Extremal Solutions Research Articles

Estimating the Spin of the Black Hole Candidate MAXI J1659-152 with the X-Ray Continuum-fitting Method

Abstract As a transient X-ray binary, MAXI J1659-152 contains a black hole candidate as its compact star. MAXI J1659-152 was discovered on 2010 September 25 during its only known outburst. Previously published studies of this outburst indicate that MAXI J1659-152 may have an extreme retrograde spin, which, if confirmed, would provide an important clue as to the origin of black hole spin. In this paper, utilizing updated dynamical binary system parameters (i.e., the black hole mass, the orbital inclination, and the source distance) provided by Torres et al., we analyze 65 spectra of MAXI J1659-152 from RXTE/PCA, in order to assess the spin parameter. With a final selection of nine spectra matching our f sc ≲ 25%, soft state criteria, we apply a relativistic thin disk spectroscopic model kerrbb2 over 3.0–45.0 keV. We find that inclination angle correlates inversely with spin, and, considering the possible values for inclination angle, we constrain spin to be −1 < a * ≲ 0.44 at a 90% confidence interval via X-ray continuum fitting. We can only rule out an extreme prograde (positive) spin. We confirm that an extreme retrograde solution is possible and is not ruled out by considering accretion torques given the young age of the system.

Biomineralization-mimetic growth of ultrahigh-load metal-organic frameworks on inert glass fibers to prepare hybrid membranes for collecting organic hazards in unconventional environment

• Pristine and ultrahigh-load metal-organic frameworks on inert glass fibers. • Hybrid membranes to collect organic hazardous substances in unconventional environs. • Presented ultrahigh-adsorption abilities to substances that included dyes and antibiotics. • Extraordinary robustness to high temperature, organic solvent, extreme alkaline solution. • Suitable for difficult environments, satisfactory recycling, and long-term operation abilities. Exploring new membrane matrices with demanding functions but inert surficial properties to prepare hybrid membranes is challenging. Inspired by biomineralization, we proposed a strategy to grow pristine and ultrahigh-load metal-organic frameworks (MOFs) on inert glass fibers (GF) to prepare GF@MOFs (ZIF-8) hybrid membranes to efficiently collect organic hazardous substance in conventional and unconventional solutions. Comparing with the poor coverage of the MOFs using the conventional method, this new method induced an ultra-high load of MOFs, and even interesting intergrown-particle-, sheet-flower-, and grain-like shapes. The GF@ZIFs exhibited adsorbability of malachite green up to 3964.8 mg g −1 , whereas that of the reported analogues only reached 1667 mg g −1 . The hybrid membranes also exhibited adsorption capability of 192.2 mg g −1 to tetracycline. More importantly, having benefited from the introduction of robust GF matrices, the robustness of the GF@ZIFs was significantly enhanced: synergetic effect derived from the GF and MOFs could be observed. Furthermore, all three types of GF@ZIFs presented well-maintained performance in 70-°C hot water, chloroform, and pH 14 NaOH solution, which are generally nonadoptive to conventional hybrid membranes. The GF@ZIF membranes were further developed as a filter device for rapid collection of over 95% malachite green (50 mg L −1 , 10 mL) in 1 h. The proposed method could create a new direction for exploring new types of matrices to fabricate hybrid materials.

A superhydrophobic TPU/CNTs@SiO2 coating with excellent mechanical durability and chemical stability for sustainable anti-fouling and anti-corrosion

Superhydrophobic materials have attracted widespread attention due to their unique anti-accretion performance to different contaminants. Over the years, numerous superhydrophobic surfaces have been designed and examined. However, most of them still suffer from the weaknesses of fragile mechanical durability and poor chemical stability, which present serious limitations to their practical applications. In this study, we prepared SiO2 particles in-situ grown on the surface of carbon nanotubes (CNTs) using tetraethyl orthosilicate (TEOS). The CNTs@SiO2 composite particles were then modified with perfluorodecyltrimethoxysilane and dispersed in thermoplastic polyurethane (TPU) matrix to obtain a superhydrophobic TPU/CNTs@SiO2 composite coating. Due to the multi-level micro/nanostructures of the CNTs@SiO2 particles and their strong bonding with TPU, the coating has excellent mechanical durability and maintains superhydrophobicity after sandpaper abrasion or tape peeling. In addition, the micro/nanostructures on the coating surface can trap air in the surface pores and thus has prevented the penetration of H+, Na+, Cl-, SO42- and OH− in liquids, leading to excellent chemical stability under extreme solution environment. The coating also has excellent self-cleaning and anti-fouling properties and expected to have great potentials in various industrial fields.

