ON STABILITY AND BIFURCATION OF PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS

EL-SHEIKH, M. M. A.,EL-MAHROUF, S. A. A. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

Design of top concrete slabs of composite space trusses

El-Sheikh, Ahmed Techno-Press 1999 Structural Engineering and Mechanics, An Int'l Jou Vol.7 No.3

The design of composite space trusses is a demanding task that involves taking several decisions on the truss depth, number of panels, member configuration, number of chord layers and concrete slab thickness and grade. The focus in this paper is on the design of top concrete slabs of composite space trusses, and in particular their thickness. Several effects must be considered in the process of designing the slab before an optimum thickness can be chosen. These effects include the inplane forces arising from shear interaction with the steel sub-truss and the flexural. and sheer effects of direct lateral slab loading. They also include a constructional consideration that the thickness must allow for sufficient cover and adequate space for placing the reinforcement. The work presented in this paper shows that the structural requirements on the concrete slab thickness are in many cases insignificant compared with the constructional requirements.

Comparative studies of double- and triple-layer space trusses

El-Sheikh, Ahmed Techno-Press 1999 Structural Engineering and Mechanics, An Int'l Jou Vol.8 No.4

In some space truss applications, particularly those with large spans, the choice of a triple-layer system might prove more cast effective than the more commonly used double-layer solution. However, there are currently no clear guidelines as to which system would be more competitive for intermediate span lengths. In this paper, comparisons in terms of the weight, stiffness and number of joints and members are made between the two system types and presented in order to simplify the choice process for the designer. The comparisons are carried out using an approximate analysis technique that is explained in this paper, and checked to be reasonably accurate and suitable for the preliminary design of space trusses.

Effect of direct member loading on space truss behaviour

El-Sheikh, Ahmed Techno-Press 2000 Structural Engineering and Mechanics, An Int'l Jou Vol.10 No.1

It is inevitable that every space truss structure would be under some form of direct member loading. At least the structure self weight certainly affects the members directly, and in structures involving top concrete slabs or cladding, their weight is also likely to apply some lateral pressure on the members. In spite of that, direct member loading is usually ignored in space truss designs and assumed to lead only to a negligible effect on truss performance. This study is intended to explore this point and identify the actual effects that can arise from direct member loading, and eventually provide an answer to the question of whether the current design practice is satisfactory or certain modifications would be needed. After presenting two analytical techniques to allow the study of space trusses with laterally loaded members, the paper describes a wide parametric study involving practical-size space trusses with different configurations, aspect ratios, boundary conditions and number of chord panels.

Design of space truss structures

El-Sheikh, Ahmed Techno-Press 1998 Structural Engineering and Mechanics, An Int'l Jou Vol.6 No.2

Space truss design usually involves two main assumptions: that truss members are pin-ended, and compression members possess brittle post-buckling characteristics. The validity of these assumptions in the design of a new group of space trusses with continuous chords and eccentric joints is questionable. With chord member continuity and the consequent improvement in compression member behaviour, current design practice might be too conservative. In this paper, it is shown that substantial improvements in overall truss strength have resulted when the true member end conditions are considered, thus indicating potential savings in truss weight with considerable magnitudes.

Tensile bond strength of four denture resins to porcelain teeth with different surface treatment

El-Sheikh, Mohamed,Powers, John The Korean Academy of Prosthodonitics 2013 The Journal of Advanced Prosthodontics Vol.5 No.4

PURPOSE. This study evaluated the bond strength between porcelain denture teeth (Bioblend 43D) and four different polymerized denture resins (Lucitone 199, Palapress, Acron MC, Triad) with and without a bonding agent and after four different types of surface treatment (polished, HF etched, sandblasted, air-abraded). MATERIALS AND METHODS. Central incisor porcelain denture teeth were divided into 32 groups of 5 each. Tensile bond strength (MPa) was determined using a testing machine at crosshead speed of 0.5 mm/min. Mean and standard deviation are listed. Data were analyzed by two-way ANOVA. Means were compared by Tukey-Kramer intervals at 0.05 significance level. RESULTS. All surface treatment increased bond strength compared to polished surface and the highest bond strength was found with Palapress resin with etched porcelain surface (8.1 MPa). Bonding agent improved the bond strength of all denture resins to porcelain teeth. Superior bonding was found with Palapress and air-abraded porcelain (39 MPa). CONCLUSION. Resins with different curing methods affect the bond strength of porcelain teeth to denture bases. Superior bonding was found with auto-polymerized resin (Palapress). Application of ceramic primer and bonding agent to porcelain teeth with and without surface treatment will improve the bond strength of all denture resins to porcelain teeth.

LIPSCHITZ STABILITY CRITERIA FOR A GENERALIZED DELAYED KOLMOGOROV MODEL

El-Sheikh, M.M.A. 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.10 No.1

Lipschitz stability and Lipschitz ø$_{o}$ - equistability of the functional differential equation x'= B(x)f(t, x, $x_{t}$), $x_{to}$ =$\theta$$_{o}$ are discussed. Sufficient conditions are given using the comparison with the corresponding scalar equation.ion.n.

Configurations of double-layer space trusses

El-Sheikh, Ahmed Techno-Press 1998 Structural Engineering and Mechanics, An Int'l Jou Vol.6 No.5

Space truss structures may be fabricated in any of several common grid configurations. With different configurations, the truss performance varies considerably affecting both its competitiveness and suitability for specific applications. The work presented in this paper is an assessment of the most commonly adopted truss configurations and their effect on truss characteristics such as the stiffness/weight value, member stress distribution, number of joints and members, degree of redundancy and cost. The study is parametric and covers wide variations of truss aspect ratios, boundary conditions and span/depth ratios. The results of this study could be of significant value to the design of space truss structures.

On the Propagation of Harmonic Heat Waves due to a Periodic System of Punches on an Infinite Strip

M. G. El-Sheikh ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2

A mixed heat conductivity problem of the Dirichlet-Neumann type in a rectangular region is reduced to a Hilbert-type singular integral equation. In this equation, the unknown is the unbounded extension of the heat flow (the Neumann condition) which can be found in L_(p), 0 < p < 4/3. Such solutions are of great physical interest. To complete the definition of the solution, the problem is further reduced to an infinite system of algebraic equations. The solution of this system through truncation is justified.

Regularity and Normality in Soft Bitopological Ordered Spaces

S. A. El-Sheikh,S. A. Kandil,S. Hussien International Journal of Computer ScienceNetwork S 2024 International journal of computer science and netw Vol.24 No.6

This paper examines regularity and normality in soft separation axioms for soft bitopological ordered spaces and their relationships with other properties. The findings expand our understanding of bitopological ordered spaces. Previous research, such as Al-Shami's work [3], has established distinctions between separation axioms in topological ordered spaces, which are more effective in describing these spaces' properties.