This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The study was underpinned by Skemp’s relational and instrumental understanding, and Kilpatrick, Swafford and Findel’s conceptual and procedural understanding to gain the (...) insights into Grade 11 learners’ understanding of the roots of quadratic equations. A case study design was espoused to answer the main research questions of this study. A written test was administered to 42 learners, and eight learners were purposively sampled to participate in a clinical interview based on their responses to the test. The findings of this study revealed that learners find it difficult to describe the roots, determine the other root when one root is given, to solve quadratic equations written in standard form, to represent the roots to determine the value of unknown variable(s), and to execute the reversal process using the given roots to find the equation. (shrink)

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to (...) Gauss and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which (...) extended causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

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)

I give concise derivations of Price's equation and the criteria for kin and group selection, prove that kin and group selection are equivalent, and discuss the controversies about altruism.

Abstract to Equations, Qualia, and Qualations -/- With regard to consciousness, we could write an equation B = black. But it is possible to rewrite this using a quale, namely, B = █. This latter equation might be called a ‘qualation’. It has the same meaning regardless of the physiology that apprehends it. This article argues a whole theory of qualations could be developed. Further, to a Dualist, it could be that a materialist is convinced by materialist arguments involving (...) the first equation, but it is unimaginable how this could ever be for a qualation. In view of the strong association of qualia with McTaggart’s A-series (future/present/past) a few notes on time are included. (shrink)

This is an English translation of Waldenfels' German essay: Equality and inequality are basic elements of law, justice and politics. Equality integrates each of us into a common sphere by distributing rights, duties and chances among us. Equality turns into mere indifference as far as we get overintegrated into social orders. When differences are fading away experience loses its relief and individuals lose their face. Our critical reflections start from the inevitable paradox of making equal what is not equal. In (...) various ways they refer to Nietzsche’s concept of order, to Marx’s analysis of money, to Lévinas’s ethics of the Other, and to novelists like Dostoevsky and Musil. Our critique turns against two extremes, on the one hand against any sort of normalism fixed on functioning orders, on the other hand against any sort of anomalism dreaming of mere events and permanent ruptures. Responsive phenomenology shows how we are confronted with extraordinary events. Those deviate from the ordinary and transgress its borders, without leaving the normality of our everyday world behind. The process of equalizing moves between the ordinary and the extraordinary. What makes the difference and resists mere indifference are creative responses which are to be invented again and again. (shrink)

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

Following a hypothesis by Marciak-Kozlowska, 2011, we consider one-dimensional Schumann wave transfer phenomena. Numerical solution of that equation was obtained by the help of Mathematica.

The objective of the study was to develop a structural model that explores the relationship between Mathematics Performance and students’ self-regulated learning skills, grit, and expectancy-value towards science, technology, engineering and mathematics (STEM). The research collected survey data from 664 senior high school students from 17 STEM high schools, and conducted a covariance-based structural equation modeling (SEM) analysis. The results of the SEM analysis indicate that the Re-specified Self-Regulated Learning Skill – Expectancy-Value towards STEM – Grit – Mathematics Performance (Re-specified (...) SRL-EV-GR-MP) model is the most parsimonious fit, offering the best empirical support for the theoretical model of the study. The research findings suggest that the mathematics performance of senior high school students in STEM curriculum is attributed to their high expectancies for success and perceived values of the STEM tasks, high grit, and high self-regulated learning skills. Moreover, the research also observed evidence of mediating and moderating grit effects in the concurrent effects of expectancy-values towards STEM and self-regulated learning skills towards students’ mathematics performance. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. (...) Each of these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. (shrink)

This study aimed to construct structural equation model of students’ competence in mathematics through selected students profile variables. The structural model revealed interesting influence of the profile variables to the competency in mathematics. It can be conveyed that better mother’s work status, higher educational level expected to complete, more confident and did not repeat kinder, have better competency in mathematics. The four variables that directly influenced the competence variables were also influenced with other profile variables such as family background. The (...) family background and confidence level consistently had the highest total effect and indirect effect to the competence in mathematics. Hence, this model can serve as a guide in making programs in the classroom or curriculum in mathematics. (shrink)

