John Venetis | NTUA - Academia.edu (original) (raw)

Papers by John Venetis

International Review of Electrical Engineering (IREE), 2023

In this paper, an analytical exact form of the Unit Step Function (or Heaviside Step Function) is... more In this paper, an analytical exact form of the Unit Step Function (or Heaviside Step Function) is presented. In particular, this piecewise-defined function, which constitutes a fundamental concept of Operational Calculus and is also involved in many other areas of applied and engineering mathematics, is explicitly performed in a very simple manner by the aid of purely algebraic representations. The novelty of this work, when compared with other analytical approximations to this discontinuous function, is that the proposed exact formula is not performed in terms of non-elementary special functions, e.g. Beta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with a pointwise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Advances in Differential Equations and Control Processes

How to cite this article: J. Venetis, Analytic evaluation of piezometric head for a creeping flow... more How to cite this article: J. Venetis, Analytic evaluation of piezometric head for a creeping flow past a fully constrained obstacle, Advances in Differential Equations and Control

Advances and Applications in Fluid Mechanics, 2015

Introduction. Appropriate treatment of diabetes requires regular intake of recommended drugs. Mul... more Introduction. Appropriate treatment of diabetes requires regular intake of recommended drugs. Multifactorial therapy, which necessitates the concomitant use of many medications, may decrease patient adherence. The purpose of the study was to assess type 2 diabetic patients' adherence to and tolerability of metformin extended-release formulation in the outpatient setting. Materials and methods. This non-interventional study was conducted in a group of 4737 patients [including 2468 (52%) women] with mean age of 60.6 ± 9.4 years, diabetes duration of 5.6 ± 4.4 years, duration of treatment with metformin extended release formulation of 8.3 ± 12 months at an average dose of 1667 ± 350 mg. The study enrolled patients aged over 18 years with type 2 diabetes if they were treated with metformin extended-release formulation at a dose of 1500-2000 mg for less than 1 year prior to the study enrollment. The exclusion criteria included: pregnancy, breast-feeding and any contraindications for metformin treatment. Treatment adherence was assessed by a tablet count (percentage of prescribed tablets taken) and using the Morisky-Green scale. Treatment adherence was defined as follows: excellent patient adherence if > 90% of prescribed tablets were taken; good: 76-90%; moderate: 51-75%; poor: ≤ 50%. Treatment tolerability was also evaluated based on the medical history focused on gastrointestinal symptoms, as well as patient preference for using specific types of metformin. Other patient data, clinical data and laboratory test results were recorded at the beginning of the study and after 3 months. Results. After 3 months of treatment with metformin extended release formulation 96% of study subjects demonstrated excellent or good adherence. Treatment adherence was significantly lower with 2 or 3 concomitant medications as compared to one (p < 0.001). Adverse events occurred in 715 patients (15% out of 4758 patients undergoing safety analysis). The occurrence of adverse events significantly decreased treatment adherence (p < 0.001). Approximately 90% of patients declared they had preferred the use of metformin extended-release formulation. Conclusions. Metformin extended-release formulation is a suitable, well tolerated therapeutic option which helps to obtain good patient cooperation based on

Transylvanian Review, 2019

Dynamic mechanical analysis (DMA) is a useful method which completes the results obtained from se... more Dynamic mechanical analysis (DMA) is a useful method which completes the results obtained from several traditional thermal analysis techniques such as Differential Scanning Calorimetry (DSC), thermogravimetric analysis (TGA), and thermal elastic analysis (TMA). Dynamic constants such as storage and loss modulus depend on temperature and supply valuable information about interfacial bonding between filler and polymeric matrix of a fibrous composite material. In the meanwhile, the glass transition temperature is defined as the point at which the specific volume versus temperature curve changes abruptly slope, marking the region between rubbery polymer and glassy polymer nature. Thus, the behavior of unidirectional fibrous composites was investigated at this region. Further, an examination of the glass transition temperature, which evidently constitutes an upper limit for the structurally important glassy region through the loss factor, was performed by its consideration as a combinat...

