Volume 8 – 2007 – 2008 Biology 1 Volume 8 – 2007 – 2008 B1. Observations on macrobenthic invertebrates and wader bird assemblages in a protected marine mudflat in Bahrain Hashim Al-Sayed, *Humood Naser, and Khalil Al-Wedaei Department of Biology, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. Aquatic Ecosystem Health & Management, 11(4):450-456, 2008. Abstract Intertidal mudflats in Bahrain provide essential feeding grounds for a good number of shorebirds. The spatial distribution of soft-sediment macrobenthic invertebrate assemblages inhabiting a mudflat designated as a natural marine protected area was investigated to characterize shorebird food supplies. Molluscs accounted for 88% of the total macroinvertebrates community, reflecting a dominance of gastropod grazers. Six species of wading birds were recorded feeding in the protected area. Bird disturbance associated with human recreational activities that may interfere with the conservational benefits of this protected area was explored. This study highlighted the crucial need for management plans for protected areas and for further research concerning bird disturbance. B2. Impact of Biochemical and Calorific Contents on the Reproductive Activity of the Marine Edible Snail Turbo coronatus Gmelin 1791 Freije, A. *and Al-Sayed, H. Department of Biology, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. J.of Arab University for Basic and Applied Sciences. Bol.6. 57-68, 2008. Abstract The edible marine snail Turbo coronatus from Shaikh Ebrahim Island spawns mainly in the spring, with a spawning peak in May in which all reserves studied (total proteins, carbohydrate, and total lipids) declined to a seasonal minimum value. A second minor but continuous spawning period was also observed between September and December. Whole, wet and dry tissue weights as well as ash-free dry weight (AFDW) were significantly lower in May and September, whereas water content was maximum in December and minimum in April. Total lipids formed the main reserve, while total proteins and carbohydrates contribution was less. The increased levels of the calorific content per AFDW were due mainly to accumulation of total lipids (42%) and secondly of carbohydrates (37.5%) and total proteins (36%) in the period prior to the major 2 Volume 8 – 2007 – 2008 spawning in May, in which gamete maturation usually takes place. The dry weight proportions of the main components were: total proteins 60.97-82.18%; carbohydrates 3.39-9.35%; total lipids 4.00-8.00%; and ash 9.13-18.79%. Calorific content varied between 3.36-4.43 kcal/g dry weight. B3. Determination of Blood Lead Levels in Adult Bahraini Citizens Prior to the Introduction of Unleaded Gasoline and the Possible Effect of Elevated Blood Lead Levels on the Serum Immunoglobulin IgG Afnan Mahmood Freije, Maheen Ghuloom Dairi, Department of Biology, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. Bahrain Medical Bulletin, 31, ( 1) 17-20, 2009 Abstract The blood lead levels of participants were found to be elevated (mean 15.3± 5.7 µg/ dl), in comparison with the standard international levels, in which blood lead levels of > 10 µg/dl are designed as lead poisoning, On the other hand, the serum immunoglobullin IgG was within the normal range (mean, 1007.1±147.1 mg/dl). However, no correlation was found between the blood lead levels and the serum IgG levels (p=0.14). B4. Ecological assessment: an initial evaluation of the ecological input in environmental impact assessment reports in Bahrain Humood Naser a, John Bythell b and Jeremy Thomason b Department of Biology, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain, School of Biology, Newcastle University, Newcastle upon Tyne NE1RU, U.K. Impact Assessment and Project Appraisal, 26(3), 201-208, 2008. Abstract Ecological assessment forms a fundamental part of environmental part of environmental impact assessment. The quality of ecological input in 15 Bahraini EIA reports concerning coastal and marine developments produced between 1996 and 2004 was evaluated using adopted criteria. The overall quality indicated that eight reports were assessed as borderline quality , and seven reports were found to be of poor quality. Major shortcomings included limited new ecological surveys, inadequate evaluation of impacts, neglecting cumulative and long-term impacts, and failing to address adequately mitigation and monitoring measures. 3 Volume 8 – 2007 – 2008 B5. MobilomeFINDER: web-based tools for in silico and experimental discovery of bacterial genomic islands Hong-Yu Ou1, Xinyi He1, Ewan M.Harrison2, Bridget R. Kulasekara3, Ali Bin Thani2, Aras Kadioglu2, Stephen Lory3, Jay C.D. Hinton4, Michael R.Barere2,5, Zixin Deng1 and Kumar Rajakumar2.5,* 1 Laboratory of Microbial Metabolism and School of Life Science & Biotechnology, Shanghai Jiaotong University, P.R. China, 2Depatment of Infection, Immunity and Inflammation, Leicester Medical School, University of Leicester, Leicester LE1 9HN, UK, 3Department of Microbiology and Molecular Genetics, Harvard Medical School, Boston MA 02115, USA, 4Molecular Microbiology Group, Institute of Food Research, Norwich Research Park, Norwich NR4 7UA and 5Department of Clinical Microbiology, University Hospitals of Leicester NHS Trust, Leicester LEI 5WW, UK. Nucleic Acids Research,2007,35 (web server issue) W97-W104. doi:10.1093/nar/gkm380. Abstract MobilomeFINDER (htt://mml.sjtu.edu.cn/MobilometFINDER) is an interactive online tool that facilitates bacterial genomic island or 'mobile genome' (mobilome) discovery; it integrates the Arrayome and tRNAcc software packages. Arrayome utilizes a microarray-derived comparative genomic hybridzation input data set to generate 'inferred contigs' produced by merging adjacent genes classified as 'present'. Collectively these 'fragments' represent a hypothetical 'microarray-visualized genome (MVG)'. Arrayome permits recognition of discordances between physical genome and MVG sizes, thereby enabling identification of strains rich in microarray-elusive novel genes. Individual tRNAcc tools facilitate automated identification of genomic islands by comparative analysis of the contents and contexts of tRNA sites and other integration hotspots in closely related sequenced genomes. Accessory tools facilitate design of hotspot-flanking primers for in silico and/or wet-science-based interrogation of cognate loci in unsequenced strains and analysis of islands for features suggestive of foreign origins; island-specific and genome-contextual features are tabulated and represented in schematic and graphical forms. To date we have used MobilomeFINDER to analyse several Enterobacteriaceae, Pseudomonas aeruginosa and Streptococcus suis genomes. MobilomeFINDER enables high-throughput island identification and characterization through increased exploitation of emerging sequence data and PCR-based profiling of unsequenced test strains; subsequent targeted yeast recombination-based capture permits full-length sequencing and detailed functional studies of novel genomic islands. 