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In chemical graph theory, various topological indices of the hexagonal lattices such as the energy, the numbers of perfect matchings and spanning trees, and so on, have been studied extensively. In this paper, we enumerate spanning trees with a perfect matching of the hexagonal lattices on the cylinder and Möbius strip. [ABSTRACT FROM AUTHOR]

Comparative analyses in education science have traditionally focused on the category of geographic location as the comparative unit. However, comparison may involve many other units of analysis, such as culture, politics, curricula, education systems, social phenomena, and other categories of the lives of societies. Still, categories are inseparably linked to one or several geographic locations. Comparative approaches are often also dictated by the availability heuristic. Studying geographic units as the foci of comparative research is a necessary step for comparative presentation of the topic. According to Bray and Thomas, a researcher must always seek preliminary insight in the geographic unit to be analyzed before making the comparison. In social science research, a unit of analysis relates to the main object of the research, as it answers the question of "who" or "what" is going to be analyzed. The most common units of analysis are people, groups, organizations, artifacts or phenomena, and social interactions. Ragin and Amoroso have noted that comparative methods can be used to explain the commonness or diversity of results. This paper shows how comparative research can be approached in ways that have not been discussed, grounded in the historically variable understanding of the very term "comparison." They are, for example, The Ogden-Richards triangle, The Porphyrian Tree, Classification strategies – Mill's Canons, The chaos of the world – the order of science, Weber's ideal types, Raymond Boudon's formula, and the Möbius strip in comparativism. [ABSTRACT FROM AUTHOR]

A new flexible bis(amidine) ligand featuring two additional N-donor groups incorporates a defined [CuIMesCu2I]2+ fragment from mesitylcopper into a triangular cluster with a reactive organometallic coordination site. Subtle changes to the reaction protocol result in the formation of an intertwined tetracuprous arrangement that adopts the shape of a Möbius strip. [ABSTRACT FROM AUTHOR]

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration into courses, reflection on ways to leverage the activity for discussion with students at the start of a course about the nature of mathematical inquiry and norms for learning through inquiry. [ABSTRACT FROM AUTHOR]

Molecules with a π-system that can be mapped onto a Möbius strip may display Möbius aromaticity. Such molecules are difficult to synthesize because they have a twisted structure. Recently, we combined chiral [6]helicene and fluorescent [7]cycloparaphenylene, and synthesized the first helicene para -phenylene ([6,7]HPP) carbon nanohoop. We have demonstrated that this design strategy ultimately provides a Möbius topology of the molecular π-electron system and, therefore, offers the potential to study Möbius aromaticity experimentally. In addition, the synthesized nanohoop exists as a mixture of conformers in solution. Some of the conformers possess a different orientability of their π-systems, i.e., they differ in their topology. As a result, the recorded circularly polarized luminescence of isolated enantiomers displays both left- and right-handedness of the emitted light, each emanating from a conformer with a different π-system topology. Therefore, [6,7]HPP provided the first experimental evidence of such topological bistability in carbon nanohoops. [ABSTRACT FROM AUTHOR]

The given text is a collection of three separate stories. The first story revolves around two men having a conversation in a restaurant about a failed marriage. The younger man hopes to reconcile with his ex-wife, but the older man, who is the brother of the ex-wife, supports his sister's decision to not see the younger man. The second story follows a man named Reuben and his deteriorating relationship with his companion, Andrei, on an island. Reuben discovers evidence that Andrei killed his wife and confronts him, resulting in a violent altercation. The third story is about Reuben's survival on the island and his eventual rescue. The stories are open-ended and leave room for interpretation. [Extracted from the article]

