Numerička aproksimacija dvodimenzionih paraboličkih problema sa delta funkcijom

Granični problemi za parcijalne diferencijalne jednačine predsta- vljaju matematičke modele najraznovrsnijih pojava, kao na primer pro- voea toplote, mehanike fluida, procesa atomske fizike itd. Samo u retkim slučajevima ovi zadaci se mogu rexiti klasiqnim metodama ma- tematičke analize, dok se u svim ostalim mora pribegavati priblinim metodama. Metoda konaqnih razlika je jedan od najčešće primeiva- nih metoda za numeričko rešavanje graničnih problema za parcijalne diferencijalne jednačine. U okviru metode konačnih razlika, jedan od glavnih problema je dokazivanje konvergencije diferencijskih shema koje aproksimiraju granične probleme. Od posebnog interesa su ocene brzine konvergencije saglasne sa glatkošću koeficijenata i rešenja početnog problema. Prilikom numeričke aproksimacije poqetno-graničnih paraboliqkih problema sa generalisanim rešenjima javljaju se i neki dodatni pro- blemi: koeficijenti nisu neprekidne funkcije, promenljivi koefici- jenti mogu biti i vremenski zavisni, koeficijenti i rešenje pripadaju nestandardnim anizotropnim prostorima Soboljeva itd. Ova disertacija se upravo bavi tim problemima.Boundary problems for partial differential equations represent mathema- tical models of the most diverse phenomena, such as heat transfer, uid me- chanics, atomic physics, etc. Only in rare cases, these tasks can be solved by classical methods of mathematical analysis, while in all other must be resort to approximate methods. Finite-difference method is one of the most commo- nly used methods for the numerical solution of boundary value problems for partial differential equations. In the context of nite-difference method, one of the main problems is proving convergence of difference schemes which appro- ximating boundary problems. Of particular interest are the estimates of the rate of convergence compatible with the smoothness of the coefficients and solution. When numerical approximations parabolic initial-boundary problems with generalized solutions, there are also some additional problems: the coefficients are not continuous functions, variable coefficients can be time-dependent coe- fficients and the solution belong to nonstandard anisotropic Sobolev spaces, etc. This dissertation is concerned with precisely these problems. The dissertation is considered a two-dimensional parabolic initial-boundary problem with concentrated capacity, that problem contains Dirac delta functi- on as the coefficient of the derivative by time. A further problem, in the case boundary problems with delta function as the coefficient, is that solution not in standard Sobolev spaces. The paper demonstrated a priori estimates of the corresponding non-standard norms. Assuming that the coefficients belong to anisotropic Sobolev spaces have been constructed the difference schemes with averaged right-hand side. The estimates of the rate of convergence in the spe- cial discrete fW2; 1 2 and fW1; 1=2 2 norms, is proved. The estimates of the rate of convergence compatible with the smoothness of the coefficients and solution, are obtained

Influence of Different Defoliation Timings on Quality and Phenolic Composition of the Wines Produced from the Serbian Autochthonous Variety Prokupac (Vitis vinifera L.)

The variety Prokupac is the dominant variety in the vineyards of Southern Serbia, which produces quality wines of characteristic and unique tastes. In the agroecological conditions of the Prokuplje vine district, the influence of manual defoliation on the phenolic profile of the wine produced from the variety Prokupac was examined. Four experimental treatments with different timings of manual defoliation were applied: early defoliation—treatment I, early defoliation— treatment II, late defoliation—treatment III and the control. The phenolic profile of the wine was determined for the three treatments of defoliation and the control treatment. Additionally, a multivariate analysis was applied on the obtained results, together with already published data (grape seeds and skins phenolic profiles). Identification and quantification of the phenolic compounds was performed using ultra-high-performance liquid chromatography (UHPLC) with an ultraviolet multi-diode detector (DAD) and mass detector with three analyzers—triple quadrupole (QQQ). Based on the obtained results, it was determined that there are significant differences between the experimental treatments in the content of individual polyphenols, total polyphenols and the antioxidant capacity. Twenty (20) phenolic compounds were identified in the wine samples of the experimental treatments. Defoliation significantly affected the variations of the contents of phenolic acids and flavonoids. In treatment III, the highest content of gallic acid was obtained, while the treatments with early defoliation did not differ in relation to the control sample. Early defoliation in treatments I and II had an effect on the phenolic composition of the wine by favoring the accumulation of flavonol, while the content of hydroxycinnamic acid and total anthocyanins (TAC) was higher in treatment III. The TAC increases with later defoliation. The wines obtained by the defoliation treatments did not show higher antioxidant activity compared to the control sample. A principal component analysis resulted in clustering of the samples based on the phenolic components characteristic for each group of samples

