We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance – modeling and ignoring non-invariant items – on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance – non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds – in simple, partial, mediated and moderated regression models where the non-invariant latent variable occupied predictor, mediator, and (...) criterion positions in the structural regression models. When non-invariance is ignored in the latent predictor, the focal group regression parameters are biased in the opposite direction to the difference in loadings and thresholds relative to the referent group (i.e., lower loadings and thresholds for the focal group lead to overestimated regression parameters). With criterion non-invariance, the focal group regression parameters are biased in the same direction as the difference in loadings and thresholds relative to the referent group. While unacceptable levels of parameter bias were confined to the focal group, bias occurred at considerably lower levels of ignored non-invariance than was previously recognized in referent and focal groups. (shrink)

The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex–valued Gaussian, looking for relevance to quantum mechanics. Here we show that the Gaussian, with all terms fully complex, acting as a propagator, leads to Schrödinger’s non-relativistic equation including scalar and vector potentials, assuming only that the norm is conserved. No physical laws need to be postulated a priori. It thereby presents as a process of irregular (...) motion analogous to the real random walk but executed under the rules of the complex number system. There is a standard view that Schrödinger’s equation is deterministic, whereas wavefunction “collapse” is probabilistic —we have now a demonstrated linkage to the central limit theorem, indicating a stochastic picture at the foundation of Schrödinger’s equation itself. It may be an example of Wheeler’s “It from bit” with “No underlying law”. Reasons for the primary role of \ are open to discussion. The present derivation is compared with recent reconstructions of the quantum formalism, which have the aim of rationalizing its obscurities. (shrink)

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an (...) class='Hi'>equational completeness theorem is shown to be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (shrink)

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.

Exact definitions in physical and biological terms of the coefficients in Volterra's (1926, 1931) original competition equations are indispensable for the understanding of the system. In agreement with Volterra's own, but not quite sufficient specifications, it is tried in this paper to give more precise definitions of the parameters used by Volterra. This leads to some consequences; i.a. that there does not exist a principle of competitive exclusion. In order to allow for competitive exclusion — or for stabilization — the (...) Volterra equations need additional biophysical specifications and mathematical modifications. Some such modifications are proposed, for instance for aggressive interference as a function of population numbers. (shrink)

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be verified (...) with observation data. (shrink)

We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classi cation of standard connectives via equations on consequence relations (these include Girard's \multiplicatives" and \additives"). We next (...) investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as.. (shrink)

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

ABSTRACT In this paper it is shown that a broad class of propositional logics can be interpreted in an equational logic based on fork algebras. This interpetability enables us to develop a fork-algebraic formalization of these logics and, as a consequence, to simulate non-classical means of reasoning with equational theories algebras.

It is well-known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems and that this formula satisfies Hilbert-Bernays derivability conditions. Recently R. Magari has suggested an algebraization of the properties of Theor, introducing the concept of diagonalizable algebra (see [7]): of course this algebraization can be applied to all these theories in which there exists a predicate with analogous properties. In this paper, by means of methods of universal algebra, we study the (...) class='Hi'>equational class of diagonalizable algebras, proving, among other things, that the set of identities satisfied by Theor which are consequences of the known ones is decidable. (shrink)

The remainder equations were introduced by S. O. Hansson. In this paper, we will give an exhaustive characterization of the set of solutions for remainder equations. Moreover, solutions to some unsolved problems proposed by Hansson are reported.

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the (...) ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EHv and BHv and the abstract tensors, the 4-vectors Ea and Ba. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST. (shrink)

I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, to of the equation exhibits an asymmetry (...) in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Moun—despite their acute similarities—exhibit an asymmetry in their mass is possible. The Moun is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been (...) criticized for using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms are similar (...) to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations. (shrink)

The author has recently proposed a “quasi-classical” theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field χ(x, t), interacting with each other via nonlinearity in the equation of motion for χ. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from χ a configuration-space wave function Ψ(x 1,x 2,t), and that the theory requires that (...) Ψ satisfy the two-particle Schrödinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrödinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a “crutch” theory which has subsequently to be “quantized.” The quasi-classical theory also suggests the existence of a preferred “absolute” gauge for the electromagnetic potentials. (shrink)

