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Main goal of this paper is to formulate possibly simple and easy to verify criteria on existence of the unique attracting probability measure for stochastic process induced by generalized iterated function systems with probabilities (GIFSPs). To do this, we study the long-time behavior of trajectories of Markov-type operators acting on product of spaces of Borel measures on arbitrary Polish space. Precisely, we get the desired geometric rate of convergence of sequences of measures under the action of such operator to the unique distribution in the Hutchinson–Wasserstein distance. We apply the obtained results to study limiting behavior of random trajectories of GIFSPs as well as stochastic difference equations with multiple delays. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of inter-comparison studies on identification of irradiated food carried out by the leading European laboratories from 1991 to 2018. In 1990s, the Federal Institute for Health Protection of Consumers and Veterinary Medicine in Germany played the leading role in the organization of the inter-laboratory tests on this subject. At the beginning of the present century, the Spanish Agency for Food Safety and Nutrition and Food National Spanish Centre took over this role. In total, 47 international tests were carried out in which nearly 500 samples of alimentary products were analysed in 37 laboratories from 14 European countries. The tests were aimed at proving the reliability of analytical methods – thermoluminescence (TL), photostimulated luminescence (PSL), and electron paramagnetic resonance (EPR) spectroscopy – for identification of specific irradiated food products and to control the analytical skills and experience of participating laboratories. The results made possible a discussion on why some irradiated food samples are more difficult for identification. In general, the tests showed that TL measurements of products such as herbs, nuts, peppers, and raisins, and EPR studies of fish and chicken bones, fresh strawberries, and dried fruits could be used as reliable control methods. The challenge that control laboratories are facing now, is related to the identification of complex food products such as diet supplements or biopharmaceuticals, in which only some additives are irradiated. [ABSTRACT FROM AUTHOR]

The stable EPR signal produced by ionizing radiation in crystalline D-mannose (C6H12O6) and separated from cranberries (Vaccinium oxycoccus) was studied. The isothermal heating of irradiated sample at 95°C for 10 minutes (melting point of D-mannose is 132°C) resulted in the modification and simplification of the EPR signal involved. The isotropic quartet has been recognized in the EPR signal of heat-treated sample. Molecular structure of the isotropic quartet identified in the complex EPR signal of D-mannose crystallite is proposed. [ABSTRACT FROM AUTHOR]

Abstract We present a new sufficient condition for existence of semiattractors for set-valued semiflows of state multifunctions associated with general cocycle mappings. We assume that a given cocycle has at least one weakly pullback contracting fiber. In particular, one can apply the result to iterated function systems having no contracting mappings. We also introduce and analyze a fiber structure of semiattractors. [ABSTRACT FROM AUTHOR]

We discuss Conley-type approach to attractive sets for lower semicontinuous multifunctions. Since every iterated function system induces a Barnsley-Hutchinson multifunction which is l.s.c. in such a case it is much more natural to consider a multifunctions of that type then closed relations on compact spaces earlier considered by some authors. We use topological (Kuratowski’s) limit instead of commonly used Hausdorff metric. [ABSTRACT FROM AUTHOR]

Background: The causes of ASD are still relatively unknown. Correlation between clinical status of patients and radiological MRI findings is of primary importance. The radiological classifications proposed by Pfirmann and Oner are most commonly used to assess intradiscal degenerative changes. The aim of the study was to assess the influence of the extension of spine fixation on the risk of developing ASD in a short time after surgery. Methods: A total of 332 patients with spinal tumors were treated in our hospital between 2010 and 2013. Of these patients, 287 underwent surgeries. A follow-up MRI examination was performed 12 months after surgical treatment. The study population comprised of 194 patients. Among metastases, breast cancer was predominant (29%); neurological deficits were detected in 76 patients. Metastases were seen in the thoracic (45%) and lumbar (30%) spine; in 25% of cases, they were of multisegmental character. Pathological fractures concerned 88% of the patients. Statistical calculations were made using the x2 test. Statistical analysis was done using the Statistica v. 10 software. A p value <0.05 was accepted as statistically significant. The study population was divided on seven groups according to applied treatment. Results: Clinical signs of ASD were noted in only seven patients. Two patients had symptoms of nerve root irritation in the lumbar spine. Twenty-two patients (11%) were diagnosed with ASD according to the MRI classifications by Oner, Rijt, and Ramos, while the more sensitive Pfirmann classification allowed to detect the disease in 46 patients (24%). Healthy or almost healthy discs of Oner type I correlated with the criteria of Pfirmann types II and III. The percentage of the incidence of ASD diagnosed 1 year after the surgery using the Pfirmann classifications was significantly higher than diagnosed according to the clinical examination. Conclusions: The incidence of ASD in patients after spine surgeries due to cancer metastases does not differ between the study groups. ASD detectability based on clinical signs is significantly lower than ASD detectability based on MR images according to the system by Pfirrmann et.al. ASD risk increase among patients with multilevel fixation. [ABSTRACT FROM AUTHOR]

