2006
30
3
3
103
DUAL SPLIT QUATERNIONS AND SCREW MOTION IN MINKOWSKI 3SPACE
2
2
In this paper, two new Hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. It is shown that finite screw motions in Minkowski 3space can be expressedby dualnumber ( 3×3 ) matrices in dual Lorentzian space. Moreover, by means of Hamilton operators, screwmotion is obtained in 3dimensional Minkowski space 3R1
1

245
258


L
KULA
Ankara University, Faculty of Science, Department of Mathematics
06100 Tandogan, Ankara, Turkey
Ankara University, Faculty of Science, Department
Turkey


Y.
YAYLI
Ankara University, Faculty of Science, Department of Mathematics
06100 Tandogan, Ankara, Turkey
Ankara University, Faculty of Science, Department
Turkey
Dual split quaternions
semiorthogonal dual matrix
screwmotion
DISTRIBUTION OF NATURAL RADIONUCLIDES ON COASTS OF BUSHEHR, PERSIAN GULF, IRAN
2
2
A reconnaissance study has been made on the distribution of 238U, 232Th, 40K, 137Cs andgeochemical features in soil and sediment samples at various locations on the coast of Bushehr in the PersianGulf. In this study a gammaray spectrometer based on a High Purity Germanium detector and a PC basedMCA and Xray fluorescence (XRF) method were used. Estimation of the measured radionuclide contenthave been made for the absorbed dose rate of gamma radiation. The Activity concentration (A), the equivalentradium (Req), and the external hazard index (Hex) which resulted from the natural radionuclides in soil andsediment are also calculated. The baseline data of radionuclides and heavy metals in view of thecommissioning of nuclear and nonnuclear industries for the coast of Bushehr, which does not yet exist, wasobtained.Activity concentration levels due to radionuclides were measured in 50 soil and sediment samplescollected from this region. The measurement was performed with respect to their gamma radioactivity for acounting time of 24 hour intervals. From the accumulated spectra, activity concentration were determined for40K (range from 108 to 520 Bq Kg1), 137Cs (from 6 to 40 Bq Kg1), 238U (from 12 to 75 Bq Kg1) and 232Th(from 8 to 33 Bq Kg1) with the lowest limit detection (LLD) of, respectively, 68, 3.2, 4.3 and 4.3 Bq Kg1.The dose rate from ambient air at the soil ranges was between 14 to 44 nGy h1 with an average of 30.56±7.86 nGy h1.
1

259
269


M. R.
ABDI
Department of Physics, University of Isfahan, Isfahan, 8174773441, I. R. of Iran
Department of Physics, University of Isfahan,
Iran


H.
FAGHIHIAN
2Department of Chemistry, University of Isfahan, Isfahan, 8174773441, I. R. of Iran,
2Department of Chemistry, University of Isfahan,
Iran


M.
KAMALI
Central Laboratory, University of Isfahan, Isfahan, 8174773441, I. R. of Iran
Central Laboratory, University of Isfahan,
Iran


M.
MOSTAJABODDAVATI
Department of Physics, University of Isfahan, Isfahan, 8174773441, I. R. of Iran
Department of Physics, University of Isfahan,
Iran


A.
HASANZADEH
Department of Physics, University of Isfahan, Isfahan, 8174773441, I. R. of Iran
Department of Physics, University of Isfahan,
Iran
Natural radionuclide
Gamma spectroscopy
Uranium
Thorium
Cesium
Potassium
HPGe
soil
Bushehr
Persian Gulf
ON PROBLEMS REDUCED TO THE GOURSAT PROBLEM FOR A THIRD ORDER EQUATION
2
2
The aim of the present paper is the investigation of some problems which can be reduced to theGoursat problem for a third order equation. Some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.
1

271
277


A.
MAHER
Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt
Department of Mathematics, Faculty of Science,
Egypt


YE. A.
UTKINA
Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt
Department of Mathematics, Faculty of Science,
Russian Federation
Third order partial differential equation
goursat problem
TEMPERATURE DEPENDENCE OF PHASE TRANSFORMATION PRESSURE IN SILICON
2
2
In this experimental work the pressure induced phase transformation of silicon and Germaniumhas been studied. It was shown that at a particular value of applied pressure, (Pt), depending on the sampletemperature, the electrical resistance of the specimen falls off to a metallic state. The main goal of this studywas to find out how the phase transformation pressure, Pt, for a ptype silicon varies with the sampletemperature. The results show that, the value of Pt decreases linearly as the temperature of the sampleincreases. Meanwhile, other related results including the rate of resistance change in accordance with appliedpressure on the sample at different temperatures (~270350K), both for the semiconductor and the metallicstate of the specimen were determined. In another effort, the amount of Pt for an ntype germanium, but onlyat room temperature, was also determined.
1

