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Full-Text Articles in Physical Sciences and Mathematics

A Fresh Look At Thermal Field Emission From Tungsten Tip, Ahmed Abdurrahman Ahmed Al-Tabbakh Jan 2012

A Fresh Look At Thermal Field Emission From Tungsten Tip, Ahmed Abdurrahman Ahmed Al-Tabbakh

Turkish Journal of Physics

Electron emission from clean tungsten tips has been investigated at different temperatures and applied electric field. Emission mechanism is analyzed on the basis of the Fowler-Nordheim (FN) model and a parameter extraction model based on elimination of field enhancement factor. The suggested extraction model of the physical and geometrical parameters is found fairly adequate to resolving the apparently confusing behavior of these parameters and shedding light on the emission mechanism. The observed linear FN plots at low temperatures confirm the predominating effect of the applied field on the electron emission. At elevated temperatures, emission is found to fall in the …


The Element Contents In Chickpeas Grown Under Organic And Conventional Farming Regimes Using Wdxrf Analysis For Human Nutrition And Health, Uğur Akbaba, Yusuf Şahi̇n, Hasan Türkez Jan 2012

The Element Contents In Chickpeas Grown Under Organic And Conventional Farming Regimes Using Wdxrf Analysis For Human Nutrition And Health, Uğur Akbaba, Yusuf Şahi̇n, Hasan Türkez

Turkish Journal of Physics

A comparative study on elemental composition of various chickpea (Cicer arientînum L) samples was conducted by using wavelength dispersive X-ray fluorescence (WDXRF). 22 elements, Al, Ca, Cu, Fe, Mn, Ni, P, S, Sr, Zn, Br, Cl, K, Mg, Na, Ba, Rb, Si, Au, Cr, La and Sn, were determined in chickpea samples (n = 10) grown under organic and conventional farming regimes. Results obtained from each group were analyzed statistically using the SPSS statistic program. It was observed that the concentration and peak intensity values of Ca, Fe, P, Cl, K, Mg and Na elements were higher in the chickpea …


Estimation Of Radiological Risk Due To Concentration Of ^{238}U, ^{226}Ra, ^{232}Th And ^{40}K In Soils Of Different Geological Origins In Northern India, Rohit Mehra, Manmohan Singh Jan 2012

Estimation Of Radiological Risk Due To Concentration Of ^{238}U, ^{226}Ra, ^{232}Th And ^{40}K In Soils Of Different Geological Origins In Northern India, Rohit Mehra, Manmohan Singh

Turkish Journal of Physics

Radioactivity of nuclides ^{238}U, ^{226}Ra, ^{232}Th and ^{40}K was measured in soil by \gamma-ray spectrometry using a HPGe detector. A criterion was set in order to analyse soil samples from plain, semi-hilly and hilly areas in northern India. More than three \gamma-ray energy peaks were used for the determination of ^{226}Ra and ^{232}Th activity concentrations to obtain more accurate results. Some of these peaks have interfering energies, which was caused by the limited resolution of the detector, but they were resolved theoretically and used in the analysis because of their significance in reducing the random error to its minimum level. …


Influence Of Aam-Lod On The Lower Stratospheric Ozone Transport Over Lagos--Nigeria, Bernadette C. Isikwue, Francisca N. Okeke Jan 2012

Influence Of Aam-Lod On The Lower Stratospheric Ozone Transport Over Lagos--Nigeria, Bernadette C. Isikwue, Francisca N. Okeke

Turkish Journal of Physics

An investigation of the relationship between Atmospheric Angular Momentum (AAM) via Length of Day (LOD) and the variability of Ozone (O_3) in the tropics with much emphasis on Lagos-Nigeria, using the global zonal wind data spanning 1997 to 2005 has been carried out. The mean O_3 concentration, O_3 temporal oscillation period, its average temporal amplitude of oscillation and its average maximum daily variation have been determined to be 273.6 \pm 0.04 DU, 5 days, 7.81 Du and 48.8 Du, respectively. The average monthly maximum and minimum O_3 concentrations were found to be 287.8 Du occurring between July and August; and …