Existence and extremal solutions in Banach algebras for a fractional order differential equation

Existence and extremal solutions in Banach algebras for a fractional order differential equation

Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases

Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases

Some qualitative properties of solutions to a nonlinear fractional differential equation involving two $ \Phi $-Caputo fractional derivatives

<abstract><p>The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function $ \Phi $. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the $ \Phi $-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results.</p></abstract>

On the extremal solutions of superlinear Helmholtz problems

Abstract: In this note, we deal with the Helmholtz equation −∆u+cu = λf(u) with Dirichlet boundary condition in a smooth bounded domain Ω of R n , n > 1. The nonlinearity is superlinear that is limt−→∞ f(t) t = ∞ and f is a positive, convexe and C 2 function defined on [0,∞). We establish existence of regular solutions for λ small enough and the bifurcation phenomena. We prove the existence of critical value λ ∗ such that the problem does not have solution for λ > λ∗ even in the weak sense. We also prove the existence of a type of stable solutions u ∗ called extremal solutions. We prove that for f(t) = e t , Ω = B1 and n ≤ 9, u ∗ is regular.

Extreme and moderate solutions of nonoscillatory second order half-linear differential equations

An existence and asymptotic theory is built for second order half-linear differential equations of the form $${\rm (A)}\qquad (p(t)|x^{\prime }|^\alpha {\rm sgn} \,x^{\prime })^{\prime } =q(t)|x|^\alpha {\rm sgn}\, x, \quad t \geq a \gt 0, $$ where $\alph

The method of lower and upper solutions for Sobolev type Hilfer fractional evolution equations

The purpose of this paper is concerned with the existence of extremal mild solutions for Sobolev type Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach spaces E. By using monotone iterative technique coupled with the method of lower and upper solutions, with the help of the theory of propagation family as well as the theory of the measure of noncompactness and Sadovskii?s fixed point theorem, we obtain some existence results of extremal mild solutions for Hilfer fractional evolution equations. Finally, an example is provided to show the feasibility of the theory discussed in this paper

Terraforming the earth

As Net Zero technology is a current hot topic in the engineering industry, our resident sci-fi author Gareth L. Powell takes a look at some more extreme solutions to the climate crisis.

Existence of solutions for fractional differential equation with periodic boundary condition

<abstract><p>We investigate the existence of solutions for a Caputo fractional differential equation with periodic boundary condition. Using the positivity of Green's function of the corresponding linear equation, we show the existence of positive solutions by using Krasnosel'skii fixed point theorem. Meanwhile, by using monotone iterative method and lower and upper solutions method, we also discuss the existence of extremal solutions for a special case.</p></abstract>

Existence of solutions of an impulsive integro-differential equation with a general boundary value condition

<abstract><p>In this paper, we discuss the existence of solutions for a first-order nonlinear impulsive integro-differential equation with a general boundary value condition. New comparison principles are developed, and existence results for extremal solutions are obtained using the established principles and the monotone iterative technique. The results are more general than those of the periodic boundary problems, which may be widely applied in this field.</p></abstract>

Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes

Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes

Uticaj Srpske pravoslavne crkve na kamatu u srpskom srednjevekovnom pravu

The loan agreement is a contract with a long and most turbulent history. Friendly loans is existed in every civilization, from the first communities to the present day. Loans with interest, however, are closely scrutinized by almost every legal system. Because these loans are very much open to abuse, governments have almost always had tendencies to prevent such outcomes by limiting interest rates. There are two extreme solutions: allowing high interest rates, as in some ancient legal systems, or as in some modern capitalist systems. On the other side of the spectrum is the suppression of interest as a „root of evil”, i.e. its complete prohibition, as suggested by the Roman Catholic Church or Islam, as well as in the formal socialist states. The Serbian Orthodox Church, as one of the local orthodox Churches, finds itself between these two extreme beliefs. Medieval Serbian states, mostly rooted in the Byzantine version of Roman law, started practicing usurious loans early. Serbian Church, mainly because of Saint Sava (Nemanjić) took a conservative attitude towards interest rates. As the economy grew, the prohibitions seemed to be less and less effective. From the time of emperor Dušan, according to the theory of symphony between the Church and State, middle ground solution was found by: prohibiting the clergy to charge interest; allowing civilians to charge interest, while limiting interest rates.The Serbian Orthodox Church would hold fast to this attitude throughout the Middle Ages, all the way to the present day. Although the Republic of Serbia is a secular state, the clergy obeys the same canonic rules. Interest rates are accordingly regulated and usurious contracts are prohibited.

Multi-valued variational inequalities in unbounded domains: existence, comparison and extremal solutions

In this paper, we study multi-valued quasilinear elliptic variational inequalities of the form in all of as well as in the exterior domain , where is the p-Laplacian, K is a closed convex subset of the Beppo-Levi space with 1<p<N, or with p = N, and is the indicator functional corresponding to K with its subdifferential . The lower order multi-valued operator is generated by a multi-valued, upper semicontinuous function , and the measurable coefficient a is supposed to decay like: Our main goals are as follows. First, we provide a new approach to an existence theory for the above multi-valued variational inequalities in all for 1<p<N as well as in the exterior domain Ω for the borderline case . Second, we establish an enclosure and comparison principle based on appropriately defined sub-supersolutions, and prove the existence of extremal solutions. Third, by means of the sub-supersolution method provided here, we show that certain rather general classes of variational-hemivariational type inequalities turn out to be only subclasses of the above class of multi-valued elliptic variational inequalities. Finally, we apply the abstract theory to a multi-valued obstacle problem.

A noncommutative spacetime realization of quantum black holes, Regge trajectories and holography

It is shown that the radial spectrum associated with a fuzzy sphere in a noncommutative phase space characterized by the Yang algebra, leads exactly to a Regge-like spectrum GMl2=l=1,2,3,…, for all positive values of l, and which is consistent with the extremal quantum Kerr black hole solution that occurs when the outer and inner horizon radius coincide r+=r−=GM. The condition GMl2=l is tantamount to the mass-angular momentum relation Ml2=lMp2 implying a mass-squared quantization in multiples of the Planck-mass-squared. Another important feature (also pointed out by Tanaka) is the holographic nature of these results that are based in recasting the Yang algebra associated with an 8D noncommuting phase space, involving xμ,pν,μ,ν=0,1,2,3, in terms of the undeformed realizations of the Lorentz algebra generators JAB corresponding to a 6D-spacetime, and associated to a 12D-phase-space with coordinates XA,PA;A=0,1,2,…,5. We finalize with a discussion of the noncommuting 3D isotropic and Born oscillators. Finding solutions to these oscillators merit investigation because they introduce explicit dynamics to the quantum black holes. We hope that the findings in this work, relating the Regge-like spectrum l=GM2 and the quantized area of black hole horizons in Planck bits, via the Yang algebra in Noncommutative phase spaces, will help us elucidate some of the impending issues pertaining the black hole information paradox and the role that string theory and quantum information will play in its resolution.

Extremal mild solutions to fractional delay integro-differential equations with non-instantaneous impulses

We study the existence of extremal mild solutions to fractional delay integro-differential equations with non-instantaneous impulses by employing the monotone iterative technique coupled with the method of lower and upper solutions. Our existence results are established by appealing to two different theories. In our first result, the semigroup generated by the linear operator associated with the problem is assumed to be compact. On the other hand, in our second result, the semigroup need not be compact and our conclusions are obtained using the theory of measures of noncompactness. In order to illustrate our results, we also discuss a concrete problem regarding heat conduction in a metal bar with predefined impulsive points.

Rotating 5D black holes: Interactions and deformations near extremality

We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with two equal angular momenta in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS_55 black holes the sign depends on the mass of the extremal solution. We discuss possible interpretations of these corrections from a gravitational and holographic perspective. We also quantify the imprint of the JT sector on the UV region, i.e. how these degrees of freedom, characteristic for the near-horizon region, influence the asymptotically far region of the black hole. This gives an interesting insight on how to interpret the IR modes in the context of their UV completion, which depends on the environment that contains the black hole.

