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Articles 1201 - 1230 of 10317
Full-Text Articles in Physical Sciences and Mathematics
A Simple Dual-Band Quasi-Yagi Antenna With Defected Ground Structures, Göksel Turan, Hayretti̇n Odabaşi
A Simple Dual-Band Quasi-Yagi Antenna With Defected Ground Structures, Göksel Turan, Hayretti̇n Odabaşi
Turkish Journal of Electrical Engineering and Computer Sciences
In this article, a dual-band compact quasi-Yagi antenna with defected ground structure (DGS) is proposed. The proposed antenna has a simple feeding mechanism consists of a microstrip and transmission line. Half of the driver and director elements are printed on the opposite side of the substrate to ensure good coupling between the antenna elements and achieve a stable radiation pattern. The ground plane is modified with one rectangular slot below the microstrip line to form dual-band operation. Also rectangular slots placed on the sides of the ground plane to improve the matching. The proposed antenna works at $f_{1}=3.35$ and $f_{2}=6.15$ …
Shape Investigations Of Structures Formed By The Self-Assembly Of Aromaticamino Acids Using The Density-Based Spatial Clustering Of Applications With Noise Algorithm, Mehmet Gökhan Habi̇boğlu, Helen W. Hernandez, Şahi̇n Uyaver
Shape Investigations Of Structures Formed By The Self-Assembly Of Aromaticamino Acids Using The Density-Based Spatial Clustering Of Applications With Noise Algorithm, Mehmet Gökhan Habi̇boğlu, Helen W. Hernandez, Şahi̇n Uyaver
Turkish Journal of Electrical Engineering and Computer Sciences
Tyrosine, tryptophan, and phenylalanine are important aromatic amino acids for human health. If they are not properly metabolized, severe rare mental or metabolic diseases can emerge, many of which are not researched enough due to economic priorities. In our previous simulations, all three of these amino acids are discovered to be self-organizing and to have complex aggregations at different temperatures. Two of these essential stable formations are observed during our simulations: tubular-like and spherical-like structures. In this study, we develop and implement a clustering analyzing algorithm using density-based spatial clustering of applications with noise (DBSCAN) to measure the shapes of …
Automatically Classifying Familiar Web Users From Eye-Tracking Data:A Machine Learning Approach, Meli̇h Öder, Şükrü Eraslan, Yeli̇z Yesi̇lada
Automatically Classifying Familiar Web Users From Eye-Tracking Data:A Machine Learning Approach, Meli̇h Öder, Şükrü Eraslan, Yeli̇z Yesi̇lada
Turkish Journal of Electrical Engineering and Computer Sciences
Eye-tracking studies typically collect enormous amount of data encoding rich information about user behaviours and characteristics on the web. Eye-tracking data has been proved to be useful for usability and accessibility testing and for developing adaptive systems. The main objective of our work is to mine eye-tracking data with machine learning algorithms to automatically detect users' characteristics. In this paper, we focus on exploring different machine learning algorithms to automatically classify whether users are familiar or not with a web page. We present our work with an eye-tracking data of 81 participants on six web pages. Our results show that …
Stability Regions In Time Delayed Two-Area Lfc System Enhanced By Evs, Ausnain Naveed, Şahi̇n Sönmez, Saffet Ayasun
Stability Regions In Time Delayed Two-Area Lfc System Enhanced By Evs, Ausnain Naveed, Şahi̇n Sönmez, Saffet Ayasun
Turkish Journal of Electrical Engineering and Computer Sciences
With the extensive usage of open communication networks, time delays have become a great concern in load frequency control (LFC) systems since such inevitable large delays weaken the controller performance and even may lead to instabilities. Electric vehicles (EVs) have a potential tool in the frequency regulation. The integration of a large number of EVs via an aggregator amplifies the adverse effects of time delays on the stability and controller design of LFC systems. This paper investigates the impacts of the EVs aggregator with communication time delay on the stability. Primarily, a graphical method characterizing stability boundary locus is implemented. …
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Turkish Journal of Mathematics
In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with several deviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations. Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples to demonstrate the results.