4 Volume 8 – 2007 – 2008 Chemistry 5 Volume 8 – 2007 – 2008 C1. Accreditation of Learning Institution. Ahmed Y. Ali-Mohamed, Department of Chemistry, College of Science, University of Bahrain and Advisor to the University President for Scientific Affairs. Kingdom of Bahrain. Al-Hawaj, Elali, & Twizell (eds) Ahlia University, Kingdom of Bahrain. 3-4 June 2007 -2008 Taylor & Francis Group, London, ISBN 978-0415-48000-0 pp 71Higher Education in the Twenty-First Century: Issues and Challenges Abstract In this paper we review the definition set up by various bodies on accreditation. Thus, accreditation is considered as a certification of academic quality of an institution of higher learning as defined by Wikipedia, 2007a. In its revised edition of characteristics of excellence in higher education, (CHE-MSA, 1994) defined accreditation as the means of self-regulation and peer review adopted by the education community. The accrediting process is intended to strengthen and sustain the quality and integrity of higher education, making it worthy of public confidence and minimizing the scope of external control. The extent to which each educational institution accepts and fulfils the responsibilities inherent in the process is a measure of its concern for freedom and quality in higher education and its commitment to striving for excellence in its endeavours. On the other hand International Accrediting for Universities (IUAA,2005) has taken into consideration the recommendations of the principles accepted by the World Conference in Higher Education sponsored by UNESCO (Budapest, 1999) as appropriate for accrediting Universities/School. The long-term outcome of the conference will be efficient and effective renovation and renewal of higher education system and institutions based in the principles of relevance and quality and with a commitment to enhance international co-operation and academic solidarity. In its clarification IUAA accrediting is a "Third Party" evaluation and "Seal of Approval" for "Quality" educational offerings for the practical training programmes. International Accrediting by IUAA is provided as a free Public Service to the Schools, to students and to the employers of the world. It is also intended to clarify that Accredited Schools are expected to maintain an ongoing programme of self-evaluation to maintain standards of excellence. Schools are expected to consider input and constructing suggestions from faculty, students, parents and the public when developing or maintaining programmes. In this paper we look at some variation by nations on the accreditation issues of an institution of higher learning and ask if it is mandatory or required by law? Discussion will be concentrated on the criteria used as a guide to meet the accreditation setup by the accreditation commissions. It will also list the accrediting organizations identified and recognized by the Council for Higher Education Accreditation (CHEA, 2006) in the U.S.A as well as the list of Wikipedia (2007b) of unrecognized accreditation associations of higher learning. 6 Volume 8 – 2007 – 2008 Mathematic 7 Volume 8 – 2007 – 2008 M1. Quantum information entropy and multi-qubit entanglement Mahmoud Abdel-Aty1 Mathematic Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. Progress in Quantum Electronic 31, 1-49, 2007 Abstract The exciting new features of entanglement are burgeoning with revolutionary new advances in the areas of quantum communication, quantum information processing and quantum computing. We review recent theoretical studies and applications of pure and mixed states entanglement of trapped ions interacting with a laser field. After an introduction to the basic concepts of traditional entanglement measures and methodology, the main phenomena and observations of two-, three- and four-level systems are summarized. In particular, we explore the influence of the various parameters of these systems on the entanglement. The particular advantages of using atomic Wehrl entropy and Shannon entropy are highlighted. A general expression of the mixed state entanglement is obtained with the physical significance and without the diagonal approximation. Based on this result, we provide a general expression for the entanglement in a multi-level system. We show that the mixed state and specific eigenstates of the two or three-level system posses remarkable entanglement properties that can reveal new insight into quantum correlations present in the multi-level models. Furthermore, we propose an intuitive picture of the behavior of mixed-state entanglement in the presence of the decoherence. After a short presentation of the entanglement measures of two qubits, each defined as an effective two-level system (negativity, Bures metric and concurrence) we discuss the general behaviors of the concurrence as a measure of entanglement. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multiphoton process is involved. M2. Emission spectra of a superconducting single-Cooper-pair box with binomial states Mahmoud Abdel-Aty a,b* , H.F. Abdel-Hameed b, N. Metwally b Ab Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. b Mathematics Department, Faculty of Science, South Balley, University of Egypt Physica C, 452, 29-34, 2007 8 Volume 8 – 2007 – 2008 Abstract We present an analytical expression for the response of a transient spectrum to a singleCooper-pair box biased by a classical voltage and irradiated by a single-mode quantized field. The exact solution of the model is obtained, by means of which we analyze the analytic form of the fluorescence spectrum using the transitions among the dressed states of the system. An interesting relation between the fluorescence spectrum and the dynamical evolution is found when the initial field states are prepared in binomial states. M3. Quantitative aspects of entanglement in optically driven quantum dots A.S.F. Obads1 and M. Abdel – Aty 2* 1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt. 2 Mathematics Department, College of Science, Bahrain University. Physical Review B75, 195310-1, 2007 Abstract We present an approach to look for the existence of maximum entanglement in a system of two identical quantum dots coupled by the Forster process and interacting with a classical laser field. Our approach is not only able to explain the existing treatments but also provides further detailed insight into the coupled dynamics of quantum-dot systems. The result demonstrates that there are two ways of generating maximum entangled states, one associated with far off-resonance interaction and (he other associated with the weakfield limit. Moreover. it is shown that exciton decoherence results in the decay of entanglement. M4. An analytical treatment of excitons in coupled three quantum dots and maximum entangled states generation Mahmoud Abdel-Aty Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. Physica A 380, 191-201, 2007 Abstract We explore and develop the mathematics of the theory of a class encompassing several widely encountered models of a solid-state quantum structure which is capable of generating rnaximally entangled states, such as Bell-states and Greenberger-HorneZeilinger (GHZ) states. 