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We study the Borsuk-Ulam theorem for triple (M;\tau; \R^n), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution \tau. The largest value of n for which the Borsuk-Ulam theorem holds is called the Z_2-index and in our case it takes value 1, 2 or 3. We fully discuss this index according to cohomological operations applied on the characteristic class x \in H^1(N; Z_2), where N = M/\tau is the orbit space. In oriented case, we obtain an expression of the index from the linking matrix of a surgery presentation of the orbit space. We illustrate our results with examples, including a non orientable one.

Accurate delay models are important for static and dynamic timing analysis of digital circuits, and mandatory for formal verification. However, F\"ugger et al. [IEEE TC 2016] proved that pure and inertial delays, which are employed for dynamic timing analysis in state-of-the-art tools like ModelSim, NC-Sim and VCS, do not yield faithful digital circuit models. Involution delays, which are based on delay functions that are mathematical involutions depending on the previous-output-to-input time offset, were introduced by F\"ugger et al. [DATE'15] as a faithful alternative (that can easily be used with existing tools). Although involution delays were shown to predict real signal traces reasonably accurately, any model with a deterministic delay function is naturally limited in its modeling power. In this paper, we thus extend the involution model, by adding non-deterministic delay variations (random or even adversarial), and prove analytically that faithfulness is not impaired by this generalization. Albeit the amount of non-determinism must be considerably restricted to ensure this property, the result is surprising: the involution model differs from non-faithful models mainly in handling fast glitch trains, where small delay shifts have large effects. This originally suggested that adding even small variations should break the faithfulness of the model, which turned out not to be the case. Moreover, the results of our simulations also confirm that this generalized involution model has larger modeling power and, hence, applicability., Comment: 9 pages, 9 figures, extended version of a paper which was accepted at DATE'18

The linearization coefficient $\mathcal{L}(L_{n_1}(x)\dots L_{n_k}(x))$ of classical Laguerre polynomials $L_n(x)$ is known to be equal to the number of $(n_1,\dots,n_k)$-derangements, which are permutations with a certain condition. Kasraoui, Stanton and Zeng found a $q$-analog of this result using $q$-Laguerre polynomials with two parameters $q$ and $y$. Their formula expresses the linearization coefficient of $q$-Laguerre polynomials as the generating function for $(n_1,\dots,n_k)$-derangements with two statistics counting weak excedances and crossings. In this paper their result is proved by constructing a sign-reversing involution on marked perfect matchings., Comment: 16 pages, 8 figures, comments welcome!

We prove that every not necessarily bounded poset P=(P,\le,') with an antitone involution can be extended to a residuated poset E(P)=(E(P),\le,\odot,\rightarrow,1) where x'=x\rightarrow0 for all x\in P. If P is a lattice with an antitone involution then E(P) is a lattice, too. We show that a poset can be extended to a residuated poset by means of a finite chain and that a Boolean algebra (B,\vee,\wedge,',p,q) can be extended to a residuated lattice (Q,\vee,\wedge,\odot,\rightarrow,1) by means of a finite chain in such a way that x\odot y=x\wedge y and x\rightarrow y=x'\vee y for all x,y\in B.

Girard Desargues (1591–1661) is one of the most intriguing figures in the history of mathematics. He wrote a profound and bold booklet on conic sections, in 1639, which might have created projective geometry nearly two centuries before its actual birth. That work was Brouillon project d’une atteinte aux evenements des rencontres d’un cone avec un plan, or A Sketch of a Study of Sections of a Cone by a Plane. Except the work was lost until La Hire’s transcription was found about 1845. Even so, Poncelet knew about involution, an invention of Desargues, when he wrote his 1822 Traite; the Brouillon project had disappeared but letters written in the vitriolic controversary about the work had survived.

