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In this study, we compare the different conditions which are used to detect the unique solvability of the absolute value equation (AVE) Ax − B|x| = b. Also, analyzing which condition is more suitable to use according to our problem and later, we will see the advantage and disadvantages of different unique solvability conditions. Further, we take an example where existing conditions are invalid to judge the unique solvability of the AVE. [ABSTRACT FROM AUTHOR]

Most leadership studies primarily focus on formal leaders, often overlooking the influence of leaders within the team. While prior research has shown that peer leaders can have a beneficial impact on various team outcomes, it is yet unclear which peer leadership behaviors precisely foster a supportive and sustainable work environment. Building upon the recent identification of 10 peer leadership roles and 37 underlying functions, the current study aims to investigate the relationships between these peer leadership roles and functions and key outcomes (i.e., job satisfaction, team cohesion, team effectiveness, and OCB). A total of 31 organizational teams, comprising 182 employees from diverse sectors, participated in a quantitative survey. Employing multilevel modeling analysis, the findings demonstrated that each leadership role and nearly every function predicted at least one outcome, highlighting their significance within organizational teams. Additionally, Necessary Condition Analysis revealed that specific roles and functions were necessary for generating one or more outcomes. Finally, we found that most of the significant relationships remained consistent across teams, regardless of their size, tenure, or level of team identification. These findings refine our understanding of shared leadership and how peer leaders can create a sustainable workplace by fostering employee well-being and productivity in organizational teams. [ABSTRACT FROM AUTHOR]

The construction waste recycling (CWR) industry in China is still in the primary stage. Thus, exploring the driving mechanisms of its development has significant theoretical worth and practical significance. Existing studies mainly focused on identifying individual key factors, while paying limited attention to the synergistic effects of multiple factors. The aim of this study is to systematically identify the primary drivers of China's CWR industry from a macro perspective and explore their conjunctional effect on the development of the CWR industry in China. Firstly, based on the PEST model, the key factors driving the development of the CWR industry were identified from political, economic, social, and technological aspects. Secondly, the fuzzy-set Qualitative Comparative Analysis (fsQCA) approach was used to explore the causal relationship between the conjunction of these factors and the development level of the CWR industry. This study yields two interesting conclusions. The first is that none of the political, economic, social, and technological factors is a necessary condition. It means that the absence of any single factor will not restrict the development of the CWR industry. The second reveals two causal paths for the high-level development of the CWR industry, namely, the configuration of policy and social factors and the individual effect of economic factors. High-level development in the CWR industry can drive the sustainable development of the construction sector. [ABSTRACT FROM AUTHOR]

In this paper we consider the multiobjective generalized semi-infinite optimization problems with nondifferentiable convex data, whereas Soroush (Journal of Mathematical Extension 16(9): 1-14, 2022) investigated them in single-objective case. We introduce some upperlevel qualification conditions for the problems, and based on these qualifications, we demonstrate some first-order necessary optimality conditions at weakly efficient and efficient solutions of the considered problem. [ABSTRACT FROM AUTHOR]

A well-known first-order necessary condition for a point to be a local minimizer of a given function is the non-negativity of the dot product of the gradient and a vector in a feasible direction. This paper proposes a series of alternative first-order necessary conditions and corresponding first-order sufficient conditions that seem not to appear in standard texts. The conditions assume a nonzero gradient. The methods use extensions of the notions of gradient, differentiability, and twice differentiability. Examples, including one involving the Karush–Kuhn–Tucker (KKT) theorem, illustrate the scope of the conditions. [ABSTRACT FROM AUTHOR]

All-or-nothing necessary conditions are critical for the unfolding of subsequent entrepreneurial outcomes. A condition is necessary when an entrepreneurial outcome emerges only in the presence or absence of that condition. While a necessary condition does not guarantee the outcome, it makes the outcome possible by virtue of its theoretical necessity. We discuss the philosophical roots and importance of necessary conditions in entrepreneurship. We offer an empirical illustration of necessary condition analysis using founder's experience, a critical concept in entrepreneurship. We argue that theory-method compatibility in entrepreneurship research can be enhanced by explicitly accounting for necessary conditions. [ABSTRACT FROM AUTHOR]