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...) able to work numerically with finite, infinite, and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and, in particular, to take advantage of infinitesimal values of h. To show the potential of the new framework a number of results is established. It is proved that the Infinity Computer is able to calculate derivatives of the solution y(x) and to reconstruct its Taylor expansion of a desired order numerically without finding the respective derivatives analytically (or symbolically) by the successive derivation of the ODE as it is usually done when the Taylor method is applied. Methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced. Numerical examples are given. (shrink)

In a rather old paper, Mario Liu described a hydrodynamic Maxwell equations. While he also discussed potential implications of these new approaches to superconductors, such a discussion of electrodynamics of superconductors is made only after Tajmar’s paper. Therefore, in this paper we present for the first time a derivation of fluidic Maxwell-Proca equations. The name of fluidic Maxwell-Proca is proposed because the equations were based on modifying Maxwell-Proca and Hirsch’s theory of electrodynamics of superconductor. It is hoped (...) that this paper may stimulate further investigations and experiments in superconductor. It may be expected to have some impact to cosmology modeling too, for instance we consider a hypothetical argument that photon mass can be origin of gravitation. Then, after combining with the so-called chiral modification of Maxwell equations (after Spröessig), then we consider chiral Maxwell-Proca equations as possible alternative of gravitation theory. Such a hypothesis has never considered in literature to the best of our knowledge. (shrink)

Science begins with mystery. What causes lightning? How did this mold stop bacterial growth? Why do we age? Arguably, the two greatest mysteries are the cosmos and consciousness—the vast world out there and the vibrant world within. Scientists captivated by one can be called to study the other, seduced by the thought that these mysteries are connected. Science writer George Musser’s book Putting Ourselves Back in the Equation reviews their progress: Can physics unlock the mystery of consciousness? Does consciousness underlie (...) fundamental physics? (shrink)

1. Schrodinger Equation, fragmentalism, total time T, Euclidean space 2. Does the A-series have the properties of qualia?

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.

A *qualation* does not contain merely references to qualia, but contains actual qualia. There are many differences to equations. Qualations are irreducibly 1st-person and are required for the statement of a hard problem.

The biochemistry of geotropism in plants and gravisensing in e.g. cyanobacteria or paramacia is still not well understood today [1]. Perhaps there are more ways than one for organisms to sense gravity. The two best known relatively old explanations for gravity sensing are sensing through the redistribution of cellular starch statoliths and sensing through redistribution of auxin. The starch containing statoliths in a gravity field produce pressure on the endoplasmic reticulum of the cell. This enables the cell to sense direction. (...) Alternatively, there is the redistribution of auxin under the action of gravity. This is known as the Cholodny-Went hypothesis [2], [3]. The latter redistribution coincides with a redistribution of electrical charge in the cell. With the present study the aim is to add a mathematical unified field explanation to gravisensing. (shrink)

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov (...) equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details. (shrink)

Inspired by “One Note Samba,” a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology (BECC). Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also discuss shortly possible link with our previous paper, where we describe Newtonian Universe with Vortex in terms of Ermakov equation.

In physics there are different opinions about the conceptual interpretation of Einstein’s famous equation that describes the equivalence between mass and energy. It is understandable that the equation has different interpretations because of the different points of view to interpret phenomenological reality. This paper is about the meaning of the equation in relation to the general concept of quantum field theory. In other words, reality is created by the underlying structure of the basic quantum fields.

