Trivial Form Research Articles

Fiktion und juristische Begriffsbildung

Legal fictions are usually defined as consciously false assumptions. This definition is suitable for distinguishing fictions from presumptions, but it conceals some important nuances about the role of fictions in a legal system. For this reason, this paper proposes an alternative definition of legal fictions as discrepancies between different conceptual systems. In doing so, it makes it possible to focus not primarily on external fictions, which consist in a discrepancy between legal terminology and colloquial language, but rather on internal fictions, which consist in a discrepancy between two versions of a legal conceptual system. The juxtaposition of two versions of a legal conceptual system makes it clear that the addition of an internal fiction, as the most trivial form of representation for the result of an analogy, increases the distinctiveness of a system in an expedient way, but at the cost of a significant loss of perspicuity. As long as the internal fiction plays only a marginal role, it can provide a clever and elegant solution. But when it assumes a structural role, it is accompanied by too great a loss of perspicuity, and is therefore an indication that the system could profitably be restructured by explicitly adjusting the meaning of some of its key concepts.

Arnold’s potentials and quantum catastrophes II

In paper I (Znojil, 2020) it has been demonstrated that besides the well known use of the Arnold’s one-dimensional polynomial potentials V(k)(x)=xk+1+c1xk−1+… in the classical Thom’s catastrophe theory, some of these potentials (viz., the confining ones, with k=2N+1) could also play an analogous role of genuine benchmark models in quantum mechanics, especially in the dynamical regime in which N+1 valleys are separated by N barriers. For technical reasons, just the ground states in the spatially symmetric subset of V(k)(x)=V(k)(−x) have been considered. In the present paper II we will show that and how both of these constraints can be relaxed. Thus, even the knowledge of the trivial leading-order form of the excited states will be shown sufficient to provide a new, truly rich level-avoiding spectral pattern. Secondly, the fully general asymmetric-potential scenarios will be shown tractable perturbatively.

No Ward-Takahashi identity violation for Abelian tensorial group field theories with a closure constraint

This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic melonic just-renormalizable $[U(1){]}^{6}$ model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows us to close the hierarchical structure of the flow equations in the melonic sector. As a consequence, there are no additional constraints on the flow equations, and then we can focus on the existence of the physical Wilson-Fisher fixed-points in the symmetric phase.

Discrete linear canonical evolution

This work builds on an existing model of discrete canonical evolution and applies it to the case of a linear dynamical system, i.e., a finite-dimensional system with vector configuration space and linear equations of motion. The system is assumed to evolve in discrete time steps. The most distinctive feature of the model is that the equations of motion can be irregular. After an analysis of the arising constraints and the symplectic form, we introduce adjusted coordinates on the phase space, which uncover its internal structure and result in a trivial form of the Hamiltonian evolution map. For illustration, the formalism is applied to the example of a massless scalar field on a two-dimensional spacetime lattice.

„Wer befehlen soll, muß im Befehlen Seligkeit empfinden.“

Abstract On the whole, the question as to the historical possibility of entrepreneurship has not been posed. Entrepreneurship has since Schumpeter simply been assumed; translated into a kind of mechanics of leadership in modern management literature in which individual characteristics rescind behind the role expectations for managers. This is logical insofar as a theory of the entrepreneur can at best only exist in a trivial form, such as in the sense of a theory of right or wrong decisions, while the entrepreneur as an individual eludes a theoretical approach in categorical terms. So while these theoretical restrictions make a theory of the entrepreneur unattainable, typological statements can still be made about the historical phenomenon of “entrepreneurship and entrepreneurial behaviour”. This is the starting point of the following article. Characteristics, behavioural patterns and lifestyle details are extracted from entrepreneurial careers of undisputed relevance in German economic and business history between roughly 1850 and 1930: these are then brought together and generalised into an “ideal type” entrepreneur. It will become apparent that entrepreneurship is ultimately based on circumstances, preconditions and attributes which economic or decision theories can only insufficiently grasp: in fact, specific aspects of each individual personality – some of which only fully develop in the course of entrepreneurial practice – determine behaviour and these are themselves again very individual. In a certain sense, entrepreneurship represents a kind of “doer type”, a quality which calls for a whole breadth of influences which in turn cannot be deduced in economic terms.