Asteroid capture holds great significance in understanding the origins of asteroids, the source of life, and the exploration of planetary mineral resources. To ensure the success of a mission aimed at capturing asteroids, it is crucial to choose asteroids that can be naturally captured by Earth. This article focuses on the orbital characteristics of temporarily captured asteroids. Through a statistical simulation of asteroid motion and an analytical derivation of the Jacobian integral, the necessary conditions for the temporary capture of asteroids by Earth are calculated. The analysis results show an approximately linear relationship between the orbit elements of temporarily captured asteroids. This condition is used to screen the currently observed near-Earth asteroids and has identified asteroids such as 2006 RH120 and 2020 CD3, which have been temporarily captured by Earth. These findings provide important suggestions for future asteroid capture missions and target selection.

Understanding the key determinants of residential water conservation is crucial for designing effective water demand management policies in arid and semiarid regions. While extant literature has frequently identified such determinants using statistical significance and correlations, there is a growing emphasis on understanding these determinants using probabilistic sufficiency and deterministic necessity logics. Integrating these two logics to test an integrated model of the Theories of Planned Behaviour (TPB) and Protection Motivation (PMT), this study identifies and differentiates the probabilistic sufficient and necessary conditions or "must have" factors that need to exist for residential water conservation intentions and behaviours to occur. Combining partial least square structural equation modeling (PLS-SEM) and necessary condition analysis (NCA) to analyse 346 responses from residents in Australia's Northern Territory (NT), we found that attitude, self-efficacy, perceived vulnerability, and response efficacy are probabilistic sufficient and necessary conditions for water conservation intention. Self-efficacy and intention further provided probabilistic sufficient and necessary conditions for water conservation behaviour. Based on the findings, the TPB-PMT constructs are categorised into four groups and the bottleneck table is used to indicate the minimum levels of the identified necessary conditions that must exist to realise the highest levels of water conservation intention and behaviour. This study further draws on these two logics to conduct a combined importance-performance map analysis (cIPMA) to provide guidelines for policymakers and water authorities on how to better prioritise water management actions to improve residential water conservation intentions and behaviours. a-Target construct is water conservation intention; b-Target construct is water conservation behaviour ● non-necessary condition construct; ◯ = necessary condition construct; Bubble size shows the percentage of cases that did not meet the required desired level outcome. [Display omitted] • The TPB constructs of attitude and self-efficacy are probabilistic sufficient and necessary conditions for intention. • PMT constructs of perceived vulnerability, self and response efficacies are sufficient and necessary factors for intention. • Self-efficacy and intention are probabilistic sufficient and necessary conditions for behaviour. • Although not probabilistic sufficient, perceived severity is a necessary condition for intention. [ABSTRACT FROM AUTHOR]

Most leadership studies primarily focus on formal leaders, often overlooking the influence of leaders within the team. While prior research has shown that peer leaders can have a beneficial impact on various team outcomes, it is yet unclear which peer leadership behaviors precisely foster a supportive and sustainable work environment. Building upon the recent identification of 10 peer leadership roles and 37 underlying functions, the current study aims to investigate the relationships between these peer leadership roles and functions and key outcomes (i.e., job satisfaction, team cohesion, team effectiveness, and OCB). A total of 31 organizational teams, comprising 182 employees from diverse sectors, participated in a quantitative survey. Employing multilevel modeling analysis, the findings demonstrated that each leadership role and nearly every function predicted at least one outcome, highlighting their significance within organizational teams. Additionally, Necessary Condition Analysis revealed that specific roles and functions were necessary for generating one or more outcomes. Finally, we found that most of the significant relationships remained consistent across teams, regardless of their size, tenure, or level of team identification. These findings refine our understanding of shared leadership and how peer leaders can create a sustainable workplace by fostering employee well-being and productivity in organizational teams.

