Infinity In Space Research Articles

Unendliche Natur

Abstract Albrecht von Haller’s ≫Unvollkommenes Gedicht uber die Ewigkeit≪ (1737/42-1748) reflects the reciprocal relationship among empirical observation of the world, imagination and human self-determination. In Haller’s poem, the grief over the death of a friendn triggers religious and secular reflections on finiteness and eternity. Faced with the knowledge of the infinity of time and space in the Copernican universe, the imagination is plunged into a crisis that leaves the speaking and reflecting ego struggling for words. The linguistic search is an open process and the poem remains unfinished - a fragment due to the subject matter. The paper analyzes the poetic process of this crisis and illustrates how the experience of the sublime, evoked by the amazement at the multiplicity of worlds, is mixed with a melancholy fear of one’s own forlornness and placelessness in the face of cosmic infinity.

On directional blow-up for a semilinear heat equation with space-dependent reaction

We consider nonnegative solutions u of the Cauchy problem for a semilinear heat equation with space-dependent reaction: ut=Δu+μ(x)up, u(x,0)=u0(x), where μ(x)≥0 satisfies some condition and the initial data u0(x)(≢0) satisfies ‖μ˜u0‖L∞(RN)<∞ with μ˜=μ1/(p−1). We study weighted solutions μ˜u which blow up at minimal blow-up time. Such a weighted solution blows up at space infinity in some direction (directional blow-up). We call this direction a blow-up direction of μ˜u. We give a sufficient and necessary condition on u0 for a weighted solution to blow up at minimal blow-up time. Moreover, we completely characterize blow-up directions of μ˜u by the profile of the initial data.

Uniqueness of lump solution to the KP‐I equation

AbstractThe KP‐I equation has family of solutions which decay to zero at space infinity. One of these solutions is the classical lump solution, which is a traveling wave, and the KP‐I equation in this case reduces to the Boussinesq equation. In this paper we classify all the ‘lump‐type’ solutions of the Boussinesq equation. Using a robust inverse scattering transform developed by Bilman–Miller for the Schrödinger equation, we show that the lump‐type solutions are rational and their functions have to be polynomials of degree for some integer . In particular, this implies that the lump solution is the unique ground state of the KP‐I equation (as conjectured by Klein–Saut). The problem studied in this paper was mentioned in Airault–McKean–Moser, our result can be regarded as a two‐dimensional analogy of their theorem on the classification of rational solutions for the KdV equation.

Глокальное пространство в Твиттер-коммуникации на испанглийском языке

The study of linguistic phenomena in media texts based on code-switching and code-mixing is a pressing issue, since their linguistic level reflects global processes of the multipolar world development. In particular, it results in post-standard modern languages and translingual idioms where language contact occurs. The article aims at determining the Spanglish language glocal space continuum at the lexical, semantic and grammatical levels. The material is based on tweets by the American satirist Rachel Figueroa, writing under the pseudonym Miguel Bloombito, for 2017–2022, selected using the continuous sampling method. A corpus of 1073 tweets was compiled and studied using morphological, syntactic, lexical and semantic analysis followed by statistical processing and mapping. The result is the identification of four modus categories that express meanings corresponding to glocal space. Methods for transmitting these meanings at the lexical, semantic and grammatical levels in Spanglish have been identified as well. Thus, it has been established that this translingual idiom boasts a full-fledged system of units and levels, which effectively conveys the meanings of all modus categories under consideration. In addition, data mapping allows us to conclude that Spanglish effectively performs communication tasks both within the same locale and between different locales. Finally, the study does not only empirically prove the validity of one of the hypotheses regarding the glocal space infinity, including its linguistic representation, but also demonstrates that modern language contact models correspond not to geography, but to the logistics of communication flows between various glocalized locales determined by geostrategic interests.

Basin delimitation and stability assessment for power systems in the projective space

This paper presents a method for determining the global basin boundary of the power systems. To show the general outline of the basin, the power system is shrink to the projective space. First, a new vector field is induced according to Poincare’s method. After the transformation, the structural stability of the system remains the same. The singularities at infinity are obtained by the proposed shrinking-projection method. The boundary of the basin which is extended to the infinity are complemented by the singularities at infinity in the projective space. The stability of the power system is then evaluated based on the distribution of the singularities at infinity. Finally, the proposed method is applied to the power system with perturbations to study the characteristic of the stochastic basin boundary. The validity of the proposed method is demonstrated on a 9-bus, 11-bus and 68-bus test system.

Everything is Infinite: Children's Beliefs About Endless Space, Time, and Number.

