Continuity Assumption Research Articles

Empirical Fitting of Periodically Repeating Environmental Data

We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R2 or the AIC). These results were consistent when the number of measurements decreased (through random removal of data). Future applications of the fitting method could account for higher-order terms in the polynomial function or refinements to the estimation of parameters in the piecewise linear function.

Simulation Relations for Abstraction-based Robust Control of Hybrid Dynamical Systems

The paper addresses the problem of robust control of hybrid dynamical systems with respect to linear-time properties. First, three notions of robust controllers are formulated, that capture imperfect measurements, actuation errors and delays, and uncertain dynamics, respectively. Under mild assumptions of uniform continuity on the transition relation, robust controller synthesis problem with respect to uncertain dynamics is shown to be more general than those with respect to measurement errors, actuation errors and delays. Hence, the paper focuses on the latter notion of robust controllers. Next, foundations for abstraction-based robust controller synthesis are explored, and uniformly continuous alternating simulation relations are shown to preserve the existence of robust controllers with respect to uncertain dynamics.

SOME FIXED POINT THEOREMS FOR (F, t)-CONTRACTIVE MAPPINGS ON INCOMPLETE METRIC SPACES

In this paper, we introduce the notion of a new type of contractive mappings and prove some fixed point results for such mappings in ordered metric spaces. Our results generalize the recent developments of Rashid et al. (Journal of Function Spaces, 2019 (2019), 1-6), which guarantees the existence of a fixed point in such cases wherein the Banach contraction principle, theorem (Proc. Amer. Math. Soc., 132 (2004), 1435-1443) and other fixed point theorems in the literature remain silent. We also provide an affirmative answer to one of the open problems posed by Rashid et al. in the paper mentioned above by relaxing the assumption of continuity to some weaker condition of continuity.

The Worlds of James Buchanan and Thaddeus Stevens: Place, Personality, and Politics in the Civil War Era. ed. by Michael J. Birkner, Randall M. Miller and John W. Quist