Numerička aproksimacija dvodimenzionih paraboličkih problema sa delta funkcijom

Granični problemi za parcijalne diferencijalne jednačine predsta- vljaju matematičke modele najraznovrsnijih pojava, kao na primer pro- voea toplote, mehanike fluida, procesa atomske fizike itd. Samo u retkim slučajevima ovi zadaci se mogu rexiti klasiqnim metodama ma- tematičke analize, dok se u svim ostalim mora pribegavati priblinim metodama. Metoda konaqnih razlika je jedan od najčešće primeiva- nih metoda za numeričko rešavanje graničnih problema za parcijalne diferencijalne jednačine. U okviru metode konačnih razlika, jedan od glavnih problema je dokazivanje konvergencije diferencijskih shema koje aproksimiraju granične probleme. Od posebnog interesa su ocene brzine konvergencije saglasne sa glatkošću koeficijenata i rešenja početnog problema. Prilikom numeričke aproksimacije poqetno-graničnih paraboliqkih problema sa generalisanim rešenjima javljaju se i neki dodatni pro- blemi: koeficijenti nisu neprekidne funkcije, promenljivi koefici- jenti mogu biti i vremenski zavisni, koeficijenti i rešenje pripadaju nestandardnim anizotropnim prostorima Soboljeva itd. Ova disertacija se upravo bavi tim problemima.Boundary problems for partial differential equations represent mathema- tical models of the most diverse phenomena, such as heat transfer, uid me- chanics, atomic physics, etc. Only in rare cases, these tasks can be solved by classical methods of mathematical analysis, while in all other must be resort to approximate methods. Finite-difference method is one of the most commo- nly used methods for the numerical solution of boundary value problems for partial differential equations. In the context of nite-difference method, one of the main problems is proving convergence of difference schemes which appro- ximating boundary problems. Of particular interest are the estimates of the rate of convergence compatible with the smoothness of the coefficients and solution. When numerical approximations parabolic initial-boundary problems with generalized solutions, there are also some additional problems: the coefficients are not continuous functions, variable coefficients can be time-dependent coe- fficients and the solution belong to nonstandard anisotropic Sobolev spaces, etc. This dissertation is concerned with precisely these problems. The dissertation is considered a two-dimensional parabolic initial-boundary problem with concentrated capacity, that problem contains Dirac delta functi- on as the coefficient of the derivative by time. A further problem, in the case boundary problems with delta function as the coefficient, is that solution not in standard Sobolev spaces. The paper demonstrated a priori estimates of the corresponding non-standard norms. Assuming that the coefficients belong to anisotropic Sobolev spaces have been constructed the difference schemes with averaged right-hand side. The estimates of the rate of convergence in the spe- cial discrete fW2; 1 2 and fW1; 1=2 2 norms, is proved. The estimates of the rate of convergence compatible with the smoothness of the coefficients and solution, are obtained

Finite difference approximation for the 2d heat equation with concentrated capacity

© 2018, University of Nis. All rights reserved. The convergence of difference scheme for two-dimensional initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficients of the space derivatives, is considered. An estimate of the rate of convergence in a special discrete Sobolev norms, compatible with the smoothness of the coefficients and solution, is proved

Finite difference approximation for parabolic interface problem with time-dependent coefficients

The convergence of difference scheme for two-dimensional initialboundary value problem for the heat equation with concentrated capacity and time-dependent coefficients of the space derivatives, is considered. An estimate of the rate of convergence in a special discrete W1,1/22 Sobolev norm, compatible with the smoothness of the coefficients and solution, is proved

Fractional order convergence rate estimate of finite-difference method for the heat equation with concentrated capacity

The convergence of difference scheme for initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficient of the space derivatives, is considered. Fractional order convergence rate estimate in a special discrete Sobolev norms, compatible with the smoothness of the coefficient and solution, is proved

Primena GWO algoritma za generisanje zatvorene putanje u optimalnoj sintezi ravnih mehanizama

The problem of optimal synthesis of four-bar linkage and adjustable slider crank mechanism for generating a closed path was considered in this paper. Two cases were considered. In the first case, the goal is to optimize the path given by a set of predefined points. In the second case, a multi-criteria optimization problem is considered, ie. the path and adjustable length of slider were optimized. The grey wolf algorithm was applied in the process of optimal synthesis. The proposed algorithm has been tested on appropriate numerical examples from the literature to demonstrate its efficiency.Publishe

Malignant fibrous histiocytoma of the right upper leg – A case report

© 2018, Inst. Sci. inf., Univ. Defence in Belgrade. All rights reserved. Introduction. Malignant fibrous histiocytoma is a fast spreading pleomorphic sarcoma with a high malignant potential. Its spreading is characterized with local invasion and distant metastazes with early onset. Most common localisations of development are extremities, trunk and retroperitoneum. Given the line of rare case and specimen, lack of a clear etiology and mechanisms of this disease, as well as adequate histopathologic findings and intraoperative documentation, we presented current status, discuss putative etiology, histopathology with variant morphology, differential diagnosis and treatment modalities. Case report. We presented a 56-years-old female Serbian with tumor in the thigh that clinically resembles incapsulated hematoma. Computed tomography revealed intramuscular tumor with a heterodense structure and compression on surround tissue. Ex tempore biopsy specimen showed malignant potential of the tumor. Wide and radical excision of the nodule has been done, and definitive histopathological verification revealed malignant fibrous histiocytoma. Conclusion. Malignant fibrous histiocytoma is a most common type of soft tissue sarcomas in adults. Frequent localization is on lower extremities, and every rapidly enlarging nodule in this localization that on computed tomography is like incapsulated hematoma with necrotic zone should alert suspicion on presence of this type of sarcoma