How do children form beliefs about the infinity of space, time, and number? We asked whether children held similar beliefs about infinity across domains, and whether beliefs in infinity for domains like space and time might be scaffolded upon numerical knowledge (e.g., knowledge successors within the count list). To test these questions, 112 U.S. children (aged 4;0-7;11) completed an interview regarding their beliefs about infinite space, time, and number. We also measured their knowledge of counting, and other factors that might impact performance on linguistic assessments of infinity belief (e.g., working memory, ability to respond to hypothetical questions). We found that beliefs about infinity were very high across all three domains, suggesting that infinity beliefs may arise early in development for space, time, and number. Second, we found that-across all three domains-children were more likely to believe that it is always possible to add a unit than to believe that the domain is endless. Finally, we found that understanding the rules underlying counting predicted children's belief that it is always possible to add 1 to any number, but did not predict any of the other elements of infinity belief.

Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity

Abstract In our previous paper [K. Ishige, S. Okabe, and T. Sato, A supercritical scalar field equation with a forcing term, J. Math. Pures Appl. 128 (2019), pp. 183–212], we proved the existence of a threshold κ ∗ &gt; 0 {\kappa }^{\ast }\gt 0 such that the elliptic problem for an inhomogeneous elliptic equation − Δ u + u = u p + κ μ -\Delta u+u={u}^{p}+\kappa \mu in R N {{\bf{R}}}^{N} possesses a positive minimal solution decaying at the space infinity if and only if 0 &lt; κ ≤ κ ∗ 0\lt \kappa \le {\kappa }^{\ast } . Here, N ≥ 2 N\ge 2 , μ \mu is a nontrivial nonnegative Radon measure in R N {{\bf{R}}}^{N} with a compact support, and p &gt; 1 p\gt 1 is in the Joseph-Lundgren subcritical case. In this article, we prove the existence of nonminimal positive solutions to the elliptic problem. Our arguments are also applicable to inhomogeneous semilinear elliptic equations with exponential nonlinearity.

The Unicity, Infinity and Unity of Space

AbstractThe article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions.

Global well-posedness to the Cauchy problem of 2D nonhomogeneous Bénard system with large initial data and vacuum

This paper establishes the global well-posedness of strong solutions to the nonhomogeneous Bénard system with positive density at infinity in the whole space R2. We obtain the global existence and uniqueness of strong solutions for general large initial data. Our method relies on the dedicate energy estimates and a logarithmic interpolation inequality.

Moduli of flat connections on smooth varieties

We study the moduli functor of flat bundles on smooth, possibly non-proper, algebraic variety $X$ (over a field of characteristic zero). For this we introduce the notion of \emph{formal boundary} of $X$, denoted by $\partial X$, which is a formal analogue of the boundary at infinity of the Betti topological space associated to $X$. We explain how to construct two derived moduli functors $Vect^{\nabla}(X)$ and $Vect^{\nabla}(\partial X)$, of flat bundles on $X$ and on $\partial X$, as well as a restriction map $R : Vect^{\nabla}(X) \rightarrow Vect^\nabla(\partial X)$ from the former to the later. This work contains two main results. First we prove that the morphism R comes equipped with a canonical shifted Lagrangian structure in the sense of [PTVV]. This first result can be understood as the de Rham analogue of the existence of Poisson structures on moduli of local systems previously studied by the authors. As a second statement, we prove that the geometric fibers of $R$ are representable by quasi-algebraic spaces, a slight weakening of the notion of algebraic spaces.

Inverse scattering transform for the complex coupled short‐pulse equation

AbstractIn this paper, we develop the Riemann–Hilbert approach to the inverse scattering transform (IST) for the complex coupled short‐pulse equation on the line with zero boundary conditions at space infinity, which is a generalization of recent work on the scalar real short‐pulse equation (SPE) and complex short‐pulse equation (cSPE). As a byproduct of the IST, soliton solutions are also obtained. As is often the case, the zoology of soliton solutions for the coupled system is richer than in the scalar case, and it includes both fundamental solitons (the natural, vector generalization of the scalar case), and fundamental breathers (a superposition of orthogonally polarized fundamental solitons, with the same amplitude and velocity but having different carrier frequencies), as well as composite breathers, which still correspond to a minimal set of discrete eigenvalues but cannot be reduced to a simple superposition of fundamental solitons. Moreover, it is found that the same constraint on the discrete eigenvalues which leads to regular, smooth one‐soliton solutions in the complex SPE, also holds in the coupled case, for both a single fundamental soliton and a single fundamental breather, but not, in general, in the case of a composite breather.