This study focuses on how admissions at selective colleges and universities represent key racialized organizations. We analyzed data from 50 individual interviews of admissions professionals, through a theory of racialized organizations to recognize admissions as practices that consistently reproduces systemic inequities. We reveal how organizational structures centering an array of institutional priorities can maintain the systemic reproduction of intersectional racial inequalities, by privileging priorities like budgetary constraints, geographic diversity, and other interests, minimizing racial diversity as a priority. Our study bears key implications for future research and practice, by demonstrating that much like a Möbius strip, admissions organizations are difficult to fundamentally change for diversity and equity goals. Even with seemingly dramatic alterations to practices (e.g. test-optional policies) in isolation, Möbius strips generally maintain their structure. Institutional priorities, especially fiscal priorities, maintain the durability in racially unequal admissions outcomes through logics of racial capitalism. Unless institutional priorities fundamentally change, admissions processes will likely continue to reproduce inequalities. Research and systemic change efforts in college admissions should go beyond focusing on isolated elements (e.g. test requirements) and approaches to admissions (e.g. percent plans) to confront admissions and enrollment management systems, by interrogating underlying institutional logics and routines. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Using tools from algebraic topology and algebraic geometry (fundamental polygons and blowups, respectively), we prove that cutting along the center of a Möbius strip yields a cylinder. [ABSTRACT FROM AUTHOR]

The article is a review of the film "Tár" directed by Todd Field. The film explores the theme of power within the context of the Berlin Philharmonic Orchestra, focusing on the character of Lydia Tár, played by Cate Blanchett. The review discusses how the film portrays the institutional, organizational, and psychological aspects of power, highlighting the dynamics of power within elite institutions and the effects of power on individuals. It also examines power from both a critical perspective, questioning the naturalness of managerial norms, and a clinical perspective, exploring the psychic mechanisms of power. The film raises thought-provoking questions about the nature and impact of power in organizations. [Extracted from the article]

The cell-cell signaling mechanisms that are the basis for all of physiology have been used to trace evolution back to the unicellular state, and beyond, to the "First Principles of Physiology". And since our physiology derives from the Cosmos based on Symbiogenesis, it has been hypothesized that the cell behaves like a functional Mobius Strip, having no 'inside or outside' cell membrane surface - it is continuous with the Cosmos, its history being codified from Quantum Entanglement to Newtonian Mechanics, affording the cell consciousness and unconsciousness/subconsciousness as a continuum for the first time. Similarly, Klein and Maimon have concluded that their 'Soft Logic' mathematics also constitutes a Mobius Strip, using both a real number axis, combined with a zero axis, numerically representing cognition. This is congruent with the cell as 'two-tiered' consciousness, the first tier being the real-time interface between the cell membrane and its environment; the second tier constituting integrated physiology, referencing the consciousness of the Cosmos. Thus, there is coherence between physiology, consciousness and mathematics for the first time. [ABSTRACT FROM AUTHOR]

This article discusses the relationship between Martin Heidegger's philosophy and Jewish thought. It explores how Jewish thinkers, such as Hannah Arendt, Hans Jonas, and Emmanuel Levinas, engaged with Heidegger's ideas in the context of the philosophical tradition of the time. The article also highlights the political implications of Heidegger's philosophy and his engagement with Nazism. The essays in this collection examine various aspects of this relationship, including affinities and differences between Heidegger and Judaism, and the potential for a nuanced understanding of both. Overall, the article provides a starting point for further exploration of this topic. [Extracted from the article]

Frances McDonald's book, "Posthumorism: The Modernist Affect of Laughter," challenges the premise of humor studies by exploring posthumorist laughter, which she argues lies outside the field. McDonald draws on affect studies to analyze various texts, including Nathanael West's "The Day of the Locust" and Hélène Cixous' "The Book of Promethea," to demonstrate how writers use language to make laughter a central focus. She also incorporates philosophical concepts from Gilles Deleuze and Félix Guattari to present posthumorist laughter as a disruptive force that goes beyond individual emotions and traditional notions of humor. While McDonald's book has been criticized for its totalizing rhetoric and overlooking the diversity of modernist art, it offers a thought-provoking critique of humor studies and opens up new possibilities for understanding laughter. [Extracted from the article]

