Infinity Research Articles

Unifying some notions of infnity in ZC and ZF

Unifying some notions of infnity in ZC and ZF

Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field

Our work focuses on investigating limit cycle bifurcation for infinity and a degenerate singular point of a fifth degree system in three-dimensional vector field. By using singular value method to compute focal values carefully, we give the expressions of the focal values (Lyapunov constants) at the origin and at infinity. Moreover, we obtain that four limit cycles at most can bifurcate from the origin and three limit cycles can bifurcate from infinity. At the same time, we show the structure of limit cycles from the origin and the infinity. It is interesting for this kind of nonlinear phenomenon that a string of large limit cycles encircle a string of small limit cycles by simultaneous Hopf bifurcation, which is hardly seen for similar published results in three-dimensional vector field, our result is new.

On the existence of polyanalytic functions

We give a sharp estimate for the codimension of the poly‐Bergman space in the poly‐Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for and the j‐polyanalytic Bergman space over the domain U is trivial precisely when the complement of U has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non‐analytic poly‐Bergman space are trivial.

‘UNBOUNDED VIEWS’: INCOMPLETE EKPHRASIS AND THE VISUAL IMAGINATION IN VIRGIL

Our imagination loves to be filled with an object or to grasp at anything that is too big for its capacity. We are flung into a pleasing astonishment at such unbounded views and feel a delightful stillness and amazement of the soul at the apprehension of them.Joseph Addison, Essay 412

Infinitely many solutions for quasilinear Schrödinger systems with finite and sign-changing potentials

We consider the following quasilinear Schrodinger system in $${\mathbb{R}^N}$$ with $${N\geq3}$$ : P $$\left\{\begin{array}{l}\sum_{i,j=1}^{N}D_j(a_{ij}(u)D_i u)-\frac{1}{2} \sum_{i,j=1}^{N}D_s a_{ij}(u) D_i u D_j u-A(x) u+F_u(u,v)=0 \\ \sum_{i,j=1}^{N}D_j(a_{ij}(v)D_iv)-\frac{1}{2} \sum_{i,j=1}^{N}D_s a_{ij}(v) D_i v D_j v-B(x)v+F_v(u,v)=0,\end{array} \right.$$ where $${D_i=\frac{\partial}{\partial x_i},\ \ D_s a_{ij}(s)=\frac{d}{ds}a_{ij}(s)}$$ , $${F(u,v)}$$ is the coupling term, $${A(x)}$$ and $${B(x)}$$ are finite and sign-changing potential functions. Using an approximation scheme and $${q}$$ -Laplacian regularization, we prove the existence of infinitely many solutions for system $${(P)}$$ .

Mathematics, Philosophical and Semantic Considerations on Infinity (II): Dialectical Vision

Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor.

On a Reformulated Convolution Quadrature Based Boundary Element Method

Boundary Element formulations in time domain suffer from two prob- lems. First, for hyperbolic problems not too much fundamental solutions are avail- able and, second, the time stepping procedure is expensive in storage and has stabil- ity problems for badly chosen time step sizes. The first problem can be overcome by using the Convolution Quadrature Method (CQM) for time discretisation. This as well improves the stability. However, still the storage requirements are large. A recently published reformulation of the CQM by Banjai and Sauter (Rapid solu- tion of the wave equation in unbounded domains, SIAM J. Numer. Anal., 47, 227- 249) reduces the time stepping procedure to the solution of decoupled problems in Laplace domain. This new version of the CQM is applied here to elastodynam- ics. The storage is reduced to nearly the amount necessary for one calculation in Laplace domain. The properties of the original method concerning stability in time are preserved. Further, the only parameter to be adjusted is still the time step size. The drawback is that the time history of the given boundary data has to be known in advance. These conclusions are validated by the examples of an elastodynamic column and a poroelastodynamic half space.

Humanity and Paternal Eros: The Father-Son Relationship in Comparative Perspective

This paper examines the human relational patterns presented in the philosophical writings of the Confucian thinker Dai Zhen (戴震1724–77) and the Jewish philosopher Emmanuel Levinas’s (1906–95) Totality and Infinity to uncover the ethical significance of the father-son relationship. I argue that for both thinkers the father-son relation is not just one type of human relationship among other social dyads, but rather, of greater significance, serves as the paradigmatic model of the ethical human relationship in bringing to light the idea of the ethical self as a responsible being in relation to others.

