THE FUNDAMENTAL GROUP OF GALOIS COVER OF THE SURFACE 𝕋 Γ— 𝕋

2008 β—½  
Vol 18 (08) β—½  
pp. 1259-1282 β—½  
Author(s):  
MEIRAV AMRAM β—½  
MINA TEICHER β—½  
UZI VISHNE
Keyword(s):  
Fundamental Group β—½  
Dimensional Torus β—½  
One Dimensional β—½  
Generic Projection β—½  
Galois Cover β—½  
The One β—½  
First Time

This is the final paper in a series of four, concerning the surface 𝕋 Γ— 𝕋 embedded in β„‚β„™8, where 𝕋 is the one-dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto β„‚β„™2, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

scholarly journals Well-posedness of the linear heat equation with a second order memory term

2020 β—½  
Vol 34 β—½  
pp. 03011
Author(s):  
Constantin Niţă β—½  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Initial Data β—½  
Heat Equation β—½  
Unique Solution β—½  
Source Term β—½  
Memory Term β—½  
Well Posedness β—½  
Dimensional Torus β—½  
One Dimensional β—½  
Linear Heat β—½  
The One

In this article we prove that the heat equation with a memory term on the one-dimensional torus has a unique solution and we study the smoothness properties of this solution. These properties are related with some smoothness assumptions imposed to the initial data of the problem and to the source term.

scholarly journals Large semigroups of cellular automata

2011 β—½  
Vol 32 (6) β—½  
pp. 1991-2010 β—½  
Author(s):  
YAIR HARTMAN
Keyword(s):  
Cellular Automata β—½  
Field Structure β—½  
The Other β—½  
Entire Space β—½  
Dimensional Torus β—½  
Semigroup Action β—½  
Closed Set β—½  
One Dimensional β—½  
Shift Space β—½  
The One

AbstractIn this article, we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to β€˜largeness’: first, a semigroup has the ID (infinite is dense) property if the only infinite invariant closed set (with respect to the semigroup action) is the entire space; the second property is maximal commutativity (MC). We shall consider two examples of semigroups: one is spanned by cellular automata transformations that represent multiplications by integers on the one-dimensional torus, and the other one consists of all the cellular automata transformations which are linear (when the symbols set is the ring β„€/sβ„€). It will be shown that these two properties of these semigroups depend on the number of symbols s. The multiplication semigroup is ID and MC if and only if s is not a power of a prime. The linear semigroup over the mentioned ring is always MC but is ID if and only if s is prime. When the symbol set is endowed with a finite field structure (when possible), the linear semigroup is both ID and MC. In addition, we associate with each semigroup which acts on a one-sided shift space a semigroup acting on a two-sided shift space, and vice versa, in a way that preserves the ID and the MC properties.

Almost free action of the one-dimensional torus on a toric variety

2006 β—½  
Vol 197 (5) β—½  
pp. 681-703 β—½  
Author(s):  
D G Il'inskii
Keyword(s):  
Toric Variety β—½  
Free Action β—½  
Dimensional Torus β—½  
One Dimensional β—½  
The One

scholarly journals A note on inverse problem for strongly damped wave equation with Gaussian white noise

2018 β—½  
Vol 20 β—½  
pp. 02003
Author(s):  
Chu Duc Khanh β—½  
Nguyen Hoang Luc β—½  
Van Phan β—½  
Nguyen Huy Tuan
Keyword(s):  
White Noise β—½  
A Priori β—½  
Gaussian White Noise β—½  
True Solution β—½  
One Dimensional β—½  
Noise Data β—½  
Ill Posed β—½  
The One β—½  
First Time β—½  
Strongly Damped

In this paper, we study for the first time the inverse initial problem for the one-dimensional strongly damped wave with Gaussian white noise data. Under some a priori assumptions on the true solution, we propose the Fourier truncation method for stabilizing the ill-posed problem. Error estimates are given in both the L2– and Hp–norms.

scholarly journals Global Components of Positive Bounded Variation Solutions of a One-Dimensional Indefinite Quasilinear Neumann Problem

