Discrete Form Research Articles

Feeling Solitary in the Seductive Republic: Narrative Deviance in Elizabeth "Harriot" Wilson and William "Amos" Wilson

Abstract: This essay examines two prominent literary narratives and tropes at the turn of the nineteenth century that constellate around the seduction plot and the hermit narrative. These two ostensibly discrete narrative forms have a curious history as they play out in the printed iterations of the Elizabeth Wilson and William Wilson stories, two siblings whose lives were marked by differing forms of tragedy. By bringing together a tale of seduction, execution, and hermitic living, I show how the account of Elizabeth Wilson's execution for infanticide shifted from being a seduction plot to a frame tale for a hermit narrative about her brother. This narrative turn moves from an account that focuses on the policing of female sexuality to instead emphasize the curious life of a man who refuses social intercourse. But that shift actually signals something more complicated about how the early Republic sought to instill ways of feeling about gender and deviance.

SOME DIAMOND INTEGRAL REVERSE HÖLDER-TYPE INEQUALITIES ASSOCIATED WITH SPECHT’S RATIO ON TIME SCALES

This paper is devoted to studying some new reverse Hölder-type inequalities associated with the dynamic integral called diamond on time scale, which is expressed as an ‘approximate’ symmetric integral on time scales. Some related inequalities are also presented. The obtained inequalities extend known results related with discrete and continuous forms.

Some novel Kulisch-Miranker type inclusions for a generalized class of Godunova-Levin stochastic processes

<abstract><p>Mathematical inequalities supporting interval-valued stochastic processes are rarely addressed. Recently, Afzal et al. introduced the notion of $ \mathtt{h} $-Godunova-Levin stochastic processes and developed Hermite-Hadamard and Jensen type inequalities in the setting of interval-valued functions. This note introduces a more generalized class of Godunova-Levin stochastic process that unifies several previously published results through the use of Kulisch-Miranker type order relations that are rarely discussed in relation to stochastic processes. Further, it is the first time that fractional version of Hermite-Hadamard inequality has been developed by using interval-valued stochastic processes in conjunction with a classical operator. Moreover, we give new modified forms for Ostrowski type results and present a new way to treat Jensen type inclusions under interval stochastic processes by using a discrete sequential form. We end with an open problem regarding Milne type results and discuss the importance of different types of order relations related to inequality terms in interval-valued settings.</p></abstract>

Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel

<abstract><p>Hepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional-order model of HBV. The qualitative assessment and well-posedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra-type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator's efficacy. We observe that the explored discrete fractional operators will be $ \chi^2 $-increasing or decreasing in certain domains of the time scale $ \mathbb{N}_j: = {j, j + 1, ... } $ by looking at the fundamental characteristics of the proposed discrete fractional operators along with $ \chi $-monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model's ability to forecast infectious diseases such as HBV and take preventive action.</p></abstract>

Information modeling of the normal forms of logical functions in Maple system

The article discusses possible ways to use the Maple computer algebra system to obtain perfect conjunctive and disjunctive normal forms. Computer algebra systems make it possible to expand the possibilities for creating, applying and using mathematical models in the daily activities of engineers, researchers, and also contribute to improving the education of students of various training profiles. In addition, the use of computer technology can help to apply various methods and expand approaches to the representation of the studied objects (Boolean functions) of discrete form, including in education. Computer algebra systems such as Maple, Mathematica, etc. are the most adapted for studying various sections of discrete mathematics and mathematics in general. The possibilities of the Maple program are shown for use at the initial stages of mastering the discrete mathematics section of the university course - Boolean functions, in particular, for work on the construction and study of perfect conjunctive and disjunctive normal forms according to the truth table.

Размышление о системном мышлении: между А. Богдановым и Л. фон Берталанфи

The article presents a comparative analysis of the concepts proposed by two influential figures in modern systems theory — Alexander Bogdanov and Ludwig von Bertalanffy. In light of the revival of systems analysis, the article addresses the need to reevaluate the systemic worldviews of these theorists, aiming to discern similarities, differences, and the potential for a systemic synthesis of their ideas. Summarizing the key principles of the new theory of economic systems and space-time analysis, the article highlights distinctions bet­ween Ludwig von Bertalanffy’s discrete (“elemental”) concept and Alexander Bogdanov’s continuous (“process”) concept. The shift in system formation from continuous to discrete forms across various fields is underscored, emphasizing the necessity for a holistic approach in 21st-century systems thinking. The article introduces a tetrad as a universal model, emphasizing its role in fostering integral, full-scale systems thinking. The concepts of Ludwig von Bertalanffy and Alexander Bogdanov can be seen as polar, reflecting a transformation in the theory and practice of system formation from the 1920s to the 1940s, moving from continuous systemic forms to discrete ones. Additionally, the article underscores distinctions between one-sided versions of systems concepts that focus on organizational structures, innovative projects, logistics processes, or intra- and external-system environments. The tetrad, serving as a comprehensive systemic worldview, incorporates object, process, design, and environmental subsystems. The article advocates for a holistic approach, uniting short- and long-term local and global subsystems, and outlines a foundational framework for integral, full-scale systems thinking in the 21st century.

