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We describe the orthogonal to the group of principal ideles with respect to the global tame symbol pairing on the group of ideles of a smooth projective algebraic curve over a field. [ABSTRACT FROM AUTHOR]

We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a certain positive projective model structure on spectra, where positivity basically means the truncation of the zero level. The localization is by the set of stabilizing morphisms or their truncated version. [ABSTRACT FROM AUTHOR]

We prove that the higher-dimensional Contou-Carrère symbol is invariant under the continuous automorphisms of algebras of iterated Laurent series over a ring. Applying this property, we obtain a new explicit formula for the higher-dimensional Contou-Carrère symbol. Unlike previously known formulas, this formula holds over an arbitrary ring, not necessarily a Q-algebra, and its derivation does not employ algebraic K-theory. [ABSTRACT FROM AUTHOR]

We study symmetric powers in the homotopy categories of abstract closed symmetric monoidal model categories, in both unstable and stable settings. As an outcome, we prove that symmetric powers preserve the Nisnevich and étale homotopy type in the unstable and stable motivic homotopy theories of schemes over a base. More precisely, if f is a weak equivalence of motivic spaces, or a weak equivalence between positively cofibrant motivic spectra, with respect to the Nisnevich or étale topology, then all symmetric powers Sym n ( f ) are weak equivalences too. This gives left derived symmetric powers in the corresponding motivic homotopy categories of schemes over a base, which aggregate into a categorical λ -structures on these categories. [ABSTRACT FROM AUTHOR]

We construct the so-called polar complex for an arbitrary locally free sheaf on a smooth variety over a field of characteristic zero. This complex is built from logarithmic forms on all irreducible subvarieties with values in a locally free sheaf.We prove that cohomology groups of the polar complex are canonically isomorphic to the cohomology groups of the locally free sheaf. Relations of the polar complex with Rost's cycle modules, algebraic cycles, Cousin complex, and adelic complex are discussed. In particular, the polar complex is a subcomplex in the Cousin complex. One can say that the polar complex is a first-order pole part of the Cousin complex, providing a much smaller, but, in fact, quasiisomorphic subcomplex. [ABSTRACT FROM AUTHOR]

Abstract: We study isomonodromicity of systems of parameterized linear differential equations and related conjugacy properties of linear differential algebraic groups by means of differential categories. We prove that isomonodromicity is equivalent to isomonodromicity with respect to each parameter separately under a filtered-linearly closed assumption on the field of functions of parameters. Our result implies that one does not need to solve any non-linear differential equations to test isomonodromicity anymore. This result cannot be further strengthened by weakening the requirement on the parameters as we show by giving a counterexample. Also, we show that isomonodromicity is equivalent to conjugacy to constants of the associated parameterized differential Galois group, extending a result of P. Cassidy and M. Singer, which we also prove categorically. We illustrate our main results by a series of examples, using, in particular, a relation between the Gauss–Manin connection and parameterized differential Galois groups. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to construct non-trivial elements in the Abel–Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a subfield in . [Copyright &y& Elsevier]

Abstract: Generalizing Atiyah extensions, we introduce and study differential abelian tensor categories over differential rings. By a differential ring, we mean a commutative ring with an action of a Lie ring by derivations. In particular, these derivations act on a differential category. A differential Tannakian theory is developed. The main application is to the Galois theory of linear differential equations with parameters. Namely, we show the existence of a parameterized Picard–Vessiot extension and, therefore, the Galois correspondence for many differential fields with, possibly, non-differentially closed fields of constants, that is, fields of functions of parameters. Other applications include a substantially simplified test for a system of linear differential equations with parameters to be isomonodromic, which will appear in a separate paper. This application is based on differential categories developed in the present paper, and not just differential algebraic groups and their representations. [Copyright &y& Elsevier]

The idea to form C 60 /CuPc dispersed nanoheterojunctions by photoexcitation of a mixture of C 60 and CuPc nanoparticles has been realized. The electronic structure of the nanoparticles and dispersed nanoheterojunctions formed in the mixture has been characterized by UV-Vis spectroscopy and the comparing with known experimental ultraviolet photoelectron spectra and theoretical models of electronic structure of these molecules. For the mixture of C 60 and CuPc nanoparticles in toluene and their coating layer on the quartz substrate the band offsets of the edges of CuPc VB and lowest unoccupied molecular orbital (LUMO) of C 60 band are ?E=1.55 eV and 1.4 eV, respectively. These results show clearly the presence of C 60 /CuPc dispersed nanoheterojunctions in the solution and on the quartz surface. [ABSTRACT FROM AUTHOR]

The experimental confirmation of the concept of the Si nanocrystallites self-formation in nanostructured Co layer (60 nm)/Si interface at the solid-state reaction between Si and Co with CoSi2 formation is presented. The following evidences have been obtained: (i) the nanostructured CoSi2 layer consists of CoSi2 particles with typical lateral size of 24–100.5 nm, separated by pores in Si, having typical depth of 0.4–6.7 nm and this relief determines the roughness of the interface layer with Si nanocrystallites embedded into CoSi2 matrix; (ii) the transverse optical (TO) phonon modes of Si nanocrystallites lattice are at wave numbers of 464 and 478 cm−1 and the vibration mode of Si&z.sbnd;Si bond is at 608 cm−1 for Si nanocrystallites of 2.5–4 nm size; (iii) the band gap of Si nanocrystallites equals Eg=1.23, 1.73, 2.74 eV in (Pt–Ir) tip-nanostructured CoSi2 layer/c-Si tunnel structures; (iv) the shape of the interface layer with these Si nanocrystallites stipulates the shape of the conductance (G)–voltage (V) curve with minimum at V=−0.6 V, which is typical for the metal-dielectric-semiconductor (MDS) structure (Si nanocrystallites as a dielectric).These arguments are further supported by our recent sensor characteristics studies on the nanostructured CoSi2 layer/c-Si structures with W probe. [Copyright &y& Elsevier]

The water-soluble fullerene C60 oxygen and hydroxyl group derivatives were prepared by means of C60 water solution visible light illumination and C60 toluene solution by ozonolysis. The experimental investigation was carried out by UV-Vis, IR, Raman spectroscopy, XPS, and AFM. The structure C60 derivatives in water solution (single molecules and its aggregates with hydrated shell, nanocrystals), chemical composition and electronic structure of C60 derivatives containing both hydroxyl groups and >C...O were studied. A comparison of these spectra for C60 derivatives water solution with the data for their adsorbed layers allowed to detection a series of oxidation products. This data for the C60 derivatives is the basis of development of efficient photosensitizers. [ABSTRACT FROM AUTHOR]

Magneto-optical methods were applied for investigating the properties of Co/Cu/Co spin-valves deposited on Si substrate. The effects of electron transport and irradiation on remagnetization of such ferromagnetic (spin-valve)/semiconductor structures were studied for various thicknesses of ferromagnetic and non-magnetic layers. [Copyright &y& Elsevier]