In this work we review the derivation of Dirac and Weinberg equations based on a “principle of indistinguishability” for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j≥1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields $\mathcal{O}(p^{2j} )$ equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG for (...) a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j= $ - \frac{1}{2}$ , there exists no Dirac-like equation for the (j,0)⊕(0,j) representation nor for the ( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ ) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)⊕( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ )⊕(0,1) representation by this method and show that the (1, $ - \frac{1}{2}$ )⊕( $ - \frac{1}{2}$ ,1) representation satisfies a Dirac-like equation which describes a multiplet of $j = \frac{3}{2}{\text{ and }}j = \frac{1}{2}$ with masses m and m/2, respectively. (shrink)

We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The "pure," propositional fragment FLR 0 turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of (...) models. (shrink)

We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The "pure," propositional fragment FLR$_0$ turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, (...) are considered. In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does (...) not assume that the desired tensor depends on the metric only up second-order partial-derivatives, that condition being a consequence of the proof. This has consequences for understanding the nature of the cosmological constant and theories of higher-dimensional gravity. Another consequence of the theorem is that it makes precise the sense in which there can be no gravitational stress-energy tensor in general relativity. Along the way, I prove a result of some interest about the second jet-bundle of the bundle of metrics over a manifold. (shrink)

The remainder set A⟂B of a set of sentences A modulo a set of sentences B is the set of all maximal subsets of A not implying any element of B. A remainder equation is an expression containing remainder sets, such as {A} = B⟂X, in which at least one set is unknown. Solutions to some classes of remainder equations are reported, and some unsolved problems are listed.

In this paper we study the connection between the use of evaluative language and the building of both personal and social identities, from the perspective of Dynamical System Theory. We primarily discuss two issues: 1) The use of evaluation ) as a means to the construction of both individual and group identities, thus exploring how the connection between linguistic choices and social identities is shaped by interactional needs for stancetaking. In order to illustrate this connection, we examine examples of the (...) use of evaluative language in a web social network, and we analyze some of the discourse elements showing ways of positioning that act as catalysts for the emergence of a multifactorial dynamic system of identities. 2) The consideration of Dynamical System Theory as a theoretical framework for the modeling of language and identity. Although originally a mathematical theory, DST has been adopted by cognitive science as a valid framework for the study of cognitive phenomena, on the grounds that natural cognition is a dynamical phenomenon. Within the realm of linguistics and pragmatics, this study is to a certain degree in line with some recent studies such as Gibbs, Geeraerts, Kristiansen and Peirsman, or Moreno Fernández. Thus, we herein focus on how linguistic evaluation intervenes in the intricate dynamical system of identity, and even though we do not engage in complex mathematical disquisition, we argue that the idea and philosophical foundation underlying DST can lead us towards the ‘integration’ of the complex equation of identity construction, and that consequently the field has great potential for further research. (shrink)

The consequences of a generalized Dirac equation are discussed for the energy levels of the hydrogen atom. Apart from the usual generalizations of the Dirac equation by adding new interaction terms, we generalize the anticommutation rule of the Dirac matrices, which leads to spin-dependent propagation properties. Such a theory can be looked at as a model theory for testing Lorentz invariance or as an outcome of pregeometric dynamical induction schemes for space-time structure.For special examples of generalized Dirac matrices including perturbation (...) terms with respect to the SRT Dirac matrices, we derive the energy level of the hydrogen atom and find a hyperfine splitting due to these perturbations. A comparison of this additional splitting with Lamb shift measurements gives us upper limits for possible perturbations, which turn out to be of measurable magnitude. Spin precession experiments give much more restrictive limits. So, it turns out that the hydrogen atom is not such a sensitive indicator for the Lorentz invariance as widely believed. (shrink)

Glymour (Philos Sci 73:369–389, 2006) claims that classical population genetic models can reliably predict short and medium run population dynamics only given information about future fitnesses those models cannot themselves predict, and that in consequence the causal, ecological models which can predict future fitnesses afford a more foundational description of natural selection than do population genetic models. This paper defends the first claim from objections offered by Gildenhuys (Biol Philos, 2011).

