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We examine whether some well-known properties of partial recursive functions are valid for ITBM-computable functions, i.e., functions which can be computed with infinite time Blum–Shub–Smale machines. It is shown that properties of graphs of ITBM-computable functions differ from the usual properties of graphs of partial recursive functions. All possible ranges of ITBM-computable functions are described, and we consider the existence problem for ITBM-computable bijections between ITBM-computable sets of the same cardinality.

Based on the results of triaxial tests for sands of various particle-size distribution, a statistical assessment of the dependence of Reynolds dilatancy on the parameters of density and stress state was carried out. An improved model, which takes into account the dependence of the dilatancy angle on the current and residual void ratios and the effective stress level, is proposed. Recommendations are given on the use of research results in the practice of geotechnical calculations.

A new monomer containing thermosetting groups of two types, namely, propargyl ether and phthalonitrile, in the structure of the molecule was synthesized and studied. It was found that thermal polymerization was accompanied by the degradation of the monomer with propargyl ether decomposition. This problem can be solved using catalysts based on Cu(i) favoring the polymerization at both the propargyl group and phthalonitrile fragments. The cured monomer has a non-porous structure and high thermal properties (Vicat softening temperature 395 °C, T5% 451 °C). The low viscosity of the melt (

We consider two kinds of reducibilities on finite families of predicates on a countable set: the definability of predicates and their complements of one family via another by means of existential formulas with parameters and the same definability on isomorphism types of families. Ordered structures of degrees generated by families of unary predicates are described. It is proved that for both reducibilities, there exist continuum many minimal nonzero degrees.

The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of investigation in computable model theory. Here we focus on the lattice structure of computably enumerable substructures of a given canonical computable structure. In particular, for a Turing degree d, we investigate the groups of d-computable automorphisms of the lattice of d-computably enumerable vector spaces, of the interval Boolean algebra Bη of the ordered set of rationals, and of the lattice of d-computably enumerable subalgebras of Bη. For these groups, we show that Turing reducibility can be used to substitute the group-theoretic embedding. We also prove that the Turing degree of the isomorphism types for these groups is the second Turing jump d′′ of d.

It is proved that the ordinal ω1cannot be embedded into a preordering Σ-definable with parameters in the hereditarily finite superstructure over the real numbers. As a corollary, we obtain the descriptions of ordinals Σ-presentable over$$ \mathbb{H}\mathbbm{F} $$(ℝ) and of Godel constructive sets of the form Lα. It is also shown that there are no Σ-presentations of structures of T-, m-, 1- and tt-degrees.

Lasing and spectroscopic properties of an LiY0.3Lu0.7F4:Pr3+ crystal grown by the Bridgman–Stockbarger method were investigated in detail. Absorption and luminescence spectra were recorded using polarized light. Lifetimes of excited states 3PJ were determined. Absorption and emission transition intensities were calculated according to f–f-transition intensity theory taking into account interconfiguration interaction. Stimulated emission transverse cross sections were determined using the Fuchtbauer–Ladenburg method. Pumping by an InGaN laser diode produced continuous-wave laser generation at 522.6 nm (3P1 → 3H5) in Pr-doped mixed fluoride crystals with a maximum output power of 0.38 W and a slope efficiency of 19%.

It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over ℍ𝔽(ℝ). It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.

Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM) are characterized via iterated Turing jumps, and we propose a normal form for these functions. It is also proved that the set of ITBM computable reals coincides with ℝ∩L ωω.

Measurements of the $\pi^{\pm}$, $K^{\pm}$, and proton double differential yields emitted from the surface of the 90-cm-long carbon target (T2K replica) were performed for the incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS using data collected during 2010 run. The double differential $\pi^{\pm}$ yields were measured with increased precision compared to the previously published NA61/SHINE results, while the $K^{\pm}$ and proton yields were obtained for the first time. A strategy for dealing with the dependence of the results on the incoming proton beam profile is proposed. The purpose of these measurements is to reduce significantly the (anti)neutrino flux uncertainty in the T2K long-baseline neutrino experiment by constraining the production of (anti)neutrino ancestors coming from the T2K target.

