p$^\dagger$q is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and realize proof-of-concept implementations of these rapid prototyping. Central this simple interface define strings second-quantized creation annihilation operators bring normal order with respect either the true vacuum state or Fermi vacuum. Tensor contractions over fully-c...

We investigate interlacing properties of zeros Laguerre polynomials Ln(α)(x) and Ln+1(α+k)(x), α>−1, where n∈N k∈{1,2}. prove that, in general, the these interlace partially not fully. The sharp t-interval within which two equal degree Ln(α+t)(x) are for every each α>−1 is 0<t≤ 2, [Driver K, Muldoon ME. Sharp interval polynomials. J Approx Theory, to appear.], consecutive Ln−1(α+t)(x) 0≤t≤ Comm...

It has been proved by Zuazua in the nineties that internally controlled semilinear 1D wave equation $\partial_{tt}y-\partial_{xx}y + g(y)=f 1_{\omega}$, with Dirichlet boundary conditions, is exactly controllable $H^1_0(0,1)\cap L^2(0,1)$ controls $f\in L^2((0,1)\times(0,T))$, for any $T>0$ and nonempty open subset $\omega$ of (0,1), assuming $g\in \mathcal{C}^1(\mathbb{R})$ does not grow faste...

chronic kidney disease is one of the most common complication of systemic lupus erythematosus, which if untreated can lead to  the end-stage renal disease (esrd). early diagnosis and adequate treatment of lupus nephritis (ln) is critical to prevent the chronic kidney disease incidence and to reduce the development of esrd. the treatment of ln has changed significantly over the past decade. in p...

The evaluation of integrals, a subject that had an important role in the 19 century, has been given a new life with the development of symbolic mathematics software such as Mathematica or Maple. The question of indefinite integrals was provided with an algorithmic approach beginning with work of J. Liouville [8] discussed in detail in Chapter IX of Lutzen [9]. A more modern treatment can be fou...

Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that PSAT (m+1)-tt = PSAT m-tt ) PSAT btt = PSAT m-tt and for all sets A FPA(m+1)-tt = FPAm-tt ) FPAbtt = FPAm-tt PA(m+1)-T = PAm-T ) PAbT = PAm-T FPA(m+1)-T = FPAm-T ) FPAbT = FPAm-T where PAm-tt is the set of languages computable by polynomial-time Turing machines that make m nonadaptiv...

The (multivalued) higher logarithms are interpreted, by studying their monodromy, as giving well-defined maps from P¿ — (3 points} into certain complex nilmanifolds with C*-actions. The purpose of this note is to exhibit a family of unipotent representations of Z * Z arising naturally from the monodromy of the higher logarithms ln¿. (see [4]), and thereby interpret each ln¿. as yielding a well-...

Language-like Optimal Linguistic universals: speakers share a universal conceptual repertoire, considering and categorizing spatial relations in a similar way, regardless of language. Coarse-grainedness (partition height) N a tu ra ln e s s ( p a rt it io n s il h o u e tt e ) Comparing across theoretically optimal k-term partitions, we take the system with the most tightly clustered categories...