The progress made in dentistry during the latest decades is due, conceptually, to the new, systemic vision of man, which has also taken place in this field of medicine. In this context, the link between organic and psychic is indestructible. Thus illness is understood as a drama in which the somatic process has a psychic value, and the mental one has a body value. It is known that the morphological and functional integrity of the dental system, health and vigorousness, gives the individual a state of well-being that affects his somatic and psychic health, as any disturbance at this level entails repercussions in psychological and social behavior. Such a disruption is the total edification that seriously alters not only the dental system but the whole organism, putting various biological and psychosocial problems to the practitioner. The total expression represents not only a physical disability but also a psychological one. A special importance in studying psychological changes at total edentulous presents the psychological aspects of senile involution. This is not only a theoretical but also a practical importance due to the increase in the number of elderly people. Through the researches of the present paper we intend to present the reality of the psychological manifestations in the total edentation, which is objectified on different methods of psychodiagnosis in the first part, in order for the second part to be addressed to problems of prosthetic psychotherapy.The study comprises a group of 43 patients, of whom 24 were men and 19 women with total uni or bimaxilar edentation. Total edentation can be and is responsible for somatopsychic alterations, along with other pathogens, general, local, social, which sometimes can take a dramatic form, converting, where the area is also favorable, a pure somatic disease, for those who are not in psychopathy or even psychosis, although these latter cases are extremely rare and especially in youngsters, which would disrupt not only the person�s behavior as an individual, but also their status, function and social integrity. The treatment of dental and psychological complex is mandatory for any patient, but especially for the elderly, where recovery is more difficult, with disease-specific disorders adding to those of senescence.

This article is not going to limit itself to presenting the traditional dualist view of good versus bad (the good is represented by average citizens manipulated by the bad, which is the capitalist media-driven society). Such views have their origin point in the Marxist or neo-Marxist school of thought, which was strictly adhered to by the (first generation) of the Frankfurt School, and it is known as critical thinking. This research supports the fundamentals of critical thinking, but additionally argues that “critical thinking” exists also to criticize itself, to overcome it, and to enter into what we call “Complex Structural Approach” (CSA). The Power is, to a large extent, the market in evolution and involution and acts today through the marginalization of universal historical memory and philosophy, among other knowledge, and is replaced by infoxication. The western citizen is not completely unaware of its dependency. The virtual-intelligent society of the 21th century connects with one of the innate characteristics of the individual: his selfishness, whether it is positive or destructive behavior, in various formats and in varying degrees.

We introduce and study affine analogues of the fixed-point-free (FPF) involution Stanley symmetric functions of Hamaker, Marberg, and Pawlowski. Our methods use the theory of quasiparabolic sets introduced by Rains and Vazirani, and we prove that the subset of FPF-involutions is a quasiparabolic set for the affine symmetric group under conjugation. Using properties of quasiparabolic sets, we prove a transition formula for the affine FPF involution Stanley symmetric functions, analogous to Lascoux and Sch\"utzenberger's transition formula for Schubert polynomials. Our results suggest several conjectures and open problems., Comment: 23 pages

Let R be a ∗−prime ring with characteristic not 2, U a nonzero ∗− (σ,τ)−Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and ∗ commutes with σ, τ, d. In the present paper it is shown that if d(U) ⊆ Z or d2(U) ⊆ Z, then U ⊆ Z.

We study KT-fields and sharply triply transitive groups with a finite or perfect involution stabilizing at least one point.

We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of$\text{K3}^{[3]}$type by a birational involution, thereby computing its Hodge numbers.

This article proposes the concept of ‘involution’ as a perspective to understand the socioeconomic dynamics of the domestic business practices within the Japanese animation (anime) sector in relation to its overseas performance. There is a counterintuitive gap between the prevalent assumption that anime is globally popular and its weak overseas performance. Leaving the detail of anime's business aspects relatively unexamined, the literature on anime has particularly failed to address the ‘inward-looking’ feature of the business of the Japanese anime sector. Based on long-term fieldwork of the business players in the Japanese anime sector in Tokyo, this article suggests ‘involution’ as a key concept to fill this void. This concept, developed by anthropologist Clifford Geertz, refers to the process by which a group develops internally by sticking to existing modes of operation rather than by opening up to the outer world. This article depicts how we might understand the socioeconomic dynamics of the Japanese anime sector's mainstream domestic market centrist mode of operation in the context of involution. It also explores how the concept could catalyse us to envision the alternative future of anime, other than assuming anime's global popularity: the involuting Japanese anime sector might be allowing Euro-American and Chinese internet conglomerates to intervene and take over, turning the Japanese anime sector into one of their subcontractors from which they can exploit the sector's creativity.

