The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy.

The ΛCDM model successfully models the expansion of matter in the universe with an expansion of the underlying metric. However, it does not address the physical origin of the big bang and dark energy. A model of cosmology is proposed, where the state of high energy density of the big bang is created by the collapse of an antineutrino star that has exceeded its Chandrasekhar limit. To allow the first neutrino stars and antineutrino stars to form naturally from an initial quantum vacuum state, it helps to assume that antimatter has negative gravitational mass. While it may prove incorrect, this assumption may also help identify dark energy. The degenerate remnant of an antineutrino star can today have an average mass density that is similar to the dark energy density of the ΛCDM model. When in hydrostatic equilibrium, this antineutrino star remnant can emit isothermal cosmic microwave background radiation and accelerate matter radially. This model and the ΛCDM model are in similar quantitative agreement with supernova distance measurements. Other observational tests of the above model are also discussed.

Cosmological models with linearly varying deceleration parameter in the cosmological theory based on Lyra’s geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a time dependent displacement field. We have also obtained the time periods during which the universe undergoes decelerated and accelerated expansions for a matter-dominated universe.

A popular approach to learning about admixture from population genetic data is by computing the allele-sharing summary statistics known as f-statistics. Compared to some methods in population genetics, f-statistics are relatively simple, but interpreting them can still be complicated at times. In addition, f-statistics can be used to build admixture graphs (multi-population trees allowing for admixture events), which provide more explicit and thorough modeling capabilities but are correspondingly more complex to work with. Here, I discuss some of these issues to provide users of these tools with a basic guide for protocols and procedures. My focus is on the kinds of conclusions that can or cannot be drawn from the results of f₄-statistics and admixture graphs, illustrated with real-world examples involving human populations.

The Vacuum Energy Parameter (VEP) of standard cosmology denotes the fraction of the critical density attributed to the accelerated expansion of the Universe. Astrophysical evidence sets the numerical range of VEP at 0.692 +, - 0.012, yet the root cause of these values is currently unknown. Drawing from the stochastic interpretation of early-Universe cosmology, we develop here a derivation of the VEP based on classical diffusion theory and the Langevin equation. Predictions are shown to be in reasonable agreement with observations.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

Mallios and Zafiris emphasize that adjoint functors or adjunctions are not only "ubiquitous" in category theory but characterize the naturality of their approach to physical geometry. Hence in this paper, the history and theory of adjoint functors is investigated. Where do adjoint functors come from mathematically and how did the concepts develop historically?

Curriculum teaching is the basic unit to realize the cultivation and achievement of students’ ability in undergraduate colleges, and it is very important to investigate the influence mechanism of the curriculum system on the achievement states of students' ability. This paper first puts forward the theoretical system and framework of curriculum chains, and constructs a “double-energy and double-space” (DEDS) which consist of the curriculum energy efficiency space and student ability space respectively. Investigating the space-time transformation relationship of curriculum chains in the DEDS, the forward transformation model, inverse transformation model and the rheological model of the achievement states in the curriculum energy efficiency space and student ability space are established. Studying the dynamic evolution mechanism of curriculum chains within the DEDS, the dynamic evolution model, which presents the relationship between achievement states of curriculum energy efficiency/students' ability and curriculum/students' dynamic potential, are established; the control methods of courses/students' dynamic potential based on the proposed dynamic evolution model are developed to ensure the achievements of the graduates’ social ability; the evaluation and detection methods of achievement states of curriculum chains in DEDS are proposed to obtain the actual achievement states of curriculum energy efficiency and students’ ability, and this will provide effective input for the control of curriculums/students’ dynamic potential; the planning and design methods of curriculum chains facing social needs are presented, which can provide theoretical basis for the formulation of the talent training scheme and curriculum system in colleges and universities.

Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between “healthy" nucleotide sequences and disrupted sequences that may be associated with various diseases. In this paper, we extend our efforts to the study of messenger RNA metabolism, showcasing the power of our approach. We investigate (i) mRNA translation in prokaryotes and eukaryotes, (ii) polyadenylation in eukaryotes, which is crucial for nuclear export, translation, stability, and splicing of mRNA, (iii) miRNAs involved in RNA silencing and post-transcriptional regulation of gene expression, and (iv) the identification of disrupted sequences that could lead to potential illnesses. To achieve this, we employ (a) infinite (finitely generated) groups fp, with generators representing the r+1 distinct nucleotides and a relation between them [e.g., the consensus sequence in the mRNA translation (i), the poly(A) tail in item (ii), and the miRNA seed in item (iii)], (b) aperiodicity theory, which connects “healthy groups" fp to free groups Fr of rank r and their profinite completion F^r, and (c) the representation theory of groups fp over the space-time-spin group SL2(C), highlighting the role of surfaces with isolated singularities in the character variety. Our approach could potentially contribute to the understanding of the molecular mechanisms underlying various diseases and help develop new diagnostic or therapeutic strategies.

In recent years, semantic communication has received significant attention from both academia and industry, driven by the growing demands for ultra-low latency and high-throughput capabilities in emerging intelligent services. Nonetheless, a comprehensive and effective theoretical framework for semantic communication has yet to be established. In particular, finding the fundamental limits of semantic communication, exploring the capabilities of semantic-aware networks, or utilizing theoretical guidance for deep learning in semantic communication are very important but yet still unresolved issues. In this paper, we delve into the pertinent advancements in semantic information theory. Grounded in the foundational work of Claude Shannon, we present the latest developments in semantic entropy, semantic rate distortion, and semantic channel capacity. Additionally, we will analyze some open problems in semantic information measurement and semantic coding, providing a theoretical basis for the design of a semantic communication system. Furthermore, we carefully review several mathematical theories and tools and evaluate their applicability in the context of semantic communication. Finally, we shed light on the challenges encountered in both semantic communication and semantic information theory.

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems of ordinary and partial differential equations, which are models of the autocatalytic chemical processes and the numbers of interacting populations, is carried out. It is analytically and numerically shown that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. In this case, irregular (chaotic) attractors in all cases are exclusively singular attractors in the sense of the FShM theory.

1) We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time $t$. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time $t_0$ under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove that both these situations cannot arise under ordinary circumstances and thus measurement processes cannot be modelled by physical Hamiltonians.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

The concept of using special electrical circuit design realize a "cold resistors", that is, an active resistor circuitry with lowered effective noise temperature, was first introduced about 80 years ago. Later on, various kinds of artificial resistors were applied in different research areas, such as gravitational wave detection, photo-amplifiers and quartz oscillators. Their proofs of concepts were experimentally proved. Unfortunately, the complete theory was not found even though several attempts had been published, sometimes with errors. In this paper, we describe a correct and complete circuit theoretical model of a cold resistor system. The results are confirmed by computer simulations. A design tools for this circuit is also shown.

Intelligence is a human construct to represent the ability to achieve goals. Given this wide berth, intelligence has been defined countless times, studied in a variety of ways and represented using numerous measures. Understanding intelligence ultimately requires theory and quantification, both of which have proved elusive. I develop a framework – the Theory of Intelligences (TIS) – that applies across all systems from physics, to biology, humans and AI. TIS likens intelligence to a calculus, differentiating, correlating and integrating information. Intelligence operates at many levels and scales and TIS distils these into a parsimonious macroscopic framework centered on solving, planning and their optimization to accomplish goals. Notably, intelligence can be expressed in informational units or in units relative to goal difficulty, the latter defined as complexity relative to system (individual or benchmarked) ability. I present general equations for intelligence and its components, and a simple expression for the evolution of intelligence traits. The measures developed here could serve to gauge different facets of intelligence for any step-wise transformation of information. I argue that proxies such as environment, technology, society and collectives are essential to a general theory of intelligence and to possible evolutionary transitions in intelligence, particularly in humans. I conclude with testable predictions of TIS and offer several speculations.

This paper introduces a Unified Field Theory through the generalization of General Relativity, following the methodology outlined by Einstein for incorporating complex metrics in the pursuit of a comprehensive Unified Field Theory.