Reviewed by: The Worlds of James Buchanan and Thaddeus Stevens: Place, Personality, and Politics in the Civil War Era. ed. by Michael J. Birkner, Randall M. Miller and John W. Quist David N. Gellman (bio) Keywords James Buchanan, Thaddeus Stevens, Sectional crises, Politics The Worlds of James Buchanan and Thaddeus Stevens: Place, Personality, and Politics in the Civil War Era. Edited by Michael J. Birkner, Randall M. Miller, and John W. Quist. (Baton Rouge: Louisiana State University Press, 2019. Pp. 288. Cloth, $47.50.) The instincts and alliances that propelled James Buchanan to the political apex also shredded the nation and his historical standing. Thaddeus Stevens left behind a more celebrated legacy by devoting his career not to sectional comity and white supremacy but to a new revolutionary foundation for the country’s future. Stephen A. Douglas, Buchanan’s Democratic Party rival and the third protagonist in this essay collection, lacked the imagination, moral or political, to find a viable path between the Democracy of the past and the Republicanism of the future. One of the striking takeaways from this compilation is how strongly conventional politicians clung to the assumption of continuity as the political world around them collapsed. Buchanan’s reputation as a northern political striver ever willing to serve the interests of the slaveholding South corresponds with aspects of his social life explored in this volume. Thomas J. Balcerski’s essay on the “Domestic Politics of Doughfacery” correlates the bachelor senator’s Washington boardinghouse friendships with southern colleagues to the votes Buchanan cast between 1834 and 1841. He saw the gag rule and slavery through the eyes of his friends. Joan E. Cashin digs deeper into gender in a brief, intriguing essay on Buchanan’s platonic friendship with Varina Davis, Jefferson Davis’s not-so-happily-married wife. The unionist-inclined spouse of the future president of the Confederacy conveyed her fondness for Buchanan as she left Washington—a dying ember of the intersectional warmth the northerner had long cultivated. Yet abiding personal loyalty to those who undertook political missions on his behalf does not appear to be a hallmark of Buchanan’s style, as William P. Mackinnon seeks to illustrate in a case study of Thomas L. Kane’s service to resolve the 1857 Utah War. The major crises of the 1850s revealed character and ideological commitments. Enter Douglas, whose presidential ambition matched Buchanan’s. The senator from Illinois shared not only a party with Buchanan but also the knowledge that a southern alliance required encouragement of territorial expansion. Managing to minimize political risk and sectional strife [End Page 519] was the tricky part. In an intriguing essay, Matthew Pinsker investigates an oft-cited 1857 exchange in which Douglas allegedly faced down Buchanan over the president’s accession to the proslavery Lecompton constitutional gambit in Kansas. When Buchanan claimed Andrew Jackson’s mantle of authority over the Democratic party, Douglas allegedly responded, “Mr. President, I wish you to remember that General Jackson is dead, sir” (83). Pinsker believes historians have been too credulous. The story first emerged in 1858 and resurfaced during the waning days of the 1860 presidential campaign. Douglas wished to appear far more resolute in opposition to proslavery machinations in Kansas than he actually had been. If he could not win the presidency, he could at least inflict some rhetorical vengeance against his nemesis in the White House. Known for their ambition-driven political acumen, these men struggled to navigate a rupturing national landscape. Douglas R. Egerton dis-mantles Stephen A. Douglas’s judgment by exposing popular sovereignty as a colossal miscalculation. The midwesterner-who-would-be-president “crafted a policy that was despised by both free-soilers and fire-eaters” (72). Politically speaking, the Illinois senator would have been better off embracing a racist, whites-only free-soil approach to the Kansas territory that would have preserved the Missouri Compromise. Instead, he paved the way for the Republican Party to flourish in the North. Buchanan’s comprehension of what was possible proved just as hopeless. Amy S. Greenberg describes how President Buchanan hewed to the old pro-southern Democratic script of Manifest Destiny, as if bullying and buying the United States’ way to...

Agamben's Theories of the State of Exception: From Political to Economic Theology

Agamben's Theories of the State of ExceptionFrom Political to Economic Theology Tim Christiaens (bio) He who, in this mystical alphabet, begins with A will inevitably end with Z; he who desires to worship God must harbour no childish illusions about the matter, but bravely renounce his liberty and humanity. —Mikhail Bakunin Giorgio Agamben's philosophy is frequently treated as continuous throughout his career. Agamben himself encourages such a reading by making explicit links between recent and earlier works. Commentators rarely question this assumption of continuity, which is odd given Agamben's long career and some statements to the contrary. The first chapter of State of Exception (2005), for example, is called "The State of Exception as a Paradigm of Government," while Agamben proclaims in a lecture some years later that "in order to understand the peculiar governmentality under which we live, the paradigm of the state of exception is not entirely adequate" (2014). As a result, secondary literature tends to focus either on the earlier volumes of the Homo Sacer project and mention the others only in passing or vice versa. I will question the assumption of continuity by examining Agamben's theory of the state of exception. I identify two approaches to the state of exception. First, I delineate how Homo Sacer (1998) conforms to Schmitt's politico-theological perspective of the state of exception as a secularized form of miraculous divine intervention. In State of Exception, there are, however, hints away from political theology and toward a view of sovereignty as an auctoritas that not only suspends but also legitimates the application of the law. In the third section, I show how The Kingdom and the Glory (2011) moves toward economic theology and [End Page 49] links the state of exception to providential government. The sovereign no longer intervenes directly by suspending the law but renders himself inactive to make a spontaneous self-government of the world under the law possible. In the final part, I address the question of the relation between the politico-theological and economico-theological models. Whereas Agamben himself favors the latter over the former in The Kingdom and the Glory, I defend the perspective from State of Exception where Agamben argues for the relevance of both depending on the degree of spontaneous obedience to the law. Under normal circumstances, the economico-theological authorization of the law suffices. The politico-theological suspension of the law, however, remains part of the sovereign's toolbox, but is only employed only in emergency situations. HOMO SACER: THE STATE OF EXCEPTION AS MIRACLE Agamben starts Homo Sacer with Aristotle's distinction between natural and sociopolitical life: "zoē, which expressed the simple fact of living common to all living beings … , and bios, which indicated the form or way of living proper to an individual or a group" (1998, 1). Communities articulate their bios via the identification of a specifically human potentiality that, if actualized, provides happiness (Whyte, 25–26; Watkin, 186). In Aristotle's polis, for instance, the cultivation of logos was deemed the utmost achievement of the good life. To actualize this potentiality, the community elaborates social rules. Agamben (1998, 20), however, agrees with Carl Schmitt (10) that the application of these rules to real-life situations is problematic. General abstract rules can be applied to particular cases only through the mediation of a decision (McLoughlin 2009, 246; Whyte, 60). The applicability of a particular law makes sense only if the decision maker can also choose not to apply the rule. The authorities can make an exception to a law by refusing to apply it in a specific case. In that instance, the case is excluded from that law but is included in the sphere of sovereign authority that decides whether this event falls under the law. The same argument holds for the legal order as a whole, where this inclusive exclusion constitutes the state of exception (Agamben 1998, 21). The applicability of the legal order depends on the sovereign's [End Page 50] willingness to apply the law and thus also on his capacity to withdraw this applicability (DeCaroli, 50): "The sovereign exception … is the presupposition of the juridical reference in the form of its...

