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Articles 1 - 29 of 29
Full-Text Articles in Physics
Amplitude Modulation Of Ion-Acoustic Waves In Magnetized Electron-Positron-Ion Plasma With Q-Nonextensive Electrons And Positrons, Basudev Ghosh, Sreyasi Banerjee
Amplitude Modulation Of Ion-Acoustic Waves In Magnetized Electron-Positron-Ion Plasma With Q-Nonextensive Electrons And Positrons, Basudev Ghosh, Sreyasi Banerjee
Turkish Journal of Physics
Using a standard reductive perturbation technique, a nonlinear Schrödinger equation has been derived that describes the nonlinear evolution of ion-acoustic waves in magnetized electron-positron-ion plasma with electrons and positrons following q-nonextensive distribution. It is shown that excitation of both bright and dark envelope solitary structures is possible in the model plasma under consideration. The conditions for the excitation and structure of these envelope solitary waves are shown to depend sensitively on the strength of the external magnetic field, obliqueness of wave propagation relative to the external magnetic field, and other plasma parameters such as the q-nonextensivity of plasma species, positron …
A Study On $^{7}$Li + $^{120}$Sn Quasi-Elastic Scattering, Murat Aygün, Zeynep Aygün
A Study On $^{7}$Li + $^{120}$Sn Quasi-Elastic Scattering, Murat Aygün, Zeynep Aygün
Turkish Journal of Physics
In the present study, we reexamine quasi-elastic scattering of $^{7}$Li by $^{120}$Sn at incident energies E$_{Lab}$ = 19.5, 20.5, and 25.0 MeV. The theoretical results are obtained by using both a phenomenological model and double-folding model (DFM) within the framework of an optical model. We also investigate the role of the surface potential, which is connected to direct reactions. The agreement between the phenomenological model and the DFM is shown in comparison to each other in connection with the experimental data. This comparison provides information about the similarities and the differences between the models used during the calculations.
A Characteristic Particle Length, Mark D. Roberts
A Characteristic Particle Length, Mark D. Roberts
Turkish Journal of Physics
It is argued that there are characteristic intervals associated with any particle that can be derived without reference to the speed of light $c$. Such intervals are inferred from zeros of wavefunctions, which are solutions to the Schrödinger equation. The characteristic length is $\ell=\beta^2\hbar^2/(8Gm^3)$, where $\beta=3.8\dots$; this length might lead to observational effects on objects the size of a virus.
Enhancing Silicon Solar Cell Efficiency With Double Layer Antireflection Coating, Mohamed Medhat, El-Sayed El-Zaiat, Samy Farag, Gamal Youssef, Reda Alkhadry
Enhancing Silicon Solar Cell Efficiency With Double Layer Antireflection Coating, Mohamed Medhat, El-Sayed El-Zaiat, Samy Farag, Gamal Youssef, Reda Alkhadry
Turkish Journal of Physics
Antireflection coating on silicon, a high refractive index substrate, was theoretically investigated. The effects of antireflection coating on electrical parameters such as the short circuit current, open circuit voltage, maximum current density, maximum voltage, maximum power, power density, and conversion efficiency of the solar cell were simulated. Various previous works in which solar cell efficiencies were investigated after applying double layer antireflection coating (DLARC) were reviewed. Ti$_{2}$O$_{3}$ and MgF$_{2}$ were then applied in a DLARC design, taking into consideration the refractive index dispersion of the two materials. The results were compared with other works in the solar spectral range (400-1200 …
Effects Of Variable Viscosity And Thermal Conductivity On Magnetohydrodynamic Free Convection Flow Of A Micropolar Fluid Past A Stretching Plate Through Porous Medium With Radiation, Heat Generation, And Joule Dissipation, Gopal Chandra Hazarika, Bandita Phukan
Effects Of Variable Viscosity And Thermal Conductivity On Magnetohydrodynamic Free Convection Flow Of A Micropolar Fluid Past A Stretching Plate Through Porous Medium With Radiation, Heat Generation, And Joule Dissipation, Gopal Chandra Hazarika, Bandita Phukan