9 Volume 8 – 2007 – 2008 This analytical treatment not only provides an unified formulation to the models belonging to the class considered but is found to uncover several new results for physical systems possessing multi- particles interaction. The concept of entanglement fidelity is used to construct explicitly general features of the system which is postulated to satisfy the maximum entangled states generation conditions. The laser pulses necessary to generate these maximally entangled states are given explicitly. We show that the fidelity yields a structure that is analogous in many dots-based respects to that of maximum entanglement. These results have significant implications for quantum information processing. The results are illustrated with an application to a specific wide-gap semiconductor quantum dots as system, like Zinc Selenide (ZnSe)-based quantum dots. The scheme for generating GHZ state using quantum dots model could be implemented using technology that is currently being developed. M5. Entanglement of a three-level trapped atom in the presence of another three-level trapped atom Mahmoud Abdel-Aty a, M.R.B. Wahiddin b, M.Sebawe Abdulla c,A.-S.F/Obada d a Mathematics Department, College of Science, University of Bahrain. Kingdom of Bahrain. B Centre for computational and Theoretical Sciences. Kulliyyah of Science. International Islamic University Malaysia, 53100 Kuala Lumpur, Malaysia. c Mathematics Department, College of Science, King Saud University, P.O.Box:2455, Riyadh 11451. Saudi Arabia. d Mathematic Department, Faulty e of Science,Al-Azhr University, Nasr City Cairo. Egpt. Optics Communications 265,551 -558, 2006 Abstract A new version of two multi-level trapped atoms interacting with laser fields is under consideration. This system is based on a three- level trapped atom interacting with laser fields in the presence of another three-level trapped atom taking into account the timedependent atom-field couplings and phase shift. The entanglement due to the concurrence is calculated and its time evolution phenomena is demonstrated within the framework of the presented theory. Our results establish an explicit relationship between the concurrence and the entanglement through the two three-level atoms and the fields interaction. We show that different non-classical effects arise in the dynamics of the atomic population inversion, due to the initial states of the system as well as the values of the Lamb-Dicke parameter. 10 Volume 8 – 2007 – 2008 M6. Quantum mutual entropy of a single four-level atom strongly coupled to a cavity field and driven by a laser field Mahmoud Abdel-Aty Mathematic Department, College of Science, University of Bahrain. Kingdom of Bahrain. Optics Communications 275, 129-134, 2007 Abstract Based on exact quantum dynamics of a single four-level atom strongly coupled to a cavity field mode and driven by a coherent laser field, we investigate quantum mutual entropy as a measure of the amount of total correlations. Through the analysis he total correlation, we show that under the influence of the decoherence, the total correlation may terminate abruptly consequences of our results include a description of total correlations of a general multi-level atomic system. M7. Fidelity of Isotropic-Coupled Oscillators Interacting with a Single Atom M.S. Abdallaa*, M.Abdel-Aty b, and A.S.F. Obadac a Mathematics Department, College of Science, King Saud University, P.O.Box:2455, Riyadh 11451 Saudi Arabia, b Mathematics Department, College of Science, University of Bahrain,P.O.Box:32038 Kingdom of Bahrain, c Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt Laser physics, 17, (9), 1151-1156, 2007 Abstract A model of a single atom interacting with isotropic two modes pumped simultaneously within a perfect cavity is examined. The quantum fidelity is employed to measure the quality of transmitted information as a function of the input state. The behavior of the quantum fidelity is studied at off-resonances between the atom and fields for different preparations of initial states. M8. Quantum Information Entropy For A MULTILEVEL SYSTEM M. Abdel-Atya, S.S. Hassanb, M.Sebawe Abdallac, and A.S.F. Obadad. a Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, b Mathematics Department, College of Science, King Saud University, P.O.Box: 2455, Riyadh 11451, Saudi Arabia c Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt. International Journal of Modern Physics B, 21 (32), 5351-5362, 2007 11 Volume 8 – 2007 – 2008 Abstract We study the uncertainty relations between photon number and canonical phase of a multilevel system. All the relevant quantities can be sampled directly from the measured phase-dependent quadrature distribution. Some comments are made on the extension of these relations to the case where the Hilbert space is of infinite dimension. We describe its theoretical basis and discuss its practical relevance, especially in comparison with already known results. Numerical calculations under specified initial conditions are presented. M9. ON KRONECKER POLYNOMIALS Ahmed Ayachea, Othman Echi*, and Mongi Naimi a Mathematic Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. To appear in Rocky Mountain Journal of Mathematics Abstract Monic polynomials with integer coefficients having all their roots in the unit disc have been studied by Kronecker; they are called Kronecker polynomials. Let n ≥ 1 be an integer. By a strong Kronecker polynomial, we mean a monic polynomial P(X) Є Z[X] of degree n - 1 and such that P(X) divides P(X-t) for each t Є {1,….n -1} We say that P(X) is an absolutely kronecker polynomial if P(X) divides P(X-t) for each positive integer t. We describe a canonical form of strong (resp. absolutely) Kronecker polynomials We, also, prove that if n is composite, then each strong Kronecker polynomial with degree n - 1 is absolutely Kronecker. If n is prime, then we prove that each strong Kronecker polynomial P(X) ≠1+X + X-2 + …+X n-1 is absolutely Kronecker M10. A Note on going down domains Ahmed Ayache Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. (To appear in communication in Algebra (2008 ) Abstract The purpose of this paper is to prove the following result: If R is a going down domain and there are no infinite chains of rings between R and S, then every intermediate ring T Є [R,S] is going down. 12 Volume 8 – 2007 – 2008 M11. Stability Analysis of A Non-Autonomous Model in Quantum Optics Sarah A. Al-Sheikh1, Shoukry S. Hassan2 1 Department of Mathematics, College of Science, King Abdul Aziz University, P.O.Box 1454, Jedadh, 21431,Kingdom of Saudi Arabia, 2 Department of Mathematics, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. International Journal of Pure and Applied Mathematics, 38 (2), 277-284, 2007 Abstract Periodic stability regions are identified for a non-autonomous system of differential equations modeling the interaction of a single 2-level atom with a coherent field and bathed in a non-classical (squeezed vacuum) reservoir. M12. Spectrum of a pulsed driven qubit S.S. Hassan1, A.Joshi2, and N.M.M. Al-Madhari3 1 Department of Mathematics, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. 2 Department of Physics, University of Arkansas. Faye tteville, AR 72701, USA, P.O.Box 20135, Al-Qateef, Saudi Arabia J.Phys. B: At. Mol. Opt. Phys., 41, 145503 (7pp) 2008, Abstract The transient spectrum of scattered radiation from a qubit (represented by a spin-1/2 system or a two-level atom) driven by a resonant rectangular pulse is calculated analytically without adopting the rotating wave approximation (RWA). Operator solutions for the non-autonomous model of Heisenberg equations of motion are obtained within an iterative approach to O (λ) where λ is the system parameter representing the ratio of the Rabi frequency of the driving pulse to its circular frequency. The spectrum in the case of an initial ground-state atom and for increasing pulse area shows asymmetric profiles outside the RWA compared with a symmetric profile within the RWA. For the qubit this asymmetry is much pronounced with splitting outside peaks, which develops to 'ringing' for larger pulse area (within and outside the RWA). As shown analytically this is attributed to the strong Rabi Oscillations and interference between various amplitude spectral components initiated by the finite atomic coherent dispersion. 13 Volume 8 – 2007 – 2008 M13.Mesoscopic multistability outside the rotating wave approximation S.S. Hassan1, and Y.A. Sharaby2 1 Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. 2 Physics Department, Faculty of Education. Suez Canal University, Suez, Egypt J.Phys. B: At. Mol. Opt. Phys., 41,(175502), 7pp, 2008, Abstract The interaction of a mesoscopic system of two-leve1 Rydberg atoms with a coherently driven single cavity mode is treated outside the rotating wave approximation (RWA). This yields a system of non-autonomous Maxwell-Bloch equations that can be solved using Fourier decomposition of both field and atomic variables up to first harmonics and to 0 ( Q - I ). where Q is the cavity quality factor. For the absorber and amplifier regimes, the first harmonic component of the output field (outside the RWA) exhibits closed hysteresis loops compared with hysteresis cycles for the non-oscillatory (fundamental) component within the RWA. A cooperative switching diagram (output field versus cooperative atomic parameter) outside the RWA shows overlapping branches in the resonant case and closed loops in the non-resonant case. M14.On Matrix Representations of Deformed Lie Algebras L.A.M. Hanna1 And S.S. Hassan2 1 Kuwait University, Faculty of Science, Department of Mathematics & Computer Sci P.O.Box 5969, Safat13060. Kuwait. 2 Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Kingdom of Bahrain. International Journal of Theoretical Physics, 13, (2), 51 -57, 2008 Abstract Faithful matrix representations of least degree are discussed for the Lie algebra : [Xo.XI]= ± rXI= [XI-:X-] = P(Xo) where. r ε R. and P is a polynomial function. The operators Xo. X- and X_ satisfy the physical properties: Xo is a real diagonal operator and X = X+† (†is for hermitian conjugation). The physical condition XI-X- must be real. is separately considered. Conditions are found for the polynomial function P to guarantee matrix representations of. 14 Volume 8 – 2007 – 2008 M15.Dispersive Switching in Mesoscopic Multistable Systems Y.A. Sharaby1 and S.S. Hassan2, 1 Physics Department, Faculty of Education. Suez Canal University, Suez, Egypt 2 Mathematics Department, College of Science, University of Bahrain. P.O.Box:32038, Bahrain. Journal Of Non linear Optical Physics & Materials,17,( 3) 339-347, 2008 Abstract Dispersive switching effect is examined for a mesoscopic system of coherently injected two-level Rydberg atoms into a driven single-mode superconducting cavity. The effect concerns the switching of the output field by simultaneously varying the atomic and cavity detuning parameters at fixed values of the coherent driving field. For certain atomic coherence parameters, symmetric and asymmetric switching diagrams are exhibited, which include one- and two-way process via multistep transitions between output field states. M16.Simulaton of Micellar-Polymer Flooding of A Layered Oil Reservoir of Nonuniform Thickness N.S. Khabeev1 and N.A. Inogamov2, 1 University of Bahrain, Manama 32038, Bahrain. 2Lomenusov Moscow State University, Moscow Journal of Applied Mechanics and Technical Physics. 49(6) 985-991. 2008 Abstract The dynamics of oil displacement from a layered reservoir of nonuniform thickness consisting hydrodynamically connected layers of different absolute permeabilty is studied. Results of numerical calculations are given. The influence of the main determining factors on the oil displacement dynamics is studied. M17.Translatory Motion of the Radially Oscillating Bubbles in Solution Nail S. Khabeev Department of Mathematics, University of Bahrain, P.O.Box 32038, Kingdom of Bahrain The 19th International Symposium on Transport Phenomena. 17-20 August, 2008, Reykjavik, ICELAND 15 Volume 8 – 2007 – 2008 Abstract The model describing the behavior of vapor bubbles in solution is presented. The model takes into account the translatory motion of the bubble accompanied by radial oscillations, and heat-mass transfer· effects. It is shown that translatory motion does not manifest itself in the dynamic stage of bubble collapse. The dominant role of the diffusion in the liquid phase was shown. The effect of diffusion is more strong in the cases when the solution consists of components with very different volatility . M18.Some Results on Proper Fuzzy Subgroup I.A. Khan M. K. Singh2 1 College of Science. University of Bahrain. P.O. Box 32038. Isa Town Kingdom of Bahrain. 