In the paper we deal with minimal closed subsets invariant with respect to set-valued semiflow. Such sets are known as supports of invariant or even ergodic measures of stochastic processes associated with such semiflows. Our motivation comes from some earlier and recent results connected with bounded noise processes, but we work in the framework of set-valued semiflows with lower semicontinuous members on general metric space rather than mostly studied by many authors continuous and compact-valued ones. Such semiflows appear naturally when nonautonomous/random dynamical systems are considered. [ABSTRACT FROM AUTHOR]

The stable and complex EPR signals produced by the action of ionizing radiation on crystalline L-sorbose (C6H12O6) separated from rowan berries (Sorbus aucuparia) were studied. Isothermal heating of the samples at the temperature close to the melting point of L-sorbose (140°C) results in the modification and simplification of the EPR signal involved. In the EPR signal of heated L-sorbose, the isotropic quartet was distinguished. In the differential spectrum obtained by subtraction of normalized spectra of unheated and heated L-sorbose, the isotropic doublet was identified in addition. The DFT fitting offers the probable assignment of the EPR signals to specific radical structures. [ABSTRACT FROM AUTHOR]

Background: Metastases of malignant neoplasms to the cervical spine are relatively rare. The most common symptom of metastatic disease is pain. Symptoms associated with roots damage or spinal cord compression indicate locally advanced disease. In a large number of patients, surgical treatment brings benefits such as pain reduction and improvement of the quality of life. Pain intensity, neurological status, and quality of patients' lives are measured with the VAS, Frankel, and Karnofsky scales.Methods: Symptoms of the disease, morphology of the metastasis and treatment outcomes were evaluated in 57 patients treated surgically because of metastases to the cervical spine over the period 2010-2014 in Brzozów. The morphology of the metastases was assessed on the basis of CT and MR examinations. Pre- and postoperative functional status of the patients was evaluated using Karnofsky scale. The intensity of pain was assessed with VAS and the neurological status was evaluated by using Frankel's grades. Anterior approach was employed in 16 patients, posterior approach in 30 patients, and postero-anterior approach in 11 patients. The inter-group differences were evaluated using the U Mann-Whitney and Wilcoxon Matched Pairs test. All statistical analyses were performed by using Statistica 10. A value of P < 0.05 was considered statistically significant.Results: The majority of patients suffered from pain associated with instability of the spine. Multi-level metastases were noted in 40 patients, while in 17 patients 1 vertebra was involved. In 51 patients the metastases caused pathological fractures of the vertebrae. The most common neurological complications was observed in patients with multi-level tumors and with pedicles involvement. After surgery patients functional status improved and pain intensity decreased. The best results (statistically significant) were observed in patients operated with anterolateral approach. Complications were scarce. Two patients required reoperation due to infection.Conclusions: Surgical treatment of metastases to the cervical spine gives good outcomes and it ought to be a treatment of choice. Proper and multifaceted qualification of the patients for different treatments is of vital importance. [ABSTRACT FROM AUTHOR]

Background: Metastatic lesions localized in the periacetabular area cause troublesome pain and reduced mobility of the patients. Radiotherapy effectively decreases pain, yet it does not restore the ability to load the joint. Surgical treatment involving resection of metastatic lesions and joint reconstruction using bone grafts is burdened with a high rate of complications. Modular tumor prostheses are being increasingly used. In some cases, it is possible to strengthen the acetabular roof with bone cement using vertebroplasty kits. The aim of the study was to demonstrate various methods of treatment of metastatic lesions localized in the periacetabular area together with the analysis of their results and effectiveness. Methods: Between 2010 and 2015, 27 patients with cancer metastases to the acetabulum were treated at our department. Qualification for surgical treatment was multifaceted with numerous aspects being considered. They included patients' general condition, type of neoplasm, clinical stage, and prognosis. CT and MRI scans of the pelvis were performed in each case. Before the surgery and 3 months following the surgery, visual analogue scale (VAS) pain intensity, Karnofsky functional status, and motor ability according to the Harris scale were evaluated. Bone cement (PMMA)-augmentation was performed in 21 patients, of whom nine had cement injected precutaneously and 12 at proximal femur resection alloplasty. Hemipelvectomy Type II combined with implantation of LUMiC resection prosthesis of the acetabulum were performed in six cases. Results: The quality of life improved in all the patients. After percutaneous cement injection, the mean pain intensity VAS score was 2.7, and the mean Karnofsky functional status score was 71.8. The mean postoperative Harris hip score (HHS) was 94 points. The patients who had undergone resection alloplasty on the proximal femur combined with periacetabular cement injection were walking using one crutch. In this group of patients, the mean postoperative pain intensity, functional status, and gait efficiency scores were 4.5, 65.7, and 82 points, respectively. The mean pain intensity VAS score in patients who had LUMiC prostheses implanted was 3.4. Their mean functional status score was 65 and the gait efficiency score 71 points. All the patients were able to walk on crutches. Conclusions: Strengthening of the acetabular roof with bone cement in a specific group of patients is an adequate method of treatment which decreases pain and allows for loading the affected limb while walking. Internal hemipelvectomy combined with LUMiC prosthesis implantation makes it possible for the patients to walk using crutches and significantly reduces pain. [ABSTRACT FROM AUTHOR]

