001124   Ilyad Md (Math Dep, Gaya College, Gaya-823 001) : On intertwining by an operator having a dense range. Math Educ 2002, 36(3), 145-8.

E. Gaya and T. satio formulated the algebriaic version of generalised Putnam-Fugledge theorem. Teh notion has been extended to quasi-normal, binormal, K-normal and K-quasi-normal operators. It has been shown tha tT is quasi-normal, binormal, K-normal and K-quasi-normal if so is S where W is an operator having a dense range such that TW=WS.

2 ref

001123   Harne S;Bijendra Singh (Mathematics Dep, PMB Gujarati Science College, Indore) : Some properties of fourth-order recurrence relations. Vikram mathl J 2000, 20, 79-84.

Fourth order recurrence relations have been made and matrices used to develop some of the properties of these recurrence relations.

10 ref

001122   Gupta V;Maheshwari P;Jain V K (School of Applied Sciences, Netaji Subhas Institute of Technology, Axad Hind Fauj Marg, Sector-3, Dwarka, New Delhi-110 045) : On the linear combination of modified beta operators. Pure appl Math Sci 2003, 58(1-2), 63-75.

Some direct theorems in Lp-approximation, for the linear combinations of modified Beta operators have been studied. Steklov means techniques have been used to prove the main theorem.

7 ref

001121   Gupta P;Saxena M (School of Studies in Statistics, Vikram University, Ujjain-456 010) : Stochastic behaviour of a system with two independent protection devices. Vikram mathl J 2000, 20, 55-67.

A single unit system with two different protection devices, operating simultaneously with the unit, is considered. The life time distribution of the operative unit changes, upon failure of the protection devices. There is a single repair facility to repair the unit and the protection devices, repairing one at a time.

3 ref

001120   Gupta K C;Taneja A K (Department of Mathematics, M.D.U.P.G. Regional Centre, Rewari) : On the expected profit of a system with rest period, patience time and various types of repair. Pure appl Math Sci 2003, 58(1-2), 101-19.

A two unit cold standby system with rest period and patience time has been examined. There is one regular repairman who always remains with the system and may get tired while repaiing a failed unit. Then a visiting assistant of an expert repairman is called. If the regular/assistant repairman is unable to repair within the patience time, the expert himself comes to complete the repair. Mean time to system failure and the profit are evaluated. Graphs are plotted and interpretations are made.

8 illus, 7 ref

001119   Gupta K C;Sindhu B S (Department of Mathematics, Maharshi Dayanand University, Rohtak P G Regional Centre, Rewari) : Analysis of two reliability models for a system with two stages of rest. Pure appl Math Sci 2003, 58(1-2), 77-92.

Two-unit cold standby system with two stages of rest have been examined. First stage is that when the regular repairman feels need of rest and can repair with reduced repair rate. Second stage is that when due to severe tiredness he becomes unable to continue the repair further. Two models have been discussed and compared graphically.

7 illus, 5 ref

001118   Gowda H;Lokesha V (Studies in Mathematics Dep, UNiversity of Mysore, Manasagangotri, Mysore-570 006) : On normed linear spaces. Math Educ 2002, 36(2), 83-6.

It has been proved that every normed linear space can be represented as a g.s.i.p space with the homogeneity property and this has been illustrated by means of an example. Also it is shown that g.s.i.p orthogonality and James normality coincide in a smooth space.

3 ref

001117   Gopalan M A;Srikantha R (Math Dep, National College, Trichy-620 001) : A note on the pell equation. Math Educ 2002, 36(2), 116-7.

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001116   Gopalan M A (Math Dep, National College, Tiruchirapalli-620 001) : Note on the diophantine equation. Math Educ 2002, 36(3), 144.

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001115   Gaur Y N;Sharma P R;Sharma R P (Mathematics Dep, M R Engineering College, Jaipur) : Mean flow and mean temperature of a non-newtonian fluid along a porous moving vertical plate in the presence of oscillating free stream. Ultra Scient phys Sci 2003, 15(1M), 103-8.

