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Purpose of Review Pediatric neuroanesthesia is a growing and still challenging subspecialty. The purpose of this review is to summarize the available knowledge and highlight the most recent findings of the literature on non-traumatic pediatric neuroanesthesia care. Recent Findings Several human studies have confirmed the negative effects of early life anesthetic exposure. According to non-human studies, volatile anesthetics and opioids contribute to tumor progression. Tranexamic acid effectively reduces perioperative blood loss; it is used in several different doses without standard guidelines on optimal dosing. The widespread use of neuromonitoring has necessitated the development of anesthetic methods that do not affect neuromuscular transmission. Summary Pediatric anesthetic neurotoxicity, management of intraoperative bleeding, and the effect of anesthesia on tumor growth are among the most debated and researched topics in pediatric neuroanesthesia. The lack of evidence and clinical guidelines underlines the need for further large prospective studies in this subspecialty.

Purpose of Review This review summarizes the anesthesiologist’s role in transferring critically ill surgical patients at different phases of care. Recent Findings Early recognition of patients at high intraoperative and postoperative risk is one of the most important first steps, followed by preoperative and intraoperative stabilization measures depending on the individual needs. It mainly is the anesthesiologist’s responsibility to decide on postoperative ICU admission. The transfer of the critically ill should be planned; the ICU staff has to be informed as early as possible. Locally developed checklists should be used during the preparation of patient transport. Trained, dedicated staff should be made available in every institution. A detailed handover using dedicated institutional flowcharts should ensure patient safety upon arrival to the ICU. Summary Transfer of critically ill patients from the OR to the ICU is an interdisciplinary task with a high probability of eventual incidents. Anesthesiologists should play a key role in all phases of the procedure to improve patient outcomes.

Aerosol particles proved to play a key role in airborne transmission of SARS-CoV-2 viruses. Therefore, their size-fractionated collection and analysis is invaluable. However, aerosol sampling in COVID departments is not straightforward, especially in the sub-500-nm size range. In this study, particle number concentrations were measured with high temporal resolution using an optical particle counter, and several 8 h daytime sample sets were collected simultaneously on gelatin filters with cascade impactors in two different hospital wards during both alpha and delta variants of concern periods. Due to the large number (152) of size-fractionated samples, SARS-CoV-2 RNA copies could be statistically analyzed over a wide range of aerosol particle diameters (70–10 µm). Our results revealed that SARS-CoV-2 RNA is most likely to exist in particles with 0.5–4 µm aerodynamic diameter, but also in ultrafine particles. Correlation analysis of particulate matter (PM) and RNA copies highlighted the importance of indoor medical activity. It was found that the daily maximum increment of PM mass concentration correlated the most with the number concentration of SARS-CoV-2 RNA in the corresponding size fractions. Our results suggest that particle resuspension from surrounding surfaces is an important source of SARS-CoV-2 RNA present in the air of hospital rooms.

There has been a long-standing opposition to genetically modified organisms (GMOs) worldwide. Some studies have tried to identify the deep-lying philosophical, conceptual as well as psychological motivations for this opposition. Philosophical essentialism, psychological essentialism, and vitalism have been proposed as possible candidates. I approach the plausibility of the claim that these notions are related to GMO opposition from a historical perspective. Vitalism and philosophical essentialism have been associated with anti-GMO stance on account of their purported hostility to species and organismic mutability. I show that vitalism has often been associated to various mutabilist theories, whereas the case for philosophical essentialism as motivating GMO opposition depends on the now discredited Essentialism Story that had constructed essentialism as a predominant view in pre-Darwinian science. Further, as philosophical essentialism taken seriously is incompatible with the reality of genetic engineering, it is unlikely to be a reason for opposition. Psychological essentialism, involving an instinctive repulsion from the practice of manipulating what is thought to be the essence of living beings, is a more likely reason for resistance to transgenesis. Yet even here, historical considerations are crucial. Not only lay people tend to essentialize genes, but scientists themselves can be shown to have been complicit in essentialist tendencies. From the advent of modern genetics, the imagery of the all-powerful genes, often depicted by scientists themselves metaphorically as material counterparts of the now obsolete vitalistic agent, has permeated the language of leading scientific figures, whose influence in shaping public opinion should not be downplayed. Enthusiasm for genetic engineering and the abhorrence from it might both derive from the same unrealistic image of the essential gene, the revision of which thus holding out the hope for transcending the present impasse of the GMO controversy.