E_{Cm}=500 Gev Clic \Gamma\Gamma Collider Based On Its Drive Beam Fel, Hüsnü Aksakal, Zafer Nergi̇z, Frank Zimmermann, Daniel Schulte, Alexander Mikhailichenko, Abbas Kenan Çi̇ftçi̇ Jan 2012

E_{Cm}=500 Gev Clic \Gamma\Gamma Collider Based On Its Drive Beam Fel, Hüsnü Aksakal, Zafer Nergi̇z, Frank Zimmermann, Daniel Schulte, Alexander Mikhailichenko, Abbas Kenan Çi̇ftçi̇

Turkish Journal of Physics

CLIC is a linear e^+e^- collider project which employs a drive beam to accelerate the main beam. Various portions of the drive beam provide RF power for corresponding units of the main linac through energy extracting RF structures. CLIC can operate over a wide range of center-of-mass energies, from 150 GeV to 3 TeV. In addition to e^+e^- collider, \gamma\gamma and \gamma e colliders based on CLIC can be realized. In order to generate high energy photons, a Free electron laser (FEL) produced from the CLIC drive beam linac can be used. In this paper we show that the CLIC …


Heat Capacity Of Trapped Bosons In A Combined Harmonic-Lattice Potential, Azza M. Elbadry Jan 2012

Heat Capacity Of Trapped Bosons In A Combined Harmonic-Lattice Potential, Azza M. Elbadry

Turkish Journal of Physics

In this paper, the heat capacity per particle C(T)/Nk_B of the trapped bosons in a combined harmonic-lattice potential is calculated within the semicalssical approximation. The main effects which can alter the ideal gas are included simultaneously in the present approach. The calculated results show that the heat capacity has a significant dependence on the lattice depth and temperature. Classical results are recovered at sufficiently high temperature, and that it reproduces the Dulong-Petit law type. Moreover, the behavior of the heat capacity in a deep lattice can be used as an indicator for the quantum phase transition superfluid-Mott insulator. It decreases …


Scale Dimension As The Fifth Dimension Of Spacetime, Sergey Fedosin Jan 2012

Scale Dimension As The Fifth Dimension Of Spacetime, Sergey Fedosin

Turkish Journal of Physics

The scale dimension discovered in the theory of infinite nesting of matter is studied from the perspective of physical implementation of well-studied four-and n-dimensional geometric objects. Adding the scale dimension to Minkowski four-dimensional space means the necessity to use the five-dimensional spacetime.


Space-Time Scaling Invariant Traveling Wave Solutions Of Some Nonlinear Fractional Equations, Tianlan He, Hui Fang Jan 2012

Space-Time Scaling Invariant Traveling Wave Solutions Of Some Nonlinear Fractional Equations, Tianlan He, Hui Fang

Turkish Journal of Physics

In this paper, a homogeneous principle is proposed to seek the space-time scaling invariant traveling wave solutions expressed by power functions for some fractional differential equations. Applying this principle to generalized fractional Benjamin-Ono equations and generalized fractional ZakharovKuznetsov equations, the traveling wave solutions expressed by power functions have been obtained under some parameter conditions.


Near-Resonant Diurnal Reactions: A Physical Model Applicable To Origin Of Life Processes, Eddwin Budding, Cüneyt Aki, Osman Demi̇rcan, Bülent Gündüz, Güngör Gündüz, Mehmet Emi̇n Özel Jan 2012

Near-Resonant Diurnal Reactions: A Physical Model Applicable To Origin Of Life Processes, Eddwin Budding, Cüneyt Aki, Osman Demi̇rcan, Bülent Gündüz, Güngör Gündüz, Mehmet Emi̇n Özel