ФАКТОР ЯЗЫКОВОЙ ВАРИАТИВНОСТИ В ФУНКЦИОНАЛЬНО-СЕМАНТИЧЕСКОЙ ОЦЕНКЕ ЛЕКСИЧЕСКИХ ЕДИНИЦ

The article puts forward the objective to disclose the means and features of language functioning in various discourse systems. The methodological basis of the research comprises the concept of language variability and the theory of synergetic linguistics. Different lexical units are explored in use within various discourse types in terms of their functions. The objective of correlating language unit functions to the discourse situation made it necessary to select the most representative discourse systems. Stemming from the basic principle that there are no ironclad borders between discrete forms of language use, the author claims that a typical discourse situation as a system-shaping attractor dictates functional specifics of language units. In distinguishing discourse types, the underlying principle is the degree of implementing the function of information and that of impact. Linguosynergetic method makes it possible to formulate universal principles of functioning language units of different types in the context of different discourse systems. These principles necessarily impose pragmatically conditioned meaning.

Matlab Class for Rapid Visualization of Missile-Target Engagement Scenarios

In this paper, the authorial Matlab Battlespace Visualization Class (MBVC) is proposed to plan, design, and compose the preliminary version of the desired computer animation, which can then be used both as a background for the discussion of the final composition and as an individual project for public presentation, providing a visual reference for missile-target engagement simulations. As a design tool, the MBVC allows us the combination of the advanced mathematical models of missile guidance loop elements (implemented in the discrete form as program scripts) with the capabilities offered by open, powerful, and flexible 3D graphical engine. As a visualization tool, the MBVC allows the designers to present their research findings in both an illustrative and informative way, providing a visual reference for the computer simulation. The class is freely available for scientific, engineering or educational use.

Li-Ion Cell in Operando Monitoring and Prognostication Using CMUT Devices

Capacitive micromachined ultrasonic transducer (CMUT) devices are ideal solutions for in operando battery monitoring applications especially for consumer electronics. Their minute size (2mm x 1mm x 0.5mm) allows direct placement on the battery without affecting the form factor of the device, the volume production techniques used for their manufacture allow for a very low-cost device, and they can be easily integrated with front-end integrated circuits either in a single device or in a discrete multichip form. Together with industry partners we have developed CMUT devices that we use to continuously monitor the behavior of a battery while it is cycling.For this work we used CMUTs (close-up shown in Fig. 1(a)) developed to operate with a low bias voltage (less than 30 V) which reduces the complexity of the driving hardware. The impulse response and its frequency content are shown in Fig. 1(b). In collapse mode, the peak frequency is 4.0 MHz and the one-way –3 dB BW is 76%, which allows flexibility in setting the drive conditions to interrogate the battery. Our testing also shows that the CMUTs show good device-to-device uniformity and they have a very stable performance in variable temperature environments (e.g. 0℃ - 60℃ ).The cell is interrogated in pulse-echo mode. The CMUT is excited by a wide-band unipolar pulse and the returned analog signal is filtered and amplified. The signal is then digitized and processed to extract features that allow us to quantify the state of the battery. Figure 1(c) depicts such signal features change under baseline cell cycling conditions (three cycles at a charge rate of C/4). These changes are the result of mechanical material property changes in the cell e.g., electrode stiffness and density [1] which directly affect the acoustic wave propagation inside the cell. Figure 1(d) depicts signal feature change due cell overcharge (red line). Ultrasound is especially sensitive to gas generation which occurs as the cell voltage extends beyond normal operating range [2]. Signal features provide early warning notice that cell is outside of normal operating conditions.Figure 1. a) Close-up image of CMUT device. b) CMUT impulse response and corresponding frequency content. c) Signal features (RMS and Time of Flight (ToF)) and thickness change during C/4 charge and discharge. d) Signal features during cell constant current overcharge. Cell overcharged after 4.4V (red line). Chang, W. et al. Measuring effective stiffness of Li-ion batteries via acoustic signal processing. Mater. Chem. A 8, 16624–16635 (2020).Appleberry, M. C. et al. Avoiding thermal runaway in lithium-ion batteries using ultrasound detection of early failure mechanisms. Journal of Power Sources 535, 231423 (2022). Figure 1

