For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum ...algebras and to a new type of Noncommutative Geometry.
The Junggar Alatau forms the northern extent of the Tian Shan within the Central Asian Orogenic Belt (CAOB) at the border of SE Kazakhstan and NW China. This study presents the Palaeozoic–Mesozoic ...post-collisional thermo-tectonic history of this frontier locality using an integrated approach based on three apatite geo-/thermochronometers: apatite U–Pb, fission track and (U–Th)/He. The apatite U–Pb dates record Carboniferous–Permian post-magmatic cooling ages for the sampled granitoids, reflecting the progressive closure of the Palaeo-Asian Ocean. The apatite fission track (AFT) data record (partial) preservation of the late Palaeozoic cooling ages, supplemented by limited evidence for Late Triassic (∼230–210 Ma) cooling and a more prominent record of (late) Early Cretaceous (∼150–110 Ma) cooling. The apatite (U–Th)/He age results are consistent with the (late) Early Cretaceous AFT data, revealing a period of fast cooling at that time in resulting thermal history models. This Cretaceous rapid cooling signal is only observed for samples taken along the major NW–SE orientated shear zone that dissects the study area (the Central Kazakhstan Fault Zone), while Permian and Triassic cooling signals are preserved in low-relief areas, distal to this structure. This distinct geographical trend with respect to the shear zone, suggests that fault reactivation triggered the Cretaceous rapid cooling, which can be linked to a phase of slab-rollback and associated extension in the distant Tethys Ocean. Similar conclusions were drawn for thermochronology studies along other major NW–SE orientated shear zones in the Central Asian Orogenic Belt, suggesting a regional phase of Cretaceous exhumation in response to fault reactivation at that time.
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•Apatite U–Pb dates record Carboniferous-Permian post-magmatic cooling ages .•Apatite thermochronology record a prominent (late) Early Cretaceous cooling phase.•Cretaceous cooling is linked to NW–SE fault reactivation in the Central Kazakhstan fault zone.•Similar major shear zones record Cretaceous cooling, suggesting a regional event for Central Asia.•We interpret extensional fault reactivation, related with slab roll-back in the Tethys Ocean.
A precise measurement of the differential cross sections dσ/dΩ and the linearly polarized photon beam asymmetry Σ_{3} for Compton scattering on the proton below pion threshold has been performed with ...a tagged photon beam and almost 4π detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS setup. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-t dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: α_{E1}=10.99±0.16±0.47±0.17±0.34, β_{M1}=3.14±0.21±0.24±0.20±0.35; in units of 10^{-4} fm^{3} where the errors are statistical, systematic, spin polarizability dependent, and model dependent.
We define quantum determinants in quantum matrix algebras related to pairs of compatible braidings. We establish relations between these determinants and the so-called column and row determinants, ...which are often used in the theory of integrable systems. We also generalize the quantum integrable spin systems using generalized Yangians related to pairs of compatible braidings. We demonstrate that such quantum integrable spin systems are not uniquely determined by the “quantum coordinate ring” of the basic space
. For example, the “quantum plane”
yields two different integrable systems: rational and trigonometric.
We report a measurement of the spin polarization of the recoiling neutron in deuterium photodisintegration, utilizing a new large acceptance polarimeter within the Crystal Ball at MAMI. The measured ...photon energy range of 300-700 MeV provides the first measurement of recoil neutron polarization at photon energies where the quark substructure of the deuteron plays a role, thereby providing important new constraints on photodisintegration mechanisms. A very high neutron polarization in a narrow structure centered around E_{γ}∼570 MeV is observed, which is inconsistent with current theoretical predictions employing nucleon resonance degrees of freedom. A Legendre polynomial decomposition suggests this behavior could be related to the excitation of the d^{*}(2380) hexaquark.
As is known, in the reflection equation (RE) algebra associated with an involutive or Hecke
-matrix, the elements
(called quantum power sums) are central. Here,
is the generating matrix of this ...algebra, and
is the operation of taking the
-trace associated with a given
-matrix. We consider the problem of whether this is true in certain RE-like algebras depending on a spectral parameter. We mainly study algebras similar to those introduced by Reshetikhin and Semenov-Tian-Shansky (we call them algebras of RS type). These algebras are defined using some current
-matrices (i.e., depending on parameters) arising from involutive and Hecke
-matrices by so-called Baxterization. In algebras of RS type. we define quantum power sums and show that the lowest quantum power sum is central iff the value of the “charge”
in its definition takes a critical value. This critical value depends on the bi-rank
of the initial
-matrix. Moreover, if the bi-rank is equal to
and the charge
has a critical value, then all quantum power sums are central.
By generalized Yangians, we mean Yangian-like algebras of two different classes. One class comprises the previously introduced so-called braided Yangians. Braided Yangians have properties similar to ...those of the reflection equation algebra. Generalized Yangians of the second class, RTT-type Yangians, are defined by the same formulas as the usual Yangians but with other quantum R-matrices. If such an R-matrix is the simplest trigonometric R-matrix, then the corresponding RTT-type Yangian is called a q-Yangian. We claim that each generalized Yangian is a deformation of the commutative algebra Sym(gl(m)t
−1
) if the corresponding R-matrix is a deformation of the flip operator. We give the explicit form of the corresponding Poisson brackets.
We diagnosed the subtypes of renal cell carcinoma on needle core biopsies using a combination of histopathology and a molecular diagnostic algorithm.
Core biopsies were taken of renal tumors ...following nephrectomy. RNA was extracted and quantitative real-time polymerase chain reaction was performed for 4 gene products to differentiate among renal cell carcinoma subtypes. Histopathological diagnosis was achieved on a second core before and after obtaining the molecular diagnostic algorithm results.
Based on the nephrectomy diagnosis 6 of 77 renal masses were nonneoplastic and 71 were tumors, including 65 renal cell carcinoma/oncocytomas. The overall diagnostic accuracy using histology and our molecular diagnostic algorithm combined was 90.0% (70 of 77). Side by side comparison of histology vs molecular diagnostic algorithm was feasible for 60 classifiable renal cell carcinoma/oncocytomas (31 clear cell, 14 papillary renal cell carcinoma, 6 chromophobe renal cell carcinoma, 2 mucinous tubular and spindle cell carcinoma, and 7 oncocytoma). In this group histology correctly predicted the final histological subtype in 83.3% (50 of 60) of cores. Addition of the molecular diagnostic algorithm to histology improved the subtyping accuracy to 95% (57 of 60), whereas the molecular diagnostic algorithm alone was accurate in 50 of 60 cases (83.3%). Dividing these 60 specimens into clear cell and nonclear cell neoplasms, the addition of the molecular diagnostic algorithm improved the sensitivity for the diagnosis of clear cell carcinoma from 87.1% (27 of 31) to 100% and the negative predictive value from 87.5% to 100%.
Core biopsies of renal tumors provide adequate material for diagnosing and subtyping renal cell carcinoma. The addition of our molecular diagnostic algorithm to histology improved the diagnostic accuracy of core biopsies of renal masses.
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