Biochar is a solid material obtained from reductive, oxygen-free processes, i.e. the thermo-chemical conversion of biomass in oxygen-limited environment. The obtained products have high carbon sequestration potential and strong nutrient-water absorption capacities because of the enlarged carbon surfaces. It is not yet clear how carbon stimulates agrochemical parameters in soil and how those characteristics are developing as time goes on a long-term basis. Samples of ancient (25, 35, 80 years old) plant coal-affected soils were collected in a temperate deciduous forest site located in the south part of the Bukk Mountains (in North Eastern Hungary). Physical–chemical soil characteristics, such as soil pH, cation exchange capacity (CEC), the organic and inorganic nitrogen (NH4 +, NH3 −) and the available nutrients (P2O5 and K2O), were estimated beside organic matter (SOM) content, measured by two different methods. Levels of polycyclic aromatic hydrocarbon (PAH) compounds in soil and in various biochar samples were assessed in relation with permissible limit values and potential toxicity. Positive correlation was found between the amount of available nutrients, total organic nitrogen content, cation exchange capacity and the age of plant coal-affected soils. The sample soils were exposed to continuous plant coal biochar effect for 25 years, during which macronutrients absorbed and accumulated in the plant coal surfaces. After this period, the degradation of carbon developed simultaneously with the reduction of the amount of available nutrients, till the end of the studied 80-year-affecting period. Measured CEC level indicated positive correlation with nutrient availability and the age of biochar-affected soils. Our results support the hypothesis that biochar in soil can improve its general agrochemical characteristics in relation with its persistence in a specific soil-plant system. Potential PAH content and toxicity of biochar products are key issues of developing proper application rates in sustainable agricultural practices.

Objectives Impaired vascular pathophysiology and increased cardiovascular (CV) mortality are associated with rheumatoid arthritis (RA). To date, no genomic analysis of RA- and RA treatment-related vascular pathophysiology has been published. In this pilot study, we performed gene expression profiling in association with vascular pathophysiology in RA patients. Methods Sixteen and 19 biologic-naïve RA patients were included in study 1 and study 2, respectively. In study 1, genetic signatures determined by microarray were related to flow-mediated vasodilation (FMD), pulse-wave velocity (PWV), and common carotid intima-media thickness (IMT) of patients. In study 2, clinical response (cR) vs non-response (cNR) to 1-year etanercept (ETN) or certolizumab pegol (CZP) treatment, as well as “vascular” response (vR) vs non-response (vNR) to biologics, were also associated with genomic profiles. Multiple testing could not be performed due to the relatively small number of patients; therefore, our pilot study may lack power. Results In study 1, multiple genes were up- or downregulated in patients with abnormal vs normal FMD, IMT, and PWV. In study 2, there were 13 cR and 6 cNR anti-tumor necrosis factor (TNF)-treated patients. In addition, 10, 9, and 8 patients were FMD-20%, IMT-20%, and PWV-20% responders. Again, vascular responder status was associated with changes of the expression of various genes. The highest number of genes showing significant enrichment were involved in positive regulation of immune effector process, regulation of glucose transport, and Golgi vesicle budding. Conclusion Differential expression of multiple genetic profiles may be associated with vascular pathophysiology associated with RA. Moreover, distinct genetic signatures may also be associated with clinical and vascular responses to 1-year anti-TNF treatment. Electronic supplementary material The online version of this article (10.1186/s13075-019-1862-6) contains supplementary material, which is available to authorized users.

Rheumatoid arthritis (RA) has been associated with osteoporosis. Quantitative computed tomography (QCT) is capable of assessing bone density and composition. We found lower bone density in RA compared to controls. Age and RA duration influenced bone density. QCT may be useful to assess bone metabolism in RA. RA is associated with generalized and periarticular osteoporosis. In addition to DXA that determines areal bone mineral density (BMD), peripheral QCT also detects volumetric BMD. QCT differentiates between total, trabecular, and cortical BMD. Here, we compared DXA and QCT in RA patients and healthy controls. BMD of 57 female RA patients and 32 age-matched healthy female controls were assessed by DXA. QCT of the forearm ultradistal region was also performed. Densitometry data were correlated with age, disease duration, disease activity, serum CRP, and anti-CCP levels. Total bone density (310.4 ± 79.7 versus 354.0 ± 54.1 mg/cm3; p = 0.007) and attenuation (0.37 ± 0.05 versus 0.40 ± 0.03 1/cm; p = 0.001), trabecular density (157.6 ± 57.0 versus 193.8 ± 48.7 mg/cm3; p = 0.005) and attenuation (0.28 ± 0.03 versus 0.32 ± 0.04 1/cm; p

In the Original Publication, the e-mail address of the author Milan Petronijevic is incorrect. The correct e-mail address is milanpetronijevic@yahoo.com.

