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First-Order Unification on Compressed Terms

Adrià Gascón, Sebastian Maneth, Lander Ramos, Marc Herbstritt
2011 International Conference on Rewriting Techniques and Applications  
In this work, STGs are used in the context of first-order unification. Hence, we want to represent terms containing first-order variables.  ...  The first-order matching problem is a particular case of first-order unification in which only one of the terms given as input may contain variables.  ...  In terms of Meta, it suffices to take n = 1, and to use large random trees.  ... 
doi:10.4230/lipics.rta.2011.51 dblp:conf/rta/GasconMR11 fatcat:5sawbklfvnfzjhxn577qxikc3y

On First-order Cons-free Term Rewriting and PTIME [article]

Cynthia Kop
2017 arXiv   pre-print
In this paper, we prove that (first-order) cons-free term rewriting with a call-by-value reduction strategy exactly characterises the class of PTIME-computable functions.  ...  We use this to give an alternative proof of the result by Carvalho and Simonsen which states that cons-free term rewriting with linearity constraints characterises this class.  ...  Cons-free Term Rewriting We assume the basic notions of first-order term rewriting to be understood.  ... 
arXiv:1711.03399v2 fatcat:n3wwedfzsbc7jefegcanzewani

First Order Hyperbolic Boundary Value Problems With a Large Oscillatory Zero Order Term [article]

Alvis Zhaodh
2021 arXiv   pre-print
We wish to establish a uniform energy estimate with respect to ϵ, which is needed in mentioned applications and justification of geometric optics solutions, but the zero order oscillatory term gives rise  ...  We study the weakly stable hyperbolic boundary value problem with a large zero order oscillatory coefficient.  ...  For the first equation in (3.49) involving σ 1 2 , the first term on the right hand side satisfies: (3.50) − E Q1 [L(∂)(I − E P )U 2 ] = −E Q1 [L(∂)(−R(L(∂)U 1 + e iθ3 M U 1 )] = −E Q1 [L(∂)(−R(L(∂)U 1  ... 
arXiv:2104.08532v2 fatcat:s4hfltoeobdjfd34fqxvu76cnq

On the comparison principle for second order elliptic equations without first and zeroth order terms [article]

Karl K. Brustad
2021 arXiv   pre-print
In Section 6 we shall see that this is also necessary when the equation is without first-and zeroth order terms.  ...  Next, |x − y| < 2t, and when recalling the definition of δ, the first term on the right-hand side is bounded by 4L 2 r t where L r is the Lipschitz constant of Q in B r (x 0 ).  ... 
arXiv:2008.08399v3 fatcat:vm4n6i4i5nhqfdjrkvptsp2dxy

Gradient estimates for nonlinear elliptic equations with first order terms [article]

Stefano Buccheri
2019 arXiv   pre-print
We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term.  ...  The presence of such a term makes the problem not coercive. The main tools are pointwise estimates of the rearrangements of both the solution and its gradient.  ...  The non coercivity is given by the presence of first order terms.  ... 
arXiv:1901.02673v2 fatcat:7y7wmsgs2feabhaokl5tcpt74y

Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences [article]

Martí Prats
2018 arXiv   pre-print
In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space F^s_p,q(Ω) in terms of first-order differences in a uniform domain Ω.  ...  First we study the term β.a β.a .  ...  Thus, one can apply only at the last norm the characterization using first order differences, which follows from [PS17, Theorem 1.2]. Corollary 1.1 (to [PS17, Theorem 1.2]).  ... 
arXiv:1804.05780v4 fatcat:mcu37vic3vcovpytacbxhur2dq

Determining nonsmooth first order terms from partial boundary measurements [article]

Kim Knudsen, Mikko Salo
2006 arXiv   pre-print
We give a similar result for determining a convection term.  ...  The following lemma shows that one may use pseudodifferential operators to conjugate away the main part Q ♯ of the first order term Q. Lemma 5.2.  ...  Elliptic equations of first order To extend the Nakamura-Uhlmann pseudodifferential conjugation method to logarithmic Carleman weights, we will need to solve first order elliptic equations with variable  ... 
arXiv:math/0609133v1 fatcat:jxan7eplwbbj3dbxygda6d7p7u

Regularizing effect and decay results for a parabolic problem with repulsive superlinear first order terms [article]

Martina Magliocca
2018 arXiv   pre-print
and long, short time decay concerning parabolic Cauchy-Dirichlet problems of the type < a r r a y > We assume that A(t,x) is a coercive, bounded and measurable matrix, the growth rate q of the gradient term  ...  As shown in [3, 4] when p = 2 and in [17] for 1 < p < N in a more general context, we need to fix (1.2) in order to get an existence result when a superlinear growth in the gradient term occurs.  ...  to rewrite (3.19) only in terms of S n,ε (G k (u)) and S n (G k (u)).  ... 
arXiv:1712.09246v3 fatcat:4ngchzprtffoxdataz3mnjuyke