JP Journal of Heat and Mass Transfer, 2018

In this work, an advanced body centered polyhedral model to simulate the periodic microstructure ... more In this work, an advanced body centered polyhedral model to simulate the periodic microstructure of hybrid composites is performed. The overall material consists of a polymeric matrix reinforced with unidirectional continuous fibers and spherical particles. According to this model, both fibers and particles are distributed inside the matrix in a deterministic manner and their configurations depend on each other. In addition, inhomogeneous interphase layers of different thicknesses are considered to surround both particles and fibers. Next, by the use of this model which takes into account the filler arrangement and contiguity along with the interphase concept, the author obtains explicit expressions to evaluate the longitudinal and transverse thermal conductivity of the composite.

The objective of this paper is to contribute towards the quality investigation of equations of co... more The objective of this paper is to contribute towards the quality investigation of equations of conservation for two dimensional incompressible flow patterns via a Complex Analysis approach. Specifically, the authors will utilize the aforementioned equations expressed in their known from literature equivalent special formulation in terms of the stream function and its partial derivatives with respect to spatial coordinates. In the sequel, by means of the Theory of Analytic Complex Functions, the authors will infer some quality information about the algebraic and geometrical properties for the family of functions which satisfy these equations for such flow patterns.

In this work, the authors present an approximate solution to three point bending equation for a g... more In this work, the authors present an approximate solution to three point bending equation for a general category of statically determinate continuum beams. The deflection of the beam due to a perpendicular point wise load is evaluated for high rates of its curvature. The load is initially assumed to be imposed at the midspan of the beam, but in continuing we perform an analytical treatment of this problem when the load is imposed at an arbitrary point. Besides, the cross sectional area of the beam is rectangular and remains as it is after its deformation. The proposed solution for both cases consists of power series throughout. Hence, since it does not contain either elliptic integrals or any other miscellaneous, or non elementary special functions, it would be more suitable for the necessary calculations dealing with conceptual or embodiment design from the engineering standpoint.

Mathematics and Statistics, 2014

ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, whic... more ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

Advances in Energy and Power, 2014

In this paper, the author investigates a generic type of the two dimensional incompressible visco... more In this paper, the author investigates a generic type of the two dimensional incompressible viscous boundary layer flows near the inflection point of a smooth curve. In particular, an approximate evaluation of velocity distribution in an "adjacent" region of the inflection point of this curve is derived. Here, it is a priory assumed that this point is unique. Besides, the flow field is supposed to be steady throughout and Prandtl's simplified assumptions for two dimensional boundary layer flows are also taken into consideration. Besides, if the cross-section of a structure can be simulated by such a curve one should denote that its inflection point is from technical aspect a very suitable place for emplacing a wind generator compared with the top of a curve, which is a stationary point, because if a wind generator was located on the top of a curve, it could be exhibited in unexpected strong blasts.

In this paper, the author obtains an analytic exact form of the unit step function, which is also... more In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently co... more In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

In this work, analytical calculations are described to estimate the elastic moduli of polymer com... more In this work, analytical calculations are described to estimate the elastic moduli of polymer composite materials consisting of short fibers, by extending and generalizing a reliable model. The fibers may have a finite length and an orientation characterized as random. An effort was made to complete and improve a previous procedure concerning transversely isotropic composites. To this end, a cylinder model with a short fiber in the centre of the matrix is considered. The elastic moduli were expressed in terms of the fiber content and fiber length. The obtained representations were used to evaluate the moduli of a randomly oriented short fiber composite. A comparison was made with theoretical values derived from two other authors who established trustworthy and accurate models. Finally, our theoretical values were also compared with obtained experimental results.

In the present paper, we shall attempt to make a contribution to approximate analytical evaluatio... more In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet’s principles, is concurrently able to be expanded in Taylor’s representation, over a particular interval of their domain of definition. Thus, we shall take into account the simultaneous validity of these two properties over this interval, in order to obtain an alternative equivalent representation of the corresponding harmonic decomposition for this category of functions. In the sequel, we shall also implement this resultant formula in the investigation of turbulence spectrum of eddies according to known from literature Von Karman’s formulation, making the additional assumption that during the evolution of such stochastic dynamic effects with respect to time, the occasional time-returning period can be actu...