PROFILING OF THE HOB MILL TOOL FOR GENERATING A PROFILE KNOWN IN DISCRETE FORM

In industrial practice, is sometimes needed to manufacture specific parts without blueprints. This part of engineering process is known as reverse engineering. Usually, this assumes that an existing piece is measured or scanned and based on this result is made a new part. If the part can be machined with universal cutting tools the manufacturing process don’t rise problems, but in case of parts which needs specific tools, these must be designed to be suitable for machining the piece. In this paper, a tool profiling algorithm is proposed, which is based on the capacity to measure and represent some surfaces in a methodical cloud of points form. The proposed profiling algorithm is based on the “virtual pole” method. This method is used together with the intermediate surface theorem for profiling tools characterized by a helical primary peripheral surface. This article will represent a continuation of a research which was been published in 2021, in Bulletin of Polytechnic Institute from Jassy. In that published article, the profiling of the hob mill tool was presented in a theoretical way and the ”virtual pole” theorem was applied for an any type of profiles. The proposed algorithm allowed the determination of the tool’s profile reciprocally enveloping with a piece’s profile known in discrete form. Now, in this paper, the discrete form profile will represent exactly a cycloidal disk from a cycloidal reducer whose coordinates were determined using specific reverse engineering processes. Considering that the determination of the relative movements between the tool and the part, as well as the determination of the enveloping condition are relatively complicated and can be a source of errors, the purpose of this work is to highlight the advantages of the ”virtual pole” method compared to the other specific methods of tool profiling that generate by enwrapping. At the same time, it is investigated if the ”virtual pole” method can provide a support for the identification of the intermediate surface, with the help of graphic design environments, for profiling, in this case, the worm tools, since the ”virtual pole” method cannot be applied as such in the case of disk-type tools, worm tools and cylindrical-frontal tools, due to the fact that the theorem is intended for the study of planar gearing. The advantages of using the ”virtual pole” method are obvious compared to the classical tool profiling methods. The results demonstrated the accuracy of the method, by the fact that, using the ”virtual pole” method, the calculation time for profiling the hob mill tool for generating a profile known in discrete form, namely the profile of the cycloidal disk, is significantly reduced.

Backstepping model‐free adaptive control for a class of second‐order nonlinear systems

SummaryThis paper proposes a backstepping model‐free adaptive control (BS‐MFAC) algorithm for the trajectory tracking control problem of a class of second‐order nonlinear systems. Firstly, the model‐free adaptive control (MFAC) is employed to track the virtual desired velocity. Then, based on the measured state data at the current moment, a virtual desired velocity is designed, combining MFAC with backstepping control in a clever manner. By designing a discrete form of Lyapunov function, it is proven that the system velocity error under this algorithm converges asymptotically and stably. Furthermore, a nonhomogeneous difference equation solution related to the system position is obtained through calculations. The analysis of the solution indicates that the system position output error will slide into a neighborhood around zero. This algorithm possesses advantages such as simple structure, model independence, and strong robustness. Additionally, a planar two‐link space robot arm model is constructed using the Mbdyn platform, a multibody dynamics simulation software. Trajectory tracking control of joint angles is achieved under the proposed control algorithm in this paper. The simulation outcomes unequivocally establish the efficacy of the algorithm, which adeptly exploits the pseudo partial derivatives (PPD) estimation for second‐order nonlinear systems in MFAC. The algorithm yields expedited and superior trajectory tracking control of said systems.

Linear and Nonlinear Splitting Schemes Conserving Total Energy and Mass in the Shallow Water Model

Two linear and one nonlinear implicit unconditionally stable finite-difference schemes of the second-order approximation in all variables are given for a shallow-water model including the rotation and topography of the earth. The schemes are based on splitting the model equation into two one-dimensional subsystems. Each of the subsystems conserves the mass and total energy in both differential and discrete (in time and space) forms. One of the linear schemes contains a smoothing procedure not violating the conservation laws and suppressing spurious oscillations caused by the application of central-difference approximations of spatial derivatives. The unique solvability of the linear schemes and convergence of iterations used to find their solutions are proved.

An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier–Stokes equations posed on a passively evolving smooth closed surface embedded in R 3 \mathbb {R}^3 . The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.

