The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on ${\mathbb C}P^3\times \Sigma_g \times {\mathbb T}^2$ with torsion $H-$flux and demonstrate in details the conjectured T-duality to ${\mathbb R}P^7\times X^3$ with no flux. In the simple case of $X^3 = {\mathbb T}^3$, T-dualizing the circles reduces to duality between ${\mathbb C}P^3\times {\mathbb T}^2 \times {\mathbb T}^2$ with $H-$flux and ${\mathbb R}P^7\times {\mathbb T}^3$ with no flux.Comment: 27 pages, tex file, no figure

Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravit

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds

Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are d-summable, the summability exponent d coinciding with the spectral dimension of the generalized laplacian operator associated with the regular harmonic structures. The characteristic tools of the noncommutative infinitesimal calculus allow to define a d-energy functional which is shown to be a self-similar conformal invariant.Comment: 16 page

Almost commuting self-adjoint matrices --- the real and self-dual cases

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover we prove that the same holds with self-dual in place of symmetric. The notion of self-dual Hermitian matrices is important in physics when studying fermionic systems that have time reversal symmetry. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin's famous theorem on almost commuting matrices. Similarly the self-dual case gives a version for matrices over the quaternions. We prove analogous results for element of real C^*-algebras of "low rank." In particular, these stronger results apply to paths of almost commuting Hermitian matrices that are real or self-dual. Along the way we develop a theory of semiprojectivity for real C^*-algebras.Comment: Expanded references. 33 page

CNS distribution, signalling properties and central effects of G-protein coupled receptor 4

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordInformation on the distribution and biology of the G-protein coupled receptor 4 (GPR4) in the brain is limited. It is currently thought that GPR4 couples to Gs proteins and may mediate central respiratory sensitivity to CO2. Using a knock-in mouse model, abundant GPR4 expression was detected in the cerebrovascular endothelium and neurones of dorsal raphe, retro-trapezoidal nucleus locus coeruleus and lateral septum. A similar distribution was confirmed using RNAscope in situ hybridisation. In HEK293 cells, overexpressing GPR4, it was highly constitutively active at neutral pH with little further increase in cAMP towards acidic pH. The GPR4 antagonist NE 52-QQ57 effectively blocked GPR4-mediated cAMP accumulation (IC50 26.8 nM in HEK293 cells). In HUVEC which natively express GPR4, physiological acidification (pH 7.4-7.0) resulted in a cAMP increase by ∼55% which was completely prevented by 1 μM NE 52-QQ57. The main extracellular organic acid, l-lactic acid (LL; 1-10 mM), suppressed pH dependent activation of GPR4 in HEK293 and HUVEC cells, suggesting allosteric negative modulation. In unanaesthetised mice and rats, NE 52-QQ57 (20 mg kg-1) reduced ventilatory response to 5 and 10% CO2. In anaesthetised rats, systemic administration of NE 52-QQ57 (up to 20 mg kg-1) had no effect on hemodynamics, cerebral blood flow and blood oxygen level dependent responses. Central administration of NE 52-QQ57 (1 mM) in vagotomised anaesthetised rats did not affect CO2-induced respiratory responses. Our results indicate that GPR4 is expressed by multiple neuronal populations and endothelium and that its pH sensitivity is affected by level of expression and LL. NE 52-QQ57 blunts hypercapnic response to CO2 but this effect is absent under anaesthesia, possibly due to the inhibitory effect of LL on GPR4.Biotechnology and Biological Sciences Research Council (BBSRC)Medical Research Council (MRC)Wellcome Trus

CNS distribution, signalling properties and central effects of G-protein coupled receptor 4

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordInformation on the distribution and biology of the G-protein coupled receptor 4 (GPR4) in the brain is limited. It is currently thought that GPR4 couples to Gs proteins and may mediate central respiratory sensitivity to CO2. Using a knock-in mouse model, abundant GPR4 expression was detected in the cerebrovascular endothelium and neurones of dorsal raphe, retro-trapezoidal nucleus locus coeruleus and lateral septum. A similar distribution was confirmed using RNAscope in situ hybridisation. In HEK293 cells, overexpressing GPR4, it was highly constitutively active at neutral pH with little further increase in cAMP towards acidic pH. The GPR4 antagonist NE 52-QQ57 effectively blocked GPR4-mediated cAMP accumulation (IC50 26.8 nM in HEK293 cells). In HUVEC which natively express GPR4, physiological acidification (pH 7.4-7.0) resulted in a cAMP increase by ∼55% which was completely prevented by 1 μM NE 52-QQ57. The main extracellular organic acid, l-lactic acid (LL; 1-10 mM), suppressed pH dependent activation of GPR4 in HEK293 and HUVEC cells, suggesting allosteric negative modulation. In unanaesthetised mice and rats, NE 52-QQ57 (20 mg kg-1) reduced ventilatory response to 5 and 10% CO2. In anaesthetised rats, systemic administration of NE 52-QQ57 (up to 20 mg kg-1) had no effect on hemodynamics, cerebral blood flow and blood oxygen level dependent responses. Central administration of NE 52-QQ57 (1 mM) in vagotomised anaesthetised rats did not affect CO2-induced respiratory responses. Our results indicate that GPR4 is expressed by multiple neuronal populations and endothelium and that its pH sensitivity is affected by level of expression and LL. NE 52-QQ57 blunts hypercapnic response to CO2 but this effect is absent under anaesthesia, possibly due to the inhibitory effect of LL on GPR4.Biotechnology and Biological Sciences Research Council (BBSRC)Medical Research Council (MRC)Wellcome Trus

