Search results for "First order"
showing 10 items of 70 documents
Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma
2017
The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L . Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L .
A constructive semantics for non-deducibility
2008
This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Unification in first-order transitive modal logic
2019
We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…
Structure and Phase Transitions in Ethylenediammonium Dichloride and its Salts with Antimony Trichloride
2000
During the mixing of ethylenediammonium dichloride and antimony trichloride except of reported earlier [NH3(CH2)2NH3]5(Sb2Cl11)2 · 4 H2O a new salt [NH3(CH2)2NH3](SbCl4)2 was obtained. The crystals are monoclinic at 295 K, space group C2/m, a = 13.829(3), b = 7.408(1), c = 7.588(2) A; β = 103.18(3)°; V = 756.9(3) A3; Z = 2; dc = 2.585, dm = 2.56(2) g · cm–3. The structure consists of anionic sublattice built of Sb2Cl82– units composed of two SbCl52– square pyramids connected by edge. The ethylenediammonium cations are located in anionic cavities. The cations are disordered. Each methylene carbon atom is split between two positions. The X-ray diffraction, DSC, TGA and dilatometric methods we…
Non-supersymmetric Extremal Black Holes: First-Order Flows and Stabilisation Equations
2013
We review the results of [1, 2] on reducing the second-order equations of motion for stationary extremal black holes in four-dimensional \({\textit{N}}\,=\,2\) supergravity to first-order flow equations and further to non-differential stabilisation equations.
Generalized transport coefficients in a gas with large shear rate
1987
We get a solution of the Bhatnagar-Gross-Krook (BGK) model kinetic equation by means of a perturbative expansion of a temperature gradient to study the transport properties in a gas with large shear rate. The irreversible fluxes are evaluated exactly to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. This dependence on shear rate is analysed and compared with previous results for several transport coefficients. Finally, we have found a solution for a simple model of constant collision frequency for which a large shear rate coexists with an arbitrary temperature gradient.
Flow properties and hydrodynamic interactions of rigid spherical microswimmers.
2017
We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals tha…
Maximale Konvergenzordnung bei der numerischen Lösung von Anfangswertproblemen mit Splines
1982
In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
A-stable spline-collocation methods of multivalue type
1989
In this paper the general classV of spline-collocation methods presented by Multhei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher.
First-order visual interneurons distribute distinct contrast and luminance information across ON and OFF pathways to achieve stable behavior
2022
The accurate processing of contrast is the basis for all visually guided behaviors. Visual scenes with rapidly changing illumination challenge contrast computation because photoreceptor adaptation is not fast enough to compensate for such changes. Yet, human perception of contrast is stable even when the visual environment is quickly changing, suggesting rapid post receptor luminance gain control. Similarly, in the fruit fly Drosophila, such gain control leads to luminance invariant behavior for moving OFF stimuli. Here, we show that behavioral responses to moving ON stimuli also utilize a luminance gain, and that ON-motion guided behavior depends on inputs from three first-order interneuro…