Rectifying Strip Patterns

Straight flat strips of inextensible material can be bent into curved strips aligned with arbitrary space curves. The large shape variety of these so-called rectifying strips makes them candidates for shape modeling, especially in applications such as architecture where simple elements are preferred for the fabrication of complex shapes. In this paper, we provide computational tools for the design of shapes from rectifying strips. They can form various patterns and fulfill constraints which are required for specific applications such as gridshells or shading systems. The methodology is based on discrete models of rectifying strips, a discrete level-set formulation and optimization-based constrained mesh design and editing. We also analyse the geometry at nodes and present remarkable quadrilateral arrangements of rectifying strips with torsion-free nodes.

Toward a Philosophy of Melodrama

Abstract This article proposes a philosophy of melodrama, following the example of Noël Carroll in The Philosophy of Horror (1990). Melodrama is defined by a distinctive mode of address in which morality is dramatized through an appeal to our emotions. More narrowly conceived as the “tearjerker,” it is designed to solicit tears through the orchestration of pathos. While melodrama is associated above all with a genre of nineteenth- century theater, it is considered here as a mode that persists from at least the medieval period into the present, encompassing discrete art forms, such as theater, opera, and film. Furthermore, as it evolves historically, it develops more complex idioms. Classical melodrama, or the melodrama of good versus evil, which dwells on the pathos of suffering innocence, is contrasted with romantic melodrama or the melodrama of moral antinomy (Singer), which explores the pathos of sacrifice. A series of distinctions are drawn between sympathy, pathos, empathy, and identification, and the relationship of each to the other and to our moral responses are briefly delineated. The article contests Murray Smith's theory of empathy as central or personal imagination and defends a distinctive concept of identification, based upon its roots in the medieval French “identifier,” to “regard as the same.” It concludes with a brief defense of melodrama against the charge that is emotionally contrived and exploits our moral sentiments for meretricious ends.

Measuring Convective Organization

Abstract Organized systems of deep convective clouds are often associated with high-impact weather and changes in such systems may have implications for climate sensitivity. This has motivated the derivation of many organization indices that attempt to measure the level of deep convective aggregation in models and observations. Here we conduct a comprehensive review of existing methodologies and highlight some of their drawbacks, such as only measuring organization in a relative sense, being biased toward particular spatial scales, or being very sensitive to the details of the calculation algorithm. One widely used metric, Iorg, uses statistics of nearest-neighbor distances between convective storms to address the first of these concerns, but we show here that it is insensitive to organization beyond the meso-β scale and very contingent on the details of the implementation. We thus introduce a new and complementary metric, Lorg, based on all-pair convective storm distances, which is also an absolute metric that can discern regular, random, and clustered cloud scenes. It is linearly sensitive to spatial scale in most applications and robust to the implementation methodology. We also derive a discrete form suited to gridded data and provide corrections to account for cyclic boundary conditions and finite, open boundary domains of nonequal aspect ratios. We demonstrate the use of the metric with idealized synthetic configurations, as well as model output and satellite rainfall retrievals in the tropics. We claim that this new metric usefully supplements the existing family of indices that can help to understand convective organization across spatial scales. Significance Statement The clustering and organization of convection is associated with high-impact weather and changes could impact climate sensitivity, but no consensus exists on how to best measure organization. Here we suggest a new metric that is robust to the calculation details and can classify scenes as random, clustered, or regular. This new metric can therefore account for spacing of organized convective systems and convective storms on scales spanning tens of kilometers to the entire tropics. We suggest that the new metric Lorg addresses many shortcomings of existing measures and can act as a useful additional tool to further understanding of convective organization.

Modeling the Water Temperature Profile of Lakes: A Physics Informed Neural Network (PINN) Approach

Water temperature plays an important role in our environment and is applicable to nearly all limnology research, as the temperature of a body of water affects biological activity and growth of organisms such as algae and bacteria. Certain organisms have a preferred temperature range within which they can survive, while others become dormant or die when the water reaches extreme temperatures. The temperature of water also governs the maximum dissolved oxygen concentration of water. Dissolved oxygen in water is important for aquatic life because of its vital role in cellular respiration. Predicting water temperature is also an important factor in determining whether a body of water is acceptable for human use. Warm bodies of water may contain pathogens that can be dangerous to humans.
 
 Our research presents a computational method of determining lake water temperature through a novel technique known as physics-informed neural networks (PINNs). PINNs can be used to model and forecast the temperature of water over a specific time period by training a neural network using the data points derived from the discrete form of a partial differential equation and taking into account the boundary conditions. Several factors such as wind, precipitation, and solar energy effects on water temperature were investigated. By using a computer simulation in place of an analytical mathematical model, a tremendous increase in run time speed can be achieved. The results can be used to determine the patterns in water temperature throughout a year, demonstrating the advantages of a PINN over an analytical model.

