Extremal Solutions Research Articles

Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative

Abstract This manuscript is committed to deal with the existence and uniqueness of positive solutions for fractional relaxation equation involving ψ-Caputo fractional derivative. The existence of solution is carried out with the help of Schauder’s fixed point theorem, while the uniqueness of the solution is obtained by applying the Banach contraction principle, along with Bielecki type norm. Moreover, two explicit monotone iterative sequences are constructed for the approximation of the extreme positive solutions to the proposed problem. Lastly, two examples are presented to support the obtained results.

Evaluating environmental and economic trade-offs in cattle feed strategies using multiobjective optimization

CONTEXTReducing livestock greenhouse gas (GHG) emissions is now central to sustainable agricultural production strategies. Feedlot systems are a significant part of the production process in many countries, and associated feeding plans can influence product emission intensity significantly. Feed formulation can be used to target several objectives including animal productive performance, direct emissions from enteric fermentation and manure decomposition, and pre-farm gate emissions associated with the feed life cycles. OBJECTIVETo explore the environmental and economic trade-offs in feed formulation for beef cattle using multiobjective optimization. METHODSWe develop a multiobjective model to derive the efficient frontier between profit maximization and environmental impact minimization in diet formulation for beef cattle in a typical French feedlot system. The nonlinear profit function includes animal performance, animal selling price, and feeding costs. The environmental impact accounts for the feed ingredient life cycles (non-renewable energy consumption, phosphorus demand, soil acidification, soil eutrophication, climate change potential, and land requirement), and for methane and nitrous oxide emissions from enteric fermentation and manure decomposition. The model is solved using a combination of optimization methods and for two scenarios with different weights representing the environmental impacts: a low carbon scenario (minimizing only CO2eq emissions), and a balanced impacts scenario (minimizing the sum of impacts with an arbitrary choice of weights derived from the literature). RESULTS AND CONCLUSIONSWe show that optimal cost-effective mitigation arises from a combined strategy, concurrently: increasing animal performance by 20% and reducing daily emissions from the feed life cycle by 50% and from enteric fermentation and manure decomposition emissions by 43%. With this strategy, both scenarios present similar maximum GHG reduction in the feedlot phase – around 42% compared to the maximum-profit solution. The similar behaviour of both scenarios shows that environmental impact transference only occurs in more extreme solutions. Finally, about 50% of the total potential reduction can be achieved at a cost of 22 € / kg CO2eq / kg CWE. SIGNIFICANCEResults suggest that significant GHG emissions reduction can be obtained solely from manipulating animal diets. Achieving these reductions cost-effectively derives from a combination of well-known strategies rather than focusing on any one individually.

Pointwise Remez inequality

The standard well-known Remez inequality gives an upper estimate of the values of polynomials on [-1,1] if they are bounded by 1 on a subset of [-1,1] of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded by 1 on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik–Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.

Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ−Caputo Fractional Boundary Value Problem

The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ. Our main results are obtained by applying the monotone iterative technique combined with the method of upper and lower solutions. Further, we consider three cases for ψ*(t) as t, Caputo, 2t, t, and Katugampola (for ρ=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.

A Two-Stage Cooperative Evolutionary Algorithm With Problem-Specific Knowledge for Energy-Efficient Scheduling of No-Wait Flow-Shop Problem.

Green scheduling in the manufacturing industry has attracted increasing attention in academic research and industrial applications with a focus on energy saving. As a typical scheduling problem, the no-wait flow-shop scheduling has been extensively studied due to its wide industrial applications. However, energy consumption is usually ignored in the study of typical scheduling problems. In this article, a two-stage cooperative evolutionary algorithm with problem-specific knowledge called TS-CEA is proposed to address energy-efficient scheduling of the no-wait flow-shop problem (EENWFSP) with the criteria of minimizing both makespan and total energy consumption. In TS-CEA, two constructive heuristics are designed to generate a desirable initial solution after analyzing the properties of the problem. In the first stage of TS-CEA, an iterative local search strategy (ILS) is employed to explore potential extreme solutions. Moreover, a hybrid neighborhood structure is designed to improve the quality of the solution. In the second stage of TS-CEA, a mutation strategy based on critical path knowledge is proposed to extend the extreme solutions to the Pareto front. Moreover, a co-evolutionary closed-loop system is generated with ILS and mutation strategies in the iteration process. Numerical results demonstrate the effectiveness and efficiency of TS-CEA in solving the EENWFSP.