We consider smallest closed invariant subsets of the phase space with respect to arbitrary set-valued semiflows. Such sets, called semiattractors, attract all trajectories of singletons but not necessary compact or bounded subsets. In particular, there are systems admitting semiattractors which do not have global attractors as usually understood. We show some sufficient conditions on the existence of such a set. We also prove lower semicontinuous dependence of semiattractors for strict semiflows of l.s.c. multifunction and the existence of semigroups of Markov operators generated by such semiflows. We are motivated by asymptotic properties of semiflows of multifunctions connected with iterated function systems as well as random dynamical systems. [ABSTRACT FROM AUTHOR]

Background: Surgical treatment of long-bone metastases requires a comprehensive approach. The indications for surgery are based on the patient's general condition, type and stage of cancer, and survival time expectancy. Tumor modular endoprostheses have been increasingly used. Surgery should provide pain relief and improve the quality of life. Methods: Between 2010 and 2013, 67 patients with malignant metastases were surgically treated with resection prostheses. We performed a retrospective analysis of the indications for the surgery, its course, the type of the prostheses used, and the implantation techniques applied. We evaluated the most important clinical parameters influencing the postoperative quality of life of the patients. Results: Breast, prostate, and lung cancers are the most common primary tumors that metastasize to bones. The most common site of the lesions is the proximal femur; sporadically, they do occur in bones distal to the knee and elbow. After the surgery, all the patients could walk, most of them without crutches. The pain, rated on a VAS scale, decreased significantly, and the Karnofsky score improved. We observed that joint mobility and the strength of the muscles in the limbs allowed for normal functioning. Postoperative complications including infections and local tumor recurrences were rarely observed. Conclusions: The use of modular prostheses is an adequate method of treatment in patients with bone metastases. A radical resection of the tumor, which prevents local recurrences and loosening of implants, gives good outcomes. Reduced joint mobility resulting from muscle attachment cutting is well tolerated and concerns mainly patients that underwent operations on the humerus. [ABSTRACT FROM AUTHOR]

We consider a Markov chain generated by random iterations of a family of mappings indexed by elements of an arbitrary measurable space. Under sufficiently weak assumptions we construct a family of place-dependent probability measures such that considered Markov chain converges to a stationary distribution. We also prove some sufficient condition for asymptotic stability of a family of i.i.d. mappings and we apply obtained result for discrete white noise random dynamical systems showing analogous probabilistic long-time behavior. [ABSTRACT FROM AUTHOR]

We consider asymptotic properties of families of multifunctions generated by cocycles, families of measures as well as Markov operators associated with such a mapping. The results we apply to random dynamical systems show connection of obtained attractors for families of multifunctions with global set attractors and also connection of supports of attracting measures for Markov families with global point attractors. The use of topological limits instead of standard Hausdorff distance lets us to get attractors under some quite general assumptions only on a cocycle mapping but without any assumptions on so-called parameter space and without standard assumption on existence of a compact absorbing set. [ABSTRACT FROM AUTHOR]

We construct continuous iteration semigroups of triangular self-mappings (skew product semiflows) of the product of compact intervals, homoeomorphic with respect to the second variable. To do that we obtain general and continuous solutions of so-called cocycle equation with values in an arbitrary group. [ABSTRACT FROM PUBLISHER]

We introduce the notion of asymptotic stability of sequences of multifunctions associated with discrete cocycles. Some sufficient conditions for existence of attracting sets are given. The use of the topological (Kuratowski's) limits, as less complicated as commonly used Hausdorff metric, let us to weaken many standard assumptions. We show that in considered case existence of attractor is a property of a cocycle mapping itself and does not depend on properties of a parameter nor a state space. The obtained results generalize earlier on iterated function systems and can be applied for non-autonomous as well as random dynamical systems. [ABSTRACT FROM AUTHOR]