Here, S is a sentence—or possibly a smaller or larger unit of meaningful expression for a language—that's written by an author and c is the circumstance in which S is used. R is defined as the language conventions holding between an author and a reader (or better yet, his readership). P, probably the most important part of the equation, is the content of S or, the intended meaning of the author. We assume that the communication between an author and a (...) reader is limited only to written text. Consequently, it is not possible to ask the author about his intention for writing S; that will have to be discovered by a reader. (shrink)

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of (...) the energy explains the balance. (shrink)

A signed -equation is an expression of the form t t or t t, where t and t are -terms (for some ranked set ). We characterize those classes of -algebras which are models of a set of signed -equations. Further we consider the problem of finding a complete deductive system analogous to equational logic for the logical consequence operation restricted to signed equations.

IntroductionWith the normalization of COVID-19 prevention and control, a large number of intergenerational audiences with different cognition preferences and value orientations have started to pour into non-acquaintance virtual communities to address their social needs by disclosing their own thoughts, feelings and experiences toward certain topics. To avoid the negative impacts of self-disclosure, this study introduced the concept of social integration into cyber society among non-acquaintance VCs, such as the topic-based VCs. Our theoretical model considers both the psychological antecedents and consequences (...) of VC audiences’ social integration and our findings have implications for public online social life. Moreover, this research could play a guiding role in improving VC audiences’ social integration status in future online learning and telecommuting scenarios.MethodTo assess the theoretical model constructed in this manuscript, we conducted an online survey in two different topic-based VCs among Microblog and yielded 472 useable responses from intergenerational audiences, among which 28.81% were born before 1985, 26.67% were born from 1985 to 1995, and 48.52% were born after 1995. Our sample consisted of 208 individuals from Health Regimen VC and 264 individuals from Star Chasing VC, 200 were men and 272 were women.ResultsOur structural equation model indicated that individuals’ self-disclosure in topic-based VCs might not directly guide them to acquire social integration. However, intimacy and cognitive communion derived from VC audiences’ self-disclosure might not only enhance their social integration, but also improve their psychological well-being. In addition, VC audiences’ social integration mediated the relationship between intimacy and psychological well-being, and the relationship between cognitive communion and psychological well-being. Moreover, VC audiences’ intimacy was found to have a direct influence on their cognitive communion.ConclusionIn the context of topic-based VCs, audiences’ self-disclosure could significantly foster their intimacy and cognitive communion with others, and both intimacy and cognitive communion are conductive to VC audiences’ social integration. Thus, audiences in topic-based VCs who wish to improve their psychological well-being need to disclose themselves and build corresponding psychological foundations to enhance their social integration. Meanwhile, topic-based VCs should pay attention to the cultivation of intimacy and cognitive communion among audiences while encouraging them to reveal themselves. (shrink)

The experience value of online education is a hot topic in both theoretical and practical circles, but research on its mechanism of action is limited. Therefore, this study systematically investigates the relationship between brand image, experience value, and continuance intention through a theoretical analysis of brand image, and discusses the boundary role of effective commitment in it. In this study, 475 users were used to conduct structural equation modeling analysis. The results of the study found that experience value had a (...) positive and significant effect on user continuance intention under the significant influence of brand image, but affective commitment did not play a positive moderating role in the relationship between experience value and continuance intention. This study examines the mechanism of the antecedents and consequences of experience value, and provides a new direction for the construction of online education and the development of online education and marketing strategies. (shrink)

