Published papers on project 1-01-254

• Paper in journal 0
  
• Summary in proceedings 4
  
• Ph.D. 1
  
• M.A. 3
  
• Mentorship 2
  
• Invited lecture 2
  

1. 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
   

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2. 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.
   

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3. 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.
   

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4. 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
   

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5. 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
   

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6. 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
   

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7. 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
   

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8. 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
   

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9. 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
   

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10. 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
    

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11. 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.
    

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12. 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.
    

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13. 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.
    

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14. Type of paper: Invited lecture
    

    Title:
    Institution: Internation centre for Mathematical Studies
    Year: 1995
    

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15. Type of paper: Invited lecture
    

    Title:
    Institution: Croatian insurance bureau
    Year: 1995
    

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