Free convection effect on mean velocity and mean temperature distributions of a non-Newtonian fluid flow along porous moving vertical plate in the presence of oscillating free stream, constant suction and constant heat flux is investigated. The governing equations of motion and energy are solved by the successive perturbation technique. The expressions of mean velocity and mean temperature are derived, shown through graphs and discussed numerically. The expression of skin-friction coefficient at the plate is derived and discussed numerically its numerical values presented through table.

2 illus, 1 table, 7 ref

001114   Ganguly A;Ganguly S (Applied Mathematics Dep, SGSITS, Indore-452 013) : On fixed point of fuzzy mappings. Ultra Scient phys Sci 2002, 14(2), 289-91.

Concept of fuzzy mappings has been used in proving fixed point theorems. A result of Khan, Kubiaczyk and Sessa has been extended to fuzzy sets.

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001113   Gajjar P A;Bhathawala P H (Applied Mathematics Dep, Sardar Vallabhbhai Regional College of Engg & Tech, Surat) : Fuzzy-rule-based model for water flow in unsaturated soil column. Ultra Scient phys Sci 2002, 14(1), 89-96.

Modeling water movement in the unsaturated zone requires a great number of parameters, such as the initial water content, the saturated moisture content, and the saturated hydraulic conductivity, which can relatively easily be assessed. Other functions such as the suction head and the relative hydraulic conductivity, which are highly nonlinear functions of the actual water content are more difficult to find. Furthermore, infiltration experiments carried out at a few locations can only define these parameters at selected locations, and a reasonable interpolation of these parameters is extremely difficult. A fuzzy logic-based model is presented for infiltration process.

2 illus, 15 ref

001112   Gajjar P A;Bhathawala P H (Math Dep, S V Regional College of Engg & Tech, Surat-395 007) : A simplified approach for combining fuzzy rule responses. Math Educ 2002, 36(3), 164-9.

It is shown that the additive combination methods with product inference lead to the simplest rule formulation using operator `AND' only.

10 ref

001111   Dubey R P;Sharma S;Singh N K (Math Dep, Bhilai Institute of Technology, Bhilai House, Durg-491 001) : Some fixed point theorems in semi-hausdorff spaces. Math Educ 2002, 36(3), 173-7.

Some fixed point theorems in Semi-Hausdorff spaces have been established, which generalize the results of Popa (1983) and Som et. al. (1984). Further, range of functions has been extended from non-negative to non-positive reals.

3 ref

001110   Daby M S (Department of Mathematics, Jai Narain Vyas University, Jodhpur-342 001) : On mix of lie theory and hypergeometric function to establish a theorem for bilinear generating relation. Pure appl Math Sci 2003, 58(1-2), 53-5.

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001109   Chauhan D S;Jakhar P K (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Non-Newtonian fluid flow and heat transfer with a power-law viscosity past an infinite naturally permeable medium. Ultra Scient phys Sci 2002, 14(1), 73-8.

The flow past an infinite naturally permeable bed with constant suction, is investigated for a power-law fluid, together with heat transfer taking viscous heating into consideration. Velocity and temperature fields are obtained and effects of permeability of the porous bed, non-Newtonian parameter and suction parameter, on velocity and temperature distributions are discussed.

2 illus, 3 tables, 8 ref

001108   Chandel S;Sharma S (Department of Mathematics, D V Postgraduate College, Orai-285001) : Hypergeometric function of four variables. Pure appl Math Sci 2003, 58(1-2), 7-18.

Investigates the generating relations, integral representations and recurrence relations for hypergeometric functions of four variables.

16 ref

001107   Bounias M;Bonaly A (Faculty of Sciences, University of Avignon, France) : Topological foundations of self-conscious perception functions in the mathematical spaces of the brain. Ultra Scient phys Sci 2002, 14(2), 218-29.

