Additional Space Dimension in Bound  Spaces Created by a Central Object

Abstract Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

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Singularly Perturbed Oscillators with Exponential Nonlinearities

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-021-10041-1 ◽

2021 ◽

Author(s):

S. Jelbart ◽

K. U. Kristiansen ◽

P. Szmolyan ◽

M. Wechselberger

Keyword(s):

Limit Cycles ◽

Space Dimension ◽

Blow Up ◽

Exponential Convergence ◽

Model System ◽

Piecewise Smooth ◽

Singularly Perturbed ◽

Model Systems ◽

Smooth System ◽

Unique Limit

AbstractSingular exponential nonlinearities of the form $$e^{h(x)\epsilon ^{-1}}$$ e h ( x ) ϵ - 1 with $$\epsilon >0$$ ϵ > 0 small occur in many different applications. These terms have essential singularities for $$\epsilon =0$$ ϵ = 0 leading to very different behaviour depending on the sign of h. In this paper, we consider two prototypical singularly perturbed oscillators with such exponential nonlinearities. We apply a suitable normalization for both systems such that the $$\epsilon \rightarrow 0$$ ϵ → 0 limit is a piecewise smooth system. The convergence to this nonsmooth system is exponential due to the nonlinearities we study. By working on the two model systems we use a blow-up approach to demonstrate that this exponential convergence can be harmless in some cases while in other scenarios it can lead to further degeneracies. For our second model system, we deal with such degeneracies due to exponentially small terms by extending the space dimension, following the approach in Kristiansen (Nonlinearity 30(5): 2138–2184, 2017), and prove—for both systems—existence of (unique) limit cycles by perturbing away from singular cycles having desirable hyperbolicity properties.

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Global small data solutions for semilinear waves with two dissipative terms

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/s10231-021-01128-z ◽

2021 ◽

Author(s):

Wenhui Chen ◽

Marcello D’Abbicco ◽

Giovanni Girardi

Keyword(s):

Wave Equations ◽

Space Dimension ◽

Full Range ◽

Small Data ◽

Decay Estimates ◽

Time Decay ◽

Nonexistence Result ◽

Derivative Type ◽

Long Time ◽

Dissipative Terms

AbstractIn this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity $$|u|^p$$ | u | p or nonlinearity of derivative type $$|u_t|^p$$ | u t | p , in any space dimension $$n\geqslant 1$$ n ⩾ 1 , for supercritical powers $$p>{\bar{p}}$$ p > p ¯ . The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive $$L^r-L^q$$ L r - L q long time decay estimates for the solution in the full range $$1\leqslant r\leqslant q\leqslant \infty $$ 1 ⩽ r ⩽ q ⩽ ∞ . The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers $$p<{\bar{p}}$$ p < p ¯ .

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Tag-based object similarity computation using term space dimension reduction

Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval - SIGIR '09 ◽

10.1145/1571941.1572130 ◽

2009 ◽

Author(s):

Yong Ki Lee ◽

Sung Jun Lee ◽

Jonghun Park

Keyword(s):

Dimension Reduction ◽

Space Dimension ◽

Similarity Computation ◽

Object Similarity

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On the Nature of R 136, the Central Object of 30 Dor. A Comparison by the Galactic Cluster NGC 3603

Symposium - International Astronomical Union ◽

10.1017/s0074180900040341 ◽

1984 ◽

Vol 108 ◽

pp. 257-258

Author(s):

Michael Rosa ◽

Jorge Melnick ◽

Preben Grosbol

Keyword(s):

Core Region ◽

H Ii Regions ◽

Central Object ◽

The Core ◽

Dominant Component ◽

Galactic Cluster ◽

H Ii Region

The massive H II region NGC 3603 is the closest galactic counterpart to the giant LMC nebula 30 Dor. Walborn (1973) first compared the ionizing OB/WR clusters of the two H II regions and suggested that R 136, the unresolved luminous WR + 0 type central object of 30 Dor, might be a multiple system like the core region of NGC 3603. Suggestions that the dominant component of R 136, i.e. R 136A, might be either a single or a very few supermassive and superluminous stars (Schmidt-Kaler and Feitzinger 1982, Savage et al. 1983) have recently been disputed by Moffat and Seggewiss (1983) and Melnick (1983), who have presented spectroscopic and photometric evidence to support the hypothesis of an unresolved cluster of stars. We have extended Walborn's original comparison of the apparent morphology of the two clusters by digital treatment of the images to simulate how the galactic cluster would look like if it were located in the LMC

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Order in Space: A General Formalism for Spatial Reasoning

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213097000232 ◽

1997 ◽

Vol 06 (04) ◽

pp. 423-450 ◽

Cited By ~ 11

Author(s):

Baher A. El-Geresy ◽

Alia I. Abdelmoty

Keyword(s):

Space Dimension ◽

Spatial Reasoning ◽

Spatial Information ◽

Spatial Objects ◽

Temporal Domain ◽

Spatial Information Systems ◽

Connected Set ◽

General Constraints ◽

Different Types ◽

Composition Table

In this paper we propose a general approach for reasoning in space. The approach is composed of a set of two general constraints to govern the spatial relationships between objects in space, and two rules to propagate relationships between those objects. The approach is based on a novel representation of the topology of the space as a connected set of components using a structure called adjacency matrix which can capture the topology of objects of different complexity in any space dimension. The formalism is used to explain spatial compositions resulting in indefinite and definite relations and it is shown to be applicable to reasoning in the temporal domain. The main contribution of the formalism is that it provides means for constructing composition tables for objects with arbitrary complexity in any space dimension. A new composition table between spatial objects of different types is presented. A major advantage of the method is that reasoning between objects of any complexity can be achieved in a defined limited number of steps. Hence, the incorporation of spatial reasoning mechanisms in spatial information systems becomes possible.

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