Z prawem na ty

S\u142owa kluczowe: dydaktyka prawa; teoria pa\u144stwa i prawa; filozofia prawa; poradniki dla nauczycieli \u2013 prawo; podstawy praw

Analytic Surgery of the zeta-determinant of the Dirac operator

We review the work of the authors and their collaborators on the decomposition of the zeta-determinant of the Dirac operator into the contribution coming from different parts of a manifold.Comment: final versio

General Spectral Flow Formula for Fixed Maximal Domain

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by the Cauchy data spaces. We provide rigorous definitions of the underlying concepts of spectral theory and symplectic analysis and give a full (and surprisingly short) proof of our General Spectral Flow Formula for the case of fixed maximal domain. As a side result, we establish local stability of weak inner unique continuation property (UCP) and explain its role for parameter dependent spectral theory.Comment: 22 page

Novel PI3Kγ Mutation in a 44-Year-Old Man with Chronic Infections and Chronic Pelvic Pain

A 44-year-old man is presented here with 14 years of chronic purulent sinusitis, a chronic fungal rash of the scrotum, and chronic pelvic pain. Treatment with antifungal therapy resulted in symptom improvement, however he was unable to establish an effective long-term treatment regimen, resulting in debilitating symptoms. He had undergone extensive work-up without identifying a clear underlying etiology, although Candida species were cultured from the prostatic fluid. 100 genes involved in the cellular immune response were sequenced and a missense mutation was identified in the Ras-binding domain of PI3Kγ. PI3Kγ is a crucial signaling element in leukotaxis and other leukocyte functions. We hypothesize that his mutation led to his chronic infections and pelvic pain

Mass-spectrometric studies of new 6-nitroquipazines—serotonin transporter inhibitors

Six synthesized 6-nitroquipazine derivatives were examined by electron ionization (EI) and electrospray ionization (ESI) mass spectrometry in positive and negative ion mode. The compounds exhibit high affinity for the serotonin transporter (SERT) and belong to a new class of SERT inhibitors. The EI mass spectra registered in negative ion mode showed prominent molecular ions for all the compounds studied. All EI mass spectra and all ESI mass spectra showed similar fragmentation pathways of molecular ions, but the pathways differed between EI and ESI. The differences were explained with the aid of theoretical evaluation of the stability of the respective radical ions (EI MS) and protonated ions (ESI MS)

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl