Obstructions to lifting automorphisms of free algebras

ABSTRACT

A monomial basis and a filtration of subalgebras for the universal enveloping algebra 𝔘(𝔤 _l ) of a complex simple Lie algebra 𝔤 _l of type A _l is given in this note. In particular, a new multiplicity formula for the Weyl module V(λ) of 𝔘(𝔤 _l ) is obtained in this note.     

A presentation for reduced extended affine weyl groups

In 1985 K. Saito [Sal] introduced the concept of an extended affine Weyl group (EAWG), the Weyl group of an extended affine root system (EARS). In [A2, Section 5J, we gave a presentation called “a presentation by conjugation” for the class of EAWGs of index zero, a subclass of EAWGs. In this paper we will give a presentation wh.ich we call a “generalized present.ation by conjugation” for the class of reduced EAWGs. If the extended affine Weyl group is of index zero this presentation reduces to “a presentation by conjugation”. Our main result states that when the nullity of the EARS is 2, these two presentations coincide that is, EAWGs of nullity 2 have “a presentation by conjugation”. In [ST] another presentation for EAWGs of nullity 2 is given.     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

Projective Quantales: A General View

Following B. Banaschewski’s work on so-called K-flat projective frames, we treat their non-commutative generalization, i.e. K-flat projective quantales. Besides a categorical definition of a K-flat projective quantale we also give an elementary characterization in terms of a binary relation on the quantale, and we prove that K-flat projective quantales are precisely the coalgebras for a certain comonad on the category of quantales. Finally we define and study a natural notion of K-coherentness for quantales. Financial Support of the Ministry of Education of the Czech Republic under the project MSM0021622409 is gratefully acknowledged.     

The middleman as a panacea for supply chain coordination problems

The prevalence of intermediaries (middlemen) in supply chains is often seen as a dying remnant of less efficient times. Despite predictions that supply chains will rapidly “cut out the middleman” as technological advances have eased logistics, middlemen have continued to thrive. In this paper, we demonstrate a transaction role of middlemen that may help clarify their staying power. In a model with self-interested decision-making by both a manufacturer and a retailer, wherein incentive misalignment creates investment and production inefficiencies, we show that the integrated (first-best) outcome can be achieved with simple cost-based contracts if and only if a middleman is present. We further show that the approach of utilizing a middleman to fully coordinate the supply chain is robust in that it can be applied to a variety of circumstances discussed in the literature, including multilateral investment/effort choices, multiple product providers, and logistical investments made by the middleman.     

A cleaner and simple spectrophotometric micro-fluidic procedure for copper determination using nitroso-R salt as chromogenic agent

A cleaner and simple spectrophotometric method using microflow analysis (muFA) was performed. It consisted of a T-junction with microcoil on a polymethyl methacrylate (PMMA) chip which was fabricated by laser ablation and a molded polydimethylsiloxane (PDMS) as top plate. The fabricated PMMA chip was integrated with light emitting diode (LED) as light source and spectrometer as detector. The proposed device was applied to determining copper in water samples using nitroso-R salt as chromogenic reagent at 495nm. It was found that the proposed muFA system was with less reagents and samples consumption with tiny waste generation. The relative standard deviation (R.S.D.) was less than 2% (n=11) with the percentage recovery of 98.0+/-1.7% (n=7). The linear range for determination of copper in water samples was over the range of 0.05-3.0mugmL(-1) with a correlation coefficient (r(2)) of 0.999. The limit of detection (3sigma) was 47ngmL(-1) with a sample throughput of 30h(-1).     

Primitive permutation groups with a regular subgroup

This paper starts the classification of the primitive permutation groups (G,Ω) such that G contains a regular subgroup X. We determine all the triples (G,Ω,X) with soc(G) an alternating, or a sporadic or an exceptional group of Lie type. Further, we construct all the examples (G,Ω,X) with G a classical group which are known to us. Our particular interest is in the 8-dimensional orthogonal groups of Witt index 4. We determine all the triples (G,Ω,X) with . In order to obtain all these triples, we also study the almost simple groups G with GPΩ_2n+1(q). The case GU_n(q) is started in this paper and finished in [B. Baumeister, Primitive permutation groups of unitary type with a regular subgroup, Bull. Belg. Math. Soc. 112 (5) (2006) 657–673]. A group X is called a Burnside-group (or short a B-group) if each primitive permutation group which contains a regular subgroup isomorphic to X is necessarily 2-transitive. In the end of the paper we discuss B-groups.     

Extreme softness of brain matter in simple shear

We show that porcine brain matter can be modelled accurately as a very soft rubber-like material using the Mooney–Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments performed on small rectangular fresh samples (2.5 cm³ and 1.1 cm³) at quasi-static strain rates. They revealed a linear shear stress–shear strain relationship $(R^2>0.97)$, characteristic of Mooney–Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting effect of non-linear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.