Analytic renormalization via continuous space dimension

1972 ◽  
Vol 4 (9) ◽  
pp. 329-332 ◽  
Author(s):  
G. M. Cicuta ◽  
E. Montaldi
Keyword(s):  
Space Dimension ◽  
Continuous Space ◽  
Analytic Renormalization

Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

scholarly journals On the quantization of folded strings in non-critical dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jacob Sonnenschein ◽  
Dorin Weissman
Keyword(s):  
Scalar Curvature ◽  
Space Dimension ◽  
Massive Particle ◽  
Open String ◽  
Closed String ◽  
Target Space ◽  
Critical Dimensions ◽  
Complete Set ◽  
Rotating String ◽  
Folding Point

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.

scholarly journals MESHFREEFLOWNET: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

2020 ◽  
Author(s):  
Chiyu lMaxr Jiang ◽  
Soheil Esmaeilzadeh ◽  
Kamyar Azizzadenesheli ◽  
Karthik Kashinath ◽  
Mustafa Mustafa ◽  
...  
Keyword(s):  
Super Resolution ◽  
Space Time ◽  
Continuous Space

scholarly journals Singularly Perturbed Oscillators with Exponential Nonlinearities

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.

scholarly journals Spatial Agglomeration of China’s Forest Products Manufacturing Industry: Measurement, Characteristics and Determinants

Forests ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 1006
Author(s):  
Zhenhuan Chen ◽  
Hongge Zhu ◽  
Wencheng Zhao ◽  
Menghan Zhao ◽  
Yutong Zhang
Keyword(s):  
Spatial Distribution ◽  
Spatial Data ◽  
Large Scale ◽  
Manufacturing Industry ◽  
Economies Of Scale ◽  
Forest Products ◽  
Spatial Data Analysis ◽  
Forest Protection ◽  
Spatial Agglomeration ◽  
Continuous Space

China’s forest products manufacturing industry is experiencing the dual pressure of forest protection policies and wood scarcity and, therefore, it is of great significance to reveal the spatial agglomeration characteristics and evolution drivers of this industry to enhance its sustainable development. Based on the perspective of large-scale agglomeration in a continuous space, in this study, we used the spatial Gini coefficient and standard deviation ellipse method to investigate the spatial agglomeration degree and location distribution characteristics of China’s forest products manufacturing industry, and we used exploratory spatial data analysis to investigate its spatial agglomeration pattern. The results show that: (1) From 1988 to 2018, the degree of spatial agglomeration of China’s forest products manufacturing industry was relatively low, and the industry was characterized by a very pronounced imbalance in its spatial distribution. (2) The industry has a very clear core–periphery structure, the spatial distribution exhibits a “northeast-southwest” pattern, and the barycenter of the industrial distribution has tended to move south. (3) The industry mainly has a high–high and low–low spatial agglomeration pattern. The provinces with high–high agglomeration are few and concentrated in the southeast coastal area. (4) The spatial agglomeration and evolution characteristics of China’s forest products manufacturing industry may be simultaneously affected by forest protection policies, sources of raw materials, international trade and the degree of marketization. In the future, China’s forest products manufacturing industry should further increase the level of spatial agglomeration to fully realize the economies of scale.

scholarly journals Global small data solutions for semilinear waves with two dissipative terms

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 ¯ .

scholarly journals A geostatistical extreme-value framework for fast simulation of natural hazard events

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150855 ◽  
Author(s):  
Benjamin D. Youngman ◽  
David B. Stephenson
Keyword(s):  
Natural Hazard ◽  
Computational Cost ◽  
Additive Model ◽  
Simulation Method ◽  
Value Theory ◽  
Extreme Value ◽  
Wind Gust ◽  
Continuous Space ◽  
Statistical Framework ◽  
Distribution Parameters

We develop a statistical framework for simulating natural hazard events that combines extreme value theory and geostatistics. Robust generalized additive model forms represent generalized Pareto marginal distribution parameters while a Student’s t -process captures spatial dependence and gives a continuous-space framework for natural hazard event simulations. Efficiency of the simulation method allows many years of data (typically over 10 000) to be obtained at relatively little computational cost. This makes the model viable for forming the hazard module of a catastrophe model. We illustrate the framework by simulating maximum wind gusts for European windstorms, which are found to have realistic marginal and spatial properties, and validate well against wind gust measurements.

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