A well-known first-order necessary condition for a point to be a local minimizer of a given function is the non-negativity of the dot product of the gradient and a vector in a feasible direction. This paper proposes a series of alternative first-order necessary conditions and corresponding first-order sufficient conditions that seem not to appear in standard texts. The conditions assume a nonzero gradient. The methods use extensions of the notions of gradient, differentiability, and twice differentiability. Examples, including one involving the Karush–Kuhn–Tucker (KKT) theorem, illustrate the scope of the conditions.

An optimal control problem with quadratic cost functional on time scales is studied and some optimality necessary conditions are derived. The main tool used is the integration by parts on time scales.

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of omnibus model tenability. The argument is exemplified with a comparison of the widely used one-parameter and two-parameter logistic models. A theoretically and practically relevant setting illustrates how discounting local fit and concentrating instead on overall model fit may lead to incorrect model selection, even if a popular information criterion is also employed. The article concludes with the recommendation for routine examination of particular parameter constraints within latent variable models as part of their fit evaluation. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with an optimal control problem for a linear stochastic differential equation (SDE) of mean-field type, where the drift coefficient of observation equation is linear with respect to the state, the control and their expectations, and the state is subject to a terminal constraint. The control problem cannot be solved by transforming it into a standard optimal control problem for an SDE without mean-field term. By virtue of a backward separation method with a decomposition technique, one optimality condition and one forward–backward filter are derived. Two linear-quadratic (LQ) optimal control problems and one cash management problem with terminal constraint and partial information are studied, and optimal feedback controls are explicitly obtained.

Abstract This paper studies an inverse problem of determining the implied volatility in the financial products linked with gold price, which has important application in financial derivatives pricing. Based on the total variation regularization strategy, the existence and necessary condition of the minimum for the control function are addressed, and the local uniqueness of the solution is also given by a modified case. Furthermore, the stability and convergence for the regularized approach are discussed. The results obtained in this paper may be useful for those who engage in hedging or risk management.

The aim of this paper is to develop a productive numerical technique to deal with a class of time partial ideal AI control issues. The classical fuzzy inference methods cannot work to their full potential in such circumstances, because the given knowledge does not cover the entire problem domain. In addition, the requirements of fuzzy systems may change over time. The use of a static rule base may affect the effectiveness of fuzzy rule interpolation due to the absence of the most concurrent (dynamic) rules. The experimental result indicates that evolved bat algorithm with our proposed fitness function presents a 93.77% success rate in average for finding the feasible solutions. The contribution of this study is that near outcomes likewise confirm that the partial administrator for a Mittag–Leffler circuit in the Caputo sense improves the execution of the AI controlled framework as far as the transient reaction, in contrast with the other fragmentary and whole number subordinate administrators. [ABSTRACT FROM AUTHOR]

This study considers the scaled consensus problem of coupled harmonic oscillators with a directed network topology. A distributed control protocol with input delay and intermittent sampled position information only is proposed. To achieve consensus, a necessary and sufficient condition depending on communication width, input delay and sampling period is derived. Furthermore, to save energy and improve the efficiency of communication among the agents and their neighbours, the authors extend their argument to investigate an impulsive control protocol. Different from intermittent control, the scaled consensus under the impulsive control cannot be achieved if there is no input delay. Numerical simulations illustrate that appropriately chosen control gains can verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Freechet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality. [ABSTRACT FROM AUTHOR]

Equating of psychometric scales and tests is frequently required and conducted in educational, behavioral, and clinical research. Construct comparability or equivalence between measuring instruments is a necessary condition for making decisions about linking and equating resulting scores. This article is concerned with a widely applicable method for examining if two scales or tests cannot be equated. A latent variable modeling method is discussed that can be used to evaluate whether the tests or parts thereof measure latent constructs that are distinct from each other. The approach can be routinely used before an equating procedure is undertaken, in order to assess whether equating could be meaningfully carried out to begin with. The procedure is readily applicable in empirical research using popular software. The method is illustrated with data from dementia screening test batteries administered as part of two studies designed to evaluate a wide range of biomarkers throughout the process of normal aging to dementia or Alzheimer's disease. [ABSTRACT FROM AUTHOR]