Topological closure allows mathematical spaces to get the physical characteristic of observability. A path (L) connecting a point interior of a set A to the interior of another closed B. Since B is closed, there also exists a second kind fixed point of the Brouwer type in the closure of the domain of fⁿ. Sequences fⁿ are generally nonlinear and the space of brain mathematics could be a mixed space composed with fractal and nonfractal components. The demonstration that a fractal space F is separated and compactifiable allows a generalization of Banach spaces to nonmetric setting, by using the nonmetric set-distance instead of the classival metric distances. Fulfilment of the conservation of topologies, finally lets appear the mappings as accounting for mental imaging, upon connection of neuronal chainings as the materialization of sequences to the observer's self-consciousness as represented by the set of points. The subset of points provide the basis for learning functions, while the reciprocal mappings reconstruct, in a eventually F-aided way, the neuronal chaining associated with a given perception. These results provide mathematical justification to the properties of non-localization and nowhere-storage of memory.

19 ref

001106   Bhattacharyya A (Pure Math Dep, University of Calcutta, 35, Ballygunge Circular Road, Calcutta-700 019) : On semi pseudo symmetric and semi pseudo RICCI symmetric Lorentzian para sasakian manifold. Math Educ 2002, 36(3), 141-3.

It is shown that a Lorentzian Para-Sasakian manifold (briefly LP-Sasakian) Mⁿ, (N<62>3) cannot be semi pseudo symmetric and semi pseudo Ricci Symmetric manifold.

7 ref

001105   Banerji P K;Goyal S P;Deroa Y (Mathematics Dep, Faculty of Science, J N V University, Jodhpur-342 005) : Integrals and partial derivatives of certain Dirichlet average. Ultra Scient phys Sci 2003, 15(1M), 123-6.

4 ref

001104   Bali R;Shukla A K (Department of Mathematics, Harcourt Butler Technological Institute, Kanpur) : A sunoke model for temperature regulation in synovial joint. Ultra Scient phys Sci 2003, 15(1M), 109-16.

The studies of the temperature regulation in synovial joint has been presented. Intra articular generation of heat is expected in any joint during its movement. The more heat is produced, the more wear occurs with the result of disorganisation of the joint and functional impairment. The articular cartilage minimises frictions and heat generation due to its poroviscoelastic and water locatable nature. It has been observed experimentally that there is hardly any rise in temperature of synovial fluid in normal state but is diseased state, the variation in temperature of synovial fluid has been observed. Analytically the problem is formulated as a two region flow and diffusion model flow and diffusion in between the cartilage. The synovial fluid has been represented by viscoelastic fluid model, the parametric values for which already have been estimated for normal, old and diseased joints. The temperature distribution is obtained by solving energy equation in both the region using proper boundary and matching conditions and perturbation technique.

5 illus, 22 ref

001103   Arora G K;Singh R P;Gupta P (A R S D College, , Dhaula Kuan, Delhi University, New Delhi) : On weighted information improvement. Pure appl Math Sci 2003, 58(1-2), 93-9.

Weighted information improvement has been defined through a generating function and it has been characterized through generalized mean value property. Particular cases and some comparison results have been presented.

3 ref

001102   Amardeep Singh;Rajput A;Saluja A S (Mathematics Dep, Govt. Motilal Vigyan Mahavidayalaya, Bhopal-462 003) : Some fixed point theorems of expansion mappings in complete metric spaces. Vikram mathl J 2000, 20, 22-30.

Some results on fixed points of expansion type maps on a complete metric space have been obtained. Several known results appear as special cases of the obtained results.

7 ref

001101   Akca I I (Department of Mathematics, Faculty of Science, Osmangazi University, 26480, Eskisehir, Turkey) : The Riemann-Roch theorem on Riemann surfaces. Pure appl Math Sci 2003, 58(1-2), 37-41.

The Riemann-Roch theorem tells something about the existence of meromorphic functions with prescribed singularities on a compact Riemann surface. The Riemann-Roch theorem on Riemann surfaces has been examined.

4 ref

001100   Ahmed S;Ahmed N (Mathematics Dep, Goalpara College, Goalpara Assam-783 101) : MHD effects on the free convection and mass transfer flow through porous medium between a long vertical wavy wall and a parallel flat wall. Ultra Scient phys Sci 2003, 15(1M), 35-44.