НЕУПРАВЛЯЕМЫЙ ТОК ФОТОЭЛЕКТРОННОГО УМНОЖИТЕЛЯ ПРИ ФОТОЭМИССИОННОМ АНАЛИЗЕ ИЗЛУЧЕНИЯ

The dependence of photon energy from energy of photoelectron is base of photoemission radiation analysis. In such photoemission measurements except current of photocathode is always exist a reverse current from the collector of electrons to the photocathode in two-electrode sensors. There are various ways of reverse and uncontrolled current eliminating or reducing their influence. The constructive method is based on creating an electron-optical system of photoelectronic device, which would be a photoelectron energy analyzer. The second method – technological. However, it requires the manufacture of the photocathode and the dynode system in different vacuum chamber with subsequent connection to a single device in vacuum environment without exposure to the atmosphere. The purpose of this article is to determinate the effect of photoemission from photocathode chamber and the first dynode of photomultiplier on energy distribution of the photoelectrons from photocathode. To solve this problem authors obtained calibration curves for measuring pyrometer module ПИФ 4/2 with ФЭУ-114 as a sensor at supply voltage 1350 V and different decelerating voltages. The effect of illumination on the value of modulation coefficient on temperature k(T) and wavelength k(λ) is shown. In temperature measurements, this effect is evident in fact that at temperatures below 1400 K linear dependence ln k – T-1 is broken. Still this linear dependence is a necessary consequence of the fact that the measured temperature is color temperature. However, this calibration curve can be used to measure low temperature if the target measurements condition and calibration conditions are identical. In wavelength calibration, curve k(λ) at λ > 760 nm is two-valued, that doesn’t allow to identify monochromatic radiation by this method and bring in errors in temperature measurements. В основе фотоэмиссионного анализа излучения лежит зависимость энергии фотоэлектрона от энергии фотона. В фотоэмиссионных измерениях, кроме тока фотокатода, всегда присутствует обратный ток с коллектора электронов на фотокатод в двухэлектродных датчиках. Существуют различные способы устранения обратного и неуправляемого токов или уменьшения их влияния. Конструктивный способ основан на создании такой электронно-оптической системы фотоэлектронного прибора, которая являлась бы энергоанализатором фотоэлектронов. Второй способ – технологический. Он требует изготовления фотокатода и динодной системы в различных вакуумных камерах с последующим их соединением в единый прибор в вакуумной среде без экспозиции на атмосферу, но этот метод является весьма трудоемким и связан с изготовлением сложного высоковакуумного оборудования. Цель данной работы состояла в том, чтобы определить влияние фотоэмиссии из катодной камеры и с первого динода фотоэлектронного умножителя на распределение по энергиям фотоэлектронов фотокатода. Для решения поставленной задачи авторами были получены градуировочные кривые для измерительного модуля пирометра ПИФ4/2 с ФЭУ-114 в качестве датчика при напряжении питания 1350 В и разных тормозящих напряжениях Uт . Показано влияние засветки на значение коэффициента модуляции по температуре k(T) и длинам волн k(λ). При измерении температур это влияние проявляется в том, что при температурах ниже 1400 К нарушается линейная зависимость ln k от T-1 , которая является необходимым следствием того, что измеряемая температура – интегральная цветовая. Однако данную градуировочную кривую можно использовать для измерения низких температур в случае, если условия градуировки и измерения температуры объекта одинаковы. При градуировке по длинам волн кривая k(λ) при λ > 760 нм делается двузначной, что не позволяет идентифицировать этим методом монохроматическое излучение и вносит погрешность в измерение температуры. Таким образом, явление обратного тока следует учитывать при освещении ФЭУ, работающего в режиме сепарации фотоэлектронов по энергиям, как непрерывным, так и монохроматическим излучением.

ТЕМПЕРАТУРНЫЕ ИЗМЕРЕНИЯ ПРИ ИМПУЛЬСНОМ ЛАЗЕРНОМ ОБЛУЧЕНИИ С ВАРЬИРУЕМЫМ НАЧАЛЬНЫМ НАГРЕВОМ

The results of measuring the temperature in a platinum filament tape, pre-heated in vacuum by direct current and irradiated a millisecond laser pulse, are presented. Gradual increase of the previous heating at a constant power irradiation density allows to receive the melted layer of different thickness without a destruction of the tape. The measurement have been carried out by photoemission method at the time resolution of 5 μs under the method and apparatus error of 0,3 % и 0,5 %, respectively. Such a method of combined heating can be used in metrological measurements under a solid-liquid phase equilibrium temperature.Приведены результаты измерения температуры платины в виде ленточного тела накала, предварительно нагретого в вакууме постоянным током и облученного миллисекундным лазерным импульсом. Постепенное увеличение предварительного нагрева при постоянной плотности энергии лазерного импульса позволяет получать на поверхности платины слой расплава различной толщины без разрушения тела накала. Измерения выполнены фотоэмиссионным методом, временное разрешение 5 мкс, методическая и приборная погрешности 0,3 % и 0,5 %, соответственно. Метод может быть использован для получения температуры фазового равновесия при плавлении в метрологических измерениях