In this work, we investigate the reliability of the probabilistic binary forecast. We mathematically prove that a necessary, but not sufficient, condition for achieving a reliable probabilistic forecast is maximizing the Peirce Skill Score (PSS) at the threshold probability of the climatological base rate. The condition is confirmed by using artificially synthesized forecast–outcome pair data and previously published probabilistic solar flare forecast models. The condition gives a partial answer as to why some probabilistic forecast system lack reliability, because the system, which does not satisfy the proved condition, can never be reliable. Therefore, the proved condition is very important for the developers of a probabilistic forecast system. The result implies that those who want to develop a reliable probabilistic forecast system must adjust or train the system so as to maximize PSS near the threshold probability of the climatological base rate.

In this article, we obtain some properties of the positive solutions to a class of fractional differential equation multipoint boundary value problems at resonance. Necessary conditions for the existence of positive solutions are established by means of the spectral theory of linear operator. As application, necessary and sufficient conditions for the existence of positive solutions are given for the case that the nonlinearity has a fixed sign. Some examples are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

The containment problem of heterogeneous multi‐agent systems with fixed time delay under directed network is considered for both continuous‐time and discrete‐time multi‐agent systems. Leaders and followers have different dynamics, modelled by double‐integrator and single‐integrator, respectively. It is also assumed that all leaders are stationary. Unlike the current approach in the literature which utilises LMIs to derive sufficient condition for containment reaching, the authors employ Laplace transform/Z ‐transform and final value theorem to obtain the necessary and sufficient condition which guarantees the containment of follower agents in the presence of communication delays. This approach gives the exact maximum allowed time delay, which is larger than the bound obtained by previous approaches. This study also proposes a noble reduced‐order dynamic method, by adding virtual agents, in order to use final value theorem for stability analysis in the presence of heterogeneity in the network. In the end, to illustrate the effectiveness of the theoretical results, simulation examples are provided. [ABSTRACT FROM AUTHOR]

An optimal control problem for backward doubly stochastic system is considered, where the control domain is not necessarily convex. By the method of classical spike variation and duality technique, one necessary condition and one sufficient condition are established for this kind of optimal control problem. The related adjoint process is characterised by the solution of a forward doubly stochastic differential equation, which formulates a forward–backward doubly stochastic differential equation coupled with the state equation. As an illustration, the authors' theoretical results are applied to study an optimal harvesting problem and a linear‐quadratic optimal control problem. Moreover, the corresponding maximum principle with an initial state constraint is obtained by Ekeland's variational principle. [ABSTRACT FROM AUTHOR]

This study is concerned with the minimal controllability problem of a connected threshold graph following the Laplacian dynamics. The goal is to find the minimum number of controllers and a small set of vertices for the controllers to connect to render the graph Laplacian controllable. A simple algorithm is provided to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a straightforward computation on its Laplacian matrix. A necessary and sufficient condition for the graph to be Laplacian controllable is then proposed. The condition suggests that the minimum number of controllers to make a connected threshold graph Laplacian controllable is the maximum multiplicity of Laplacian eigenvalues of the graph, and this minimum can be achieved using a binary control matrix. If a controller can be connected to one vertex only, the minimum number is the difference between the number of vertices in the graph and the number of vertices with different degrees. The condition also implies that the controllers ensuring the Laplacian controllability should be connected to the vertices with repeating degrees to break the symmetry of the network topology. Several examples are provided to illustrate the authors' results. [ABSTRACT FROM AUTHOR]

This mainly studies the mean square stabilisability, interval stability and stabilisation of mean‐field stochastic control systems. A necessary and sufficient condition for stabilisation of continuous‐time mean‐field stochastic systems is presented via operator spectrum technique. The unremovable spectrum is generalised to mean‐field stochastic differential equations (MF‐SDEs), and a necessary and sufficient condition for unremovable spectrum is obtained. Three operators defined in different domains are given to characterise the stabilisability of MF‐SDEs. As applications, an example is given to illustrate their relationships. Interval stability and stabilisation are generalised to MF‐SDEs, and a necessary condition for interval stability is given to show the relationship among interval stability, the decay rate of the system state response and the Lyapunov exponent. A sufficient condition for interval stabilisation is proposed via linear matrix inequality approach. [ABSTRACT FROM AUTHOR]