Generically split octonion algebras and 𝔸1-homotopy theory

We study generically split octonion algebras over schemes using techniques of ${\mathbb A}^1$-homotopy theory. By combining affine representability results with techniques of obstruction theory, we establish classification results over smooth affine schemes of small dimension. In particular, for smooth affine schemes over algebraically closed fields, we show that generically split octonion algebras may be classified by characteristic classes including the second Chern class and another "mod $3$" invariant. We review Zorn's "vector matrix" construction of octonion algebras, generalized to rings by various authors, and show that generically split octonion algebras are always obtained from this construction over smooth affine schemes of low dimension. Finally, generalizing P. Gille's analysis of octonion algebras with trivial norm form, we observe that generically split octonion algebras with trivial associated spinor bundle are automatically split in low dimensions.

Local large deviations principle for occupation measures of the stochastic damped nonlinear wave equation

We consider the damped nonlinear wave (NLW) equation driven by a noise which is white in time and colored in space. Assuming that the noise is non-degenerate in all Fourier modes, we establish a large deviations principle (LDP) for the occupation measures of the trajectories. The lower bound in the LDP is of a local type, which is related to the weakly dissipative nature of the equation and is a novelty in the context of randomly forced PDE’s. The proof is based on an extension of methods developed in (Comm. Pure Appl. Math. 68 (12) (2015) 2108–2143) and (Large deviations and mixing for dissipative PDE’s with unbounded random kicks (2014) Preprint) in the case of kick forced dissipative PDE’s with parabolic regularization property such as, for example, the Navier–Stokes system and the complex Ginzburg–Landau equations. We also show that a high concentration towards the stationary measure is impossible, by proving that the rate function that governs the LDP cannot have the trivial form (i.e., vanish on the stationary measure and be infinite elsewhere).

Equilibrium forms of a liquid on the interior surface of a rotating cylinder and their stability

The problem of the viscous liquid, partially filling the cylindrical cavity of a finite length, which rotates with a constant angular velocity, is considered (the rimming flow) . It is assumed that the gravity force is absent. If the wetting angle is equal to π /2, equilibrium forms with cylindrical free surface exist (trivial forms of equilibrium). There exist values of the Weber number (bifurcation values) at which the nontrivial forms branch off from the trivial form of equilibrium. Graphics of the axisymmetric equilibrium forms of the liquid are constructed numerically. With the Weber number growth, the nontrivial forms increasingly deviate from the cylindrical equilibrium state. With a further increase in the values of the Weber number the topology of equilibrium forms changes, as the form contacts the cavity wall (when the liquid layer is thin) or its axis (when the liquid layer is thick).The stability of equilibrium states is investigated using Lagrange’s stability theorem and its converse. The cylindrical state is unstable when the values of the Weber numbers are less than the bifurcation value or slightly exceed the bifurcation value. The value of the Weber number, for which the trivial form of equilibrium becomes stable, is obtained. Nontrivial forms of equilibrium are unstable for all admissible values of the Weber number.

Interpretation miniatures

Most physicists do not have patience for reading long and obscure interpretation arguments and disputes. Hence, to attract attention of a wider physics community, in this paper various old and new aspects of quantum interpretations are explained in a concise and simple (almost trivial) form. About the “Copenhagen” interpretation, we note that there are several different versions of it and explain how to make sense of “local nonreality” interpretation. About the many-world interpretation (MWI), we explain that it is neither local nor nonlocal, that it cannot explain the Born rule, that it suffers from the preferred basis problem, and that quantum suicide cannot be used to test it. About the Bohmian interpretation, we explain that it is analogous to dark matter, use it to explain that there is no big difference between nonlocal correlation and nonlocal causation, and use some condensed-matter ideas to outline how nonrelativistic Bohmian theory could be a theory of everything. We also explain how different interpretations can be used to demystify the delayed choice experiment, to resolve the problem of time in quantum gravity, and to provide alternatives to quantum nonlocality. Finally, we explain why is life compatible with the second law.

Le lecteur comme copiste et naufragé. Une lecture presque romanesque des “Petits traités”

The reader of Pascal Quignard’s work is, we might say, robbed of the faculty of interpretation and reduced to the state of copyist, which is in fact the state that Pascal Quignard also attributes to the author, since it goes hand in hand with a certain desire for all-inclusiveness. This encyclopaedic aspect is boundless and embarks the reader on a sort of odyssey which leads to another figure the writer also associates with the reader, that of the shipwreck victim. Therefore, the act of reading is not related to the notions of invention or originality, although the question of origin repeatedly crops up. The act of reading is seen in its most trivial, sensorial and material form, as a gesture and posture of abandonment. In Petits traités, the “romantic” perspective is connected with the author’s fondness for the sordidissima.