Differential diagnosis of patients with Sjögren's syndrome (SS), IgG4-related disease (IgG4-RD) and SS patients having high risk for lymphoma (LHR) can be challenging. Some patients with IgG4-RD might be misdiagnosed as having SS. There are special symptoms of SS that raise the possibility of IgG4-RD whereas other symptoms identify patients as having LHR. The purpose of this study was to characterize and compare patients with SS, possible IgG4-RD and SS patients with LHR. Sixty-five SS patients were divided into 4 subgroups according to having possible IgG4-RD (n = 15), LHR (n = 16), eligible for both aforementioned groups (n = 20) and not eligible for either group (n = 14), respectively. Four patients fulfilled the diagnostic criteria for IgG4-RD. The serum levels of IgG4 were significantly higher in patients suspicious for IgG4-RD compared to that of LHR patients (0.46 g/l vs. 0.12 g/l, p = 0.032). Shared features of the patient groups (salivary gland swelling (SGS) and lymphadenopathy), were separately analysed: SGS patients had higher IgG4/IgG ratio (p = 0.036), lymphadenopathic patients had higher IgG4 levels (p = 0.042). Some patients may be "hidden" under the diagnosis of SS. Although patients with LHR and patients with possible IgG4-RD share some symptoms, they differ significantly regarding IgG4 levels and IgG4/IgG ratio.

A fast and reliable diagnostic system has been developed for the detection of Mangalica meat in foods. This qualitative test is based on a recombinase polymerase amplification which can be performed on the field, in situ, where it may be necessary to determine Mangalica content in food products at once. The required equipments for the procedure are pipettes, a portable homogenizer and a portable thermostat. DNA amplification is carried out at a constant temperature, and the detection is based on antibody reaction. The detection limit is one copy of the target sequence in 1 μl reaction volume. The test can be used for uncovering falsification of local brands on the spot within a very short (25–45 min) period of time. The present approach can be adopted for the detection of other food ingredients, if the species-specific target DNA sequence is known, e.g. in case of chicken, turkey, horse, and cattle.

The blood pressure (BP) of most patients on antihypertensive monotherapy or bitherapy remains uncontrolled. Our study evaluated the efficacy of triple therapy with perindopril, amlodipine, and indapamide sustained release (SR) in patients with uncontrolled hypertension on previous antihypertensive therapy. This 4-month, multicenter, prospective, observational, open-label study included patients switched from previous antihypertensive therapy to triple therapy with perindopril, amlodipine, and indapamide SR. The main outcome was change in office BP from baseline to 4 months, as well as changes in 24-h ambulatory BP monitoring (ABPM) parameters in a subgroup of patients. Age was 62.8 ± 11.3 years in 6,088 patients (55 % were male). Office BP at baseline was 158.1 ± 13.0/92.6 ± 8.8 mmHg. By 4 months, office BP decreased by 26.7 ± 13.3/12.9 ± 9.4 mmHg (p

Objectives To compare the efficacy and safety of infliximab-biosimilar with other biological drugs for the treatment of active ankylosing spondylitis (AS). Methods Systematic literature review for randomized controlled trials (RCTs) with adalimumab, etanercept, golimumab, infliximab and infliximab-biosimilar in AS was performed and indirect meta-analysis (Bayesian mixed treatment comparison) was carried out. The proportion of patients reaching 20 % improvement by the assessment of Spondyloarthritis International Society response criteria (ASAS20) at weeks 12 and 24 was used as efficacy endpoints, and the occurrence of serious adverse events at week 24 was applied to compare the safety of the biologicals. Results Altogether, 13 RCTs, identified by the systematic literature search, were included in the analysis. Results on the ASAS20 efficacy endpoint were reported for week 12 in 12 RCTs involving 2,395 patients, and for week 24 in 5 RCTs comprising 1,337 patients. All the five biological agents proved to be significantly superior to placebo. Infliximab showed the highest odds ratio (OR) of 7.2 (95 % CI 3.68–13.19) compared to placebo, followed by infliximab-biosimilar with OR 6.25 (95 % CI 2.55–13.14), both assessed at week 24. No significant difference was found between infliximab-biosimilar and other biological treatments regarding their efficacy and safety. Conclusions This is the first study which includes a biosimilar drug in the meta-analysis of biological treatments in AS. The results have proven the similar efficacy and safety profile of infliximab-biosimilar treatment compared to other biologicals.