Is it sensical to ascribe psychological predicates to AI systems like chatbots based on large language models (LLMs)? People have intuitively started ascribing emotions or consciousness to social AI (‘affective artificial agents’), with consequences that range from love to suicide. The philosophical question of whether such ascriptions are warranted is thus very relevant. This paper advances the argument that LLMs instantiate language users in Ludwig Wittgenstein’s sense but that ascribing psychological predicates to these systems remains a functionalist temptation. Social AIs (...) are not full-blown language users, but rather more like Italo Calvino’s literature machines. The ideas of LLMs as Wittgensteinian language users and Calvino’s literature-producing writing machine are combined. This sheds light on the misguided functionalist temptation inherent in moving from equating the two to the ascription of psychological predicates to social AI. Finally, the framework of mortal computation is used to show that social AIs lack the basic autopoiesis needed for narrative façons de parler and their role in the sensemaking of human (inter)action. Such psychological predicate ascriptions could make sense: the transition ‘from quantity to quality’ can take place, but its route lies somewhere between life and death, not between affective artifacts and emotion approximation by literature machines. (shrink)

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton (...) method to solve the PDEs. We submit wholeheartedly Robert Kurucz’s hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)

Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, (...) and yet scientists and mathematicians do effective work there (McLarty 2023, Elder 2023). Building on extant accounts of structural scientific explanation (Bokulich 2011, Leng 2021), I argue that philosophical accounts of the role of equations in scientific explanation need not rely on scientists’ ability to solve equations independently of their understanding of the empirical or experimental context. For instance, the process of formulating solutions to equations can involve significant appeal to information about experimental contexts (Curiel 2010) or of physically similar systems (Sterrett 2023). Working from a close analysis of work in fluid mechanics by Martin Bazant and Keith Moffatt (2005), I propose an account of heuristic structural explanation in mathematics (Einstein 1921, Pincock 2021), which explains how physical explanations can be constructed even in domains where basic equations cannot be solved directly. (shrink)

In recent years, there are a number of proposals to consider collision-based soliton computer based on certain chemical reactions, namely Belousov-Zhabotinsky reaction, which leads to soliton solutions of coupled Nonlinear Schroedinger equations. They are called Manakov System. But it seems to us that such a soliton computer model can also be based on solitary wave solution of Maxwell-Dirac equation, which reduces to Choquard equation. And soliton solution of Choquard equation has been investigated by many researchers, therefore it seems more (...) profound from physics perspective. However, we consider both schemes of soliton computer are equally possible. More researches are needed to verify our proposition. (shrink)

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

The study's general objective is to determine the students' stance on the most appropriate model of writing skills, using Structural Equation Modeling (SEM) as a basic design in the relationship of self-regulated learning strategies, communicative learning strategies, learning grammatical strategies, and writing skills. This study used a mixed-method sequential explanatory design, in which quantitative design is more widely used than qualitative Creswell, J., & Creswell, D. (2017). The researcher used the stratified random sampling technique for selecting respondents and, by using (...) the Raosoft sample size calculator, identified 390 respondents using a four-part questionnaire to collect data. Purposive sampling is the method for determining participants in a qualitative design using a guided questionnaire to obtain data from In-Depth Interviews and Focus Group Discussions. Model 5 was the best-fitting model for writing skills, showing significant correlations with the exogenous variables: self-regulated learning strategies, communicative learning strategies, learning grammatical strategies, and writing skills as endogenous variables. Both the exogenous and endogenous variables obtained a high level of overall description, meaning that students often practiced strategies to cultivate writing skills. The participants' stance on the most appropriate model is essential for tertiary students to have different strategies for developing writing skills. It is necessary to reach the full description of the highest level by using different strategies to build writing skills. (shrink)

Recent studies tend to explain the importance of communication in the organisation as well as prescribing the most commonly practised techniques adopted by school managers. Studies on financial management are quite limited with the available ones suggesting that poor financial management is a source of conflict between school leaders and host communities. Little seems to be known on the connection between principals’ communication patterns and funds’ management as predictors of school-community relationship. This study builds on existing studies and appears to (...) be the first to assess the linkages between principals’ communication patterns, fund management practices and school- community relationship based on empirical rather than subjective data. A structural modelling approach was adopted to examine the nexus using quantitative primary data obtained from a random sample of 2108 respondents. A questionnaire which was designed and validated by the researchers served as the data collection device. Collected data were subjected to Exploratory and Confirmatory Factor Analyses, as well as Multiple Regression Analysis. Findings revealed various significant communication, funds management and school-community relationship practices that are available for adoption. However, it was found that the extent to which principals utilised such practices were below expected minimum standards. It was also found that there were no significant partial and composite effects of principals’ communication and funds management practices on school-community relationship (SCR). Based on these results, relevant theoretical, policy and practical implications are discussed. (shrink)

