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In this paper, we consider the graph regularization Q-weighted nonnegative matrix factorization problem in multi-view clustering. Based on the Q-weighted norm property, this problem is transformed into the minimization problem of the trace function. The necessary condition for the existence of a solution is given. The proximal alternating nonnegative least squares method and its acceleration method are designed to solve it. The convergence theorem is also given. The feasibility and effectiveness of the proposed methods are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

We consider the most basic concept of bivariate symmetry, referred to as general symmetry or conditional symmetry and provide a necessary condition for it based on the joint probability density function and the associated cumulative distribution function. This condition is then used to provide a test of general bivariate symmetry by using the sample analog of the necessary condition as a test statistic. We derive the asymptotic distribution of the test statistic under the null hypothesis and exhibit the performance of the proposed test through simulations. The test is then applied to a couple of real datasets, one coming from an insurance company and the other from a medical trial of Mayo Clinic. [ABSTRACT FROM AUTHOR]

In this contribution, the Schemper–Henderson measure of explained variation for survival outcomes is extended to accommodate competing events (CEs) in addition to events of interest. The extension is achieved by moving from the unconditional and conditional survival functions of the original measure to unconditional and conditional cumulative incidence functions, the latter obtained, for example, from Fine and Gray models. In the absence of CEs, the original measure is obtained as a special case. We define explained variation on the population level and provide two different types of estimates. Recently, the authors have achieved a multiplicative decomposition of explained variation into degrees of necessity and degrees of sufficiency. These measures are also extended to the case of competing risks survival data. A SAS macro and an R function are provided to facilitate application. Interesting empirical properties of the measures are explored on the population level and by an extensive simulation study. Advantages of the approach are exemplified by an Austrian study of breast cancer with a high proportion of CEs. [ABSTRACT FROM AUTHOR]

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]

The purpose of the present study was to investigate the stress—burnout link in entrepreneurship by employing the role stress theory's tri-component conceptualization (i.e., role conflict, role ambiguity, and role overload) using a novel statistical method entitled, Necessary Condition Analysis (NCA). The NCA is based on necessity logic, in contrast to variance-based methodologies (e.g., regression analysis and structural equation modeling) based on sufficiency logic, which seeks to assess whether an increase in the predictor variable is associated with an increase in the outcome variable. NCA aims to determine if there is a critical (necessary) determinant for an event to occur. In other words, NCA helps to answer questions, which allows identification of the necessity in type and the degree of concern for necessity linkages. Data were collected from self-identified American entrepreneurs (N = 285). The NCA's results were consistent with the conclusion of several variance-based research that identified the overall role of stress as a prerequisite for burnout. However, the three components of entrepreneurial role stress were not the necessary conditions for the development of entrepreneurial burnout. The present study is the first to use the NCA to investigate the role stress-burnout link in entrepreneurship, which has important theoretical and methodological implications. Theoretically, future studies should frame the necessary for developing entrepreneurial role stress in a broader manner, going beyond the tri-component conceptualization of role stress. And, methodologically, sufficiency logic analyses should be accompanied and supported by necessary logic analyses to deepen our understanding regarding various aspects of entrepreneurs' well-being. [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]

A variation method for solving the inverse problems of determining of the complex quantum potential in a nonlinear non-stationary Schrödinger-type equation with final and boundary observations is considered. The existence and uniqueness theorem of the solution of the variation formulation of the inverse problem is proved, the continuity and continuous differentiability of the quality criterion are established, the formula for its gradient is found, the necessary condition of optimality is proved and iterative regularization of the solution is indicated. [ABSTRACT FROM AUTHOR]

In the first part of the study, we proposed that logicians adopt from linguists their detailed distinction of conditions on a scale of varying degrees of satisfiability from factually true via potentially satisfiable to absolutely irreal. On this basis, we have proposed a suitable distinction for the logico-semantic investigation of conditionals of the following kinds: Factual, hypothetical (agnostic), counterfactual, and counterpossible. We consider the syntactic-semantic distinction between potentially and absolutely irreal conditions to be crucial. Therefore, we think that the conditional mode in the form of antepreterite is an appropriate syntactic signal for identifying the absolute irreality of the condition and, especially in scientific and artistic style, we consider it functional. On the other hand, the distinction between sufficient and necessary conditions could be inspiring for linguists. In classical logic, these are the basic kinds of conditions and are associated with the rules of deductive reasoning modus ponens and modus tollens, respectively. These rules are central to the application of logic. It turns out that these tools are not sufficiently established in Slovak linguistics, as there is no systematic distinction between sufficient and necessary conditions. The situation in czech dictionaries is similar. Finally, we have put forward a hypothesis why the conjunction unless is considered in Slovak linguistics as a double – in our opinion wrongly – of the conjunction only: There is a "forgotten" ellipsis behind it, which is not brought to the reader's attention. [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]

The terms "sufficient condition" and "necessary condition" are related to conditional sentences (those of the form "If A, then B"). The meaning of the former depends on the use of the latter, and conditional sentences are used differently. A conditional sentence could express material implication, but it could also express formal implication. The terms "sufficient condition" and "necessary condition" reflect this difference, each taking on respectively (at least) two different meanings. In the text, I indicate and analyze these meanings. The difference between them is significant because, as it turns out, according to one of them (corresponding to the cases where conditional sentences express material implications), if several conditions together are a sufficient condition for something, then (by logical necessity) only one of them is also a sufficient condition for it, which is not the case with the other meaning (corresponding to the cases in which conditional sentences express formal implications). If the difference in meaning is not taken into account, it is not improbable for situations to arise where mixing them up leads to logical problems. An example of this is given in the text. [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]

Tis research aims to reveal the combinations of conditions leading to Korean teacher job satisfaction. The data of this study are derived from the 2018 Teaching and Learning International Survey (TALIS). Teacher job satisfaction was approached as a composite scale with two dimensions: job satisfaction with profession and job satisfaction with work environment. The explanatory variables were preparation for pedagogical content knowledge, teacher self-efficacy in general, teacher self-efficacy in multicultural classrooms, teachers' innovative climate, teacher-student relations, social perceptions of teacher value, and professional development barriers. The findings using fsQCA are as follows; 1) the presence of social perceptions of teacher value is a necessary condition for a high level of job satisfaction with the profession. 2) Four distinct paths were extracted to explain the high level of job satisfaction with the profession. 3) Four distinct paths were shown clearly to explain the low level of job satisfaction with the profession. 4) None of the conditions is a necessary condition for job satisfaction with the work environment. 5) Five distinct paths were singled out to explain the high level of job satisfaction with the work environment. 6) Three distinct paths were identified to explain the low level of job satisfaction with the work environment. The findings revealed Korean teacher job satisfaction in multicultural secondary schools by outlining several combinations of factors that lead to paths explaining job satisfaction with profession and job satisfaction with work environment. Some implications and a few recommendations to improve teacher job satisfaction are suggested. [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.

In 2017 the US imposed several tariffs on imports from China. In our study, we derive both the necessary and the sufficient conditions for the tariff to be welfare-enhancing using the ex-post approach. We found the data satisfies both the necessary and the sufficient conditions. So, we conclude that U.S. welfare has improved due to US import tariff on Chinese products. [ABSTRACT FROM AUTHOR]

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. [ABSTRACT FROM AUTHOR]

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.

Objective: Although many factors predict adolescent depression, risks that operate as necessary conditions (ie, absence of the factor conveys absence of the outcome) have been largely unexplored. This study aimed to evaluate which psychosocial risk factors might serve as necessary conditions for future onset of depression across adolescence., Method: At baseline, cognitive and personality risks, symptom severity, stressful events, and past depression history were assessed among 382 adolescents (225 girls; mean age = 12.6), who were then followed over 2 years with repeated diagnostic interviews to ascertain depression onset. An innovative statistical approach in mental health research, necessary condition analysis, was applied., Results: Baseline rumination (d = 0.50), stressful events (d = 0.37), depressive symptoms (d = 0.23), and self-criticism (d = 0.35) all emerged as significant necessary conditions for adolescents to be diagnosed with a depressive disorder over the subsequent 24 months. Overall, 13.5% of the sample did not show all the necessary conditions (ie, they lacked 1 or more conditions) and were therefore virtually immune from experiencing 1 or more major depressive episodes over the follow-up, and 65.5% did not meet all those conditions for experiencing 3 or more major depressive episodes (ie, recurrent depression)., Conclusion: These findings can inform future theory building and testing as well as clinical applications via screening of necessary risk to future pediatric depression so that youth who may most benefit from effective interventions can be identified., Study Preregistration Information: The Necessary Conditions for Depressive Symptoms and Major Depression in Adolescence; https://osf.io/b5ced., Diversity & Inclusion Statement: We worked to ensure race, ethnic, and/or other types of diversity in the recruitment of human participants. We worked to ensure sex and gender balance in the recruitment of human participants. One or more of the authors of this paper self-identifies as a member of one or more historically underrepresented sexual and/or gender groups in science., (Copyright © 2024 American Academy of Child and Adolescent Psychiatry. Published by Elsevier Inc. All rights reserved.)

