Ranking Templates for Linear Loops

We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

The Role of Certain Species of Small Mammals in the Persistence of Natural Focality in the Territory of Forest-Steppe Zone of the Natural Tularemia Focus of the Stavropol Region

Epizootiological monitoring of the forest-steppe area of the natural tularemia focus in the Stavropol region has revealed that the role of particular species of small mammals in the persistence of natural tularemia focality is unequal. Epizootic activity of the focus in 1959-1970 was determined by the numerous species of rodents: Microtus arvalis , mice of Syvaemus genus and Mus musculus . In 1972-2010 there occurred significant changes in the grouping of the main tularemia agent carriers under the influence of strong anthropogenic pressure. Nowadays the leading role is played by the widely-spread and subsistent mice of Sylvaemus genus and C. suaveolens , the latter ones being responsible for 31.2 % of overall, isolated from small mammals, tularemia agent strains. In addition to this, epizootic significance of M. arvalis has greatly changed. Index of strains isolated from field vole has lowered from 55.3 up to 28.4. Numbers of M. arvalis and Mus musculus are continuously on the low level, which is due to the absence of favorable breeding conditions. It reduces their impact on the persistence of natural focality in the territory under surveillance significantly

NMR Study of Disordered Inclusions in the Quenched Solid Helium

Phase structure of rapidly quenched solid helium samples is studied by the NMR technique. The pulse NMR method is used for measurements of spin-lattice $T_1$ and spin-spin $T_2$ relaxation times and spin diffusion coefficient $D$ for all coexisting phases. It was found that quenched samples are two-phase systems consisting of the hcp matrix and some inclusions which are characterized by $D$ and $T_2$ values close to those in liquid phase. Such liquid-like inclusions undergo a spontaneous transition to a new state with anomalously short $T_2$ times. It is found that inclusions observed in both the states disappear on careful annealing near the melting curve. It is assumed that the liquid-like inclusions transform into a new state - a glass or a crystal with a large number of dislocations. These disordered inclusions may be responsible for the anomalous phenomena observed in supersolid region.Comment: 10 pages, 3 figure

On The Mobile Behavior of Solid 4^4He at High Temperatures

We report studies of solid helium contained inside a torsional oscillator, at temperatures between 1.07K and 1.87K. We grew single crystals inside the oscillator using commercially pure $^4$He and $^3$He-$^4$He mixtures containing 100 ppm $^3$He. Crystals were grown at constant temperature and pressure on the melting curve. At the end of the growth, the crystals were disordered, following which they partially decoupled from the oscillator. The fraction of the decoupled He mass was temperature and velocity dependent. Around 1K, the decoupled mass fraction for crystals grown from the mixture reached a limiting value of around 35%. In the case of crystals grown using commercially pure $^4$He at temperatures below 1.3K, this fraction was much smaller. This difference could possibly be associated with the roughening transition at the solid-liquid interface.Comment: 15 pages, 6 figure

A Survey of Satisfiability Modulo Theory

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches. We also cover quantifiers, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201

Local modes, phonons, and mass transport in solid 4^4He

We propose a model to treat the local motion of atoms in solid $^{4}$He as a local mode. In this model, the solid is assumed to be described by the Self Consistent Harmonic approximation, combined with an array of local modes. We show that in the bcc phase the atomic local motion is highly directional and correlated, while in the hcp phase there is no such correlation. The correlated motion in the bcc phase leads to a strong hybridization of the local modes with the T$_{1}(110)$ phonon branch, which becomes much softer than that obtained through a Self Consistent Harmonic calculation, in agreement with experiment. In addition we predict a high energy excitation branch which is important for self-diffusion. Both the hybridization and the presence of a high energy branch are a consequence of the correlation, and appear only in the bcc phase. We suggest that the local modes can play the role in mass transport usually attributed to point defects (vacancies). Our approach offers a more overall consistent picture than obtained using vacancies as the predominant point defect. In particular, we show that our approach resolves the long standing controversy regarding the contribution of point defects to the specific heat of solid $^{4}$He.Comment: 10 pages, 10 figure

A glassy contribution to the heat capacity of hcp 4^4He solids

We model the low-temperature specific heat of solid $^4$He in the hexagonal closed packed structure by invoking two-level tunneling states in addition to the usual phonon contribution of a Debye crystal for temperatures far below the Debye temperature, $T < \Theta_D/50$. By introducing a cutoff energy in the two-level tunneling density of states, we can describe the excess specific heat observed in solid hcp $^4$He, as well as the low-temperature linear term in the specific heat. Agreement is found with recent measurements of the temperature behavior of both specific heat and pressure. These results suggest the presence of a very small fraction, at the parts-per-million (ppm) level, of two-level tunneling systems in solid $^4$He, irrespective of the existence of supersolidity.Comment: 11 pages, 4 figure

Norbornadiene as a Universal Substrate for Organic and Petrochemical Synthesis

A wide range of rare polycyclic hydrocarbons can be obtained through catalytic processes involving  norbornadiene (NBD). The problem of selectivity is crucial for such reactions. The feasibility of controlling selectivity and reaction rate has been shown for cyclic dimerization, co-dimerization, isomerization and allylation of NBD. Kinetic rules have been scrutinized. Consistent mechanisms have been proposed. Factors affecting directions of the reactions and allowing us to obtain individual stereoisomers quantitatively, have been established. A series of novel unsaturated compounds has been synthesized; they incorporate a set of double bonds with different reactivity and can find an extremely wide range of applications

Measurement of the Pion Form Factor in the Energy Range 1.04-1.38 GeV with the CMD-2 Detector

The cross section for the process $e^+e^-\to\pi^+\pi^-$ is measured in the c.m. energy range 1.04-1.38 GeV from 995 000 selected collinear events including 860000 $e^+e^-$ events, 82000 $\mu^+\mu^-$ events, and 33000 $\pi^+\pi^-$ events. The systematic and statistical errors of measuring the pion form factor are equal to 1.2-4.2 and 5-13%, respectively.Comment: 5 pages, 2 figure

Computation in Real Closed Infinitesimal and Transcendental Extensions of the Rationals.

Abstract. Recent applications of decision procedures for nonlinear real arithmetic (the theory of real closed fields, or RCF) have presented a need for reasoning not only with polynomials but also with transcendental constants and infinitesimals. In full generality, the algebraic setting for this reasoning consists of real closed transcendental and infinitesimal extensions of the rational numbers. We present a library for computing over these extensions. This library contains many contributions, including a novel combination of Thom’s Lemma and interval arithmetic for representing roots, and provides all core machinery required for building RCF decision procedures. We describe the abstract algebraic setting for computing with such field extensions, present our concrete algorithms and optimizations, and illustrate the library on a collection of examples. 1 Overview and Related Work Decision methods for nonlinear real arithmetic are essential to the formal verification of cyber-physical systems and formalized mathematics. Classically, thes