Effects of magnetic field on the two dimensional free convective and mass transfer flow of a viscous incompressible fluid through a porous medium bounded by a vertical wavy wall and a parallel flat wall have been analysed. The equations governing the fluid flow and heat transfer have been soved subject to a set of appropriate boundary conditions. The solution consists of two parts : a mean part and a perturbed part. To solve the perturbed part, long wave approximation has been applied. To obtain the solution of mean part, the well known approximation used by Ostrach has been utilised. The zeroth order and first order velocity profile, temperature profile and the skin friction, heat transfer at the walls are demonstrated graphically for different values of the parameters involved

9 illus, 5 ref

000099   Zorlutuna I;Kucuk Y (Mathematics Dep, Faculty of Sci, Cumhuriyet Univ, 58140, Turkey) : On the upper lower faintly continuous multifunctions. Far East J mathl Sci 2003, 9(3), 241-53.

Upper (lower) faintly continuous multifunctions have been defined and some characterizations using single valued map and some basic properties of such a multifunction have been obtained. Also, some relationships between the concept of faint continuity and known concepts of continuity and weak continuity are given.

12 ref

000098   Weaver A (NO, , 800 Riverside Drive, Apt. 6B, New York, N.Y. 10032, USA) : Odd-Irder group actions on surfaces. J Ramanujan Mathl Soc 2003, 18(3), 211-20.

For the lagest odd-order group of automorphisms N(g) that a compact Riemann surface of genus g can admit, sharp upper and lower bounds for N(g) have been obtained at least once. It has been shown that the lower bound is attained at least once. Infinite sequences of genera in which the upper bound is attained and inifinte sequences in which it is not attained have been exhibited. Also an infinite family of metacyclic groups which attain the upper bound has been constructed.

19 ref

000097   Wang Y;Liu X (Statistics Dep, Shandong Economic University, Jinan, Shandong 250 014, People's Republic of China) : Positive solutions of singular boundary value problem of negative exponent Emden-Fowler equation. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 195-205.

Investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition of the existence of C¹[0, 1] positive solution as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.

9 ref

000096   Vinocha O P;Bhullar J S (Math Dep, S.G.N. Khalasa College, Sri Ganganagar-335 001) : The generalized non. additive measue of useful information. Appl Sci Period 2003, 5(3), 152-61.

The utility of distribution plays a very important role in study of useful information by using the sum properties and solutions of new functional equation give the new non-additive useful informactio measure.

10 ref

000095   Vasantha W B;Kannan S R;Neelakantan N R (Mathematics and Chemical Engineerng Dep, IIT Madras, Chennai-600 036) : Operability study on decision tables in a chemical plant using hierarchical genetic fuzzy control algorithms. Vikram mathl J 1999, 19, 48-59.

In chemical plants the main components of information are stored in the form of decision tables. In the functioning of the decision tables, the output states are largely dependent on the internal states. The internal states, in general, in most of the chemical plants are too many and some of them are not compatible enough to give a proper output, resulting in loss of time, engineering cost, and damage to the very system. To overcome these problems hierarchical genetic fuzzy control algorithms are used. Operability study is a method to study the decision tables in a chemical plant. This method examines the safety of chemical plants by systematically identifying every conceivable process deviations and it can reduce the time and the engineering. The tools for the operability study are guidewords, property words and decision tables. HGFCA method has been described, by the use of genetic algorithms to decision tables of operability study. By using HGFCA, The system performance with minimal valid conditions in decision tables improves.

12 illus, 4 tables, 3 ref

000094   Upadhyayaya L N;Singh H P (Indian School of Mines, Vikram University, Dhanbad, Jharkhand) : An estimator for population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram mathl J 1999, 19, 14-7.

An estimator for the population variance of the study variable using information on population variable x, and kurtosis of an auxiliary variance has been proposed and its properties analy. The merits of the suggested estimator is judged through an numerical illustration.

1 table, 2 ref

000093   Turkoglu D;Fisher B (Mathematics Dep, Faculty of Scinence and Arts, University of Kirikkale, 71450-Yashihan Kirikkale, Trkey, ) : Fixed point of multivalued mapping in uniform spaces. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 183-7.

Some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces have been proved.

8 ref

000092   Theriault N (Mathematics Dep, University of Toronto, Toronto, Ontario, Canada, M5S 3G3) : Weil descent attack for Kummer extensions. J Ramanujan Mathl Soc 2003, 18(3), 281-312.

