Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras

A molecule is a nonzero non-unit element of an integral domain (resp., commutative cancellative monoid) having a unique factorization into irreducibles (resp., atoms). Here we study the molecules of Puiseux monoids as well as the molecules of their corresponding semigroup algebras, which we call Puiseux algebras. We begin by presenting, in the context of numerical semigroups, some results on the possible cardinalities of the sets of molecules and the sets of reducible molecules (i.e., molecules that are not irreducibles/atoms). Then we study the molecules in the more general context of Puiseux monoids. We construct infinitely many non-isomorphic atomic Puiseux monoids all whose molecules are atoms. In addition, we characterize the molecules of Puiseux monoids generated by rationals with prime denominators. Finally, we turn to investigate the molecules of Puiseux algebras. We provide a characterization of the molecules of the Puiseux algebras corresponding to root-closed Puiseux monoids. Then we use such a characterization to find an infinite class of Puiseux algebras with infinitely many non-associated reducible molecules.Comment: 21 pages, 2 figure

The Increase of the Micoporosity and CO2 Adsorption Capacity of the Commercial Activated Carbon CWZ-22 by KOH Treatment

The chemical modification of CWZ-22—commercial activated carbon (AC) with KOH‐ to enhance CO2 adsorption was examined. The effect of different impregnation ratios KOH:CWZ-22 from 1 to 4 was studied. The ACs were characterized by CO2 and N2 sorption, Fourier transform infrared (FTIR), SEM, and XRD methods

On certain infinite extensions of the rationals with Northcott property

A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states that sets of bounded degree have the Northcott property. Bombieri, Dvornicich and Zannier raised the problem of finding fields of infinite degree with this property. Bombieri and Zannier have shown that \IQ_{ab}^{(d)}, the maximal abelian subfield of the field generated by all algebraic numbers of degree at most $d$, is such a field. In this note we give a simple criterion for the Northcott property and, as an application, we deduce several new examples, e.g. \IQ(2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...) has the Northcott property if and only if $2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...$ tends to infinity

Ground states for a class of deterministic spin models with glassy behaviour

We consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the discrete sine Fourier transform. The ground state found by these authors for $N$ odd and $2N+1$ prime is shown to become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes, and to disappear for $N$ even. This last result is based on the explicit construction of a set of eigenvectors for $J$, obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the $2$-torus.Comment: 15 pages, plain LaTe

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups

How to treat hypertension more effectively? Patients&#8217; education program in Polish Project of 400 Cities