We show that in Jackiw-Teitelboim (JT) gravity, late-time two-point functions can get a leading non-decaying contribution from a spacetime with the topology of a Möbius strip (a disk with one crosscap). There is an interesting interplay between this contribution and the standard "plateau". The two can add together or cancel, depending on topological weighting factors. We match this behavior to Random Matrix Theory (RMT) and the N mod 8 periodicity of Sachdev-Kitaev-Ye (SYK) results. [ABSTRACT FROM AUTHOR]

We extend the analysis of Misaligned Supersymmetry to orientifold vacua. The lack of modular invariance in the Klein bottle, annulus and Möbius strip amplitudes implies that the IR properties of the physical spectrum are related to the UV behaviour of closed strings freely propagating between D-branes and O-planes, and vice versa. We thus build sector averaged sums 〈d(n)〉 associated to both representations of each Riemann surface. We find that the 〈d(n)〉's associated to the loop channel control the coupling of closed-string tachyons to D-branes and/or O-planes, and therefore their vanishing is a necessary, but not sufficient, condition for stability in the closed sector. Similarly, the sector averaged sums associated to the tree-level amplitudes encode the presence of tachyons in the physical spectrum, and their vanishing is a sufficient, but not necessary, condition for classical stability. Using this technology, it is difficult, if not impossible, to formulate necessary and sufficient criteria for the absence of tachyons since, in orientifold vacua, they can be removed from the spectrum by the orientifold projection. Although in these cases one would naively expect a cancellation between 〈d(n)〉's associated to different amplitudes, this does not occur in practice. We provide several examples in ten and lower dimensions supporting our results. [ABSTRACT FROM AUTHOR]

Mobius strip is an infinite loop having one‐sided surface with no boundaries, also known as twisted cylinder. Möbius strips being widely used in different fields of engineering are of important nature in research. Being different in sizes and shapes, these can be visualized in Euclidean space but few cannot be. Topology of Mobius strips makes it a rare Euclidean representation of the infinite nature. Researchers expanded this concept and generalized it in the form of Klein bottles. In this article, we have derived various polynomials and respective topological indices for the Hexagonal Möbius graphs having each face as a hexagon. Also, inverse relationship between heat of formation and crystal size is developed for the calculated indices. [ABSTRACT FROM AUTHOR]

During combat activities, the consequences of contusive and traumatic injuries to the spine, which lead to myofascial pain, in particular in the neck area, are of great importance. Myofascial pain syndrome, localized in the muscles and fascia, can range from mild discomfort to excruciating pain. To optimize personal rehabilitation programs in health care practice, for additional visualization of educational and practical activities, it was suggested to consider the rehabilitation process as a "motor and mental dialogue" at the same time, and also to use a topological object - the Möbius strip as a visual, multi-vector, interdisciplinary, plastic model of rehabilitation. The paper focuses on the study of the effectiveness of using the ecological approach in rehabilitation practice. The research was conducted on the basis of the Municipal Enterprise "Poltava Regional Clinical Hospital for War Veterans" of Poltava Regional Council. 42 military servicemen - participants of combat activities with a diagnosis of the myofascial pain syndrome of the cervical area were included in the study. As a component of the ecological approach, an individually developed program of comprehensive rehabilitation intervention aimed at the biomechanically interconnected muscle spirals, the diaphragm and masticatory muscles, and the temporomandibular joint was used. The method of active rehabilitation in patients using a program of comprehensive rehabilitation intervention for biomechanically interconnected muscle spirals, diaphragm and masticatory muscles, and temporomandibular joint, was based on a course of training with a multidisciplinary rehabilitation team lasting 21 days - 3 - 5 sessions with the doctor every day and 6-8 sessions according to the video sample recorded by the doctor. A statistically significant decrease in the intensity of pain according to VAS and an increase in the angle of painless lateral movement with an element of rotation may indicate the effectiveness of rehabilitation measures already on the seventh day of treatment. A decrease in the intensity of pain and an increase in the angle of painless lateral movement with an element of rotation in the experimental group, as compared to the control group, may indicate the advantage of using the proposed program at the same time as standard approaches in rehabilitation. The model proposed in the study can act not only as a treatment and rehabilitation tool but also as a visual training tool for future specialists, which has several advantages over traditional models. In particular, it involves low cost and ease of implementation, and it should be noted that the comprehensive, at first glance, rehabilitation process is simplified due to mathematical logic, sequence, creativity, and game form.