Central neurocytoma is generally considered to be a benign tumor and the literature suggests that a cure may be attained by surgery ± adjuvant focal irradiation. However, there is a need for change in the therapeutic strategy for the subgroup of patients with aggressive central neurocytoma. An example case is presented and the literature on central neurocytoma cases with malignant features and dissemination via the cerebrospinal fluid is reviewed and the radiotherapeutic strategies available for central neurocytoma treatment is discussed. Nineteen cases including the present report with a malignant course and cerebrospinal fluid dissemination have been described to date, most of them involving an elevated MIB-1 labeling index. Our case exhibited atypical central neurocytoma with an initially elevated MIB-1 labeling index (25-30 %). The primary treatment included surgery and focal radiotherapy. Three years later the disease had disseminated throughout the craniospinal axis. A good tumor response and symptom relief were achieved with repeated radiation and temozolomide chemotherapy. Central neurocytoma with an initially high proliferation activity has a high tendency to spread via the cerebrospinal fluid. The chemo- and radiosensitivity of the tumor suggest a more aggressive adjuvant therapy approach. Cases with a potential for malignant transformation should be identified and treated appropriately, including irradiation of the entire neuroaxis and adjuvant chemotherapy may be considered.

We investigate the boundary value problems for nonlinear fractional impulsive differential equations with p-Laplacian operator. By applying some standard fixed point theorems, we obtain new results on the existence and uniqueness of solutions. Examples are given to show the applicability of our results.

In this paper, we consider existence and uniqueness of solutions for nonlinear boundary value problems involving Riemann–Liouville fractional integro-differential equations with advanced arguments. By establishing a new comparison theorem and applying the monotone iterative technique, we show the existence of extremal solutions.

Physical therapy in ankylosing spondylitis (AS) is important for maintaining or improving mobility, fitness, functioning, and global health. It also plays a role in the prevention and management of structural deformities. In this study we assessed the functional status of AS patients in relation to disease duration and activity. Furthermore, in volunteering patients we analyzed the efficacy of a controlled, individualized physiotherapeutic program. Altogether, clinical data of 75 AS patients were retrospectively analyzed. Anthropometrical data, duration since diagnosis and disease activity, pain intensity, tender points, sacroiliac joint involvement determined by X-ray, functional condition, and physical activity level were recorded. Subjective, functional, and physical tests were performed. Out of the 75 patients, 10 volunteered to undergo a complex physical exercise program twice a week for 3 months. The program included 1.5 h of general posture reeducation, manual mobilization of the spine, and pelvic-, upper-, and lower-extremity exercises, stretching with joint prevention strategies and functional exercises. In AS, pain intensity recorded on a 10-cm visual analog scale (VAS), BASFI, BASDAI, modified Schober index, chest expansion and occiput-to-wall distance values showed significant correlation with disease activity. The 3-month physical therapy improved several subjective and functional parameters, and markedly reduced pain intensity and spine stiffness. A complex, individualized physical therapy program may be useful and should be introduced to AS patients in order to maintain and increase spine mobility, preserve functional capacity, decrease the pain and stiffness.

Abbreviations ABVD Doxorubicin 25mg/m2, bleomycin 10mg/m2, vinblastine 6 mg/m2, dacarbazine 375 mg/m2 Anti-SSA Anti-Sjogren’s syndrome A (SSA) Anti-SSB Anti-Sjogren’s syndrome B (SSB) ASCT Autologous stem cell transplantation Bwkg Body weight kilogramm CA 19–9 Carbohydrate antigen 19–9 CD Cluster of differentiation EBV Epstein-Barr virus HL Hodgkin’s lymphoma NHL Non-Hodgkin lymphoma PET-CT Positron emission tomography—computed tomography PTLD Posttransplant lymphoproliferative disorder SCT Stem cell transplantation VAD Vincristine 2 mg i.v., doxorubicin 9 mg/m2 i.v. es dexamethasone 40 mg WHO World health organisation Background

We give a description of the terms in the Ringel-Hall product of preinjective Kronecker modules. We characterize in this way all the short exact sequences of preinjective modules. As an application we also give an explicit solution to the column completion challenge for pencils with only minimal indices for columns (corresponding to preinjective modules) and to the row completion challenge for pencils with only minimal indicies for rows (corresponding to preprojective modules).