Mathematics and Statistics, 2014

ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, whic... more ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

Advances in Energy and Power, 2014

In this paper, the author investigates a generic type of the two dimensional incompressible visco... more In this paper, the author investigates a generic type of the two dimensional incompressible viscous boundary layer flows near the inflection point of a smooth curve. In particular, an approximate evaluation of velocity distribution in an "adjacent" region of the inflection point of this curve is derived. Here, it is a priory assumed that this point is unique. Besides, the flow field is supposed to be steady throughout and Prandtl's simplified assumptions for two dimensional boundary layer flows are also taken into consideration. Besides, if the cross-section of a structure can be simulated by such a curve one should denote that its inflection point is from technical aspect a very suitable place for emplacing a wind generator compared with the top of a curve, which is a stationary point, because if a wind generator was located on the top of a curve, it could be exhibited in unexpected strong blasts.

In this paper, the author obtains an analytic exact form of the unit step function, which is also... more In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 2021

The intention of this paper is to investigate the boundary roughness of a mounted obstacle which ... more The intention of this paper is to investigate the boundary roughness of a mounted obstacle which is inserted into an incompressible, external and viscous flow field of a Newtonian fluid. In particular, the present study focuses on the cross – sectional area of the obstacle, which is assumed to be a non deformable body (rigid object) with a predefined shape of random roughness. For facility reasons and without violating the generality, one may select the cross – section of the body which contains its center of gravity and is perpendicular to the main flow direction. The boundary of this cross – sectional area is mathematically simulated as the polygonal path of the length of a single – valued continuous function. Evidently, this function should be of bounded variation. The novelty of this work is that the formulation of the random roughness of the boundary has been carried out in a deterministic manner.

Procedia Structural Integrity, 2018

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently co... more In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

International Review of Electrical Engineering (IREE), 2023

In this paper, an analytical exact form of the Unit Step Function (or Heaviside Step Function) is... more In this paper, an analytical exact form of the Unit Step Function (or Heaviside Step Function) is presented. In particular, this piecewise-defined function, which constitutes a fundamental concept of Operational Calculus and is also involved in many other areas of applied and engineering mathematics, is explicitly performed in a very simple manner by the aid of purely algebraic representations. The novelty of this work, when compared with other analytical approximations to this discontinuous function, is that the proposed exact formula is not performed in terms of non-elementary special functions, e.g. Beta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with a pointwise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Advances in Differential Equations and Control Processes

How to cite this article: J. Venetis, Analytic evaluation of piezometric head for a creeping flow... more How to cite this article: J. Venetis, Analytic evaluation of piezometric head for a creeping flow past a fully constrained obstacle, Advances in Differential Equations and Control

Advances and Applications in Fluid Mechanics, 2015

Introduction. Appropriate treatment of diabetes requires regular intake of recommended drugs. Mul... more Introduction. Appropriate treatment of diabetes requires regular intake of recommended drugs. Multifactorial therapy, which necessitates the concomitant use of many medications, may decrease patient adherence. The purpose of the study was to assess type 2 diabetic patients' adherence to and tolerability of metformin extended-release formulation in the outpatient setting. Materials and methods. This non-interventional study was conducted in a group of 4737 patients [including 2468 (52%) women] with mean age of 60.6 ± 9.4 years, diabetes duration of 5.6 ± 4.4 years, duration of treatment with metformin extended release formulation of 8.3 ± 12 months at an average dose of 1667 ± 350 mg. The study enrolled patients aged over 18 years with type 2 diabetes if they were treated with metformin extended-release formulation at a dose of 1500-2000 mg for less than 1 year prior to the study enrollment. The exclusion criteria included: pregnancy, breast-feeding and any contraindications for metformin treatment. Treatment adherence was assessed by a tablet count (percentage of prescribed tablets taken) and using the Morisky-Green scale. Treatment adherence was defined as follows: excellent patient adherence if > 90% of prescribed tablets were taken; good: 76-90%; moderate: 51-75%; poor: ≤ 50%. Treatment tolerability was also evaluated based on the medical history focused on gastrointestinal symptoms, as well as patient preference for using specific types of metformin. Other patient data, clinical data and laboratory test results were recorded at the beginning of the study and after 3 months. Results. After 3 months of treatment with metformin extended release formulation 96% of study subjects demonstrated excellent or good adherence. Treatment adherence was significantly lower with 2 or 3 concomitant medications as compared to one (p < 0.001). Adverse events occurred in 715 patients (15% out of 4758 patients undergoing safety analysis). The occurrence of adverse events significantly decreased treatment adherence (p < 0.001). Approximately 90% of patients declared they had preferred the use of metformin extended-release formulation. Conclusions. Metformin extended-release formulation is a suitable, well tolerated therapeutic option which helps to obtain good patient cooperation based on