The article discusses a unique experience at a shop called Imaginary Medical Solutions, where the protagonist encounters a variety of unusual and seemingly fictional medical devices. The shopkeeper presents items like a Universal Communicator, Narrative Arc, and Gestalt Spectrometer, each with peculiar functions. Despite the odd encounter, the protagonist ends up with an Automated Empathic Defibrillator, hinting at the shop's mysterious offerings. The narrative raises questions about reality and perception, leaving the reader intrigued about the potential of revisiting the shop for more unconventional solutions. [Extracted from the article]

The interesting properties of Mobius structure and boron-carbon-nitride (BCN) inspired this research to study different characteristics of Mobius BCN (MBCN) nanoribbon. The structural stability and vibrational, electrical and optical properties are analysed using the density functional theory. The gas-sensing ability of the modelled MBCN structure was also studied for methane, hydrogen sulfide, ammonia, phosgene and methanol gases. The negative adsorption energy and alteration of electronic bandgap verified that MBCN is very sensitive toward the selected gases. The complex structures showed a high absorption coefficient with strong chemical potential and 7 ps–0.3 ms recovery time. The negative change in entropy signifies that all the complex structures were thermodynamically stable. Among the selected gases, the MBCN showed the strongest interaction with methanol gas.

The enumerative problem of spanning trees of graphs is one of the fundamental problems in the field of graph theory, which has attracted the attention of mathematicians and physicists. For a connected graph G , let T be a spanning tree of G. In this paper, we call T to be a pm - t r e e of G if T contains a perfect matching. Recently, Li and Yan (Applied Mathematics and Computation, 456 (2023), 128125.) gave an explicit expression for the number of pm-trees in linear hexagonal chains on the plane, cylinder and Möbius strip, respectively. In this paper, we extend the results above and obtain the explicit formula for the number of pm-trees in linear polygonal chains with n polygons of 4 k + 2 vertices on the plane, cylinder and Möbius strip, respectively. [ABSTRACT FROM AUTHOR]

In this contribution, we explore the chiroptical properties of achiral PF6BT blended with three chiral polyfluorene derivatives using the same 1:9 chiral/achiral ratio. Circular dichroism spectroscopy (CD) revealed that the sergeants and soldiers principle was operating in annealed thin films, reaching a CD intensity of 1400 mdeg, signal unequivocally associated to the PF6BT backbone. Dissymmetry factor obtained in two blends were superior to that of pristine chiral polymers. Atomic force and confocal microscopies were employed to explore the morphological properties. Confocal analysis results showed that different types of chiral:achiral aggregations were evidenced in the blends. AFM height images revealed several self-assembled helical fibers and nanotoroids, and a rare supramolecular topological morphology, a Möbius strip. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents a conceptual overview of the main figures that Lacan borrowed in his approach to surface topology; the aim is to fathom the theoretical implications and the ontological consequences of these schemes regarding central psychoanalytic concepts such as subject, jouissance, object, fantasy, among others. It develops a logical sequence of iconic topological figures in Lacan, from the torus to the cross-cap, passing through the Möbius strip and the Klein bottle. It concludes with the cross-cap because it specifies the novel contribution of concepts re-articulated from these new tools. Theoretical terms such as subject and object, as well as their complex relationship, are clarified from a critical conception of dualism and by offering an alternative that surpasses the spheroid topologies. [ABSTRACT FROM AUTHOR]