A formulation of the Density Functional Theory (DFT) is constructed as an application of the method of maximum entropy for an inhomogeneous fluid in thermal equilibrium. The use of entropy as a systematic method to generate optimal approximations is extended from the classical to the quantum domain. This process introduces a family of trial density operators that are parametrized by the particle density. The optimal density operator is that which maximizes the quantum entropy relative to the exact canonical density operator. This approach reproduces the variational principle of DFT and allows a simple proof of the Hohenberg-Kohn theorem at finite temperature. Finally, as an illustration, we discuss the Kohn-Sham approximation scheme at finite temperature

The Quantum-Cosmos Nexus Theory delves into the intricate web of relationships that tie together fundamental constants, cosmological properties, and the boundaries of our comprehension in the realm of physics. It unveils a profound interconnection between the gravitational constant (G), the speed of light (c), and the parameters of the observable universe. It introduces a unification equation that hints at a connection between the fundamental constants. It also introduces a new constant, , which is similar to the Planck constant but, on a large scale, signifies the ultimate unit of action or energy on a cosmic scale. With this new constant, new units similar to Planck units have been introduced. They are the equivalence of Planck units in the sense that they represent the limits of our current understanding of physics on the largest scale. The theory also shows that most of the fundamental constants of nature, including the gravitational constant (G), the speed of light (c), vacuum permittivity (ε₀) vacuum permeability (u₀), the Boltzmann constant (K_B), and the fine-structure constant (α), can be derived from these new units and Planck units. The first derived equation suggests a potential weakening of the gravitational constant over time, assuming the density remains relatively constant. Although this is a matter of speculation, it has the potential to explain observations related to dark matter. The theory also makes use of the Planck force, defining it as the maximum force on the quantum and cosmic scales. It also emphasizes that the Planck scale is not the ultimate limit and reveals our observational constraints, offering a unique perspective on the universe's fundamental workings. The Quantum-Cosmos Nexus Theory reveals how fundamental constants, cosmic dynamics, and the limits of our understanding converge, opening the door to fresh perspectives on the underlying principles of the universe.

A new model of gravity is presented here similar to the earlier work of Verlinde on Emergent Gravity but without the use of Verlinde's main assumption on the nature of gravity as an entropic force using the First Law of Thermodynamics. Instead, the model will be shown to be consistent with the Second Law of Thermodynamics as used in Black Hole Physics. Moreover, it does not use the Equipartition Theorem such that there is no need to define a thermal bath enclosed within a holographic screen. The theory uses $E=NE_{p}$, for the total energy of a massive object where $E_{p}$ is the Planck Energy while $N$ is the number of Planck Energy to represent the maximum possible density of information that can reside in matter. The theory uses also the Holographic Principle as the basis for an information-theoretic approach to the nature of gravity. It is shown here that gravity emerges whenever there is an updating of the information within a given volume of space by the presence of matter.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

Quantum mechanics is often described as irreducibly non-local. A tacit element of this picture is the assumption that one and the same sub-ensemble of quanta is post-selected in every measurement combination of a Bell test. Yet, this expectation was recently shown to be formally inconsistent with quantum theory (Cetto et al., 2020) and even to be experimentally falsifiable (Mardari 2021). The need to make sense of this development motivated a rigorous conceptual analysis of quantum non-locality, especially as it relates to the basic principles of quantum mechanics. The simple conclusion is that quantum theory and quantum non-locality are fundamentally incompatible. This is not a loophole around the predictions of quantum mechanics, but rather an insight into the essential conditions that make them accurate.

