Coupled fractional differential systems with random effects in Banach spaces

The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

Bi-interior Ideal Elements in ∧e-semigroups

All the results on semigroups obtained using only sets, can be written in an abstract form in a more general setting. Let us consider a recent paper to justify what we say. The bi-interior ideals of semigroups introduced and studied by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. in 2018, follow for more general statements about ordered semigroups. The same holds for every result of this sort on semigroups based on right (left) ideals, bi-ideals, quasi-ideals, interior ideals etc. for which we use sets. As a result, we have an abstract formulation of the results on semigroups obtained by sets that is in the same spirit with the abstract formulation of general topology (the so-called topology without points) initiated by Koutsk ́y, Nöbeling and, even earlier, by Chittenden, Terasaka, Nakamura, Monteiro and Ribeiro. As a consequence, results on ordered Γ-hypersemigroups and on similar simpler structures can be obtained.

Decidability in robot manipulation planning

Consider the problem of planning collision-free motion of n objects movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of $$m \le n$$ m ≤ n objects simultaneously. This represents the abstract formulation of a general class of manipulation planning problems that are proven to be decidable in this paper. The tools used for proving decidability of this simplified manipulation planning problem are, in fact, general enough to handle the decidability problem for the wider class of systems characterized by a stratified configuration space. These include, e.g., problems of legged and multi-contact locomotion, bi-manual manipulation. In addition, the approach described does not restrict the dynamics of the manipulation system modeled.

Ograničenje predmeta postupka za raspravljanje zaostavštine pred sudom države članice – primena Cl. 12 EU uredbe o nasleđivanju

In the following paper we are dealing with certain application aspects regarding the article 12 of Regulation (EU) No 650/2012 of the European Parliament and of the Council of 4 July 2012 on jurisdiction, applicable law, recognition and enforcement of decisions and acceptance and enforcement of authentic instruments in matters of succession and on the creation of a European Certificate of Succession. The author’s primary concern is to analyze the justification of its constitution in principle, and then to deal with certain issues regarding the possibility of its effective application. Particular attention is paid to interpreting the conditions underlying the application of the article 12, whose abstract formulation can, in certain aspects, represent a problem for the the member state courts upon their decision not to administrate assets of the estate located in a third country. Moreover, there will be a word as regards to the influence that limitation of proceedings before member state courts has on realization of the principle of unity of succession established by the Succession Regulation, which will be followed by hypothetical example and a suggestion of a possible solution concerning scission of succession, one that would not disrupt the coordination with the third country legal orders.

Abstract Formulation of the Miura Transform

Miura transform is known as the transformation between Korweg de-Vries equation and modified Korweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed. This fact sheds light on the logarithmic type transformations as an origin of a certain kind of nonlinearity in the soliton equations. In this article, based on the logarithmic representation of operators in infinite-dimensional Banach spaces, a structure common to both Miura and Cole-Hopf transforms is discussed. In conclusion, the Miura transform is generalized as the transform in abstract Banach spaces, and it is applied to the higher order abstract evolution equations.

A channel-based perspective on conjugate priors

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions – say Gaussians – as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the ‘conjugate priors’ of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions and (3) an extension to multiple updates. The theory is illustrated with several standard examples.

An abstract formulation of a theorem of Sierpiński on the nonmeasurable sum of two measure zero sets

Here we give an abstract formulation (in uncountable commutative groups) of a classical theorem of Sierpiński on the nonmeasurability of the algebraic sum of measure zero sets.

Informational Structures and Informational Fields as a Prototype for the Description of Postulates of the Integrated Information Theory

Informational Structures (IS) and Informational Fields (IF) have been recently introduced to deal with a continuous dynamical systems-based approach to Integrated Information Theory (IIT). IS and IF contain all the geometrical and topological constraints in the phase space. This allows one to characterize all the past and future dynamical scenarios for a system in any particular state. In this paper, we develop further steps in this direction, describing a proper continuous framework for an abstract formulation, which could serve as a prototype of the IIT postulates.

Metanomianism and Religious Praxis in Martin Buber’s Hasidic Tales

It is well known that Martin Buber abandoned Jewish law as a binding code. Scholars have identified him accurately as a religious anarchist, and his perspective is best characterized as metanomian—that is, one that locates the essence of religiosity outside of any fixed system, without necessarily opposing that system as a matter of principle. And yet, such general characterizations offer only a very vague picture of Buber’s stance. This paper demonstrates that it is especially illustrative for us to turn to Buber’s Hasidic tales. First of all, precisely because Buber’s concept of practice was irreducible to any static system or code, the genre of narrative conveys far more than any abstract formulation can. Moreover, inasmuch as Buber’s Hasidic tales were his own hermeneutical refractions of earlier sources, which were in themselves teeming with images of practice, our intertextual investigations reveal at once narrative representations of religious life and Buber’s personal interpretations of those narratives. What emerges from this study, then, is a textured and vivid vision of religious practice, which was not merely a peripheral concern but a life-encompassing core of Buber’s thought.