This paper begins with crucial inquiries about the process of Indonesian civilization growth: Why is the Indonesian self-identity different from those of its neighboring nations? Is there anything amiss in its process of self-making? How exactly did this nation come into being in relation with the roles of the actors involved in that process? The questions above will be responded with hypothetical answers through a historical review of the social and political behavior of the Indonesian society since its independence. Indonesia’s self-making process will be reviewed back from the period of its independence to see how its civilization grew in comparison to other nations around it. Is it true that the revolution of independence had disjointed this nation’s civilization growth process, or is there any other cause? In comparison with those of its neighboring nations, the Indonesia’s civilization growth is ratherinvolutive than evaluative, and this may not change at least for the foreseeable future. This paper aims to analyze it in a hypothetical review. The implication of this paper is the suggestion for Indonesian nation to be alert of the potential continuation of conflicts that may perpetuate the involution process, which can hamper Indonesia’s civilization growth.

This essay traces the evolution of children's geographies as a concept through three phases. First, in the early 1970s as a beginning impression influenced heavily by developmental and environmental psychology. Second, beginning around 1990, children's geographies cohered politically as geographers focused on young people's identity through feminism and Marxism, and global policy initiatives on children's rights. The third phase, covering the last couple of decades, coming from issues of political identity, challenges what we think we know about young people and their geographies, and also advocates a set of loose theories about the ways young people create and re-create spaces and themselves. Cognate disciplines coming to geography for insights about children and their worlds characterize this current phase. To offset this seeming linear progression the essay also notes an involution of the concept that defies clear categories and sequences, but suggests the fluidity of tensions and accommodations that comprises children's geographies. This article is protected by copyright. All rights reserved.

For a closure operation c and an involution i defined on a language family M , we define N c , i M ( L ) as the number of distinct languages which can be obtained from a language L by repeated applications of c and i. The orbit O M ( c , i ) of c and i is defined as the set of all these numbers. We show that for the families of all languages and all regular languages over some alphabet and some classical closure operators c on languages, there are involutions i such that the orbit O M ( c , i ) contains arbitrary large numbers or contains infinity (which is in contrast to Kuratowski's complement-closure theorem). Moreover, we show that it is undecidable whether infinity occurs in the orbit.

We propose a new type of group game, the involution game. The group resources are fixed, and individuals compete for the fixed resources by effort. We assume binary strategies: more effort and less effort. More effort means paying more cost to occupy more resources than less effort does. If everyone adopts more effort, they will acquire the same amount of resources as if everyone adopts less effort, but each pays a meaningless extra cost, that is, the involution. We use the method of replicator dynamics in an infinite well-mixed population to investigate the model. The results show that more abundant resources promote involution, and an increase in the relative utility of more effort also aggravates involution. Increasing the cost of more effort may aggravate involution in some parameter ranges, but it ultimately leads to a disincentive to involution. This new type of game may contain considerable potential to explore.

In [WW1] and [WW2], the author constructed the complex associated to 1-regular functions. This complex is the equivalent of Dolbeault's complex for holomorphic functions if we replace the Cauchy-Riemann equations by the Cauchy-Fueter equations. In this paper, using the Cartan theory of linear Pfaffian system, we give a direct construction for the Cauchy-Fueter complex, at least in $\R^8$. Moreover, we give a sufficient condition in terms of Cartan's theory, to ensure that a complex associated to a linear PDE system with constant coefficients of order one, contains only operators of order one. In fact, the Cauchy-Fueter equation in $\R^8$ is an illuminating example for which this condition is not satisfied, Comment: Preliminary version. Comments are welcome

In this paper, we consider the pseudo-conjugation and its variations on the sets of partitions with restricted cranks and involutions on Frobenius symbols. We give several partition identities revealing relations between the number of equivalence classes in the set of partitions arising from an involution and the number of partitions satisfying a certain parity condition.

In this paper we deal with the problems of the eigenfunction expansions related to the differential operators with involution. The mean value formula for the eigenfunction is obtained with application of the transformation methods of the operators in the symmetric regions. The obtained formula is applied to estimate the eigenfunctions of the given differential operator in the ball. For domains with smooth boundary, the solution to these differential operator problems involves eigenfunction expansions associated with biharmonic-type operator with Navier boundary conditions.

Mixed partial differential equation of parabolic type with involution is considered. The sufficient conditions of the existence and uniqueness of the solution for the parabolic type equations with involution is obtained. The Fourier method is used to find a classical solution of the mixed problem for the transformed parabolic type equation with involution.

This paper explains that a symmetrical element on a ring having a Moore Penrose general inverse is commutative with a Generalized Moore Penrose inverse. This is due to the properties of the involution in the ring. By using these results and the main properties of Generalized Moore Penrose invers obtained directly from definition Generalized Moore Penrose invers, several theorems that discuss the necessary and sufficient of an element in a ring that has Generalized Moore Penrose invers and also symmetric had been found.

