DYNAMICS OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Linear Difference Equations with Constant Coefficients Linear Difference Equations with Variable Coefficients Stability Stability in the Non-Hyperbolic Case Bifurcations Dynamica Session Symbolic Dynamics for One-Dimensional Maps Dissipative Maps and Global Attractivity Parametrisation and Poincare Functional Equation Exercises DYNAMICS OF TWO-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Linear Theory Equilibrium Solutions The Riccati Equation Linearized Stability Analysis Dynamica Session Period Doubling Bifurcation Lyapunov Numbers Box Dimension Semicycle Analysis Stable and Unstable Manifold Dynamica Session on Henon's Equation Invariants Lyapunov Functions, Stability, and Invariants Dynamica Session on Lyness' Map Dissipative Maps and Systems Dynamica Session on Rational Difference Equations Area-preserving Maps and Systems Biology Applications Projects Applications in Economics Exercises SYSTEMS OF DIFFERENCE EQUATIONS, STABILITY, AND SEMICYCLES Introduction Linear Theory Stability of Linear Systems The Routh-Hurwitz and Schur-Cohn Criterion Nonlinear Systems and Stability Limit Sets and Invariant Manifolds Dissipative Maps Stability of Difference Equations Semicycle Analysis Dynamica Session on Semicycles Exercises INVARIANTS AND RELATED LYAPUNOV FUNCTIONS Introduction Invariants for Linear Equations and Systems Invariants and Corresponding Lyapunov Functions for Nonlinear Systems Invariants of Special Class of Difference Equations Applications Dynamica Session on Invariants Dynamica Session on Lyapunov Functions Invariance under Lie Group Transformations Exercises DYNAMICS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Dynamica Session on Third Order Difference Equations Dissipative Difference Equation of Third Order Dynamica Session on Local Asymptotic Stability of Period-Two Solution Dynamica Session on Todd's Difference Equation Biology Applications Projects Exercises FRACTALS GENERATED BY ITERATED FUNCTIONS SYSTEMS Introduction Basic Definitions and Results Iterated Function System Basic Results on Iterated Functions Systems Calculation of Box Dimension for IFS Dynamica Session Exercises BIBLIOGRAPHY INDEX

Cystatin C is a natural inhibitor of the cysteine proteinases papain, and mammalian lysosomal cathepsins B, H, L and S. This protein is thought to serve an important physiological role as a local regulator of enzyme activity. The changes of levels of cystatin C in extracellular fluids have shown themselves having potential clinical importance. We have purified cystatin C from urine of patients with chronic renal failure by procedure using affinity chromatography on CM-papain Sepharose, gel filtration on Sephacryl S-200, and ion exchange chromatography on CM-cellulose. After isolation we obtained three inhibitory peaks (pI's from 7.8 to 9.2) which represent isoforms of the same protein. These isoforms are immunologically identical and differ in N-terminal sequence of the molecule. The form with pI 9.2 represents the intact inhibitor form, whereas the form with pI 7.8 is shortened for 8 amino-acid residues at N-terminal end. Purified cystatin C pI 9.2 was used for immunization of rabbits. Polyclonal antibodies, produced in rabbits, were isolated from rabbit sera by affinity chromatography on Protein A Sepharose. Enzyme immunoassay (ELISA) for cystatin C is developed on the basis of purified antibodies. Using ELISA test we determined amount of cystatin C in urine and serum samples of patients with chronic renal failure. The concentration of the inhibitor in the urine of these patients was approximately 100-fold more than in normal urine. In the serum from the same patients we found concentrations of cystatin C to be five times higher in comparison with the serum of healthy individuals.

Posttraumatic Stress Disorder (PTSD) very often occurs accompanied with other psychiatric disorders such as: Alcohol and Drug abuse, Personality Disorder, General Anxiety Disorder, Obsessive Compulsive Disorder, Schizophrenia etc. Sometimes it might be a problem for clinicians to differ PTSD symptoms from symptoms of coexisting psychic disorders. The aim of this study was to present the most common PTSD coexisting psycho-disorders. This research was conducted during the period from April 1998 to October 1999. Participants were divided in two groups each containing 30 examinees. The first group consisted of 30 participants with symptoms of PTSD only while the second group included participants who suffered from both PTSD and other psychic disorders (co-morbidity). Both groups were quite similar regarding participants gender and age. The scientific tools used in the research were: Standard Psychiatric Interview, Harvard Trauma Questionnaire (HTQ), Hamilton Anxiety Rating Scale, Hamilton Depression Rating Scale, and Drug and Alcohol Abuse Checklist. Our research results are indicating that PTSD symptoms are most common in middle-aged persons, regardless of their gender and age. We have found following coexisting psychic disorders: personality disorder 46.6% (from which 13.3% is permanent personality disorder after the traumatic experience); depression 29.9% (depression without psychotic symptoms 23.3% and depression with coexisting psychotic symptoms 6.6%); drug abuse 13.3; alcohol abuse 6.7% and dissociative (conversion) disorder 3.3%. The results of our work are suggesting that co-morbid psychic symptoms have significant regressive influence on PTSD course and prognosis.

Lethal and sublethal genetical factors, including Rh factor, represent endogenous risk factors of the pregnancy outcome. These factors are most frequently inherited in recessive way and they often lead to the negative outcome of pregnancies. They represent pregnancy (a prirori) risk of various degrees. Inheritance of Rh system blood groups is linked to chromosome 1 and it could be explained by two alternative theories; molecular Rh system genetics has not yet been completely explained. The first formal-genetic theory postulates three closely linked gene sites (loci C, D and E) while the second theory has a monogenic character (one locus with several allele genes). Data on 755 pregnancies, which were (for various reasons) estimated as increased risk pregnancies, were registered at Gynaecology Clinic, Clinical Centre of University of Sarajevo, during the period from 1989 to 1992. These data were collected from pregnant women who, according to the certain indications from their familiar and personal anamnesis, demanded genetic consultations. The result of investigation of the basic Rh system phenotype distribution shows no statistically significant difference between monitored pregnant women. This result is assumed as valid for both pregnant women and their partners. The same result is suggesting that the observed increased risk pregnancy samples do not significantly differ from the previously studied population samples. Therefore, it has been concluded that Rh factor is not closely related to the increased risk of individual pregnancy outcomes, that is, it does not have relevant influence on the observed reproduction parameters. This result is very interesting and deserves particular medical attention and further evaluation in the future, particularly considering known immunological phenomena resulting from relations between reproduction partners belonging to the basic Rh system phenotypes.

Sustained-release theophylline pellets formulation for once-daily evening administration significantly improved patients compliance and adjusted serum levels profile of the drug. The patients conversion from i.v. to p.o. therapy is one of the most critical steps in the treatment of asthma according to its chronopathophysiological character. In our study we have examined safety and efficiency of this conversion in twelve hospitalised asthmatic patients who were given the new sustained-release theophylline pellets formulation for once-daily evening administration. The lung function parameters (FEV1, VC, RV, and Rt) and serum theophylline concentrations were monitored. So, the values obtained for the last day of i.v. therapy and the fifth day of p.o. therapy were compared. We found that 75% of the patients had no change or improved lung function on the conversion. Our results indicate that this conversion from i.v. to p.o. theophylline therapy is safe and could be efficacious. Also, the maximum theophylline serum levels could safely be predicted by measuring only one serum concentration in p.o. therapy with sustained-release theophylline pellets formulation for once-daily evening administration.