Asymptotically polynomial solutions of difference equations of neutral type

Asymptotic properties of solutions of difference equation of the form $$\Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n$$ are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or all nonoscillatory solutions are asymptotically polynomial. We use a new technique which allows us to control the degree of approximation

Qualitative approximation of solutions to difference equations

We present a new approach to the theory of asymptotic properties of solutions of difference equations. Usually, two sequences $x,y$ are called asymptotically equivalent if the sequence $x-y$ is convergent to zero i.e., $x-y\in c_0$, where $c_0$ denotes the space of all convergent to zero sequences. We replace the space $c_0$ by various subspaces of $c_0$. Our approach is based on using the iterated remainder operator. Moreover, we use the regional topology on the space of all real sequences and the `regional' version of the Schauder fixed point theorem

Components of metabolic syndrome in the first trimester of pregnancy as predictors of adverse perinatal outcome

Objectives: It is the prospective observational study aimed at early prediction of pregnancy complications in women with symptoms of MS. Material and methods: 124 Caucasian women in singleton pregnancies 11th to the 13th wks 6 days of gestation with MS criteria compared to 30 healthy controls. Perinatal maternal and fetal results were analyzed. Results: Increased in the MS group were: age (32.9 y vs. 28.6 y; p = 0,00), weight 11 to 13 + 6 weeks of gestation (79.0 kg vs. 59.7 kg; p = 0.00), BMI (29 kg/m2 vs. 21.6 kg/m2; p = 0.00), waist–hip ratio (WHR) (0.9 vs. 0.8; p = 0.00). Maternal serum parameters were higher in the MS group: LDL-cholesterol (124.1 vs. 109.6 mg/dL; p = 0.02), t-PA (2556.8 vs. 1949.5 pg/mL; p < 0.00), GGTP (16.8 vs. 13.3 IU/L; p = 0.02) and lower values for: adiponectin (6.4 vs. 7.5 μg/mL; p = 0.01), SHBG (273.4 vs. 338.4 nmol/L; p = 0.001). MS group neonates higher body weight (3594.4 vs. 3312.2 g; p = 0.01), significantly frequent macrosomic neo­nates (> 4000 g) (20.9% vs. 6.6%; p = 0.042), GDM (12% vs. 0; p = 0.019). Conclusions: Higher E-selectin serum concentration, GGTP and lower SHBG in first trimester are additionally to fasting maternal glucose, higher BMI and maternal age predictive for GDM. Higher E-selectin, fasting glucose, increased BMI and lower adiponectin serum concentration in first trimester are significant predictors of fetal macrosomia. Maternal BMI > 24.5 kg/m2 is the best predictor of increased risk of fetal macrosomia and gestational diabetes mellitus

Asymptotic behavior of solutions to difference equations in Banach spaces

We investigate the asymptotic properties of solutions to higher order nonlinear difference equations in Banach spaces. We introduce a new technique based on a vector version of discrete L’Hospital’s rule, remainder operator, and the regional topology on the space of all sequences on a given Banach space. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we are dealing with the problem of approximation of solutions. Our technique allows us to control the degree of approximation of solutions

Ciąża heterotopowa u pacjentki bez czynników ryzyka – trudności diagnostyczne

Heterotopic pregnancy (HP) is a rare entity occurring in 1:30000 pregnancies but its incidence raises as a result of assisted reproductive techniques (ART) to 1:100-1:500. The aim of this report was to present a rare case of simultaneous intrauterine and extrauterine tubal pregnancy in a natural conception cycle. The ectopic pregnancy was not diagnosed in the first trimester scan and at 14 and 16 weeks of gestation led to severe hemoperitoneum and two exploratory laparotomies. Diagnostic problems were discussed and literature was reviewed.Ciąża heterotopowa występuje z częstością 1:30000 ciąż, ale częstość jej wzrasta, w konsekwencji stosowania technik wspomaganego rozrodu, do 1:100-1:500. Celem tej pracy jest opis rzadkiego przypadku ciąży jajowodowej współistniejącej z ciążą wewnątrzmaciczną. Ciąża ektopowa nie była zdiagnozowana w pierwszym trymestrze ciąży a w 14 i 16 tygodniu ciąży dwukrotnie doprowadziła do laparotomii z powodu obfitego krwawienia do jamy brzusznej. W pracy przedstawiono problemy diagnostyczne oraz przegląd aktualnej literatury

Approximative solutions of difference equations

Asymptotic properties of solutions of difference equations of the form $$\Delta^m x_n=a_nf(n,x_{\sigma(n)})+b_n$$ are studied. Using the iterated remainder operator and fixed point theorems we obtain sufficient conditions under which for any solution $y$ of the equation $\Delta^my=b$ and for any real $s\leq 0$ there exists a solution $x$ of the above equation such that $\Delta^kx=\Delta^ky+\mathrm{o}(n^{s-k})$ for any nonnegative integer $k\leq m$. Using a discrete variant of the Bihari lemma and a certain new technique we give also sufficient conditions under which for a given real $s\leq m-1$ all solutions $x$ of the equation satisfy the condition $x=y+\mathrm{o}(n^s)$ where $y$ is a solution of the equation $\Delta^my=b$. Moreover, we give sufficient conditions under which for a given natural $k<m$ all solutions $x$ of the equation satisfy the condition $x=y+u$ for a certain solution $y$ of the equation $\Delta^my=b$ and a certain sequence $u$ such that $\Delta^ku=\mathrm{o}(1)$

Ocena czterech wariantów klasyfikacji TIRADS w grupie pacjentów z wolem guzkowym — badanie wstępne

Purpose The goal this study was to evaluate the utility of four variants of the Thyroid Imaging Reporting and Data System (TIRADS) in the differentiation of focal lesions in individuals with multinodular goiter.   Materials and Methods The study was approved by the Local Bioethical Committee. Each patient gave informed consent before enrolment. A total of 163 nodules in 124 patients with multinodular goiter were evaluated by ultrasound. B-mode and PD imaging and strain elastography were performed. Archived images were evaluated via retrospective analysis using four different proposed TIRADS classifications   Results Sensitivity and specificity of the Horvath, Park, Kwak, and Russ classifications were 0.625 and 0.769, 0.813 and 0.864, 0.938 and 0.667, and 0.875 and 0.293, respectively. Positive and negative predictive values were 0.227 and 0.95, 0.394 and 0.977, 0.234 and 0.99, and 0.119 and 0.956, respectively. Receive operating characteristic analysis suggests that the best differentiation potential was demonstrated by the Kwak classification with an area under the curve (AUC) of 0.896, followed by the Park (AUC = 0.872), Horvath (AUC = 0.774), and Russ (AUC = 0.729) classifications.   Conclusion The TIRADS classification proposed by Kwak can be a useful tool in daily practice for the evaluation of thyroid cancer in individuals with multinodular goiter, particularly for selecting cases that require biopsy, which may improve and simplify clinical decision making. To adopt a definitive, comprehensive variant of the TIRADS classification with potential for universal, practical application, further prospective studies that include improvement of the lexicon and evaluation of the full spectrum of thyroid malignancy are warranted.Wstęp: Celem tej pracy była ocena przydatności 4 wariantów systemu raportowania badań ultrasonograficznych tarczycy (TIRADS) do różnicowania zmian ogniskowych u pacjentów z wolem guzkowym. Materiał i metody: Badanie było zatwierdzone przez właściwą komisję bioetyczną. Każdy pacjent wyraził świadomą zgodę przed przy­stąpieniem do badania. W badaniu ultrasononograficznym analizowano 163 zmiany ogniskowe u 124 pacjentów z wolem guzowatym. Wykonano obrazowanie w skali szarości, z dopplerem mocy oraz elastografię odkształceń względnych. Zarchiwizowane obrazy zostały poddane analizie retrospektywnej z zastosowaniem 4 wariantów klasyfikacji TIRADS. Wyniki: Czułość i swoistość klasyfikacji Horvath, Park, Kwak i Russ wyniosły odpowiednio 0,625 i 0,769, 0,813 i 0,864, 0,938 i 0,667 oraz 0,875 i 0,293. Dodatnie i ujemne wartości predykcyjne wynosiły odpowiednio 0,227 i 0,95, 0,394 i 0,977, 0,234 i 0,99 oraz 0,119 i 0,956. Analiza ROC sugeruje, że najlepszy potencjał w różnicowaniu prezentuje wariant Kwak z polem pod krzywą (AUC) of 0,896, następnie Park (AUC = 0,872), Horvath (AUC = 0,774) i Russ (AUC = 0,729). Wnioski: Klasyfikacja TIRADS proponowana przez Kwaka może być przydatnym narzędziem w codziennej praktyce oceny pod kątem raka tarczycy u pacjentów z wolem guzkowym, szczególnie do wyselekcjonowania przypadków wymagających biopsji, co może polepszyć i uprościć podjęcie decyzji klinicznej. Wskazane są dalsze badania prospektywne, obejmujące ulepszenie leksykonu i ocenę pełnego spektrum guzów złośliwych tarczycy, aby ostatecznie przyjąć optymalny wariant klasyfikacji TIRADS, co zapewne umożliwi jej uniwersalne praktyczne zastosowanie

Asymptotic behavior of solutions of the mth-order nonhomogeneous difference equations

AbstractAsymptotic behavior of solutions of the mth-order difference equation of the form (E1) Δmxn + ƒ(n, xn,…, Δm−1xn) = hn and some special case (E2) of these equation are investigated