As is well known, Einstein was dissatisfied with the foundation of quantum theory and sought to find a basis for it that would have satisfied his need for a causal explanation. In this paper this abandoned idea is investigated. It is found that it is mathematically not dead at all. More in particular: a quantum mechanical U(1) gauge invariant Dirac equation can be derived from Einstein's gravity field equations. We ask ourselves what it means for physics, the history of (...) physics and for the actual discussion on foundations. (shrink)

We propose to simplify the problem of the unified theory of Quantum-Gravity through dealing first with the simple case of non-relativistic equations of Gravity and Quantum Mechanics. We show that unification of the two non-relativistic formalisms can be achieved through the joined classical and Quantum postulate that every natural body is composed of N identical final particles. This includes the current 'elementary' particles of the standard model such as quarks, photons, gluons, etc. Furthermore, we show that this opens a (...) new route toward a Generalized Equation of Quantum-Gravity that takes the effects of both of velocity and acceleration into account. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in (...) which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

An ongoing mystery in sensory science is how sensation magnitude F(I), such as loudness, increases with increasing stimulus intensity I. No credible, direct experimental measures exist. Nonetheless, F(I) can be inferred algebraically. Differences in sensation have empirical (but non-quantifiable) minimum sizes called just-noticeable sensation differences, ∆F, which correspond to empirically-measurable just-noticeable intensity differences, ∆I. The ∆Is presumably cumulate from an empirical stimulus-detection threshold I_th up to the intensity of interest, I. Likewise, corresponding ∆Fs cumulate from the sensation at the stimulus-detection (...) threshold, F(I_th ), up to F(I). Regarding the ∆Is, however, it is unlikely that all of them will be known experimentally; the procedures are too lengthy. The customary approach, then, is to find ∆I at a few widely-spaced intensities, and then use those ∆Is to interpolate all ∆Is using some smooth continuous function. The most popular of those functions is Weber’s Law, ∆I⁄I=K. But that is often not even a credible approximation to the data. However, there are other equations for ∆I⁄I. Any such equation for ∆I⁄I can be combined with any equation for ∆F, through calculus, to altogether obtain F(I). Here, two assumptions for ∆F are considered: ∆F=B (Fechner’s Law) and (∆F⁄F)=g (Ekman’s Law). The respective integrals involve lower bounds I_th and F(I_th ). This stands in broad contrast to the literature, which heavily favors non-bounded integrals. We, hence, obtain 24 new, alternative equations for sensation magnitude F(I) (12 equations for (∆I⁄I) × 2 equations for ∆F). (shrink)

Horizontal gene transfer (HGT) has been a paramount mechanism of interest in recent literature addressing the origins of biological evolution. However, research on lightning-triggered electroporation represents the innovative and still insufficiently grasped approach to HGT (Kotnik, 2013). On the other hand, prebiotic synthesis is a fundamental process for chemical evolution. Recently, the effects of volcanic lightning on nitrogen fixation and phosphate reduction have also been considered (NavarroGonzález and Segura, 2004). This paper aims to present a top-down approach to the question (...) of the origin of life on early Earth. By considering the conditions necessary for the emergence of biological and chemical evolution, emphasizing electrostatic discharges, we will attempt to link previous theoretical and experimental research. Furthermore, we will present a recent endeavor at applying the Drake equation to calculating the probability of volcanic lightning impact on the prebiotic synthesis and derive a similar use in estimating the contribution of lightning to HGT (Weaver, 2013). We will also display that choosing a type of probability appropriate for the context of life sciences is not necessarily a quantitative issue. Finally, we will show that significant conceptual constraints, like determining the relevant factors and sources of uncertainty when considering the origin of life on early Earth, are fundamentally philosophical issues. We hope that the results of our research – deriving Drake’s equation in the domain of chemical evolution and considering Bayesian and counterfactual types as potentially more suitable candidates for calculating probabilities in the evolutionary framework – will contribute to developing new discussions in life sciences. (shrink)

Some years ago, Hidding et al. suggest that the emergence of intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers’ equation. The solution to this equation can be obtained from a geometrical formalism. The resulting Adhesion formalism provides deep insight into the dynamics and topology of the Cosmic Web. It uncovers a direct connection between the conditions in the very early Universe and the complex spatial patterns (...) that emerged out of these under the influence of gravity. In the present paper, we describe a cellular automaton model of the Burgers’ equation, which can be investigated via a fast computer simulation. In the end, this suggests a Cellular Automata Adhesion Model of the Universe. (shrink)

In contemporary mathematics, a Colombeau algebra of Colombeau generalized functions is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Remark 1.1.1.Such a multiplication of distributions has been a long time mistakenly believed to be impossible because of Schwartz’ impossibility result, which basically states that there cannot be a differential algebra containing the space of distributions and (...) preserving the product of continuous functions. However, if one only wants to preserve the product of smooth functions instead such a construction becomes possible, as demonstrated first by J.F.Colombeau [1],[2]. As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial differential equations, geophysics, microlocal analysis and general relativity so far. (shrink)

While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory 's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime (...) setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that their basic principles are simply incompatible with this theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name General Relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say , Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993). Of other hand from the mathematical point view the “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996). So, during a time, the declaration of quantum theorists:“I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996)seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradicts fundamental assumptions of the theory of Relativity. These observations are in disagree from predictions of the theory of Relativity. (Hatch, 2004a, 2004b, 2007). The mathematical model was developed first by Grossmann who presented it, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann ́s spacetimes. In this paper, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch and, course, we conclude that a Einstein ́s gravity theory does not exist. (shrink)

This book deals with Colombeau solutions to Einstein field equations in general relativity: Gravitational singularities, distributional SAdS BH spacetime-induced vacuum dominance. This book covers key areas of Colombeau nonlinear generalized functions, distributional Riemannian, geometry, distributional schwarzschild geometry, Schwarzschild singularity, Schwarzschild horizon, smooth regularization, nonsmooth regularization, quantum fields, curved spacetime, vacuum fluctuations, vacuum dominance etc. This book contains various materials suitable for students, researchers and academicians of this area.

Many have taken Sellars’s critique of empiricism in “Empiricism and the Philosophy of Mind” (EPM) to be aimed at his teacher C. I. Lewis. But if so, why do the famous arguments of its opening sections carry so little force against Lewis’s views? Understandably, some respond by denying that Lewis’s epistemology is among the positions targeted by Sellars. But this is incorrect. Indeed, Sellars had earlier offered more trenchant (if already familiar) critiques of Lewis’s epistemology. What is original about EPM (...) is that it criticizes empiricist positions like Lewis’s not because of their foundationalism, but because of their psychologism about meaning. Since psychologism turns out to be unacceptable by Lewis’s own lights, EPM has a compelling (if implicit) critique of Lewis to offer after all, one that strikes at the heart of his philosophical system. (shrink)

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)

Latin American religious political thought includes colonial Spanish and Portuguese ideologies that preceded independence but have survived into the post-independence era, authoritarian ideologies supportive of military governments in the twentieth century, and progressive liberation theologies. In this article, I present a distinct tradition: a version of classical liberal thought. This tradition is skeptical of big government, opposed to caste systems, supportive of a high degree of federalism, uneasy with militarism, and supportive of democratic institutions while affirming religious social norms. This (...) ideology was developed in northeastern Brazil in the early nineteenth century by a Carmelite activist named Frei Caneca (Brother Mug), who published a newspaper titled the Typhis Pernambucano (Tiphys of the State of Pernambuco). (shrink)