Advances of Relativity Theory are in the replacement of the space-time model with time-invariant universal space that has a variable energy density. Every physical object with mass m and energy E is diminishing the energy density of space exactly for the amount of its energy. Lorentz factor has its origin in the variable energy density of universal space, we call it "superfluid quantum space" - SQS that is the primordial energy of the universe. Universal SQS is the absolute frame of reference for all observers as confirmed experimentally by the GPS system, which demonstrates that the relative rate of clocks is valid for all observers. A planet's perihelion precession and the Sagnac effect are the results of the SQS dragging effect.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

According to the standard cold dark matter (CDM) cosmology, the structure of dark halos including those of galaxy clusters reflects their mass accretion history. Older clusters tend to be more concentrated than younger clusters. Their structure, represented by the characteristic radius $r_s$ and mass $M_s$ of the Navarro-Frenk-White (NFW) density profile, is related to their formation time. In this study, we show that $r_s$, $M_s$, and the X-ray temperature of the intracluster medium (ICM), $T_X$, form a thin plane in the space of $(\log r_s, \log M_s, \log T_X)$. This tight correlation indicates that the ICM temperature is also determined by the formation time of individual clusters. Numerical simulations show that clusters move along the fundamental plane as they evolve. The plane and the cluster evolution within the plane can be explained by a similarity solution of structure formation of the universe. The angle of the plane shows that clusters have not achieved “virial equilibrium” in the sense that mass/size growth and pressure at the boundaries cannot be ignored. The distribution of clusters on the plane is related to the intrinsic scatter in the halo concentration--mass relation, which is originated from the variety of cluster ages. The well-known mass--temperature relation of clusters ($M_\Delta\propto T_X^{3/2}$) can be explained by the fundamental plane and the mass dependence of the halo concentration without the assumption of virial equilibrium. The fundamental plane can also be used for calibration of cluster masses.

This hypothesis is the result of my conviction that science will oneday prove everything in space and time is part of a unification. In "A Brief History of Time", Stephen Hawking wrote, "If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation." The goal: to establish a “proof of concept” to which equations can be added. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.

Quantum theory is the land of indiscernible things, of things that in some situations cannot be put apart. This contrasts in much with standard mathematics and classical logic, which were elaborated to deal with \textit{individuals}, discernible things. Many thinkers, among them the mathematician Yuri Manin, have proposed that a more general theory of `sets' than standard set theories (where sets are collections of discernible elements) should be elaborated to cope with quantum physics. Quasi-set theory was proposed with such an aim. In this paper, we consider some aspects of this theory and discuss the way we can use such a theory as a framework for constructing deformable (not rigid) structures where indiscernible things can be considered but with one additional and fundamental detail: these structures cannot be extended to rigid structures as it happens in the standard frameworks. Really, the way of dealing with indiscernible (or indistinguishable) elements within a `standard' framework such as a `classical' set theory (like the ZFC system) requires the confinement of the discussion to deformable (non-rigid) structures. But in ZFC every structure can be extended to a rigid structure (encompassing only the trivial automorphism -- the identity function), so that in the extended structure (or in the whole universe) one can realize that the supposed indiscernible objects are not indiscernible at all. Quasi-set theory is such that the universe of quasi-sets is deformable and in such a theory one can construct deformable structures which cannot be extended to rigid ones. The aim of this paper is to put these things in a clear way.

We first of all define the arrow of time. Definition of the arrow of time will allow choosing different initial starting points. One of the issues we will also discuss is the interconnection be-tween the arrow of time, entropy and quantum information. Seth Lloyd in his 2001 work made a linkage between entropy, bits, and information via an axiomatic approach involving time in-tervals. Our take is a bit more general. We will discuss as well the t’Hooft’s statement as to in-itial conditions and times arrow, and how different cosmological models may influence initial conditions. Spoilers alert, if a nonsingular start to expansion existed, this would provide the most straightforward way to avoid a datum from classical relativity. That is, that in the actual equations of classical GR, there is no reason to have time asymmetry. Time asymmetry is built into initial conditions and we will detail several candidates. The first half of the paper brings up cosmology models and forming the arrow of time. The second is related to entropy itself and the problem of information. .