It has been shown that the Weil descent attack of Gaudry, Hess and Smart can be adapted to work for some hyperelliptic curves defined over fields of odd characteristic. This attack applies to a family of hyperelliptic and superelliptic curves defined over fields of odd characteristic. This attack applies to a family of hyperelliptic and superelliptic curves over quadratic field extensions, as well as two families of hyperelliptic curves defined over cubic extensions. It has been shown that those are the only families of nonsingular curves defining Kummer extensions for which this method will work.

24 ref

000091   Tamilarasi A;Thangaraj P (Math Dep, Kongu Engineering College, Perundurai, Erode-638 052) : Some fixed point theorems of a fuzzy metric space. Appl Sci Period 2003, 5(3), 162-6.

Some fixed point theorems for mappings of a fuzzy metric space have been obtained.

6 ref

000090   Sujivrathan N S (NO, Govt Ay College, Puthiyakavu, Tripunithura-682 301) : Formula for the volume of right triangular prism. Appl Sci Period 2003, 5(3), 182.

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000089   Srivastava A;Khadke A (Sch Stud Math, Vikram Univ, Ujjain-456010 MP) : Variation of α-coincidence sets. Bull Calcutta Mathl Soc 2003, 95(4), 301-6.

In many familiar cases the upper semi-finite topology on the set of closed subsets is the largest topology making the coincidence function continuous, when the collection of functions is given the graph topology. For continuous maps f, h: X→Y and for fixed map α: Y→Y, where the α-coincidence set consists of points such that α. f and αo h coincide, many of the results have been obtained.

7 ref

000088   Srivastava A;Gupta D (Sch Stud Math, Vikram Univ, Ujjain-456010) : On H-singular set of a composition mapping. Bull Calcutta Mathl Soc 2003, 95(4), 281-4.

H-singular set of the composition of two mappings between locally H-closed, paces is obtained in terms of the H-singular set of the individual mappings when one map is the embedding of the space in one of its H-closed extensions.

9 ref

000087   Somashekara D D;Noor Fathima S (Studies in Mathematics Dep, Univ of Mysore, Manasagangothri, Mysore-570 006) : An interesting generalization of Jacobi's triple product identity. Far East J mathl Sci 2003, 9(3), 255-9.

An interesting generalization of Jacobi's triple product identity has been obtained. A number of eta-function identities have been deduced thereform

12 ref

000086   Som T (Math Dep, Assam Univ, Silchar-788011) : Few common fixed point results for compatible mappings. Bull Calcutta Mathl Soc 2003, 95(4), 307-12.

Few common fixed point results are obtained for a weaker type of mappings than commuting or weakly commuting, called compatible mappings, satisfying a more general inequality condition.

17 ref

000085   Singh M;Sharma M;Sharma R K (Mathematical Sciences and Computer Applications Dep, Bundelkhand University, Jhansi, U P) : Weak compability and common fixed points in generalized fuzzy metric spaces. Vikram mathl J 1999, 19, 60-9.

Concepts of S-weak commutativity and S-weak compatibility of maps are introduced and some common fixed point theorems in recently developed space S-fuzzy metric space are proved.

11 ref

000084   Singh J P;Prasad A;Tiwari R K (Mathematical Sciences Dep, A P S Univ, Rewa) : Bianchi type V perfect fluid cosmological models with constant active gravitational mass. Vikram mathl J 1999, 19, 23-30.

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000083   Shandil R G;Jagjit Singh (Mathematics Dep, H.P. University, Shimla-171 005) : Bounds on the phase velocity in the linear instability of viscous shear flow problem in the β-plane. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 207-12.

Results obtained by Joseph for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived.

9 ref

000082   Sarangi K C;Chaturvedi R (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Steady heat transfer through parallel porous discs of different permeability: upper disc is rotating. Appl Sci Period 2003, 5(3), 167-70.

Heat transfer for laminar flow through parallel porous discs of different permeability is investigated. The discs are kept at constant temperatures. The expression of temperature distribution is derived, discussed numerically and show through graph. The expression of Nusselt number at the discs is also derived, discussed numerically and numerical values are presented through table.