Turkish Journal of Physics
The effects of temperature-dependent viscosity and thermal conductivity on free convection magnetohydrodynamic flow of an optically thin gray, viscous, and incompressible micropolar fluid and heat transfer past a stretching plate through porous medium in the presence of radiation, heat generation, and Joule dissipation were studied. The fluid viscosity and thermal conductivity were assumed to vary as inverse linear functions of temperature. Using similarity transformation, the governing partial differential equations of motion were reduced to ordinary ones, which were solved numerically for prescribed boundary conditions using the shooting method. Numerical results for the velocity, angular velocity, and temperature profiles are shown …
Effects Of Variable Viscosity And Thermal Conductivity On Magnetohydrodynamic Free Convection Dusty Fluid Along A Vertical Porous Plate With Heat Generation, Gopal Chandra Hazarika, Jadav Konch
Effects Of Variable Viscosity And Thermal Conductivity On Magnetohydrodynamic Free Convection Dusty Fluid Along A Vertical Porous Plate With Heat Generation, Gopal Chandra Hazarika, Jadav Konch
Turkish Journal of Physics
The present study investigated the effects of variable viscosity and thermal conductivity on a two-dimensional steady laminar magnetohydrodynamic (MHD) free convective boundary layer flow of a dusty fluid over a vertical porous flat plate with viscous dissipation, Joule heating, and heat generation/absorption. Governing partial differential equations of motion were reduced to a system of ordinary differential equations using similarity transformations. The resulting boundary value problem was then solved numerically using the shooting technique. Velocity, temperature, and species concentration profiles of fluid and solid particles were obtained for different flow governing parameters. The results are presented in graphs. We found that …
Radon Concentration Measurements At A University Campus In Turkey, Melekşah Altinsöz, Emel Alğin, Celal Aşici, Haci Soğukpinar
Radon Concentration Measurements At A University Campus In Turkey, Melekşah Altinsöz, Emel Alğin, Celal Aşici, Haci Soğukpinar
Turkish Journal of Physics
In this study we measured radon (222Rn) concentrations in offices at the Meşelik campus of Eskişehir Osmangazi University to estimate the effective dose of 222Rn and its progeny for office occupants. The measurements were performed four times in 2011 over a period of 3 months using solid state nuclear track detectors (LR-115). A total of 381 LR-115 detectors were installed in 110 different offices, choosing three offices on each floor in the same building. 222Rn concentrations obtained in the first, second, third, and fourth measurement periods were 163 (73) Bq m-3, 77 (43) Bq m-3, and 164 (70) Bq m-3 …
Pp-Waves In Modified Gravity, Ahmet Baykal
Pp-Waves In Modified Gravity, Ahmet Baykal
Turkish Journal of Physics
The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a self-contained and coherent manner by using a variant of the null coframe formulation of Newman and Penrose and the exterior algebra of differential forms on pseudo-Riemannian manifolds.
Supergravity Backgrounds And Symmetry Superalgebras, Ümi̇t Ertem
Supergravity Backgrounds And Symmetry Superalgebras, Ümi̇t Ertem
Turkish Journal of Physics
We consider the bosonic sectors of supergravity theories in ten and eleven dimensions corresponding to the low energy limits of string theories and M-theory. The solutions of supergravity field equations are known as supergravity backgrounds and the number of preserved supersymmetries in those backgrounds are determined by Killing spinors. We provide some examples of supergravity backgrounds that preserve different fractions of supersymmetry. An important invariant for the characterization of supergravity backgrounds is their Killing superalgebras, which are constructed out of Killing vectors and Killing spinors of the background. After constructing Killing superalgebras of some special supergravity backgrounds, we discuss the …