For India, achieving environmental sustainability in the midst of faster growth remains a challenging objective. Therefore, we are revisiting the nature of the Environmental Kuznets Curve (EKC) at different stages of economic growth through both necessary and sufficient conditions under the cubic model specifications in India. Further, we extend the EKC framework by incorporating energy consumption, agricultural value added, trade, the world uncertainty index, and geopolitical risk as additional variables into the three preferred disaggregated greenhouse gas emission (GHG) models. This study employs an auto-regressive distributed lag model (ARDL). The empirical findings show evidence of the valid N-shaped EKC through both necessary and sufficient conditions for carbon dioxide (CO 2) and nitrous oxide (N 2 O) and exhibit the presence of two real and distinct income turning points for both valid EKCs. In contrast, only the necessary condition supports the N-shaped EKC for methane (CH 4) emissions in India. Further, the results highlight that trade has a positive impact, whereas the world uncertainty index has a negative impact on disaggregated GHGs. Similarly, geopolitical risk has a negative effect on CH 4 and N 2 O, whereas energy consumption has a positive impact on CO 2 emissions. Moreover, agricultural value added has a negative effect on CH 4 and a positive effect on N 2 O emissions. Our empirical findings suggest policy recommendations that can collectively work as a roadmap for India to become emission-neutral by 2070. [ABSTRACT FROM AUTHOR]

In the energy transition context, restructuring energy systems and making informed decisions on the optimal energy mix and technologies is crucial. Energy system optimisation models (ESOMs) are commonly used for this purpose. However, their focus on cost minimisation limits their usefulness in addressing other factors like environmental sustainability and social equity. Moreover, by searching for only one global optimum, they overlook diverse alternative solutions. This paper aims to overcome these limitations by exploring near-optimal spaces in multi-objective optimisation problems, providing valuable insights for decision-makers. The authors extend the concepts of epsilon-optimality and necessary conditions to multi-objective problems. They apply this methodology to a case study of the Belgian energy transition in 2035 while considering both cost and energy invested as objectives. The results reveal opportunities to reduce dependence on endogenous resources while requiring substantial reliance on exogenous resources. They demonstrate the versatility of potential exogenous resources and provide insights into objective trade-offs. This paper represents a pioneering application of the proposed methodology to a real-world problem, highlighting the added value of near-optimal solutions in multi-objective optimisation. Future work could address limitations, such as approximating the epsilon-optimal space, investigating parametric uncertainty, and extending the approach to other case studies and objectives, enhancing its applicability in energy system planning and decision-making. [Display omitted] • We present an approach to exploring near-optimal spaces in multi-objective problems. • Using necessary conditions, better insights can be provided to decision-makers. • The methodology is applied to a case study of the Belgian energy transition. • We reveal minimum resource needs to achieve a reasonable cost and EROI. [ABSTRACT FROM AUTHOR]

Increasingly high bandwidths are desired in modern navigation and autonomous RF ranging signal design to achieve better pseudo-noise (PN) ranging accuracy. However, fulfilling the Nyquist criterion for such high-bandwidth signals would be a challenging issue for system design. Considering that the Nyquist criterion is not a necessary condition for PN code tracking, sub-Nyquist sampling can be adopted as a feasible solution to this issue. Nevertheless, it is at the expense of an increase in thermal noise caused by tracking error. This problem is particularly prominent for tracking weak signals such as navigation signals, which limits the applicability of this sampling scenario. As far as high-precision autonomous PN ranging is concerned, however, the tracking error due to digital implementation is not negligible and even becomes the dominating factor instead of thermal noise. This means that the performance loss incurred by sub-Nyquist sampling can be eliminated under high-signal-to-noise ratio conditions. Exploiting this fact, this Letter proposes a novel PN code tracking approach based on sub-Nyquist and non-commensurate sampling, providing a solution to achieving high-ranging accuracy while breaking the bounds of the Nyquist sampling theorem without performance degradation. The approach is very attractive for precise PN ranging applications demanding miniaturised implementation. [ABSTRACT FROM AUTHOR]