An Evolutionary Multi-objective Approach for Coordinating Supplier–Producer Conflict in Lot Sizing

Context. This paper deals with bilateral joint decision making in supply chains, and more specifically focuses on coordinating the decisions taken by the supplier and the producer in lot sizing. Research gap. Previous existing works in lot sizing have modeled the coordination task as a bi-level optimization problem. Unfortunately, the bi-level model causes a hierarchy between the two actors by making the leader imposing the decisions that suits his/her interests to the follower. This induces a significant conflict of interest between the two stakeholders because the leaders benefit is always greater than the follower’s one. Objective. The main goal of this work is to attenuate the conflict of interest issue between both actors by proposing a multi-objective model that alleviates the hierarchy and creates a win–win situation. Method. We propose an effective multi-objective lot sizing model, called Supplier-Producer Multi-Objective Lot Sizing (SP-MOLS); that alleviates the hierarchy between the actors’ objectives by assigning them the same importance degree and hence optimizing them simultaneously. The resolution of our SP-MOLS model using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), as an effective meta-heuristic search engine, provides a set of trade-off solutions, each expressing a compromise degree between the two actors: the supplier and the producer. Results. To validate our approach, we use five test problems each containing 100 instances with a planning horizon of 10 periods and we analyze the obtained trade-off solutions using the compromise degree and the gap between costs as main consensus metrics. The obtained results reveal that a small sacrifice in the leader’s benefit could produce a significant improvement in the follower’s one. For instance, a 10% increase of the producer’s cost may generate a 42% decrease in the supplier’s one. Reciprocally, a 0.4% increase of the supplier’s cost may generate a 49% decrease in the producer’s cost. Method algorithmic improvement. As solutions of interests for both stakeholders are usually located within the extreme regions of the Pareto front, we propose NSGA-II with Focus on Extreme Regions (NSGA-II-FER) as a new variant of NSGA-II that focuses the search in the extreme regions of the Pareto front thanks to a modified crowding measure that is adaptively managed during the evolution process. This variant has shown its ability to eliminate dominance-resistant solutions and thus to come up with better extreme regions. Based on the experimental results, NSGA-II-FER is shown to have the ability to provide the decision makers with more convergent and more diversified extreme non-dominated solutions, expressing better trade-off degrees between both actors’ costs. Managerial implications. The promising results obtained by our proposal encourage decision makers’ to adopt a multi-objective approach rather than a bi-level one. From our personal perspective, we recommend running the three models (the multi-objective model and the two bi-levels ones); then analyzing the solutions of all models in terms of compromise degrees and logistic costs. This would allow both actors to observe how the hierarchy incurred by the bi-level models increases conflicts, while the multi-objective one generates solutions with much improved consensus degrees. Such observations will convince the supply chain stakeholders to adopt our multi-objective approach, while keeping an eye on the bi-level models’ solutions and the consensus degrees. Finally, we also recommend focusing on the extreme regions of the Pareto front since they contain rich solutions in terms of consensus. Such solutions are more convincing in the negotiation process and thus could lead to better win–win situations.

Finite Element Analysis of the Lower Extrtemity - Hinge Knee Behavior Under Dynamic Load

A key goal of joint endoprosthesis is to become a full-featured functional and anatomical replacement. The joint damage may occur for several reasons - primarily a disease of different nature and magnitude, resulting in gradual and irreversible changes and in an extreme solution in the implantation of artificial joints. However, there should be also mentioned accidents leading to joint destruction, which are often "trigger mechanism" of the disease. This work therefore presents a dynamic computational finite element analysis of a hinge-type knee replacement, which aim to streamline and accelerate the development of knee endoprosthesis. It tackles a question of the overall strength of the implant and detects sites of elevated concentrations of stresses that may be potential sources of implant damages. It also studies the behavior of the endoprosthesis under dynamic loads with emphasis on the study of the shape and size of the contact surfaces, which are closely related to the size of the contact pressure and material wear. Aside the hinged knee replacement, the computational model consisted of femur, fibula, tibia, patella and 25 most important muscles of the lower limb. Due to realistic definition of the boundary conditions, this model is suitable for investigation of invivo knee joint replacement behavior.