Projective method for the equation of risk theory in the arithmetic case

We consider a discrete model of operation of an insurance company whose initial capital can take any integer value. In this statement, the problem of nonruin probability is naturally solved by the Wiener – Hopf method. Passing to generating functions and reducing the fundamental equation of risk theory to a Riemann boundary-value problem on the unit circle, we establish that this equation is a special one-sided discrete Wiener – Hopf equation whose symbol has a unique zero, and, furthermore, this zero is simple. On the basis of the constructed solvability theory for this equation, we justify the applicability of the projective method to the approximation of ruin probabilities in the spaces l₁⁺ and c₀⁺ . Conditions for the distributions of waiting times and claims under which the method converges are established. The delayed renewal process and stationary renewal process are considered, and approximations for the ruin probabilities in these processes are obtainedРозглядається дискретна модель функцiонування страхової компанiї, початковий капiтал якої може набувати довiльного цiлого значення. У такiй постановцi проблема обчислення ймовiрностi стiйкостi компанiї природно розв’язується методом Вiнера – Хопфа. При переходi до твiрних функцiй i зведеннi фундаментального рiвняння теорiї ризику до граничної задачi Рiмана на одиничному колi з’ясовано, що розглядуване рiвняння є особливим одностороннiм дискретним рiвнянням Вiнера – Хопфа, символ якого має єдиний нуль i цей нуль є простим. На базi побудованої теорiї розв’язностi цього рiвняння обґрунтовано застосування проективного методу до апроксимацiї ймовiрностей банкрутства у просторах l₁⁺ і c₀⁺. Отримано умови на розподiли часiв очiкування вимог i розмiрiв виплат для збiжностi методу. Розглянуто процес вiдновлення iз запiзненням i стацiонарний процес вiдновлення, а також наближення для ймовiрностей банкрутства у цих процеса

Exact non-ruin probabilities in arithmetic case

Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times Ti and claims Zi in ordinary renewal process, an exact non-ruin probabilities for an insurance company in terms of the factorization of the symbol of the discrete Feller-Lundberg equation, are obtained. The delayed stationary process is introduced and generating function for delay is given. It is proved that the stationary renewal process in arithmetic case is ordinary if and only if, when the inter-arrival times have the shifted geometrical distribution. A formula for exact non-ruin probabilities in delayed stationary process is obtained. Illustrative examples when the distributions of Ti and Zi are shifted geometrical or negative binomial with positive integer power are considered. In these cases the symbol of the equation is rational functions what allows us to obtain the factorization in explicit form

Exact non-ruin probabilities in infinite time

Using the Wiener-Hopf method, for the fundamental equation of the risk theory it is obtained an exact solution in terms of the Fourier transforms and factorization

Deposition and Resorption of Calcified Matrix in Vitro by Rat Marrow Cells

Rat bone marrow derived cells were cultured using a-Minimal Essential Medium supplemented with antibiotics, ascorbic acid and !3-glycerphosphate in the presence of 10-8M dexamethasone, on polystyrene and hydrophilic fluorocarbon substrata for periods of 2 - 4 weeks. During this time, a large yield of bone nodules was achieved and the elaborated tissue was examined by both scanning and transmission electron microscopy. The matrix produced by the cells contacting the underlying substratum was an afibrillar, globular, calcified material which formed a layer approximately 0.5μm thick. The calcium and phosphorus content of this material was confirmed by energy dispersive X-ray dot mapping analysis. The collagenous matrix of the forming bone nodules was intimately associated with, and anchored to, this layer. The bulk of the bone nodule, above the interfacial zone, was of a normal appearance with osteocytes buried in a collagenous matrix exhibiting spheritic foci of mineralization. The cells, but not the extracellular matrix, of this culture were then removed using a trypsin citrate saline solution and the dishes containing these nodules reseeded with fresh bone marrow cells. These second stage cultures were maintained in supplemented medium, without dexamethasone. During this second period, osteoclasts resorbed both the afibrillar and collagen containing calcified matrices laid down in the first stage of the culture, producing characteristic scalloped osteoclast resorption lacunae

Mineralized Matrix Production by Osteoblasts on Solid Titanium In Vitro

Rat bone marrow cells were cultured on solid commercially pure titanium discs. Extracellular matrix (ECM) formed by the cells and the ECM/metal interface developed were examined by both scanning and transmission electron microscopy. The ECM most intimately associated with the substratum comprised afibrillar calcium phosphate globular accretions produced by the colonizing osteoblasts. The presence of calcium and phosphorus was confirmed by energy dispersive X-ray analysis. This initial layer acted as a site of anchorage for collagen fibres, produced by the osteoblasts. However, flaps of tissue elaborated during the culture period and manually reflected created a tissue division immediately above the afibrillar layer which indicated that the latter was adherent to the underlying metal oxide surface. The collagen matrix, consisting of networks of fibres, became mineralized with time in culture and also enveloped osteocytes which possessed radiating cell processes to form a bone nodule. This in vitro study suggests that while a calcified matrix layer, produced by osteoblasts, may adhere to titanium surfaces, subsequently formed bone is separated from this layer by a zone rich in both proteoglycans (as demonstrated by ruthenium red staining) and collagen fibres