Extremal Solutions for Caputo Conformable Differential Equations with p-Laplacian Operator and Integral Boundary Condition

The Caputo conformable derivative is a new Caputo-type fractional differential operator generated by conformable derivatives. In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. We also establish two comparison principles and prove the extremal solutions for nonlinear fractional p -Laplacian differential system with Caputo conformable derivatives by utilizing the monotone iterative technique. An example is given to verify the validity of the results.

Monotone iterative method for nonlinear fractional p‐Laplacian differential equation in terms of ψ‐Caputo fractional derivative equipped with a new class of nonlinear boundary conditions

The aim of this paper is to deal with the existence of extremal solutions for a novel class of nonlinear fractional p‐Laplacian differential equation in terms of ψ‐Caputo fractional derivative equipped with a new class of nonlinear boundary conditions. Initially, we focus on the linear problem and we give an explicit form of the solutions, from which we derive new comparison results which is crucial for the proof of the main theorem of this paper. Secondly, with the help of the monotone iterative method along with its accompanying upper and lower solutions, the existence of extremal solutions for the aforementioned problem is investigated. Then, based on the proposed method, we can construct two types of successive approximations which converge uniformly monotonically to minimal and maximal solutions of the given problem. Finally, we illustrate our results with an example.

Test, analysis, and design of ovally‐perforated vertically‐flexible steel plate shear wall (OVSPW)

AbstractA new type of steel plate shear wall (SPSW) with oval‐curved architectural openings and vertically flexible horizontal connection elements is proposed. The vertical flexibility of the wall accommodates the construction settlement introduced by column contraction under the dead loads of the upper stories and allows sequential installation from the lower stories. A quasi‐static cyclic loading test and finite element (FE) analysis verified the stable seismic behaviors of the ovally‐perforated vertically‐flexible steel plate shear wall (OVSPW). The results of FE parametric analysis showed that an OVSPW with an appropriate thickness of boundary elements effectively accommodated the construction settlement that could lead to large in‐plane compression for a conventional SPSW. The horizontal connection elements made of steel tubes realized the vertical stiffness of OVSPW to less than 2% of the original value without changing the lateral stiffness. New design equations of the OVSPW were derived through integral and extreme value solutions to predict the mechanical behavior of OVSPW.

The topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We investigate the large-N asymptotics of the topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of mathcal{N} = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual mathcal{N} = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

Transversality conditions for the existence of solutions of first-order discontinuous functional differential equations

We are concerned with the existence of extremal solutions to a large class of first-order functional differential problems under weak regularity assumptions. Our technique involves multivalued analysis and the method of lower and upper solutions in order to obtain a new existence result to a scalar Cauchy problem. As a consequence of this result and a monotone iterative method for discontinuous operators, we derive our main existence result which is illustrated by several examples concerning well-known models: a generalized logistic equation or second-order problems in the presence of dry friction.

Die „Magie des Extrems“ in philosophischen Neuorientierungen. Nietzsches neue extreme Problemstellungen und -lösungen und das alte Beispiel des Sokrates

Abstract The later Nietzsche developed the “magic of the extreme” as a special strategy in order to make his philosophical reorientations successful. He needed this strategy not only to be heard at all; also the problems he faced called for it. The article first gives an overview of the most important problems Nietzsche coped with and the extreme solutions he offered. Then, we show how, according to Nietzsche, even Socrates, who stands for the beginning of the European Enlightenment, used the “magic” of extreme irritation and fascination to get this Enlightenment on its way.

Abstract P368: Caveolin-3 Prevents Swelling-induced Cell Lysis Via Regulation Of I Cl,swell Expression And Activity

Background: Caveolae membrane structures harbor mechanosensitive chloride channels (MCCs) which form a swelling-activated chloride current ( I Cl,swell ) and play an important role in cell volume regulation and mechano-electrical signal transduction. However, the role of muscle-specific caveolar scaffolding protein caveolin-3 (Cav3) in regulation of MCCs expression, activity, and contribution to cell viability in response to mechanical stress remains unclear. We hypothesized that Cav3-based mechano-protection is enabled by complimentary expression of MCCs. Methods and Results: Experiments were performed on native (Cav3-) and Cav3-transfected (Cav3+) HEK-293 cells. Cell stretch was mimicked by light (220 mOsM) or extreme hypoosmotic swelling (<20mOsM). Cav3+ HEK-293 cells were significantly resistant to extreme hypotonic solutions (15 minute incubation) compared to Cav3- HEK-293 cells, and this mechano-protection was significantly reduced when exposed to I Cl,swell selective inhibitor DCPIB (1 μM). We found that three MCCs (ClC-2, ClC-3, and SWELL1, also known as LRRC8A) contain caveolin-binding motifs in their structure, indicating their possible localization in caveolae structures. Co-IP analysis confirmed association of SWELL1 with Cav3. Interestingly, Cav3+ HEK-293 cells showed a significant (by 2-fold) increase of SWELL1 protein level, while ClC-2/3 protein levels remained unchanged. This was accompanied by a 2-fold increase of I Cl,swell , but no change in mRNA expression levels. FRET analysis showed a <10 nm membrane and intracellular association between Cav3 and tested MCCs. Furthermore, Cav3/SWELL1 membrane FRET efficiency was halved in light hypoosmotic solution, as well as after disruption of caveolae structures via cholesterol depletion by 1-hour treatment with 10 μM methyl-β-cyclodextrin. Cav3/ClC-2/3 average membrane FRET efficiency remained unchanged in hypotonic solution. Conclusions: We concluded that of MCCs tested, SWELL1 abundance and activity is regulated by Cav3 and that their association relies on membrane tension and caveolae integrity. The present study highlights the mechano-protective properties of Cav3 which are partially facilitated by complimentary SWELL1 expression and activity.

Die „Magie des Extrems“ in philosophischen Neuorientierungen. Nietzsches neue extreme Problemstellungen und -lösungen und das alte Beispiel des Sokrates

Abstract The later Nietzsche developed the “magic of the extreme” as a special strategy in order to make his philosophical reorientations successful. He needed this strategy not only to be heard at all; also the problems he faced called for it. The article first gives an overview of the most important problems Nietzsche coped with and the extreme solutions he offered. Then, we show how, according to Nietzsche, even Socrates, who stands for the beginning of the European Enlightenment, used the “magic” of extreme irritation and fascination to get this Enlightenment on its way.

Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

US COVID-19 EXAM FAILURE MAKES WORLD LEERY ABOUT AMERICAN EXCEPTIONALISM AND LEADERSHIP

For a newbie in the USA, heath care, education, science and economy are presented as exceptional; the best of the world, but these nice words are not backed by reality, and it is hard to openly talk about these issues as they turn into an inconvenient truth, and the fact that truth is anti-American and anti-human makes it more difficult to correct the problems, as it turns difficult to openly acknowledge the issues and look for solutions. Trump and revealed a bunch of American truths, removed the of kindness and exceptionalism, and put in the limelight a lot of inconvenient realities of the actual USA, a country ideologically divided and under Lord , a nation sunk in alternate realities and facts, with a political leadership inept for progress. Looking to understand why this aberrant behavior in front of SARS-CoV-2 pandemic, we discovered that the F++ grade USA obtained at this “ecologic” exam, is routed in education of the last 50 years, that produced such population with very low real IQ, but loud arrogant and oblivious of their situation, with little respect for reality and knowledge.
 From the education stand point, the thinks appear even more complicated, because failures in education are routed in society, and the education system produced exactly what society asked and paid for, everything becoming a “chicken or egg” problem, under “what to solve first” dilemma
 The present research was looking to find an answer to this very complex problem, at minimum to openly list the issues, and propose idealistic solutions, looking to become a wake-up moment not only for the USA but for many other nations which are confronted with the same issues, of a decadent democracy and consumerist economy, without pleading for extreme left solution manifested autocratic regimes.