Copyright of Enthymema is the property of Enthymema, International Journal of Literary Criticism, Literary Theory & Philosophy of Literature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The structure of the 9 vertex obstructive graphs for the nonorientable surface of the genus 2 is established by the method of (-transformations of the graphs. The problem of establishing the structural properties of 9 vertex obstruction graphs for the surface of the undirected genus 2 by the method of phi-transformation of graphs is considered. The article has an introduction and 5 sections. The introduction contains the main definitions, which are illustrated, to some extent, in Section 1, which provides several statements about their properties. Sections 2 – 4 investigate the structural properties of 9 vertex obstruction graphs for an undirected surface by presenting as a phi-image of several graphs homeomorphic to one of the Kuratovsky graphs and at least one planar or projective-planar graph. Section 5 contains a new version of the proof of the statement about the peculiarities of the minimal embeddings of finite graphs in nonorientable surfaces, namely, that, in contrast to oriented surfaces, cell boundaries do not contain repeated edges. Also in section 5 the other properties peculiar to embeddings of graphs to non-oriented surfaces and the main result are given. The main result is Theorem 1. Each obstruction graph H for a non-oriented surface N2 of genus 2 satisfies the following. 1. An arbitrary edge u,u = (a,b) is placed on the Mebius strip by some minimal embedding of the graph H in N3 and there exists a locally projective-planar subgraph K of the graph H \ u which satisfies the condition: (tK({a,b},N3)=1)and(tK\u({a,b},N2)=2), where tK({a,b},N) is the number of reachability of the set {a,b} on the nonorientable surface N. 2. There exists the smallest inclusion of many different subgraphs Ki of a 2-connected graph H homeomorphic to the graph K+e, where K is a locally planar subgraph of the graph H (at least K+e is homemorphic to K5 or K3,3), which covers the set of edges of the graph H.

If you cut a mobius strip in half, the edges form a Trefoil Knot, which can be untied to form a circle, proving it's a true mathematical knot. The cell is a homologue of the mathematical knot since it, too, must be able to unknot itself to form the egg and sperm meiotically in order to reproduce. The homology between a knot and a cell is thought-provoking biologically because the Trefoil Knot is a metaphor for the endoderm, ectoderm and mesoderm, the three germ layers of the gastrula that ultimately produce the embryo, beginning with the zygote. Upon further consideration, the cell membrane is like a mobius strip, forming one continuous surface between the inner environment of the cell and the outer environment. However, it is not formed by taking a circular surface, cutting it, twisting it and attaching the two ends as you would conventionally to form a mobius strip. Conversely, David Bohm's Explicate Order forms a boundary with the Implicate Order. That lipid boundary is the prima facie mobius strip that divides the infinite surface of the Implicate Order into inside and outside by 'recalling' its pre-adapted state as lipid molecules before there was an inside or outside. • The cell membrane separates the inside of the cell from the environment. • The cell membrane functions like a mobius strip. • The cell membrane was pre-adapted as lipid molecules before there was an inside or outside of the cell. • The cell membrane mobius strip 'remembers' when it did not exist, emerging from micelles. [ABSTRACT FROM AUTHOR]

Cyclothianthrenes, a series of sulphur‐embedded hydrocarbon belts proposed a decade ago, were successfully constructed through a stepwise bottom‐up synthesis. The belt [6]cyclothianthrene ([6]CT) is the smallest and most strained member of the family yet reported. Both [6]CT and [8]CT are the first examples of cyclothianthrene characterized by single crystal X‐ray diffraction. An unprecedented chiral belt [7]CT and a Möbius‐shaped [9]CT were also achieved via modular synthesis. Crystallographic and computational studies show that belts [6]CT‐[8]CT have prism‐like conformations with well‐defined tubular cavities which have potential for guest molecule inclusion. Cyclic voltammograms further revealed that these belts are redox‐active. The success of constructing sulphur‐embedded hydrocarbon belts, that is, cyclothianthrenes, greatly enriches the chemistry of heteroatom‐doped molecular belts and tubes. [ABSTRACT FROM AUTHOR]