In this paper we study the connection between the use of evaluative language and the building of both personal and social identities, from the perspective of Dynamical System Theory . We primarily discuss two issues: 1) The use of evaluation (in the sense given to the term by Alba-Juez and Thompson (forthcoming)) as a means to the construction of both individual and group identities, thus exploring how the connection between linguistic choices and social identities is shaped by interactional needs for (...) stancetaking. In order to illustrate this connection, we examine examples of the use of evaluative language in a web social network, and we analyze some of the discourse elements showing ways of positioning that act as catalysts for the emergence of a multifactorial dynamic system of identities. 2) The consideration of Dynamical System Theory (DST) as a theoretical framework for the modeling of language and identity. Although originally a mathematical theory, DST has been adopted by cognitive science as a valid framework for the study of cognitive phenomena, on the grounds that natural cognition is a dynamical phenomenon. Within the realm of (socio) linguistics and pragmatics, this study is to a certain degree in line with some recent studies such as Gibbs (2010), Geeraerts, Kristiansen and Peirsman (2010), or Moreno Fernández (2012). Thus, we herein focus on how linguistic evaluation intervenes in the intricate dynamical system of identity, and even though we do not engage in complex mathematical disquisition, we argue that the idea and philosophical foundation underlying DST can lead us towards the ‘integration’ of the complex equation of identity construction, and that consequently the field has great potential for further research. (shrink)

One of the most commonplace worries about humanitarian intervention relates to the perverse incentives that it might create, or the adverse reactions that it might provoke. For instance, it is sometimes said that by weakening the norm of sovereignty humanitarian intervention can encourage unscrupulous states to wage aggressive wars of self-interest using human rights as a pretense. It is feared, in other words, that humanitarian intervention—even when it has the purest motives—might ultimately do more harm than good by inciting unwanted (...) reactions from other states or substate groups. I will refer to these kinds of knock-on effects as the mediated consequences of intervention. They are brought about via the interceding agency of parties other than the intervener. It is generally assumed that when judging the proportionality of a humanitarian intervention, these consequences must be factored into the equation. If an intervention is expected to provoke adverse reactions the accumulated costs of which will outweigh the benefits that the intervention will deliver, then the intervention is thought to be disproportional and, therefore, unjustified. I want to challenge this assumption. I begin by considering what the principle of proportionality can reasonably demand of rebels who are defending their own basic rights against an oppressive government. I argue that a rebellion in such circumstances cannot plausibly be rendered impermissible solely by the expectation of negative mediated consequences, even when those consequences outweigh the anticipated benefits of the rebellion. This would seem to imply that rebels may discount mediated consequence from the proportionality calculus. But if this is so, do we have sound reasons for withholding the same prerogative from humanitarian interveners pursuing similar ends and using similar means? Can we justify asymmetric standards of proportionality? (shrink)

The Lorentz-Dirac equation is analyzed for the case of a charged particle injected into a step-function electric field of finite extent. It is shown that for small exit velocities, the relation between entrance and exit velocities is “inverted” in the sense that the larger the entrance velocity, the smaller the exit velocity. As a consequence, some entrance velocities can yield at least two distinct exit velocities. Numerical evidence bearing on the possibility of experimentally detecting this dichotomy is presented.

Parental burnout is a unique and context-specific syndrome resulting from a chronic imbalance of risks over resources in the parenting domain. The current research aims to evaluate the psychometric properties of the Spanish version of the Parental Burnout Assessment across Spanish-speaking countries with two consecutive studies. In Study 1, we analyzed the data through a bifactor model within an Exploratory Structural Equation Modeling on the pooled sample of participants obtaining good fit indices. We then attained measurement invariance across both gender (...) and countries in a set of nested models with gradually increasing parameter constraints. Latent means comparisons across countries showed that among the participants’ countries, Chile had the highest parental burnout score, likewise, comparisons across gender evidenced that mothers displayed higher scores than fathers, as shown in previous studies. Reliability coefficients were high. In Study 2, we tested the relations between parental burnout and three specific consequences, i.e., escape and suicidal ideations, parental neglect, and parental violence toward one’s children. The medium to large associations found provided support for the PBA’s predictive validity. Overall, we concluded that the Spanish version of the PBA has good psychometric properties. The results support its relevance for the assessment of parental burnout among Spanish-speaking parents, offering new opportunities for cross-cultural research in the parenting domain. (shrink)