In this paper we consider a control problem with pointwise observation for a one-dimensional parabolic equation which arises in a mathematical model of climate control in industrial greenhouses. We study a general equation with variable diffusion coefficient, convection coefficient, and depletion potential. For the extremum problem of minimizing an integral weighted quadratic cost functional, we establish the existence and uniqueness of a minimizing function. We also study exact controllability and dense controllability of the problem. Necessary conditions for an extremum are obtained, and qualitative properties of the minimizing function are studied. [ABSTRACT FROM AUTHOR]

This research shows the importance of supervisor organizational embodiment (SOE) for the relationship between ethical leadership and organizational identification. Drawing on the social identity model of organizational leadership, we propose that ethical leaders promote organizational identification and subsequently extra-role performance only when employees perceive that their leader shares the values and norms of their organization. In a two-wave study and a multi-source study, our findings suggest that the benefits of ethical leadership for organizational identification and consequently extra-role performance are dependent on high levels of SOE; when it is low, ethical leadership does not foster organizational identification, rendering SOE a necessary condition for this relationship. Further, the stability of the effects using multiple research designs strengthens the robustness of our findings. Theoretical and practical implications are discussed. [ABSTRACT FROM AUTHOR]

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.

A special case of a fundamental result of Loewner and Horn [Trans. Amer. Math. Soc. 136 (1969), pp. 269–286] says that given an integer n \geqslant 1, if the entrywise application of a smooth function f : (0,\infty) \to \mathbb {R} preserves the set of n \times n positive semidefinite matrices with positive entries, then f and its first n-1 derivatives are non-negative on (0,\infty). In a recent joint work with Belton–Guillot–Putinar [J. Eur. Math. Soc., in press], we proved a stronger version, and used it to strengthen the Schoenberg–Rudin characterization of dimension-free positivity preservers [Duke Math. J. 26 (1959), pp. 617–622; Duke Math. J. 9 (1942), pp. 96–108]. In recent works with Belton–Guillot–Putinar [Adv. Math. 298 (2016), pp. 325–368] and with Tao [Amer. J. Math. 143 (2021), pp. 1863-1929] we used local, real-analytic versions at the origin of the Horn–Loewner condition, and discovered unexpected connections between entrywise polynomials preserving positivity and Schur polynomials. In this paper, we unify these two stories via a Master Theorem (Theorem A) which (i) simultaneously unifies and extends all of the aforementioned variants; and (ii) proves the positivity of the first n nonzero Taylor coefficients at individual points rather than on all of (0,\infty). A key step in the proof is a new determinantal / symmetric function calculation (Theorem B), which shows that Schur polynomials arise naturally from considering arbitrary entrywise maps that are sufficiently differentiable. Of independent interest may be the following application to symmetric function theory: we extend the Schur function expansion of Cauchy's (1841) determinant (whose matrix entries are geometric series 1 / (1 - u_j v_k)), as well as of a determinant of Frobenius [J. Reine Angew. Math. 93 (1882), pp. 53–68] (whose matrix entries are a sum of two geometric series), to arbitrary power series, and over all commutative rings. [ABSTRACT FROM AUTHOR]

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.

Focusing on regime-switching diffusions with mean-fields interactions, this paper is devoted to obtaining a general maximum principle. A main feature is that conditional mean-field is used in the controlled dynamic systems and the optimization process. Analysis of variational and adjoint equations using forward and backward stochastic differential equations with regime-switching and conditional mean-field is carried out. Necessary conditions for optimality are obtained without assuming the convexity of the control space. An example on conditional mean-variance portfolio selection with regime switching is given to illustrate the sufficient conditions for optimality. [ABSTRACT FROM AUTHOR]

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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]

We extend Peng's maximum principle for semilinear stochastic partial differential equations (SPDEs) in one space dimension with nonconvex control domains and control-dependent diffusion coefficients to the case of general cost functionals with Nemytskii-type coefficients. Our analysis is based on a new approach to the characterization of the second order adjoint state as the solution of a function-valued backward SPDE. [ABSTRACT FROM AUTHOR]

