Isomorphic and isometric structure of the optimal domains for Hardy-type operators

We investigate structure of the optimal domains for the Hardy-type operators including, for example, the classical Ces\`aro, Copson and Volterra operators as well as for some of their generalizations. We prove that, in some sense, the abstract Ces\`aro and Copson function spaces are closely related to the space $L^1$, namely, they contain "in the middle" a complemented copy of $L^1[0,1]$, asymptotically isometric copy of $\ell^1$ and also can be renormed to contain an isometric copy of $L^1[0,1]$. Moreover, the generalized Tandori function spaces are quite similar to $L^\infty$ because they contain an isometric copy of $\ell^\infty$ and can be renormed to contain an isometric copy of $L^\infty[0,1]$. Several applications to the metric fixed point theory will be given. Next, we prove that the Ces\`aro construction $X \mapsto CX$ does not commutate with the truncation operation of the measure space support. We also study whether a given property transfers between a Banach function space $X$ and the space $TX$, where $T$ is the Ces\`aro or the Copson operator. In particular, we find a large class of properties which do not lift from $TX$ into $X$ and prove that the abstract Ces\`aro and Copson function spaces are never reflexive, are not isomorphic to a dual space and do not have the Radon--Nikodym property in general.Comment: 34 pages; we changed the title and added some corrections compared to the first versio

Conformational degrees of freedom and stability of splay-bend ordering in the limit of a very strong planar anchoring

We study the self-organization of flexible planar trimer particles on a structureless surface. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of (quasi-)liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend ($S_{SB}$) and chiral smectic A ($S_A^*$) phases. The $S_{SB}$ phase is also stable in the limit, where only cis-conformers are allowed. The second phase occupying a considerable portion of the phase diagram is $S_A^*$ with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis-conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the $S_A^*$ phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay bend ($N_{SB}$) phase for trimers, the free energy of the $N_{SB}$ and $S_{SB}$ phases is calculated within DFT for the cis-conformers, for densities where simulations show stable $S_{SB}$. It turns out that the $N_{SB}$ phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of $S_{SB}$, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition

Sphinx: Monte Carlo Program for Polarised Nucleon-Nucleon Collisions

This program can be used to simulate polarised nucleon - nucleon collisions at high energies. Spins of colliding particles are taken into account. The program allows to calculate cross sections for various processes.Comment: 33pp, LaTe

Phenomenology of diphoton photoproduction at next-to-leading order

We develop the analysis of diphoton exclusive photoproduction in the kinematics where a collinear QCD factorization framework applies, namely nearly forward large invariant mass diphoton production. We work at the leading twist level and at the next-to-leading order (NLO) in the strong coupling constant $\alpha_S$. We compare our predictions for cross-sections with Born order calculations for the experimental conditions accessible to JLab experiments and show the interesting sensitivity of our results to various models of generalized parton distributions (GPDs). The NLO corrections are rather large and negative but do not prevent the studied reaction from being a promising tool for the extraction of C-dd GPDs, which do not contribute to either spacelike or timelike deeply virtual Compton scattering amplitudes

Creating reliable and resilient logistics organizations for unpredictable conditions and unexpected future

PURPOSE: The objective of this paper is to develop a general concept for creating resilient logistics organizations under the deep uncertainty that arises from unpredictable conditions and unexpected future, and to integrate it with a framework for ensuring the reliable operation of these organizations under conditions of predictable change.DESIGN/METHODOLOGY/APPROACH: The research methodology was based on a transdisciplinary approach because logistics organizations have the nature of complex systems with different types of systems such as physical, cybernetic and social ones. The research approach used is based on a critical analysis of the literature and case studies from the authors' own experience. The research is supported by Ackoff's 'idealized design' approach and assumptions from The IRGC Risk Governance Framework.FINDINGS: It was found that complex logistics organizations can be successfully modelled as Engineered System of Systems and managed according to the principles applicable to such systems. Furthermore, it was shown that it is possible to combine two different concepts, namely High Reliability Organization and Resilient Enterprise, into one coherent whole in the form of a Reliable and Resilient Logistics Organization.PRACTICAL IMPLICATIONS: For practical use of the developed concept, a framework was designed in the form of an algorithm describing the process of creating Reliable and Resilient Logistics Organization in the form of successive stages of action and decisions.ORIGINALITY/VALUE: The concept of the Reliable and Resilient Logistics Organization is wholly original and is the result of many years of our research into the behavior of complex sociotechnical systems under uncertainty. The added value of the work is the model developed, which in the form of a framework can be used in practice in logistics organizations to ensure their continuous and effective operation under various conditions, both predictable and unpredictable changes in the environment.The project is funded under the program of the Minister of Science and Higher Education titled “Regional Initiative of Excellence” in 2019-2022, project number 018/RID/2018/19, the amount of funding PLN 10 788 423,16.peer-reviewe

Collectivist logic in comparative genocide studies and in the battles for memory

The article aims to present the mechanisms of collectivist logic as it functions in three areas: (1) in the historical comparative analysis of genocides – the basic method of genocide studies; (2) in the activities of the organizations of victims and survivors, as well as in actions undertaken by animal rights activists; (3) in nationalist discourses and in the politics of memory. Collectivist logic is a set of operations that address human communities – groups of individuals linked together by significant social bonds and interests, and perceived as culturally distinctive – as the subject of history. As a result of the application of such logic, we may think about collective guilt and collective merit. The article discusses the advantages and disadvantages of historical comparative analysis as an essential methodological tool of genocide studies. The argument further focuses upon the use of the symbolic capital attributed to the term “genocide” in studies involving analyses comparing other crimes – as well as the industrial exploitation of animals – to genocides. Finally, the author describes the relationship between the state policy of memory, nationalist discourses, and the academic integrity of genocide scholars