scholarly journals Academician CAIUS IACOB – a Brilliant Mathematician Fascinated by Mechanics

2020 ◽  
Vol 12 (1) ◽  
pp. 243-248
Author(s):  
Nicolae-Florin ZAGANESCU ◽  
Rodica ZAGANESCU ◽  
Constantin-Marcian GHEORGHE
Keyword(s):  
Compressible Flow ◽  
Applied Mathematics ◽  
Flow Theory ◽  
Mathematical Statistics ◽  
French Mathematician ◽  
Mathematics Section ◽  
Romanian Academy ◽  
Brilliant Mathematician ◽  
Phd Thesis

The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912–1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about “Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics”. Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the “Mathematical introduction to the mechanics of fluids”. This book, providing original ways to work with classical hydrodynamics and compressible-flow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the “Romanian Academy Institute of Applied Mathematics”. In 2001 the institute merged with the “Centre for Mathematical Statistics”, which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the “Gheorghe Mihoc – Caius Iacob Institute of Mathematical Statistics and Applied Mathematics” of the Romanian Academy.

APPROXIMATIVE PROPERTIES OF ABEL–POISSON-TYPE OPERATORS ON THE GENERALIZED HÖLDER CLASSES

2021 ◽  
Vol 1 ◽  
pp. 76-83
Author(s):  
Yuri I. Kharkevich ◽  
◽  
Alexander G. Khanin ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Applied Mathematics ◽  
Continuous Functions ◽  
Elliptic Type ◽  
Periodic Functions ◽  
French Mathematician ◽  
First Order ◽  
Function Classes ◽  
In The Beginning ◽  
Poisson Type

The paper deals with topical issues of the modern applied mathematics, in particular, an investigation of approximative properties of Abel–Poisson-type operators on the so-called generalized Hölder’s function classes. It is known, that by the generalized Hölder’s function classes we mean the classes of continuous -periodic functions determined by a first-order modulus of continuity. The notion of the modulus of continuity, in turn, was formulated in the papers of famous French mathematician Lebesgue in the beginning of the last century, and since then it belongs to the most important characteristics of smoothness for continuous functions, which can describe all natural processes in mathematical modeling. At the same time, the Abel-Poisson-type operators themselves are the solutions of elliptic-type partial differential equations. That is why the results obtained in this paper are significant for subsequent research in the field of applied mathematics. The theorem proved in this paper characterizes the upper bound of deviation of continuous -periodic functions determined by a first-order modulus of continuity from their Abel–Poisson-type operators. Hence, the classical Kolmogorov–Nikol’skii problem in A.I. Stepanets sense is solved on the approximation of functions from the classes by their Abel–Poisson-type operators. We know, that the Abel–Poisson-type operators, in partial cases, turn to the well-known in applied mathematics Poisson and Jacobi–Weierstrass operators. Therefore, from the obtained theorem follow the asymptotic equalities for the upper bounds of deviation of functions from the Hölder’s classes of order from their Poisson and Jacobi–Weierstrass operators, respectively. The obtained equalities generalize the known in this direction results from the field of applied mathematics.

scholarly journals Blended Proposal of Orientation Scientific Works by Comparison Face-to-Face and Online Processes

10.28945/3074 ◽  
2007 ◽  
Author(s):  
Pollyana Mustaro
Keyword(s):  
Intrinsic Motivation ◽  
Development Process ◽  
Learning Theories ◽  
Face To Face ◽  
Academic Orientation ◽  
Communication Structures ◽  
Digital Generation ◽  
Phd Thesis ◽  
Virtual Interactions

The execution of academic researches - such as Undergraduate work, Master’s or PhD Thesis - is often supervised by a research advisor. The development process of such works could be characterized as face-to-face, remote or blended orientation, which combines both of former ones. The construction of a proposal for blended academic orientation involves mapping and analysis of elements, as well as didactical and communication structures that would differs face-to-face meetings from virtual interactions. The paper presents some considerations about relevant characteristics related to digital generation and learning theories that value interaction in order to built knowledge, thus allowing the determination of a blended methodology that aims to enhance intrinsic motivation and investigative posture of students at any level.

