39 research outputs found
Nicht konstruktiv beweisbare SĂ€tze der Analysis
Nach allgemeiner Ueberzeugung können gewisse SĂ€tze der Analysis nicht konstruktiv bewiesen werden. Man denke etwa an den folgenden Satz: Eine monotone und beschrĂ€nkte Folge a(n) von rationalen Zahlen konvergiert, d.h. es gibt eine solche ganzzahlige Funktion k(m), daĂ Unter einem konstruktiven Beweis dieses Satzes hĂ€tte man etwa die Angabe eines Verfahrens zu verstehen, das gestattet, die Funktion k(m) auf Grand der Folge a(n) rekursiv zu definieren. Wenn ein solcher Beweis vorlĂ€ge, wĂ€re insbesondere gezeigt, daĂ es zu einer rekursiv definierten Folge a(n) mit den verlangten Eigenschaften stets eine rekursiv definierbare Konvergenzfunktion k(m) gibt. Es soil nun im folgenden von einigen grundlegenden SĂ€tzen der reellen Analysis gezeigt werden, daĂ sie nicht konstruktiv bewiesen werden könnenâkonstruktiv in dem Sinn, der eben angedeutet wurde. Wir stĂŒtzen uns dabei auf die Begriffe der rekursiven und der berechenbaren Funktion; rekursive und berechenbare Funktionen sind zahlentheoretische Funktionen. Unter einer rekursiven Funktion möge vorlĂ€ufig eine primitiv rekursive Funktion verstanden werden (vgl. etwa D. Hilbert und P. Bernays [3], S.286); berechenbar meint berechenbar im Sinne von A. Church [1], S. C. Kleene [4], A. M. Turing [6]. Der Begriff der "konstruktiv definierten Funktionâ wird durch die Bestimmung als "rekursive Funktionâ eher eng, durch die Bestimmung als "berechenbare Funktionâ eher weit gefaĂt. Definition I. Eine Folge rationaler Zahlen Ί(n) heiĂt rekursiv,(berechenbar), wenn es solche rekursiven (berechenbaren) Funktionen Ï{n), Ï(n) und Ï(n) gibt, daĂ Ï(n) â§1 und . Definition II. Eine Folge Ί(n) von rationalen Zahlen heiĂt rekursiv (berechenbar) konvergent, wenn es eine solche rekursive (berechenbare) Funktion v(m) gibt, daĂ Wir werden zeigen (Satz I): Es gibt eine rekursive, monotone und beschrĂ€nkte Folge rationaler Zahlen, die nicht berechenbar konvergiert. Bei unserer Auffassungsweise ist darin enthalten, daĂ der zu Beginn erwĂ€hnte Satz nicht konstruktiv bewiesen werden kan
The Ring of Polyfunctions over
We study the ring of polyfunctions over a commutative ring with unit
element, i.e., the ring of functions which admit a polynomial
representative in the sense that for all .
This allows to define a ring invariant which associates to a commutative
ring with unit element a value in . The function
generalizes the number theoretic Smarandache function. For the ring
we provide a unique representation of polynomials
which vanish as a function. This yields a new formula for the number
of polyfunctions over . We also investigate algebraic
properties of the ring of polyfunctions over . In
particular, we identify the additive subgroup of the ring and the ring
structure itself. Moreover we derive a new formula for the size of the ring of
polyfunctions in several variables over .Comment: 22 page
Determination of islet cell antibodies using an ELISA system with a preparation of rat insulinoma (RIN A2) cells
An enzyme-linked immunosorbent assay (ELISA) was established for the detection of islet cell antibodies in human sera. The antigen was prepared from rat insulinoma (RIN A2) cells. Cells were dissociated in lysis buffer and the lysate was centrifuged at 100,000 x g. The supernatant was used to coat microtiter ELISA plates (10 micrograms protein/ml in PBS pH 7.2). Non-specific binding sites on the plates were blocked with 2% PBS-BSA. Human test sera were preabsorbed on separate plates using 2% PBS-BSA and incubated on precoated plates at an optimal dilution of 1/10 in 60 mM PBS for 60 min at 37 degrees C. Phosphatase-labeled anti-human IgG serum and phosphatase substrate were applied and the reaction was stopped by adding 3 M NaOH. Out of 90 sera from type I diabetic patients, 47 (52.2%) reacted in the new ELISA whereas none of 15 type II diabetics, 50 sera containing non-islet specific antibodies or 100 normal controls were positive. In the same group of patients, ICA were positive in 63.3%. When both, the ELISA and conventional ICA testing were applied, the number of positives was increased to 83%. The ICA-ELISA with the above described antigen preparation provides a well standardized and reproducible test method which is highly specific for type I diabetes. It may therefore be useful for large screening procedures
The German National Registry of Primary Immunodeficiencies (2012-2017)
Introduction: The German PID-NET registry was founded in 2009, serving as the first national registry of patients with primary immunodeficiencies (PID) in Germany. It is part of the European Society for Immunodeficiencies (ESID) registry. The primary purpose of the registry is to gather data on the epidemiology, diagnostic delay, diagnosis, and treatment of PIDs.
Methods: Clinical and laboratory data was collected from 2,453 patients from 36 German PID centres in an online registry. Data was analysed with the software StataÂź and Excel.
Results: The minimum prevalence of PID in Germany is 2.72 per 100,000 inhabitants. Among patients aged 1â25, there was a clear predominance of males. The median age of living patients ranged between 7 and 40 years, depending on the respective PID. Predominantly antibody disorders were the most prevalent group with 57% of all 2,453 PID patients (including 728 CVID patients). A gene defect was identified in 36% of patients. Familial cases were observed in 21% of patients. The age of onset for presenting symptoms ranged from birth to late adulthood (range 0â88 years). Presenting symptoms comprised infections (74%) and immune dysregulation (22%). Ninety-three patients were diagnosed without prior clinical symptoms. Regarding the general and clinical diagnostic delay, no PID had undergone a slight decrease within the last decade. However, both, SCID and hyper IgE- syndrome showed a substantial improvement in shortening the time between onset of symptoms and genetic diagnosis. Regarding treatment, 49% of all patients received immunoglobulin G (IgG) substitution (70%âsubcutaneous; 29%âintravenous; 1%âunknown). Three-hundred patients underwent at least one hematopoietic stem cell transplantation (HSCT). Five patients had gene therapy.
Conclusion: The German PID-NET registry is a precious tool for physicians, researchers, the pharmaceutical industry, politicians, and ultimately the patients, for whom the outcomes will eventually lead to a more timely diagnosis and better treatment