Does Education Really Cause Domestic Violence? Replication and Reappraisal of "for Better or for Worse? Education and the Prevalence of Domestic Violence in Turkey"

Using the 2008 Turkish National Survey of Domestic Violence against Women, Erten and Keskin (2018, henceforth EK), published in AEJ–Applied Economics, find that women's education increases the psychological violence and financial control behavior that they face from their partners. The authors also claim that the incidence of financial control behavior rises because women become more likely to be employed—supporting the instrumental violence hypothesis. They present this evidence only for women who live in what they call areas during childhood. EK's findings are an artifact of the way the authors create two key variables: the variable that classifies women into rural vs. urban childhood location and the variable measuring financial control behavior. EK misclassify the variable on childhood rural status. We find that once this variable is defined properly, the evidence for all their findings vanishes. EK make use of two of the three variables related to financial control behavior in the dataset. We show that using all three variables—or any other combination of two of the three variables—generates no evidence of a policy effect on financial control behavior. Even after ignoring these problems, the evidence EK provide in their paper is highly specification sensitive and the standard checks of the continuity assumption in RDD fail for their key outcomes. Moreover, the results obtained from the analysis of urban areas—not provided in their paper—are inconsistent with the instrumental violence hypothesis. In addition, EK claim—using RDD graphs with high-order polynomials but no estimation results—that the policy has no effect on men's schooling, contrary to the findings of the previous literature. However, we show a clear and substantial policy effect on men's schooling, resulting in the failure of their exclusion restriction assumption.

انعكاسات جائحة كورونا على تطبيق الفروض والمبادئ والمحددات المحاسبية: بحث نظري (Reflections of the Corona Pandemic on Implementation of the Accounting Assumptions, Principles and Determinants: Theoretical Research)

Arabic Abstract: استهدف البحث دراسة التداعيات الاقتصادية والاجتماعية لجائحة كورونا وانعكاساتها على تطبيق الفروض والمبادئ والمحددات المحاسبية، واعتمد على المنهج الوثائقي (Documentary Approach)، الذي تطلب جمع البيانات من إصدارات المنظمات المحاسبية المهنية الدولية وشركات المحاسبة والمراجعة الدولية الكبرى، وتم تحليل الآراء والإرشادات الواردة في هذه الوثائق باستخدام التحليل الموضوعي (Thematic analysis)، واستمد البحث أهميته من حداثة وأهمية موضوعه، وخلص إلى نتائج أبرزها: أن جائحة كورونا أفرزت مؤشرات اقتصادية ومالية قد تلقي بظلال من الشك على تطبيق فرض الاستمرارية، مما يترتب عليه تأثير سلبي على فرض الوحدة الاقتصادية والمبادئ والمحددات المحاسبية، كما أن مبدأ القياس يواجه صعوبة في التطبيق في ظل جائحة كورونا؛ نتيجة عدم توفر بعض مدخلات القياس الموثوق بها ولجوء المحاسبين للإفراط في استخدام التقديرات الشخصية، خاصة عند استخدام القيمة العادلة، كما تتطلب جائحة كورونا إعادة النظر في تطبيق مبدأ تحقق المصروف ومبدأ تحقق الإيراد وسياسات الاعتراف المحاسبي المعدة على هذين المبدأين، وتزداد الحاجة إلى الإفصاح عن المعلومات المالية وغير المالية في ظل جائحة كورونا، خاصة تلك المتعلقة بالمخاطر والاحتمالات المستقبلية، كما يحتاج المحاسب في ظل آثار هذه الجائحة إلى إعادة النظر في تحليلات التكلفة والمنفعة عند إنتاج المعلومات المحاسبية وزيادة التطبيقات القائمة على الحيطة والحذر، وبناء على هذه النتائج تم اقتراح بعض التوصيات التي من شأنها أن تساعد المحاسبين وأصحاب المصلحة أثناء وبعد جائحة كورونا. English Abstract: This research focuses on the economic and social implications of the Corona pandemic on the implementation of the accounting assumptions, principles, and determinations, based on the Documentary Approach, which require Collects the data from the publications of the international accounting organizations, international accounting, and auditing firms to analyze the opinions and instructions by thematic analysis. The importance of the research lies in the novelty of the topic. The conclusion of this study includes several results, the most important of which are: many financial and economic indicators show up because of the pandemic, these indicators may cast doubt on applications of the continuity assumption, which may hurt unity assumption, accounting principles, and determinations. Besides, the measurement principle faces difficulties on applying according to the lack of reliable measurement inputs which excess the accountants using the personal estimates, especially when using the fair value. Moreover, the pandemic requires a reconsideration of the applying of the principle of expense recognition, the principle of revenue recognition, and accounting recognition policies for these principles. The need for more disclosure of information increases especially those related to future risks and possibilities according to the pandemic. Furthermore, the accountant needs to reconsider the cost-benefit analysis when producing accounting information and the practice that concerns conservatism. According to these results, several recommendations propose to assist the accountants and the stakeholders during and after the pandemic.

A Second Order Dynamical System and Its Discretization for Strongly Pseudo-monotone Variational Inequalities

We consider a second order dynamical system for solving variational inequalities in Hilbert spaces. Under standard conditions, we prove the existence and uniqueness of strong global solution of the proposed dynamical system. The exponential convergence of trajectories is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. A discrete version of the proposed dynamical system leads to a relaxed inertial projection algorithm whose linear convergence is proved under suitable conditions on parameters. We discuss the possibility of extension to general monotone inclusion problems. Finally some numerical experiments are reported demonstrating the theoretical results.

Deslocamentos sociais provocados pelo ensino superior: as ações e percepções de mediadores formados no curso Educação do Campo da Transamazônica e Xingu

As reflexões do presente artigo centram-se nos egressos do curso de Licenciatura em Educação do Campo da UFPA-Campus de Altamira, vistos, para efeito desta análise, enquanto agentes mediadores, os quais se auto declaram pertencentes às ações coletivas ligadas ao campesinato. Objetivamos analisar, a partir de uma abordagem qualitativa de pesquisa, a dimensão histórica manifesta no pressuposto de continuidade da classe (o nominado, genericamente, Movimento Social da Transamazônica) que os mediadores portam, aliada aos sentidos de mudança que os mesmos têm incorporado diante da formação universitária recebida que repercutem sobre os espaços de mediação dos egressos. Os dados produzidos através das técnicas de entrevistas individuais e de grupo focal permitem inferir que a incorporação e o uso de outras formas de capitais (institucionalizados por meio do ensino superior) têm contribuído para a emergência de mediadores, alguns advindos da posição de lideranças locais, outros assumindo esse lugar de intermediar demandas, recursos, etc; em ambos os casos, é possível que estejam construindo instâncias locais de poder, criando espaços de inclusão política, ou ainda questionando internamente a própria ação coletiva.
 Palavras-chave: educação do campo, deslocamentos sociais, mediadores, Transamazônica e Xingu.
 
 Social dislocations caused by college education: actions and perceptions of mediators graduated in Countryside Education of Campo da Transamazônica and Xingu
 ABSTRACT. The present work focuses on individuals with Licentiate degree in Countryside Education of UFPA – Campus of Altamira, regarded as mediating agents who consider themselves participants in peasantry-related actions. The main objective of this study is to analyze, through a qualitative research approach, the historical dimension present in class continuity assumption supported by these mediating groups (referred as Social Movement of Transamazônica), associated with the sense of change they have developed in college thus affecting their mediating scope. The data obtained through techniques of individual and focus groups interviews reveal that incorporating and using certain forms of capital (institutionalized through college education) has contributed to the emergency of mediators, some of them deriving from local leadership positions and others intermediating demands, resources, etc. In both cases, these groups may be building local instances of power, by creating chances of political inclusion or even questioning internally the collective action itself.
 Keywords: countryside education, social dislocations, mediators, Transamazônica, Xingu.
 
 Desplazamientos sociales provocados por la enseñanza superior: las acciones y percepciones de facilitadores egresos del curso de Licenciatura en Educación del Campo, de la UFPA - Altamira Campus
 RESUMEN. El presente artículo busca focalizar las acciones y reflexiones de militantes de las acciones vinculadas al campesinado en la zona Transamazônica y Xingu, egreso en el curso de Licenciatura en Educación del Campo de la UFPA- Campus Altamira, tomando como presupuesto, a efectos de este análisis, el encargo de facilitadores. El objetivo es hacer un estudio, desde un abordaje cualitativo a través de una anchura histórica expresa en el presupuesto de continuidad de acción clasista llevada a cabo por el denominado genéricamente ‘Movimento Social da Transamazônica’, al que los facilitadores, añaden, así como los sentidos del cambio en sus performances de militantes. Los datos producidos tras las técnicas de entrevistas individuales y por equipos focalizados, asienten la deducción de que la incorporación del habitus académico, bien como el uso de maneras referente al capital cultural reunido a través del acceso de los militantes a la enseñanza superior, hayan aportado para que los mismos tomen sus posiciones de liderazgo y de fundamental importancia para el intermedio junto al Estado de exigencias comunales, sino también a la capacitación de demandas. Los facilitadores intervienen buscando la construcción de peticiones regionales de poder, creando espacios de inclusión política, cuestionando internamente el propio entorno colectivo.
 Palabras clave: educación del campo, esplazamientos sociales, facilitadores, Transamazônica e Xingu.

An accelerated forward-backward algorithm with a new linesearch for convex minimization problems and its applications

We study and investigate a convex minimization problem of the sum of two convex functions in the setting of a Hilbert space. By assuming the Lipschitz continuity of the gradient of the function, many optimization methods have been invented, where the stepsizes of those algorithms depend on the Lipschitz constant. However, finding such a Lipschitz constant is not an easy task in general practice. In this work, by using a new modification of the linesearches of Cruz and Nghia [ 7 ] and Kankam et al. [ 14 ] and an inertial technique, we introduce an accelerated algorithm without any Lipschitz continuity assumption on the gradient. Subsequently, a weak convergence result of the proposed method is established. As applications, we apply and analyze our method for solving an image restoration problem and a regression problem. Numerical experiments show that our method has a higher efficiency than the well-known methods in the literature.

Data-Driven Estimation of Infinitesimal Generators of Stochastic Systems

Abstract This paper is concerned with a data-driven approach for the estimation of infinitesimal generators of continuous-time stochastic systems with unknown dynamics. We first approximate the infinitesimal generator of the solution process via a set of data collected from trajectories of the unknown system. The approximation utilizes both time discretization and sampling from the solution process. Assuming proper continuity assumptions on dynamics of the system, we then quantify the closeness between the infinitesimal generator and its approximation while providing a priori guaranteed confidence bound. We demonstrate that both the time discretization and the number of data play significant roles in providing a reasonable closeness precision. Moreover, for a fixed size of data, variance of the estimation converges to infinity when the time discretization parameter goes to zero. The formulated error bound shows how to pick proper data size and time discretization jointly to prevent this counter-intuitive behavior. The proposed results are demonstrated on a case study.

Rounding and other pitfalls in meta-studies on p-hacking and publication bias: A comment on Brodeur et al. (2020)

Brodeur et al. (2020) study a large number of hypothesis tests from economic articles and find evidence for p-hacking or publication bias, in particular for studies using an IV or DID approach. We show that a crucial continuity assumption is violated because many collected estimates and standard errors are reported with just a single significant digit. These rounding errors cause bunching of computed z-statistics, particularly at exactly 2. We propose and compare different adjustments. Under every adjustment evidence for p-hacking from randomization and caliper tests at the 5% significance threshold substantially reduces. We find no more significant results for DID studies, but effects remain similar and significant for IV studies. Brodeur et al. (2020) perform additional tests that seem less affected by rounding errors. Yet, we highlight several problems of these tests.

Linear programming-based reconstruction algorithm for limited angular sparse-view tomography

The reconstruction of high-quality images from limited angular sparse-view tomography data is desired in many fields, including low-dose computed tomography and nondestructive detection. In this study, two regularization terms based on the assumptions of image continuity and nonzero pixels are utilized to reconstruct an image from incomplete data. By transforming the original nonlinear reconstruction model into a linear programming, the proposed method can obtain the optimal solution rather than the local minimum point, which helps to accurately reconstruct the images. To demonstrate the effect of the proposed method, we designed a simulation experiment under limited angle, few-view, and limited angular sparse-view conditions, and evaluated the reconstruction results using the structural similarity index, peak signal-to-noise ratio, and cosine distance. The experimental results show that our method can effectively overcome the adverse effects of sparse-view conditions and a limited scanning range. In the tomographic results of our method, streak artifacts do not appear, even when using projection data from 20 views of a 180° scanning angular range.

Methods Matter: p-Hacking and Publication Bias in Causal Analysis in Economics: Comment

Brodeur et al. (2020) study a large number of hypothesis tests from top economic articles and find evidence for p-hacking or publication bias, in particular for articles using DID or IV as causal identification method. We show that a crucial continuity assumption is violated because many collected estimates and standard errors are reported with just a single significant digit. These rounding errors cause bunching of computed z-statistics at exactly 2. We adjust for rounding errors and then find no evidence for p-hacking or publication bias in the DID and pooled data, but evidence remains for IV.

L 1-Norm Sparse 2-D Phase Unwrapping Algorithm Based on Reliable Redundant Network

Multitemporal interferometric synthetic aperture radar (InSAR) technology has become an important tool for digital elevation model (DEM) generation and surface deformation monitoring. The prerequisite is to obtain the correct unwrapped phase of the interferograms. However, it is still challenging to obtain reliable results by traditional 2-D phase unwrapping (PU) algorithms and even 3-D PU algorithms, when the phase continuity assumption fails due to large deformation gradients or abrupt topographic changes. This letter proposes an L¹-norm sparse 2-D PU algorithm based on reliable redundant network in the phase discontinuous region, which is obtained by implementing ambiguity detector on free network within a given distance. Experiment on real synthetic aperture radar (SAR) interferograms covering urban tall buildings verified that the algorithm can obtain more reliable results in phase discontinuous regions than traditional PU algorithms.

A kind of stricter Hyers–Ulam stability of second order linear differential equations of Carathéodory type

The purpose of this article is to establish a kind of stricter Hyers–Ulam stability of second order linear differential equation of Carathéodory type. More explicitly, we prove that if x is an approximate solution satisfying a kind of stricter condition of the differential equation x′′(t)+b1x′(t)+b0x(t)=f(t) without the assumption of continuity of f(t), then there exists an exact solution of the differential equation near to x.

Characterizations of nonconvex optimization problems via variational inequalities

ABSTRACT In this paper, we deal with two problems from the theory of nonconvex nonsmooth analysis; The characterization of nonsmooth quasiconvex functions, and connections between nonsmooth constraint optimization problems via variational inequalities. For the first problem, we provide different characterizations for nonsmooth quasiconvex functions, while for the second problem, a full connection between constraint optimization problems and Stampacchia and Minty variational inequalities is provided, in both cases, neither differentiability nor convexity nor continuity assumptions are considered. As a corollary, we recover well-known results from convex analysis.

A NOTE ON THE PAPER “ON COMPLETENESS IN METRIC SPACES AND FIXED POINT THEOREMS"

In the present note, we show that the assumption of continuity used in the fixed point theorem of Gregori et al. (Results Math. 73 (2018), no. 4, Art. 142, 13) can be relaxed to some weaker version of continuity. More precisely, we prove a fixed point theorem for orbitally continuous and k-continuous mappings in weak G-complete metric space and provide an appropriate example to show that our result is not only valid for continuous mappings but also for some discontinuous mappings. Moreover, we apply our main result to establish a common fixed point theorem for two self-mappings

Structural Aspect of Checking the Continuity of the Enterprise during Internal Audit

The article presents the results of the study and the further development of approaches to assessing the continuity risks associated with the internal audit of the enterprise. Particular attention is given in the article to the organization of internal audit of termination of activity for groups of events or conditions, which alone or in the aggregate may call into question the validity of the assumption of continuity of activity.
 The purpose of the article is to research and further develop approaches to assessing the risk assessment of the impact of internal audit effectiveness on the auditor’s assessment of the risk of termination of the enterprise.
 Current practice research shows that the implementation of an element of internal control, such as internal audit, is either not used at all, or is carried out in a purely formal manner. In particular, it concerns the control over the financial statements, which indicate the probability of termination of the enterprise. In turn, the lack or low efficiency of the internal audit service, whose main task is to monitor the internal control system, causes an increase in audit risk of control, which in turn increases the overall level of audit risk. This situation necessitates an increase in volumes and as a result of audit time.
 In view of the results of the conducted researches of the current practice of functioning of the internal audit service at the enterprises, in most cases there is a purely formal approach to its functions, in particular in the aspect of ensuring control over the financial status indicators, the critical values of which can directly lead to the termination of the activity of the enterprise.
 The analysis of the scientific and methodological base shows the lack of materials, the organization of an effective system of internal control over strategic financial indicators, and as a consequence of the lack of an effective concept of its monitoring by the internal audit.
 We have proposed a comprehensive functional model that includes the following elements: 1) setting an assignment for the internal audit service; 2) identification of sources of necessary information and method of assessment of its reliability; 3) conceptual basis for ensuring the performance of internal audit functions.

Modelling Intercalation Induced Stresses in All Solid State Batteries Using Discrete Element Method

Recently, all-solid-state lithium-ion batteries (ASSLiB) has emerged as one of the most promising candidates for next-generation power sources for electric vehicles (EVs) and energy storage. The main reason is the introduction of non-flammable solid electrolyte (SE) which substantially reduces the risk of battery fires. However, more research is needed in order to improve the durability and the overall performance.High charge capacity active material (AM) such as Si have been developed but their high expansion during charging and discharging reduces the durability. 1 During charge, AM in the cathode will absorb Lithium by intercalation and expand. A reverse contraction process occurs in the anode. This is known as Vegards expansion/contraction and cause buildup of high stresses, so called intercalation induced stresses. Although materials with less expansion/contraction have been developed, it is unclear how much expansion/contraction the materials in AM and SE can tolerate.Previous studies that model intercalation induced stress can be found in the literature. Most of the research is focused on the intercalation induced stresses either inside the AM or inside SE material. In the study of Bucci et al., 2 the stress in the SE due to Vegards expansion of AM was modelled by the finite element method (FEM) and the location of cracks could be predicted. However, according to Sun et al., 3 the critical region of failure is not within AM and SE but at the interface. Moreover, in FEM it is difficult to resolve the grained boundaries at the interfaces and the continuity assumption may not be valid as there are often void spaces between SE particles. These issues can be solved by modelling AM and SE as particles as in the Discrete Element Methods (DEM).In this study we perform DEM simulations and utilize the multisphere method for the AM particles. In the multisphere method, non-spherical particles are represented as a cluster of spherical sub-particles as illustrated in Figure 1 (a). We assume elliptical shapes which is in agreement with TEM image of graphite AM. In the DEM solver, the particle motion is determined from the forces acting on each particle. The elastic contact force between two particles with radii Ri and Rj is calculated by the Herzian contact law: F elastic = 4/3∙E eff δ 3/2 R eff 1/2 (1)where R eff = RiRj /(Ri + Rj ) is the effective radius and E eff is the effective elastic modulus given by1/E eff = (1-ν i 2)/E i +(1-ν j 2)/E j (2) where E i and E j are the Young modulus of elasticity of the particles. In the DEM solver, collision damping force and the tangential forces due to static and kinetic friction are also calculated. The motion and rotation of each particle was calculated from the sum of forces and torques acting on the particles.A series of DEM simulations were conducted. Different aspect ratios of the elliptical shapes were generated and the relationship between the aspect ratio and circularity agreed well with the experimental results. A gravity driven packing simulation was conducted followed by a press simulation at 500 MPa and a release simulation to stack pressure at 25 MPa. In order to solve for the intercalation induced stresses, expansion of AM particle was calculated by gradually increasing the particle radius. The results of the spatial distribution of the stresses of the SE material is shown in Figure 2 in the case of a volume expansion of 10%.During cold pressing of ASSLiB electrode, the contact force is not perfectly elastic but plasticity effects of SE plays a role large role and is an important design parameter 4. In cold pressing applications the normal force is often modeled as follows 5 F normal = min(F elastic , F plastic ) (3)where F plastic is the plastic force. A model is currently under development that can simulate the effect of plasticity on stress and damage during cold pressing and intercalation. The model can aid in the development and selection of favorable of materials for ASSLiB electrode.This research was supported by Grants-in-Aid for Scientific Research on Innovative Areas, “Science on Interfacial Ion Dynamics for Solid State Ionics Devices” MEXT, Japan FY2019-2023. References M. N. Obrovac, L. Christensen, D. B. Le, and J. R. Dahn, J. Electrochem. Soc., 154, A849 (2007).G. Bucci, T. Swamy, Y.-M. Chiang, and W. C. Carter, ArXiv170300113 Cond-Mat (2017) http://arxiv.org/abs/1703.00113.C. Sun, J. Liu, Y. Gong, D. P. Wilkinson, and J. Zhang, Nano Energy, 33, 363–386 (2017).K. Nagao et al., Solid State Ion., 308, 68–76 (2017).C. L. Martin, D. Bouvard, and S. Shima, J. Mech. Phys. Solids, 51, 667–693 (2003). Figure 1