Approaching the social dilemma of autonomous vehicles with a general social welfare function

We consider the social dilemma related to the trolley problem in ethics regarding the driving behavior of an autonomous vehicle (AV) when there are passengers in the AV and pedestrians on the street. To investigate the optimal driving behaviors in different concepts of values, we introduce a general social welfare function (SWF) into our model that encompasses the three types of Bentham- (ρ=0), Nash- (ρ→1), and Rawls-type (ρ→∞) SWFs as a special case. Parameter ρ is key and represents the inequality aversion. We first demonstrate that the optimal solution continuously and monotonically moves from ρ=0 to ρ→∞. This result implies that the optimal solutions involving the Bentham- and Rawls-type SWFs are extreme (maximum or minimum value) solutions, whereas solutions involving the Nash-type SWF can be intermediate. Although some empirical studies have stated that it is better for a policymaker or AV manufacturer to employ Benthamism, our results suggest that care should be applied when choosing a driving behavior. Second, if the total utility of the passengers (or pedestrians) at the optimum is relatively large, our results indicate that the AV will likely go straight and hit the pedestrians (or swerve and crash into a wall) as ρ increases (or decreases). Finally, we discuss the applicability of our results in controlling AVs worldwide. We confirm that setting ρ=0 is preferred in the U.S., Canada, Australia, and some Western European countries, whereas setting ρ>0 is preferred in some African and Asian countries, such as China, India, and Japan.

On a class of nonlinear nonlocal fractional differential equations

We investigate the existence of extremal solutions for a class of fractional differential equations in the area of fluid dynamics. By establishing a new comparison theorem and applying the classical monotone iterative approach, we establish sufficient conditions to ensure the existence of the extremal solutions and construct twin convergent monotone explicit iterative schemes. Generalized nonlinear nonlocal Bagley-Torvik equation and generalized Basset equation with nonlinear source functions are some special cases of our discussed problem.

Gravitational perturbations from NHEK to Kerr

We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS2 holography.

Nonlinear fractional differential equations with advanced arguments

In this paper, we develop the existence and uniqueness theory of fractional differential equation involving Riemann-Liouville differential operator of order $0 < alpha< 1$, with advanced argument and integral boundary conditions. We investigate the uniqueness of the solution by using Banach fixed point theorem, we apply the comparison result to obtain the existence and uniqueness of solution by monotone iterative technique also by using weakly coupled extremal solution for the nonlinear boundary value problem (BVP). As an application of this technique, existence and uniqueness results are obtained.

Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

Abstract Our purpose of this paper is to study positive solutions of Lane-Emden equation − Δ u = V u p i n R N ∖ { 0 } $$\begin{array}{} -{\it\Delta} u = V u^p\quad {\rm in}\quad \mathbb{R}^N\setminus\{0\} \end{array}$$ (0.1) perturbed by a non-homogeneous potential V when p ∈ [ p c , N + 2 N − 2 ) , $\begin{array}{} p\in [p_c, \frac{N+2}{N-2}), \end{array}$ where pc is the Joseph-Ludgren exponent. When p ∈ ( N N − 2 , p c ) , $\begin{array}{} p\in (\frac{N}{N-2}, p_c), \end{array}$ the fast decaying solution could be approached by super and sub solutions, which are constructed by the stability of the k-fast decaying solution wk of −Δ u = up in ℝ N ∖ {0} by authors in [9]. While the fast decaying solution wk is unstable for p ∈ ( p c , N + 2 N − 2 ) , $\begin{array}{} p\in (p_c, \frac{N+2}{N-2}), \end{array}$ so these fast decaying solutions seem not able to disturbed like (0.1) by non-homogeneous potential V. A surprising observation that there exists a bounded sub solution of (0.1) from the extremal solution of − Δ u = u N + 2 N − 2 $\begin{array}{} -{\it\Delta} u = u^{\frac{N+2}{N-2}} \end{array}$ in ℝ N and then a sequence of fast decaying solutions and slow decaying solutions could be derived under appropriated restrictions for V.