Turkish Journal of Physics

We adopt that the large residual chemical potential energy (CPE) among reagents of the biosphere constitutes the key physical problem posed by life. We associate the formation of this CPE with the near-resonant behaviour of a two-stage `A-B' molecular process that behaves as a self-sustaining parametric oscillator. Under suitable conditions, such an oscillator generates CPE when forced by a periodic (daily) insolation. The net growth factor required to explain the current mean excess of biospheric CPE is \sim 5 x 10^{-12} d^{-1}. This aligns with the mean exponential coefficient of secular oxygen generation in the terrestrial atmosphere. It is also …


Neotectonic Evolution Of An Actively Growing Superimposed Basin In Western Anatolia: The Inner Bay Of İzmir, Turkey, Bora Uzel, Hasan Sözbi̇li̇r, Çağlar Özkaymak Jan 2012

Neotectonic Evolution Of An Actively Growing Superimposed Basin In Western Anatolia: The Inner Bay Of İzmir, Turkey, Bora Uzel, Hasan Sözbi̇li̇r, Çağlar Özkaymak

Turkish Journal of Earth Sciences

İzmir Bay is an actively growing shallow marine basin controlled by active faults trending NE, NW, N-S and E-W, in the West Anatolian Extensional Province. The bay of İzmir is a lazy L-shaped superimposed basin which is topographically divided into an E-W-trending inner bay and a NW-trending outer bay. The Inner Bay of İzmir is an asymmetric graben structure approximately 5-7 km wide and 25 km long containing (i) upper Cretaceous-Palaeocene basement, (ii) an older succession of lower to upper Miocene basin fill, overlain with angular unconformity by (iii) a younger Plio-Quaternary basin fill. The older succession contain a 0.5- …


Stratigraphy And Some Structural Features Of The İstanbul Paleozoic, Necdet Özgül Jan 2012

Stratigraphy And Some Structural Features Of The İstanbul Paleozoic, Necdet Özgül

Turkish Journal of Earth Sciences

Palaeozoic rocks crop out across large areas in the İstanbul region. The Palaeozoic sequence starts with the Lower Ordovician fluviatile and lacustrine deposits (Kocatöngel and Kurtköy formations). The area was transgressed by the sea during the Late Ordovician-Early Silurian, represented by the feldspathic quartzwacke and quartz-arenites of the Kınalıada and Aydos formations. The basin became progressively deeper and more stable during the Silurian and Devonian. In this period, micaceous siltstones and sandstones of the Yayalar Formation (Upper Ordovician (?)-Lower Silurian), shelf-type carbonates of the Pelitli Formation (Lower Silurian-Lower Devonian), fossil-rich micaceous shales with rare limestone intercalations representing a low-energy open …


Dynamic Stability Enhancement Of A Multimachine Electric Power System Using Statcom, Hasan Fayazi Boroujeni, Reza Hemmati, Sayed Mojtaba Shirvani Boroujeni Jan 2012

Dynamic Stability Enhancement Of A Multimachine Electric Power System Using Statcom, Hasan Fayazi Boroujeni, Reza Hemmati, Sayed Mojtaba Shirvani Boroujeni

Turkish Journal of Electrical Engineering and Computer Sciences

With the expansion of electric power systems, the size and complexity of the network is increased. One of the most important drawbacks of network expansion is the reduction in the damping torque of the whole system. The lack of damping torque can lead to fluctuations and instability in the power system. With regard to this problem, power system stabilizers (PSSs) have been widely utilized to improve power system stability. However, due to some drawbacks of the conventional PSSs, the need for finding a better substitution still remains. Therefore, in this paper, the application of a static synchronous compensator (STATCOM) to …


On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids, Karim Ahmadidelir, Hossein Doostie Jan 2012

On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids, Karim Ahmadidelir, Hossein Doostie

Turkish Journal of Mathematics

This paper investigates the automorphism group of monogenic [4] semigroups (or monoids) to find its relationship with the automorphism group of cyclic groups. Then, by considering a presentation related to the direct product of monogenic semigroups, verify the relationship between the automorphism group of These and the automorphism group of the group presented by the same presentation. This study gives us some [4]explicit formulas for computing the order of automorphism groups of these algebraic structures.


Best Constants In Second-Order Sobolev Inequalities On Compact Riemannian Manifolds In The Presence Of Symmetries, Mohammed Ali Jan 2012

Best Constants In Second-Order Sobolev Inequalities On Compact Riemannian Manifolds In The Presence Of Symmetries, Mohammed Ali

Turkish Journal of Mathematics

Let (M,g) be a smooth compact 3\leq n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.


On \Alpha-Skew Mccoy Modules, Jian Cui, Jianlong Chen Jan 2012

On \Alpha-Skew Mccoy Modules, Jian Cui, Jianlong Chen

Turkish Journal of Mathematics

Let \alpha be a ring endomorphism. Extending the notions of McCoy modules and \alpha-skew McCoy rings, we introduce the notion of \alpha-skew McCoy modules, which can also be regarded as a generalization of \alpha-skew Armendariz modules. A number of illustrative examples are given. Various properties of these modules are developed, and equivalent conditions for \alpha-skew McCoy modules are established. Furthermore, we study the relationship between a module and its polynomial module.


On Cise-Normal Subgroups Of Finite Groups, Yong Xu, Tao Zhao, Xianhua Li Jan 2012

On Cise-Normal Subgroups Of Finite Groups, Yong Xu, Tao Zhao, Xianhua Li

Turkish Journal of Mathematics

A generalized normality CISE of subgroups of a finite group is introduced. Let F be a saturated formation containing the class of all supersolvable groups. We give a characterization of F by using CISE-normality of subgroups.


Note On Hilbert-Type Inequalities, Predrag Vukovic Jan 2012

Note On Hilbert-Type Inequalities, Predrag Vukovic

Turkish Journal of Mathematics

The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a general homogeneous kernel, thus generalizing a result obtained in [Namita Das and Srinibas Sahoo, A generalization of multiple Hardy-Hilbert's integral inequality, Journal of Mathematical Inequalities, 3(1), (2009), 139--154].


Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen Jan 2012

Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen

Turkish Journal of Mathematics

Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference \Delta^nf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.


Application Of Asymmetrical Periodic Signals As Test Vectors For Analog Fault Detection: A Novel Perspective Of Classical Concepts, Badar Ud Din Ahmed, Wang Youren, Najam-Ud-Din Ahmed Jan 2012

Application Of Asymmetrical Periodic Signals As Test Vectors For Analog Fault Detection: A Novel Perspective Of Classical Concepts, Badar Ud Din Ahmed, Wang Youren, Najam-Ud-Din Ahmed

Turkish Journal of Electrical Engineering and Computer Sciences

Analog fault diagnosis is a field of paramount importance, and test signal generation is an important prerequisite for analog fault detection. Several stimuli have been used as input test vectors. This study presents a novel approach for the adoption of classical methods and signals for fault detection. This involves the use of asymmetrical periodic signals and comparison of their effectivity in maximizing output response between faulty and conforming circuits. The technique helps to determine a minimal set of test signals for a circuit. It also enables the test designer to identify the parts of the frequency spectra of various signal …


Effects Of Routing Algorithms On Novel Throughput Improvement Of Mobile Ad Hoc Networks, Barbaros Preveze, Aysel Şafak Jan 2012

Effects Of Routing Algorithms On Novel Throughput Improvement Of Mobile Ad Hoc Networks, Barbaros Preveze, Aysel Şafak

Turkish Journal of Electrical Engineering and Computer Sciences

A cognitive method called most congested access first (MCAF), minimizing the packet loss ratio and improving the throughput of a multihop mobile WiMAX network, is proposed. MCAF combines both the time division multiple access and the orthogonal frequency division multiple access methods. MCAF additionally uses spectral aid and buffer management methods, which are proposed in this paper, to manage both spectrum access and packets in the buffers. By using these novel methods, real-time video and voice packet transmission is achieved, data packet loss rate is minimized, and the system throughput per node is improved. Effects of fastest path and ant …


Considering Transmission Loss For An Economic Dispatch Problem Without Valve-Point Loading Using An Ep-Epso Algorithm, Sevugarathinam Muthu Vijaya Pandian, Keppanagowder Thanushkodi Jan 2012

Considering Transmission Loss For An Economic Dispatch Problem Without Valve-Point Loading Using An Ep-Epso Algorithm, Sevugarathinam Muthu Vijaya Pandian, Keppanagowder Thanushkodi

Turkish Journal of Electrical Engineering and Computer Sciences

Economic dispatch (ED) is one of the most important optimization problems in a power system. The objective of ED is sharing the power demand among the online generators while keeping the minimum cost of generation as a constraint. The aim of this paper is to operate an electric power system as economically as possible within its security limits. This paper proposes the following 2 new particle swarm optimization (PSO) algorithms to solve a nonconvex economic dispatch problem: an efficient PSO is termed as efficient particle swarm optimization (EPSO), and a hybrid of evolutionary programming (EP) and EPSO is termed as …


An Active Composite Pull-Apart Basin Within The Central Part Of The North Anatolian Fault System: The Merzifon-Suluova Basin, Turkey, Fuat Bora Rojay, Ali̇ Koçyi̇ği̇t Jan 2012

An Active Composite Pull-Apart Basin Within The Central Part Of The North Anatolian Fault System: The Merzifon-Suluova Basin, Turkey, Fuat Bora Rojay, Ali̇ Koçyi̇ği̇t

Turkish Journal of Earth Sciences

The North Anatolian Fault System (NAFS) that separates the Eurasian plate in the north from the Anatolian microplate in the south is an intracontinental transform plate boundary. Its course makes a northward convex arch-shaped pattern by flexure in its central part between Ladik in the east and Kargı in the west. A number of strike-slip basins of dissimilar type and age occur within the NAFS. One of the spatially large basins is the E-W-trending Merzifon-Suluova basin (MS basin), about 55 km long and 22 km wide, located on the southern inner side of the northerly-convex section of the NAFS. The …


Late Cretaceous-Eocene Geological Evolution Of The Pontides Based On New Stratigraphic And Palaeontologic Data Between The Black Sea Coast And Bursa (Nw Turkey), Zahi̇de Özcan, Aral Okay, Ercan Özcan, Aynur Hakyemez, Sevi̇nç Altiner Jan 2012

Late Cretaceous-Eocene Geological Evolution Of The Pontides Based On New Stratigraphic And Palaeontologic Data Between The Black Sea Coast And Bursa (Nw Turkey), Zahi̇de Özcan, Aral Okay, Ercan Özcan, Aynur Hakyemez, Sevi̇nç Altiner

Turkish Journal of Earth Sciences

The Late Cretaceous-Eocene geological evolution of northwest Turkey between the Black Sea and Bursa was studied through detailed biostratigraphic characterization of eleven stratigraphic sections. The Upper Cretaceous sequence in the region starts with a major marine transgression and lies unconformably on a basement of Palaeozoic and Triassic rocks in the north (İstanbul-type basement) and on metamorphic rocks and Jurassic sedimentary rocks in the south (Sakarya-type basement). Four megasequences have been differentiated in the Late Cretaceous-Eocene interval. The first one, of Turonian to Late Campanian age, is represented by volcanic and volcanoclastic rocks in the north along the Black Sea coast, …


On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang Jan 2012

On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang

Turkish Journal of Mathematics

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')^n and g + a(g')^n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.


Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu Jan 2012

Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu

Turkish Journal of Mathematics

We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B\rangle of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided.


Optimal In Vitro Realization Of Pulsatile Coronary Artery Flow Waveforms Using Closed-Loop Feedback Algorithms With Multiple Flow Control Devices, Serdar Yilmaz, Onur Toker, Nurullah Arslan, Herman Sedef Jan 2012

Optimal In Vitro Realization Of Pulsatile Coronary Artery Flow Waveforms Using Closed-Loop Feedback Algorithms With Multiple Flow Control Devices, Serdar Yilmaz, Onur Toker, Nurullah Arslan, Herman Sedef

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, we study optimal in vitro realization of pulsatile coronary artery flows using newly proposed closed-loop feedback algorithms with a clearly defined mathematical performance objective, and we compare several flow control device technologies in terms of their ability to generate pulsatile flow signals as accurately as possible. In the literature, there are several published results for in vitro pulsatile flow realization systems. However, most of the proposed systems operate in an open-loop setting and use a single flow control device, and their performance is assessed mostly by graphical means without a clearly defined mathematical performance objective. Furthermore, some …


Dating Subduction Events In East Anatolia, Turkey, Oberhaensli Roland, Bousquet Romain, Osman Candan, Aral Okay Jan 2012

Dating Subduction Events In East Anatolia, Turkey, Oberhaensli Roland, Bousquet Romain, Osman Candan, Aral Okay

Turkish Journal of Earth Sciences

Metamorphic studies in the cover sequences of the Bitlis complex allow the thermal evolution of the massif to be constrained using metamorphic index minerals. Regionally distributed metamorphic index minerals such as glaucophane, carpholite, relics of carpholite in chloritoid-bearing schists and pseudomorphs after aragonite in marbles record a LT-HP evolution. This demonstrates that the Bitlis complex was subducted and stacked to form a nappe complex during the closure of the Neo-Tethys. During late Cretaceous to Cenozoic evolution the Bitlis complex experienced peak metamorphism of 1.0-1.1 GPa at 350-400°C. During the retrograde evolution temperatures remained below 460°C. 39Ar/40Ar dating of white mica …


The Unaz Formation: A Key Unit In The Western Black Sea Region, N Turkey, Okan Tüysüz, İsmai̇l Ömer Yilmaz, Lilian Svabenicka, Sabri̇ Ki̇ri̇ci̇ Jan 2012

The Unaz Formation: A Key Unit In The Western Black Sea Region, N Turkey, Okan Tüysüz, İsmai̇l Ömer Yilmaz, Lilian Svabenicka, Sabri̇ Ki̇ri̇ci̇

Turkish Journal of Earth Sciences

The Pontide magmatic belt in the Western Pontides, which developed in response to the northward subduction of the northern branches of the Tethys Ocean, consists of two different volcanic successions separated by an Upper Santonian pelagic limestone unit, the Unaz Formation. The first period of volcanism and associated sedimentation started during the Middle Turonian and lasted until the Early Santonian under the control of an extensional tectonic regime, which created horst-graben topography along the southern Black Sea region. The lower volcanic succession, the Dereköy Formation, was deposited mainly within these grabens. This extensional period probably represents the rifting of magmatic …


Weight And Nonlinearity Of Boolean Functions, Lavinia Corina Ciungu Jan 2012

Weight And Nonlinearity Of Boolean Functions, Lavinia Corina Ciungu

Turkish Journal of Mathematics

In this paper we analyze the weight and the nonlinearity of various types of Boolean functions. We give some general results related to rotation symmetric Boolean functions, and in particular, we prove partially a conjecture stated by Cusick and Stanica in [3].


Pointwise Slant Submanifolds In Almost Hermitian Manifolds, Bang-Yen Chen, Oscar J. Garay Jan 2012

Pointwise Slant Submanifolds In Almost Hermitian Manifolds, Bang-Yen Chen, Oscar J. Garay

Turkish Journal of Mathematics

An interesting class of submanifolds of almost Hermitian manifolds (\tilde M,\tilde g,J) is the class of slant submanifolds. Slant submanifolds were introduced by the first author in [6] as submanifolds M of (\tilde M,\tilde g,J) such that, for any nonzero vector X \in T_pM, p \in M, the angle \theta(X) between JX and the tangent space T_pM is independent of the choice of p\in M and X \in T_pM. The first results on slant submanifolds were summarized in the book [7]. Since then slant submanifolds have been studied by many geometers. Many nice results on slant submanifolds have been obtained …