The gravitational Hamiltonian, first order action, Poincaré charges and surface terms

Alejandro Corichi, Juan D Reyes
2015 Classical and quantum gravity  
More precisely, our starting point is the gravitational first order Holst action with surface terms and fall-off conditions that make the variational principle and the covariant phase space formulation  ...  Unlike the case of the Einstein-Hilbert action with Gibbons-Hawking-York or Hawking-Horowitz terms, here we do recover the ADM energy-momentum from the covariant surface term also when more general variations  ...  FIRST ORDER ACTION WITH BOUNDARY TERMS Our starting point is the covariant and Lorentz-gauge invariant first-order Holst action [15] with the additional surface integral term first put forward in [17  ... 
doi:10.1088/0264-9381/32/19/195024 fatcat:xi3lnjr72rfhldmafxjzgwpkl4

Optimal control of a first order Fokker-Planck equation with reaction term and density constraints [article]

Adrien Seguret
2021 arXiv   pre-print
Sobolev regularity, for the solution of a first order MFG, has been established in [34] , and improved in [42] ; see also [25] . The paper is organized as follows.  ...  In order to analyze (3.1) we now introduce several notations.  ...  From its definition, S i satisfies for any (t, τ, x) ∈ [0, T ] × [0, T ] × [0, 1]: deriving both terms in (A.3) w.r.t. x, it comes: Since ∂ x S τ,x i (τ ) = 1, solving (A.4) gives the result (A.2).  ... 
arXiv:2109.12836v2 fatcat:m5lexqlqyjgqzbnzw5bryzk2oe

On the Liouville property for fully nonlinear equations with superlinear first-order terms [article]

Marco Cirant, Alessandro Goffi
2021 arXiv   pre-print
order terms are two.  ...  Nonetheless, it is also by now well-known that the perturbation of second-order operators with suitable nonlinearities, such as zero-th and first-order terms,  ... 
arXiv:2107.13262v2 fatcat:iwgmwlyt4veyrp4dptds5c6d3m

The recursive path and polynomial ordering for first-order and higher-order terms

M. Bofill, C. Borralleras, E. Rodriguez-Carbonell, A. Rubio
2012 Journal of Logic and Computation  
The ordering is extended to higher-order terms, providing a new fully automatable use of polynomial interpretations in combination with betareduction.  ...  In most termination tools two ingredients, namely recursive path orderings (RPO) and polynomial interpretation orderings (POLO), are used in a consecutive disjoint way to solve the final constraints generated  ...  In order to ease the reading, the ordering is first presented in Section 3 for first-order terms and later on for higher-order terms.  ... 
doi:10.1093/logcom/exs027 fatcat:mzp6vkpzufgsxal2obzvkyfgym

Long-term Hydrodynamic Simulations on the Planetesimals Trapped in the First-order Mean Motion Resonances [article]

He-Feng Hsieh, Ing-Guey Jiang
2019 arXiv   pre-print
We perform long-term 2D hydrodynamic simulations to study the dynamics of planetesimals in the j:(j+1) first-order exterior resonances, and reexamine the theoretical expressions.  ...  In this study, we focus on the j : (j + 1) first-order exterior resonances.  ...  In this paper, we perform long-term hydrodynamic simulations to study the dynamics of planetesimals trapped in the first-order resonances, and reexamine the analytical expressions of the equilibrium eccentricity  ... 
arXiv:1904.07552v3 fatcat:7am65xjgsvepjhmwm3depkrzyy

First-Order Phase Transition in Three-Dimensional QED with Chern-Simons Term

K. -I. Kondo, P. Maris
1995 Physical Review Letters  
In the presence of a Chern--Simons term, the chiral phase transition turns out to be first order, in sharp contrast to the phase transition in pure three-dimensional QED.  ...  We have studied the chiral phase transition in three-dimensional QED in the presence of a Chern--Simons term for the gauge field.  ...  In this letter we show that there is a rst-order chiral phase transition in the presence of an explicit CS term.  ... 
doi:10.1103/physrevlett.74.18 pmid:10057688 fatcat:3i5oltcxw5avtglop54cadgrke

Identifiability at the boundary for first-order terms

Russell M. Brown, Mikko Salo
2006 Applicable Analysis  
We also consider a steady state heat equation with convection term ∆+2W ·∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map.  ...  Ours are not the first results on identifiability at the boundary for first-order terms.  ...  The identifiability at the boundary is often a first step in recovering the coefficients in the interior.  ... 
doi:10.1080/00036810600603377 fatcat:wdui3oeo35asxdnu6liijzm2rm
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