Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predi...

In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be realized as the lengths of certain specia...

Previous research has shown that households are sensitive to commuting distance. In particular, households beyond a threshold distance move closer to the job when they change residence. The questions which motivate this paper are-how does race affect the probability of moving closer to the job when households change residence, and is there a trade off between commuting distance and neighborhood...

In this paper, we analyze the spatial distribution of US employment and earnings against an urban wage-efficiency background, where leisure and effort at work are complementary. Using data from the American Time Use Survey (ATUS) for the period 2003-2014, we analyze the spatial distribution of employment across metropolitan areas. We also empirically study the relationship between individual ea...

We discuss the concept of what we refer to as semi-commuting linear differential operators. Such operators hold commuting operators as a special case. In particular, we discuss a heuristic by which one may construct such operators. Restricting to the case in which one such operator is of degree two, we construct families of linear differential operators semi-commuting with some named operators ...

OBJECTIVES Promoting active commuting is viewed as one strategy to increase physical activity and improve the energy balance of more sedentary individuals thereby improving health outcomes. However, the potential effectiveness of promotion policies may be seriously undermined by the endogenous choice of commute mode. Policy to promote active commuting will be most effective if it can be demonst...

In this paper, we study properties of extended commuting operators. particular, provide the polar decomposition product (?,?)-commuting operators where ? and are real numbers with ?? > 0. Furthermore, find restriction for quasihyponormal to be quasihyponormal. We also give spectral local relations between ?-commuting Moreover, show that a unilateral shift representable as weighted composition

BACKGROUND Long commutes by car are stressful. Most research studying health effects of commuting have summarized cross-sectional data for large regions. This study investigated whether the levels of stress and individual characteristics among 30-60 min car commuters were similar across different places within the county of Scania, Sweden, and if there were changes over time. METHODS The stud...

The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps) associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table). The need of a canonical chain of groups to establish a complete set of commuting operators is emphasize...