This paper discusses complexity theory, that is, the many theories that have been proposed for emergence of complexity from the underlying physics. Our aim is to identify which aspects have turned out to be the more fundamental ones as regards the emergence of biology, engineering, and digital computing, as opposed to those that are in fact more peripheral in these contexts. In the cases we consider, complexity arises via adaptive modular hierarchical structures that are open systems involving broken symmetries. Each emergent level is causally effective because of the meshing together of upwards and downwards causation that takes place consistently with the underlying physics. Various physical constraints limit the outcomes that can be achieved. The underlying issue concerns the origin of consciousness and agency given the basis of life in physics, which is structured starting from symmetries and variational principles with no trace of agency. A possible solution is to admit that consciousness is an irreducible emergent property of matter.

In this work, we explore new constraints on phantom scalar field cosmologies with a scalar field employing early times catalogues related to CMB measurements, along with the local standard observables, like Supernovae Type Ia (SNIa), H(z) measurements (Cosmic Clocks), and Baryon Acoustic Oscillations (BAO) baselines. In particular, we studied a tracker phantom field with hyperbolic polar coordinates that have been proposed in the literature. The main goal is to obtain precise cosmological constraints for H0 and σ8, in comparison to other constructions that present tension in early cosmological parameters. Our results show that phantom scalar field cosmologies have a reduced statistical tension on H0 that it is less than 3σ using model-independent CMB catalogues as SPT-3G+WMAP9 and ACTPol DR-4+WMAP9 baselines. This suggests these models using a different phantom potential might address the Hubble constant problem and reduce the systematics involved.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigated a formulation of quantum gravity based on the Wheeler-DeWitt (WDW) equation combined with the classical concepts of the branch-cut cosmology, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction phase, prior to the primordial singularity, and the subsequent expansion phase. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched cosmology as well as the corresponding conjugate momentum to the category of quantum operators. As a novelty, ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted to the integers α=[0,1,2], since non-integers have no physical meaning, allowing this way a broader class of solutions for the wave function of the Universe. As another novelty, additional energy-dependent parametrizations are considered, more specifically, in addition to a branched universe filled with underlying background vacuum energy, matter and radiation, in order to make contact with standard model calculations, we additionally supplement the formulation with baryon matter, dark matter and quintessence contributions. As an additional novelty, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate this way, as a novelty conclusion, the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early universe in contrast to the classic branched cosmology view of a smooth transition.

We show that the accelerating expansion phase of the universe can emerge from the group field theory formalism, a candidate theory of quantum gravity. The cosmological evolution can be extracted from condensate states using mean field approximation, in a form of modified FLRW equations. By introducing an effective equation of state w, we can reveal the relevant features of the evolution, and show that with proper choice of parameters, w will approach to −1, corresponds to the behaviour of cosmological constant, results in a late time acceleration and leads to de Sitter spacetime asymptotically.

We are encouraged to look beyond ɅCDM as there are no satisfactory explanations for either dark energy or dark matter. A data centred phenomenological approach supports an explanation where dark energy is Holographic Dark Information Energy, HDIE. HDIE explains many effects attributed separately to Ʌ and CDM. HDIE mimics Ʌ with sufficient energy and an equation of state parameter, w= -1.03±0.05 at redshifts z<1.35 to account for accelerating expansion. HDIE is clumped around galaxies at densities that distort space-time, explaining many CDM attributed effects. The present ratio of HDIE/baryons ~2.15, required for the observed expansion history, is equivalent to a dark matter fraction ~68%, consistent with many galaxies. The HDIE/baryon model is based largely on proven physics, provides a common explanation for dark energy and dark matter, and solves the cosmological coincidence problem. At earlier times, z > ~1.35, HDIE was phantom, w = -1.82±0.08, enabling the model to be falsified. HDIE fits Planck dark energy wo-wa plots at least as well as Ʌ, and is consistent with other results that suggest dark energy was phantom at earlier times. A new w-parameterisation is proposed, as the usual CPL parameterisation is biased and unsuitable for distinguishing between HDIE/baryon and ɅCDM models.