The well-known effect "measurability implies continuity" in the theory of functional equations is shown for solutions of some equations generalizing the classical translation and cocycle ones. All the obtained results are consequences of a single rather general theorem concerning continuity of measurable function f satisfying [formula] [ABSTRACT FROM AUTHOR]

Background: Thoracic spine cancer metastases is frequently the cause of neurological deficits. Despite the availability of diagnostics, delays in treatment are still quite common. The aim of this work is to analyze the reasons for delayed diagnostics and treatment, in patients with neurological deficits in the course of metastatic spine disease. Methods: In our study patients medical data was analyzed from 2013 to 2015. The analysis covered the following aspects: symptoms of metastases, time of neurological deficits occurrence, where and when initial diagnostics were performed, time from diagnosis to proper surgical treatment in an oncological centre. In total, 411 patients were consulted and 287 were operated on. Of 112 patients with neurological deficits, 64 underwent surgeries. Women represented the majority of the patients. The most common primary neoplasms were breast cancer and myeloma. Results: In 75% of the patients neurological symptoms occurred prior to admission to a hospital. The average time between the onset of neurological symptoms and medical consultation was 4 days. The patients were diagnosed mainly at neurologic, orthopedic and emergency departments. The mean time between undergoing radiological examinations and receiving the examinations results was 2.4 days for CT and 2.8 days for MRI. The average time between a patients’ admission from the department where they were initially diagnosed, to the orthopedic oncology ward was 4.5 days. Conclusions: The most common cause of the delayed treatment of patients with neurological deficits, in the course of metastatic spine disease, is a combination of the lack of knowledge among patients and healthcare personnel regarding the necessity of early diagnosis. [ABSTRACT FROM AUTHOR]

Background: Metastatic lesions localized in the pelvis cause pain, pathological fractures and decrease quality of patients life. Limited data are avaliable to compare the oncological, surgical and functional outcomes after different surgeries in patients with metastatic pelvic tumors. Most of the works presents the results of hemipelvectomy performed in patients with primary malignant bone tumors. The objectives of this study were to assess the outcome of patients after internal hemipelvectomy due to cancer metastases. Methods: Over the period 2010–2015 at the Department of Orthopaedic Oncology in Brzozów, 34 patients with metastases to the pelvis were treated. This study group comprised of 21 men and 13 women. The mean age was 67 (range: 51–79) for men and 56 (range: 41–77) for women. The majority of the treated patients suffered from myeloma (12 patients) and breast cancer (8 patients). Following the Enneking system classification guidelines, tumours were found in zone I (5 cases), zone II (18 cases), zone III (4 cases). Tumour involvement of both zones (II and III) considered 7 patients. The following resections were accomplished: wide in 11 cases, marginal in 17 cases, and intralesional in 6 cases. 18 patients were postoperatively treated with 8 Gy single-dose radiotherapy. 25 patients underwent bone reconstruction using either Lumic prostheses (9 cases) or the Harrington technique (16 cases). The mean follow-up period was 2.1 years (range: 1.2–6 years). The analysis covered patients’ survival, number of local recurrences, functional results and effectiveness of surgical treatment, considering the type, number and reason of complications. Results: Eight patients died. Overal survival calculated with Kaplan- Meier curve was 48.2% for 34 patients. Mean survival was 3.85 years. There were no statistically significant differences in overall survival depending on the type of metastasis resection. In this group, local tumour recurrences concerned 6 patients. The extent of tumour resection and the use of postoperative radiotherapy were statistically significantly related to local recurrences. Functional results were better in a group of patients without reconstruction. Postoperative VAS score was 2.7, Karnofsky status 71 and MSTS 23(86%). After Lumic prostheses implantation VAS score was 3.4, Karnofsky status 65 and MSTS 19(63%). The worst results were observed after Harrington procedure. We noticed 9 perioperative complications in 6 (18%) of patients. Most frequently, the problems included impaired wound healing due to infection (4 patients) and dislocation of Lumic prosthesis (2 patients). Conclusions: The frequency of local recurrences after hemipelvectomies is related to the radicality of tumour resection and the postoperative application of radiotherapy. Survival time depends on the type and stage of cancer and does not depend on the type of tumour resection. The best functional results were obtained in patients after type I resection followed by no reconstruction of the bone. Lumic prosthesis implantation gave better results than Harrington procedure. [ABSTRACT FROM AUTHOR]