On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.Comment: 27 pages; 1 figur

Asymptotic behavior of a system of linear fractional difference equations

We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a + xn)/(b + yn), yn+1 = (d + yn)(e + xn), n = 0,1…, where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equilibrium, of this system

Balint Groups as a Driving Force of Ego Development

This paper gives an overview of one of the main components in the process of Balint groups. The paper is based on the authors\u27 research on the work of Balint groups and the study of literature which deals with the development of ego and the role of Balint groups in the development of participants’ ego. This field is of great interest to the Balint movement and education in medicine. The special place in the discussions on the Balint method is given to the issue of benefit and the nature of influence of the Balint groups on participants. The Balint movement is of special interest for Croatia since it was perhaps among the first in the world to introduce Balint seminars as an official part of education of family doctors. The Croatian Society of Balint Groups as early as in 1970\u27s became a part of the International Federation of Balint Groups. Professor Betlheim was Michael Balint\u27s friend and his followers introduced the method not only in medicine but also in other professions: social work, pedagogy, psychology, sociology etc. The Balint’s method is also very interesting and useful to stomatologists, orthopedists and physiotherapists. Croatian dentists joined the Balint Groups in 1983 and orthopaedists in 1987. These were the unique cases in the European context. The Balint groups are very efficient and necessary in the process of strenghtening ego and selfawarness of these professionals. The paper also discusses the increase of the doctor\u27s self-awareness and selfconsciousness during the process of training in the Balint Groups. The Balint Groups only insist on the doctor-patient relationship and do not interfere with the unconscious of the doctor’s preoccupations. The approach of Enid Balint strives to find harmony between the Balint’s approach and the psychoanalytic approach to the object of the research. According to her understanding, the development of the group atmosphere is similar to the one in the family. The authors reach a similar conclusion in their research

Invariant Manifolds for Competitive Systems in the Plane

Let $T$ be a competitive map on a rectangular region $\mathcal{R}\subset \mathbb{R}^2$, and assume $T$ is $C^1$ in a neighborhood of a fixed point $\bar{\rm x}\in \mathcal{R}$. The main results of this paper give conditions on $T$ that guarantee the existence of an invariant curve emanating from $\bar{\rm x}$ when both eigenvalues of the Jacobian of $T$ at $\bar{\rm x}$ are nonzero and at least one of them has absolute value less than one, and establish that $\mathcal{C}$ is an increasing curve that separates $\mathcal{R}$ into invariant regions. The results apply to many hyperbolic and nonhyperbolic cases, and can be effectively used to determine basins of attraction of fixed points of competitive maps, or equivalently, of equilibria of competitive systems of difference equations. Several applications to planar systems of difference equations with non-hyperbolic equilibria are given.Comment: 20 pages, 2 figure

Health Status as Geneologic Burden in Aging Process

Knowledge of modern molecular biology is leading to the idea that aging and diseases of the aged are two different entities. Healthy life is relatively limited by the specific number of chronic conditions which are present more in old age. Up to now the idea of aging as a process in relation to the individual, organ, tissue, cell or a molecule. There are only few studies on the influence of aging within a single family and even less of aging within several generations of the same family. Genealogic level is one way of getting into the process of family system and aging throughout time. The aim of the study was to determine the significance of genealogical burden with regard to the health status in examinees with different cognitive capabilities. The difference according to sex and age was not significant between the two groups. Health status of the examinees proband in both groups showed 34.4% healthy examinees in the group D and 65.3% in group G. The difference between the two groups was statistically significant. The difference of health status of parents (II. generation) was statistically significant in both groups. Morbidity of diseases was not statistically significant. Most of the ancestors from the grandmothers and grandfathers (III generation) died. (group G–97.5%, group D–100%). Statistically significant difference is present among the diseases of the circulatory system and those of digestive system in this generation. Data on the ancestors of the IV. generation showed that all the relatives died in both groups. Conclusion: the health status of the examinees with higher impairment in the test of cognitive capabilities is worse and they come from the families with worse health status

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form xn+1 = x2n-1/(ax2n + bxnxn-1 + cx2n-1), n = 0, 1, 2, …, where the parameters a, b, and c are positive numbers and the initial conditions x−1 and x0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable

Balint Groups as a Driving Force of Ego Development

This paper gives an overview of one of the main components in the process of Balint groups. The paper is based on the authors\u27 research on the work of Balint groups and the study of literature which deals with the development of ego and the role of Balint groups in the development of participants’ ego. This field is of great interest to the Balint movement and education in medicine. The special place in the discussions on the Balint method is given to the issue of benefit and the nature of influence of the Balint groups on participants. The Balint movement is of special interest for Croatia since it was perhaps among the first in the world to introduce Balint seminars as an official part of education of family doctors. The Croatian Society of Balint Groups as early as in 1970\u27s became a part of the International Federation of Balint Groups. Professor Betlheim was Michael Balint\u27s friend and his followers introduced the method not only in medicine but also in other professions: social work, pedagogy, psychology, sociology etc. The Balint’s method is also very interesting and useful to stomatologists, orthopedists and physiotherapists. Croatian dentists joined the Balint Groups in 1983 and orthopaedists in 1987. These were the unique cases in the European context. The Balint groups are very efficient and necessary in the process of strenghtening ego and selfawarness of these professionals. The paper also discusses the increase of the doctor\u27s self-awareness and selfconsciousness during the process of training in the Balint Groups. The Balint Groups only insist on the doctor-patient relationship and do not interfere with the unconscious of the doctor’s preoccupations. The approach of Enid Balint strives to find harmony between the Balint’s approach and the psychoanalytic approach to the object of the research. According to her understanding, the development of the group atmosphere is similar to the one in the family. The authors reach a similar conclusion in their research

Health Status as Geneologic Burden in Aging Process

Knowledge of modern molecular biology is leading to the idea that aging and diseases of the aged are two different entities. Healthy life is relatively limited by the specific number of chronic conditions which are present more in old age. Up to now the idea of aging as a process in relation to the individual, organ, tissue, cell or a molecule. There are only few studies on the influence of aging within a single family and even less of aging within several generations of the same family. Genealogic level is one way of getting into the process of family system and aging throughout time. The aim of the study was to determine the significance of genealogical burden with regard to the health status in examinees with different cognitive capabilities. The difference according to sex and age was not significant between the two groups. Health status of the examinees proband in both groups showed 34.4% healthy examinees in the group D and 65.3% in group G. The difference between the two groups was statistically significant. The difference of health status of parents (II. generation) was statistically significant in both groups. Morbidity of diseases was not statistically significant. Most of the ancestors from the grandmothers and grandfathers (III generation) died. (group G–97.5%, group D–100%). Statistically significant difference is present among the diseases of the circulatory system and those of digestive system in this generation. Data on the ancestors of the IV. generation showed that all the relatives died in both groups. Conclusion: the health status of the examinees with higher impairment in the test of cognitive capabilities is worse and they come from the families with worse health status

Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation

By using the KAMtheory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1 = (2axn)/(1 + x2n) – xn-1, n = 0, 1, …, where x-1, x0, ∈ (−∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions