A repetition-free hypersequent calculus for first-order rational Pavelka logic

We present a hypersequent calculus \text{G}^3\text{\L}\forall for first-order infinite-valued {\L}ukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In \text{G}^3\text{\L}\forall, there are no structural rules, all the rules are invertible, and designations of multisets of formulas are not repeated in any premise of the rules. The calculus \text{G}^3\text{\L}\forall proves any sentence that is provable in at least one of the previously known hypersequent calculi for the given logics. We study proof-theoretic properties of \text{G}^3\text{\L}\forall and thereby provide foundations for proof search algorithms.Comment: 21 pages; corrected a misprint, added an appendix containing errata to a cited articl

Comparing Calculi for First-Order Infinite-Valued Łukasiewicz Logic and First-Order Rational Pavelka Logic

We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for one of the hypersequent calculi considered.

Spin Asymmetry and Gerasimov-Drell-Hearn Sum Rule for the Deuteron

An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes photodisintegration, single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed whereas for double pion production an effective Lagrangean approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 $\mu$b to be compared to the sum rule value 0.65 $\mu$b.Comment: 4 pages, 5 figures, revtex

Numerical modelling of heat transfer during impact of a molten droplet on a surface

SPH-based numerical technique for modelling of impact of molten drops on a surface with heat transfer and phase transitions effects is proposed. Computational algorithm uses SPH with procedure of restoring of particle consistence and variational approach to calculation of acceleration field. Also, boundary algorithm for free and contact surfaces in 3D setting are develope

The interaction of the projectile with moving plates and rods

The study of the problem of protecting the elements of constructions from impact loadings is very important due to the need of constant perfection of the means of shock-wave impact on the objects of modern technology. The problem of creating a reliable protective system dictates necessity of studying different ways to counteract to high-velocity elongated projectiles. The interaction of projectiles with plates and rods which are thrown towards by HE is investigated. The strain and fracture of the projectile sharply reduce its penetrating ability

Determination of gas temperature in the plasmatron channel according to the known distribution of electronic temperature

An analytical method to calculate the temperature distribution of heavy particles in the channel of the plasma torch on the known distribution of the electronic temperature has been proposed. The results can be useful for a number of model calculations in determining the most effective conditions of gas blowing through the plasma torch with the purpose of heating the heavy component. This approach allows us to understand full details about the heating of cold gas, inpouring the plasma, and to estimate correctly the distribution of the gas temperature inside the channel

Poisson geometry of monic matrix polynomials

We study the Poisson geometry of the first congruence subgroup $G_1[[z^{-1}]]$ of the loop group $G[[z^{-1}]]$ endowed with the rational r-matrix Poisson structure for $G=GL_m$ and $SL_m$. We classify all the symplectic leaves on a certain ind-subvariety of $G_1[[z^{-1}]]$ in terms of Smith Normal Forms. This classification extends known descriptions of symplectic leaves on the (thin) affine Grassmannian and the space of $SL_m$-monopoles. We show that a generic leaf is covered by open charts with Poisson transition functions, the charts being birationally isomorphic to products of coadjoint $GL_m$ orbits. Finally, we discuss our results in terms of (thick) affine Grassmannians and Zastava spaces.Comment: Version 2: results extended, proofs simplified. To appear in IMR