NOVA COSMÓPOLIS: AS FRONTEIRAS COMO OBJETOS DE CONFLITO NO MUNDO CONTEMPORÂNEO

A globalização não suprimiu as fronteiras: ela as transforma, as desloca, as dissocia umas das outras. Algumas atividades econômicas, por exemplo, não têm o mesmo alcance das atividades políticas ou das comunicações. As fronteiras se multiplicam, se alargam e se tornam, assim, simultaneamente mais frágeis e incertas. O momento atual do processo de globalização nos traz duas questões referentes à possibilidade de viver em uma escala global. Por um lado, um número cada vez maior de fronteiras se transformam em muros, mais migrantes morrem em mares, desertos e montanhas ao tentar atravessar fronteiras fechadas. Por outro lado, a questão filosófica e política do cosmopolitismo volta à ordem do dia em um contexto diferente daquele do Iluminismo, mas que formula, concretamente, as mesmas perguntas. A partir de etnografias de “homens-fronteira” e “lugares-fronteira” (Borderlands), proporei pensarmos uma nova cosmópolis, considerada como um mundo em movimento que antecipa a forma banal e quotidiana do cosmopolitismo. Na esfera antropológica, trata-se de uma nova situação onde a cultura e a sociabilidade se definem em situações de fronteira que se tornam cada vez mais constantes.

Ordinary ethics and craft consumption: A Southern perspective

Geography has recently experienced something of an ‘ethical turn’, and much attention has been focused on consumption as a site of ethical practice. Studies of ethical consumption tend to focus on explicitly socially or environmentally responsible purchasing decisions, but a growing body of research on ‘ordinary ethics’, starting from the premise that most consumption has a moral dimension, has opened up the notion of what counts as ethical to include everyday habits, considerations and desires. There remains, however, relatively little appreciation of the ethical agency of consumers within the global South, and little consideration of how enactments of ordinary ethics within Southern contexts may deepen understandings of the practices and meanings of diverse forms of consumption. Addressing this gap, this paper explores accounts of producers and consumers of craft in informal trading spaces in Cape Town, a city that 20years after apartheid’s end remains deeply racially segregated and has seen numerous incidents of xenophobic violence. It is in this context that I unpack the ethical dimensions of a seemingly trivial form of consumption, arguing that sites of informal trade may provide spaces for the expression and enactment of care for the other. While not always entirely positive, these interactions reveal a complex moral landscape where shared identities and mutual recognition underpin mundane economic transactions. The paper concludes that ordinary ethics of care for the other go beyond explicit, rational responsibility, and that informal spaces of trade should be considered as key sites for the exploration of consumer ethics.

Admit or Reject? Preserve or Drop?

Server failures on the cloud introduce acute operational dilemmas as now the cloud management entity needs to handle existing task preservations in addition to new task admissions. These admission and preservation decisions have significant impact on the cloud performance and operational cost, as they impact future system decisions. Should a cloud manager prefer to use resources for new task admissions and increase the risk of dropping an already admitted task in the future? Or should he/she prefer to maintain resources for potential future task preservations at the expense of new task admissions? These dilemmas are even more critical in Distributed Cloud Computing (DCC) due to the small scale of the micro Cloud Computing Center (mCCC). In this paper we will address these questions through the use of Markov Decision Process (MDP) analysis. We will show that even though the problem appears to be rather complicated (as the two decision rules are coupled), our analysis reveals that it can be significantly simplified (as one of the rules is of a trivial form). These results enables us to compose a holistic framework for cloud computing task management.

«Dejarse caer para después poder quizá levantarse ...» o el tema mitológico del descenso a los infiernos en Rayuela de Julio Cortázar*

En la novela Rayuela, definida por Luis Harss (81978, 269) como «una obra terapéutica», el autor, Julio Cortázar, pone en la boca de Traveler, el amigo y el segundo yo del protagonista Horacio Oliveira, el consejo siguiente:Lo malo en vos – dijo Traveler – es que cualquier problema lo retrotraés a la infancia. Ya estoy harto de decirte que leas un poco a Jung, che (41: 391)1.