1 illus, 1 table, 9 ref

000081   Sahoo A K (Mathematics Dep, Government Kolasib College, P.B. No.23, Kolasib-796 081) : On the absolute N_qα-summability of rth derived conjugate series. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 223-41.

Studies the absolute N_{qα - summability of rth derived conjugate series generalizing a known result.}

10 ref

000080   Sabu N (T.I.F.R. Centre, IISc Campus, Bangalore-560 012, , ) : Vibrations of thin piezoelectric shallow shells: two-dimensional approximation. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 333-52.

Considers the eigenvalue problem for piezoelectric shallow shells and shows that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a two dimensional eigenvalue problem.

9 ref

000079   Roy J P;Verma Lalan B K (Mathematics Dep, Dr. L.K.V.D. College, Tajpur-848 130) : On characterisation of probability measures in banach space. Appl Sci Period 2003, 5(3), 171-4.

Discusses full Levy's measures on Rⁿ and express it in terms of operator decomposability. Some properties of the sets E(λ) and A (λ) have been derived. The concept of uniformly infinitesimal in terms of random variables has been discussed by M. Loeve and P. Levy. The symmetrisation aspect its domain to has been extended to Branch-valued random variables.

4 ref

000078   Rhoades B E;Savas E (Mathematics Dep, Indiana University, Bloomington, IN 47405-7106, USA) : Necessary and sufficient conditions for inclusion relations for absolute summability. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 243-50.

A set of necessary and sufficient conditions for <157>N^-, p_n<157>k to imply <157>N, q_n<157>s for 1 <60> k ≤ s <60> ∞ have been obtained. Using this result several inclusion theorems as well as conditions for the equivalence of <157>N^-, p_n<157>k and <157>, q_n<157>s have been established.

6 ref

000077   Raychaudhuri P (Appl Math Dep, Calcutta Univ, Kolkata-700 009) : One of the possible solutions of the solar neutrino problems. Bull Calcutta Mathl Soc 2003, 95(4), 343-50.

The solar neutrino flux observation from the existing solar neutrino detectors has been explained and it has been found that if the neutrions can be a mixture of electron neutrino types and muon neutrino types and if the neutrino interaction cross section for Ev ≤0.5 MeV is different from the neutrino interaction cross section 0.5 <60>Ev≤20 MeV then it is possible to explain the solar neutrino problems in a coherent manner. In the stated framework solar neutrino flux from the standard solar model remains the same but the cross section is different from the electroweak interaction in the mentioned neutrino energy region. It has also been predicted the ratio of σ(ve+²D→p+n+ve)/(ve+²D<142>p+p+e^-) is in between 2 and 4 for the Sudbury Neutrino Observatory detector. If the interpretation is correct then all the neutrino absorption process and the neutral current phenomena must be reexamined very carefully for the neutrino energy region 0.233 MeV≤Ev≤20MeV before to get a definite solution.

1 table, 22 ref

000076   Rane V V (Mathematics Dep, The Institute of Science, 15, Madam Cama Road, Mumbai-400 032) : Analogues of Euler and Poisson summation formulae. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 213-21.

Euler-Maclaurin and Poisson analogues of the summations ∑_{a<60>n≤b d⁽ⁿ⁾ χ⁽ⁿ⁾ ƒ⁽ⁿ⁾, ∑a<60>n≤b d⁽ⁿ⁾ ƒ⁽ⁿ⁾, ∑a<60>n≤b χ⁽ⁿ⁾ ƒ⁽ⁿ⁾ have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence; d(n) is the divisor function and ƒ(x) is a sufficiently smooth function on [a,b]. A generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables have been stated.}

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000075   Ramsamujh T I (Mathematics Dep, Florida International Univ, Miami, Florida 33199, U.S.A.) : The levels and complexity of hypersets. Far East J mathl Sci 2003, 9(3), 327-41.

The minimal representation of a hyperset is obtained by a transfinite algorithm. This leads to Aczel's minimal anti-foundation axiom and to the internal complexity of a hyperset. Some results about the levels and complexity of hypersets then follow.

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