The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim (...) \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$. (shrink)

In a previous paper by Pollock and Singh, it was proven that the total entropy of de Sitter space-time is equal to zero in the spatially flat case K=0. This result derives from the fundamental property of classical thermodynamics that temperature and volume are not necessarily independent variables in curved space-time, and can be shown to hold for all three spatial curvatures K=0,±1. Here, we extend this approach to Schwarzschild space-time, by constructing a non-vacuum interior space with line element (...) ds 2=e2λ(r) dt 2−e−2λ(r) dr 2−r 2(dθ 2+sin2 θdϕ 2), where $\mathrm{e}^{2{\lambda }(r)}=-\frac{1}{2}(1-\frac{r^{2}}{R_{0}^{2}})$ , which matches onto the vacuum exterior Schwarzschild metric in such a way that e2λ and d(e2λ )/dr are both continuous at the Schwarzschild radius R 0=2M. Then we show that the volume entropy is equal to A/4, where $A\equiv 4\pi R_{0}^{2}$ is the area of the apparent horizon, as found by Hawking. (shrink)

This paper is devoted to theoretical and methodical considerations on our study and understanding of macroscopic transitions in the world of Sanskrit intellectuals from the sixteenth to the eighteenth century (cf. Pollock, Indian Economic and Social History Review 38(1):3–31, 2001). It is argued that compared to his immediate predecessors Bhaṭṭoji Dīkṣita’s contribution to Prakriyā grammars was modest. It was to a large extent on account of changed circumstances—over the centuries mainly a slow but steady decline—in the position of Sanskrit (...) and the general public’s need for a simple definition of authoritatively correct Sanskrit that Bhaṭṭoji’s grammar met with success so quickly, so widely, and so solidly. I once knew a little boy in England who asked his father, “Do fathers always know more than sons?” and the father said “Yes.” The next question was, “Daddy, who invented the steam engine?” and the father said “James Watt.” And then the son came back with “But why didn’t James Watt’s father invent it?” Gregory Bateson (1972, p. 21). (shrink)

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

Provability, Computability and Reflection.

LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and nice description (...) (see Figure 2) while the latticeL(V 0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V 0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with free generators. Each of the quasivarietiesV 0,V 1, andV 2 is generated by a 2-element algebra inD 2. (shrink)

In their “social contextual view” of emotional mimicry, authors Hess and Fischer (2022) put forward emotional mimicry as a social regulator, considering it a social act, bound to certain affiliative contexts or goals. In this commentary, we argue that the core function of mimicry is to ease predicting conspecifics’ behaviours and the environment, and that as a consequence, this often smoothens social interactions. Accordingly, we make three main points. First, we argue that there is no good reason to believe that (...) the mimicry of negative expressions is fundamentally different than the mimicry of positive or ambiguous or autonomic expressions. Second, we give examples of empirical evidence that mimicry is not always a social act. Third, we show that mimicry has primary benefits for the mimicker. As such, we will briefly summarise and elaborate on the relevant findings in these respects, and propose a comparative, multi-method and ecologically valid approach which can explain the multifaceted character of the phenomenon. (shrink)

The relevance of the research is the intensity of noise emitted by lorries depends on the regime of the vehicle movement. One of the main negative factors caused by road vehicles is air pollution with exhaust gases. The article presents results for noise caused by lorries and gas usage while the vehicle is accelerating. The subject of the study is 4 lorries, and they also feature fuel recording systems which are less than 5 years old. Research methodology. The level of (...) noise emitted by heavyweight transport vehicles is measured according to Lithuanian standard LST ISO 1996-2:2008 requirements. During the tests the noise levels of L A,eq, L C,eq, L C,peak were measured. The tests were done 5 times each and the results are presented as arithmetical averages. Fuel consumption is registered in vehicle data registration system. The researched vehicles have to comply with environmental safety normative requirements; that the vehicle carbon monoxide, particulate matter, nitrogen oxides, unburned fuel and other hazardous substances contained in the combustion gases must not exceed the prescribed limits. The results of the experimental studies show that EURO6 lorries noise level is the lowest compared to the EURO4 and EURO5. After carrying out the analysis of the caused noise and gas usage, it was found that noise pollution and gas usage are higher without speed control system. The noise caused by lorries can be described in square polynomial which defines the noise inclination change while vehicle is accelerating. Scientific novelty of the research a complex research on noise and fuel consumption of lorries by using and not using speed control system. Research idea and problem is to achieve sustainable transport development objectives, in particular the reduction of greenhouse gas emissions under the Kyoto Protocol. It is very important to find ways to forecast and reduce transport noise pollution, while also reducing overall pollution, as well as mitigating the impact on the global climate., Conclusion – after conducting a lorry noise and fuel consumption analysis, it was determined that not using speed control system increases the noise and fuel consumption and if the system is used both of these factors decrease drastically. (shrink)

In 2001, Le Bars proved that there exists an existential monadic second-order sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence.

We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if is a regular ultrafilter on λ such that and M is a model whose theory is countable, then is λ+-saturated iff it realizes all φ-types of size λ.

The same research proposal was submitted to 24 district health authority (DHA) research ethics committees in different parts of the country. The objective was to obtain permission for a multi-centre research project. The study of neonatal care in different types of unit (regional, subregional and district), required that four health authorities were approached in each of six widely separated health regions in England. Data were collected and compared concerning aspects of processing, including application forms, information required, timing and decision-making. The (...) key finding was that ethics committees received and processed the applications variably, reflecting individual factors and local problems. To improve consensus and facilitate multicentre studies, standard forms and instructions are suggested and the establishment of a national committee or advisory group advocated. (shrink)

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, (...) syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS''s). This generalization allows us to define BRS''s in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers. (shrink)

Let T 1 , T 2 be countable first-order theories, M i ⊨ T i , and ������ any regular ultrafilter on λ ≥ $\aleph_{0}$ . A longstanding open problem of Keisler asks when T 2 is more complex than T 1 , as measured by the fact that for any such λ, ������, if the ultrapower (M 2 ) λ /������ realizes all types over sets of size ≤ λ, then so must the ultrapower (M 1 ) λ /������. (...) In this paper, building on the author's prior work [12] [13] [14], we show that the relative complexity of first-order theories in Keisler's sense is reflected in the relative graph-theoretic complexity of sequences of hypergraphs associated to formulas of the theory. After reviewing prior work on Keisler's order, we present the new construction in the context of ultrapowers, give various applications to the open question of the unstable classification, and investigate the interaction between theories and regularizing sets. We show that there is a minimum unstable theory, a minimum TP 2 theory, and that maximality is implied by the density of certain graph edges (between components arising from Szemerédi-regular decompositions) remaining bounded away from 0, 1. We also introduce and discuss flexible ultrafilters, a relevant class of regular ultrafilters which reflect the sensitivity of certain unstable (non low) theories to the sizes of regularizing sets, and prove that any ultrafilter which saturates the minimal TP 2 theory is flexible. (shrink)

Some theorists, worried about liberalism’s potential as a foundation for public health ethics, suggest that republicanism provides a better background of justification for public health policies, interventions, etc. In this article, this suggestion is put to the test, and it is argued that (i) contemporary (civic) republicanism and liberalism are not nearly as opposed as it is sometimes suggested, and that (ii) the kind of republicanism which one leading scholar in the field, Bruce Jennings, as an alternative to liberalism, does (...) not reflect the contemporary understanding of republicanism as held by, e.g. Phillip Pettit et al. (shrink)

This article develops an account of the nature and limits of the state’s legislative authority that closely attends to the challenge of harmonizing Kant’s ethical and juridical theories. It clarifies some key Kantian concepts and terms, then explains the way in which the state’s three interlocking authorities – legislative, executive, and judicial – are metaphysically distinct and mutually dependent. It describes the emergence of the Kantian state and identifies the preconditions of its authority. Then it offers a metaphysical model of (...) the Kantian state and uses it to argue that the activity of juridical lawgiving is an act of the omnilateral will itself. Legislative authority is limited in the sense that it does not include the capacity to create juridical laws that are conceptually incompatible with the idea of universal external freedom. I argue that my proposed account of the legislative authority is wholly consistent with that authority’s exclusive lawgiving capacity and does not threaten the possibility of ‘distributive justice’ – the legal finality that is the sine qua non of a civil condition. (shrink)

A comprehensive, critical evaluation of the ideas of the Italian philosopher Benedetto Croce, including a summary of his life.