2019 β—½  
Vol 19 (3) β—½  
pp. 437-473 β—½  
Author(s):  
Julian López-Gómez β—½  
Pierpaolo Omari
Keyword(s):  
Neumann Problem β—½  
Positive Solutions β—½  
Bounded Variation β—½  
Connected Components β—½  
One Dimensional β—½  
Linearized Problem β—½  
Bounded Variation Functions β—½  
The One β—½  
First Time β—½  
Prime 2

Abstract This paper investigates the topological structure of the set of the positive solutions of the one-dimensional quasilinear indefinite Neumann problem \begin{dcases}-\Bigg{(}\frac{u^{\prime}}{\sqrt{1+{u^{\prime}}^{2}}}\Bigg{)}^{% \prime}=\lambda a(x)f(u)\quad\text{in }(0,1),\\ u^{\prime}(0)=0,\quad u^{\prime}(1)=0,\end{dcases} where {\lambda\in\mathbb{R}} is a parameter, {a\in L^{\infty}(0,1)} changes sign, and {f\in C^{1}(\mathbb{R})} is positive in {(0,+\infty)} . The attention is focused on the case {f(0)=0} and {f^{\prime}(0)=1} , where we can prove, likely for the first time in the literature, a bifurcation result for this problem in the space of bounded variation functions. Namely, the existence of global connected components of the set of the positive solutions, emanating from the line of the trivial solutions at the two principal eigenvalues of the linearized problem around 0, is established. The solutions in these components are regular, as long as they are small, while they may develop jump singularities at the nodes of the weight function a, as they become larger, thus showing the possible coexistence along the same component of regular and singular solutions.

The Derivation of 1/N Energy-Solutions to the harper-Equation and Related Magnetizations

1998 β—½  
Vol 12 (18) β—½  
pp. 1847-1870 β—½  
Author(s):  
C. Micu β—½  
E. Papp
Keyword(s):  
Energy Spectrum β—½  
Fermi Level β—½  
Quantum Gas β—½  
One Dimensional β—½  
Implicit Form β—½  
Field Independent β—½  
The One β—½  
First Time β—½  
Harper Equation

Proofs are given for the first time that the energy-spectrum of the Harper-equation can be derived in a closed implicit form by using the one-dimensional limit of the 1/N-description. Explicitly solvable cases are discussed in some more detail for Ξ”=1. Here Ξ” expresses the Harper-parameter discriminating between metallic (Ξ”<1) and insulator (Ξ”>1) phases. Related magnetizations have been established by applying both Dingle- and quantum-gas approaches, now for a fixed value of the Fermi-level. The first description leads to large paramagnetic-like magnetizations oscillating with nearly field-independent amplitudes increasing with the temperature. In the second case one deals with magnetization-oscillations centered around the zero-value, such that the amplitudes decrease both with the field and the temperature.

THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)

2007 β—½  
Vol 17 (03) β—½  
pp. 507-525 β—½  
Author(s):  
MEIRAV AMRAM β—½  
MINA TEICHER β—½  
UZI VISHNE
Keyword(s):  
Fundamental Group β—½  
Hirzebruch Surface β—½  
Generic Projection β—½  
Galois Cover β—½  
Hirzebruch Surfaces β—½  
Galois Covers β—½  
Branch Curve

This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is [Formula: see text] where c = gcd (a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in β„‚2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to [Formula: see text].

The decay of a plane shock wave

1970 β—½  
Vol 43 (4) β—½  
pp. 737-751 β—½  
Author(s):  
H. Ardavan-Rhad
Keyword(s):  
Analytic Solution β—½  
Weak Shock β—½  
Simple Wave β—½  
Plane Shock β—½  
One Dimensional β—½  
Conductive Medium β—½  
Expansion Theory β—½  
Particular Solution β—½  
The One β—½  
First Time

An analytic solution of the non-isentropic equations of gas-dynamics, for the one-dimensional motion of a non-viscous and non-conductive medium, is derived in this paper for the first time. This is a particular solution which contains only one arbitrary function. On the basis of this solution, the interaction of a centred simple wave with a shock of moderate strength is analyzed; and it is shown that, for a weak shock, this analysis is compatible with Friedrichs's theory. Furthermore, in the light of this analysis, it is explained why the empirical methods employed by the shock-expansion theory, including Whitham's rule for determining the shock path, work.

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