There is a great deal of evidence that method bias is really sure influences item validities, measurement error, correlation and covariance between latent constructs and thus leading the researchers to erroneous conclusion due to inflation or deflation during hypothesis testing. To remedy this, the study provides a guideline to minimize the method bias in the context of structural equation modeling employing the covariance method (CB-SEM) using medical tourism model. A practical approach is illustrated for the identification of method bias based (...) on the new construct namely common latent factor. Using this latent construct, we managed to identify which item has potential to permeate more variance from common latent factor. Nevertheless, we figure out that the method bias is do not exist in our developed model. Therefore, this measurement model is appropriate for structural model in order to achieve the research hypotheses. We hope that this discussion will help the researchers anticipate which items are likely exposed on method bias before proceed to advance modeling. (shrink)

Previous research has interlinked alcohol consumption (AC), mental stress (MS), psychotic experiences (PE), and academic performance (AP) of students and psychological behavior of the general population. The current study seems to be the first to consider the joint and partial mediation effects of MS and PE in linking AC to graduates’ job performance in specific areas such as teamwork (TW), communication competence (CC), customer service (CS), and job functions (JF). A virtual cross-section of 3,862 graduates with self-reported cases of having (...) taken alcohol in the past participated in the study. These participants responded to an electronic questionnaire that was mailed to them. The instrument used for data collection had acceptable psychometric properties. The study used the partial least squares structural equation modeling (PLS-SEM) to achieve its objectives. The inner and outer models were all evaluated for quality and goodness of fit. Results showed a significant negative effect of AC and MS on graduates’ job performance in terms of TW, CC, CS, and JF, respectively. AC had a significant positive effect on MS and PE. MS had a significant positive effect on PE. A significant joint mediation effect of MS and PE was found in linking AC to graduates’ TW, CC, and CS, excluding JF. MS partially mediated AC’s paths to all the graduates’ job performance indicators. PE was only a significant partial mediator of the connection between AC to JF, but not TW, CC, and CS. This study’s result can help improve graduates’ work effectiveness and has revealed some negative predictors. Therefore, it is recommended that graduates avoid alcohol or only consume mild quantities of it to enable them to discharge services effectively at the workplace. (shrink)

Reading tough books to achieve excellent marks, perform well in class, and gain attention from teachers and parents is less likely to drive students. Students used to evaluate their language learning requirements, define the abilities they wished to develop, pick effective study techniques, and set aside gadgets when studying. They also used to read the question before looking for hints in the relevant content, extract the essential lines that convey the major ideas, concentrate on titles, names, numbers, quotations, or instances, (...) and comprehend the overall context to infer an option. The survey discovered that most of the time, students utilized it to determine the progress of their learning and create learning objectives. It was also found that there was a link between the exogenous variables and the academic performance of students. (shrink)

The Comprehensive Human Decision-Making Equation presents a robust model for understanding Holistic Free Will (HFW), conceptualizing decision-making as an autonomous, non-deterministic process within a complex network of influences. This model addresses the Infinite Regress issue by portraying free will as an emergent property of interacting layers, including internal beliefs, external contexts, emotional responses, cognitive biases, and habitual tendencies. Departing from traditional linear models, the equation adopts a systemic framework where each choice reflects a cumulative utility, integrating multiple components such as (...) personal, ethical, social, and temporal utilities. This holistic approach emphasizes the probabilistic nature of free will, challenging deterministic interpretations and highlighting the ethical and relational dimensions of autonomy. By situating free will within a structured yet adaptive process, the model supports the notion that true autonomy is ethically aligned, relational, and embedded in a flexible reality, thereby promoting communal and ethical development. (shrink)

We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the two basic (...) equations of the physics cannot be reconciled. 1. (shrink)

Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that general relativity theory may be reduced to the Newton's gravity theory in the limit of a weak gravitational field and slow motion of the material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be mathematically, physically and dimensionally (...) wrong and also the geometrization of gravity is not really necessary. (shrink)

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation .