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Articles 1 - 30 of 412
Full-Text Articles in Physical Sciences and Mathematics
Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao
Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao
Turkish Journal of Mathematics
Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.
Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir
Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir
Turkish Journal of Mathematics
We investigate here the connected graphs with the property that any pair of vertices are missed by some longest paths (or cycles), embeddable in n-dimensional lattices L^n where L denotes the set of integers.
On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇
On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇
Turkish Journal of Mathematics
The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that a^{m+r}=a^m, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T_n, which we call transformations of index 1.
Horizontally Submersions Of Contact Cr-Submanifolds, Fortune Massamba, Tshikunguila Tshikuna-Matamba
Horizontally Submersions Of Contact Cr-Submanifolds, Fortune Massamba, Tshikunguila Tshikuna-Matamba
Turkish Journal of Mathematics
In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf …
Coloring Hypercomplete And Hyperpath Graphs, Yusuf Ci̇van, Demet Taylan
Coloring Hypercomplete And Hyperpath Graphs, Yusuf Ci̇van, Demet Taylan
Turkish Journal of Mathematics
Given a graph G with an induced subgraph H and a family F of graphs, we introduce a (hyper)graph H_H(G;F)=(V_H, E_H), the hyper-H (hyper)graph of G with respect to F, whose vertices are induced copies of H in G, and \{H_1,H_2,\ldots,H_r\} \in E_H if and only if the induced subgraph of G by the set \cup_{i=1}^r H_i is isomorphic to a graph F in the family F, and the integer r is the least integer for F with this property. When H is a k-complete or a k-path of G, we abbreviate H_{K_k}(G;F) and H_{P_k}(G;F) to H_k(G;F) and HP_k(G;F), respectively. …
Euler-Seidel Matrices Over F_P, Nesri̇n Tutaş
Euler-Seidel Matrices Over F_P, Nesri̇n Tutaş
Turkish Journal of Mathematics
A Euler--Seidel matrix is determined by an infinite sequence whose elements are given by recursion. The recurrence relations are investigated for numbers and polynomials such as hyperharmonics, Lucas numbers, and Euler and Genocchi polynomials. Linear recurring sequences in finite fields are employed, for instance, in coding theory and in several branches of electrical engineering. In this work, we define the period of a Euler--Seidel matrix over a field F_p with p elements, where p is a prime number. We give some results for the matrix whose initial sequence is \{s_r(n)\}_{n=0}^{\infty}, where s_r(n)=\sum_{k=0}^n {\binom{n}{k}}^r, n \geq 0, and r is a …
On Betti Series Of The Universal Modules Of Second Order Derivations Of \Frac{K[X_1,X_2,...,X_S]}{(F)}, Ali̇ Erdoğan, Hali̇se Meli̇s Teki̇n Akçi̇n
On Betti Series Of The Universal Modules Of Second Order Derivations Of \Frac{K[X_1,X_2,...,X_S]}{(F)}, Ali̇ Erdoğan, Hali̇se Meli̇s Teki̇n Akçi̇n
Turkish Journal of Mathematics
Let R be a coordinate ring of an affine irreducible curve represented by \frac{k[x_1,x_2,...,x_s]}{(f)} and m be a maximal ideal of R. In this article, the Betti series of \Omega_2(R_m) is studied. We proved that the Betti series of \Omega_2(R_m), where \Omega_2(R_m) denotes the universal module of second order derivations of R_m, is a rational function under some conditions.
Some Results On T-Noncosingular Modules, Rachid Tribak
Some Results On T-Noncosingular Modules, Rachid Tribak
Turkish Journal of Mathematics
The notion of T-noncosingularity of a module has been introduced and studied recently. In this article, a number of new results of this property are provided. It is shown that over a commutative semilocal ring R such that Jac(R) is a nil ideal, every T-noncosingular module is semisimple. We prove that for a perfect ring R, the class of T-noncosingular modules is closed under direct sums if and only if R is a primary decomposable ring. Finitely generated T-noncosingular modules over commutative rings are shown to be precisely those having zero Jacobson radical. We also show that for a simple …
A Class Of Uniquely (Strongly) Clean Rings, Orhan Gürgün, Ayşe Çi̇ğdem Özcan
A Class Of Uniquely (Strongly) Clean Rings, Orhan Gürgün, Ayşe Çi̇ğdem Özcan
Turkish Journal of Mathematics
In this paper we call a ring R \delta_r-clean if every element is the sum of an idempotent and an element in \delta(R_R) where \delta(R_R) is the intersection of all essential maximal right ideals of R. If this representation is unique (and the elements commute) for every element we call the ring uniquely (strongly) \delta_r-clean. Various basic characterizations and properties of these rings are proved, and many extensions are investigated and many examples are given. In particular, we see that the class of \delta_r-clean rings lies between the class of uniquely clean rings and the class of exchange rings, and …
On The Structure Of Some Modules Over Generalized Soluble Groups, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin, Vasiliy Anatolievich Chupordya
On The Structure Of Some Modules Over Generalized Soluble Groups, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin, Vasiliy Anatolievich Chupordya
Turkish Journal of Mathematics
Let R be a ring and G a group. An R-module A is said to be Artinian-by-(finite rank) if Tor_R(A) is Artinian and A/ Tor_R(A) has finite R-rank. We study a module A over a group ring RG such that A/C_A(H) is Artinian-by-(finite rank) (as an R-module) for every proper subgroup H.
On 2 Nonsplit Extension Groups Associated With Hs And Hs:2, Jamshid Moori, Thekiso Seretlo
On 2 Nonsplit Extension Groups Associated With Hs And Hs:2, Jamshid Moori, Thekiso Seretlo
Turkish Journal of Mathematics
The group HS:2 is the full automorphism group of the Higman--Sims group HS. The groups 2^{4.}S_6 and 2^{5.}S_6 are maximal subgroups of HS and HS:2, respectively. The group 2^{4.}S_6 is of order 11520 and 2^{5.}S_6 is of order 23040 and each of them is of index 3 850 in HS and HS:2, respectively. The aim of this paper is to first construct \overline{G} = 2^{5.}S_6 as a group of the form 2^{4.}S_6.2 (that is, \overline{G} = G_1.2) and then compute the character tables of these 2 nonsplit extension groups by using the method of Fischer--Clifford theory. We will show that …
On Finsler Metrics With Vanishing S-Curvature, Akbar Tayebi, Hassan Sadeghi, Esmaeil Peyghan
On Finsler Metrics With Vanishing S-Curvature, Akbar Tayebi, Hassan Sadeghi, Esmaeil Peyghan
Turkish Journal of Mathematics
In this paper, we consider Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We study these metrics with vanishing S-curvature. We find some conditions under which such a Finsler metric is Berwaldian or locally Minkowskian.
Conformally Parallel Spin(7) Structures On Solvmanifolds, Selman Uğuz
Conformally Parallel Spin(7) Structures On Solvmanifolds, Selman Uğuz
Turkish Journal of Mathematics
In this paper we review the Spin(7) geometry in relation to solvmanifolds. Starting from a 7-dimensional nilpotent Lie group N endowed with an invariant G_2 structure, we present an example of a homogeneous conformally parallel Spin(7) metric on an associated solvmanifold. It is thought that this paper could lead to very interesting and exciting areas of research and new results in the direction of (locally conformally) parallel Spin(7) structures.
Geometry Of Almost Cliffordian Manifolds: Classes Of Subordinated Connections, Jaroslav Hrdina, Petr Vasik
Geometry Of Almost Cliffordian Manifolds: Classes Of Subordinated Connections, Jaroslav Hrdina, Petr Vasik
Turkish Journal of Mathematics
An almost Clifford and an almost Cliffordian manifold is a G--structure based on the definition of Clifford algebras. An almost Clifford manifold based on O:= Cl (s,t) is given by a reduction of the structure group GL(km, R) to GL(m, O), where k=2^{s+t} and m \in N. An almost Cliffordian manifold is given by a reduction of the structure group to GL(m, O) GL(1, O). We prove that an almost Clifford manifold based on O is such that there exists a unique subordinated connection, while the case of an almost Cliffordian manifold based on O is more rich. A class …
Ree Geochemical Characteristics Of Titanium-Rich Bauxites: The Permian Kanigorgeh Horizon, Nw Iran, Ali Abedini, Ali Asghar Calagari
Ree Geochemical Characteristics Of Titanium-Rich Bauxites: The Permian Kanigorgeh Horizon, Nw Iran, Ali Abedini, Ali Asghar Calagari
Turkish Journal of Earth Sciences
The Permian Kanigorgeh bauxite horizon is one of the typical titanium-rich bauxite deposits in the northeast of Bukan, West Azerbaijan Province, NW Iran. It is a part of the Irano-Himalayan karst bauxite belt and was developed as discontinuous stratified layers and lenses in Upper Permian carbonates. Mineralogically, diaspore and kaolinite are 2 major mineral phases accompanied by boehmite, smectite, illite, rutile, anatase, hematite, goethite, chlorite, quartz, and plagioclase as minor phases. Geochemical considerations for a selected profile indicate that the concentration values of rare earth elements (REEs) in the bauxite ores range from 8.9 to 200.4 ppm. Eu and Ce …
Coherence Analysis On Thermal Effect For Power Cables Under Different Environmental Conditions, Sezai̇ Taşkin, Şahi̇n Serhat Şeker, Özcan Kalenderli̇, Murat Karahan
Coherence Analysis On Thermal Effect For Power Cables Under Different Environmental Conditions, Sezai̇ Taşkin, Şahi̇n Serhat Şeker, Özcan Kalenderli̇, Murat Karahan
Turkish Journal of Electrical Engineering and Computer Sciences
There are 2 important aspects of this research; these are the experimental study and the data analysis, which are based on coherence analysis. In this study, a low-voltage power cable is tested under 2 different environments, air and water, and the variations in temperature are measured for the conductor, the sheath parts of the cable, and the environment. The recorded test data are analyzed using such as coherence analysis. This in turn provides the means to determine the relationship among the sheath, conductor, and the environment. In conclusion, high correlated peaks in the frequency domain are used to determine the …
Btsql: Nested Bitemporal Relational Database Query Language, Canan Atay, Abdullah Uz Tansel
Btsql: Nested Bitemporal Relational Database Query Language, Canan Atay, Abdullah Uz Tansel
Turkish Journal of Electrical Engineering and Computer Sciences
A nested bitemporal relational data model and its query language are implemented. The bitemporal atom (BTA) is the fundamental construct to represent temporal data and it contains 5 components: a value, the lower and upper bounds of valid time, and the lower and upper bounds of the recoding time. We consider 2 types of data structures for storing BTAs: 1) string representation and 2) abstract data-type representation. We also develop a preprocessor for translating a bitemporal structured query language (BtSQL) statement into standard SQL statements. The BtSQL includes the select, insert, delete, and update statements of the SQL, extended for …
Expert Doctor Verdis: Integrated Medical Expert System, Aytürk Keleş
Expert Doctor Verdis: Integrated Medical Expert System, Aytürk Keleş
Turkish Journal of Electrical Engineering and Computer Sciences
Innovative medical technologies are developing day by day, as there is an important need for integrated medical expert systems (ESs) that will help to effectively manage and control diagnosis and treatment processes. These systems, with new approaches, have improved the experiences and capabilities of physicians to make the diagnosis of diseases. In this work, an integrated medical ES called Expert Doctor Verdis (Ex-Dr Verdis) is developed, which combines an advanced medical information system containing various medical services supported by information technologies, with ES capabilities in a single system. This system is also one kind of decision support system. Implementation of …
Design And Realization Of A Welding Oscillator, Muci̇z Özcan
Design And Realization Of A Welding Oscillator, Muci̇z Özcan
Turkish Journal of Electrical Engineering and Computer Sciences
Welding is one of the most popular methods to combine metal pieces in manufacturing processes. Arc welding, among all welding techniques, is the most commonly used in manufacturing due to its cost and flexibility. During the manufacturing process, arc welding is either performed by an operator or by automatic tools such as welding oscillators. Using automatic tools has advantages over manual use, as the process will be faster, cheaper, and have less welding flaws. In this paper, a homemade welding oscillator and the method to manufacture it are presented. The presented welding oscillator can be manufactured for a very low …
The Results Of The First Photonuclear Reaction Performed In Turkey: The Zinc Example, İsmai̇l Boztosun, Haris Dapo, Süleyman Fati̇h Özmen, Yi̇ği̇t Çeçen, Mesut Karakoç, Abdullah Çoban, Alp Cesur, Tanfer Caner, Edi̇p Bayram, Gi̇zem Büşra Keller, Beyza Küçük, Abdullah Güvendi̇, Melek Derman, Deni̇z Kaya
The Results Of The First Photonuclear Reaction Performed In Turkey: The Zinc Example, İsmai̇l Boztosun, Haris Dapo, Süleyman Fati̇h Özmen, Yi̇ği̇t Çeçen, Mesut Karakoç, Abdullah Çoban, Alp Cesur, Tanfer Caner, Edi̇p Bayram, Gi̇zem Büşra Keller, Beyza Küçük, Abdullah Güvendi̇, Melek Derman, Deni̇z Kaya
Turkish Journal of Physics
We have investigated the decays of several zinc isotopes produced by photonuclear reactions, which were induced by bremsstrahlung photon beams from a clinical e-linac. A photon beam of 18 MeV endpoint energy was directed at a target consisting of primarily zinc isotopes in their natural abundances. Subsequently, the induced decays of unstable zinc isotopes were measured with an HPGe detector twice, once shortly after irradiation and once on the following day. Decays of Zn-63, Zn-65, Zn-69m, and Cu-67 were measured and fitted. In addition, the gamma energy levels of the daughters of these decays were measured with good accuracy. All …
Theoretical Investigations Of Pt_3x (X = Al, Sc, Hf, Zr) Ground State, Adewumi Isaac Popoola, Lesley Heath Chown, Lesley Alison Cornish
Theoretical Investigations Of Pt_3x (X = Al, Sc, Hf, Zr) Ground State, Adewumi Isaac Popoola, Lesley Heath Chown, Lesley Alison Cornish
Turkish Journal of Physics
The electronic structure of Pt_3X compounds showed that Pt_3Hf and Pt_3Zr were more stable for the D0_{24} structure, rather than L1_2. The compound Pt_3Al was predicted to be the hardest and most ductile, but not with the L1_2 structure at ground state. The density of states showed that Pt_3Hf, Pt_3Zr, and Pt_3Al can be stabilized to the L1_2 phase with suitable element addition. All calculations were done within the density functional theory framework.
Evidence That Photons Have Extension In Space, Randy Wayne
Evidence That Photons Have Extension In Space, Randy Wayne
Turkish Journal of Physics
Satyendra Nath Bose realized that there was a logical inconsistency in the derivation of Planck's radiation law since the derivation used to obtain the temperature-independent prefactor in the blackbody radiation law had been based in part on classical wave hypotheses, such as the number of degrees of freedom of the ether. Bose worked out a strictly quantum derivation by combining the quantum hypothesis with statistical mechanics to determine the number of states of each mode that would occupy a 6-dimensional phase space. Here I use the model of an extended photon to show that the temperature-independent prefactor of Planck's radiation …
Thermodynamic Properties Of A Rotating Bose-Einstein Condensation In A Deep Optical Lattice, Hend A. Abdel-Gany, Ali Y. Ellithi, Abdelhamid A. Galal, Ahmed Hassan
Thermodynamic Properties Of A Rotating Bose-Einstein Condensation In A Deep Optical Lattice, Hend A. Abdel-Gany, Ali Y. Ellithi, Abdelhamid A. Galal, Ahmed Hassan
Turkish Journal of Physics
In this paper, we suggest a conventional semiclassical approximation to calculate several thermodynamic quantities of a rotating Bose-Einstein condensation in a deep optical lattice. Expressions for the condensation fraction, critical temperature, and heat capacity are derived analytically. These expressions are obtained by considering the standard harmonic approximation of the deep optical lattice potential. The suggested approach is able to include the the finite size and the positive chemical potential effects simultaneously. The advantage of our suggested approach is in its simplicity, in comparison to the quantum-mechanical calculations (Bose-Hubbard model). Moreover, its generality allows the treatment of a finite temperature regime
Transmission Of A Broadband Light Through A Fiber Optic Loop: Effect Of Nonlinear Refractive Index, Erkin Zakhidov, Abdumutallib Kokhkharov, Farrukh Mirtagjiev, Sherzod Nematov, Ilkhom Todjiboev, Olga Trunilina
Transmission Of A Broadband Light Through A Fiber Optic Loop: Effect Of Nonlinear Refractive Index, Erkin Zakhidov, Abdumutallib Kokhkharov, Farrukh Mirtagjiev, Sherzod Nematov, Ilkhom Todjiboev, Olga Trunilina
Turkish Journal of Physics
The results of studies of broadband light transmission through a fiber loop and a double loop under the effect of nonlinear refractive index are presented in this paper. Fiber loop and double loop transmission/reflection vs. a coupler splitting ratio at various powers of the light with a spectral width of approximately 35 nm are studied and high efficient nonlinear light switching is demonstrated. It is shown that a double loop formed by consecutive connecting 2 fiber loops allows us to exclude the strong spectral dependence of light transmission/reflection and to distribute input light equally between them. Such all-fiber devices can …
A Model Of The Multijunction Ac Josephson Effect In A Superconductor, Mohammed Rafiqul Islam, Habibur Rahman
A Model Of The Multijunction Ac Josephson Effect In A Superconductor, Mohammed Rafiqul Islam, Habibur Rahman
Turkish Journal of Physics
We present a model of the multijunction ac Josephson effect in a superconductor. Josephson predicted that at a finite applied voltage (V_o) an alternating supercurrent of frequency \omega_J =2eV_o/\hslash flows between 2 superconductors separated by an insulating layer, called the ac Josephson effect. Adding 2 or more Josephson junctions (so-called multijunction) with an applied voltage, we have shown that the resultant current (which is equivalent to the vector sum of the currents in each junction) has the same frequency as the single Josephson junction. The amplitude of the resultant current for the multijunction is increased with the increasing number of …
Analytical Solution Of The Klein-Gordon Equation Under The Coulomb-Like Scalar Plus Vector Potential With The Laplace Transforms Approach, Ebrahim Momtazi, Ali Akbar Rajabi, Bentol Hoda Yazarloo, Hassan Hassanabadi
Analytical Solution Of The Klein-Gordon Equation Under The Coulomb-Like Scalar Plus Vector Potential With The Laplace Transforms Approach, Ebrahim Momtazi, Ali Akbar Rajabi, Bentol Hoda Yazarloo, Hassan Hassanabadi
Turkish Journal of Physics
In this paper, analytical solution of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials is obtained exactly. We considered the Laplace transform approach in our calculation. The exact bound state energy eigenvalues and the corresponding eigenfunctions are reported for various values of the quantum numbers n and l.
Aldimine Derivatives As Photosensitizers For Dye-Sensitized Solar Cells, Amal Y. Batniji, Rami Morjan, Monzir S. Abdel-Latif, Taher M. El-Agez, Sofyan A. Taya, Hatem S. El-Ghamri
Aldimine Derivatives As Photosensitizers For Dye-Sensitized Solar Cells, Amal Y. Batniji, Rami Morjan, Monzir S. Abdel-Latif, Taher M. El-Agez, Sofyan A. Taya, Hatem S. El-Ghamri
Turkish Journal of Physics
Five aldimine derivatives were prepared by condensation of the appropriate amine with salicylaldehyde (m1-m4) and 4-aminobenzoic acid with 2-thiophene carboxaldehyde (m5). A molar ratio of 1:1 was used and the mixture was refluxed in ethanol for 2 h to obtain the corresponding aldimine derivative. These derivatives were used as photosensitizers for dye-sensitized solar cells (DSSCs). The best performance was obtained for the DSSC sensitized with 2-(2-hydroxybenzylideneamino)benzoic acid, for which a short-circuit current of 2.86 mA/cm^2, an open-circuit voltage of 0.562 V, and an efficiency of 0.575% were obtained.
Xrd, Xps, And Optical Characterizations Of Al-Doped Zno Film Grown On Gaas Substrate, Ebru Şenadim Tüzemen, Hülya Şahi̇n, Kamuran Kara, Sezai̇ Elagöz, Ramazan Esen
Xrd, Xps, And Optical Characterizations Of Al-Doped Zno Film Grown On Gaas Substrate, Ebru Şenadim Tüzemen, Hülya Şahi̇n, Kamuran Kara, Sezai̇ Elagöz, Ramazan Esen
Turkish Journal of Physics
A ZnO:Al (10%) thin film was prepared on GaAs(100) substrate by using a pulsed filtered cathodic vacuum arc deposition (PFCVAD) system. The ZnO:Al thin film was thermally annealed for 1 h at 2 different temperatures in air. The film structure was investigated as a function of annealing temperature by X-ray diffraction (XRD). ZnO:Al film annealed at 500 °C by PFCVAD method resulted in an amorphous film. However, after annealing ZnO:Al film at 600 °C, it showed (100) and (002) peaks at around 32° and 34°, respectively. The chemical state of ZnO:Al (AZO) film on GaAs substrate was investigated by using …
Influence Of Composition On The Structure And Optoelectronic Properties Of Pb_Xin_{25-X}Se_{75} Thin Films, Hesham Azmi Elmeleegi, Zeinab El Sayed El Mandouh, Ahmed Abdel Moez
Influence Of Composition On The Structure And Optoelectronic Properties Of Pb_Xin_{25-X}Se_{75} Thin Films, Hesham Azmi Elmeleegi, Zeinab El Sayed El Mandouh, Ahmed Abdel Moez
Turkish Journal of Physics
Pb_xIn_{25-x}Se_{75} thin films with 2 compositions were prepared by thermal evaporation. The surface topography of these films was studied by transmission electron microscope. The optical reflectance and transmittance were studied in order to determine the optical parameters such as optical energy gap, refractive index, extinction coefficient, dielectric loss, and dielectric tangent loss for these films. A single oscillator theory equation was applied for these films in order to determine both dispersion energy and oscillating energy, and the ratio of free carrier concentration/effective mass (N/m*) was determined optically. It was found that change in the composition of these films affects strongly …
Representation Of Electromagnetic And Gravitoelectromagnetic Poynting Theorems In Higher Dimensions, Mustafa Emre Kansu, Murat Tanişli, Süleyman Demi̇r
Representation Of Electromagnetic And Gravitoelectromagnetic Poynting Theorems In Higher Dimensions, Mustafa Emre Kansu, Murat Tanişli, Süleyman Demi̇r
Turkish Journal of Physics
This study investigates whether the electromagnetic and gravitoelectromagnetic energy conservation equations are obtained together by using octonion algebra or not. Maxwell and Maxwell-like equations for linear gravity with magnetic monopole terms are used in the SI unit system. A new complex octonionic field term is suggested for the first time. The complex octonionic source equation is then obtained. Finally, Poynting theorems for both electromagnetism and gravitoelectromagnetism are defined for the first time by using higher dimensional algebra.