We introduce a class of existentially Steinitz structures containing, in particular, the fields of real and complex numbers. A general result is proved which implies that if $$ \mathfrak{M} $$ is an existentially Steinitz structure then the following structures cannot be embedded in any structure Σ-presentable with trivial equivalence over ℍ $$ \mathbb{F} $$ ( $$ \mathfrak{M} $$ ): the Boolean algebra of all subsets of ω, its factor modulo the ideal consisting of finite sets, the group of all permutations on ω, its factor modulo the subgroup of all finitary permutations, the semigroup of all mappings from ω to ω, the lattice of all open sets of real numbers, the lattice of all closed sets of real numbers, the group of all permutations of ℝ Σ-definable with parameters over ℍ $$ \mathbb{F} $$ (ℝ), and the semigroup of such mappings from ℝ to ℝ.

A series of symmetric and nonsymmetric tetrahydroindenyl zirconium complexes was obtained by the reaction of ZrCl4 or (CpTMS)ZrCl3 with lithium salts of the corresponding tetrahydroindenes. Activated with methylalumoxane, these complexes exhibit high activity in polymerization of ethylene (up to 6.8∙106 g PE (mol Zr h)–1), as well as in copolymerization of ethylene and hex-1-ene (up to 8.6∙106 g PE (mol Zr h)–1).

We study linear orders definable over negative and positive equivalences and their computable automorphisms. Special attention is paid to equivalences like η(α) = α 2∪id ω , α ⊆ ω. In particular, we describe orders that have negative presentations over such equivalences for co-enumerable sets α. Presentable and nonpresentable order types are exemplified for equivalences with various extra properties. We also give examples of negative orders with computable automorphisms whose inverses are not computable.

We prove the nonexistence of universal Σ-presentable linear orderings as well as the effective infinity of the class of Σ-presentations of the natural order on ℝ over an admissible set ℍ $$ \mathbb{F} $$ (ℝ).

It is proved that every two Σ-presentations of an ordered field $ \mathbb{R} $ of reals over $ \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) $ , whose universes are subsets of $ \mathbb{R} $ , are mutually Σ-isomorphic. As a consequence, for a series of functions $ f:\mathbb{R} \to \mathbb{R} $ (e.g., exp, sin, cos, ln), it is stated that the structure $ \mathbb{R} $ = 〈R, +, ×

We define the automorphism spectrum of a computable structure $$ \mathcal{M} $$ , a complexity measure of the symmetries of $$ \mathcal{M} $$ , and prove that certain sets of Turing degrees can be realized as automorphism spectra, while certain others cannot.

Under study are the automorphism groups of computable formal contexts. We give a general method to transform results on the automorphisms of computable structures into results on the automorphisms of formal contexts. Using this method, we prove that the computable formal contexts and computable structures actually have the same automorphism groups and groups of computable automorphisms. We construct some examples of formal contexts and concept lattices that have nontrivial automorphisms but none of them could be hyperarithmetical in any hyperarithmetical presentation of these structures. We also show that it could be happen that two formal concepts are automorphic but they are not hyperarithmetically automorphic in any hyperarithmetical presentation.

We study the isomorphism types of ordered structures of concepts for computable formal contexts from the point of view of computable model theory. We show that, although these structures could have the cardinality of the continuum or—if they are countable—could have an arbitrary high hyperarithmetical complexity, they are in some sense very close to computable orderings. We give some sufficient conditions for these orderings to have computable presentations. A full description is given of the isomorphism types of discrete concept lattices. We also give some counterexamples.

We compute the levels of complexity in analytical and arithmetical hierarchies for the sets of the Σ-formulas defining in the hereditarily finite superstructure over the ordered field of the reals the classes of open, closed, clopen, nowhere dense, dense subsets of ℝn, first category subsets in ℝn as well as the sets of pairs of Σ-formulas corresponding to the relations of set equality and inclusion which are defined by them. It is also shown that the complexity of the set of the Σ-formulas defining connected sets is at least Π11.

We study Σ-definability of countable models over hereditarily finite {ie193-01} superstructures over the field ℝ of reals, the field ℂ of complex numbers, and over the skew field ℍ of quaternions. In particular, it is shown that each at most countable structure of a finite signature, which is Σ-definable over {ie193-02} with at most countable equivalence classes and without parameters, has a computable isomorphic copy. Moreover, if we lift the requirement on the cardinalities of the classes in a definition then such a model can have an arbitrary hyperarithmetical complexity, but it will be hyperarithmetical in any case. Also it is proved that any countable structure Σ-definable over {ie193-03}, possibly with parameters, has a computable isomorphic copy and that being Σ-definable over {ie193-04} is equivalent to being Σ-definable over {ie193-05}.

The main result of the paper is describing all definable subsets in the group Aut 〈ℚ; ⩽〉 of all automorphisms of the natural ordering on the rational numbers, and also in groups of the form Aut I 〈ℚ; ⩽〉, where I is a Turing ideal consisting of elements of Aut 〈ℚ; ⩽〉 whose Turing degree is contained in I. This description is properly a uniform method for proving definability of all basic properties appearing in works on the theory of groups Aut I 〈ℚ; ⩽〉, as well as definability of a number of new sets. Also, we describe automorphism groups for such groups Aut I 〈ℚ; ⩽〉 and state a number of structure properties for elementary subgroups in Aut 〈ℚ; ⩽〉.

We introduce and study the notions of computable formal context and computable formal concept. We give some examples of computable formal contexts in which the computable formal concepts fail to form a lattice and study the complexity aspects of formal concepts in computable contexts. In particular, we give some sufficient conditions under which the computability or noncomputability of a formal concept could be recognized from its lattice-theoretic properties. We prove the density theorem showing that in a Cantor-like topology every formal concept can be approximated by computable ones. We also show that not all formal concepts have lattice-theoretic approximations as suprema or infima of families of computable formal concepts.

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations.

We introduce the notion of F-parametrizable model and prove some general results on elementary submodels of F-parametrizable models. Using this notion, we can uniformly characterize all elementary submodels for the field of real numbers and for the group of all permutations on natural numbers in the first order language as well as in the language of hereditarily finite superstructures. Assuming the constructibility axiom, we obtain a simpler characterization of elementary submodels of F-parametrizable models and prove some additional properties of the structure of their elementary submodels.

Use of a single term, i.e., “dew point,” for the quantitative characteristic of gas moisture expressed in units of a thermometric scale is substantiated. Features and conditions of the correct application of this term and also calculation methods for evaluating phase equilibrium parameters in a water in the condensed state-compressed gas system are described.

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a lightlike straight line., To appear in Geometriae Dedicata

A criterion is obtained for existence of two isomorphic but not hyperarithmetically isomorphic tuples in a hyperarithmetical model. This criterion is used to show that such a situation occurs in the models of well-known classes.

We study effective presentations and homeomorphisms of effective topological spaces. By constructing a functor from the category of computable models into the category of effective topological spaces, we show in particular that there exist homeomorphic effective topological spaces admitting no hyperarithmetical homeomorphism between them and there exist effective topological spaces whose autohomeomorphism group has the cardinality of the continuum but whose only hyperarithmetical autohomeomorphism is trivial. It is also shown that if the group of autohomeomorphisms of a hyperarithmetical topological space has cardinality less than 2ω then this group is hyperarithmetical. We introduce the notion of strong computable homeomorphism and solve the problem of the number of effective presentations of T0-spaces with effective bases of clopen sets with respect to strong homeomorphisms.

An experimental procedure for determining the solvent efficiency index in cleaning and degreasing is proposed and substantiated.

It is shown that the class of all possible families of Σ-subsets of finite ordinals in admissible sets coincides with a class of all non-empty families closed under e-reducibility and ⊕. The construction presented has the property of being minimal under effective definability. Also, we describe the smallest (w.r.t. inclusion) classes of families of subsets of natural numbers, computable in hereditarily finite superstructures. A new series of examples is constructed in which admissible sets lack in universal Σ-function. Furthermore, we show that some principles of classical computability theory (such as the existence of an infinite non-trivial enumerable subset, existence of an infinite computable subset, reduction principle, uniformization principle) are always satisfied for the classes of all Σ-subsets of finite ordinals in admissible sets.

Reducibility on admissible sets is studied which is a stronger version of the usual Σ-presentability of models. One of its informal prototypes is the interpretability of one computational device in the other. We obtain criteria of reducibility for recursively listed and pure sets, introduce the notion of jump, and prove exact boundaries for the ordinals of jumps. We also show that this reducibility is lifted to \(\mathbb{H}\mathbb{Y}\mathbb{P}\)-superstructures. Several results are proven on the relations of this reducibility to some known reducibilities.

