tel.: +385 1 459 44 44, fax: +385 1 459 44 69

E-mail: ured@znanost.hr

**Type of paper**:*Paper in journal*

**Title:**Basis of splines associated with some singular differential operators

**Authors:**- Rogina, Mladen (95213)

**Journal**: BIT

**Number**: 32

**Year**: 1992

**Pages**: from 496 to 505

**Number of references**: 16

**Language**: engleski

**Summary**: Functions being piecewise in the kernel of D(k)DpD are a special case of Chebyshev splines having one nontrivial weight and also a special case of singular splines. An algorithm is designed which enables calculating with related B-splines and their derivatives. If p(x) is approximated by a piecewisw constant, an interesting recurrence for calculating with polynomial splines is obtained.

**Keywords**: spline,Chebyshev systems,recurrence relations,collocation,singular boundary value problems

**Type of paper**:*Paper in journal*

**Title:**Incommensurate periodic configurations in systems with real order parameter

**Authors:**- Dananiš, Vladimir
- Bjelić, Aleksandar
- Rogina, Mladen (95213)

**Journal**: Physical Review A

**Number**: 6

**Volume**: 46

**Year**: 1992

**Pages**: from 3551 to 3555

**Number of references**: 12

**Language**: engleski

**Summary**: Considering the standard Landau model we demonstrate that the phase diagrams for the lock-in to the uniformed and dimerized ordering contain a novel class of periodic configurations. They are formed as sequences of local commnesurate and incommensurate modulation. The simplest representatives are calculated numerically. Being stable in narrow ranges of control parameter, these configurations might be the source og global hysteresis and memory effects seen in particular systems.

**Type of paper**:*Paper in journal*

**Title:**Prediction Power of Mathematical Models for Tumor Growth

**Authors:**- Marućiš, Miljenko (125056)
- Vuk-Pavloviš, Stanimir

**Journal**: Journal of Biological Systems

**Number**: 1

**Volume**: 1

**Year**: 1993

**Pages**: from 69 to 78

**Language**: engleski

**Summary**: We compared the Gompertz model, the generalized Gompertz model, the Piantadosi model, the autostimulation model and the polynomials for the power to predict growth of multicellular tumor spheroids as paradigms of the prevascular phase of tumor growth. For the comparison of models we developed a criterion that established the Gompertz model as the model with the best prediction power. The prediction power of the remaining models was ranked in the declining order: the generalized Gompertz model; the mutually indistinguishable Piantadosi model and the autostimulation model; and the polynomials. The ranking of models was not affected by the applied minimization criteria of weighted least squares, unweighted least squares and fitting to logarithmically transformed data, but the prediction power was affected by these criteria. The best predictions were obtained by weighted least squares, closely followed by fitting to logarithmically transformed data. The unweighted least-squares minimization was much less applicable for prediction (and description) of growth.