Blow-up at space infinity for a quasilinear parabolic equation with space-dependent reaction

We consider a nonnegative solution $u$ of the Cauchy problem for a quasilinear parabolic equation $u_t=\Delta u^m+\mu(x)u^p$ with the initial data $u_0(x)\,(\not\equiv 0)$ satisfying $\| \tilde\mu u_0\|_{L^{\infty}(\mathbf R^N)}<\infty$, where nonnegative function $\mu(x)$ satisfies some condition and $\tilde\mu=\mu^{1/(p-1)}$. We give sufficient conditions on $u_0$ for a weighted solution $\tilde\mu u$ to blow up at space infinity and for a direction $\psi \in \mathbf S^{N-1}$ to be a blow-up direction of $\tilde\mu u$. We also show that such a weighted solution $\tilde\mu u$ blows up completely at the blow-up time of $\tilde\mu u$.

Cosmological evolution with quadratic gravity and nonideal fluids

Some cosmological models based on the gravitational theory f(R)=R+zeta R^2, and on fluids obeying to the equations of state of Redlich–Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different cosmic epochs. A dynamical system analysis reveals that these models contain fixed points which correspond to an inflationary, a radiation dominated and a late-time accelerating epoch, and a nonsingular bouncing solution, the latter being an asymptotic fixed point of the compactified phase space. The infinity of the compactified phase space is interpreted as a region in which the non-ideal behaviors of the previously mentioned cosmic fluids are suppressed. Physical constraints on the adopted dimensionless variables are derived by demanding the theory to be free from ghost and tachyonic instabilities, and a novel cosmological interpretation of such variables is proposed through a cosmographic analysis. The different effects of the equation of state parameters on the number of equilibrium solutions and on their stability nature are clarified. Some generic properties of these models, which are not sensitive to the particular fluid considered, are identified, while differences are critically examined by showing that the Redlich–Kwong scenario admits a second radiation-dominated epoch and a Big Rip Singularity.

Lipschitz Continuous Hypersurfaces with Prescribed Curvature and Asymptotic Boundary in Hyperbolic Space

Abstract We prove the existence of a complete locally Lipschitz continuous hypersurface in weak sense with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under certain assumptions.

SHAKESPEARE’S THEATER OF LIFE AND PHILOSOPHY OF BAROQUE THEATER: «FAUSTIAN SPIRIT» OVERTAKES ANCIENT FORM

Purpose of the article is to identify the components of creative method and anthropology of Shakespeare’s theater, to compare Shakespeare’s theater to Baroque theater, to analyze various conceptions of Shakespeare. Methods: hermeneutic, cultural anthropology, historical and cultural, analytical, psychoanalysis. From philosophical and anthropological positions, creative method and creative works of W. Shakespeare have been analyzed, a strong connection of theater and philosophy of Shakespeare’s theater with Baroque theater has been revealed (mysticism, fabulousness, hyperrealism, formal features are replaced by effective ones, usage of parable and utopia (image of King Lear in particular), motives of vanitas (vanity), duality of the world, allegory, «figureness»). Shakespeare suggests a new philosophy of theater based on elimination of borders between reality and art, «baroqueivisation», theatricalization of reality, masks are used as symbols of a real person without distorting it but rather revealing his or her deepest essence, sincerity. It is also reflected in understanding of Shakespeare’s authorship problem where mask of a clown and a buffoon are used in order to convey the deepest and most philosophical thoughts to society. Baroque reform of the theater suggested by Shakespeare, reduces theater to universal anthropological model both synchronically and diachronically. Theater runs around the actor, not only art but life of the universe is carried out via actor. This new philosophy of theater cannot be considered only within the «culture of meanings» (G.U. Gumbrecht) but on principle is within the limits of «culture of presence», which helps to understand the ideological idea of Shakespeare’s theater, to view biography and personality of Shakespeare in a new way because Shakespearean Studies was within the culture of meanings and tried to consider only the hidden codes and symbols of Shakespeare’s theater. Beyond these philosophical hermeneutics remained the transforming, effective power of Shakespeare’s theater. Humanization of theater also takes place: based on the old Antique form a new humanistic content is built, where much attention is paid to «life of soul», love, kindness, wits, passion, vengeance, etc., sinfulness of a soul and its ability to clear of evil. Theatre is considered to be not an external spectacle but a deep instrument of immersion in life of a soul and its gradual growth. Since theater is the whole world (in philosophy of culture it can also be identified with the formation of «Faustian soul» (O. Spengler), «Faustian spirit» focused on the infinite formation, the infinity of space), it requires the creation of a corresponding dictionary because the word itself becomes a word-action. A special role of allegory genre for philosophy of Shakespeare’s theater is considered, his philosophy is compared to philosophy of F. Bacon.