2 Head. Dept. of Maths G. B. College. Ramgarh. Kaimur A Un.it of V. K. S. U. ,Ara (ANUSANDHAN,IX (14),139-142, 2007) Abstract In this paper we have derived some result in fuzzy proper subgroup of a group G M19. On two natural Riemannian metrics on a tube. M. Labbi. Department of Mathematics College of Science, University of Bahrain, P.O.Box 32038, Kingdom of Bahrain. Balkan Journal of Geometry and its Applications, 12, ( 2) , 81-86, 2007 Abstract During an operation of surgery on a Riemannian manifold and along a given embedded submanifold, (see [1,2,3]), one needs to replace the (old) metric induced by the exponential map on a tubular neighborhood of the submanifold by the Sasakian metric. So a good understanding of the behavior of these two metrics is important, this is our main goal in this paper. In particular, we prove that these two metrics are tangent up to the order one if and only if the submanifold is totally geodesic. In the case where the ambient space is an Euclidean space, we prove that the difference of these two metrics is quadratic in the radius of the tube and depends only on the second fundamental form of the submanifold. Also the case of spherical and hyperbolic space forms are studied. 16 Volume 8 – 2007 – 2008 M20.On Gauss-Bonnet curvatures Mohammed Labbi Department of Mathematics, College of Science, University of Bahrain 32038, Bahrain This paper is a contribution to the proceedings of the 2007 Midwest Georetry Conference in honor of Thomas P. Branson. SIGMA 3, 118, 2007 Abstract The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k =1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds. M21. Variational properties of the Gauss-Bonnet curvatures M.Labbi. Department of Mathematics, College of Science, University of Bahrain, P.O.Box 32038, Isa Town, Bahrain Calculus of Variations and PDE’s, 32, ( 2), 175-189, 2008 Abstract The Gauss-Bonnet curvature of order 2k is a generalization to higher dimensions of the Gauss-Bonnet integrand in dimension 2k, as the scalar curvature generalizes the two dimensional Gauss-Bonnet integrand. In this paper, we evaluate the first variation of the integrals of these curvatures seen as functionals on the space of all Riemannian metrics on the manifold under consideration. An important property of this derivative is that it depends only on the curvature tensor and not on its covariant derivatives. We show that the critical points of this functional once restricted to metrics with unit volume are generalized Einstein metrics and once restricted to a pointwise conformal class of metrics are metrics with constant Gauss-Bonnet curvature. 17 Volume 8 – 2007 – 2008 M22.On 2k-minimal submanifolds. Mohammed Labbi Mathematics Department, College of Science, University of Bahrain,Sakier 32038, Isa Kingdom of Bahrain Results in Mathematics, 52, (3-4), 323-338, 2008 Abstract Recall that a submanifold of a Riemannian manifold is said to be minimal if its mean curvature is zero. It is classical that minimal submanifolds are the critical points of the volume functional. In this paper, we examine the critical points of the total 2k-th Gauss-Bonnet curvature functional, called 2k-minimal submanifolds. We prove that they are characterized by the vanishing of a higher mean curvature, namely the (2k+ 1) –mean curvature. Furthermore, we show that several properties of usual minimal submanifolds can be naturally generalized to 2k-minimal submanifolds. M23.Entanglement and Pancharatnam Phase for Two Two-Level Atoms Interacting with a Single Mode Field Nasser Metwally Mathematics Department, College of Science, Bahrain University, Sakier 32038, Kingdom of Bahrain. Int J. Theor Phys, 47, 623 – 633, 2008 Abstract A model of two 2-level atoms interacts with a single quantized electromagnetic field is considered. We study the effect of the mean photon number and the structure of the initial states of the two atoms on the dynamics of the atomic system from the separability point of view. It is found that, if we start from a product mixed atomic state, the probability of generating long living entangled states is increased as the mean photon number increases. Starting from excited atomic system in product state, one generates a more stable entangled states with high degree of entanglement. Also, the effect of the mean photon number on atomic system prepared initially in entangled states is investigated. It is found that the entangled state generated from the initially partial entangled states are more robust than those obtained from a maximum entangled state. The Pancharatnam phase for the separable and entangled states is studied under the effect of the mean photon number and the structure of the initial state'. We find that for the separable states, the collapses decrease and the amplitude of the revivals is smaller than that for the entangled state, so there are long-living entangled phases. This property give us a great chances to store safely information in entangled state. 18 Volume 8 – 2007 – 2008 M24. NEW ASPECTS OF THE PURITY AND INFORMATION OF AN ENTANGLED QUBIT PAIR NASSER IVlETWALLY Mathematics Department, Bahrain University, College of Science, 32038 Kingdom of Bahrain International Journal of Quantum Information, 6, (1), 187-200, 2008 Abstract In this article, we investigate the purity dynamics of entangled 2 two-level atoms interacting with a single quantized electromagnetic field. We show that the purity of the qubit pairs depends on the initial state of the atomic system. It is found that the superposition case is the best choice to generate entangled states with high purity and hence high entanglement. It is clear that the purity of one qubit can be purified at the expense of the other pair through the phenomena of purity swapping. The mean photon number plays an important role in increasing the purity. The robustness of the quantum channel is investigated in the presence of individual attacks, where we study the separability of these channels and evaluate its fidelity. Finally, we use the partial entangled states as quantum channels to perform the original coding protocol. We find that Bob can obtain the coded information with reasonable percentage. The inequality of security is tested, where we determine the interval of times in which Alice and Bob can communicate securely. These intervals depend on the type of error and the structure of the initial atomic system. M25.Some Theorems on Generating Functions Mohmoud Ahmad Pathan a , Mohannad Jamal S. Shahwan b a Department of Mathematics, Aligarh Muslilm, University, Aligarh-202002, India. b Department of Mathematics, University of Bhrain, P.O.Box 32038, Kingdom of Bahrain. KYUNGPOOK Math. J. 47, 373-380, 2007 Abstract In this paper, we derive some generating relations involving Konhauser polynomials, Gauss, Humbert, Appell and Kampe de Feriet hypergeometric functions with the help of four general theorems on generating functions (partly unilateral and partly bilateral) of one and two variables. 