With the negative impact of COVID-19, the continuous recession of economic globalization, and the increasing market competition, enterprise transformation gradually becomes the theme of enterprise management. Although more and more scholars and companies have paid attention to the importance of enterprise transformation, most of the research on it is still at the qualitative level of theoretical descriptions and lacks a comprehensive consideration and empirical research on its motivation and performance. In view of this, this study analyzes the overall driving effect (...) of technological innovation and the internal and external environment on enterprise transformation from the perspective of its drivers and analyzes in depth its causes and consequences for different industries. The study also analyzes the antecedents and consequences of enterprise transformation and its differences in different industries. In this study, a sample of middle and senior management of 10 companies with a valid sample of 401 is collected. Structural equation modeling results indicate that competitive advantage, technological innovation, and market pressure significantly affect enterprise transformation, which is an antecedent of corporate performance. Further, the results of the multiple-group analysis also reveal some significant differences between the theoretical models of the construction and real estate communities. Finally, suggestions are made based on the findings. (shrink)

Econometrics : Ideology in Equations ? Within the terms of the dominant theory, unemployment can only be the consequence of excessive wage-levels. The procedures resorted to in support of such a hypothesis do however tend to violate a reality which remains stubbornly recalcitrant, even when the most sophisticated devices of formalisation are adopted. Since the domination exercised by the dominant economic model is not a function of its actual epistemological productiveness, it is worthwhile to reflect on the operational conditions (...) governing a field that is polarised between theory and ideology. (shrink)

The free Schrödinger equation is shown to be a consequence of spacetime homogeneity in the non-relativistic domain. This may help understand the origin of the wave equations in quantum theory.

The aim of this study was to investigate the level of specificity of the different regulation types described by Self-Determination Theory, and to evaluate its impact on the links with its antecedents and consequences, in an academic context. In line with the school-subject-specificity hypothesis, we postulated that autonomous motivation types would be more specific to the situational level than controlled motivation types. Moreover, we hypothesized that AM types would be, at this level, more strongly associated with its antecedents and consequences (...) than CM types. Three hundred fourteen university students were asked to complete online questionnaires assessing their motivation, motivational antecedents and consequences in various courses. As expected, results from structural equation modeling confirmed that AM types were more specific to the situational level than CM types. Moreover, a higher number of significant correlations were found between motivation and its antecedents and consequences in the corresponding course for AM than for CM types. Educational implications and directions for future research are discussed. (shrink)

A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of electromagnetic (...) interaction, the Lagrangian for this optimal, nonclassical path coincides with the Lagrangian of the Dirac particle. The nonrelativistic, or diffusion, limit is shown to be a formal consequence of Einstein's dynamical equilibrium condition; the continuity equation reduces to the same diffusion equation derived from Schrödinger's equation. The relativistic, massless limit, which would describe a neutrino, is comparable (in the sense of analytic continuation) to a nonviscous liquid whose molecules possess internal degrees of freedom. (shrink)

In the nation of Belize, and in particular the south side of Belize City, the main metropolitan area of the nation, significant economic disparities have led to child and adolescent exposure to high rates of violent crime, gang activity, unsafe neighborhoods, sexual, and physical violence. Problems associated with poor Social-Emotional Character Development are especially prevalent among boys. Consequently, valid culture-relevant measures are required that identify problematic behavior for policy-based intervention and evaluation of educational programs designed to ameliorate this problem. The (...) present study demonstrates the application of Exploratory Structural Equation Modeling to existing measures through the investigation of structural validity and generalizability of the Social-Emotional and Character Development Scale with a large sample of children from schools in Belize. Exploratory structural equation modeling results demonstrate the original factor correlations were reduced, providing less biased estimates than confirmatory factor analysis. Moreover, a multi-group Exploratory Structural Equation Modeling analysis illuminates significant differences between latent factor scores of males and females for most factors. Using this newer factor analytic procedure, original factors are reconceptualized to better situate the Social Emotional Character Development Scales into the larger body of Social-Emotional Learning competencies literature. (shrink)

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of (...) the energy explains the balance. (shrink)