We read with interest the recent article from Kensler and colleagues ([1][1]), “Automated measures of terminal duct lobular unit involution and breast cancer risk.” This article represents an important first effort to use computational quantitative methods to assess age-related involution of

Old age, like any other age, is a cultural and historical phenomenon. In the culture and mass consciousness the viewpoint about elderly and old age as the period of involution is still prevalent. At the same time, there has been a change in attitude toward this age. Many authors emphasize the perspective of using the potential of older people in society, the value of continued employment to maintain social and intellectual activity in old age. This is possible only if a person realized the need for continuous creation of themselves and their living conditions. Currently, the ending of the life of modern people has moved from 60 to 80 years. Thus, after retirement, the person has a chance to live around 20 years of valuable productive life. This means that contemporary people’s life path has a completely new period, which did not exist before. At that time, when the previous life attitudes were realized, the person opens up new possibilities of self-development in other areas. People on their life become able to realize the potential of self-development and to resist the pressure of adverse cultural forces. At any age the opinion about people’s abilities has a significant impact on the life eÿciency and quality. Conscious and productive change in the trajectory of person’s own life path not only questioned the idea of the inevitability of negative changes in the quality of life in old age, but also "removes" the problems of this age, as constant depression, deficiency and weakness.

The article is oriented on explanation of the theoretical framework of the transition theory. The origin of this theory, terminology development and approaches how to adapt to it in practice are presented. Three basic approaches are developed in research and practice: a) a drop-out phenomenon between stages, b) a stage of involution and dual career, c) a long-term talent development. The acceptance of biodromal and holistic approach are stressed which means that the principles of sports training should be accompanied with the perception of importance of a social environment (parents, coaches, peers, sports club policy). A classic model of the theory consists of four developmental stages with typical markers in each stage (from early childhood up to the period of involution). The theory can be applied in both recreational participation in one’s daily life-span development, and in the sports talent development and professional sports career including the stage of involution.

Every residuated lattice can be considered as an idempotent semiring. Conversely, if an idempotent semiring is finite, then it can be organized into a residuated lattice. Unfortunately, this does not hold in general. We show that if an idempotent semiring is equipped with an involution which satisfies certain conditions, then it can be organized into a residuated lattice satisfying the double negation law. Also conversely, every residuated lattice satisfying the double negation law can be considered as an idempotent semiring with an involution satisfying the mentioned conditions.

This article analyses the democratic involution in Hungary, which was followed by the country embracing a pro-Russian policy in 2010. These processes came to be viewed as a rare case of authoritari...

It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski’s other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski’s axiom system.

We often hear about hybrid wars, using this artificial and not commonly used construct in the tactics of mutual deterrence of the East and the West, Russia, and the United States. I am surprised by...

Known projective transformations, namely their private types such as harmonism and involution are considered. It is known that projective transformations are collinear, at their performance the order, the cross ratio of fours of elements (on a straight line — the cross ratio of four points, in a bunch of straight lines — the cross ratio of this bunch’s four straight lines, this property (invariant) is similarly preserved for a bunch of planes, i.e. in considering of first step forms) is preserved. At a constructive approach to such transformations there are some ways for definition of position for corresponding elements which students use when studying discipline "Affine and projective geometry" on preparation profiles 09.03.01 — “CAD Systems" and 09.03.03 — “Applied Informatics in Design”. The received constructions are checked by analytical calculations, proceeding from known dependences for harmonism and involutions. In such a case results both for a range of points, and for a bunch of straight lines which pass through these points are analytically compared. The provided computational and graphic work contains three sections: prospects, harmonism and involution, and is carried out by students on individual options with application of the graphic editor Microsoft Visio or the graphic package CO MPAS voluntary. In the present paper some constructions in definition of corresponding points in elliptic and hyperbolic involution are considered, some of these constructions are published for the first time. Besides, a proposition has been formulated: in a rectangular coordinate system the work for coordinates of two points related to a circle intersection with one coordinate axis is equal to the product for coordinates of two other points related to this circle intersection with the other coordinate axis. This proposition is fairly for imaginary points of circle intersection with coordinate axes as well.