Catalytic C-phenylation of methyl acrylate to methyl cinnamate with the Ph4SbX complexes (X = F, Cl, Br, OH, OAc, O2CEt) in the presence of the palladium compounds PdCl2, Pd(OAc)2, Pd2(dba)3, Pd(Ph3P)2Cl2, and Pd(dppf)Cl2 (dba is dibenzylideneacetone and dppf is bis(diphenylphosphinoferrocene)) was studied in organic solvents (MeCN, THF, DMF, MeOH, and AcOH). The highest yield of methyl cinnamate (73% based on the starting organometallic compound) was obtained for the Ph4SbCl—PdCl2 (1 : 0.04) system in acetonitrile.

We show that not each model can be replaced by a model of finite signature so that its automorphism group remains the same.

A new method for testing the gas-tightness of the basic material of insulators of sulfur hexafluoride (SF6) circuit breakers is justified. The law of penetration of gases through porous materials is considered analytically and investigated experimentally.

Neurotoxicological profile of actoprotector bromantane was studied on rats using S. Irwin's protocol of multi-test observation. The drug in doses of 30-300 mg/kg stimulated and in doses of 600-9600 mg/kg suppressed behavioral activity. Spontaneous motor activity increased after single treatment with bromantane in doses of 30-300 mg/kg, did not change after treatment in doses of 600 mg/kg, and was inhibited after treatment in doses above 600 mg/kg. In doses of 300-600 mg/kg the drug reduced pain sensitivity threshold and in doses above 600 mg/kg elevated the pain threshold and tactile sensitivity and reaction to knock. Bromantane induced mydriasis in all studied doses; in doses above 10 g/kg the preparation induced blepharoptosis. In doses above 5 g/kg bromantane slightly increased respiration rate and depth (Kussmaul-like respiration). In some animals bromantane in high doses induced regurgitation, diarrhea, and polyuria. Rectal temperature decreased by 0.5-1°C after virtually all doses. Behavioral effects of bromantane in doses of 30 and 600 mg/kg were associated with stimulation of the central dopamine and suppression of muscarinic and nicotinic cholinergic structures, n-cholinolytic effects of bromantane was more pronounced at a dose of 30 mg/kg than at a dose of 600 mg/kg.

Basics and results on groups of computable automorphisms are collected in [1].We recall the main definitions. A computable model $$\mathfrak{M} = \langle A,f_0^{n_0 } ,...;P_0^{m_0 } ,...\rangle $$ is a model in which A is a computable subset of the set ! of natural numbers, the mappings i 7! ni(the number of arguments of fi) and i ↦ mi (the number of arguments of Pi) are computable, andall operations fi and predicates Pi are computable uniformly in i. A computable automorphism ofa computable model M is an automorphism of \(\mathfrak{M}\) which is a computable function on its universe. Allsuch automorphisms form a group denoted by Autc \(\mathfrak{M}\).

A new RNA of about 900 nt was found in the virions of cocksfoot mottle virus (CfMV) and in infected plants by RNA hybridization and RT-PCR. Structural features suggested that this RNA is a defective interfering RNA (diRNA). The CfMV diRNA was shown to consist of a 35-nt 5′-terminal genomic region, which formed a hairpin, and a 3′-terminal genomic region, which included the coat protein (CP) gene lacking the first 120 nt.In vitro translation of the diRNA started at the third Met codon to produce truncated CP. The CfMV diRNA was assumed totrans-activate synthesis of the CP subgenomic RNA (sgRNA).

We construct a two-generated group with the co-recursively enumerable word problem that has no presentation by recursive permutations. This answers Higman’s question and exemplifies a group with the minimal possible number of generators. The previous article [1], in which that question was claimed settled, contains an incorrigible error.

The adamantane derivatives adapromine, midantane, and bromantane modify bioelectrical activity of brain cortex and subcortical structures. Neurophysiological effects of these preparations indicate that they possess psychostimulating activity. The effect of bromantane on electrical potentials from left and right sensorimotor cortex, dorsal hippocampus, and lateral hypothalamus was stronger than that of adapromine and midantane. This effect was observed as greater quantitative changes in the characteristics of electroencephalogram and changes practically in all characteristics of the power spectrum of electroencephalogram.