Neutron Stars: Compact Objects With Relativistic Gravity, Kazim Yavuz Ekşi̇
Neutron Stars: Compact Objects With Relativistic Gravity, Kazim Yavuz Ekşi̇
Turkish Journal of Physics
General properties of neutron stars are briefly reviewed with an emphasis on the indispensability of general relativity in our understanding of these fascinating objects. In Newtonian gravity the pressure within a star merely plays the role of opposing self-gravity. In general relativity all sources of energy and momentum contribute to the gravity. As a result, the pressure not only opposes gravity but also enhances it. The latter role of pressure becomes more pronounced with increasing compactness, $M/R$, where $M$ and $R$ are the mass and radius of the star, and sets a critical mass beyond which collapse is inevitable. This …
Exact Solutions To The Geodesic Equations Of Linear Dilaton Black Holes, Alan Hameed Hussein Hamo, Izzet Sakalli
Exact Solutions To The Geodesic Equations Of Linear Dilaton Black Holes, Alan Hameed Hussein Hamo, Izzet Sakalli
Turkish Journal of Physics
In this paper, we analyze the geodesics of the 4-dimensional linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-dilaton theory. LDBHs have nonasymptotically flat geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the Weierstrass P-function ($\wp $-function), which …
Structure And Stability Of Primordial Stars, Aysel İbrahi̇m Karafi̇stan
Structure And Stability Of Primordial Stars, Aysel İbrahi̇m Karafi̇stan
Turkish Journal of Physics
For decades large-scale cosmic structures have been modeled as the gravitational amplification of small-density perturbations of the cosmological recombination epoch of the Big Bang. In astrophysics, cosmological nucleosynthesis is considered responsible for the production of the pristine gas, which should be found in the first-generation stars in the form of hydrogen and helium as the main constituents. In the later type of second-generation stars, hydrogen is converted into helium by the CN-cycle reactions, in which heavier elements are produced. These elements are believed to enrich the intergalactic medium by possible star bursts at the last stages of evolution. Stability criteria …
The Observational Status Of Simple Inflationary Models: An Update, Nobuchika Okada, Vedat Nefer Şenoğuz, Qaisar Shafi
The Observational Status Of Simple Inflationary Models: An Update, Nobuchika Okada, Vedat Nefer Şenoğuz, Qaisar Shafi
Turkish Journal of Physics
We provide an update on five relatively well-motivated inflationary models in which the inflaton is a Standard Model singlet scalar field. These include i) the textbook quadratic and quartic potential models but with additional couplings of the inflaton to fermions and bosons, which enable reheating and also modify the naive predictions for the scalar spectral index $n_s$ and $r$, ii) models with Higgs and Coleman-Weinberg potentials, and finally iii) a quartic potential model with nonminimal coupling of the inflaton to gravity. For $n_s$ values close to 0.96, as determined by the WMAP9 and Planck experiments, most of the considered models …
Revisiting The Dyonic Majumdar-Papapetrou Black Holes, Seyedhabibollah Mazharimousavi, Mustafa Hali̇lsoy
Revisiting The Dyonic Majumdar-Papapetrou Black Holes, Seyedhabibollah Mazharimousavi, Mustafa Hali̇lsoy
Turkish Journal of Physics
We extend the Majumdar-Papapetrou solution of the Einstein-Maxwell equations, which are implied generally for static electric charge in nonrotating metrics, to encompass equally well magnetic charges. In the absence of Higgs and non-Abelian gauge fields, 'dyonic' is to be understood in this simpler sense. Cosmologically this may have far-reaching consequences, to the extent that existence of multimagnetic monopole black holes may become a reality in our universe. Infalling charged particle geodesics may reveal, through particular integrals, their inner secrets, which are screened from our observation.