COMPREHENSIVE INVESTIGATION OF EXTRUSION OF П-SHAPED BRACKETS. REPORT 6. KINEMATIC AND STRESSED STATES OF BLANKET DURING RESTRICTED EXTRUSION. PART 2

2021 ◽  
pp. 38-43
Author(s):  
A. L. Vorontsov ◽  
◽  
S. M. Karpov ◽  
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Plane Deformation ◽  
Flow Theory ◽  
Equation System ◽  
Extrusion Process ◽  
Thick Wall ◽  
Comprehensive Investigation ◽  
Flow Velocities

On the basis of the complete equation system of the plastic flow theory, the solution continuation of the determination problem of the kinematic and stressed states of a blanket during restricted extrusion of П-shaped brackets under conditions of plane deformation in the general case of a nonaligned placement of the punch and the die is stated. The determination of flow velocities and stresses in the area of plastic deformation, located under the punch end near the formed thick wall of the bracket has been carried out. The formulae were obtained, which are required for identification of the main parameters of the extrusion process of П-shaped products with a relatively thin horizontal bridge.

scholarly journals Kinematics of Orion Association Members

1995 ◽  
Vol 164 ◽  
pp. 373-373
Author(s):  
R.L. Smart
Keyword(s):  
Proper Motions ◽  
Linear Approximations ◽  
Orion Association ◽  
Phd Thesis

We discuss the determination of the expansion of the Orion association. Previous estimates of expansion in associations have employed simplified linear approximations which only required the observation of proper motions (cf. Lesh, J.R., ApJ, 152, 905, 1968). We have used proper motions obtained by Smart (PhD Thesis, Univ. of Florida, 1993) with previously obtained membership criteria to investigate this hypothesised expansion without conclusive results.

Photoelast Method and Possible Applications of Mathematical Statistics in Prediction of Stress State of Structural Elements

2014 ◽  
Vol 611 ◽  
pp. 405-411 ◽  
Author(s):  
Oskar Ostertag ◽  
Eva Ostertagová ◽  
Peter Frankovský
Keyword(s):  
Stress State ◽  
Stress Concentration ◽  
Stress Field ◽  
Statistical Methods ◽  
Mathematical Statistics ◽  
Structural Elements ◽  
State Development ◽  
Stress States ◽  
Structural Parts

The presented article is dedicated to stress state development while assessing the concentration of stresses in samples with continuously changing notches. These samples represent connecting elements of structural parts. The stress states of selected samples were determined experimentally by means of reflection photoelasticity. This method is suitable mainly for determination of stress state in the whole area in question, predominantly though for the analysis of stress concentration and its gradient in the notched area. Within the method of reflection photoelasticity, a layer was used to analyse the stress field. When loaded, this layer exhibits the ability of temporal birefringence. One of the statistical methods was selected in order to predict the stress state of other samples with bigger notches.

A compressible flow theory for regenerative compressors with aerofoil blades

2003 ◽  
Vol 217 (11) ◽  
pp. 1241-1257 ◽  
Author(s):  
J W Song ◽  
M Raheel ◽  
A Engeda
Keyword(s):  
Compressible Flow ◽  
Performance Prediction ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Flow Theory ◽  
Point Of View ◽  
Code Design ◽  
Governing Equations ◽  
Compression Process ◽  
Positive Displacement

Regenerative flow compressors (RFCs) are rotodynamic machines capable of producing high heads at very low flowrates. They have very low specific speed and share some of the characteristics of positive displacement machines such as a roots blower, but without the problems of lubrication and wear. They can produce heads equivalent to that of several centrifugal stages from a single rotor with comparable tip speed. The compression process is usually not regarded as efficient. Typically they produce efficiency of less than 50 per cent but still they have found many applications because they allow the use of fluid dynamic compressors in place of positive displacement compressors for duties requiring high heads at low flowrates. There are very few mathematical models in the literature that explain the behaviour of regenerative turbomachines and predict the performance. Most of these models assumed incompressible flow, thus limiting their use to only pumps and blowers. Moreover, they needed extensive experimental support for performance prediction. Hence, it is very interesting from an industrial point of view to find efficient theoretical means that are able to forecast regenerative compressor performances, using easy to find geometric and fluid dynamic parameters. A compressible flow theory is thus presented for the first time in this paper to describe complex three-dimensional corkscrew flow patterns in regenerative compressors. Conventional RFC were designed with radial, non-radial or semicircular impeller blades. In the present investigation, the authors have discussed RFCs with aerofoil blades and an annular flow channel containing a core to direct circulating flow to the blades with a minimum amount of losses. The effects of various geometric elements on the performance of RFCs are studied. All the major sources of losses in blade and channel region are identified. Governing equations for the flow in the compressor are derived and a performance prediction code based on governing equations and loss models is developed. Theoretical performance results are compared with published test data on aerofoil blade RFCs. Based on sensitivity analysis from the code, design changes are suggested for performance improvement.

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