Scanning Electron Microscopy of the Osteoclast-Bone Interface In Vivo

Rat femoral bones were studied by scanning electron microscopy to demonstrate the morphology of osteoclast- bone matrix interfacial relationships. Two general morphological types of actively resorbing osteoclasts were observed . One cell type was approximately ovoid with highly fimbriated borders, fully attached and closely adapted to the resorption surface. The ruffled border of such cells was composed of a number of individual filopodia which were of uniform , regular shape and approximately 2-3 μm in length and 150 nm in diameter. They were found to penetrate the bone matrix to a depth of 1 μm and interdigitated with the surrounding bone. The other cell type was elongated, covered smaller lining cells, and attached to the bone surface by pseudopodia. The bone-contacting face of pseudopodia formed a network of irregular membranous branches apposed closely to the underlying bone matrix. The results revealed the three dimensional ultrastructure of in situ relationship of osteoclast to bone matrix and necessitate a reinterpretation of the geometry of the secondary lysosome of these cells

Cytotoxic chemotherapy for incurable colorectal cancer: living with a PICC-line

<b>Aims.</b> (i) To determine which aspects of living with a peripherally inserted central catheter (PICC) line cause Modified de Gramont (MdG) patients most difficulty. (ii) To explore MdG patients' views of the PICC-line experience. (iii) To determine if patients view PICC-lines as a benefit or a burden when receiving ambulatory MdG chemotherapy. <b>Design.</b> A two-stage, descriptive study. <b>Methods.</b> Phase 1 comprised semi-structured interviews. Phase 2 surveyed the MdG population. Phase 1 interview data informed the Phase 2 questionnaire. The setting was a West of Scotland Cancer Care Centre and the sample was: Phase 1, a convenience sample of 10 MdG patients; Phase 2, 62 consecutive patients. <b>Results.</b> A response rate of 93·9% for Phase 2. The majority of PICC-line patients held favourable views towards having a PICC-line and adapted well with minimal disruption to daily life. Concerns were evident regarding coping at home with a PICC-line, chemotherapy spillage, dealing with complex information and the responsibility of patients/carers regarding PICC-line management. Patients preferred ambulatory chemotherapy to in-patient treatment. <b>Conclusions.</b> PICC-lines should be considered for more chemotherapy patients but service development is necessary to ensure individual needs are addressed. <b>Relevance to clinical practice.</b> Contributes to the PICC-line literature by providing a national patient perspective on a range of daily living activities (DLAs). PICC-line patients prefer out-patient ambulatory chemotherapy rather than in-patient treatment. The longer a patient has a PICC-line, the more able they are to manage activities such as dressing. Concerns remain over chemotherapy spillage, partner/carer responsibility for PICC-line maintenance and the proper balance between required information and what the patient wants to know

Complications of Peripherally Inserted Central Venous Catheters: A Retrospective Cohort Study

Background and Aim The use of venous catheters is a widespread practice, especially in oncological and oncohematological units. The objective of this study was to evaluate the complications associated with peripherally inserted central catheters (PICCs) in a cohort of patients. Materials and Methods In this retrospective cohort study, we included all patient carrying PICCs (n = 603) inserted at our institute between October 2010 and December 2013. The main variables collected were medical diagnosis, catheter care, location, duration of catheterization, reasons for catheter removal, complications, and nursing care. Complications were classified as infection, thrombosis, phlebitis, migration, edema, and/or ecchymosis. Results All patients were treated according to the same “nursing care” protocol. The incidence rate of complications was two cases per 1000 days of catheter duration. The most relevant complications were infection and thrombosis, both with an incidence of 0.17 cases per 1000 days of the total catheterization period. The total average duration of catheterization was 170 days [SD 6.06]. Additionally to “end of treatment” (48.42%) and “exitus”, (22.53%) the most frequent cause of removal was migration (displacement towards the exterior) of the catheter (5.80%). Conclusions PICCs are safe devices that allow the administration of long-term treatment and preserve the integrity of the venous system of the patient. Proper care of the catheter is very important to improve the quality life of patients with oncologic and hematologic conditions. Therefore, correct training of professionals and patients as well as following the latest scientific recommendations are particularly relevant