systems. Furthermore, we correct the existing material models with the use of distribution theory in order to obtain their causal formulations. In addition to the well-known Kramers–Krönig (K–K) relations, we overview four further methods which can be used to assess causality of given dispersion relations, when calculations of integrals involved in the K–K relations are challenging or even impossible. Depending on the given problem, optimal approaches allowing us to prove either the causality or lack thereof are pointed out. These methodologies should be useful for scientists and engineers analyzing causality problems in electrodynamics and optics, particularly with regard to photonic materials, when the involved mathematical distributions have to be invoked.

In this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality of the system is investigated; its output is an electromagnetic signal propagating in media described by the time-domain two-sided fractional derivative. It is demonstrated that, for the derivative order in the range [1,+∞), the transfer function describing attenuated signal propagation is not causal for any value of the asymmetry parameter of the derivative. On the other hand, it is shown that, for derivative orders in the range (0,1), the transfer function is causal if and only if the asymmetry parameter is equal to certain specific values corresponding to the left-sided Grünwald–Letnikov derivative. The results are illustrated by numerical simulations and analyses. Some comments on the Kramers–Krönig relations for logarithm of the transfer function are presented as well.

In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function $\varphi$ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval $[a,b]\subset\mathbb{R}$ the Leray–Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some approximation techniques, we prove that there exist at least two such branches.