In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein’s celebrated energy-mass relation E=mc 2 is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein’s energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both (...) the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements. (shrink)

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not (...) derived’ according to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems. (shrink)

This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format (...) may display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization. (shrink)

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with (...) preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'. (shrink)

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands of (...) system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. (shrink)

This paper engages with the following closely related questions that have recently received some attention in the literature: what is the status of the equivalence principle in general relativity?; how does the metric field obtain its property of being able to act as a metric?; and is the metric of GR derivative on the dynamics of the matter fields? The paper attempts to complement these debates by studying the spin-2 approach to gravity. In particular, the paper argues that three lessons (...) can be drawn from the spin-2 approach: different from what is sometimes claimed in the literature, central aspects of the non-linear theory of GR are already derivable in classical spin-2 theory; in particular, ‘universal coupling’ can be considered a derived ‘theorem’ in both the classical and the quantum spin-2 approach; this provides new insights for the investigation of the equivalence principle; the ‘second miracle’ that Read et al. argue characterises GR is explained in the classical as well as in the quantum version of the spin-2 approach; the spin-2 approach allows for an ontological reduction of the metrical part of spacetime to the dynamics of matter fields. (shrink)

Religions “in the wild” are the varied set of religious activities that occurred before the emergence of organized religions with doctrines, or that persist at the margins of those organized traditions. These religious activities mostly focus on misfortune; on how to remedy specific cases of illness, accidents, failures; and on how to prevent them. I present a general model to account for the cross-cultural recurrence of these particular themes. The model is based on features of human psychology—namely, epistemic vigilance, the (...) set of systems whereby we evaluate the quality of information and of sources of information, and threat-detection psychology, the set of evolved systems geared at detecting potential danger in the environment. Given these two sets of systems, the dynamics of communication will favor particular types of messages about misfortune. This makes it possible to predict recurrent features of religious systems, such as the focus on nonphysical agents, the focus on particular cases rather than general aspects of misfortune, and the emergence of specialists. The model could illuminate not just why such representations are culturally successful, but also why people are motivated to formulate them in the first place. (shrink)

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers (...) who have offered a general epistemic justification of such practices. (shrink)

Background Dynamic consent has been proposed as a process through which participants and patients can gain more control over how their data and samples, donated for biomedical research, are used, resulting in greater trust in researchers. It is also a way to respond to evolving data protection frameworks and new legislation. Others argue that the broad consent currently used in biobank research is ethically robust. Little empirical research with cohort study participants has been published. This research investigated the participants’ (...) opinions of adding a dynamic consent interface to their existing study. Methods Adult participants in the Extended Cohort for E-health, Environment and DNA longitudinal cohort study who are members of the EXCEED Public and Participant Engagement Group were recruited. Four focus groups were conducted and analysed for thematic content. Discussion topics were derived from a review of the current literature on dynamic consent. Results Participants were in favour of many aspects of a dynamic consent interface, such as being able to update their information, add additional data to their records and choose withdrawal options. They were supportive provided it was simple to use and not intrusive. Participants expressed a markedly high level of trust in the study and its investigators and were unanimously happy with their current participation. No strong support was found for adding a dynamic consent interface to EXCEED. Conclusions Trust in the study researchers was the strongest theme found. Openness and good data security were needed to retain their trust. While happy to discuss dynamic consent, participants were satisfied with the current study arrangements. There were indications that changing the study might unnecessarily disturb their trust. This raised the question of whether there are contexts where dynamic consent is more appropriate than others. This study was limited by the small number of participants who were committed to the study and biased towards it. More research is needed to fully understand the potential impact of adding a dynamic consent interface to an existing cohort study. (shrink)

In this article, the dynamical behaviors of two classes of chaotic systems are considered based on generalized Lyapunov function theorem with integral inequalities. Explicit estimations of the ultimate bounds are derived. The results presented in this article contain the existing results as special cases. Computer simulation results show that the proposed method is effective. © 2014 Wiley Periodicals, Inc. Complexity 21: 363–369, 2015.

In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness, as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a formal model of awareness change, and (...) to derive from it logics of awareness change. In the first part of the paper, the model of epistemic states of bounded agents proposed in Hill (Stud Log 89(1):81–109, 2008a ) is extended with operations modelling awareness change. In the second part of the paper, it is shown how this model naturally extends the “standard” logic of awareness to yield a logic of awareness change. (shrink)

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth’s rotation. The Fourier operators (...) and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework. (shrink)

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. (...) Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results. (shrink)

In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is (...) found that for ω = ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. (shrink)