It Is Sufficient To Set The Cosmological Constant To Zero Or To A Small Number At An Initial Time, Recai̇ Erdem
It Is Sufficient To Set The Cosmological Constant To Zero Or To A Small Number At An Initial Time, Recai̇ Erdem
Turkish Journal of Physics
I point out a simple but usually overlooked fact about the cosmological constant problem: to solve the cosmological constant problem it is sufficient to find a symmetry or mechanism that sets the cosmological constant to zero or to a tiny value at some time in the past, provided that general relativity is the relevant theory of gravity, and the energy-momentum tensor (excluding the part of the form of a cosmological constant) is conserved. The relevant symmetry or mechanism need not be applicable today. Any additional cosmological constant term induced by a phase transition in the energy-momentum tensor in this case …
Crystal Dynamics Of Zinc Chalcogenides Iii: An Application To Znte, Jay Prakash Dubey, Raj Kishor Tiwari, Kripa Shankar Upadhyaya, Pramod Kumar Pandey
Crystal Dynamics Of Zinc Chalcogenides Iii: An Application To Znte, Jay Prakash Dubey, Raj Kishor Tiwari, Kripa Shankar Upadhyaya, Pramod Kumar Pandey
Turkish Journal of Physics
We report the results of a theoretical study on phonon dispersion curves (PDCs) along the three principal symmetry directions, Debye temperature variation, combined density of states (CDS) curves, two-phonon Raman/IR peaks, and anharmonic elastic properties (third order elastic constants and their pressure derivatives) of ZnTe. This new van der Waals three-body force rigid shell model (VTRSM) incorporates the effect of van der Waals interactions and three-body interactions into the rigid shell model of zinc blende structure, where the short range interactions are operative up to the second neighbors. Our results are in good agreement with the available measured data for …
The Magnetic Properties Of A Quantum Dot In A Magnetic Field, Ayham Shaer, Mohammad Elsaid, Musa Elhasan
The Magnetic Properties Of A Quantum Dot In A Magnetic Field, Ayham Shaer, Mohammad Elsaid, Musa Elhasan
Turkish Journal of Physics
We calculate the magnetization and susceptibility of two interacting electrons confined in a quantum dot presented in a magnetic field by solving the Hamiltonian using the exact diagonalization method. We investigate the dependence of the magnetization and susceptibility on temperature, magnetic field, and confining frequency. The singlet-triplet transitions in the ground state of the quantum dot spectra and the corresponding jumps in the magnetization curves are shown. The comparisons show that our results are in very good agreement with reported works.
Properties Of Asymmetric Semiinfinite Nuclear Systems In The Extended Thomas-Fermi Model, Mohamed Abdalla
Properties Of Asymmetric Semiinfinite Nuclear Systems In The Extended Thomas-Fermi Model, Mohamed Abdalla
Turkish Journal of Physics
We start from the energy density of the Skyrme interaction and perform a leptodermous expansion for an asymmetric semiinfinite nuclear system. We get a liquid drop model formula for the energy of such a system. We use the obtained analytic formulae for volume, surface, and curvature energies to study the properties of asymmetric nuclear systems. We also study the effect of the asymmetry parameter on the volume, surface, and curvature properties.
A Comparative Study Of The Electronic Properties Of Aluminum Nitride Compounds, Rezek Mohammad, Şenay Katircioğlu
A Comparative Study Of The Electronic Properties Of Aluminum Nitride Compounds, Rezek Mohammad, Şenay Katircioğlu
Turkish Journal of Physics
Electronic properties of aluminum nitride in wurtzite, zinc-blende, and rock-salt phases are investigated by a full potential-linearized augmented plane waves method based on density functional theory within standard local density approximation and its four improved versions. Local density approximation corrected by the generalized gradient functional of Perdew-Wang-Engel-Vosko is found to be more successful than the other generalized gradient functional approximations considered in this work for providing reasonable lattice constants, energy gaps, effective electron and hole masses, and optical features for AlN phases. Although local density approximation corrected by modified Becke-Johnson potential underestimates the static dielectric constants, it provides the largest …
An Approach Based On Neural Computation To Simulate Transition Metals Using Tight Binding Measurements, Adel Belayadi, Boualem Bourahla, Leila Ait-Gougam, Fawzia Mekideche-Chafa
An Approach Based On Neural Computation To Simulate Transition Metals Using Tight Binding Measurements, Adel Belayadi, Boualem Bourahla, Leila Ait-Gougam, Fawzia Mekideche-Chafa
Turkish Journal of Physics
A theoretical study of neural networks modeling, based on the tight binding approach, is proposed in this study. The aim of the present contribution is to establish a network topology to compute the binding energy parameters of transition metals. However, because of the different types of crystallization fcc, bcc, hcp, and sc of transition metals, neural network topology determination cannot be easily established, i.e. it would not be able to collect the data to feed the neurocomputing model. Hence, in order to overcome this problem, it would be helpful to distinguish one common structure from fcc, bcc, hcp, and sc. …
Validity Of Ehrenfest's Theorem For Generalizedfields Of Dyons, Gaurav Karnatak, Praveen Singh Bisht, Om Prakash Singh Negi
Validity Of Ehrenfest's Theorem For Generalizedfields Of Dyons, Gaurav Karnatak, Praveen Singh Bisht, Om Prakash Singh Negi
Turkish Journal of Physics
The validity of Ehrenfest's theorem with its classical correspondence has been justified for the manifestly covariant equations of dyons. We have also developed accordingly the Lagrangian formulation for electromagnetic fields in a minimum coupled source giving rise to conserved current of dyons. Applying the Gupta subsidiary condition we have extended the validity of the Ehrenfest's theorem for $U\left(1\right)\times U\left(1\right)$ Abelian gauge theory of dyons. It is shown that the expectation value of the quantum equation of motion reproduces the classical equation of motion, which is the generalized form of Ehrenfest's theorem in quantum field theory.