279
283


B.
SALEHPOUR
Faculty of Physics, University of Tabriz, I. R. of Iran
Faculty of Physics, University of Tabriz,
Iran


M.
OMIDFAR
Faculty of Physics, University of Tabriz, I. R. of Iran
Faculty of Physics, University of Tabriz,
Iran
Phase transformation pressure
Silicon
Germanium
metallic state
temperature dependence
COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES
2
2
Let (M,g ) be a compact immersed hypersurface of (Rn+1,<,>) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, A the shape operator, vol (M ) the volume of M,and S the scalar curvature of M. In this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2M MA dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2M 1 Mdv S dvn nα ρ ≥ ρ∫ − ∫ ,3) If the scalar curvature S and the first nonzero eigenvalue λ1 satisfy S = λ1 (n −1) , then[ ] 2 1 2 0Mdvn∫ α − λ ρ ≥ ,4) Suppose that the Ricci curvature of M is bounded below by a positive constant k. Thus( )2 2 2 ( )M 1 Mdv k gradf dv vol Mn nα ρ ≥ +∫ − ∫ ,5) Suppose that the Ricci curvature is bounded and the scalar curvature satisfy S = λ1 (n −1) and L=k2S>0 is a constant. Thus( ) 1 2 2 2 2 .M Mvol M k dv S dvL L≥ − λ ∫ ψ αρ − ∫ α ρ
1

285
289


M.
BEKTAS
Department of Mathematics, Fırat University, 23119 Elazig, Turkey
Department of Mathematics, Fırat University,
Turkey


M.
ERGUT
Department of Mathematics, Fırat University, 23119 Elazig, Turkey
Department of Mathematics, Fırat University,
Turkey
First Eigenvalue
Support Function
NUMERICAL SOLUTION OF THIRDORDER BOUNDARY VALUE PROBLEMS
2
2
In this paper, we use a third degree Bspline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. Severalexamples are given to illustrate the efficiency of the proposed technique.
1

291
295


G. B.
LOGHMANI
Department of Mathematics, Yazd University, Yazd, I. R. of Iran
Department of Mathematics, Yazd University,
Iran


M.
AHMADINIA
Department of Mathematics, University of Qom, Qom, I. R. of Iran
Department of Mathematics, University of
Iran
Bspline
least square method
third order BVPs
FUZZY β −IRRESOLUTE FUNCTIONS AND FUZZY β −COMPACT SPACES IN FUZZIFYING TOPOLOGY
2
2
In this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.
1

297
314


O. R.
SAYED
Department of Mathematics, Faculty of Science,
Assiut University, Assiut 71516, Egypt
Department of Mathematics, Faculty of Science,
Ass
Egypt


M.
AZAB ABDALLAH
Department of Mathematics, Faculty of Science,
Assiut University, Assiut 71516, Egypt
Department of Mathematics, Faculty of Science,
Ass
Egypt
Lukasiewicz logic
fuzzifying topology
β − irresoluteness
fuzzifying compactness
β − compactness
NETWORK OPTIMIZATION WITH PIECEWISE LINEAR CONVEX COSTS
2
2
The problem of finding the minimum cost multicommodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. The arcpath model and overflowmodel are presented to formulate the problem. The results suggest that the new overflow model outperformsthe classical arcpath model for this problem. The classical revised simplex, Frank and Wolf and a heuristicmethod are compared for the problem.
1

315
323


S.
KETABI
Department of Management, University of Isfahan, I. R. of Iran
Department of Management, University of Isfahan,
Iran
Multicommodity network flow problem
piecewise linear and convex costs
Arcpath Model
Overflow Model
Frank and Wolfe Method
BRAIDING FROM 2GROUPS TO 2GROUPOIDS
2
2
We give the concept of ‘braiding’ for 2groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.
1

325
341


E.
ULUALAN
Department of Mathematics, Faculty of Science, University of Dumlupınar, Kütahya, Turkey
Department of Mathematics, Faculty of Science,
Turkey
Braided crossed modules
catgroups
internal category
monoidal category
SEMIANALYTICAL SOLUTION OF STABILITY OF COMPOSITE ORTHOTROPIC CYLINDRICAL SHELLS UNDERTIME DEPENDENT APERIODIC AXIALCOMPRESSIVE LOAD
2
2
In this study, the stability problem of a circular orthotropic cylindrical shell under the effect of anaxial compression varying with a power function of time is considered. At first, the modified Donnell typedynamic stability and compatibility equations are obtained using Love’s shell theory. Applying the Galerkinmethod and RayleighRitz variational techniques to these equations and taking the large values of loadingparameters into consideration, analytics are obtained for critical parameter values. The results show thatcritical parameters are affected by loading parameters variations, ratio of the Young’s moduli variations,radius to thickness variations and the power of time in the axial compression expression variations.Comparing results with those in the literature validates the present analysis.
1