β-catenin and E cadherin are both membrane-associated proteins which are essential regulators and providers of cellular adhesion. In the metastatic cascade of malignant tumours, detachment of tumour cells from each other is a very important step. It has been shown in several tumour types, that reduced expression of these proteins is important. The aim of our study was to clarify the expression profile of these proteins, and correlate the findings with the metastasizing potential of early stage colon and rectal cancers. Formalin fixed and paraffin embedded samples from 79 Dukes B2 stage colorectal cancer were examined using a tissue microarray approach. The expression of β-catenin and E-cadherin proteins was determined immunohistochemically. Our findings indicated that there is a tendency for metastatic spread in cases when membranous expression of β-catenin is lost (p = 0.062). Similarly metastases in negative cases developed more rapidly, than in positive ones (p = 0.05). Survival rate was worse in the negative cases. The risk of metastasis in rectal cancer was significantly higher in the β-catenin membranously negative than positive groups (p = 0.024) and in case of β-catenin nuclear expression the risk was also higher (p = 0.047). Reduced E-cadherin expression also correlated with development of metastatic disease, but this association was statistically not significant. The immunohistochemical analysis of 79 cases shows that in Dukes B2 stage colorectal tumours clarification of β-catenin and E-cadherin expression patterns is reliable for predicting the metastatic potential of early stage rectal cancer and hence the method may have relevant implications in the therapeutic management of these cancers.

Ankylosing spondylitis (AS) and rheumatoid arthritis (RA) are two distinguished representatives of inflammatory rheumatic diseases. The two diseases differ significantly in their etiology, pathology, clinical signs, and in the nature of articular manifestations. Their association has been a rarity in the literature. Here, authors describe a case of a 55-year-old female patient with AS associated with RA. Her spinal symptoms started in 1979, and the diagnosis of AS was established based on the typical clinical picture and X-ray. She developed severe spinal deformity during the next decades. In 2005, peripheral polyarthritis developed, although neither the diagnosis nor the treatment was modified. In 2007, authors diagnosed seropositive RA. Therapy included anti-inflammatory therapy and traditional disease-modifying agents, eventually followed by biological therapy.

International audience; The objectives of this study were to assess the costs of psoriatic arthritis (PsA) in Hungary and to identify key cost drivers among demographic and clinical variables and to compare cost-of-illness of PsA and rheumatoid arthritis (RA). Cross-sectional retrospective survey of 183 consecutive patients from eight rheumatology centres was conducted. Mean direct medical, direct non medical, indirect and total costs were 1,876, 794, 2,904 and 5,574 euros/patient/year, respectively. Total costs were in significant linear relationship with health assessment questionnaire score and psoriatic area severity index. Costs of RA were higher in all domains than of PsA. Our study was the first from the Eastern European region that provides cost-of-illness data on PsA. Our study revealed that functional status and severity of skin symptoms were the key cost drivers. The costs of PsA in Hungary were lower than in the high-income European countries.

We show the existence of a cubic system having at least one limit cycle bounded by two invariant parabolas. We will also obtain the necessary and sufficient conditions for the critical point in the interior of the bounded region to be a center.

A class of Kukles differential systems of degree five having an invariant conic is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, under perturbations of the coefficients of the systems.

Rheumatoid nodules are well established manifestations of rheumatoid arthritis but in the lungs they are very rare according to the literature. In our study we present the case of a 34-year-old woman with rheumatoid arthritis and secondary Sjogren’s syndrome who developed multiplex rheumatoid nodules in the lungs 3 years after initiating leflunomide therapy. During leflunomide therapy we did not detect inflammation in the joints. Surprisingly, in November 2005 she started to cough, had low grade fever and low back pain. On the chest X-ray there were multiplex necrobiotic nodules in the lungs. All bacteriological, viral and fungal investigations including tuberculosis, serological tests and cytology were negative. The X-ray, video-associated thoracoscopy and repeated biopsy of the lung followed by histology of the samples proved intrapulmonary rheumatoid nodules, caused by leflunomide.

