On the environmental zero-point problem in microevolutionary climate response predictions

It is well documented that populations adapt to climate change by means of phenotypic plasticity, but few reports on adaptation by means of genetically based microevolution caused by selection. Disentanglement of these separate effects requires that the environmental zero-point is defined, and this should not be done arbitrarily. Together with parameter values, the zero-point can be estimated from environmental, phenotypic and fitness data. A prediction error method for this purpose is described, with the feasibility shown by simulations. An estimated environmental zero-point may have large errors, especially for small populations, but may still be a better choice than use of an initial environmental value in a recorded time series, or the mean value, which is often used. Another alternative may be to use the mean value of a past and stationary stochastic environment, which the population is judged to have been fully adapted to, in the sense that the mean fitness was at a global maximum. An exception is here cases with constant phenotypic plasticity, where the microevolutionary change per generation follows directly from phenotypic and environmental data, independent of the chosen environmental zero-point.

Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

The ordered implicit relations and related fixed point problems in the cone $ b $-metric spaces

<abstract><p>In this paper, we introduce an ordered implicit relation. We present some examples for the illustration of the ordered implicit relation. We investigate conditions for the existence of the fixed points of an implicit contraction. We obtain some fixed point theorems in the cone $ b $-metric spaces and hence answer a fixed-point problem. We present several examples and consequences to explain the obtained theorems. We solve an homotopy problem and show existence of solution to a Urysohn Integral Equation as applications of the obtained fixed point theorem.</p></abstract>

Analisis Butir Soal Ulangan Semester Ganjil Mata Pelajaran Matematika Kelas VIII SMP

This study aims to know the quality of Grain Analysis of Odd Semester Test Questions Of Mathematics Subjects Grade VIII at State Junior High School 1 Kediri In The Academic Year 2018/2019 which is reviewed in terms of Validity, Reliability, Difficulty Level, Differentiating Power, and Effectiveness of Phishing. This is a descriptive research. The result of this research shows that: in terms of Validity, the amount of valid questions up to 14 points of the question (70%) and invalid question are up to 6 points of question (30%); in terms of Reliability, including questions that have high reliability is with a coefficient 0.79; in terms of Difficulty Level, the number of questions that are include in the difficult categorythere are 2 points (10%), which belongs to the moderate category there are 17 items (85%), and include in easy category there is 1 item(5%); in terms of Differentiating power, the number of problems categorized as very bad as 1 item (5%), bad category as much as 1 item (5%), categorized enough as many as 9 points (45%), good category as much as 6 items (30%) and very high category 3 items (15%); reviewed in terms of Effectiveness of phishing, there are 15 points of question (75%) with excellent outwits, 5 points of question (25%) with a good phishing, 0 point problem (0%) with a less bad phishing and with a bad phishing 0 point problem (0%).

Cyclic Mappings and Further Results in B-Metric-Like Spaces

Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.

A Class of Recursive Optimal Stopping Problems with Applications to Stock Trading

In this paper, we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multidimensional Markovian setting, we show that the problem is well posed in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues, and we determine the optimal stopping rule in that case.

On Mann-Type Subgradient-like Extragradient Method with Linear-Search Process for Hierarchical Variational Inequalities for Asymptotically Nonexpansive Mappings

We propose two Mann-type subgradient-like extra gradient iterations with the line-search procedure for hierarchical variational inequality (HVI) with the common fixed-point problem (CFPP) constraint of finite family of nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. Our methods include combinations of the Mann iteration method, subgradient extra gradient method with the line-search process, and viscosity approximation method. Under suitable assumptions, we obtain the strong convergence results of sequence of iterates generated by our methods for a solution to HVI with the CFPP constraint.