Stability and Performance of the X-CMFD Method for Multiphysics Reactor Calculations

This paper presents an innovative approach to efficiently perform deterministic direct whole-core transport calculations with multiphysics feedback for steady-state problems. Traditionally, Picard iteration combined with coarse mesh finite difference (CMFD) acceleration has been used, but it can suffer from instability and inefficiency in certain scenarios. In this work, we introduce the X-CMFD method, supported by Fourier analysis, to enhance the stability of the multiphysics iteration scheme. A new and efficient variation of the X-CMFD method for practical simulations is also present. Additionally, we explore the theoretical convergence rates of nonlinear fully coupled diffusion acceleration (NFCDA), a class of diffusion acceleration methods that formalizes similar ideas of previous research. NFCDA uses a low-order diffusion problem that is fully coupled with equivalent nonlinear multiphysics feedback to accelerate the high-order transport problem with feedback. The theoretical analysis shows that NFCDA offers similar convergence rates to nonlinear diffusion acceleration (NDA) in problems without feedback. This provides theoretical support for numerical experiments conducted by other researchers. X-CMFD, which is a discretized form of NFCDA, leverages typical coarse mesh concepts and operators from CMFD while applying feedback to cross sections in the low-order diffusion problem at each power iteration of the low-order problem. To reduce computational costs, we optimize the implementation of X-CMFD in MPACT by introducing an equivalent low-order approximation to the cross-section updates in the nonlinear low-order problem. Numerical results from pressurized water reactor problems demonstrate that X-CMFD, along with its practical implementation, outperforms current relaxed Picard iteration methods in terms of robustness and efficiency, irrespective of the presence of multiphysics feedback.

Sociocultural Analysis of Millennials in Russia

The present article provides a sociocultural analysis of parameters of the millennials, the generation which will become the main workforce in Russia in the next ten years. This is what gives the paper its relevance. The paper focuses on the market and micro-interactionist influence of basic traits of millennials. The issue of how to behave towards millennials is faced both at the sociological and managerial levels. It is said that the large number of conflicts between millennials and older generations leads to systematic disruption and turbulence, as it does not allow young employees to integrate into corporate cultures and increase labour efficiency, which simultaneously affects older employees, management and corporative performance. Another aspect of the core issue raised by the author is educating the youth. Understanding the set of core values of millennials, their strategies and behavioural tactics in the workplace is also a prerequisite for teachers and instructors to successfully train students of this generation in universities. Like many recent studies, this research considers the distinctive features that can be used to characterize millennials. They, being digital natives, shift to more rapid, discrete and depersonalized forms of communication. Focused on managing their personal image and identity, millennials prefer to play socially desirable roles and tend to reframe their own failures into external misfortunes. This brings about the issue of meeting set goals, and nowadays the youth tends to plan less and thrives on regular feedback that they expect to be positive. These features are most likely to breed intergenerational misunderstanding. However, millennials tend to be more flexible and tolerant than other generations, which is useful for settling controversies and speaks to the overall success of interaction and effort on the part of this generation. The author, addressing the challenges of communication with the modern youth, offers recommendations based on her own pedagogical experience of interaction with millennials. These are: provide basic guidelines, time plans, and assessment benchmarks. Managerial staff should also dedicate more effort to mentorship and peer-level communication.

Optimization of the mode of movement of the boom system of the loader crane

The article presents a method for solving the problem of eliminating vibrations of the load, which is fixed on a rigid articulated suspension at the time of simultaneous movement of two links of the boom system. The essence of the method is to optimize the mode of simultaneous movement of two links of the boom system of the loader crane with horizontal movement of the load during the start-up period. The problem is solved according to two optimization criteria, namely: according to the optimization criterion of the root-mean-square value of the generalized force and the optimization criterion of the root-mean-square value of the power of drive mechanisms. The developed criteria reflect the undesirable properties of the links of the boom system and drive mechanisms, so their value was minimized.
 The solution of the optimization problem is presented in a discrete form. For this purpose, the particle swarm optimization (ME-PSO) method was used. This helped to obtain discrete values of the kinematic and power characteristics of the boom system of the loader crane.
 Since the optimization criterion is an integral functional, the methods of the calculus of variations are used for its optimization. The solution of the variational optimization problem is presented in the form of many parametric functions that satisfy the boundary conditions of motion and minimize the obtained dimensionless criteria. For this purpose, the particle swarm optimization (ME-PSO) method was used. This made it possible to obtain the dependence of the optimal energy and power characteristics of the boom system and the drive mechanisms of the loader crane. The mode of movement of the boom system links obtained as a result of optimization improved the power and energy characteristics of the loader crane, which made it possible to increase its reliability and productivity.