Rovibrational laser jet-cooled spectroscopy of the NH3–Ar complex in the ν2 umbrella region of NH3: comparison between new infrared data and an ab initio calculated spectrum*

ABSTRACT

Five ortho and para bands of the ν₂ umbrella mode of the NH₃–Ar van der Waals complex have been recorded at high resolution using jet-cooled infrared laser spectroscopy. A rovibrational analysis provides accurate band centres and upper state rotational constants for the Π_s(j?=?1,k?=?0)?←?Σ_a(j,k?=?0) and Σ_s(j?=?1,k?=?0)?←?Σ_a(j,k?=?0) ortho bands. The puzzling para bands observed in the region of the lower and upper components of the inversion splitting doublet have been assigned by comparison with rovibrational and tunnelling levels and transitions calculated ab initio. The latter calculations are based on the four-dimensional potential energy surface reported by Loreau et al. [J. Chem. Phys. 141, 224303 (2014)], which takes explicitly into account the umbrella motion of the ammonia molecule. The very good agreement found between Π_s/a,lower(j?=?1,k?=?1)?←?Σ_a(j?=?1,k?=?1) and Π_s/a,upper(j?=?1,k?=?1)?←?Σ_s(j?=?1,k?=?1) experimental and calculated transitions has been exploited to determine precisely two different inversion splittings in the ν₂ state (32.003(1) and 36.008(1)?cm^?1) from extrapolated Q(0) line frequencies and to obtain a qualitative picture of Coriolis couplings present in both the ν₂?=?0 and ν₂?=?1 states.     

Proper Efficiency in Vector Optimization on Real Linear Spaces

In this paper, we use an algebraic type of closure, which is called vector closure, and through it we introduce some adaptations to the proper efficiency in the sense of Hurwicz, Benson, and Borwein in real linear spaces without any particular topology. Scalarization, multiplier rules, and saddle-point theorems are obtained in order to characterize the proper efficiency in vector optimization with and without constraints. The usual convexlikeness concepts used in such theorems are weakened through the vector closure.     

A categorical characterization of varieties

A simple, direct proof of the following characterization of varieties of (finitary) algebras is presented: a cocomplete category is equivalent to a variety iff it has an algebraic generator, i.e., a regular generator which is exactly projective and finitely generated. This improves somewhat a recent restatement, due to Pedicchio and Wood, of the classical characterization theorem of Lawvere. A bijective correspondence between algebraic theories and algebraic generators is established.     

Injective hulls are not natural

In a category with injective hulls and a cogenerator, the embeddings into injective hulls can never form a natural transformation, unless all objects are injective. In particular, assigning to a field its algebraic closure, to a poset or Boolean algebra its Mac-Neille completion, and to an R-module its injective envelope is not functorial, if one wants the respective embeddings to form a natural transformation. Received January 21, 2000; accepted in final form August 10, 2001. RID="h1" RID="h2" RID="h3" ID="h1"The hospitality of York University is gratefully acknowledged by the first author. ID="h2"Third author partially supported by the Grant Agency of the Czech Republic under Grant no. 201/99/0310, and the hospitality of York University is also acknowledged. ID="h3"Partial financial assistance by the Natural Sciences and Engineering Councel of Canada is acknowledged by the fourth author.     

Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey.     

Algebraic and differential equations for spinning particles on the sphere

We revise the mathematical formulation of the theory of a particle in a spherical surface, in particular we show that the system of relations between two sets of generators of theSU(2) group lead to a formulation of nonrelativistic spinone half theory on the sphereS ³. First we examine various possibilities to extend this approach in the case of relativistic motion, then we give formulation for the Dirac and Maxwell equations in homogeneous space-time where a geometrical point is associated with the notion of relativistic top. Finally we formulate these equations in aS ³ surface embedded inR ⁵, using spherical system of coordinates, and examine the eigenvalue problem.     

Influence of the coulomb interaction on the liquid-gas phase transition and nuclear multifragmentation

The liquid-gas phase transition is analyzed from the topologic properties of the event distribution in the observables space. A multicanonical formalism allows one to directly relate the standard phase transition with neutral particles to the case where the nonsaturating Coulomb interaction is present, and to interpret the Coulomb effect as a deformation of the probability distributions and a rotation of the order parameter. This formalism is applied to a statistical multifragmentation model and consequences for the nuclear multifragmentation phase transitions are drawn.     

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.     

Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.