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THE p-BINOMIAL TRANSFORM, CAUCHY NUMBERS AND FIGURATE NUMBERS
BORISLAV STANISHEV BORISOV 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.4
The concepts binomial transform and Pascal triangle are generalized in this paper as the p-binomial transform and the Pascal trapezium. To prove some properties of the p-binomial transform a generalization of the parallel summation identity is derived. It is shown that the Cauchy numbers used in the equation of the center in celestial mechanics are a special case of the p-binomial transform of n-tuples. This result is used to find a relation between the Cauchy numbers and the binomial coefficients. Finally it is shown that some of the figurate numbers are also the p-binomial transform of n-tuples. Using this it is derived an identical form for presenting them with only three parameters.
Socratic Style Support for Transferability of Math Knowledge and Skills
( Borislav Lazarov ) 한국수학교육학회 2014 수학교육 학술지 Vol.2014 No.2
The transferability of knowledge and skills into another context is an indicator for existence or lack of students` synthetic competence. Two teaching experiments took place in 2010/2011 and 2012/2013 scholastic year to clarify some parameters of the Socratic style teaching, in particular how this approach supports decontextualization of the knowledge and skills in dynamic geometry software (DGS) environment. The experimental groups were of advanced students in upper secondary school. The outcomes were similar for the both groups which give us reason to claim that our findings could have more general application in mathematics education in DGS environment.
Socratic Style Support for Transferability of Math Knowledge and Skills
( Borislav Lazarov ) 한국수학교육학회 2014 뉴스레터 Vol.30 No.5
The transferability of knowledge and skills into another context is an indicator for ?existence or lack of students`` synthetic competence. Two teaching experiments took place in 2010/2011 and 2012/2013 scholastic year to clarify some parameters of the Socratic style teaching, in particular how this approach supports decontextualization of the knowledge and skills in dynamic geometry software (DGS) environment. The experimental groups were of advanced students in upper secondary school. The outcomes were similar for the both groups which give us reason to claim that our findings could have more general application in mathematics education in DGS environment.
Developing Synthetic Competence along Individual Educational Trajectory
( Lazarov Borislav ) 한국수학교육학회 2013 수학교육 학술지 Vol.2013 No.-
The paper presents a kind of case study on the effect of implementation of a general model for building mathematics synthetic competence. The momentous of the individual education with an advanced student are given in narrative style. The concept of mathematics synthetic competence is considered in the context of medial term student`s activity which outcome was a new geometrical construction and some results on it. The Socratic style we adopted allowed having a closer look on the interaction of different types of the student`s knowledge and skills in a new context. Evidences for transfer of knowledge and skills are given. An effective upgrade of the synthetic competence was registered.
POLICY INITIATIVES FOR IMPROVING YUGOSLAV ECONOMIC PERFORMANCE
SKEGRO, BORISLAV,GAPINSKI, JAMES H .,ANUSIC, ZORAN 한국국제경제학회 1989 International Economic Journal Vol.3 No.4
With the aid of a timely econometric model, this paper examines policies for improving Yugoslav economic performance. It establishes a baseline path to evaluate the efficacy of policy instruments such as money, government consumption, the exchange rate, technical-progress incentives, and wage-price controls. It then exercises the instruments individually to ascertain their strengths and their patterns of effect. Because the separate scenarios suggest that initiatives might be used advantageously in combination, two policy packages are treated, and both demonstrate that economic performance can be improved comprehensively and dramatically. Sobering thoughts about the politics of the economics close the discussion.
Pero Latkoski,Borislav Popovski 보안공학연구지원센터 2009 International Journal of Multimedia and Ubiquitous Vol.4 No.2
The improvement of the communication systems is conducted through communication protocol engineering and optimization process. This paper presents an effort to upgrade the IEEE 802.16 and IEEE 802.16e protocol performance regarding the delay during subscriber network entry or base station handover. Our communication protocol engineering process of WiMax protocol and its optimization resulted in a new UCD-aware initial ranging transmission opportunity slots distribution. Using an analytical and numerical performance evaluation, we prove the relevance of the new algorithm and the increase of the IEEE 802.16-based network performance.
Goran Stimac,Borislav Spajic,Ante Reljic,Josip Katusic,Alek Popovic,Igor Grubisic,Davor Tomas 대한비뇨의학회 2014 Investigative and Clinical Urology Vol.55 No.8
Purpose: We are often confronted with patients in the “gray zone” (prostate-specific antigen[PSA]<10 ng/mL) whose biopsies reveal no malignancy but only inflammation. We investigated the relationship between histological inflammation and total PSA(tPSA), free PSA (fPSA), and percentage of free PSA (f/tPSA) levels in patients withoutprostate cancer (PC). Materials and Methods: We studied 106 men with tPSA<10 ng/mL who had undergonebiopsy that was negative for PC and who had no clinical prostatitis. Inflammation observedat biopsies was scored for inflammation type in each biopsy core by use of afour-point scale and was then correlated with tPSA, fPSA, and f/tPSA. Results: Different patterns of inflammation were found in each set of biopsies. Regression factor analysis was used to form two groups according to inflammation type:more chronic and more acute. Median tPSA, fPSA, and f/tPSA levels in the more chronicand more acute inflammation groups were 6.4 ng/mL, 1.09 ng/mL, and 15%, and 7.3ng/mL, 0.79 ng/mL, and l2%, respectively. A significant difference was found in fPSA(p=0.003) and f/tPSA (p<0.001), whereas the difference in tPSA was not significant(p=0.200). Total PSA correlated with fPSA (r=0.4, p<0.001) but not with inflammationtype (r=0.12, p>0.010). A correlation existed between inflammation type and fPSA(r=–0.31, p=0.001) and f/tPSA (r=–0.43, p<0.001) in that the fPSA and f/tPSA were lowerin the group with more acute inflammation. Conclusions: Subclinical inflammation has a significant influence on fPSA in patientswith tPSA<10 ng/mL but without PC or clinical prostatitis. Subclinical inflammationis not characterized by elevated tPSA alone but also by a decreased fPSA, a tendencysimilar to that in PC.
Multi-output fuzzy inference system for modeling cutting temperature and tool life in face milling
Pavel Kovac,Dragan Rodic,Vladimir Pucovsky,Borislav Savkovic,Marin Gostimirovic 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.10
This paper proposes a method for cutting parameters identification using the multi-inputs-multi-outputs fuzzy inference system(MIMO-FIS). The fuzzy inference system (FIS) was used to identify the initial values for cutting parameters (cutting speed, feed rate anddepth of cut) and flank wear using cutting temperature and tool life as outputs. The objective was to determine the influence of cuttingparameters on cutting temperature and tool life. The model for determining the cutting temperature and tool life of steel AISI 1060 wastrained (design rules) and tested by using the experimental data. The average deviation of the testing data for tool life was 11.6 %, whilethat of the cutting temperature was 3.28 %. The parameters used in these testing data were different from the data collected for the designrules. The test results showed that the proposed MIMO-FIS model can be used successfully for machinability data selection. The effect ofparameters and their interactions in machining is analyzed in detail and presented in this study.