ABSTRACTHigh-level judgement and decision-making tasks display dynamic bidirectional relationships in which salient cues determine how responses are evaluated by decision-makers, and these responses in turn determine the cues that are considered. In this paper, we propose Kosko's bidirectional associative memory network, a minimal two-layer recurrent neural network, as a mathematically tractable toy model with which the properties of existing bidirectional models, and the behavioural implications of these properties, can be studied. We first derive results regarding the dynamics of the (...) BAM network, and then show how these results can be used to provide an analytically sound explanation for a number of important findings, including coherence shifts in judgement and choice, anchoring effects, and reference point effects. (shrink)

This work presents a post-positivist research framework for explaining any surprising or anomalous fact in the evolutionary path of a complex, dynamic, and contingent social process. Firstly, it elaborates on the reconciliation betweenthe ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Next, the research method is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledge patterns of sequences of events, either involving individual action or interaction between (...) actors within a real social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible through comparison between cases belonging to the same category, but differing in some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that explain this surprising fact, and the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests a hierarchy of classes of grammars for middle-range explanations based on the ontological assumption of the generative nature of social reality. (shrink)

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have (...) derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

Knowledge based privacy policies are more declarative than traditional action based ones, because they specify only what is permitted or forbidden to know, and leave the derivation of the permitted actions to a security monitor. This inference problem is already non trivial with a static privacy policy, and becomes challenging when privacy policies can change over time. We therefore introduce a dynamic modal logic that permits not only to reason about permitted and forbidden knowledge to derive the permitted actions, (...) but also to represent explicitly the declarative privacy policies together with their dynamics. The logic can be used to check both regulatory and behavioral compliance, respectively by checking that the permissions and obligations set up by the security monitor of an organization are not in conflict with the privacy policies, and by checking that these obligations are indeed enforced. (shrink)

Knowledge based privacy policies are more declarative than traditional action based ones, because they specify only what is permitted or forbidden to know, and leave the derivation of the permitted actions to a security monitor. This inference problem is already non trivial with a static privacy policy, and becomes challenging when privacy policies can change over time. We therefore introduce a dynamic modal logic that permits not only to reason about permitted and forbidden knowledge to derive the permitted actions, (...) but also to represent explicitly the declarative privacy policies together with their dynamics. The logic can be used to check both regulatory and behavioral compliance, respectively by checking that the permissions and obligations set up by the security monitor of an organization are not in conflict with the privacy policies, and by checking that these obligations are indeed enforced. (shrink)

The dynamical equations for black-body radiation are derived from the vanishing of the stress-energy tensor and shown to imply a theorem which generalizes that of Tolman and Ehrenfest[Phys. Rev. 36,1791 (1930)]. A method for finding the general solution of these equations is given.

‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of PD. PD applies to (...) both subjectivist and frequentist theories. ‘Straight PD’ (SPD) produces associative and commutative mergers of evidence, in which evidences of positive credence are mutually reinforcing. ‘Offsetting PD’ (OPD) sets off conflicting evidences against each other. Subjectivist PD is a quantified second-order logic of action. Frequentist PD relates to descriptions of physical states of affairs. Acceptance of evidence α 1 X = [c 1; d 1 X ] at t 1 updates α 0 X = [c 0; d 0 X ] at t 0 into SPD-merger or OPD-merger . Given ‘co-evidence’ at t 0 < t 1, ‘indirect’ PD accepts evidence at t 1 and produces support for update α 10 X = [c10;d 10 X α 0 X such that in SPD and in OPD. For binary X and Y, with α 0 X = [c 0; P 0(X)] at t 0 (short-hand for ) and the accepted evidence, the support is ; ; where ρ0(X, Y) is the correlation coefficient of X and Y, and update α 10 X of α 0 X is with ‘accord’ λ = 1 in SPD and in OPD. As , tends toward update P 1(Y) of P 0(Y), but P 10(X) does not converge toward ‘ ’ of ‘probability kinematics’. Therefore PD is not compatible with probability kinematics. A process of ‘normalization’ interprets ‘β-evidence’ [[c 1; q 1]& . . . &[c m ; q m ]; U m X ]] with [c j ; q j ] on and m ≥ 3, as an α-evidence on {X 1, . . . , X m }. It is shown that SPD- and OPD-updates can be derived from updated cumulative functions. Time-biased updates are discussed. A PD-based theory of confirmation (PDCT) is presented. (shrink)

Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e., C[F and (...) G] = C[F][G]), it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e., C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e., bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). (shrink)