One of the main objectives of historical studies, is the study of the causes of historical events. In the present article in the first place, the four kinds of causalities that are used for historical explanation, that is, necessary and insufficient condition, sufficient and unnecessary condition, necessary and sufficient condition, and unnecessary and insufficient condition, are explained. History-based researchers of social sciences mainly search for specific results in one or few cases. Attempts have been made in the preset study to show that such historical analyses normally rely on counterfactual analysis. In other words, it is argued that if one tries to conduct a causal study of the past or evaluate a historical explanation, there is no other option than relying on counterfactual analysis. In the next step, the relationship between causal analysis with historical chain explanations has been studied. These analyses refer to the sequence or interconnected causal factors and explain historical events through interconnected events that unfold in the process of time.

Most leadership studies primarily focus on formal leaders, often overlooking the influence of leaders within the team. While prior research has shown that peer leaders can have a beneficial impact on various team outcomes, it is yet unclear which peer leadership behaviors precisely foster a supportive and sustainable work environment. Building upon the recent identification of 10 peer leadership roles and 37 underlying functions, the current study aims to investigate the relationships between these peer leadership roles and functions and key outcomes (i.e., job satisfaction, team cohesion, team effectiveness, and OCB). A total of 31 organizational teams, comprising 182 employees from diverse sectors, participated in a quantitative survey. Employing multilevel modeling analysis, the findings demonstrated that each leadership role and nearly every function predicted at least one outcome, highlighting their significance within organizational teams. Additionally, Necessary Condition Analysis revealed that specific roles and functions were necessary for generating one or more outcomes. Finally, we found that most of the significant relationships remained consistent across teams, regardless of their size, tenure, or level of team identification. These findings refine our understanding of shared leadership and how peer leaders can create a sustainable workplace by fostering employee well-being and productivity in organizational teams.

This work studies the conditions on which the outputs of linear heterogeneous (i.e. non‐identical) agents are asymptotically synchronised, where the dynamics of the agents and the dimensions of the state variables might widely differ among themselves. With the constraint that the relative outputs of the agents are the only measurements, it is shown that the reflexive generalised inverses play a key role in characterising the conditions, and give rise to the synchronisation stability of the agents. Together with the internal model principle for synchronisation, this results in a necessary and sufficient condition for reaching the asymptotic output synchronisation. This necessary and sufficient characterisation has its own geometric interpretation as the reflexive generalised inverses are related to the projections onto subspaces. Finally, it is shown that the condition is in fact a natural generalisation of the state synchronisability of homogeneous (i.e. identical) linear agents. A computer simulation is also provided to verify the result. [ABSTRACT FROM AUTHOR]

How to find the minimum number of control agents needed to guarantee the strategy consensus of networked evolutionary games (NEGs) is studied. First, the minimal‐agent consensus control (MACC) problem is formulated, and given a set of control agents, a necessary and sufficient condition is presented for the consensus of NEGs based on the algebraic form. Second, using the necessary and sufficient condition, an algorithm is established to solve the MACC problem. Third, the consensus of NEGs with switching topology is considered, and a necessary and sufficient condition is presented by introducing the concept of switching reachability. Finally, three illustrative examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This study addresses the distributed H∞ and H2 consensus control problems for multi‐agent systems with general integrator dynamics and undirected topology. First, based on the frequency domain description of linear multi‐agent systems, a sufficient and necessary condition is imposed on each controller to achieve consensus. Second, both H∞ and H2 optimal controllers are computed analytically according to the corresponding performance indices. The novel controllers not only can optimise the reference tracking performance but also has a simple tuning way to trade off the nominal performance and robustness. Finally, by application to the formation control of autonomous surface vessels shows the effectiveness of the proposed two control strategies. [ABSTRACT FROM AUTHOR]