Carboxypeptidase-M (CPM) is a membrane-bound peptidase that metabolizes peptides, and is present in pneumocytes. CPM hydrolyses the C-terminal arginine of epidermal growth factor (EGF) resulting in des-Arg53-EGF which binds to the EGF receptor (EGFR) with an equal or greater affinity than native EGF. Therefore, this study focused on the possible presence of CPM in human lung adenocarcinomas (ADC) and evaluated the relationship between CPM and EGFR by assessing the impact of expressions on patient clinical outcome. This is a retrospective study of 110 patients who underwent resection of the primary tumour (92) or metastatic tissues (18) for treatment or diagnosis. Immunohistochemistry (IHC) for CPM and EGFR was made in serial sections using standard methods. This study demonstrates for the first time that 23.6% of ADCs express carboxypeptidase-M (26/110), mainly in membrane-bound forms. The amounts and the extent of CPM within tumours vary from low levels to obviously overexpressed forms. The immunohistochemical positivity (+) for CPM in ADCs negatively correlated with disease survival. In addition, 80% of CPM+ adenocarcinomas (21/26) showed a coexpression with EGFR suggesting a high prevalence for coexistence. The follow up data indicated a significantly shorter 5-year survival time for patients with CPM+–EGFR+ (double-positive) tumours compared to those harbouring neoplasias negative for both proteins (9.5 vs. 60.4% survivals, P

Sjögren's syndrome (SS) is a prototypical systemic autoimmune disease, where autoimmune processes lead to the dysfunction of the exocrine glands. The key feature of the disease is autoimmune exocrinopathy, causing reduced tear secretion and subsequent keratoconjunctivitis sicca (KCS). The aim of this study was to investigate the connection between the presence of autoantibodies to lachrymal gland antigens and the reduced tear production in patients with primary SS. Ninety-nine patients, 90 women and 9 men, were investigated in the study. Twenty healthy young women served as controls. Enzyme-linked immunosorbent assay (ELISA) and Western blotting were applied to detect autoantibodies to antigen fractions prepared from the human lachrymal gland membrane and cytosolic fractions. Autoantibodies of the IgG, IgA and IgM isotypes to the lachrymal membrane and cytosolic fractions were detected in about one third (27%) of the patients with primary SS. IgA antobodies to the membrane and cytosolic fractions occurred most frequently in SS patients. A significant difference was found in the presence of IgA antibodies to the membrane lachrymal fraction between patients and controls given in ELISA indices (1.23 +/- 0.3 vs 1 +/- 0.19, p0.001). IgG, IgA, and IgM isotypes of autoantibodies directed to the membrane lachrymal fraction of 200-180, 120-116, 80-70, 58, 50, 48.5, 40 and 28.8 kDa were also identified in patients. Membrane IgG antibody levels showed a positive correlation (R = 0.998; p = 0.045) with the clinical loss of secretory function (Schirmer's test values). Positive correlation was found between membrane IgM and anti-SS-A levels (R = 0.962; p = 0.038) and also between cytosolic IgM antibodies and anti-SS-A levels (R = 0.982; p = 0.018). IgG, IgA and IgM types of autoantibodies may play a role in the development of the impaired lachrymal secretion and therefore may be involved in the pathogenesis of KCS.

The paper presents the results of radiological investigation of several mushroom samples collected in the fall of 2004 in different parts of Europe. The work was performed in order to support decision making to develop and produce a certified reference material for quality assurance of radionuclide measurements in environmental samples. The levels of 137Cs in mushrooms varied widely ranging from 0.6 to 4300 Bq/kg on dry mass basis, while those of natural 40K were relatively constant. In one sample 60Co of unknown origin was detected (25±2 Bq/kg dry mass), while 90Sr concentrations were usually below the detection limit (

For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, we prove that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations we can have at most two small amplitude limit cycles.

We present formulas for the structure constants (Hall numbers) of the Hall algebra \(+AFw-mathcal{H}(kK)\) associated to the Kronecker algebra. The formulas which in some cases involve the classical Hall polynomials \(g^{+AFw-lambda}_{(r)+AFw-mu}\) enable us to determine every Hall number. Using again these formulas we construct new PBW-bases with simple structure constants for the composition algebra \(+AFw-mathcal{C}(kK)\), making possible the definition of the generic composition algebra via Hall polynomials.