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Journal articles on the topic 'Η - circumference of a point'

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Published: 5 June 2025

Last updated: 24 June 2025

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1

Ducotey, K. S., and J. K. Good. "The Effect of Web Permeability and Side Leakage on the Air Film Height Between a Roller and Web." Journal of Tribology 120, no. 3 (1998): 559–65. http://dx.doi.org/10.1115/1.2834587.

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Air entrained between a web and roller can cause a loss in traction that can affect web quality. The entrained air causes an air layer to form which separates the web from the roller. Insufficient traction exists at this point and an idler roller will be unable to be driven by the web. Other applications, however, such as newsprint moving around a turnbar, require complete clearance. An equation for predicting the air film height between a permeable web and roller was developed using foil bearing theory. The separation distance (h) between the roller and web is a function of the roller radius (R), web tension (T), air viscosity (η), summation of the web and roller velocities (U), and the web permeability (α). The air film height was found to decrease linearly around the circumference (θ) of the roller in the constant pressure region. Therefore, the air film height can be expressed simply as, h=0.643R[(6ηU)/T]2/3−2[(αT)/U]θ The slope of the air film height is a function of the web/roller velocity, web tension, and the permeability of the paper. A correction factor for side leakage was also incorporated into the result.

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2

Fox, Patrick J., Sergo Jindariani, and Vladimir Shiltsev. "DIMUS: super-compact Dimuonium Spectroscopy collider at Fermilab." Journal of Instrumentation 18, no. 08 (2023): T08007. http://dx.doi.org/10.1088/1748-0221/18/08/t08007.

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Abstract While dimuonium (μ + μ -) — the “smallest QED atom” — has not yet been observed, it is of utmost fundamental interest. By virtue of the larger mass, dimuonium has greater sensitivity to beyond the standard model (BSM) effects than its cousins positronium or muonium, both discovered long ago, while not suffering from large QCD uncertainties. Dimuonium atoms can be created in e + e - collisions with large longitudinal momentum, allowing them to decay a small distance away from the beam crossing point and avoid prompt backgrounds. We envision a unique cost-effective and fast-timeline opportunity for copious production of (μ + μ -) atoms at the production threshold via a modest modification of existing Fermilab Accelerator Science and Technology (FAST) facility to arrange collisions of 408 MeV electrons and positrons at a 75° angle. This compact 23 m circumference collider (DIMUS) will allow for precision tests of QED and open the door for searches for new physics coupled to the muon. The FAST facility is perfectly suited for DIMUS as there are existing SRF accelerators and infrastructure, capable of producing high energy, high current electron and positron beams, sufficient for O(1032)cm2 s-1 luminosity and ∼0.5 million dimuons per year. The expansion will require installation of a second SRF cryomodule, positron production and accumulation system, fast injection/extraction kickers and two small circumference intersecting rings. An approximately meter-sized detector with several layers of modern pixelated silicon detector and crystal-based electromagnetic calorimeters will ensure observation of the decays of dimuonium to electron-positron pairs in presence of the Bhabba scattering background. An expansion of the system to include solenoidal magnet outside of the calorimeter system, a layer of steel shielding behind the magnet, and a set of dedicated muon detectors would extend the physics program of DIMUS to include precision studies of rare processes with muons, pions, and η mesons produced in e + e - collisions.

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3

Antczak, Tadeusz. "Saddle point criteria and duality in multiobjective programming via an η-approximation method". ANZIAM Journal 47, № 2 (2005): 155–72. http://dx.doi.org/10.1017/s1446181100009962.

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AbstractIn this paper, Antczak's η-approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the η-saddle points of the associated η-approximated vector optimisation problems. We introduce an η-Lagrange function for a constructed η-approximated vector optimisation problem and present some modified η-saddle point results. Furthermore, we construct an η-approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between η-approximation vector optimisation problems and their duals (that is, an η-approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.

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4

Jung, Soon-Mo, Ji-Hye Kim, and Young Woo Nam. "Hyers–Ulam Stability of Two-Dimensional Flett’s Mean Value Points." Mathematics 7, no. 8 (2019): 733. http://dx.doi.org/10.3390/math7080733.

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If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) - f ( a ) = f ′ ( η ) ( η - a ) , then the point η is called a Flett’s mean value point of f in [ a , b ] . The concept of Flett’s mean value points can be generalized to the 2-dimensional Flett’s mean value points as follows: For the different points r ^ and s ^ of R × R , let L be the line segment joining r ^ and s ^ . If a partially differentiable function f : R × R → R and an intermediate point ω ^ ∈ L satisfy f ( ω ^ ) - f ( r ^ ) = ω ^ - r ^ , f ′ ( ω ^ ) , then the point ω ^ is called a 2-dimensional Flett’s mean value point of f in L. In this paper, we will prove the Hyers–Ulam stability of 2-dimensional Flett’s mean value points.

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5

Hussain, N., M. A. Kutbi та P. Salimi. "Fixed Point Theory inα-Complete Metric Spaces with Applications". Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/280817.

