On computation of the first Baues--Wirsching cohomology of a freely-generated small category

The Baues--Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues--Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues--Wirsching cohomology whose kernel is the vector space of inner derivations.Comment: 11 page

Duality between quantum symmetric algebras

Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.Comment: 15 pages. Letters in Math. Phy., to appear soo

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres' theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres' theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.Comment: Aug 25 replacement has corrected margin width

D-Koszul algebras

AbstractIn this paper we study d-Koszul algebras which were introduced by Berger. We show that when d⩾3, these are classified by the Ext-algebra being generated in degrees 0, 1, and 2. We show the Ext-algebra, after regrading, is a Koszul algebra and present the structure of the Ext-algebra

The effects of graded levels of calorie restriction : III. Impact of short term calorie and protein restriction on mean daily body temperature and torpor use in the C57BL/6 mouse

GRANT SUPPORT This work was supported by BBSRC BB009953/1 awarded to JRS and SEM. PK and CD were funded by the Erasmus exchange programme. JRS, SEM, DD, CG, LC, JJDH, YW, DELP, DL and AD are members of the BBSRC China Partnership Award, BB/J020028/1.Peer reviewedPublisher PD

Tilting mutation of weakly symmetric algebras and stable equivalence

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a weakly symmetric algebra A, presented by a quiver with relations, we give a detailed description of the quiver and relations of the algebra obtained by mutating at a single loopless vertex of the quiver of A. In this form the mutation procedure appears similar to, although significantly more complicated than, the mutation procedure of Derksen, Weyman and Zelevinsky for quivers with potentials. By definition, weakly symmetric algebras connected by a sequence of tilting mutations are derived equivalent, and hence stably equivalent. The second aim of this article is to study these stable equivalences via a result of Okuyama describing the images of the simple modules. As an application we answer a question of Asashiba on the derived Picard groups of a class of self-injective algebras of finite representation type. We conclude by introducing a mutation procedure for maximal systems of orthogonal bricks in a triangulated category, which is motivated by the effect that a tilting mutation has on the set of simple modules in the stable category.Comment: Description and proof of mutated algebra made more rigorous (Prop. 3.1 and 4.2). Okuyama's Lemma incorporated: Theorem 4.1 is now Corollary 5.1, and proof is omitted. To appear in Algebras and Representation Theor

Viability of primordial black holes as short period gamma-ray bursts

It has been proposed that the short period gamma-ray bursts, which occur at a rate of $\sim 10 {\rm yr^{-1}}$, may be evaporating primordial black holes (PBHs). Calculations of the present PBH evaporation rate have traditionally assumed that the PBH mass function varies as $M_{{\rm BH}}^{-5/2}$. This mass function only arises if the density perturbations from which the PBHs form have a scale invariant power spectrum. It is now known that for a scale invariant power spectrum, normalised to COBE on large scales, the PBH density is completely negligible, so that this mass function is cosmologically irrelevant. For non-scale-invariant power spectra, if all PBHs which form at given epoch have a fixed mass then the PBH mass function is sharply peaked around that mass, whilst if the PBH mass depends on the size of the density perturbation from which it forms, as is expected when critical phenomena are taken into account, then the PBH mass function will be far broader than $M_{{\rm BH}}^{-5/2}$. In this paper we calculate the present day PBH evaporation rate, using constraints from the diffuse gamma-ray background, for both of these mass functions. If the PBH mass function has significant finite width, as recent numerical simulations suggest, then it is not possible to produce a present day PBH evaporation rate comparable with the observed short period gamma-ray burst rate. This could also have implications for other attempts to detect evaporating PBHs.Comment: 5 pages, 2 figures, version to appear in Phys. Rev. D with additional reference

Dynamics of the QCD String with Light and Heavy Quarks

The generalization of the effective action [1] of the quark--antiquark system in the confining vacuum is performed for the case of arbitrary quark masses. The interaction of quarks is described by the averaged Wilson loop for which we use the minimal area law asymptotics. The system is quantized by the path integral method and the quantum Hamiltonian is obtained. It contains not only quark degrees of freedom but also the string energy density. As well as in the equal masses case [1] two dynamical regimes are found [2]: for large orbital excitations ($l \gg 1$) the system is represented as rotating string, which leads to asymptotically linear Regge trajectories, while at small $l$ one obtains a potential-like relativistic or nonrelativistic regime. In the limiting cases of light-light and heavy-light mesons a unified description is developed [2]. For the Regge trajectories one obtains nearly straight-line patterns with the slope very close to $1/2 \pi \sigma$ and $1/ \pi\sigma$ correspondingly. The upper bound on the light quark(s) masses which doesn't change considerably this property of the trajectories is also found.Comment: 31 pages, preprint ITEP 62-9

Detonation E. O. S. patterns for several explosives

The available overdriven shockwave data for a number of explosives have been analyzed and compared. The data follow neither a constant gamma pattern nor the JWL EOS that fits expansion data to high accuracy. Modifications of the JWL function are proposed to correct for discrepancies and also to allow for the appropriate volume dependence of the Grueneisen constant indicated by previous and more recent work. The deviations from the JWL form of the equation of state appear directly above the CJ point for 9404 and PETN while Pentolite and TNT agree with this form over a portion of the Hugoniot. The comparisons with other experiments and a theoretical EOS indicate nonequilibrium behavior