A teoria diz que as primeiras coisas a existir no universo e no momento atual foram impulsionadas pela necessidade imperiosa; ou seja, os espaços físicos influenciam a existência de elementos e fatos a partir das inúmeras observações nos espaços físicos em relação a elementos e fatos. A existência de elementos obrigatórios no espaço é motivada pelas características dos espaços que oferecem condições para tal obrigação. A teoria afirma que o universo não surgiu por acaso; Ou seja, o universo surgiu por determinação influenciada pelo que o rodeia. O objetivo do estudo é ajudar a explicar os elementos e fatos do universo desde a origem até o presente.

Clinical work conducted over the last seventeen years at the EEG Institute in Los Angeles and by other neurofeedback providers around the world has demonstrated the utility of extending frequency-based neurofeedback deep into the infra-low frequency (ILF) region, using the method of endogenous neuromodulation described herein. The method is characterized by the absence of any overt reinforcements, which makes it possible to extend the clinical reach to extremely low frequencies. As the training frequency is lowered, the signal becomes more difficult to discriminate, and ultimately it can only be discerned by the brain itself, in the process of endogenous neuromodulation. The method emulates how the brain does skill learning in general: It must observe itself performing the skill, with feedback on its performance. While the immediate target of ILF neurofeedback is enhanced self-regulatory competence--with symptomatic relief and functional recovery the secondary consequences, progressive lowering of the target frequencies has led to improved outcomes in application to challenging dysfunctions such as episodic suicidality, migraine, seizures, and bipolar mood swings. The work has also yielded insights into how the frequency domain is organized. The training proceeds best at frequencies that are specific to each individual, and these are referred to as optimal response frequencies (ORFs). These frequencies differ for various placements but stand in two fixed relationships to one another, one that holds over the EEG spectral range, and another that holds over the entire ILF range. Training in the ILF region engages the dynamics of the glial-neuronal networks, which govern tonic, resting state regulation. The collective clinical experience with ILF neuromodulation within a large practitioner network supports the case for making protocol-based, individualized ‘homeodynamic’ regulation a therapeutic priority, particularly for our most impacted clinical populations: addiction, trauma formations, traumatic brain injury, and the dementias. The case is made for further outcome studies and foundational research.

The exact, non perturbative, response theory developed within the field of nonequilibrium molecular dynamics, also known as TTCF (Transient Time Correlation Function) applies to quite general dynamical systems. Its key element is called dissipation function, because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time independent external perturbations, and then it has been extended to time dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated withe.g. linear response theory. The present work includes time dependent stochastic perturbations, in the theory, using the Karhunen-Loeve theorem. This leads to three different investigations of a given process. One in which a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigations, one averages over both initial conditions and stochastic coefficients. We conclude illustrating the applicability of the resulting exact response theory with simple examples.

There are gravitational field and baryonic matter (star, planet, gases etc.) in our world; gravitational field is much more fundamental for that the relativistic mass of the gravitational field of a neutron star is almost 10²¹ times the mass of the neutron star. And, it is astonishing that the relativistic mass density of the gravitational field on the surface of a neutron star can be larger than the mass density of the neutron star. It is well known that, in the weak gravitational field a light line appears a straight line while in the strong field it is a curved line. It is stressed that the result measured in the strong field is more fundamental for that in a galaxy the measurable object is generally with strong field. It results in that the way that the result measured on the Earth with weak field is used as the universal standard need be revised as gravity is studied in the scale of a galaxy. It seems that a new theory of gravity need be developed for the new observations.

Diffuse optical tomography (DOT) is a medical imaging procedure using light to measure the geometric and working properties of cells, for instance, oxygen consumption, water content, and fat percentage in the tissue by performing three-dimensional visualization of the tissue. This paper aims to explain the theory behind diffuse optical tomography imaging and how the technology works. The paper explains how photon migration techniques based on diffusion theory can be used to image the optical properties of tissue. There are several reasons why near-infrared (NIR) imaging is the most effective method in terms of recovering optical parameters quantitatively in the near-infrared region. The author discusses the methods in detail. This research also presents various advantages, practical uses, and potential problems that have been related to DOT in this work. There is also a brief discussion of current research developments in medical imaging using near-infrared wavelengths, and what the future holds for that area.