Federations are concerned about attracting new sportsmen and sportswomen and increasing the number of members. The purpose of this research was to describe karate federations' strategies for attracting and retaining members through happiness. The analysis was carried out by designing a structural equation modeling, which allowed to analyze the main variables that influenced the happiness of the karate athlete and consequently to study their effect on people's loyalty to sports federations. In particular, Partial least squares SEM was applied in an (...) overall model when it was possible to understand the happiness role in relation with other traditional relevant variables on loyalty. The data were obtained through primary sources employing a survey sent to the autonomous federations in the discipline of karate, obtaining a sample of 682 federated members in Spain. The results of the model revealed that consumer satisfaction, engagement, and meaningful influence on consumer happiness, but engagement was the most important and relevant variable for affecting this variable. Finally, consumer satisfaction and consumer happiness influence loyalty, and consumer satisfaction was the most important variable, but consumer happiness showed a real alternative for improving loyalty in karate sports federations. Then, one of the implications of this work was that it helped to explain how the federations can be managed to achieve loyal consumers together with a more considerable increase in the number of federated members. (shrink)

This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.

Dans cet article, je discuterai de l’idée selon laquelle l’École polytechnique au xixe siècle ne permettait pas aux acteurs de réaliser des travaux mathématiques originaux. En fait, plusieurs historien⋅ne⋅s pensent que les programmes d’examens empêchaient les élèves et les enseignants de prendre des initiatives. J’essayerai de nuancer cette idée, en prenant en compte plusieurs exemples liés à l’enseignement des équations numériques au cours du xixe siècle. Plus précisément, je présente dans cet article trois théorèmes attribués à trois enseignants de l’École (...) polytechnique et qui ont circulé parmi les élèves de l’École et parmi des milieux d’enseignement. Ces exemples sont intéressants car ils donnent des informations à propos de l’École polytechnique et à propos de l’enseignement et de l’apprentissage qui s’y pratiquaient. Ils permettent aussi de mieux connaître la façon dont la recherche de résultats mathématiques nouveaux pouvait, dans ce contexte, être liée à des activités pédagogiques et je vais expliquer comment ce lien a de nombreuses conséquences sur l’activité d’un enseignant comme Edmond Laguerre par exemple. (shrink)

We define a new class of Kripke structures for the second-order λ-calculus, and investigate the soundness and completeness of some proof systems for proving inequalities as well as equations. The Kripke structures under consideration are equipped with preorders that correspond to an abstract form of reduction, and they are not necessarily extensional. A novelty of our approach is that we define these structures directly as functors A: → Preor equipped with certain natural transformations corresponding to application and abstraction . We (...) make use of an explicit construction of the exponential of functors in the Cartesian-closed category Preor, and we also define a kind of exponential ΠΦs ε T to take care of type abstraction. However, we strive for simplicity, and we only use very elementary categorical concepts. Consequently, we believe that the models described in this paper are more palatable than abstract categorical models which require much more sophisticated machinery . We obtain soundness and completeness theorems that generalize some results of Mitchell and Moggi to the second-order λ-calculus, and to sets of inequalities. (shrink)

After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications (...) and extensions of this result.Topics considered here include equational definability in first order logic, an extended notion of definability in equational logic and the synonymy of equational theories.The final two sections briefly review some of the history of equational logic. (shrink)