19 Volume 8 – 2007 – 2008 Physics 20 Volume 8 – 2007 – 2008 P1. Evolution of the Time-Lag and Variability Luminosity Relations for Long Gamma-Ray Bursts 1Azzam, Walid, Alothman, Mohamed2, Guessoum, Nidhal3 1( University of Bahrain),2(University of Bahrain),3 (American University of Sharjah) 37th COSPAR Scientific Assembly. Held 13-20 July 2008, in Montreal, Canada., p.151 Symposium E, session 18 (poster). Paper No. E18-0045-2008 Abstract Several luminosity relations currently exist for long gamma-ray bursts. Some were derived from the light curves; others were obtained from the spectra. In this study, we consider two of these luminosity relations: the time-lag, i, relation and the variability, V, relation and investigate their possible dependence on (or "evolution" with) the redshift. The data we use are taken from Schaefer's (2007) analysis of 69 long gamma-ray bursts. The method consists of binning the data by redshift, z, then writing the time-lag relation in the form 10g(L) = A + B log[T/(1 +z)] and extracting the fit parameters A and B for each redshift bin; likewise, for the variability relation, which we write in the form 1og(L)= A + B 1og [V(1 +z)]. The objective is then to see whether the fitting parameters A and B evolve in any systematic way with the redshift. Our preliminary analysis indicates that the B parameter does indeed evolve with z in a systematic way, while the A parameter shows a weak dependence on z. Throughout the analysis a flat universe with ΏM = 0.3 and H0 = 70 km/s.Mpc is assumed. P2. The missing host galaxies of (some)gamma-ray bursts Guessoum, Nidhal 1, Al-Dallal , Shawqi2, Azzam, Walid2 1 American University of Sharjah, 2University of Bahrain, 37th COSPAR Scientific Assembly. Held 13-20 July 2008, in Montreal, Canada., p.II 04 Abstract The detection of Gamma-Ray Bursts (GRBs) has increased by at least an order of magnitude with the launch of Swift. On the other hand, the number of host galaxies observed for GRBs has remained limited; moreover, the observed host galaxies do not seem to be correlated with redshift (distance). A recent (Ovaldsen et al. 2007) search on 24 GRBs with the Danish 1.54 m telescope at ESO/La Silla did not detect host galaxies for more than half of the sample. More baffling, though, was the case of GRB 070125, for which no galaxy was found even after a search with the 10 meter Keck I telescope. We here consider possible explanations for these observations. We have tabulated relevant data (fluence, redshift, extinction coefficients, etc.) of all GRBs for which such 21 Volume 8 – 2007 – 2008 information could be found, and we have undertaken a statistical analysis in order to determine the probability that there is some systematic effect on some properties of the GRBs or the galactic environments that may explain the absence of host galaxies in various cases/searches. We report our preliminary results and analysis including: distance effect, extinction, intrinsic burst properties and other related parameters. P3. The dc and ac properties of potassium trioxalatoferrate (Ill) trihydrate A.A. Dakhel College of Science, University of Bahrain, P.O.Box 32038, Bahrain Current Applied Physics, 8, 134-137, 2008 Abstract The complex potassium trioxalatoferrate (Ill) trihydrate {K3Fe(C204h)3.3H20)} was synthesised and characterised by energy dispersion X-ray fluorescence (XRF) and X-ray diffraction (XRD). The electrical and dielectric properties of the complex pellet were studied by ac- and dc-techniques in room temperature and in a temperature range of 293373 K. The data of the ac conductivity as a function of frequency in a frequency range of 1-100 kHz follow the correlated barrier hopping CBH model and the parameters of the model were determined and connecting them with the optical properties. The temperature dependence of dc conductivity shows that the semi-conducting behavior of conduction phenomenon in the complex is realised by hopping mechanism between localised states and the minimum hopping distance was determined. High relative permittivity of about 30 at 100 kHz was obtained for the complex, which can find technological applications like alternative for the Si02 insulator in MOS devices. P4. Correlated structural and optical study of Zn-Mn-O system thin films A.A. Dakhel Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Bahrain Materials Chemistry and Physics, 107, 518-523, 2008 Abstract Zinc-manganese oxide thin films prepared on glass and Si substrates have been annealed at different conditions in order to create different crystalline structures and agitate a solidstate reaction. The films were characterised by energy dispersion X-ray fluorescence (EDXRF), X-ray diffraction (XRD), and UV-vis absorption spectroscopy. The EDXRF spectrum was used to determine the weight fraction ratio of Mn/Zn in the prepared samples. The XRD method was used to determine the crystalline structure of the phases created in the sample during the pre-annealing processes at different temperatures 22 Volume 8 – 2007 – 2008 (400, 600, 800, and 1000 oC) in air and in vacuum. The spectral transmittance and reflectance of amorphous and polycrystalline Zn-Mn oxide samples grown on glass substrates in the fundamental absorption region of the spectrum were studied. The spectral refractive index as well as extinction coefficient was determined. The optical bandgap and its variation under crystallisation were determined. The spectral real and imaginary parts of the optical dielectric constant were calculated and explained by a molecular energy diagram. P5. dc-Conduction mechanism in lanthanum-manganese oxide films grown on p-Si substrate A.A. Dakhel Department of Physics, College of Science, University of Bahrain, P.D. Box 32038, Bahrain Microelectronics Reliability, 48, 395-400, 2008 Abstract Thin films of (La-Mn) double oxide were prepared on p-Si substrates for electrical investigations. The samples have been characterrised by X-ray fluorescence (XRF) and X-ray diffraction (XRD) methods. The XRF spectrum was used to determine the weight fraction ratio of Mn to La in the prepared samples. The XRD study shows the formation of grains of LaMn03 compound through a solid-state reaction for annealing at 800°C. Samples used to study the electrical characteristics of the prepared films were constructed in form of a metal-oxide-Si MOS structures. Those MOS structures were characterised by the measuring their capacitance as a function of gate volltage C(Vg) in order to determine the oxide charge density Qox, the surface density of states Dit at the oxide/Si interface, and to extract the oxide voltage in terms of gate voltage. The extracted dielectric constant of the double oxide film is lower than that of pure La203 film and larger than that of pure Mn203 film, but the formation of LaMn03 grains by a solid-state reaction at 800°C increases the relative permittivity to 11.5. These experimental conclusions might be useful to be used in the field of Si-oxide alternative technique. The leakage dc current density vs. oxide field J(Eox) relationship for crystalline films follow the mechanism of Richardson-Schottky (RS), from which the field-lowering coefficient and the dynamic relative permittivity were determined. Nevertheless, the leakage current density measured in a temperature range of (293-363 K) was not controlled by the RS mechanism. It was observed that the temperature dependence of the leakage current in crystalline (La-Mn) oxide insulating films has metallic-like temperature behavior, which might be important in the technical applications. 