In this article key results in general relativity are studied and the dynamics of quantum fields in curved spacetime is reviewed. It has been shown geometrically how dark energy breaks strong energy condition. We study tan-hyperbolic inflation for an open FRWL universe and show that over half and full period scalar field remains in it's initial state.

The Action Control Theory (ACT) is an enactive theory of perception and mental imagery with six components: Schemata, Objects, Actions, Affect, Goals and Others’ Behavior. The evidence support-ing these six connected processes is reviewed in light of research on mental imagery vividness. The six processes and their interconnections receive empirical support from a wide range of studies. All six domains of perception and mental imagery are influenced by individual differences in vividness. Real-world applications of ACT show interesting potential to improve human well-being in both healthy people and patients. Mental imagery can be applied in creative ways to make new collective goals and actions for change that are necessary to maximize the future prospects of the planet.

We have introduced a sign operator of energy, analogous to the operator helicity, but in the direction of what we call energy vector. However, this energy vector needs a time vector. To give physical senses to the components of such a time vector, we try to explain the time dilation in special relativity and try to relate the components of the time vector to the tunneling times when an electron crosses a potential barrier.

Assuming a Winterberg model for space where the vacuum consists of a very stiff two component superfluid made up of positive and negative mass planckions, theory is the hypothesis, that Planck charge, , was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where equals Apery's constant, , and, , is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, equals, , and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere , within the vacuum made up of these particles. On the surface of the earth, where, , the displacement amounts to, . All of these displacements are due to increased gravitational pressure within the vacuum, which in turn are caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = -1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the Moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck units increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is being considered.

We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH₀ and dc/dt = 1.8cH₀ with H₀ as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH₀. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string.

This paper investigates the recently found \cite{migdal2023exact} reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the quantum statistical theory of free fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the statistical limit $N\to \infty$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the charge density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without assumptions, approximations, or fitted parameters. We compute resulting integrals in \Mathematica{} and present effective indexes for the energy decay as a function of time Fig.\ref{fig::NPlot} and the energy spectrum as a function of the wavevector at fixed time Fig.\ref{fig::SPIndex}. In particular, the asymptotic value of the effective index in energy decay $n(\infty) = \frac{7}{4}$, but the universal function $n(t)$ is neither constant nor linear.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

A Teoria das diferenças entre elementos explica as razões das diferenças nos conceitos físicos entre diferentes elementos, como a Física Quântica e a Teoria da Relatividade Geral, sendo explicada através de observações. Assim, é possível concluir a partir das observações que as diferenças são motivadas pelas reações entre os elementos, pela composição dos elementos, e pela influência dos espaços que promovem perdas e ganhos de características; portanto, não há semelhança geral entre a física quântica e a teoria geral da relatividade. O estudo tem como objetivo compreender os elementos e seus conceitos físicos que compõem o Universo.

We show that quantum mechanics can be constructed as a classical field theory that correctly describes all basic quantum effects, by combining the Maxwell and Dirac equations. It is shown that for a self-consistent union of the Maxwell and Dirac equations into a unified classical field theory, it is necessary to introduce an additional short-range tensor field, which compensates the intrinsic electrostatic field of the electron wave inside the atom. For the combined Maxwell-Dirac field, the stress-energy tensor is constructed. We show that in the nonrelativistic limit this theory naturally transforms into the self-consistent Maxwell-Pauli theory and allows describing all basic quantum effects in the framework of classical field theory without any quantization.

A grand unification of electroweak and strong forces is presented based on a new idea called Unified Charged Vectors. Using this new concept, it is shown that: The electroweak and strong forces can be unified into a single electro-weak-strong force. The various charges and coupling constants of fermions (like the electroweak mixing angle) can be predicted, rather than presupposed. The Lagrangian symmetries can be predicted rather than presupposed. The standard model Lagrangian can be cast into a simple unified form.