The convex hull swampland distance conjecture and bounds on non-geodesics

The Swampland Distance Conjecture (SDC) restricts the geodesic distances that scalars can traverse in effective field theories as they approach points at infinite distance in moduli space. We propose that, when applied to the subset of light fields in effective theories with scalar potentials, the SDC restricts the amount of non-geodesicity allowed for trajectories along valleys of the potential. This is necessary to ensure consistency of the SDC as a valid swampland criterion at any energy scale across the RG flow. We provide a simple description of this effect in moduli space of hyperbolic space type, and products thereof, and obtain critical trajectories which lead to maximum non-geodesicity compatible with the SDC. We recover and generalize these results by expressing the SDC as a new Convex Hull constraint on trajectories, characterizing towers by their scalar charge to mass ratio in analogy to the Scalar Weak Gravity Conjecture. We show that recent results on the asymptotic scalar potential of flux compatifications near infinity in moduli space precisely realize these critical amounts of non-geodesicity. Our results suggest that string theory flux compactifications lead to the most generic potentials allowing for maximum non-geodesicity of the potential valleys while respecting the SDC along them.

Эволюция систем расселения в аспекте классической теории центральных мест

Considering the features of the evolutionary development of central places' systems, we establish that, contrary to the prevailing point of view, in the general case there is no pronounced relationship between the share of urban population and the number of central places of a lower hierarchy level subordinate to the central place of a given level. Moreover, the axiom of the theory, stating the heterogeneous distribution of only the urban population, should be replaced by the following: “Space is homogeneous and isotropic in all respects, with the exception of the distribution of the entire population or part of it.” Thus, the existence of central systems without rural population does not contradict the theory itself in its classic version. The evolution of central places' systems within an infinite lattice takes place by sequentially filling the hierarchy levels (increasing the value of the K -parameter for a given level), interrupted by the appearance of subsystems (increasing the number of hierarchy levels with constant K )—at least after filling the second and the fifth levels. The article substantiates the possibility of considering the isolated sections of the lattice. In this regard, the axiom of the “rational” consumer behavior can be considered excessive, and the postulate of the infinity of space is rejected. Only two initial axioms—on the polymorphism of central places' systems and on the most compact “packaging” of their parts—can be considered unshakable.

Asymptotics for a parabolic equation with critical exponential nonlinearity

We consider the Cauchy problem: $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _{t}u = \Delta u - u+ \lambda f(u) &{} \text {in } (0,T) \times {\mathbb {R}}^{2}, u(0,x)=u_{0}(x) &{} \text {in } {\mathbb {R}}^{2}, \end{array}\right. } \end{aligned}$$ where $$\lambda >0$$ , $$\begin{aligned} f(u){:=}2 \alpha _0 u e^{\alpha _{0}u^{2}}, \quad \text {for some } \alpha _{0}>0, \end{aligned}$$ with initial data $$u_0\in H^{1}({\mathbb {R}}^{2})$$ . The nonlinear term f has a critical growth at infinity in the energy space $$ H^{1}({\mathbb {R}}^{2})$$ in view of the Trudinger-Moser embedding. Our goal is to investigate from the initial data $$u_0\in H^{1}({\mathbb {R}}^{2})$$ whether the solution blows up in finite time or the solution is global in time. For $$0<\lambda <\frac{1}{2\alpha _0}$$ , we prove that for initial data with energies below or equal to the ground state level, the dichotomy between finite time blow-up and global existence can be determined by means of a potential well argument.

ARCHITECTURAL IDEAS OF F. KIESLER IN THE DESIGN OF CONTEMPORARY CULTURAL AND ENTERTAINMENT OBJECTS

The life and career of Friedrich Kiezler is an example of constant research of world achievements in various fields of science and culture. This search was reflected in his own creative method of "flexible" architecture, based on the idea of the infinity of space, which later established itself in the direction of "correalism", which was based on constant interaction between people and the natural and technological environment.

Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction

We perform a thorough study of the blow up profiles associated to the following second order reaction-diffusion equation with non-homogeneous reaction:∂tu=∂xx(um)+|x|σup, in the range of exponents 1<p<m and σ>0. We classify blow up solutions in self-similar form, that are likely to represent typical blow up patterns for general solutions. We thus show that the non-homogeneous coefficient |x|σ has a strong influence on the qualitative aspects related to the finite time blow up. More precisely, for σ∼0, blow up profiles have similar behavior to the well-established profiles for the homogeneous case σ=0, and typically global blow up occurs, while for σ>0 sufficiently large, there exist blow up profiles for which blow up occurs only at space infinity, in strong contrast with the homogeneous case. This work is a part of a larger program of understanding the influence of unbounded weights on the blow up behavior for reaction-diffusion equations.