«Dejarse caer para después poder quizá levantarse ...» o el tema mitológico del descenso a los infiernos en Rayuela de Julio Cortázar*

En la novela Rayuela, definida por Luis Harss (81978, 269) como «una obra terapéutica», el autor, Julio Cortázar, pone en la boca de Traveler, el amigo y el segundo yo del protagonista Horacio Oliveira, el consejo siguiente:Lo malo en vos – dijo Traveler – es que cualquier problema lo retrotraés a la infancia. Ya estoy harto de decirte que leas un poco a Jung, che (41: 391)1.

Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’

Let (X t )0 ≤ t ≤ T be a one-dimensional stochastic process with independent and stationary increments, either in discrete or continuous time. In this paper we consider the problem of stopping the process (X t ) ‘as close as possible’ to its eventual supremum M T := sup0 ≤ t ≤ T X t , when the reward for stopping at time τ ≤ T is a nonincreasing convex function of M T - X τ. Under fairly general conditions on the process (X t ), it is shown that the optimal stopping time τ takes a trivial form: it is either optimal to stop at time 0 or at time T. For the case of a random walk, the rule τ ≡ T is optimal if the steps of the walk stochastically dominate their opposites, and the rule τ ≡ 0 is optimal if the reverse relationship holds. An analogous result is proved for Lévy processes with finite Lévy measure. The result is then extended to some processes with nonfinite Lévy measure, including stable processes, CGMY processes, and processes whose jump component is of finite variation.

Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’

Let (Xt)0 ≤ t ≤ T be a one-dimensional stochastic process with independent and stationary increments, either in discrete or continuous time. In this paper we consider the problem of stopping the process (Xt) ‘as close as possible’ to its eventual supremum MT := sup0 ≤ t ≤ TXt, when the reward for stopping at time τ ≤ T is a nonincreasing convex function of MT - Xτ. Under fairly general conditions on the process (Xt), it is shown that the optimal stopping time τ takes a trivial form: it is either optimal to stop at time 0 or at time T. For the case of a random walk, the rule τ ≡ T is optimal if the steps of the walk stochastically dominate their opposites, and the rule τ ≡ 0 is optimal if the reverse relationship holds. An analogous result is proved for Lévy processes with finite Lévy measure. The result is then extended to some processes with nonfinite Lévy measure, including stable processes, CGMY processes, and processes whose jump component is of finite variation.

Modified Regge calculus as an explanation of dark energy

Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein–de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance DL is related to graphical proper distance Dp by the equation , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through versus log z gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using Ho = 69.2 km s−1 Mpc, ΩM = 0.29 and ΩΛ = 0.71. The best fit EdS gives SSE = 2.68 using Ho = 60.9 km s−1 Mpc. The best-fit MORC gives SSE = 1.77 and Ho = 73.9 km s−1 Mpc using R = A−1 = 8.38 Gcy and m = 1.71 × 1052 kg, where R is the current graphical proper distance between nodes, A−1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating.

On BICM Receivers for TCM Transmission

Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is in fact the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are also presented. It is shown that the minimum distance of the code is not the relevant optimization criterion for BICM-T. Optimal convolutional codes for different constrain lengths are tabulated and asymptotic gains of about 2 dB are obtained. These gains are found to be the same as those obtained by Ungerboeck's one-dimensional trellis coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be asymptotically as good as 1D-TCM.

The Gnat, the Hammer, and the Cruise Ship

Hammer oerwhelms said gnat?then what? Everybody shrugs? Maybe some people titter, some people squirm, some people shop, some people cry foul, some people jam the phone lines calling home from Edmonton or Boston to see is Sister Maddie Cousin Trevor Uncle Bernie doing okay, while the usual suspects does hold rally, shout slogan, wear out vocal cords chanting: poor poor gnat, sledgehammers really ought to stop behaving this way. Counter-deplorers hoot Nuke the Gnat. Pierced by grandiloquent eloquence of power, TV viewers study rigor of the ham mer. Yes, from where we sit, the focus is all on Hammerism. As virile virtue, imperial perfidy, Blood and Guts and Hardware cunningly com mingled. An irrelevant few concern themselves briefly with the ant s pedi gree. As in: was that gnat an ant, in point of fact? A wasp? A bumblebee? How would we know, since our eyes were glued to the tool and we couldn't very well study the trivial insect form as it slid beneath the compass of the hammer s awesome shadow? (As it writhed within that compass.) What if it was a butterfly, what if it was a horsefly, what if it was a beetle? Silverfish, ladybug? Even congaree?1 What difference would that make? (Congaree you would hear a crispy crunch.)