Dynamic resilience is a novel concept that aims to quantify how individuals are coping while operating in dynamic and complex task environments. A recently developed dynamic resilience measure, derived through autoregressive modeling, offers an avenue toward dynamic resilience classification that may yield valuable information about working personnel for industries such as defense and elite sport. However, this measure classifies dynamic resilience based upon in-task performance rather than self-regulating cognitive structures; thereby, lacking any supported self-regulating cognitive (...) links to the dynamic resilience framework. Vagally mediated heart rate variability (vmHRV) parameters are potential physiological measures that may offer an opportunity to link self-regulating cognitive structures to dynamic resilience given their supported connection to the self-regulation of stress. This study examines if dynamic resilience classifications reveal significant differences in vagal reactivity between higher, moderate and lower dynamic resilience groups, as participants engage in a dynamic, decision-making task. An amended Three Rs paradigm was implemented that examined vagal reactivity across six concurrent vmHRV reactivity segments consisting of lower and higher task load. Overall, the results supported significant differences between higher and moderate dynamic resilience groups' vagal reactivity but rejected significant differences between the lower dynamic resilience group. Additionally, differences in vagal reactivity across vmHRV reactivity segments within an amended Three Rs paradigm were partially supported. Together, these findings offer support toward linking dynamic resilience to temporal self-regulating cognitive structures that play a role in mediating physiological adaptations during task engagement. (shrink)

The theoretical description of particle decay by a single particle theory requires the use of a probability density in time that is not present in conventional theories. The problem of single particle decay is consistently described here within the context of a single particle, relativistic dynamical theory. We derive experimentally testable differences between the standard model and Relativistic Dynamics for a two-state system: the neutral K-meson (K 0) system. We show that the estimate of mass difference between the two states (...) is theory dependent. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static (...) agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

Several tasks in artificial intelligence require the ability to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper, we exploit the algebraic framework of mathematical morphology in the context of propositional logic and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation (...) and tractability are addressed, and simple examples illustrate the main results. (shrink)

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system (...) through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz. (shrink)

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states (...) of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation. (shrink)

I introduce a new method for validating models—including stochastic models—that gets at the reliability of a model’s predictions under intervention or manipulation of its inputs and not merely at its predictive reliability under passive observation. The method is derived from philosophical work on natural kinds, and turns on comparing the dynamical symmetries of a model with those of its target, where dynamical symmetries are interventions on model variables that commute with time evolution. I demonstrate that this method succeeds in testing (...) aspects of model validity for which few other tools exist. (shrink)

We examine notions of genericity intermediate between 1-genericity and 2-genericity, especially in relation to the Δ20 degrees. We define a new kind of genericity, dynamic genericity, and prove that it is stronger than pb-genericity. Specifically, we show there is a Δ20 pb-generic degree below which the pb-generic degrees fail to be downward dense and that pb-generic degrees are downward dense below every dynamically generic degree. To do so, we examine the relation between genericity and array noncomputability, deriving some structural (...) information about the Δ20 degrees in the process. (shrink)

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

The transition from classical physics to quantum mechanics has been mysterious. Here, we mathematically derive the space-independent von Neumann equation for electron spin from the classical Bloch equation. Subsequently, the space-independent Schrödinger–Pauli equation is derived in both the quantum mechanical and recently developed co-quantum dynamic frameworks.

In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras . One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended (...) to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders–von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them. (shrink)

We study the dynamics of a vortex in superfluid He4. This is carried out by deriving the effective Lagrangian for the center of the vortex by starting with the time-dependent Ginzburg-Landau formalism. From the resultant equation of motion for a vortex, we arrive at a novel aspect for the Magnus force which has long been known in fluid dynamics. This force has a geometric origin and is expected to occur in other form of condensates such as vortex excitations for quantum (...) Hall fluids or ferromagnets. We also consider the force of non geometric origin, the pinning force coming from the impurity. (shrink)

A theorem is derived that enables a systematic enumeration of all the linear superoperators ℒ (associated with a two-level quantum system) that generate, via the law of motion ℒρ= $\dot \rho$ , mappings ρ(0) → ρ(t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state ρ(t → ∞) that is in some cases independent of ρ(0).

The Michelson-Morley result is described empirically by generalized Doppler equations. If the phase of a light wave is not invariant, in agreement with the quantum nature of light, special-relativistic kinematics need not be assumed. Einstein particle dynamics and Maxwell-Lorentz electrodynamics in a moving system are derived without assuming special-relativistic kinematics. An alternative explanation for the decay rate of moving radioactive particles is presented. The observation of a third-order Doppler effect may yield the velocity of the closed laboratory.

