Complete Cone Research Articles

Ciric type fixed point theorems under c-distance on non-normal cone metric spaces over Banach algebras

In this paper, we obtain Ciric type fixed point theorems for continuous or non-continuous mappings under c-distance on mapping-orbitally complete cone metric spaces over Banach algebras without normalities.

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.

Common Fixed Point in Cone Metric Space for $mathbf{s}-mathbf{varphi}$-contractive

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric space has been introduced. We have defined $s-phi$-contractive and obtained common fixed point theorem for a mapping $f,s$ which satisfies $s-phi$-contractive.

Complete flat cone metrics on punctured surfaces

We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.

Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras

The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. An example to illustrate main theorem is given. Finally, applications of our main result to cyclic mappings and weak contraction type mappings are given.

On The Solution of Existence of Nonlinear Integral-and Integrodifferential Equations

In this paper we study the existence and uniqueness for mixed Volterra – Fredholm integral and integrodifferential equations By using the extensions of Banach's contraction principle in complete cone metric space

Design of SECAR a recoil mass separator for astrophysical capture reactions with radioactive beams

A recoil mass separator SECAR has been designed for the purpose of studying low-energy (p,γ) and (α,γ) reactions in inverse kinematics with radioactive beams for masses up to about A = 65. Their reaction rates are of importance for our understanding of the energy production and nucleosynthesis during explosive hydrogen and helium burning. The radiative capture reactions take place in a windowless hydrogen or He gas target at the entrance of the separator, which consists of four Sections. The first Section selects the charge state of the recoils. The second and third Sections contain Wien Filters providing high mass resolving power to separate efficiently the intense beam from the few reaction products. In the following fourth Section, the reaction products are guided into a detector system capable of position, angle and time-of-flight measurements. In order to accept the complete kinematic cone of recoil particles including multiple scattering in the target in the center of mass energy range of 0.2 MeV to 3.0 MeV, the system must have a large polar angle acceptance of ± 25 mrad. This requires a careful minimization of higher order aberrations. The present system will be installed at the NSCL ReA3 accelerator and will be used with the much higher beam intensities of the FRIB facility when it becomes available.

Playing frequency of conical reed instruments

Several factors explain the difference between the resonance frequencies of the resonator of reed instruments and their playing frequency: the flow rate due to the reed displacement, the reed dynamics, the resonator inharmonicity, and the temperature gradient. For conical instruments, the truncation of the cone entails non-negligible inharmonicity effects. This is true even if the inharmonicity is reduced by a proper choice of the mouthpiece volume. The playing frequency was calculated by using a minimum, ab initio model of self-sustained oscillations, and compared to analytical results. Furthermore, the “reactive power rule” (Boutillon, 1989) provides a link between the pressure spectrum and inharmonicity. Compared to the natural frequency of the complete cone, which is a well known approximation, the playing frequency is slightly higher: typical discrepancies are 50 cents for short truncated cones (higher notes) and 10 cents for long truncated cones (lower notes). This discrepancy, due to inharmonicity, depends on the excitation parameters, and the influence of the second and third harmonics is found to be significant.

Hearing the transformation of conical to closed-pipe resonances

The harmonics for an open cone with slant length are the same as the harmonics for an open pipe with length . When the cone is transformed through phases of closed–open conical frusta into a cylinder of length closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using boundary conditions is presented in order to understand this remarkable fact. A new free interactive HMTL5 application is provided which enables the user to hear the resonances of a complete cone transform into the pitches of a conical frustum closed at the small end, and eventually into the odd harmonics of a closed cylindrical pipe.

English

English

Teoreme o fiksnoj tački u konusnom metričkom prostoru primenom c-distance

In this paper we achieved the results related to determining the fixed point using c-distance. The existence of a fixed point in a cone metric space is proved when the mapping is continuous. The existence of a fixed point in a complete cone metric space is proved when the cone is normal but when the mapping is not continuous for different types of contractive mapping.

Energetic electron precipitation into the middle atmosphere—Constructing the loss cone fluxes from MEPED POES

AbstractThe impact of energetic electron precipitation (EEP) on the chemistry of the middle atmosphere (50–90 km) is still an outstanding question as accurate quantification of EEP is lacking due to instrumental challenges and insufficient pitch angle coverage of current particle detectors. The Medium Energy Proton and Electron Detectors (MEPED) instrument on board the NOAA/Polar Orbiting Environmental Satellites (POES) and MetOp spacecraft has two sets of electron and proton telescopes pointing close to zenith (0°) and in the horizontal plane (90°). Using measurements from either the 0° or 90° telescope will underestimate or overestimate the bounce loss cone flux, respectively, as the energetic electron fluxes are often strongly anisotropic with decreasing fluxes toward the center of the loss cone. By combining the measurements from both telescopes with electron pitch angle distributions from theory of wave‐particle interactions in the magnetosphere, a complete bounce loss cone flux is constructed for each of the electron energy channels >50 keV, >100 keV, and >300 keV. We apply a correction method to remove proton contamination in the electron counts. We also account for the relativistic (>1000 keV) electrons contaminating the proton detector at subauroral latitudes. This gives us full range coverage of electron energies that will be deposited in the middle atmosphere. Finally, we demonstrate the method's applicability on strongly anisotropic pitch angle distributions during a weak geomagnetic storm in February 2008. We compare the electron fluxes and subsequent energy deposition estimates to OH observations from the Microwave Limb Sounder on the Aura satellite substantiating that the estimated fluxes are representative for the true precipitating fluxes impacting the atmosphere.

A Common Fixed Point Result in Ordered Complete Cone Metric Spaces

In this paper, we prove a common fixed point theorem for ordered contractions in ordered cone metric spaces without using the continuity. Our result generalizes some recent results existing in the references.

COMMON COUPLED FIXED POINT THEOREMS OF TWO MAPPINGS SATISFYING GENERALIZED CONTRACTIVE CONDITION IN CONE METRIC SPACE

In this paper, we prove the existence and uniqueness of a common coupled fixed point theorem in complete cone metric space for a pair of mappings satisfying a generalised contractive condition. Some results are also given in the form of corollaries. The results are also verified with the help of example.

Fixed point theorems for (p, q)-quasi-contraction mappings in cone metric spaces

In this work, the authors introduce the concept of (p, q)-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a (p, q)-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order 2.

On Quasi-Contractions in Metric Spaces with a Graph

In the present work, we introduce G -quasi-contractions using directed graphs in metric spaces with a graph and we show that this contrac- tion generalizes a large number of contractions. the existence of xed points for We then investigate G -quasi-contractions under two dif- ferent conditions and discuss the main theorem. Finally, we list some consequences of our theorem where either the contractive condition is replaced with a stronger one or the underlying space is changed to a complete metric space or a complete cone metric space.

Convergence of Noor-type iteration scheme with errors in a convex cone metric space

A convergence criterion of a Noor-type iteration scheme with errors is proved for approximation of common fixed points of three sequences of uniformly quasi-Lipschitzian self-mappings of a closed convex subset in a complete convex cone metric space.

Local existence in retarded time under a weak decay on complete null cones

In the previous paper (see Li and Zhu (2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman (1993), we proved the local existence in retarded time, which means the solution to the vacuum Einstein equations exists in a uniform future neighborhood, while the global existence in retarded time is the weak cosmic censorship conjecture. In this paper, we prove that the local existence in retarded time still holds when the data is assumed to decay slower, like that in Bieri’s work (2007) on the extension to the stability of Minkowski spacetime. Such decay guarantees the existence of the limit of the Hawking mass on the initial null cone, when approaching to infinity, in an optimal way.

Canonical polygons for the hyperbolic structures on the torus with a single cone point

Let T0 be the once-punctured torus and θ a real number with 0<θ<2π. Let ρ˜ be a representation of π1(T0) to SL(2,R) which sends the peripheral loop to an elliptic element with trace −2cos⁡(θ/2). Let ρ be the PSL(2,R)-representation induced from ρ˜, and assume it satisfies Bowditch's Q-condition. In this paper, we construct a certain polyhedron, which is obtained as a variation of Jorgensen's theory to cone manifolds, and construct a complete cone hyperbolic structure on the 3-dimensional cone manifold obtained as the product of the torus with a single cone point and R which induces ρ as the holonomy representation.

Partial kilovoltage cone beam computed tomography, complete kilovoltage cone beam computed tomography, and electronic portal images for breast radiation therapy: A dose-comparison study

PurposeThe purpose of this study was to compare absorbed dose with the treated breast and organs at risks (OARs) with weekly image guidance using electronic portal imaging (EPI), complete kilovoltage cone beam computed tomography (kV CBCT), and partial kV CBCT. Methods and materialsUsing a thorax female phantom, we determined absorbed doses to treated and contralateral breast, ipsilateral and contralateral lung, heart, and skin for tangential EPI, complete kV CBCT, and partial kV CBCT. Doses were measured by use of ionization chambers and compared with treatment planning system calculations. With simulation of breast tangential irradiation to a standard dose of 50 Gy in 25 fractions, dose to each organ was measured for each image guidance technique. ResultsUse of weekly EPI was associated with a significantly increased dose to the treated breast compared with weekly complete and partial kV CBCT (4.44 ± 0.04 vs 1.00 ± 0.07 vs 0.576 ± 0.003 cGy, respectively). Dose to the contralateral breast, ipsilateral and contralateral lung, heart, and contralateral skin was lower with EPI than with either complete or partial kV CBCT (0.042 ± 0.004 vs 0.36 ± 0.01 vs 0.23 ± 0.01 cGy, 0.06 ± 0.04 vs 0.42 ± 0.02 vs 0.31 ± 0.01 cGy, 0.004 ± 0.002 vs 0.29 ± 0.01 vs 0.22 ± 0.01 cGy, 0.03 ± 0.08 vs 0.36 ± 0.02 vs 0.25 ± 0.01 cGy, and 0.20 ± 0.02 vs 0.80 ± 0.06 vs 0.40 ± 0.03 cGy, respectively). Compared with complete CBCT, the use of partial CBCT allowed dose reductions of 42%, 37%, 27%, 24%, and 28% to the ipsilateral breast, contralateral breast, ipsilateral lung, contralateral lung, and heart, respectively. Additional dose from weekly CBCT was significantly lower than treatment-related scatter dose for all OARs. ConclusionsUse of CBCT was associated with decreased dose to ipsilateral breast and increased dose to all OARs compared with EPI. Significant dose reduction can be achieved with the use of partial CBCT, while generally maintaining image quality.