The Dirichlet problem at infinity on Hadamard manifolds

Let M be an n -dimensional Hadamard manifold, that is, a complete simply connected C ∞ Riemannian manifold with nonpositive sectional curvatures. Making use of geodesic rays, Eberlein and O’Neill [11] constructed a compactification = M S (∞) of M which gives a homeomorphism of ( M, S(∞ )) with the Euclidean pair ( B n , S n-1 ). In this paper we shall study the asymptotic Dirichlet problem for the Laplace-Beltrami operator, which is stated as follows:

W. Large, Levinas' "Totality and Infinity"

W. Large, Levinas' "Totality and Infinity"

Lusting for Infinity: A Spiritual Odyssey, by Tom W. Boyd

Lusting for Infinity: A Spiritual Odyssey, by Tom W. Boyd

Somos islas hechas de infinidad de fronteras. Entrevista a Rey Andújar

Entrevista realizada al escritor dominicano Rey Andújar. Ganador del premio ALBA narrativa 2015.

Group Actions On The Sphere And Multiplicity Results For The Cr-Yamabe Equation

We will show that the CR-Yamabe equation has several families of infinitely many changing sign solutions, each of them having different symmetries. The problem is variational but it is not Palais-Smale: using different complex group actions on the sphere, we will find many closed subspaces on which we can apply the minmax argument.

Servo System Pid Control of Neural Network Algorithm Based on Lugre Model

Considering the parameters of the traditional PID control algorithm are not capable of online adjustment and do not have adaptive capability once they are determined, which can not satisfied the precision control requirement of servo system with complex nonlinear friction, a PID controller based on radial basis function neural network (RBFNN) is designed, the advantages of RBFNN such as infinity approaching nonlinear system, little operation quantity and speedy constringency are combined with PID control technology organically to obtain high position tracking accuracy. The simulate results show that compared with common PID control, the RBFNN PID controller can adaptively adjust the controller parameters, greatly improving the control precision of the system.

Levinas' Totality and infinity

Levinas' Totality and infinity

Minimizing Energy Consumption of the Mobile Charger in a Wireless Rechargeable Sensor Network

＂Wireless Rechargeable Sensor Networks＂ (WRSNs) have received wide attention in recent years due to their potential to solve the energy problem. With a Mobile Charger (MC), the lifetime of a WRSN can be prolonged significantly, or theoretically speaking, to infinity. An important issue in deploying WRSNs is to minimize the total energy consumption of the MC. To address the problem, this paper proposes a method of service station deployment, and an energy efficient charging scheme. These methods are developed based on the fact that energy consumption of sensor nodes in a WRSN is extremely imbalanced. Simulation results validate the energy efficiency of the two methods.

On the uniform spread of almost simple linear groups

Let G be a finite group, and let k be a nonnegative integer. We say that G has uniform spread k if there exists a fixed conjugacy class C in G with the property that for any k nontrivial elements x 1,…,xk in G there exists y ∊ C such that G = ‹xi,y› for all i. Further, the exact uniform spread of G, denoted by u(G), is the largest k such that G has the uniform spread k property. By a theorem of Breuer, Guralnick, and Kantor, u(G) ≥ 2 for every finite simple group G. Here we consider the uniform spread of almost simple linear groups. Our main theorem states that if G = ‹PSL n (q),g› is almost simple, then u(G) ≥ 2 (unless G ≅ S 6), and we determine precisely when u(G) tends to infinity as |G| tends to infinity.

Bi-space Global Attractors for a Class of Nonclassical Parabolic Equations with Arbitrary Polynomial Growth in Unbounded Domain

In this article, we consider the dynamical behavior of the nonclassical diffusion equation in unbounded domain while the nonlinearity satisfy the arbitrary order polynomial growth conditions. Using the tail-estimated method and the asymptotic a priori estimate method, we obtain the existence of \({(H^1(\Omega)\cap L^{p}(\Omega),L^{2}(\Omega))}\)-global attractor, \({(H^1(\Omega)\cap L^{p}(\Omega),L^{p}(\Omega))}\)-global attractor, \({(H^1(\Omega)\cap L^{p}(\Omega),H^{1}(\Omega))}\)-global attractor and \({(H^1(\Omega)\cap L^{p}(\Omega),H^1(\Omega)\cap L^{p}(\Omega))}\)-global attractor.

The logic of infinity

The logic of infinity

The Heesch number for multiple prototiles is unbounded

In this paper we show that, for all integers k⩾3 and n⩾1, there exists a protoset consisting of k prototiles, whose Heesch number is n. This disproves a conjecture by Grünbaum and Shephard.