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The aim of this paper is to introduce new concepts ofα-η-complete metric space andα-η-continuous function and establish fixed point results for modifiedα-η-ψ-rational contraction mappings inα-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems forψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

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6

Baccelli, François, and Eliza O'Reilly. "Reach of repulsion for determinantal point processes in high dimensions." Journal of Applied Probability 55, no. 3 (2018): 760–88. http://dx.doi.org/10.1017/jpr.2018.49.

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Abstract Goldman (2010) proved that the distribution of a stationary determinantal point process (DPP) Φ can be coupled with its reduced Palm version Φ0,! such that there exists a point process η where Φ=Φ0,!∪η in distribution and Φ0,!∩η=∅. The points of η characterize the repulsive nature of a typical point of Φ. In this paper we use the first-moment measure of η to study the repulsive behavior of DPPs in high dimensions. We show that many families of DPPs have the property that the total number of points in η converges in probability to 0 as the space dimension n→∞. We also prove that for some DPPs, there exists an R∗ such that the decay of the first-moment measure of η is slowest in a small annulus around the sphere of radius √nR∗. This R∗ can be interpreted as the asymptotic reach of repulsion of the DPP. Examples of classes of DPP models exhibiting this behavior are presented and an application to high-dimensional Boolean models is given.

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Hussain, N., M. A. Kutbi, S. Khaleghizadeh та P. Salimi. "Discussions on Recent Results forα-ψ-Contractive Mappings". Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/456482.

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We establish certain fixed point results forα-η-generalized convex contractions,α-η-weakly Zamfirescu mappings, andα-η-Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

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8

Pourhadi, Ehsan, Reza Saadati, and Sotiris K. Ntouyas. "Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem." Mathematics 7, no. 6 (2019): 526. http://dx.doi.org/10.3390/math7060526.

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Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

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Sitthiwirattham, Thanin, and Jessada Tariboon. "Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/569313.

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By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problemΔ2u(t-1)+a(t)f(u(t))=0,t∈{1,2,…,T},u(0)=β∑s=1ηu(s),u(T+1)=α∑s=1ηu(s), wherefis continuous,T≥3is a fixed positive integer,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),andΔu(t-1)=u(t)-u(t-1). We show the existence of at least one positive solution iffis either superlinear or sublinear.

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Sun, Jian-Ping, Xue-Mei Yang, and Ya-Hong Zhao. "Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs." Journal of Function Spaces 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/6874643.

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We are concerned with the following system of third-order three-point boundary value problems:u′′′(t)+f(t,v(t))=0,t∈(0,1),v′′′(t)+g(t,u(t))=0,t∈(0,1),u(0)=u′′(0)=0,u′(1)=αu(η),v(0)=v′′(0)=0, andv′(1)=αv(η), where0<η<1and0<α<1/η. By imposing some suitable conditions onfandg, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.

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11

Akbar, Sobia, and Azad Hussain. "Nonviscous Oblique Stagnation Point Flow towards Riga Plate." Mathematical Problems in Engineering 2021 (November 20, 2021): 1–9. http://dx.doi.org/10.1155/2021/2227269.

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Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

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12

Tariq, Muhammad, Muhammad Arshad, Eskandar Ameer, Ahmad Aloqaily, Suhad Subhi Aiadi та Nabil Mlaiki. "On Relational Weak Fℜm,η-Contractive Mappings and Their Applications". Symmetry 15, № 4 (2023): 922. http://dx.doi.org/10.3390/sym15040922.

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In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results for cyclic-type weak Fℜm,η-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form ξα=∫0αAα,σ,ξσmσ+Ψα,α∈0,1.

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13

Das, Susanta, Ashis Biswas та Kanak Kanti Baishya. "η-Ricci soliton on η-Einstein-like LP-Sasakian manifolds". Annals of West University of Timisoara - Mathematics and Computer Science 58, № 1 (2022): 76–84. http://dx.doi.org/10.2478/awutm-2022-0006.

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Abstract The object of the present article is to study the notion of η-Einstein-like LP-Sasakian manifolds admitting η-Ricci soliton. Furthermore, we study the η-Ricci soliton on LP-Sasakian manifolds when the potential vector field V is point-wise collinear.

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14

Reitzner, M., E. Spodarev, and D. Zaporozhets. "Set Reconstruction by Voronoi Cells." Advances in Applied Probability 44, no. 04 (2012): 938–53. http://dx.doi.org/10.1017/s0001867800005991.

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For a Borel set A and a homogeneous Poisson point process η in of intensity λ&gt;0, define the Poisson–Voronoi approximation A η of A as a union of all Voronoi cells with nuclei from η lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AΔ A η) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(A η) and Vol(AΔ A η) together with their asymptotics for large λ are obtained as well.

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15

Basok, M. "On some degeneracy loci in the moduli space of pointed odd spin curves." St. Petersburg Mathematical Journal 32, no. 5 (2021): 819–45. http://dx.doi.org/10.1090/spmj/1672.

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Let C C be a smooth projective curve of genus g ≥ 3 g\geq 3 and let η \eta be an odd theta characteristic on it such that h 0 ( C , η ) = 1 h^0(C,\eta ) = 1 . Pick a point p p from the support of η \eta and consider the one-dimensional linear system | η + p | |\eta + p| . In general this linear system is base-point free and all its ramification points are simple. The locus in the moduli space of odd spin curves is studied where the linear system | η + p | |\eta + p| fails to have this general behavior. This locus is stratified with respect to multiplicities of degeneracies; these strata are called degeneracy schemes and their geometry is explored. Conormal spaces to these schemes are described in intrinsic terms and some consequences of this are presented.

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Furqan, Salman, Hüseyin Işık, and Naeem Saleem. "Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results." Journal of Function Spaces 2021 (May 20, 2021): 1–8. http://dx.doi.org/10.1155/2021/9936992.

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In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.

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Baleanu, Dumitru, Shahram Rezapour, and Hakimeh Mohammadi. "Some existence results on nonlinear fractional differential equations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1990 (2013): 20120144. http://dx.doi.org/10.1098/rsta.2012.0144.

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In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D α u ( t )= f ( t , u ( t )) with a Riemann–Liouville fractional derivative via the different boundary-value problems u (0)= u ( T ), and the three-point boundary condition u (0)= β 1 u ( η ) and u ( T )= β 2 u ( η ), where T >0, t ∈ I =[0, T ], 0< α <1, 0< η < T , 0< β 1 < β 2 <1.

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Kutbi, Marwan Amin, Muhammad Arshad та Aftab Hussain. "ON Modified(α-η)-Contractive Mappings". Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/657858.

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Hussain et al. (2013) established new fixed point results in complete metric space. In this paper, we prove fixed point results ofα-admissible mappings with respect toη, for modified contractive condition in complete metric space. An example is given to show the validity of our work. Our results generalize/improve several recent and classical results existing in the literature.

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Gaba, Yaé Ulrich, Hassen Aydi та Nabil Mlaiki. "(ρ,η,μ)-Interpolative Kannan Contractions I". Axioms 10, № 3 (2021): 212. http://dx.doi.org/10.3390/axioms10030212.

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We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.

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Bekri, Zouaoui, and Slimane Benaicha. "Existence of solution for nonlinear fourth-order three-point boundary value problem." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (2018): 67–82. http://dx.doi.org/10.5269/bspm.v38i1.34767.

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In this paper, we study the existence of nontrivial solution for the fourth-order three- point boundary value problem having the following formu(4) (t) + f (t, u(t)) = 0, 0 < t < 1,u(0) = α(η), u'(0) = u''(0) = 0, u(1) = βu(η),where η ∈ (0, 1), α, β ∈ R, f ∈ C ([0, 1] × R, R). We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. And by using the Leray-Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.

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Zhou, Dai-Mei, Xu Cai, Yun Cheng, Yu-Liang Yan, Bao-Guo Dong, and Ben-Hao Sa. "Elliptic flow parameter in Au+Au and p+Au collisions at top RHIC energy." International Journal of Modern Physics: Conference Series 29 (January 2014): 1460214. http://dx.doi.org/10.1142/s2010194514602142.

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The new issue of parton and hadron cascade model PACIAE 2.1 is utilized investigating the charged particle elliptic flow parameter v2 in Au + Au and p+ Au collisions at top RHIC energy. If the transverse momenta px and py of particles from string fragmentation are randomly sampled on the circumference of an ellipse instead of circle originally the PHENIX charged particle v2(η) and v2(pT) data in the 20-40% and 40-50% central Au + Au collisions at [Formula: see text] are fairly reproduced by the PACIAE 2.1 calculations, respectively. In addition, the charged particle v2(η) and v2(pT) in the p+ Au collisions at [Formula: see text] are predicted. It turned out that the charged particle elliptic flow parameter v2 may reach a measurable value of ~0.04 in the above p+ Au collisions.

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Chang, Jianming. "Normality, Quasinormality and Periodic Points." Nagoya Mathematical Journal 195 (2009): 77–95. http://dx.doi.org/10.1017/s0027763000009715.

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AbstractLet M > 1 be a positive number. Let be a family of holomorphic functions f in some domain D ⊂ ℂ for which there exists an integer k = k(f) > 2 such that |(fk)′(ζ)| ≤ Mk for every periodic point ζ of period k of f in D. We show first that is quasinormal of order at most one in D. This strengthens a result of W. Bergweiler. Secondly, for the case M = 1, we prove that is normal in D if there exists a positive number K < 3 such that | f(η)| ≤ K for each f ∈ and every fixed point η of f in D. This improves a result of M. Esséen and S. J. Wu. We also construct an example which shows that the condition |f’(η)| ≤ K < 3 can not be replaced by | f′(η) | < 3.

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23

Petters, A. O. "A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing." Symposium - International Astronomical Union 173 (1996): 281–82. http://dx.doi.org/10.1017/s0074180900231550.

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Consider a gravitational lens system with K planes. If light rays are traced back from the observer to the light source plane, then the points on the first lens plane where a light ray either terminates, or, passes through and terminates before reaching the light source plane, are “obstruction points.” More precisely, tracing rays back to the source plane induces a K-plane lensing map η : U ⊆ R2 → R2 of the form η(x1) = x1 −∑i=1k αi(xi(xi)). We then define an obstruction point of η to be a point a of U where limx1→a |αi(xi(x1))| = ∞ for some “deflection angle” αi.

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ANTCZAK, TADEUSZ. "AN η-APPROXIMATION APPROACH IN NONLINEAR VECTOR OPTIMIZATION WITH UNIVEX FUNCTIONS". Asia-Pacific Journal of Operational Research 23, № 04 (2006): 525–42. http://dx.doi.org/10.1142/s0217595906001029.

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In this paper, the so-called η-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function η. In this method, an equivalent η-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated η-approximated vector optimization problem. Finally, the description of the η-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.

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Ayoob, Irshad, Ng Zhen Chuan, and Nabil Mlaiki. "Double-Composed Metric Spaces." Mathematics 11, no. 8 (2023): 1866. http://dx.doi.org/10.3390/math11081866.

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The double-controlled metric-type space (X,D) is a metric space in which the triangle inequality has the form D(η,μ)≤ζ1(η,θ)D(η,θ)+ζ2(θ,μ)D(θ,μ) for all η,θ,μ∈X. The maps ζ1,ζ2:X×X→[1,∞) are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form D(η,μ)≤αD(η,θ)+βD(θ,μ) for all η,θ,μ∈X. In our new space, the control functions α,β:[0,∞)→[0,∞) are composed of the metric D in the triangle inequality, where the control functions ζ1,ζ2:X×X→[1,∞) in a double-controlled metric-type space are multiplied with the metric D. We establish some fixed-point theorems along with the examples and applications.

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Haurysh, V. Y., and V. V. Andreev. "Two-photon decay of the pseudoscalar meson in the relativistic quark model." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 59, no. 4 (2024): 315–27. http://dx.doi.org/10.29235/1561-2430-2023-59-4-315-327.

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In the relativistic quark model, based on the point form of Poincaré-invariant quantum mechanics, an integral representation of the form-factor of the pseudoscalar P0(π0,η,η′) meson of P0 (qq̅)→γγ decay is obtained taking into account the anomalous magnetic moments of u-, d- and s-quarks. IIn the developed formalism the values of the constituent quark masses and the parameters of the wave functions are calculated using the lepton decay P±(qQ̅ ) → ℓ±νℓ± constant fP± and the pseudoscalar density constant gP±. It is shown that taking into account the gluonium component in η/η′-mesons and using the structure functions of light sector quarks lead to the behavior of the form factors of pseudoscalar π0-, η-, η′-mesons in the area of a small transferred momentum to the lepton pair, which is consistent with the modern experimental data

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Hüsken, Nils, Kay Demmich та Alfons Khoukaz. "η meson physics with WASA-at-COSY". EPJ Web of Conferences 199 (2019): 01006. http://dx.doi.org/10.1051/epjconf/201919901006.

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In recent years, the η meson has been a focal point of research for the WASA experiment at the Cooler Synchrotron COSY of the Research Center Jülich. Production experiments using nucleon-nucleon and nucleon-nucleus collisions have been performed, studying the η − N interaction in various configurations. A better understanding of this interaction is a key aspect in the ongoing search for η-nuclear bound states. In addition, the η meson itself represents an ideal laboratory for precision studies of the strong and electromagnetic interactions as well as for searches for beyond Standard Model physics. Large datasets were assembled using the WASA experiment to enable studies on rare and forbidden decay modes. An overview over recent highlights of the WASA η meson physics programme was given.

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Al-Omari, Ahmad, and Hanan Al-Saadi. "Impulsive fractional order integrodifferential equation via fractional operators." PLOS ONE 18, no. 3 (2023): e0282665. http://dx.doi.org/10.1371/journal.pone.0282665.

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In this paper, we establish the existence and uniqueness of the solution to fractional equations abstract integrodifferential equation with impulsive as d η w ( z ) d z η + ζ w ( z ) = f ( z , w ( z ) ) + K ( w ) ( z ) , z > z 0 , z ≠ z k , 0 < η ≤ 1 , Δ w | z = z k = I k ( w ( z k - ) ) , k = 1 , . . . , m , w ( z 0 ) + φ ( w ) = w 0 ∈ X , where K ( w ) ( z ) = ∫ z 0 z q ( z - s ) g ( s , w ( s ) ) d s , and we used the fixed point theorems due to Banach space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. Finally, in support, an example is presented to validate the obtained results.

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Sakurai, Kazuhiko. "Leaf Size Recognition and Evaluation of Some Attelabid Weevils (1) Chonostropheus Chujoi." Behaviour 106, no. 3-4 (1988): 279–99. http://dx.doi.org/10.1163/156853988x00296.

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AbstractLeaf recognition of the female during cradle formation was studied using model leaves, young oak leaves moulded in several shapes; observation of behaviour preceding cutting and numerical analysis of cutting points were carried out. Females repeatedly perform a sequence of walking along the circumference via the leaf apex and then cut the leaf. Circumference length is the most probable determinant of the cutting point. It is hypothesized that females perceive the most protrusive point of the leaf, the leaf apex, and the circumference length by walking. A scheme, which consists of two mechanisms for circumference measurement, for the cutting point decision is proposed. Although females do not adjust the cutting point with respect to the number of eggs to be laid in the cradle, they perceive and use leaf area or something correlative to it, for the decision as to egg number.

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Murata, Minoru, and Tetsuo Tsuchida. "Monotonicity of non-Liouville property for positive solutions of skew product elliptic equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (2019): 1429–49. http://dx.doi.org/10.1017/prm.2018.138.

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AbstractWe consider a second-order elliptic operator L in skew product of an ordinary differential operator L1 on an interval (a, b) and an elliptic operator on a domain D2 of a Riemannian manifold such that the associated heat kernel is intrinsically ultracontractive. We give criteria for criticality and subcriticality of L in terms of a positive solution having minimal growth at η (η = a, b) to an associated ordinary differential equation. In the subcritical case, we explicitly determine the Martin compactification and Martin kernel for L on the basis of [24]; in particular, the Martin boundary over η is either one point or a compactification of D2, which depends on whether an associated integral near η diverges or converges. From this structure theorem we show a monotonicity property that the Martin boundary over η does not become smaller as the potential term of L1 becomes larger near η.

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Peralta, Andrade Karla Alexandra, and Rojas Marcos Ali Palacio. "Abdominal circumference cut-off point: an overview." Archivos Venezolanos de Farmacología y Terapéutica 41, no. 3 (2022): 299–306. https://doi.org/10.5281/zenodo.6981770.

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Introduction: Obesity is currently considered as a “pandemic” because it is a health challenge both in developed and developing countries, reducing life expectancy by up to 20 years. Abdominal circumference (AC) serves for the diagnosis and prognosis of associations with chronic noncommunicable diseases. Objective: To provide an overview of the cut- off point for AC. Methods: A literature review was performed; the sources of information were Medline, Scopus, Embase, Pubmed, ScienceDirect and Springer Link in Spanish and English, between 2016 and 2021. Results: With the bibliography collected, it can be determined that this anthropometric value reflects clinical usefulness for prognosis and diagnosis. The study showed there is a discrepancy regarding the reference point of the AC between WHO, ATPIII and ALAD. Conclusion: The impact of this review lies in the urgent search for a cut-off point for AC to provide a reference for health personnel in each country.

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Liu, Jian, Hanying Feng, and Xingfang Feng. "Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/603203.

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This paper is concerned with the following second-order three-point boundary value problemu″t+β2ut+λqtft,ut=0,t∈0 , 1,u0=0,u(1)=δu(η), whereβ∈(0,π/2),δ>0,η∈(0,1), andλis a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values ofλby means of the fixed point index theory.

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33

Craig, I. J. D. "The Evolution of Disturbed Neutral Point Equilibria." Publications of the Astronomical Society of Australia 9, no. 2 (1991): 225–28. http://dx.doi.org/10.1017/s1323358000023924.

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AbstractWe consider the linear and non-linear evolution of a perturbed X-type neutral point. A semi-analytic treatment is given for the case of small disturbances of the equilibrium field. This problem admits well defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that the longest lived modes are purely radial and decay of the timescale τ ≈ |ln η| where η defines the resistivity of the coronal plasma. Higher azimuthal modes decay much faster, generally on a fraction (O(m−1)) of the Alfvén timescale for the outer field.We go on to perform finite amplitude calculations that demonstrate the implosive current build-up that precedes the reconnective phase of the relaxation. In general both linear and non-linear studies support the idea of an initial implosive stage which rapidly releases the bulk of the energy associated with arbitrary field disturbances.

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Lin, Xiaojie, and Zhengmin Fu. "Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem." Discrete Dynamics in Nature and Society 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/937670.

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We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problemu‴(t)+λa(t)f(u(t))=0,0<t<1,u(0)=u′(0)=0,u″(1)=∝u″(η), whereλis a positive parameter,∝∈(0,1),η∈(0,1),f:(0,∞)→(0,∞),a:(0,1)→(0,∞)are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

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35

Hirata, Kentaro. "Estimates for the Products of the Green Function and the Martin Kernel." Nagoya Mathematical Journal 188 (December 2007): 1–18. http://dx.doi.org/10.1017/s0027763000009429.

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AbstractLet Ω be a proper subdomain of ℝn, n ≥ 2, and let x0∈ Ω be fixed. By GΩ and KΩ we denote the Green function and the Martin kernel for Ω, respectively. Under a certain assumption on Ω near a boundary point ξ, we show that the product GΩ(x, x0)KΩ(x, ξ) is comparable to |x - ξ|2-n for x in a nontangential cone with vertex at ξ. We also give an estimate for the product KΩ(x, ξ)KΩ(x,η) in a uniform domain, where η is another boundary point.

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Ahmari, Hadi, and Mohammad Chalkesh Amiri. "On the relationship between surface tension and viscosity of fluids." Chemical Engineering Research Bulletin 18, no. 1 (2016): 18. http://dx.doi.org/10.3329/cerb.v18i1.26217.

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<p>Relating surface tension and viscosity of liquids not only is important conceptually but it can also be used to test the validity of some measured data. Schonhorn modified Pelofsky’s equation by introducing the concept of the vapor viscosity η<sub>v</sub> in equilibrium with the liquid, i.e.γ= Aexp(-B/(η<sub>l</sub>-η<sub>v</sub>)) This empirical relation can be applied to both organic and inorganic solutions of pure and mixed components. As surface tension is a strong function of surfactant, they neglected to emphasis that mixed components must not be surface active agents. Both Pelofsky and Schonhorn indicated that A may be an indication of the surface tension of the liquid at the temperature where η=∞. They were not successful in correlating the temperature where and the surface tension at the melting point. In this work, a new empirical equation for relating surface tension and viscosity has been developed, i.e., γ((Tc – Tm)/( Tc – T)) = δ(1-β/η). This equation not only satisfies the extreme conditions but it also reveals a physical concept for δ, that is, it should equal the surface tension at the melting point of the liquid.</p><p>Chemical Engineering Research Bulletin 18(2015) 18-22</p>

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Wang, Ruibo, Lingen Chen, Yanlin Ge, and Huijun Feng. "Optimizing Power and Thermal Efficiency of an Irreversible Variable-Temperature Heat Reservoir Lenoir Cycle." Applied Sciences 11, no. 15 (2021): 7171. http://dx.doi.org/10.3390/app11157171.

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Applying finite-time thermodynamics theory, an irreversible steady flow Lenoir cycle model with variable-temperature heat reservoirs is established, the expressions of power (P) and efficiency (η) are derived. By numerical calculations, the characteristic relationships among P and η and the heat conductance distribution (uL) of the heat exchangers, as well as the thermal capacity rate matching (Cwf1/CH) between working fluid and heat source are studied. The results show that when the heat conductances of the hot- and cold-side heat exchangers (UH, UL) are constants, P-η is a certain “point”, with the increase of heat reservoir inlet temperature ratio (τ), UH, UL, and the irreversible expansion efficiency (ηe), P and η increase. When uL can be optimized, P and η versus uL characteristics are parabolic-like ones, there are optimal values of heat conductance distributions (uLP(opt), uLη(opt)) to make the cycle reach the maximum power and efficiency points (Pmax, ηmax). As Cwf1/CH increases, Pmax-Cwf1/CH shows a parabolic-like curve, that is, there is an optimal value of Cwf1/CH ((Cwf1/CH)opt) to make the cycle reach double-maximum power point ((Pmax)max); as CL/CH, UT, and ηe increase, (Pmax)max and (Cwf1/CH)opt increase; with the increase in τ, (Pmax)max increases, and (Cwf1/CH)opt is unchanged.

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Russell, Christopher M. P., Michael F. Corcoran, Atsuo T. Okazaki, Thomas I. Madura та Stanley P. Owocki. "X-Ray modeling of η Carinae & WR 140 from SPH simulations". Proceedings of the International Astronomical Union 6, S272 (2010): 630–31. http://dx.doi.org/10.1017/s1743921311011641.

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AbstractThe colliding wind binary (CWB) systems η Carinae and WR140 provide unique laboratories for X-ray astrophysics. Their wind-wind collisions produce hard X-rays that have been monitored extensively by several X-ray telescopes, including RXTE. To interpret these RXTE X-ray light curves, we apply 3D hydrodynamic simulations of the wind-wind collision using smoothed particle hydrodynamics (SPH). We find adiabatic simulations that account for the absorption of X-rays from an assumed point source of X-ray emission at the apex of the wind-collision shock cone can closely match the RXTE light curves of both η Car and WR140. This point-source model can also explain the early recovery of η Car's X-ray light curve from the 2009.0 minimum by a factor of 2-4 reduction in the mass loss rate of η Car. Our more recent models account for the extended emission and absorption along the full wind-wind interaction shock front. For WR140, the computed X-ray light curves again match the RXTE observations quite well. But for η Car, a hot, post-periastron bubble leads to an emission level that does not match the extended X-ray minimum observed by RXTE. Initial results from incorporating radiative cooling and radiative forces via an anti-gravity approach into the SPH code are also discussed.

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39

GOMAA, ADEL MAHMOUD. "ON THE SOLUTION SETS OF FOUR-POINT BOUNDARY VALUE PROBLEMS FOR NONCONVEX DIFFERENTIAL INCLUSIONS." International Journal of Geometric Methods in Modern Physics 08, no. 01 (2011): 23–37. http://dx.doi.org/10.1142/s021988781100494x.

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We consider the multivalued problem [Formula: see text] under four boundary conditions u(0) = x0, u(η) = u(θ) = u(T) where 0 < η < θ < T and for F is a multifunctions from [0, T] × ℝn × ℝn to the nonempty compact subsets of ℝn not necessary convex. We give a lemma which is useful in the study of four boundary problems for the differential equations and the differential inclusions. Further we have results that improve earlier theorems.

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WYPER, PETER F., та REKHA JAIN. "Torsional magnetic reconnection: The effects of localizing the non-ideal (ηJ) term". Journal of Plasma Physics 77, № 6 (2011): 843–55. http://dx.doi.org/10.1017/s0022377811000262.

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AbstractMagnetic reconnection in three dimensions (3D) is a natural extension from X-point reconnection in two dimensions. Of central importance in the 3D process is a localized non-ideal region within which the plasma and magnetic field decouple allowing for field line connectivity change. In practice, localized current structures provide this localization; however, mathematically a similar effect can be achieved with the localization of plasma resistivity instead. Physically though, such approaches are unrealistic, as anomalous resistivity requires very localized currents. Therefore, we wish to know how much information is lost in localizing η instead of current? In this work we develop kinematic models for torsional spine and fan reconnection using both localized η and localized current and compare the non-ideal flows predicted by each. We find that the flow characteristics are dictated almost exclusively by the form taken for the current profile with η acting only to scale the flow. We do, however, note that the reconnection mechanism is the same in each case. Therefore, from an understanding point of view, localized η models are still important first steps into exploring the role of non-ideal effects.

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41

Nishiyama, Yoshihiro. "Transverse-field XY spin chain with the competing long-range interactions: multi-criticality around the XX-symmetric point." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 8 (2023): 083102. http://dx.doi.org/10.1088/1742-5468/aceb55.

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Abstract The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1 / r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transverse-field-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY-anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ F . Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XX-symmetric point in a systematic manner. As a preliminary survey, with η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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Li, Zuxiong, Shengnan Fu, Huili Xiang, and Hailing Wang. "Qualitative Analysis of a Single-Species Model with Distributed Delay and Nonlinear Harvest." Mathematics 9, no. 20 (2021): 2560. http://dx.doi.org/10.3390/math9202560.

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In this paper, a single-species population model with distributed delay and Michaelis-Menten type harvesting is established. Through an appropriate transformation, the mathematical model is converted into a two-dimensional system. Applying qualitative theory of ordinary differential equations, we obtain sufficient conditions for the stability of the equilibria of this system under three cases. The equilibrium A1 of system is globally asymptotically stable when br−c>0 and η<0. Using Poincare-Bendixson theorem, we determine the existence and stability of limit cycle when br−c>0 and η>0. By computing Lyapunov number, we obtain that a supercritical Hopf bifurcation occurs when η passes through 0. High order singularity of the system, such as saddle node, degenerate critical point, unstable node, saddle point, etc, is studied by the theory of ordinary differential equations. Numerical simulations are provided to verify our main results in this paper.

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Rao, Sabbavarapu Nageswara. "Multiplicity of Positive Solutions for Fractional Differential Equation withp-Laplacian Boundary Value Problems." International Journal of Differential Equations 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/6906049.

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We investigate the existence of multiple positive solutions of fractional differential equations withp-Laplacian operatorDa+β(ϕp(Da+αu(t)))=f(t,u(t)), a<t<b,uja=0, j=0,1,2,…,n-2,u(α1)(b)=ξu(α1)(η),ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), whereβ∈(1,2],α∈(n-1,n], n≥3,ξ∈(0,∞),η∈(a,b),β1∈(0,1],α1∈{1,2,…,α-2}is a fixed integer, andϕp(s)=|s|p-2s, p>1, ϕp-1=ϕq, (1/p)+(1/q)=1, by applying Leggett–Williams fixed point theorems and fixed point index theory.

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Salem, Ahmed, and Aeshah Al-Dosari. "Hybrid Differential Inclusion Involving Two Multi-Valuedoperators with Nonlocal Multi-Valued Integral Condition." Fractal and Fractional 6, no. 2 (2022): 109. http://dx.doi.org/10.3390/fractalfract6020109.

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The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition η(0)∈∫0σΔs,η(s)ds, where Δ is a multi-valued map. Relative compactness of the set ∫0σΔs,η(s)ds in L2(0,ε),R is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.

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I. Sabri, Raghad, та Buthainah A. Ahmed. "Best Proximity Point Results for Generalization of α ̌–η ̌ Proximal Contractive Mapping in Fuzzy Banach Spaces". Indonesian Journal of Electrical Engineering and Computer Science 28, № 3 (2022): 1451. http://dx.doi.org/10.11591/ijeecs.v28.i3.pp1451-1462.

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<p>The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems provide an approximate solution to the fixed-point equation Tҳ = ҳ. It is used to solve the problem to determine an approximate solution that is optimum. The main goal of this paper is to present new types of proximal contraction for nonself mappings in a fuzzy Banach space. At first, the notion of the best proximity point is presented. We introduce the notion of α ̌–η ̌-β ̌ proximal contractive. After that, the best proximity point theorem for such type of mappings in a fuzzy Banach space is proved. In addition, the concept of α ̌–η ̌-φ ̌ proximal contractive mapping is presented in a fuzzy Banach space and under specific conditions, the best proximity point theorem for such type of mapping is proved. Additionally, some examples are supplied to show the results' applicability.</p>

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Lafuente, Miguel, Raúl Gouet, F. Javier López, and Gerardo Sanz. "Near-Record Values in Discrete Random Sequences." Mathematics 10, no. 14 (2022): 2442. http://dx.doi.org/10.3390/math10142442.

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Given a sequence (Xn) of random variables, Xn is said to be a near-record if Xn∈(Mn−1−a,Mn−1], where Mn=max{X1, …, Xn} and a>0 is a parameter. We investigate the point process η on [0,∞) of near-record values from an integer-valued, independent and identically distributed sequence, showing that it is a Bernoulli cluster process. We derive the probability generating functional of η and formulas for the expectation, variance and covariance of the counting variables η(A),A⊂[0,∞). We also derive the strong convergence and asymptotic normality of η([0,n]), as n→∞, under mild regularity conditions on the distribution of the observations. For heavy-tailed distributions, with square-summable hazard rates, we prove that η([0,n]) grows to a finite random limit and compute its probability generating function. We present examples of the application of our results to particular distributions, covering a wide range of behaviours in terms of their right tails.

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Anwar, Sanam, Bushra Aleem, Hajir H. Rashid, and Ghadeer J. Moslhey. "Which is a better marker for overweight: waist height ratio or waist circumference?" International Journal of Research in Medical Sciences 7, no. 2 (2019): 462. http://dx.doi.org/10.18203/2320-6012.ijrms20190354.

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Background: The global prevalence of obesity has been increasing. Body mass index, waist circumference and waist height ratio have been widely used for nutritional assessment. Waist height ratio has the advantage of taking into account abdominal obesity as well as height associated with body fat accumulation or distribution. The objective of this study was to suggest cut off points for waist circumference and waist height ratio to identify overweight in Omani adults.Methods: Weight, height, waist circumference and waist height ratio were measured for all participants. Pearson’s correlation was used to determine correlation of BMI with waist circumference and waist height ratio. ROC curve was used to identify AUC and specific cut off point for anthropometric indicators.Results: The largest proportion of overweight was picked up by waist height ratio across both the genders. Correlation of BMI with waist height ratio was stronger (r=0.699) than correlation with waist circumference (r=0.589) for both the genders. Maximum AUC was for waist height ratio in males (AUC=0.833, 95% CI=0.791-0.875). The specific cut off point for waist circumference in males and females was 89.5cm and 87.6cm respectively. The specific cut off point for waist height ratio in males and females was 0.53 and 0.57 respectively.Conclusions: Maximum participants were found overweight by waist height ratio followed by waist circumference and the least by BMI. The higher cut off points should be used in this population for identifying overweight people.

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V., Govindan S. Pinelas and N. Gunasekaran. "Generalized U-H stability of cubic mappings." Annals of Communications in Mathematics 3, no. 2 (2020): 152–57. https://doi.org/10.5281/zenodo.10046357.

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In this work, we investigate the generalized Ulam-Hyers stability of the ωdimensional cubic functional equation ℘( Xω κ=1 κκi) = Xω κ=1;κ6=λ6=η ℘(κκκ + λκλ + ηκη) + (3 − n) Xω κ=1;κ6=λ6=η ℘(κκκ + λκλ) + ω 2 − 5ω + 6 2 ωX−1 κ=0 (κ + 1)3℘(κκ + 1) where ω ≥ 4, in Banach spaces using direct and fixed point methods.

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Petwal, Sudheer, Anita Tomar, and Meena Joshi. "On unique and non-unique fixed point in parametric N _b −metric spaces with application." Acta Universitatis Sapientiae, Mathematica 14, no. 2 (2022): 278–307. http://dx.doi.org/10.2478/ausm-2022-0019.

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Abstract We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and η b −regularity in parametric N b -metric spaces to determine a unique fixed point, a unique fixed circle, and a greatest fixed disc. Further, we investigate the geometry of non-unique fixed points of a self mapping and demonstrate by illustrative examples that a circle or a disc in parametric N b −metric space is not necessarily the same as a circle or a disc in a Euclidean space. Obtained outcomes are extensions, unifications, improvements, and generalizations of some of the well-known previous results. We provide non-trivial illustrations to exhibit the importance of our explorations. Towards the end, we resolve the system of linear equations to demonstrate the significance of our contractions in parametric N b −metric space.

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Sitthiwirattham, Thanin, Jessada Tariboon, and Sotiris K. Ntouyas. "Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions." Discrete Dynamics in Nature and Society 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/104276.

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We consider a discrete fractional boundary value problem of the formΔαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T]ℕ0:={0,1,…,T}, u(α-2)=0, u(α+T)=Δ-βu(η+β),where1<α≤2,β>0,η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, andf:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝis a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.

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