Thermal Diffusion In Thin Plates And Coatings: Influence Of Thickness And Substrate Material, Harshan Soumya, Jacob Philip
Thermal Diffusion In Thin Plates And Coatings: Influence Of Thickness And Substrate Material, Harshan Soumya, Jacob Philip
Turkish Journal of Physics
The dependence of thermal diffusivity/conductivity on thickness for a variety of coatings and free-standing thin metallic plates was measured using a traveling photothermal technique. The selected materials have large differences in terms of their thermal conductivity. Measurements were carried out on coatings prepared on substrates with two widely different values for thermal conductivity to bring out the influence of substrate thermal conductivity on the thermal diffusivity/conductivity of the coating. Thermal diffusivity/conductivity increases exponentially with coating thickness with the value saturating at a definite thickness. The variation follows an empirical relation, which can predict thermal diffusivity of a coating at any …
Calculation Of Thermophysical Properties Of Magnesium Antimonide ($\Alpha $-Mg$_{3}$Sb$_{2})$, Seçki̇n Dündar Günay
Calculation Of Thermophysical Properties Of Magnesium Antimonide ($\Alpha $-Mg$_{3}$Sb$_{2})$, Seçki̇n Dündar Günay
Turkish Journal of Physics
Magnesium antimonide ($\alpha $-Mg$_{3}$Sb$_{2})$ is investigated by molecular dynamics simulation to find thermophysical properties. Lattice parameters and heat capacities are calculated from room temperature to the melting point. Nearest neighbor distances of ions are measured from the radial distribution function and compared with experimental values. Bulk properties like elastic constants and bulk and shear moduli are found and tabulated with first-principle and experimental data.
Magnetic Effect On The Phase Properties Of Neodymium-Activated Yttrium Disilicate Nanomaterials, Murat Erdem, Ci̇hat Boyraz
Magnetic Effect On The Phase Properties Of Neodymium-Activated Yttrium Disilicate Nanomaterials, Murat Erdem, Ci̇hat Boyraz
Turkish Journal of Physics
Under varying temperature conditions, undoped Y$_{2}$Si$_{2}$O$_{7}$ and neodymium-doped Y$_{2}$Si$_{2}$O$_{7}$ nanopowders were synthesized by the sol-gel method. The phase transitions from $\alpha $ to $\delta $ were observed in neodymium nanopowders by XRD measurements. TEM images showed ball-shaped structure forms for synthesized samples. The elemental compositions of all samples were established and quite close stoichiometry to all compound formulas was found using an attached component for TEM. To reveal the Nd dopant effect in different-phased Y$_{2}$Si$_{2}$O$_{7}$ nanopowders, diffuse reflectance measurements were conducted. To establish the magnetic properties of undoped Y$_{2}$Si$_{2}$O$_{7}$ and neodymium-doped Y$_{2}$Si$_{2}$O$_{7}$ nanopowders, an extensive study was carried out including …
Determination Of The Effective Atomic Numbers Of Fe$_{X}$Cu$_{1-X} $Binary Ferroalloys Using A Nondestructive Technique: Rayleigh-To-Compton Scattering Ratio, Mehmet Büyükyildiz
Determination Of The Effective Atomic Numbers Of Fe$_{X}$Cu$_{1-X} $Binary Ferroalloys Using A Nondestructive Technique: Rayleigh-To-Compton Scattering Ratio, Mehmet Büyükyildiz
Turkish Journal of Physics
The aim of the present study is to determine effective atomic numbers ($Z_{eff})$ of Fe$_{x}$Cu$_{1-x} $ binary ferroalloys using scattering of 59.54 keV gamma photons at 130$^{\circ}$ ($x=4.36{{\unicode{x212B}}}^{-1})$ scattering angle. For this purpose, the Rayleigh ($R)$ and Compton ($C)$ scattering intensities for the given alloys were measured using a monoenergetic beam of 59.54 keV gamma rays and the Rayleigh-to-Compton scattering ratio $R/C $was determined. Then the $Z_{eff}$ values of these alloys were determined by interpolating the $R/C$ of the material using the $R/C$ data of adjacent elements in between the $R/C$ of the alloys. For comparison, $Z_{eff}$s of alloys were …