Materials Anddevices For Integrated Room Temperature Quantum Spintronics, Mehmet Cengi̇z Onbaşli
Materials Anddevices For Integrated Room Temperature Quantum Spintronics, Mehmet Cengi̇z Onbaşli
Turkish Journal of Physics
Recent advances in precise stoichiometry control and high-resolution characterization of advanced spintronicmaterials allowed for the development of integrated spintronic devices, which might enable ultralow power magnonicdevices with multi-THz spin wave bandwidth and topologically protected spin wavefunctions that are robust for fabrica-tion imperfections. In addition, advances in microwave and optical excitation and control of quantum states in diamondnitrogen-vacancy systems (diamond-NV) allowed for ultrasensitive magnetometry and integrated quantum logic applica-tions. Here, an integrated spintronic garnet/diamond-NV quantum system has been reviewed and discussed for logic andmemory applications. After an overview of the recent advances in the growth and characterization of insulating magneticiron garnets, …
Hollow-Core Optical Fiber With Eight-Pointed Star Cladding Structure For Low-Loss Transmission In Telecom Bands, Mustafa Ordu
Hollow-Core Optical Fiber With Eight-Pointed Star Cladding Structure For Low-Loss Transmission In Telecom Bands, Mustafa Ordu
Turkish Journal of Physics
In this study, a novel negative curvature hollow-core fiber is proposed for low-loss transmission in thenear-infrared region. We numerically investigate the effect of the cladding structure, which is formed of concentricallyinterlaced squares, to the confinement losses using the finite element modelling. The design has eight cladding tubeswith nested elements placed to the outer edge of the tubes. The confinement losses of the interlaced square core fiberis calculated as low as 0.12 dB/km in the range of 1.3 to 1.65 $\mu$m. The loss profile of the noncircular core design is comparable with the circular cores, and have improved transmission performance at …
$\Psi(2s)$ And $J/\Psi$ Production In Pp Collisions At $\Sqrt{S}$ = 7, 8 And 13 Tev, Yasir Ali, Uzma Tabassam, Syed Uzair Ahmed Shah, Atif Arif, Mais Suleymanov, Zain Ul Abidin
$\Psi(2s)$ And $J/\Psi$ Production In Pp Collisions At $\Sqrt{S}$ = 7, 8 And 13 Tev, Yasir Ali, Uzma Tabassam, Syed Uzair Ahmed Shah, Atif Arif, Mais Suleymanov, Zain Ul Abidin
Turkish Journal of Physics
Proton-proton collision is an essential part of high energy physics, as it is a baseline for nucleus-nucleus and hadron-nucleus collisions. Quark-gluon plasma, an exotic state of strongly interacting QCD matter, is routinely produced in heavy nuclei high-energy collisions. Charmonium, the bound states of $c\bar{c}$ produced at the early stages of collisions, are nice probes to examine the properties of matter through which they pass. The differential cross-sections of inclusive $\psi(2S)$ in pp collisions at energies of $\sqrt{s}$ = 7, 8 and 13 TeV have been studied. PYTHIA 8.1 event generator is used for the simulation of data. The differential cross-section …
The Effect Of Sn Doping On The Electronic And Mechanical Properties Of Ti${}_{3}$Al${}_{1-X}$Sn${}_{X}$C${}_{2}$ Max Phases, Ayşenur Gencer, Aytaç Erki̇şi̇
The Effect Of Sn Doping On The Electronic And Mechanical Properties Of Ti${}_{3}$Al${}_{1-X}$Sn${}_{X}$C${}_{2}$ Max Phases, Ayşenur Gencer, Aytaç Erki̇şi̇
Turkish Journal of Physics