23 Volume 8 – 2007 – 2008 P6. Structural and electrical properties of Zn doped Mn oxide thin films grown on p-Si substrates A.A. Dakhel * Department of Physics, College of Science, University of Bahrain, P.O. Box 32038,Bahrain Journal of Alloys and Compounds,454, 24-30,2008 Abstract In the present work, Zn-Mn oxide thin films were prepared on p-Si(l 00) substrates for structural and electrical studies. The X-ray fluorescence (XRF) technique was used to determine the relative weight fraction ratio of Mn/Zn in the prepared samples. The X-ray diffraction (XRD) study shows that films annealed at 400 oC have amorphous structure and they were crystallised under pre-annealing at 600 oC or more. Moreover, Zn oxide cannot crystallise alone, but instead it diffuses into Mn oxide grains. A comprehensive study on electrical properties was carried on. The ac-conductance and capacitance as a function of gate voltage, frequency, and temperature were studied on samples made in form of metal/oxide film/Si MOS devices. The fixed charge and interface state densities were determined and their variation with annealing process was studied and explained. It was found that the "correlated barrier hopping" CBH model controls the frequency dependence of the conductivity, while Kramers-Kronig (KK) relations explain the frequency dependence of the relative permittivity. The parameters of CBH model were determined showing that the ac-conduction is realised by single-polaron hopping mechanism. dc-Conduction properties were also studied through the voltage and temperature dependence of the leakage dc-current density. The obtained dc-data follow a Richardson-Schottky (RS) mechanism. P7.Charge trapping and ac-electrical conduction in nanocrystalline erbium manganate film on Si substrate A.A. Dakhel Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Bahrain Journal of Alloys and Compounds, 458, 77-82, 2008 24 Volume 8 – 2007 – 2008 Abstract Thin film of nanocrystalline ErMn03 was prepared by thermal annealing of Er-Mn oxide film deposited on p-Si(l00) substrates. The X-ray fluorescence (XRF) and X-ray diffraction (XRD) technique were used to investigate the structure of the prepared Er-Mn oxide films. XRD study shows that films pre-annealed at 400 oC have amorphous structure and they were crystallised forming ErMn03 compound under pre-annealing at 800 oC or more. Moreover, in the prepared Er-Mn oxide films, Er oxide or Mn oxide cannot be crystallised each alone, but instead they interact chemically with each other forming ErMn03 compound. A comprehensive study on electrical properties was carried on. The ac-conductance and capacitance as a function of gate voltage, frequency, and temperature were studied on samples made in form of metal/oxide film/Si MOS devices. The fixed charge and interface state densities were determined and their variation with annealing process was studied and explained. It was found that the "correlated barrier hopping" CBH model controls the frequency dependence of the ac-conductivity, while Kramers-Kronig (KK) relations explain the frequency dependence of the relative permittivity. The parameters of CBH model were determined showing that the acconduction is realised by bipolaron hopping mechanism. dc conduction properties were also studied through the voltage and temperature dependence of the leakage dc-current density. The obtained dc-data follow a space charge limited current (SCLC) mechanism. P8. Correlated transport and optical phenomena in Ga-doped CdO films A.A. Dakhel Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Bahrain Solar Energy, 82, 513-519, 2008 Abstract Series of samples of lightly Ga-doped CdO thin films (3%, 6%, and 9%) have been prepared by evaporation method on glass substrate. The prepared films were characterized by X-ray diffraction (XRD), UV-VIS-NIR absorption spectroscopy, and dc-electrical measurements. The investigation shows that Ga doping widens the energygap of Cd0. The optical properties were easily explained by using Tauc et al. bandto-band transitions and classical Drude theory. The electrical behavior of the samples shows that they are degenerate semi-conductors. The 6% Ga-doped CdO sample shows increase its mobility by 3.2 times, increase its conductivity by 1.5 times, increase its intrinsic bandgap, and a slight increase its transmittance relative to undoped CdO film. Explanation was given concerning these variations. From transparent conducting oxide (TCO) point of view, Ga is not sufficiently effective for CdO doping comparing to other dopants like In, Sn, Sc, and Y. 25 Volume 8 – 2007 – 2008 P9. Influence of hydrogenation on the electrical and optical properties of CdO thin films A.A. Dakhel Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Kingdom of Bahrain Semicond.Sci. Technol. 23(2008)055017 (6pp) Doi.10.1088/0268-1242/23/5/055017 Abstract The electrical and optical properties of CdO films post-annealed in hydrogen atmosphere for different durations (15 min, 30 min and 60 min) were studied. The prepared films were subjected to structural characterization by the x-ray diffraction method and optical characterization by the UV-VIS-NIR absorption spectroscopy method. Experimental data indicate that annealing in H2-atmosphere slightly compresses the CdO unit cell and widens the energy gap of CdO from 2.31 eV to 2.42 eV via a Burstein-Moss energy level shift. The optical properties were easily explained within the framework of Hamberg et al band-to-band transitions and classical Drude theory. It was found that the greatest enhancement of electrical parameters that related to the transparent-conducting-oxide (TCO) function occurs by annealing in H2-atmosphere for 30 min when the resistivitydecreases, the conduction carrier concentration increases and the mobility increases. The results of the present work are important from a technical point of view for TCO production. P10.Linear and nonlinear optical properties of gold nanoparticle-Eu