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Deif investigates the face angle of Egypt's pyramids. Although it relies on the culmination o... more Deif investigates the face angle of Egypt's pyramids. Although it relies on the culmination of Sirius, the brightest star in the sky, it is rounded to match the nearest Egyptian unit, seqed When the Egyptians witnessed the rising of Sirius just before dawn (known as the heliacal rising), they knew that the Nile would soon flood; for they depended upon the flooding for the agriculture and fertility of their land. The heliacal rising, which falls close to the summer solstice, marked the beginning of the New Year coinciding with the month of Thoth. Since Sirius brought prosperity to Egypt, tracing of the star was crucial. At the Isis-Hathor Temple of Denderah there is a statue of Isis which was oriented to the rising of Sirius. When the priests saw the rays from Sirius penetrating the temple to fall upon the gemstone she wore, they announced that a New Year had begun. In the temple appears the inscription, "Her majesty Isis shines into the temple on New Year's Day, and she...
To the earliest Egyptians, Sirius/Sothis was the home of departed souls. Assem Deif*shows how the... more To the earliest Egyptians, Sirius/Sothis was the home of departed souls. Assem Deif*shows how the triad Osiris-Isis-Nephthys affected other cultures The place is the Isis-Hathor Temple of Denderah, where the priests hasten along the columned aisle to witness an important event. The principal temple is dedicated to Hathor, whereas a small adjacent one is dedicated to Isis in which a statue of the goddess is located at the end of the aisle. It is a little before 5am on 22 July, 700 BC, the summer solstice; the priests wait to watch Sirius rise and its rays penetrate the temple to fall on Isis's gem. As they arrive the sun is still below the horizon, and they gaze impatiently for the apparent heliacal rising of the Dog Star. For the priests already knew that the appearance of Sepdet lasts only for a brief moment before Ra brightens the sky. When the star begins to flicker low on the horizon it marks the beginning of a New Year in Ancient Egypt. The festivities will soon begin. The ...
A wealth of lunacy is associated with the Great Pyramid. Assem Deif* suggests that unorthodox vie... more A wealth of lunacy is associated with the Great Pyramid. Assem Deif* suggests that unorthodox views ignore the provenance of the pyramid and its place in the context of the overall pyramid complex and necropolis It has variously been claimed that the pyramids served as power plants, water pumps, astronomical observatories, sources of ill-defined pyramid-power energy vortices, guidance beacons for alien spacecraft sites for mystery initiation ceremonies. Unfortunately there remains no known written record as to how the most famous of the more than 100 pyramids in Egypt, the Great Pyramid of Giza, was built, nor have any reliefs depicting the building ever been found. The Greek geographer Herodotus, writing in the fifth century BC, mentioned the theory that levers were used to lift pyramid stones. Perhaps this is the most tenable of the alternate theories; as reported by Egyptologist Selim Hassan in his opus Ancient Egypt, Part 1, Cairo, 2000, p. 288. Hassan verified Herodotus's t...
For thousands of years, the riddle of the Pyramids has puzzled observers. Assem Deif*looks to the... more For thousands of years, the riddle of the Pyramids has puzzled observers. Assem Deif*looks to the skies for an answer Speaking of Egypt, it is the Pyramids that spring to mind. Their grandeur, their mystery and their architecture have caused more debate than any other structure on Earth. Since the time of Herodotus geographers and historians have tried to solve their riddles. The Great Pyramid of Khufu, in particular, has a design so striking that some thought only a deity could have created it. No wonder it was listed as one of the Seven Wonders of the Ancient World. Despite their size, the precise number of pyramids in Egypt remains unknown. Pyramidal structures that were demolished or hidden under the sand are constantly being found, and Egyptologists now put their number at about 100. There are thought to be some 28 pyramid complexes dating from the third to the sixth dynasties, all standing along a narrow stretch of the desert from Abu Ruwash south to Meidum. No two of them, wh...
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1983
ABSTRACT It is shown that, whenA is singular, (A+eA1)-1 can be expanded into a Laurent's ... more ABSTRACT It is shown that, whenA is singular, (A+eA1)-1 can be expanded into a Laurent's series ine. The coefficients of the expansion are given in an explicit form. The case where ?A+?A1? vanishes identically ine is also studied and a generalized inverse ofA+?A1 is given.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986
Computing, 1992
We describe a method for enclosing the set of real eigenvalues of an interval matrix pertaining t... more We describe a method for enclosing the set of real eigenvalues of an interval matrix pertaining to eigenvectors of a given sign pattern.
Computing, 1994
ABSTRACT In this paper a necessary and sufficient condition for the existence of a solution for t... more ABSTRACT In this paper a necessary and sufficient condition for the existence of a solution for the interval Sylvester equation is given. A modified Oettli's inequality is derived to characterize the solution. Many direct methods for solving the equation are suggested and compared to each other. These methods are based on different techniques such as simulation, linear programming, correspondence between an interval Sylvester equation and an interval linear system as well as sensitivity analysis. An iterative technique for solving the interval Sylvester equation is provided with special conditions to guarantee the convergence. The square root of an interval matrix is calculated as an application to solving interval Sylvester equations.
Applied Mathematical Modelling, 1980
ABSTRACT This work is a kind of feasibility study mixed with optimization techniques to decide up... more ABSTRACT This work is a kind of feasibility study mixed with optimization techniques to decide upon the possibility of achieving a certain manpower structure together with a complete removal of illiteracy after a certain planning period. Changing the manpower structure is achieved by controlling the proportions of students who enter the different channels of formal education. The removal of illeteracy is achieved by accepting more and more students into the compulsory stage. It will be found that there is more than one option for achieving these objectives through the many control paths available.It is not easy to fulfil these two aims; the obstacles are the non-availability of teachers as well as the universal budget constraint. This will result in a limited number of feasible opportunity paths to choose from.In this paper the solution to the above problem is given. First the feasibility problem is dealt with by examining the possibility of changing the manpower structure after a certain planning period and subject to the above constraints. Once this is found possible, the optimal path regarding the admission of the students to the compulsory stage is given for the quickest removal of illiteracy.
Applied Mathematical Modelling, 1981
Applied Mathematical Modelling, 1984
IEEE Transactions on Circuits and Systems, 1975
ABSTRACT First-order perturbation theory is used to find the shifts in the eigenvalues of the sta... more ABSTRACT First-order perturbation theory is used to find the shifts in the eigenvalues of the state matrix due to changes in the values of the reactive elements and due to the introduction of losses in electrical networks. A set of simultaneous equations are found to realize the invariance of the eigenvalues and the results can be used to compensate for small perturbations in networks. The results are then applied to lossy reactive networks to compensate for the shifts in the natural frequencies due to the introduction of small losses.
International Journal of Electronics, 1979
The state matrix ofR-L-C networks has been dealt with by a number of authors. However, the case o... more The state matrix ofR-L-C networks has been dealt with by a number of authors. However, the case of networks containing lossy reactances, where the losses in the reactive elements are represented by resistances in series with the inductors and conductances in parallel with the capacitors, merits special attention as a number of practical networks fall into this category. In this paper a relation is derived between the state matrix of the network before and after losses are introduced. The special cases of non-degenerate networks and of networks with equal loss factors in their inductors and equal loss factors in their capacitors arc considered, The results are useful when state-space techniques are used in filter design to compensate for the losses in the reactive elements. The results are applied to a lossy low-pass and a high-pass filter.
Linear Algebra and its Applications, 1991
Deif investigates the face angle of Egypt's pyramids. Although it relies on the culmination o... more Deif investigates the face angle of Egypt's pyramids. Although it relies on the culmination of Sirius, the brightest star in the sky, it is rounded to match the nearest Egyptian unit, seqed When the Egyptians witnessed the rising of Sirius just before dawn (known as the heliacal rising), they knew that the Nile would soon flood; for they depended upon the flooding for the agriculture and fertility of their land. The heliacal rising, which falls close to the summer solstice, marked the beginning of the New Year coinciding with the month of Thoth. Since Sirius brought prosperity to Egypt, tracing of the star was crucial. At the Isis-Hathor Temple of Denderah there is a statue of Isis which was oriented to the rising of Sirius. When the priests saw the rays from Sirius penetrating the temple to fall upon the gemstone she wore, they announced that a New Year had begun. In the temple appears the inscription, "Her majesty Isis shines into the temple on New Year's Day, and she...
To the earliest Egyptians, Sirius/Sothis was the home of departed souls. Assem Deif*shows how the... more To the earliest Egyptians, Sirius/Sothis was the home of departed souls. Assem Deif*shows how the triad Osiris-Isis-Nephthys affected other cultures The place is the Isis-Hathor Temple of Denderah, where the priests hasten along the columned aisle to witness an important event. The principal temple is dedicated to Hathor, whereas a small adjacent one is dedicated to Isis in which a statue of the goddess is located at the end of the aisle. It is a little before 5am on 22 July, 700 BC, the summer solstice; the priests wait to watch Sirius rise and its rays penetrate the temple to fall on Isis's gem. As they arrive the sun is still below the horizon, and they gaze impatiently for the apparent heliacal rising of the Dog Star. For the priests already knew that the appearance of Sepdet lasts only for a brief moment before Ra brightens the sky. When the star begins to flicker low on the horizon it marks the beginning of a New Year in Ancient Egypt. The festivities will soon begin. The ...
A wealth of lunacy is associated with the Great Pyramid. Assem Deif* suggests that unorthodox vie... more A wealth of lunacy is associated with the Great Pyramid. Assem Deif* suggests that unorthodox views ignore the provenance of the pyramid and its place in the context of the overall pyramid complex and necropolis It has variously been claimed that the pyramids served as power plants, water pumps, astronomical observatories, sources of ill-defined pyramid-power energy vortices, guidance beacons for alien spacecraft sites for mystery initiation ceremonies. Unfortunately there remains no known written record as to how the most famous of the more than 100 pyramids in Egypt, the Great Pyramid of Giza, was built, nor have any reliefs depicting the building ever been found. The Greek geographer Herodotus, writing in the fifth century BC, mentioned the theory that levers were used to lift pyramid stones. Perhaps this is the most tenable of the alternate theories; as reported by Egyptologist Selim Hassan in his opus Ancient Egypt, Part 1, Cairo, 2000, p. 288. Hassan verified Herodotus's t...