In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes either anisotropic or metabolic over all extensions of the ground field. A similar result is obtained for the case where this algebra with involution is Brauer-equivalent to a quaternion algebra and it becomes adjoint to a bilinear Pfister form over all splitting fields of the algebra.

Debbora Battaglia’s essay opens portals to entire worlds that turn around plants, sites in which people and their attendant techniques, technologies, and magic get caught in the spiralling whorl of...

For a long time, Gilbert Simondon’s work was known only as either a philosophy restricted to the problem of technology or as an inspirational source for Gilles Deleuze’s philosophy of difference. As Simondon’s thinking is now finally in the process of being recognized in its own right as one of the most original philosophies of the twentieth century, this also entails that some critical work needs to be done to disentangle it from an all too hasty identification with (or even subsumption under) Deleuzian categories. While both Simondon and Deleuze have made crucial contributions towards a theory of differential individuation that significantly diverges from other authors associated with French poststructuralism insofar as they insist on the dynamic and vital dimension of difference, they also differ on crucial points. Whereas Simondon sees the process of becoming as transductive amplification, Deleuze theorizes it as intensifying involution, leading to two notably distinct concepts of difference.

A class of finite-dimensional Hopf algebras which generalise the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a pair in involution, that is, to not have a group-like and a character implementing the square of the antipode. As a consequence we prove the existence of an infinite set of examples of finite-dimensional Hopf algebras without such pairs. This has implications for the theory of anti-Yetter-Drinfeld modules as well as biduality of representations of Hopf algebras. This article has been accepted for publication in Communications in Algebra, published by Taylor & Francis., 15 pages

International audience; We introduce the prototype of a digital timing simulation and power analysis tool for integrated circuit (Involution Tool) which employs the involution delay model introduced by Függer et al. at DATE'15. Unlike the pure and inertial delay models typically used in digital timing analysis tools, the involu-tion model faithfully captures pulse propagation. The presented tool is able to quantify for the first time the accuracy of the latter by facilitating comparisons of its timing and power predictions with both SPICE-generated results and results achieved by standard timing analysis tools. It is easily customizable, both w.r.t. different instances of the involution model and different circuits, and supports automatic test case generation, including parameter sweeping. We demonstrate its capabilities by providing timing and power analysis results for three circuits in varying technologies: an inverter tree, the clock tree of an open-source processor, and a combinational circuit that involves multi-input NAND gates. It turns out that the timing and power predictions of two natural types of involution models are significantly better than the predictions obtained by standard digital simulations for the inverter tree and the clock tree. For the NAND circuit, the performance is comparable but not significantly better. Our simulations thus confirm the benefits of the involution model, but also demonstrate shortcomings for multi-input gates.

This introductory chapter was prepared to place Buck’s Land Utilization in China study within a broader economic framework. The chapter provides an overview of the peasant economy and the conditions prevalent at the time. It explores the notion of “involution” and frames the economic issues in 1930s agriculture in the context of low- and high-level equilibrium poverty traps.

This paper addresses the changes in Brazil’s agrarian pact during to the post-neoliberal period established in 2003 and intensified after the controversial impeachment process of the president in 2016. Basing on the analysis of agricultural data, legislation, and governmental acts, this paper shows that, in the name of legal security claiming to foster agriculture and development in general, a considerable involution is being imposed to the protection of social well-being; such an involution involves territorial liabilities of the policy that induces land grabbing

We study the maximal amount of energy that can be extracted from a finite quantum system by means of projective measurements. For this quantity we coin the expression "metrotropy" $\mathcal{M}$, in analogy with "ergotropy" $\mathcal{W}$, which is the maximal amount of energy that can be extracted by means of unitary operations. The study is restricted to the case when the system is initially in a stationary state, and therefore the ergotropy is achieved by means of a permutation of the energy eigenstates. We show that i) the metrotropy is achieved by means of an even combination of the identity and an involution permutation; ii) it is $\mathcal{M}\leq\mathcal{W}/2$, with the bound being saturated when the permutation that achieves the ergotropy is an involution., Comment: 12 pages, 3 figures. Contribution to the special issue of JSTAT "New Trends in Nonequilibrium Statistical Mechanics: Classical and Quantum Systems - nesmcq18". v2 = published version

For every $n\geq 1$, we calculate the Hochschild homology of the quantum monoids $M_q(n)$, and the quantum groups $GL_q(n)$ and $SL_q(n)$ with coefficients in a 1-dimensional module coming from a modular pair in involution., Comment: 16 pages, 3 figures