Transylvanian Review, 2019

Dynamic mechanical analysis (DMA) is a useful method which completes the results obtained from se... more Dynamic mechanical analysis (DMA) is a useful method which completes the results obtained from several traditional thermal analysis techniques such as Differential Scanning Calorimetry (DSC), thermogravimetric analysis (TGA), and thermal elastic analysis (TMA). Dynamic constants such as storage and loss modulus depend on temperature and supply valuable information about interfacial bonding between filler and polymeric matrix of a fibrous composite material. In the meanwhile, the glass transition temperature is defined as the point at which the specific volume versus temperature curve changes abruptly slope, marking the region between rubbery polymer and glassy polymer nature. Thus, the behavior of unidirectional fibrous composites was investigated at this region. Further, an examination of the glass transition temperature, which evidently constitutes an upper limit for the structurally important glassy region through the loss factor, was performed by its consideration as a combinat...

JP Journal of Heat and Mass Transfer, 2018

In this work, an advanced body centered polyhedral model to simulate the periodic microstructure ... more In this work, an advanced body centered polyhedral model to simulate the periodic microstructure of hybrid composites is performed. The overall material consists of a polymeric matrix reinforced with unidirectional continuous fibers and spherical particles. According to this model, both fibers and particles are distributed inside the matrix in a deterministic manner and their configurations depend on each other. In addition, inhomogeneous interphase layers of different thicknesses are considered to surround both particles and fibers. Next, by the use of this model which takes into account the filler arrangement and contiguity along with the interphase concept, the author obtains explicit expressions to evaluate the longitudinal and transverse thermal conductivity of the composite.

The objective of this paper is to contribute towards the quality investigation of equations of co... more The objective of this paper is to contribute towards the quality investigation of equations of conservation for two dimensional incompressible flow patterns via a Complex Analysis approach. Specifically, the authors will utilize the aforementioned equations expressed in their known from literature equivalent special formulation in terms of the stream function and its partial derivatives with respect to spatial coordinates. In the sequel, by means of the Theory of Analytic Complex Functions, the authors will infer some quality information about the algebraic and geometrical properties for the family of functions which satisfy these equations for such flow patterns.

In this work, the authors present an approximate solution to three point bending equation for a g... more In this work, the authors present an approximate solution to three point bending equation for a general category of statically determinate continuum beams. The deflection of the beam due to a perpendicular point wise load is evaluated for high rates of its curvature. The load is initially assumed to be imposed at the midspan of the beam, but in continuing we perform an analytical treatment of this problem when the load is imposed at an arbitrary point. Besides, the cross sectional area of the beam is rectangular and remains as it is after its deformation. The proposed solution for both cases consists of power series throughout. Hence, since it does not contain either elliptic integrals or any other miscellaneous, or non elementary special functions, it would be more suitable for the necessary calculations dealing with conceptual or embodiment design from the engineering standpoint.

Mathematics and Statistics, 2014

ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, whic... more ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

Advances in Energy and Power, 2014

In this paper, the author investigates a generic type of the two dimensional incompressible visco... more In this paper, the author investigates a generic type of the two dimensional incompressible viscous boundary layer flows near the inflection point of a smooth curve. In particular, an approximate evaluation of velocity distribution in an "adjacent" region of the inflection point of this curve is derived. Here, it is a priory assumed that this point is unique. Besides, the flow field is supposed to be steady throughout and Prandtl's simplified assumptions for two dimensional boundary layer flows are also taken into consideration. Besides, if the cross-section of a structure can be simulated by such a curve one should denote that its inflection point is from technical aspect a very suitable place for emplacing a wind generator compared with the top of a curve, which is a stationary point, because if a wind generator was located on the top of a curve, it could be exhibited in unexpected strong blasts.