Discussions in English of Benedetto Croce’s concept of the pure or logical concept are few in comparison with treatments of his aesthetics and theory of history. Yet an understanding of the Crocean concrete universal is a necessary prerequisite for a comprehension of his humanistic philosophy. With regard to Croce’s aesthetics, for instance, the autonomy of art depended upon his view of the relations that existed among the categories of thought and will; and his theory of history followed from his definitions (...) of pure concept and pseudoconcept. (shrink)

Paperback. The book treats two general questions: 1. Whether Erasmanism and Erasmian Humanism existed as a recognizable attitude during the sixteenth and early seventeenth centuries; 2. Whether Erasminism represented a definable middle way between the confessional conflicts of these times. How important was Erasmanism in these respects? The treatment of these two questions is geographically limited to those countries where Erasmus himself was active: Italy, The Netherlands, Holy Roman Empire, Switzerland and England.Erasmanism as a concept has hardly been studied before, (...) although the term is used freely by scholars of the early modern period. This book is a first attempt at a begriffsgeschichte of Erasminism. (shrink)

Since the 1930s, scientists studying the neurological disease scrapie had assumed that the infectious agent was a virus. By the mid 1960s, however, several unconventional properties had arisen that were difficult to reconcile with the standard viral model. Evidence for nucleic acid within the pathogen was lacking, and some researchers considered the possibility that the infectious agent consisted solely of protein. In 1982, Stanley Prusiner coined the term `prion' to emphasize the agent's proteinaceous nature. This infectious protein hypothesis was denounced (...) by many scientists as `heretical'.This essay asks why the concept of an infectious protein was considered controversial. Some biologists justified their evaluation of this hypothesis on the grounds that an infectious protein contradicted the `central dogma of molecular biology'. Others referred to vague theoretical constraints such as molecular biology's `theoretical structure' or `framework'. Examination of the objections raised by researchers reveals exactly what generalizations were being challenged by a protein model of infection.This two-part survey of scrapie and prion research reaches several conclusions: (1) A theoretical framework is present in molecular biology, exerting its influence in hypothesis formation and evaluation; (2) This framework consists of several related, yet separable, generalizations or `elements', including Francis Crick's Central Dogma and Sequence Hypothesis, plus notions concerning infection, replication, protein synthesis, and protein folding; (3) The term `central dogma' has stretched beyond Crick's original 1958 definition to encompass at least two other `framework elements': replication and protein synthesis; and (4) From the study of scrapie and related diseases, biological information has been delineated into at least two classes: sequential and what I call `conformational'.In Part I of this essay, a brief review of the central dogma, as outlined by both Francis Crick and James Watson, will be given. The developments in scrapie research from 1965 to 1972 will then be traced. This section will summarize many of the puzzling, non-viral-like properties of the scrapie agent. Alternative hypotheses to the viral explanation will also be presented, including early versions of a protein-only hypothesis. Part II of this essay will follow the developments in scrapie and prion research from the mid 1970s through 1991. The growing prominence of a protein-only model of infection will be balanced by continued objections from many researchers to a pathogen devoid of nucleic acid. These objections will help illuminate those generalizations in molecular biology that were indeed challenged by a protein-only model of infection. (shrink)

For a first-order formula φ(x; y) we introduce and study the characteristic sequence ⟨P n : n < ω⟩ of hypergraphs defined by P n (y₁…., y n ):= $(\exists x)\bigwedge _{i\leq n}\varphi (x;y_{i})$ . We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of φ and vice versa. The main results are a characterization of NIP and of simplicity in terms of persistence of configurations in the characteristic sequence. Specifically, we show that (...) some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence property manifest themselves in the persistence of complicated configurations under localization. (shrink)