Dans cet article, je discuterai de l’idée selon laquelle l’École polytechnique au xixe siècle ne permettait pas aux acteurs (les élèves et les enseignants) de réaliser des travaux mathématiques originaux. En fait, plusieurs historien⋅ne⋅s pensent que les programmes d’examens empêchaient les élèves et les enseignants de prendre des initiatives. J’essayerai de nuancer cette idée, en prenant en compte plusieurs exemples liés à l’enseignement des équations numériques au cours du xixe siècle. Plus précisément, je présente dans cet article trois théorèmes attribués (...) à trois enseignants de l’École polytechnique et qui ont circulé parmi les élèves de l’École et parmi des milieux d’enseignement. Ces exemples sont intéressants car ils donnent des informations à propos de l’École polytechnique et à propos de l’enseignement et de l’apprentissage qui s’y pratiquaient. Ils permettent aussi de mieux connaître la façon dont la recherche de résultats mathématiques nouveaux pouvait, dans ce contexte, être liée à des activités pédagogiques et je vais expliquer comment ce lien a de nombreuses conséquences sur l’activité d’un enseignant comme Edmond Laguerre par exemple. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Subjective Knowledge, Mental Disorders, and MedsHow to Parse the EquationMark D. Rego (bio)Keywordspsychopathology, antidepressants, suicidality, subjective experience, pre-reflectiveA few weeks, ago I was walking down the hall to my office when I spotted my brother-in-law coming the other way. This was odd on two accounts. First, he lives in Kentucky (I am in Connecticut) and second, he is at least a foot taller than the man in my hallway. (...) Nonetheless, I struggled to figure out why he was there. The resemblance was so striking it took me a minute or two to convince myself it was not him. Even after such convincing, the feeling that it was him remained.Later, I imagined that had I just returned from a crack cocaine den I would have been hypervigilant, if not paranoid, and consequently would be certain that my brother-in-law had arrived unannounced. Furthermore, I would probably assume that he was up to no good.How did I retain a strong feeling of recognition, the feeling that maybe it was really him, when I already concluded otherwise? And why, were I on crack cocaine, would the obvious facts be useless in rendering a decision about the identity of the man in the hall? Last, why would the post-cocaine man in the hall become a nefarious brother-in-law rather than a benign one?If I just computed some symbols to figure this out, wouldn't the feeling have gone away? If I activated a brother-in-law neural network, how did I come to acquire an evil brother-in-law neural network? And why wouldn't that go away either?In his article in this issue of Philosophy, Psychiatry, & Psychology, Hadreas looks at questions like these through the prism of before and after effects of people treated with selective serotonin reuptake inhibitors (SSRIs). Hadreas investigates the implications of a straightforward recomputation of self-awareness when treated with these medicines and finds such approaches unsatisfying and incomplete in their explanatory power. (My example looks at a type of awareness, but not specifically self-awareness, as does Hadreas. Furthermore, my paradigm asks about computational conclusions using language more common in psychiatric literature, whereas Hadreas uses standard philosophical terms. Although not isomorphic, I believe the interchange of the two remains true to the issues Hadreas is addressing). [End Page 57]In my example, there is clearly something else going on than the incorrect arrangement of symbols or the misfiring of nodes in a network that influences how I feel and what I think. Neither reason nor empiricism seem to serve me well here. Hadreas utilizes Husserl to begin to unpeel the layers of self-awareness and self-states that intermix to form the shifts and contradictions which are so common in psychiatric treatment (and in common experience as I describe).This is a welcome reckoning; the psychiatric literature is overflowing with unquestioned premises about the neuropsychiatric correlates of reason and empirical approaches (described more as computation and neural networks in the literature—again, not strictly analogous, but the same criticisms apply) Hadreas is critical of. Unfortunately, Hadreas has navigated through a sea of highly questionable assumptions about the psychopharmacology of depression to illustrate his points. This is due in large part to the common practice of consulting literary narratives and critics rather than one of immersion in the literature as a whole and the daily life of patients and active clinicians. He arrived at his destination despite this, because many of these details did not affect his particular analysis. However, to look forward to a continuation of this work and clarify some important issues I devote most of my commentary to these issues. The points I raise are more extensively discussed in a previous edition of this journal (Rego 2005).Affect to Reason ShiftLet's begin with the idea that SSRIs work by dampening emotions. An extension of this idea is that they dampen negative emotions and strengthen positive ones like assertiveness, confidence, and optimism. An even further development in this direction is that, by dampening strong emotions, cognitive enhancement takes place with SSRI treatment. A summary observation then is that SSRIs facilitate... (shrink)

According to the mainstream position in the bioethical definition of death debate, death is to be equated with the cessation of an organism. Given such a perspective, some bioethicists uphold the position that brain-dead patients are dead, while others claim that they are alive. Regardless of the specific opinion on the status of brain-dead patients, the mere bioethical concept of death, according to many bioethicists, has the merit of being unanimous and univocal, as well as grounded in biology. In the (...) present article, we challenge such a thesis. We provide evidence that theoretical biology operates with a plurality of equally valid organismic concepts, which imply different conclusions regarding the organismal status of a brain-dead patient. Moreover, the theoretical biology concepts of an organism are very distant from the view on an organism that appears by way of bioethicists theorizing on death. We conclude that if death is to be understood as the cessation of an organism, there is no single correct answer to the question of whether a brain-dead patient is alive or dead. (shrink)