For thousands of years, the riddle of the Pyramids has puzzled observers. Assem Deif*looks to the... more For thousands of years, the riddle of the Pyramids has puzzled observers. Assem Deif*looks to the skies for an answer Speaking of Egypt, it is the Pyramids that spring to mind. Their grandeur, their mystery and their architecture have caused more debate than any other structure on Earth. Since the time of Herodotus geographers and historians have tried to solve their riddles. The Great Pyramid of Khufu, in particular, has a design so striking that some thought only a deity could have created it. No wonder it was listed as one of the Seven Wonders of the Ancient World. Despite their size, the precise number of pyramids in Egypt remains unknown. Pyramidal structures that were demolished or hidden under the sand are constantly being found, and Egyptologists now put their number at about 100. There are thought to be some 28 pyramid complexes dating from the third to the sixth dynasties, all standing along a narrow stretch of the desert from Abu Ruwash south to Meidum. No two of them, wh...
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1983
ABSTRACT It is shown that, whenA is singular, (A+eA1)-1 can be expanded into a Laurent's ... more ABSTRACT It is shown that, whenA is singular, (A+eA1)-1 can be expanded into a Laurent's series ine. The coefficients of the expansion are given in an explicit form. The case where ?A+?A1? vanishes identically ine is also studied and a generalized inverse ofA+?A1 is given.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986
Computing, 1992
We describe a method for enclosing the set of real eigenvalues of an interval matrix pertaining t... more We describe a method for enclosing the set of real eigenvalues of an interval matrix pertaining to eigenvectors of a given sign pattern.
Computing, 1994
ABSTRACT In this paper a necessary and sufficient condition for the existence of a solution for t... more ABSTRACT In this paper a necessary and sufficient condition for the existence of a solution for the interval Sylvester equation is given. A modified Oettli's inequality is derived to characterize the solution. Many direct methods for solving the equation are suggested and compared to each other. These methods are based on different techniques such as simulation, linear programming, correspondence between an interval Sylvester equation and an interval linear system as well as sensitivity analysis. An iterative technique for solving the interval Sylvester equation is provided with special conditions to guarantee the convergence. The square root of an interval matrix is calculated as an application to solving interval Sylvester equations.
Applied Mathematical Modelling, 1980
ABSTRACT This work is a kind of feasibility study mixed with optimization techniques to decide up... more ABSTRACT This work is a kind of feasibility study mixed with optimization techniques to decide upon the possibility of achieving a certain manpower structure together with a complete removal of illiteracy after a certain planning period. Changing the manpower structure is achieved by controlling the proportions of students who enter the different channels of formal education. The removal of illeteracy is achieved by accepting more and more students into the compulsory stage. It will be found that there is more than one option for achieving these objectives through the many control paths available.It is not easy to fulfil these two aims; the obstacles are the non-availability of teachers as well as the universal budget constraint. This will result in a limited number of feasible opportunity paths to choose from.In this paper the solution to the above problem is given. First the feasibility problem is dealt with by examining the possibility of changing the manpower structure after a certain planning period and subject to the above constraints. Once this is found possible, the optimal path regarding the admission of the students to the compulsory stage is given for the quickest removal of illiteracy.
Applied Mathematical Modelling, 1981
Applied Mathematical Modelling, 1984
IEEE Transactions on Circuits and Systems, 1975
ABSTRACT First-order perturbation theory is used to find the shifts in the eigenvalues of the sta... more ABSTRACT First-order perturbation theory is used to find the shifts in the eigenvalues of the state matrix due to changes in the values of the reactive elements and due to the introduction of losses in electrical networks. A set of simultaneous equations are found to realize the invariance of the eigenvalues and the results can be used to compensate for small perturbations in networks. The results are then applied to lossy reactive networks to compensate for the shifts in the natural frequencies due to the introduction of small losses.
International Journal of Electronics, 1979
The state matrix ofR-L-C networks has been dealt with by a number of authors. However, the case o... more The state matrix ofR-L-C networks has been dealt with by a number of authors. However, the case of networks containing lossy reactances, where the losses in the reactive elements are represented by resistances in series with the inductors and conductances in parallel with the capacitors, merits special attention as a number of practical networks fall into this category. In this paper a relation is derived between the state matrix of the network before and after losses are introduced. The special cases of non-degenerate networks and of networks with equal loss factors in their inductors and equal loss factors in their capacitors arc considered, The results are useful when state-space techniques are used in filter design to compensate for the losses in the reactive elements. The results are applied to a lossy low-pass and a high-pass filter.
Linear Algebra and its Applications, 1991