Most researchers who touch on the problem of students' technical creativity believe that the most important means of developing students' creative technical thinking is their independent solution of a system of gradually becoming more complex problematic problems. The essence of these problems lies in the fact that on the basis of some data in the condition of the problem, presented explicitly or assumed to be known to the student, and the requirements of the problem, the solver must solve the problem, find what is sought, while carrying out, that is, in the course of the solution, one or several procedures of creative activity. A special role in the formation of a creative personality, capable of high-performance work in the future, technically rich production activity, is assigned to the lessons of technology. [ABSTRACT FROM AUTHOR]

Random context picture grammars are used to generate pictures through successive refinement. There exist several subclasses of these grammars, e. g., context-free picture grammars, random permitting context picture grammars, random forbidding context picture grammars and table-driven context-free picture grammars. These classes generate context-free galleries (cfpls), random permitting context galleries (rPcpls), random forbidding context galleries (rFcpls) and table-driven context-free galleries (Tcfpls), respectively. For all these classes of galleries, necessary conditions have been proven. In particular, for cfpls, there exists a pumping-shrinking lemma, for rPcpls, a pumping lemma and for rFcpls, a shrinking lemma. For Tcfpls, two necessary conditions have been proven. Recently, a new necessary condition related to the size of a subpicture was proven for each of the abovementioned classes of galleries. We now prove theorems that are an alternative to the existing necessary conditions. This is done by adapting Ogden's idea of marking parts of a word for the picture case. We illustrate the new conditions with examples. For rPcpls and Tcfpls, we also give examples of galleries for which the marking is necessary. [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.

The purpose of this paper is to extend to ordinal and nominal outcomes the measures of degree of necessity and of sufficiency defined by the authors for dichotomous and survival outcomes in a previous paper. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. The degrees of necessity and sufficiency, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic regression models; the measures, however, do not require any particular model. In addition, we study in detail the relationship between the proposed measures and the related explained variation summary for dichotomous outcomes, which are the common root for the developments for ordinal, nominal, and survival outcomes. We introduce and analyze the Austrian covid-19 data, with the aim of quantifying effects of age and other potentially prognostic factors on covid-19 mortality. This is achieved by standard regression methods but also in terms of the newly proposed measures. It is shown how they complement the toolbox of prognostic factor studies, in particular when comparing the importance of prognostic factors of different types. While the full model's degree of necessity is extremely high (0.933), its low degree of sufficiency (0.179) is responsible for the low proportion of explained variation (0.193). [ABSTRACT FROM AUTHOR]

The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient conditions" SCOs"), together denoted as NSCOs, for the optimality (OP) of the state constrained problem (SCP) are stated and proved. [ABSTRACT FROM AUTHOR]

Various guidelines for the social implementation of autonomous robots have been developed so far; however, how these guidelines are used remains an issue. In this study, the concept of legitimacy is used as a criterion to evaluate such guidelines. From the perspective of legitimacy, sociological acceptance, moral legitimacy, and future expectations can be considered constitutional and legal perspectives when addressing the necessary conditions for the social implementation of autonomous robots. At the same time, the article considers that resources, reflections, expertise, recognitions, and results are required as sufficient conditions of the elaboration likelihood model. As a case study, an examination of the Japanese government's approach to ethics extracted the need for moral legitimacy and the need for resources and advice from a professional perspective on ethics to obtain adequate outcomes. It has contributed to this paper by presenting a review process, in which the necessary and sufficient conditions for consideration must be examined from the perspective of legitimacy. [ABSTRACT FROM AUTHOR]

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.

This paper offers a unified analysis of the coded meaning of Spanish conditional marker si es que: it conventionally conveys conditionality and the speaker's lack of commitment to the proposition. This second meaning differentiates si es que from the general conditional marker si. It is also argued that si es que has two values: suspending a proposition and expressing a necessary condition, and established that these two share the conventional meaning but differ in the discourse status of the proposition: suspension takes place when the proposition was explicitly evoked in previous discourse, while the marking of necessary conditionals takes place when the proposition is not evoked, but typically new information. The analysis of Spanish si es que contributes to determining the relationship between the operation of suspending a content and the expression of conditionality. [ABSTRACT FROM AUTHOR]

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]