oxide composite thin films [DOI:10.1063/1.2967711] F. Z. Henari1 and A. A. Dakhel2 1 Royal College of Surgeons in Ireland, Medical University of Bahrain, P.O. Box 15503, Bahrain 2 Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Bahrain JOURNAL OF APPLIED PHYSICS 104, 033110 (2008) Abstract In this work, nanogold particles incorporated onto europium oxide films at levels of 4% and 7% were fabricated by a vacuum evaporation technique on glass and silicon substrates held at 200 oC. Samples were investigated by x-ray diffraction and linear and 26 Volume 8 – 2007 – 2008 nonlinear optical absorption. The linear optical absorption data were measured in the UVvisible-near infrared spectral regions and from these data the energy gap and the surface plasmon resonance were determined. The third order nonlinear optical properties of the nanogold particles incorporated onto europium oxide films were measured using the Zscan technique. Nonlinear absorption and refraction were performed using a continuous wave laser at 633 nm. A large value of third order nonlinearities was obtained with the samples. P11.Linear and N onlinear Optical Properties of Hydrogenated CdO Thin Films F.Z. Henari a, * and A. A. Dakhel b a Royal College of Surgeons in Ireland, Medical University of Bahrain, PO. Box 15503, Kingdom of Bahrain b Department of Physics, College of Science, University of Bahrain, P. O. Box 32038, Kingdom of Bahrain Laser Physics, 18, ( 12), 1557-1561, 2008 Original Text © Astro, Ltd., 2008. Abstract The linear and nonlinear optical properties of a CdO film post-annealed in a hydrogen atmosphere for 30 min (CdO:H) were studied. The prepared CdO and CdO:H films were characterized by X-ray diffraction and UV- VIS-NIR absorption spectroscopy. Experimental data indicated that annealing in an H2 atmosphere slightly compresses the CdO unit cell and widens the energy gap of CdO by about 3% relative to a nonhydrogenated film. This effect can be explained by the Burstem-Moss energy. effect. The nonlinear absorption and nonlinear refractive index coefficients were determined and found to be higher than the values previously determined for nonhydrogenated CdO. P12.Effect of thallium doping on the electrical and optical properties of CdO thin films A. A. Dakher Department of Physics, College of Science, University of Bahrain, P.O. Box 32038, Kingdom of Bahrain Physical Status Solid(a),205(11), 2704-2710,2008 27 Volume 8 – 2007 – 2008 Abstract A series of lightly TI-doped CdO thin films (1%. 1.5%, 2%, 2.5%, and 3%) have been prepared by a vacuum evaporation method on glass and Si wafer substrates. The prepared films were subjected to structural study by X-ray diffraction, optical characterization by UV-VIS-NIR absorption spectroscopy, and dc-electrical measurements. Experimental data indicate the TI3+ doping slightly stretching stresses the CdO crystalline structure and changes the optical and electrical properties. It was observed that TI doping widens the energy gap of CdO from 2.22 eV to 2.83 eV via a Burstein-Moss energy level shift. The band gap shrinkage was also observed for carrier concentrations N 22>1.13x1020 cm-3, which was explained by merging of the impurity band with the conduction band. The optical properties were explained by using Hamberg et al.'s band-to-band transitions and classical Drude theory. The electrical behavior of the samples shows that they are degenerate semiconductors. The 2% TI-doped CdO sample shows an increase in its mobility by about 1.4 times, conductivity by 5 times, and carrier concentration by 3.6 times relative to the undoped CdO film. From the transparentconducting-oxide point of view, TI is sufficiently effective for CdO doping but does not emulate other dopants like In, Sn, Sc, and Y. P13.Influence of hydrogenation on the electrical and optical properties of CdO:TI thin films A.A. Dakhel * Department af Physics, College of Sdence, University of Bahrain, P.O. Box 32038. Bahrain Thin Solid Films, 517,886,890 (2008) Abstract Electrical and optical properties of Tl-doped CdO films ((dO:TI) post-annealed in hydrogen atmosphere for different durations (15 min, 30 min, 45 min, and 60 min) were studied. The prepared films were characterized by the X-ray diffraction method and UVVIS-NIR absorption-reflection spectroscopy. Experimental data indicate that annealing in H2-atmosphere removes gradually with time the internal structural micro-stress that created as a consequence of Tl doping into CdO structure. The band gap of the hydrogenated TI-doped CdO samples changes with H2-annealing time following the changing in the free-electron concentration. These results were found to be in agreement with the available bandgap widening and narrowing models. The optical properties were easily explained within the framework of Hamberg bandto-band transitions and classical Drude theory. It was found that the greatest enhancement of the electrical conduction parameters occurs by annealing of CdO:Tl films in H2-atmosphere for 30-45 min when the conductivity increased by about 37% and the free-electron concentration increased by about 6%. The results of the present investigation are important for the transparent conducting oxide preparation technique. 28 Volume 8 – 2007 – 2008 P14.OPTICAL AND STRUCTURAL PARTICLES Eu OXIDE FILMS PROPERTIESOF Ag NANO- A. A. DAKHEL Department of Physics, College of Science University of Bahrain P. O. Box 32038, Bahrain International Journal of NanoScience, 7(6), 339-344 (2008) Abstract Silver-incorporated europium oxide thin films have been prepared by the successive evaporation method on quartz and silicon substrates. The silver concentration was 2.5% and 8.9% respectively, as measured by X-ray fluorScence. X-ray diffraction revealed that the Eu oxide of these samples remained amorphous after preannealing at 450oC; however, it crystallized in bcc structure at 800°C. The lattice parameter of the crystallized Eu oxide was larger than that of the bulk, due to the adsorption of Ag ions, which have a higher ionic radius. The optical absorption of the samples manifested the surface plasmon resonance (SPR) phenomenon, which varied with the Ag content and preannealings of the samples at different temperatures. The Ag nanoparticle radius was estimated with the Mie classical theory by using the SPR data analysis. 29 Volume 8 – 2007 – 2008 Addendum 30 Volume 8 – 2007 – 2008 Addendum to the previous volume 7 (2006/07) The following articles appeared in volume 7 (2006/07) as accepted papers. Now they have appeared in their reported journals as follows: M4 Ayache, A., N. Jarboui Answer to Dobbs conjecture about treed domains J.of Algebra, 320, 3720-3725, (2008) M5 Ayache, A. Nooman Jarboui Universally ca narian domains of the type A+I Ricerche.mat., 52 (1), 27-42, 2008 31