Effect Of Glow Discharge Plasma On Step Index Polymer Optical Fiber Parameters, Mohamed Medhat, El-Sayed El-Zaiat, Mohamed Sauday, Mona Omar, Hassanein Shaaban
Effect Of Glow Discharge Plasma On Step Index Polymer Optical Fiber Parameters, Mohamed Medhat, El-Sayed El-Zaiat, Mohamed Sauday, Mona Omar, Hassanein Shaaban
Turkish Journal of Physics
DC glow discharge plasma of power 40 W was applied to step index polymer optical fibers for different exposure times. Nitrogen, oxygen, and hydrogen gases were used to obtain the glow discharge. The fiber core material was poly methyl methacrylate and the cladding was fluorinated polymer. The effect of plasma on the optical parameters, such as core index profile, cladding index, and the numerical aperture, was studied by multiple beam interference fringes and Fourier transformation of infrared spectroscopy spectra. It was found that the plasma treatment affected the optical parameters of both the cladding and the core regions of optical …
Structural And Optical Properties Of Gallium Sulfide Thin Film, Hüseyi̇n Ertap, Tarik Baydar, Mustafa Yüksek, Mevlüt Karabulut
Structural And Optical Properties Of Gallium Sulfide Thin Film, Hüseyi̇n Ertap, Tarik Baydar, Mustafa Yüksek, Mevlüt Karabulut
Turkish Journal of Physics
Structural, morphological, and optical properties of gallium sulfide film grown by chemical bath deposition have been investigated by XRD, SEM, AFM, and optical absorption techniques. The XRD spectrum indicated that the gallium sulfide film grew in crystalline form and the phase was identified as GaS. Gallium sulfide film had an island-like structure with a random distribution on a glass substrate. The particle size of the crystallites and surface roughness of the film were found to be 28-48 nm and 11.84 nm, respectively. The direct and indirect band gaps of gallium sulfide thin film were calculated from the absorption spectra as …
Isospin Mixing And Fermi Transitions For Some Deformed Nuclei, Serdar Ünlü, Hasan Ali̇ Aygör, Necla Çakmak, Cevad Selam
Isospin Mixing And Fermi Transitions For Some Deformed Nuclei, Serdar Ünlü, Hasan Ali̇ Aygör, Necla Çakmak, Cevad Selam
Turkish Journal of Physics
We have tried to give a self-consistent explanation of isospin mixing and Fermi beta decays for 54 $\le $ Z $\le $ 68 deformed nuclei. The effect of isospin impurity in nuclear ground states on Fermi beta transitions has been investigated considering the restoration of symmetry violations stemming from the mean field approximation. The isobar analogue excitations in neighbor odd-odd nuclei have been obtained by following the proton-neutron quasiparticle random phase approximation (pnQRPA) procedure. The dependence of isospin admixture probability on the deformation parameter has been determined for various isotopes of Z = 54-68 nuclei. Then the variations of isobar …
Recursion Formula For The Green's Function Of A Hamiltonian For Several Types Of Dirac Delta-Function Potentials In Curved Spaces, Fati̇h Erman
Turkish Journal of Physics
In this short article, we nonperturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Dirac delta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentials supported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulation allows us to find the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.