The purpose of this article is to introduce, interpret, and develop two incompatible process -ontological theories of personal identity that have received little attention in analytic metaphysics. The first theory derives from the notion of personal identity proposed in Alfred North Whitehead’s philosophy, but I interpret this notion differently from previous commentators. The Whiteheadian theory may appeal to those who believe that personal identity involves an entity or entities that are essentially dynamic, but has nothing to do with diachronic (...) objectual identity : the binary equivalence relation that every entity bears to itself, and only to itself, even after undergoing intrinsic change. The Whiteheadian theory may also find favor with those who, like Whitehead, reject the possibility of pure processes and hold that in every becoming, something—which need not be an object, thing, or individual substance—becomes. The second theory derives from the notion of recurrent dynamics presented in Johanna Seibt’s General Process Theory. The Seibtian theory may appeal to those who believe that personal identity involves not only an entity or entities that are essentially dynamic, but also the relation of diachronic objectual identity. The Seibtian theory may also find favor with those who, like Broad and Sellars, find reason to postulate pure processes. (shrink)

This paper aims at investigating the dynamic characteristics of a microring driven by dual arch electrodes because they are basic elements of microelectrostatic motors. The dual arch electrodes surround the periphery of the microring and are arranged symmetrically to the center of the ring. The electrodes are fixed while the microring is flexible. The electrostatic force will deform the microring, while the deflection of the microring changes the gap between the microring and the electrodes, thereby changing the electrostatic force. (...) Therefore, this is an electromechanical coupling effect. The nonlinear partial-differential equation that governs the motion of the microring is derived based on thin shell theory. Then, based on the assumption of small deflection, the nonlinear governing equation is linearized by truncating the higher-order terms of the Taylor series expansion of the nonlinear electrostatic force. After that, the linearized governing equation is discretized into a set of ordinary differential equations using Galerkin method in which the mode shape functions of the ring are adopted. The influences of the structural damping of the microring and the span of the arch electrodes on the forced response and dynamical stabilities of the microring are investigated. The results show that the damping ratio has a great influence on the system instability during high-frequency excitation. The unstable region of the system can increase with the increase of the electrode span; the response amplitude can also be increased within a certain range. (shrink)

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures. That is, for example, rather than using a complete set of orthogonal (...) projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, ] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors. We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical. (shrink)

In recent years, the method of the complex network has been applied to various fields. Dynamics research in complex networks is also an important branch. There are many types of research into dynamic complex network, but few scholars use bibliometrics to study it. Therefore, this paper adopts the method of bibliometrics to analyze the development history and status quo of dynamic complex network, providing a summary description of this research field. We used CiteSpace and Pajek to analyze 2936 (...) relevant papers on the website of Web of Science and further interpreted and summarized the analysis results. To fully show the bibliometric results, we further derive the productive countries, institutions, sources, and authors and some main research directions in the dynamic complex network research. The research results show that the dynamic complex network research method was applied to various fields after the dynamic research method had been integrated into the complex network. According to the subject analysis of the cited papers, we find that the dynamic complex network method has been widely used in various subjects. Through emergent analysis, we found that the latest hot research trends are the study of infectious diseases and applications in neural networks. At the same time, through the main path analysis, we find the essential literature to elaborate on the development context of a dynamic complex network at different time points. This paper gives a comprehensive analysis of dynamic complex network research and provides some enlightenment for the future research direction. (shrink)

This paper will suggest a mapping for human dynamics to see where emerging digital technology currently and could further affect the dynamics of the human, technological and natural, and the cultural forms that define them. Emerging technology will be seen to reveal and surpass the limitations of human measures built on human abilities and perception. and the social structures that are derived from them. The formation of this conceptual mapping is based on the premise that digital technology has the ability (...) to better relay and hence refine dynamics working at points where culture is created and necessitated in our perception of a shared reality. Technology thus alleviates the layering, representation, labelling, and reification notions of culture that are based in human perceptual limitations. Information as referential will be seen against the tendency of technology to offer succinct mediation and direct actions as a format for any change and application with refined cultural constructions. The mapping presents a notion of homeostasis or more bereft of balance at the point where the proximal dynamics of the unit, that is, the individual, is closely supported by the technology with a changing orientation to the dynamics of a natural environment. The notion of a person as an individual is also reconsidered in terms of technology and how this changing definition is part of how we conceptualize a balanced world. Nonlinear mapping rendered in a complex will be introduced to align these mixed dynamics. Complex is here defined as a concurrence of dynamics evident in shifts of change that act as a whole and where each action affects the whole. As measures are revealed so, too, will be the source of notions of linearity and nonlinearity; mapping; point of view as a basis of complexity; and evolutionary theory as a function of a labeling of cultural dynamics. (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due (...) to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

Minimizers are widely acknowledged cross-linguistically to denote a minimal quantity, extent or degree. With respect to minimizers in Mandarin Chinese, Shyu claims that their so-called negative polarity is purely syntactically determined and is facilitated by the lian…dou EVEN construction. Within the framework of Dynamic Syntax which allows for interaction between syntactic, semantic and pragmatic information, we demonstrate that the total negation is actually derived from the interaction between syntax, semantics and pragmatics, rather than being determined by purely syntactic means.

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman equation on time scales is obtained. Finally, an example is employed to illustrate our main results.