Quantum number conservation in statistical models and its application top $$\bar p$$ -annihilatoin at rest

Zeitschrift für Physik C Particles and Fields - We investigate the role of exact quantum number conservation in small statistical systems and illustrate the consequences forp $$\bar p$$...     

Cross-Section Calculation of ( $${n,p}$$ ) and ( $${n,2n}$$ ) Reactions for High Temperature Reactors Construction Materials Tungsten and Rhenium

Physics of Atomic Nuclei - In this study, cross-section calculations for ( $$n,2n$$ ) and ( $$n,p$$ ) reactions of Tungsten isotopes and Rhenium isotopes have been investigated using different...     

Neutron Polarization Observables in $$d(\vec {\gamma },\vec {n})p$$ at Low Energies of Interest to Astrophysics

JETP Letters - A model-independent theoretical analysis of neutron polarization observables in $$d(\vec {\gamma },\vec {n})p$$ using circularly polarized photons at the range of energies of...     

Higher spin $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ s l 2 R-matrix from equivariant (co)homology

Letters in Mathematical Physics - We compute the rational $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ R-matrix acting in the product of two spin- $$\ell \over 2$$ ( $${\ell \in {\mathbb {N}}}$$ )...     

Analysis of Angular $$\boldsymbol{t{-}\gamma}$$ Correlations in the Reaction $${}^{\boldsymbol{27}}$$ Al $$\boldsymbol{(\alpha,t)^{28}}$$ Si(2 $${}^{\boldsymbol{+}}$$ )

Physics of Atomic Nuclei - Angular $$t$$ – $$\gamma$$ correlations measured earlier in the reaction $${}^{27}$$ Al $$(\alpha,t)^{28}$$ Si(2 $${}^{+}$$ ) occurring at $$E_{\alpha}=30.3$$ MeV...     

Investigation of Excitation of $${K}$$ Isomers $${}^{{179m2}}$$ Hf and $${}^{{180m}}$$ Hf in ( $${\gamma,\gamma^{\prime}}$$ ) Reactions

Physics of Atomic Nuclei - The weighted-average cross sections for $${}^{179m2}$$ Hf and $${}^{180m}$$ Hf population in ( $$\gamma,\gamma^{\prime}$$ ) reactions induced by gamma rays of...     

Lifshitz Tails for the Fractional Anderson Model

Journal of Statistical Physics - We consider the d-dimensional fractional Anderson model $$(-\Delta )^\alpha + V_\omega $$ on $$\ell ^2({\mathbb {Z}}^d)$$ where $$0<\alpha \leqslant 1$$....     

Experimental and Evaluated Data on the Photodisintegration of $${}^{{197}}$$ Au

Physics of Atomic Nuclei - The cross sections evaluated for the ( $$\gamma,1n$$ ) and ( $$\gamma,2n$$ ) partial photoneutron reactions on $${}^{\textrm{197}}$$ Au by means of objective physical...     

Finite State and Finite Stop Quantum Languages

We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition, the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq) and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. In this way, we establish two proper inclusion relations (fsqa) ⊂ (ftqa) and (icftq) ⊂ (vcftq), where the symbol means languages, and two infinite language hierarchies (fsqa) ⊂ (fsqa), (icftq) (icftq).     

Reliability of Results of Photonuclear Experiments for $${}^{58}$$ Ni

Physics of Atomic Nuclei - The reliability of experimental data on the cross sections ( $$\gamma,1n$$ ) and ( $$\gamma,2n$$ ) partial reaction cross sections measured for $${}^{58}$$ Ni nuclei in...     

Double Product Integrals and Enriquez Quantisation of Lie Bialgebras II: The Quantum Yang–Baxter Equation

For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra , let be the vector space of tensors over equipped with the Itô Hopf algebra structure derived from the associative multiplication in . It is shown that a necessary and sufficient condition that the double product integral satisfy the quantum Yang–Baxter equation over is that satisfy the same equation over the unital associative algebra got by adjoining a unit element to . In particular, the first-order coefficient r₁ of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of is where is the inverse of in we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on in the unital associative subalgebra of consisting of formal power series whose zero order coefficient lies in the space of symmetric tensors. The deformation coproduct acts on by conjugating the undeformed coproduct by and the coboundary structure r of is given by where is the flip.Mathematical Subject Classification (2000). 53D55, 17B62     

$${\mathsf{N}}$$ -Complexes as Functors,Amplitude Cohomology and Fusion Rules

We consider -complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology (called generalized cohomology by M. Dubois-Violette) only vanishes on injective functors providing a well defined functor on the stable category. For left truncated -complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive -complexes is proved to be isomorphic to an Ext functor of an indecomposable -complex inside the abelian functor category. Finally we show that for the monoidal structure of -complexes a Clebsch-Gordan formula holds, in other words the fusion rules for -complexes can be determined. This work has been supported by the projects PICT 08280 (ANPCyT), UBACYTX169, PIP-CONICET 5099 and the German Academic Exchange Service (DAAD). The second author is a research member of CONICET (Argentina) and a Regular Associate of ICTP Associate Scheme.     

An efficient and green reaction of isatins, 3-amino-1-phenyl-2-pyrazolin-5-one (3-amine-1H-pyrazole), and β-diketone in aqueous medium

Molecular Diversity - An efficient and green reaction of isatins, 3-amino-1-phenyl-2-pyrazolin-5-one (3-amine-1H-pyrazole), and $$\beta $$ -diketone in aqueous medium in the presence of $$\hbox...     

Counting Regions with Bounded Surface Area

Define a cubical complex to be a collection of integer-aligned unit cubes in d dimensions. Lebowitz and Mazel (1998) proved that there are between and complexes containing a fixed cube with connected boundary of (d − 1)-volume n. In this paper we narrow these bounds to between and . We also show that there are connected complexes containing a fixed cube with (not necessarily connected) boundary of volume n.     

Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators

We construct a continuous transition density of the semigroup generated by for and b in the Kato class on . For small time the transition density is comparable with that of the fractional Laplacian. Partially supported by KBN and MEN.     

The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra {\mathfrak{osp}(1|2n)}

It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters. NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). An erratum to this article can be found at     

The <Emphasis Type="Italic">N</Emphasis> = 1 Triplet Vertex Operator Superalgebras

We introduce a newfamily of C ₂-cofinite N = 1 vertex operator superalgebras , m ≥ 1, which are natural super analogs of the triplet vertex algebra family , p ≥ 2, important in logarithmic conformal field theory. We classify irreducible -modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible characters. Finally, we contemplate possible connections between the category of -modules and the category of modules for the quantum group , , by focusing primarily on properties of characters and the Zhu’s algebra . This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008). The second author was partially supported by NSF grant DMS-0802962.