In this paper, the author obtains an analytic exact form of the unit step function, which is also... more In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently co... more In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

In this work, analytical calculations are described to estimate the elastic moduli of polymer com... more In this work, analytical calculations are described to estimate the elastic moduli of polymer composite materials consisting of short fibers, by extending and generalizing a reliable model. The fibers may have a finite length and an orientation characterized as random. An effort was made to complete and improve a previous procedure concerning transversely isotropic composites. To this end, a cylinder model with a short fiber in the centre of the matrix is considered. The elastic moduli were expressed in terms of the fiber content and fiber length. The obtained representations were used to evaluate the moduli of a randomly oriented short fiber composite. A comparison was made with theoretical values derived from two other authors who established trustworthy and accurate models. Finally, our theoretical values were also compared with obtained experimental results.

In the present paper, we shall attempt to make a contribution to approximate analytical evaluatio... more In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet’s principles, is concurrently able to be expanded in Taylor’s representation, over a particular interval of their domain of definition. Thus, we shall take into account the simultaneous validity of these two properties over this interval, in order to obtain an alternative equivalent representation of the corresponding harmonic decomposition for this category of functions. In the sequel, we shall also implement this resultant formula in the investigation of turbulence spectrum of eddies according to known from literature Von Karman’s formulation, making the additional assumption that during the evolution of such stochastic dynamic effects with respect to time, the occasional time-returning period can be actu...

Mathematics and Statistics, 2014

ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, whic... more ABSTRACT In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

Advances in Energy and Power, 2014

In this paper, the author investigates a generic type of the two dimensional incompressible visco... more In this paper, the author investigates a generic type of the two dimensional incompressible viscous boundary layer flows near the inflection point of a smooth curve. In particular, an approximate evaluation of velocity distribution in an "adjacent" region of the inflection point of this curve is derived. Here, it is a priory assumed that this point is unique. Besides, the flow field is supposed to be steady throughout and Prandtl's simplified assumptions for two dimensional boundary layer flows are also taken into consideration. Besides, if the cross-section of a structure can be simulated by such a curve one should denote that its inflection point is from technical aspect a very suitable place for emplacing a wind generator compared with the top of a curve, which is a stationary point, because if a wind generator was located on the top of a curve, it could be exhibited in unexpected strong blasts.

In this paper, the author obtains an analytic exact form of the unit step function, which is also... more In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 2021

The intention of this paper is to investigate the boundary roughness of a mounted obstacle which ... more The intention of this paper is to investigate the boundary roughness of a mounted obstacle which is inserted into an incompressible, external and viscous flow field of a Newtonian fluid. In particular, the present study focuses on the cross – sectional area of the obstacle, which is assumed to be a non deformable body (rigid object) with a predefined shape of random roughness. For facility reasons and without violating the generality, one may select the cross – section of the body which contains its center of gravity and is perpendicular to the main flow direction. The boundary of this cross – sectional area is mathematically simulated as the polygonal path of the length of a single – valued continuous function. Evidently, this function should be of bounded variation. The novelty of this work is that the formulation of the random roughness of the boundary has been carried out in a deterministic manner.

Procedia Structural Integrity, 2018

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently co... more In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

In this paper, an analytical exact form of Rump Function is presented. This seminal function cons... more In this paper, an analytical exact form of Rump Function is presented. This seminal function constitutes a fundamental concept of digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, Rump Function is performed in a simple manner as the limit of a sequence of real functions letting tend to infinity. This limit is zero for strictly negative values of the real variable whereas it coincides with the independent variable for strictly positive values of the variable. The novelty of this work when compared to other research studies concerning analytical expressions of the Ramp Function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g. Gamma Function, Biexponential Function or any other special functions such as Error Function, Hyperbolic Function, Orthogonal polynomials etc. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into digital signal processing techniques and other engineering practices.

In this paper, a further mathematical analysis of some previous results of the author's ongoing i... more In this paper, a further mathematical analysis of some previous results of the author's ongoing investigation regarding Prandtl's equations is accomplished. In particular, the objective of the present work is the performance of an approximate explicit solution to Prandtl's system of equations for a laminar, isothermal, incompressible and steady boundary layer flow of a Newtonian fluid, over an infinite horizontal flat plate.