This paper develops the Möbius strip as an 'ordering theory' (Sandberg and Alvesson, 2020) that brings CCT studies into dialogue with mainstream marketing approaches. The aim is to work toward a transdisciplinary understanding of market spatiality, a topic that has become increasingly important for theorists and practitioners (Warnaby and Medway, 2013; Castilhos et al., 2016; Chatzidakis et al., 2018). Building on psychosocial interpretations of the Möbius strip as a 'tactical' way of thinking, a range of insights and ideas are organized along a single strip of theorization. This paper maps a continuous plane of logic between the concepts of space, place, emplacement, spatiality, implacement, and displacement. The potential applications of the Möbius strip are then demonstrated by showing how the transdisciplinary topic of 'atmosphere' can be theorized from multiple perspectives. The paper concludes by exploring how the Möbius strip might also be employed in other areas of marketing theory and practice, potentially generating further transdisciplinary conversations between CCT and the marketing mainstream. [ABSTRACT FROM AUTHOR]

In this work, the electromagnetic response of a mathematically interesting shape—a Möbius strip—is presented, along with a ring resonator for comparison. Both resonators consist of a central lossy dielectric layer bounded by perfectly conducting layers. For the case of the Möbius strips, the computational results show that there are a family of half-integer wavelength modes within the dielectric layer. These additional modes result in increased absorption, and a corresponding reduction in the radar cross section. Interestingly, rotational scans show that these modes can be excited over a large angular range. This investigation gives an understanding of the electromagnetic response of these structures, paving the way for future experiments on Möbius strip resonators. [ABSTRACT FROM AUTHOR]

Examples illustrating the use of one of the simplest and remarkable geometric bodies of all, the Möbius strip (loop, tape) are considered. A survey of the most characteristic patented designs of working and auxiliary elements of equipment in the chemical, petrochemical, and related industries along with ways of using the properties of the Möbius strip in the fabrication and operation of equipment is presented. [ABSTRACT FROM AUTHOR]

We determine p-colorability of the paradromic rings. These rings arise by generalizing the experiment of bisecting a Möbius strip. Instead of joining the ends with a single half twist, use m half twists, and, rather than bisecting (n = 2), cut the strip into n sections. Replacing each thin strip with its midline results in the m, n paradromic link. Using the notion of p-colorability from knot theory, we determine, for each m and n, which primes p can be used to color the link. Amazingly, almost all admit 0, 1, or an infinite number of prime colorings! This is reminiscent of solutions sets in linear algebra. Indeed, the problem quickly turns into a study of the eigenvalues of a large, nearly diagonal matrix. [ABSTRACT FROM AUTHOR]

Climate change causing large seasonal fluctuations is likely to lead to an increase in the average threshold of the Allee effect as well as an increase in its seasonal variability. In this paper, we show that a seasonally synchronized predator-prey system can be strongly destabilized by these changes in the threshold of the Allee effect. The typical result first leads to two-year and multiyear cycles by the principle of period doubling on a folded Möbius strip, up to the emergence of a chaotic and hyper-chaotic attractor living close to the trivial equilibrium corresponding to the extinction of populations. Moreover, this instability of the ecosystem can be hidden for a long time and the transition to its basin of attraction can occur by external perturbation in a random and irreversible manner. We also reveal a double folding of the 1:1 synchronized cycle manifold inside the corresponding Arnold tongue and hysteresis similar to well-known Duffing oscillator. • Increase in level and fluctuation of Allee effect destabilize seasonally synchronized system. • Period doubling route to chaos on folded Möbius strip inside 1:1 Arnold tongue. • Local dynamics of a subsystem and global chaotic dynamics of a seasonally driven system connected. • Instability can stay long-time hidden and lead to extinction of populations. • 1:1 cycle manifold double folding inside Arnold tongue and hysteresis similar to Duffing oscillator. [ABSTRACT FROM AUTHOR]