**Type of paper**:*Summary in proceedings*

**Title:**

**Authors:**- Marućiš, Miljenko (125056)
- Bajzer, Željko
- Freyer, J.
- Vuk-Pavloviš, Stanimir

**Proceedings title**: Proceedings of Annual Meeting of the American Association for Cancer Researc

**Language**: engleski

**Place**: Houston, Texas, USA

**Year**: 1991

**Meeting**: Annual Meeting of the American Assocation for Cancer Research

**Held**: from 05/15/91 to 05/18/91

**Type of paper**:*Summary in proceedings*

**Title:**

**Authors:**- Marućiš, Miljenko (125056)
- Bajzer, Željko
- Vuk-Pavloviš, Stanimir

**Proceedings title**: Proceedings of 2.ICIAM

**Language**: engleski

**Year**: 1991

**Meeting**: 2. ICIAM

**Held**: from 07/08/91 to 07/12/91

**Type of paper**:*Summary in proceedings*

**Title:**

**Authors:**- Marućiš, Miljenko (125056)
- Rogina, Mladen (95213)

**Proceedings title**: Proceeding of 2. ICIAM

**Language**: engleski

**Place**: Washington, DC, USA

**Year**: 1991

**Meeting**: 2. ICIAM

**Held**: from 07/08/91 to 07/12/91

**Type of paper**:*Summary in proceedings*

**Title:**

**Authors:**- Marućiš, Miljenko (125056)

**Proceedings title**: Proceedings of ICIAM 95.

**Language**: engleski

**Place**: Hamburg, Germany

**Year**: 1995

**Meeting**: ICIAM 95

**Held**: from 07/03/95 to 07/07/95

**Type of paper**:*Ph.D.*

**Title:**New recurrent relations for Chebyshev splne functions and their applications

**Faculty**: Prirodoslovno-matematički Zagreb

**Author**: ROGINA MLADEN

**Date of defense**: 04/01/94

**Language**: hrvatski

**Number of pages**: 125

**Summary**: A recurrence relation for derivatives of Chebyshev splines is developed. In case of piecewise constant weights, it is shown that an algorithm for computing local basis of B-splines can be deduced for parabolic and cubic splines with jumps in derivatives. For hermitic splines a most general two-term recurrence relation of deBoor-Cox type is obtained. A stable knot insertion algorithm is given for cubic splines with jumps in second derivatives, and a problem of computing a local basis thus solved completely. Some Chebyshev and polynomial splines are used in methods of colloaction type for solving boundary value problems. Algorithms for solving these problems numerically, and an optimal choice of collocation points are discused.

**Keywords**: Chebyshev splines,differential equations,collocation,singular boundary value problems,knot insertion algorithms

**Type of paper**:*M.A.*

**Title:**Collocation by Spline in Tension

**Faculty**: Prirodoslovno-matematički Zagreb

**Author**: MARUŠIĆ MILJENKO

**Date of defense**: 04/01/92

**Language**: hrvatski

**Number of pages**: 94

**Summary**: Uniform error estimates aer developed for interpolation by spline in tension. These are used for proof of convergence of the collocation method for second order boundary value problems. Specially, singular boundary value problems can be treated nicely.

**Keywords**: Spline in tension,interpolation,collocation,second order boundary value problems

**Type of paper**:*M.A.*

**Title:**Solution of linear boundary value problems by approximating coefficients

**Faculty**: Prirodoslovno-matematički Zagreb

**Author**: ČIŽMEŠIJA ALEKSANDRA

**Date of defense**: 05/01/94

**Language**: hrvatski

**Number of pages**: 155

**Summary**: Numerical testing of the Pruess method for regular Sturm-Liouville problems, based on piecewise polynomial approximation of the coeficients in the differential equations. The case of piecewise constant approximation of coefficients in considerd in greater depth. Numerical experimenting has been performed by the Pruess's software package SLEDGE.

**Keywords**: Eigenvalues, differential operators, collocation

**Type of paper**:*M.A.*

**Title:**

**Faculty**: Prirodoslovno-matematički Zagreb

**Date of defense**: 02/23/95

**Language**: hrvatski

**Number of pages**: 126

**Summary**: Using truncation, we obtain numerical methods from the stochastic Ito-Taylor formula. The implementatin of such methods requires the generation of multiple stochastic integrals of higher order. These being very difficult to simulate, numerical result with a higher order are not proposed.

**Type of paper**:*Mentorship*

**Title:**Solutions of linear boundary value problems by approximating the coefficients

**Faculty**: Prirodoslovno-matematički Zagreb

**Mentor**: COFFOU EMIL

**Date of defense**: 05/01/95

**Number of pages**: 155

**Author**: Čižmešija mr Aleksandra

**Degree level**: M.A.

**Type of paper**:*Mentorship*

**Title:**Collocation by spline in tension

**Faculty**: Prirodoslovno-matematički Zagreb

**Mentor**: COFFOU EMIL

**Date of defense**: 01/01/92

**Number of pages**: 95

**Author**: Marućiš Mr Miljenko

**Degree level**: M.A.

**Type of paper**:*Invited lecture*

**Title:**

**Institution**: Internation centre for Mathematical Studies

**Year**: 1995

**Type of paper**:*Invited lecture*

**Title:**

**Institution**: Croatian insurance bureau

**Year**: 1995

Ministry of Science and Technology |
Croatian language |
Svibor homepage |
Alphabetic list |
Sorted on project code |
Sorted on institutions |
Search | Help |

Information: svibor@znanost.hr