This paper studies an inverse problem of determining the implied volatility in the financial products linked with gold price, which has important application in financial derivatives pricing. Based on the total variation regularization strategy, the existence and necessary condition of the minimum for the control function are addressed, and the local uniqueness of the solution is also given by a modified case. Furthermore, the stability and convergence for the regularized approach are discussed. The results obtained in this paper may be useful for those who engage in hedging or risk management. [ABSTRACT FROM AUTHOR]

Peer in marriage contract is defined as equality and similar dignity of spouse in some issues. There is a difference of opinion among Imamiya jurists and also the Sunnite scholars concerning the issues and criterion of equality in marriage. Reputed Imamiya jurists consider Islam & belief in the Imamate of the twelve Imams (PBUT) to be the criterion for the equality and similar ranking of the man and the woman. Yet, from the perspective of another group, only Islam in its broadest sense of the word is the only condition required. Still others believe that Islam, faith, and the ability to pay alimony is enough to elaborate the term kefaat (peer). In addition to the equality of spouses in Islam, most of the general jurists consider parentage, liberty and career, equality between men and women -in terms of health and defect- for the termination of the marriage (contract) as criterion for equality. This paper seeks to answer to this question: ‘Indeed, what issues can be the examples of equality in marriage in Islam?’ By expressing the opinions and reasons of both Imamiya jurists and Sunnite scholars and their critiques that other than “Islam” in the broadest sense of the word, no other criterion is a condition for equality. This conclusion can be formed that affairs such as parentage, liberty and occupation, from the viewpoint of the four religions, are the necessary conditions, and are not the condition of the validity of marriage and from Imamiya jurists’ point of view they are neither a condition for (marriage) nor a condition for the validity thereof.

Containment control problems for high‐order linear Markov jump swarm systems with a dynamic output feedback under directed interaction topologies are investigated. A necessary and sufficient condition for Markov jump swarm systems to guarantee output containment is proposed. A sufficient condition is further presented to ensure the scalability of the criteria. Finally, numerical simulations show that the swarm system achieves output containment under the sufficient condition. [ABSTRACT FROM AUTHOR]

Simpson's paradox is a challenging topic to teach in an introductory statistics course. To motivate students to understand this paradox both intuitively and statistically, this article introduces several new ways to teach Simpson's paradox. We design a paper toss activity between instructors and students in class to engage students in the learning process. We show that Simpson's paradox widely exists in basketball statistics, and thus instructors may consider looking for Simpson's paradox in their own school basketball teams as examples to motivate students’ interest. A new probabilistic explanation of Simpson's paradox is provided, which helps foster students’ statistical understanding. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Partial shading (PS) is an unavoidable condition which significantly reduces the efficiency and stability of a photovoltaic (PV) system. With PS, the system usually exhibits multiple-peak output power characteristics, but single-peak is also possible under special PS conditions. In fact it is shown that the partial shading condition (PSC) is the necessary but not sufficient condition for multiple-peak. Based on circuit analysis, this paper shows that the number of peak points can be determined by short-circuit currents and maximum-power point currents of all the arrays in series. Then the principle is established based on which the number of the peak points is to be determined. Furthermore, based on the dynamic characteristic of solar array, this paper establishes the rule for determination of the relative position of the global maximum power point (GMPP). In order to track the GMPP within an appropriate period, a reliable technique and the corresponding computer algorithm are developed for GMPP tracking (GMPPT) control. It exploits a definable nonlinear relation has been found between variable environmental parameters and the output current of solar arrays at every maximum power point, obtained based on the dynamic performance corresponding to PSC. Finally, the proposed method is validated with MATLAB®/Simulink® simulations and actual experiments. It is shown that the GMPPT of a PV generation system is indeed realized efficiently in a realistic environment with partial shading conditions. [ABSTRACT FROM AUTHOR]

In the paper, the problem of determination of the coe±cient at the first time derivative of a hyperbolic equation with integral overdetermination condition is reduced to an optimal control problem. A theorem on the existence of optimal control is proved, the gradient of the functional is calculated and the necessary optimality condition is derived in the form of an integral inequality. [ABSTRACT FROM AUTHOR]