The phase pure synthesis of Ti${}_{3}$AlC${}_{2}$ MAX phase is quite difficult and some additives are required to get a phase pure Ti${}_{3}$AlC${}_{2}$ such as Sn. In this study, Sn doped Ti${}_{3}$AlC${}_{2}$ MAX phase has been investigated taking into account the experimental synthesis conditions where some Sn atoms could replace Al atoms in the structure. For this purpose, Ti${}_{3}$Al${}_{1-x}$Sn${}_{x}$C${}_{2}$ with x ranging from 0 to 1 with 0.1 interval has been studied using the first principles method and the results show that all compositions are thermodynamically stable. The electronic properties of these compositions have been studied using band filling theory in …
Hydrogen Sensing Properties Of Pd Loaded Tio$_2$ Nanorods, Serkan Büyükköse
Hydrogen Sensing Properties Of Pd Loaded Tio$_2$ Nanorods, Serkan Büyükköse
Turkish Journal of Physics
The hydrogen sensing performance of palladium (Pd) catalyst loaded TiO$_2$ nanorods based sensors were investigated. TiO$_2$ nanorods were grown on Al$_2$O$_3$ substrate by a facile hydrothermal process. TiO$_2$ nanorods (NRs) were functionalized with Pd metal by RF magnetron sputtering. Samples were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques for structural and morphological analysis. Sensor measurements toward H$_2$ and some volatile organic compounds (VOCs) such as acetone, ethanol, xylene and toluene were performed by varying gas concentrations at different temperatures. The sensors were found to exhibit excellent sensitivities towards different hydrogen concentrations ranging from 25 to 1000 …
The Effect Of Two Different Substituted Atoms In Lithium Positions On The Structureof Garnet-Type Solid Electrolytes, Sevda Saran, Osman Murat Özkendi̇r, Ülfet Atav
The Effect Of Two Different Substituted Atoms In Lithium Positions On The Structureof Garnet-Type Solid Electrolytes, Sevda Saran, Osman Murat Özkendi̇r, Ülfet Atav
Turkish Journal of Physics
Li${}_{7}$La${}_{3}$Zr${}_{2}$O${}_{12}$ (LLZO), lithium lanthanum zirconate is a promising garnet-type solid electrolyte that is being intensively studied for solid-state lithium batteries. The properties of LLZO such as compatibility with the lithium electrode, stability, and ionic conductivity make them to be used in all solid-state batteries. Moreover, lithium ion concentration and distribution, doping different cations, chemical composition, and interaction between different dopants have remarkable effects on the ionic conduction of LLZO material. Herein, we investigate the solid electrolyte, Li${}_{6.4}$(Ga${}_{(1-y)}$In${}_{(y)}$)${}_{0.2}$La${}_{3}$Zr${}_{2}$O${}_{12}$ (y = 0.05, 0.10, 0.15, 0.20), by probing the influence of indium substitution to gallium sites at the same lithium concentration on the …
The Investigation Of The Complex Dielectric And Electric Modulus Of Al/Mg${}_{2}$Si/P-Si Schottky Diode And Its Ac Electrical Conductivity In A Wide Frequency Range, Ömer Sevgi̇li̇
Turkish Journal of Physics
The Al/Mg${}_{2}$Si/p-Si Schottky diode was fabricated using spin coating. The real ($\varepsilon$$\mathrm{\prime}$) and imaginary ($\varepsilon$$\mathrm{\prime}$$\mathrm{\prime}$) components of complex dielectric ($\varepsilon$*), the real (M$\mathrm{\prime}$) and imaginary (M$\mathrm{\prime}$$\mathrm{\prime}$) components of complex electric modulus (M*) and AC electrical conductivity ($\sigma$${}_{AC}$) of the fabricated Al/Mg${}_{2}$Si/p-Si Schottky diode (SD) were examined by using the impedance spectroscopy (IS) measurements in a wide frequency range of 1 kHz-1 MHz. The $\varepsilon$$\mathrm{\prime}$ and $\varepsilon$$\mathrm{\prime}$$\mathrm{\prime}$ were obtained using the value of measured capacitance and conductance while the values of dielectric loss tangent (tan$\delta$, M$\mathrm{\prime}$, M$\mathrm{\prime}$$\mathrm{\prime}$ and $\sigma$${}_{AC}$${}_{\ }$were obtained using the value of $\varepsilon$$\mathrm{\prime}$ and $\varepsilon$$\mathrm{\prime}$$\mathrm{\prime}$. While the values …
Sputtered 2d Transition Metal Dichalcogenides: From Growth To Deviceapplications, Merve Acar, Emre Gür
Sputtered 2d Transition Metal Dichalcogenides: From Growth To Deviceapplications, Merve Acar, Emre Gür
Turkish Journal of Physics
Starting from graphene, 2D layered materials family has been recently set up more than 100 different materials with variety of different class of materials such as semiconductors, metals, semimetals, superconductors. Among these materials, 2D semiconductors have found especial importance in the state of the art device applications compared to that of the current conventional devices such as (which material based for example Si based) field effect transistors (FETs) and photodetectors during the last two decades. This high potential in solid state devices is mostly revealed by the transition metal dichalcogenides (TMDCs) semiconductor materials such as MoS${}_{2}$, WS${}_{2}$, MoSe${}_{2}$ and WSe${}_{2}$. …
Investigating The Effect Of Self-Trapped Holes In The Current Gain Mechanism Of $ \Beta \Mathbf{-}{\Mathbf{Ga}}_{\Mathbf{2}}{\Mathbf{O}}_{\Mathbf{3}}$ Schottky Diode Photodetectors, Fati̇h Akyol
Turkish Journal of Physics
Monoclinic gallium oxide $(\beta\mathrm{-}{\mathrm{Ga}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}})$ has found great research interest in solar blind photodetector (SBP) applications due to its' bandgap $\mathrm{\sim}$4.85 eV and availability of high quality native crystal growth. Applications including missile guidance, flame detection, underwater/intersatellite communication and water purification systems require SBPs. $\beta\mathrm{-}{\mathrm{Ga}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}$ SBPs with high responsivity values have been published indicating internal gain in these devices. The gain has been attributed to accumulation of self-trapped hole (STH) below Schottky metal which the lowers Schottky barrier in these devices based on some approximations rather than a proper device simulation. In this paper, technology computer-aided design (TCAD) simulation of $\beta\mathrm{-}{\mathrm{Ga}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}$ …
Vacuum Polarization Energy Of The Kinks In The Sinh-Deformed Models, Ishmael Takyi, Benedict Barnes, Joseph Ackora-Prah
Vacuum Polarization Energy Of The Kinks In The Sinh-Deformed Models, Ishmael Takyi, Benedict Barnes, Joseph Ackora-Prah
Turkish Journal of Physics
We compute the one-loop quantum corrections to the kink energies of the sinh-deformed $\phi^{4}$ and $\varphi^{6}$ models in one space and one time dimensions. These models are constructed from the well-known polynomial $\phi^{4}$ and $\varphi^{6}$ models by a deformation procedure. We also compute the vacuum polarization energy to the non-polynomial function $U(\phi)=\frac{1}{4}(1-\sinh^{2}\phi)^{2}$. This potential approaches the $\phi^{4}$ model in the limit of small values of the scalar function. These energies are extracted from scattering data for fluctuations about the kink solutions. We show that for certain topological sectors with nonequivalent vacua the kink solutions of the sinh-deformed models are destabilized.
Fano Enhancement Of Second Harmonic Field Via Dark-Bright Plasmon Coupling, Mehmet Günay
Fano Enhancement Of Second Harmonic Field Via Dark-Bright Plasmon Coupling, Mehmet Günay
Turkish Journal of Physics
Surface plasmon resonances, the coherent oscillation of free electrons, can concentrate incident field into small volumes much smaller than the incident wavelength. The intense fields at these hot spots enhance the light-matter interactions and may lead to the appearance of nonlinearity. Controlling such nonlinearities is significant for various practical applications. The existence of the long-lived particles in these hotspots may lead to creating Fano resonances in both linear and nonlinear fields. Here we demonstrate that by coupling plasmonic dark modes to the first and the generated second harmonic modes separately, one can gain control over both fields. We find that …
Modern Quantum Mechanics, Why We Need It, How To Use It?, Vahid Karimipour
Modern Quantum Mechanics, Why We Need It, How To Use It?, Vahid Karimipour
Turkish Journal of Physics
A new field of research centered on quantum science and technology is emerging. This rapidly developing field deals with the study and control of single quantum entities, i.e. atoms, ions, photons, which are no longer isolated but are parts of a larger system. Manipulation of these quantum entities forms the basis of modern quantum technology, from quantum computation to quantum communication and quantum sensing. One, therefore, needs to reconsider the basic concepts of state, evolution, and measurement for these so-called open quantum systems. This is a pedagogical review paper on the rudiments of modern quantum mechanics, which keeps citations to …
Contrasting The Fuzzball And Wormhole Paradigms For Black Holes, Bin Guo, Marcel Hughes, Samir Mathur, Madhur Mehta
Contrasting The Fuzzball And Wormhole Paradigms For Black Holes, Bin Guo, Marcel Hughes, Samir Mathur, Madhur Mehta
Turkish Journal of Physics
We examine an interesting set of recent proposals describing a `wormhole paradigm' for black holes. These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon. We prove the `effective small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside. This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation. We try to illustrate various proposals for nonlocality by making simple bit …
An Improvement Of Current Driving And Electrical Conductivity Properties Incovetics, Mesut Atasoyu, Emi̇n Argun Oral, Mehmet Ertuğrul
An Improvement Of Current Driving And Electrical Conductivity Properties Incovetics, Mesut Atasoyu, Emi̇n Argun Oral, Mehmet Ertuğrul
Turkish Journal of Physics
Compared to pure Cu, Cu lattice retaining carbon atoms, called a covetic material, can have better electrical conductivity. Furthermore, the incorporation of carbon nanostructures into Cu-alloys could improve the mechanical properties of Cu-alloys. In the simulation study, we investigated Joule heating due to applied DC current on molten Cu metal concerning how to improve current density of covetic materials. In addition, we will discuss interfacial effects on covetic-metal electrodes to meet better current driving performance. The covetic composite excited at one electrode (width = 10 nm) has a higher current drive capability as a value of 3.54 $10^{7}$ $A /m^{2}$, …
A Simulation And Experimental Validation Of Third-Order Coma In Nodal Aberrationtheory With A Cassegrain Telescope, Özgür Karci
A Simulation And Experimental Validation Of Third-Order Coma In Nodal Aberrationtheory With A Cassegrain Telescope, Özgür Karci
Turkish Journal of Physics
This study presents a simulation and experimental validation of third-order coma in Nodal Aberration Theory (NAT) with a custom-designed Cassegrain system. The Cassegrain system uses a piezo-driven flexure tool to align the telescope's secondary mirror with respect to the primary mirror. This alignment mechanism is also used to misalign the telescope's secondary mirror to induce the intentional aberrations. The third-order Fringe Zernike coma (Z$_{7/8}$) was simulated utilizing the Cassegrain telescope's real ray-trace model (e.g., in Code V) and analyzed for both the telescope's nominal aligned and misaligned states. The simulated aberration of third-order coma was induced utilizing the secondary mirror …
Mixing Angles Between The Tetraquark States With Two Heavy Quarks Within Qcdsum Rules, Selçuk Bi̇lmi̇ş
Mixing Angles Between The Tetraquark States With Two Heavy Quarks Within Qcdsum Rules, Selçuk Bi̇lmi̇ş
Turkish Journal of Physics
LHCb collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated; hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is …
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Turkish Journal of Mathematics
IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Turkish Journal of Mathematics
This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variable-order and fixed initial valuable. By applying Krasnoselskii's fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it. For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.
Hilbert Series Of Tangent Cones For Gorenstein Monomial Curves In $\Mathbb{A}^{4}(K)$, Anargyros Katsabekis
Hilbert Series Of Tangent Cones For Gorenstein Monomial Curves In $\Mathbb{A}^{4}(K)$, Anargyros Katsabekis
Turkish Journal of Mathematics
In this paper, we study the Hilbert series of the tangent cone of Gorenstein monomial curves in the 4-dimensional affine space. We give an explicit formula for the reduced Hilbert series of the tangent cone of a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen-Macaulay.
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
Let $G$ be a finite abelian group. Ferraz, Guerreiro, and Polcino Milies (2014) proved that the number of $G$-equivalence classes of minimal abelian codes is equal to the number of $G$-isomorphism classes of subgroups for which corresponding quotients are cyclic. In this article, we prove that the notion of $G$-isomorphism is equivalent to the notion of isomorphism on the set of all subgroups $H$ of $G$ with the property that $G/H$ is cyclic. As an application, we calculate the number of non-$G$-equivalent minimal abelian codes for some specific family of abelian groups. We also prove that the number of non-$G$-equivalent …
Close-To-Convexity Of A Class Of Harmonic Mappings Defined By A Third-Order Differential Inequality, Eli̇f Yaşar, Si̇bel Yalçin Tokgöz
Close-To-Convexity Of A Class Of Harmonic Mappings Defined By A Third-Order Differential Inequality, Eli̇f Yaşar, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonic polynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.
Existence Of Nonnegative Solutions For Discrete Robin Boundary Value Problems With Sign-Changing Weight, Yan Zhu
Turkish Journal of Mathematics
In this paper,~we are concerned with the following discrete problem first $$\left\{ \begin{array}{ll} -\Delta^{2}u(t-1)=\lambda p(t)f(u(t)), &t\in[1,N-1]_{\mathbb{Z}},\\ \Delta u(0)=u(N)=0,\\ \end{array} \right. $$ where $N>2$~is an integer,~$\lambda>0$~is a parameter,~$p:[1,N-1]_{\mathbb{Z}}\rightarrow\mathbb{R}$~is a sign-changing function,~$f:[0,+\infty)\rightarrow[0,+\infty)$~is a continuous and nondecreasing function.~$\Delta u(t)=u(t+1)-u(t)$,~$\Delta^{2}u(t)=\Delta(\Delta u(t))$.~By using the iterative method and Schauder's fixed point theorem,~we will show the existence of nonnegative solutions to the above problem. Furthermore, we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights.
Volume Properties And Some Characterizations Of Ellipsoids In ${\Bbb E}^{N+1}$, Dong-Soo Kim, Incheon Kim, Young Ho Kim
Volume Properties And Some Characterizations Of Ellipsoids In ${\Bbb E}^{N+1}$, Dong-Soo Kim, Incheon Kim, Young Ho Kim
Turkish Journal of Mathematics
Suppose that $M$ is a strictly convex and closed hypersurface in ${\Bbb E}^{n+1}$ with the origin $o$ in its interior. We consider the homogeneous function $g$ of positive degree $d$ satisfying $M=g^{-1}(1)$. Then, for a positive number $h$ the level hypersurface $g^{-1}(h)$ of $g$ is a homothetic hypersurface of $M$ with respect to the origin $o$. In this paper, for tangent hyperplanes $\Phi_h$ to $g^{-1}(h)$ ($0
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In the present paper, using the triangular $A-$statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on $\left[ 0,\infty \right)\times \left[ 0,\infty \right) $ with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.