343
347


H.
SOFIYEV
1Department of Civil Engineering, Suleyman Demirel University, Isparta, Turkey
1Department of Civil Engineering, Suleyman
Turkey


AL. H.
SOFIYEV
Technical Sciences Department, Kazakh Branch, Azerbaijan Teachers Institute, Kazakh, Azerbaijan
Technical Sciences Department, Kazakh Branch,
Azerbaijan


E.
YUSUFOGLU
Department of Mathematics, Dumlupinar University, Kutahya, Turkey
Department of Mathematics, Dumlupinar University,
Turkey


Z.
KARACA
Department of Civil Engineering, Ondokuz Mayis University, Samsun, Turkey
Department of Civil Engineering, Ondokuz
Turkey
orthotropic material
cylindrical shell
dynamic critical axial load
dynamic factor
REGRESSION ANALYSIS IN MARKOV CHAIN
2
2
In a finite stationary Markov chain, transition probabilities may depend on some explanatoryvariables. A similar problem has been considered here. The corresponding posteriors are derived andinferences are done using these posteriors. Finally, the procedure is illustrated with a real example.
1

349
354


A. Y.
ALAMUTI
Department of Statistics, Shahid Beheshti University, Evin, Tehran, 19838, I. R. of Iran
Department of Statistics, Shahid Beheshti
Iran


R.
MESHKANI
Department of Statistics, Shahid Beheshti University, Evin, Tehran, 19838, I. R. of Iran
Department of Statistics, Shahid Beheshti
Iran
Bayes
Empirical Bayes
estimation
Markov chain
maximum likelihood
Regression
transition probability matrix
TOPOLOGICAL RINGGROUPOIDS AND LIFTINGS
2
2
We prove that the set of homotopy classes of the paths in a topological ring is a topological ringobject (called topological ringgroupoid). Let p : X → X be a covering map and let X be a topological ring.We define a category UTRCov(X) of coverings of X in which both X and X have universal coverings, and acategory UTRGdCov( π1X ) of coverings of topological ringgroupoid π1X , in which X and R0 = X haveuniversal coverings, and then prove the equivalence of these categories. We also prove that the topologicalring structure of a topological ringgroupoid lifts to a universal topological covering groupoid.
1

355
362


A.
FATIH OZCAN
Inonu University, Science and Art Faculty
Department of Mathematics, Malatya, Turkey
Inonu University, Science and Art Faculty
Departme
Turkey


I.
ICEN
Inonu University, Science and Art Faculty
Department of Mathematics, Malatya, Turkey
Inonu University, Science and Art Faculty
Departme
Turkey


M.
HABIL GURSOY
Inonu University, Science and Art Faculty
Department of Mathematics, Malatya, Turkey
Inonu University, Science and Art Faculty
Departme
Turkey
Fundamental groupoids
topological coverings
topological ringgroupoids
SOME MAXIMAL INEQUALITIES FOR RANDOM VARIABLES AND APPLICATIONS
2
2
In this paper, we extend some famous maximal inequalities and obtain strong laws of largenumbers for arbitrary random variables by use of these inequalities and martingale techniques.
1

363
367


M.
AMINI
Department of Statistics, Ferdowsi University, Mashhad, I. R. of Iran
Department of Statistics, Ferdowsi University,
Iran


A.
BOZORGNIA
Department of Statistics, Ferdowsi University, Mashhad, I. R. of Iran
Department of Statistics, Ferdowsi University,
Iran
Kolmogorove's inequality
HajekRenyi inequality
Strong law of large numbers
Martingale
EXISTENCE OF THREE SOLUTIONS FOR THE DIRICHLET PROBLEM INVOLVING THE PLAPLACIAN AND MINIMAX INEQUALITY FOR RELEVANT FUNCTIONALS
2
2
In this paper, we establish some results on the existence of at least three weak solutions for aDirichlet problem involving pLaplacian using a variational approach.
1

369
374


G. A.
AFROUZI
Department of Mathematics, Faculty of Basic Sciences,
Mazandaran University, Babolsar, I. R. of Iran
Department of Mathematics, Faculty of Basic
Iran


S.
HEIDARKHANI
Department of Mathematics, Faculty of Basic Sciences,
Mazandaran University, Babolsar, I. R. of Iran
Department of Mathematics, Faculty of Basic
Iran
Dirichlet problem
critical point
three solutions
multiplicity results
minimax inequality