Wstęp Nadciśnienie tętnicze stanowi najczęstszą patologię układu krążenia. Skuteczność leczenia, pomimo dostępności sprawdzonych metod, jest nadal wysoko niezadowalająca. Chorzy na nadciśnienie tętnicze obarczeni są szczególnie wysokim ryzykiem powikłań sercowo-naczyniowych. Jedną z głównych przyczyn nieskuteczności leczenia jest brak współpracy pacjenta z lekarzem. PP400M to wieloośrodkowy projekt interwencyjny i badawczy, mający na celu poprawę wykrywania i skuteczności terapii najczęstszych czynników ryzyka chorób układu sercowo- naczyniowego oraz poszerzenie wiedzy na temat zdrowego żywienia. Celem badania była ocena skuteczności programu edukacji realizowanego wśród pacjentów dotychczas nieleczonych, z niedawno wykrytym nadciśnieniem tętniczym oraz zaburzeniami gospodarki lipidowej i węglowodanowej. Materiał i metody W 268 miejscowościach, liczących poniżej 8000 mieszkańców, w latach 2003-2005 przeprowadzono zajęcia edukacyjne dla 10 720 pacjentów z nowo wykrytym nadciśnieniem lub zaburzeniami metabolicznymi. W każdym z tych ośrodków utworzono i przeszkolono zespół edukacyjny, składający się z lekarza i pielęgniarki. Edukacja nowo wykrytych chorych prowadzona była przez zespoły edukatorskie w ośmioosobowych grupach. Wyszkolone w programie zespoły edukacyjne po zakończeniu realizacji programu mogą dalej uczyć pacjentów, używając przekazanych nieodpłatnie pomocy edukacyjnych. Analizą skuteczności programu objęto 10 720 pacjentów (kobiety 66,39%, mężczyźni 33,61%, śr. wiek 59,39 &plusmn; 13,2 roku, BMI 27,95 &plusmn; 5,13 kg/m2, śr. RR 147,75 &plusmn; 27,393/90,82 &plusmn; 13,602 mm Hg). Wyniki Większość chorych z niedawno wykrytym nadciśnieniem oczekuje informacji na temat chorób układu krążenia (91%), a jedynie 9% ocenia swoją wiedzę jako wystarczającą. Po zajęciach edukacyjnych większość pacjentów chciałaby mieć wpływ na swoje leczenie (90,77%) oraz deklaruje chęć wykonywania pomiarów tętniczych w domu (92,52%). Ponad 90% zdaje sobie sprawę iż pomiary wykonywane w domu mają znaczenie w leczeniu nadciśnienia tętniczego. Po przeprowadzeniu szkolenia wzrósł poziom wiedzy na temat czynników ryzyka chorób układu krążenia, jak również wpływu ich modyfikacji na skuteczność leczenia nadciśnienia tętniczego. W wyniku przeprowadzonych zajęć edukacyjnych zaobserwowano wzrost poziomu wiedzy pacjentów na temat zasad postępowania farmakologicznego; 58,51% pacjentów przed edukacją zanegowało stwierdzenie, że prawidłowe ciśnienie tętnicze w trakcie leczenia usprawiedliwia odstawienie przepisanego leku, po edukacji - 76,20%. Zaobserwowano wzrost świadomości pacjentów na temat występowania potencjalnych działań niepożądanych. Wnioski Istnieje duże zapotrzebowanie na informacje dotyczące chorób układu krążenia wśród osób z noworozpoznanymi zaburzeniami - nadciśnieniem tętniczym i zaburzeniami gospodarki lipidowej i węglowodanowej. Pacjenci z dopiero co rozpoznanym nadciśnieniem tętniczym dobrze identyfikują czynniki ryzyka chorób układu krążenia, jednak poziom ich wiedzy o zasadach farmakoterapii jest niewystarczający. Edukacja pacjentów jest skutecznym narzędziem, pomagającym przekazać i rozszerzyć wiadomości na temat choroby, czynników ryzyka i sposobów terapii.Background Hypertension is the most common cardiovascular pathology. Treatment efficacy, despite effective methods, is still highly unsatisfactory. Hypertensive patients are at high risk of cardiovascular complications. One of the reasons for treatment poor effects is lack of patient-doctor cooperation. PP400M is multicenter, intervention and research project which aim was to improve efficacy of screening and reduction of major cardiovascular risk factors and improvement of healthy diet knowledge. The aim of the study was to evaluate effectiveness of educational program designed for newly diagnosed patients with hypertension, dyslipidaemia and glucose intolerance. Material and methods In 268 small cities and villages of up to 8000 habitants in years 2003-2005 the educational program was implemented. 10 720 patients with newly diagnosed metabolic disturbances were invited to participate in education program. The meetings were held by teams of nurse and a physician. The eight people groups met during two meetings, held weekly. The first meeting was devoted to risk factors, diet and self blood pressure measurement, during second meeting the rules of hypertension pharmacotherapy were discussed. Teams instructed to implement the program were given free educational materials to continue with the program later. Participants in education meetings 66.39% were women and 33.61% men. The efficacy analysis was performed on 10 720 patients (mean age 59.39 &plusmn; 13.2 ys., BMI 27.95 &plusmn; 5.13 kg/m2, mean RR 147.75 &plusmn; 27.393/90.82 &plusmn; 13.602 mm Hg). Results Most patients (91%) with newly diagnosed hypertension expect to be offered more information on cardiovascular diseases, only 9% asses their knowledge as good. After education meetings most of the patients (90.77%) want to be involved in treatment process, and declare the will to perform blood pressure measurement at home (92.52%). More than 90% of patients realize that home blood pressure measurement is important in hypertension management. After education knowledge level on risk factors increases as well as awareness on importance of lifestyle modification in treatment of hypertension. After education there is a marked improvement in knowledge on hypertension pharmacotherapy rules. We also observed increase of side effects awareness among patients after education meetings. Conclusions There is a strong need for information concerning cardiovascular diseases among newly diagnosed patients with hypertension, dyslipidaemia and glucose intolerance. Newly diagnosed patients identify well cardiovascular risk factors, but knowledge about pharmacotherapy rules is very poor. Patient education is an effective tool in improving patients knowledge on disease, risk factors and methods of therapy

V*-algebras, independence algebras and logic

Independence algebras were introduced in the early 1990s by specialists in semigroup theory, as a tool to explain similarities between the transformation monoid on a set and the endomorphism monoid of a vector space. It turned out that these algebras had already been defined and studied in the 1960s, under the name of v*-algebras, by specialists in universal algebra (and statistics). Our goal is to complete this picture by discussing how, during the middle period, independence algebras began to play a very important role in logic

Abnormalities in autonomic function in obese boys at-risk for insulin resistance and obstructive sleep apnea.

Study objectivesCurrent evidence in adults suggests that, independent of obesity, obstructive sleep apnea (OSA) can lead to autonomic dysfunction and impaired glucose metabolism, but these relationships are less clear in children. The purpose of this study was to investigate the associations among OSA, glucose metabolism, and daytime autonomic function in obese pediatric subjects.MethodsTwenty-three obese boys participated in: overnight polysomnography; a frequently sampled intravenous glucose tolerance test; and recordings of spontaneous cardiorespiratory data in both the supine (baseline) and standing (sympathetic stimulus) postures.ResultsBaseline systolic blood pressure and reactivity of low-frequency heart rate variability to postural stress correlated with insulin resistance, increased fasting glucose, and reduced beta-cell function, but not OSA severity. Baroreflex sensitivity reactivity was reduced with sleep fragmentation, but only for subjects with low insulin sensitivity and/or low first-phase insulin response to glucose.ConclusionsThese findings suggest that vascular sympathetic activity impairment is more strongly affected by metabolic dysfunction than by OSA severity, while blunted vagal autonomic function associated with sleep fragmentation in OSA is enhanced when metabolic dysfunction is also present