Biological technologies are fundamentally unlike any other because biology evolves. Bioengineering therefore requires novel design methodologies with evolution at their core. Knowledge about evolution is currently applied to the design of biosystems ad hoc. Unless we have a unified engineering theory of evolution, we will neither be able to meet evolution’s potential as a design tool, nor understand or limit its unintended consequences on our designs. Our concept of the evotype offers a conceptual framework for engineering the evolutionary potential of biosystems. We show how a biosystem’s evolutionary properties might be rationally designed by engineering aspects of genetic variation, designed function, and natural selection. This idea could apply to all biosystems – from individual proteins to communities of whole-cells or even entire ecosystems – whether the goal is to direct evolution in the design process, or to limit its impacts during application. These principles could even be used beyond the realm of bioengineering to design entirely synthetic evolving auto-adaptive technologies.

This article integrates existing theory from distributed computing and cryptology with anecdotal material from the cryptocurrency industry, to provide a comprehensive description of the minimum requirements of the hypothetical academic blockchain. The paper argues that such a community could significantly reduce the biases and misconduct that now exist in the academic peer review process. Theory suggests such a system could operate effectively as a distributed encrypted telecommunications network where nodes are anonymous, do not trust each other, and there is minimal central authority. To incentivize the academic community to join such a proposed community, the paper proposes a pseudo-cryptocurrency called litcoin (literature coin). This litcoin-based system would create economic scarcity based on proof of knowledge (POK), which is a synthesis of the proof of work (POW) mechanism used in bitcoin, and the proof of stake (POS) mechanism used in various altcoin communities. The paper argues that the proposed POK system would enable the academic community to more effectively develop the research it finds valuable.

The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. This is known as the strong Goldbach's conjecture. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A principal complexity class is NSPACE(S(n)) for some S(n). We show if the weak Goldbach's conjecture is true, then the problem PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n). This proof is based on the assumption that if some language belongs to NSPACE(S(n)), then the unary version of that language belongs to NSPACE(S(log n)) and vice versa. However, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples. Since Harald Helfgott proved that the weak Goldbach's conjecture is true, then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples, where the case of infinite number of counterexamples statistically seems to be unlikely. In addition, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Twin prime conjecture is true. Moreover, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Beal's conjecture is true. Since the Beal's conjecture is a generalization of Fermat's Last Theorem, then this is also a simple and short proof for that Theorem. In mathematics, the Riemann hypothesis is consider to be the most important unsolved problem in pure mathematics. If PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Riemann hypothesis is true.

The QBIT theory is an attempt toward solving the problem of consciousness based on empirical evidence provided by various scientific disciplines including quantum mechanics, biology, information theory, and thermodynamics. This theory formulates the problem of consciousness in the following four questions: (1) What is the nature of qualia? (2) How are qualia generated? (3) Why are qualia subjective? (4) Why does a quale have a particular quality or meaning?In sum, the QBIT theory proposes that (1) when a pack of quantum information is compressed beyond a certain threshold, a quale is generated; (2) a quale is a superdense pack of maximally entangled qubits in a pure state; (3) when information-theoretic certainty of a system about an external stimulus exceeds a particular level, the system becomes conscious of that stimulus; (4) subjectivity of consciousness is due to the fact that maximally entangled pure states are private and unshareable.

Several specific types of generalized compactness of generalized topological spaces have been defined, investigated and related to compactness in ordinary topological spaces from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized compactness in a generalized topological space is reported herein as a starting point for more generalized classes.

Several specific types of ordinary and generalized connectedness in a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new type of generalized connectedness in a generalized topological space is reported herein as a starting point for more generalized types.

Several specific types of generalized maps of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

Several specific types of generalized sets of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized sets of a generalized topological space is reported herein as a starting point for more generalized classes.

We suggest progress regarding the following six physics opportunities. List all elementary particles. Describe dark matter. Explain ratios of dark matter to ordinary matter. Explain eras in the history of the universe. Link properties of objects. Interrelate physics models. We use models based on Diophantine equations.

Our study essentially concerns the dynamic behavior of an SIRS epidemic model in discrete time. Two equilibrium points are obtained; one is disease-free while the other is endemic. We are interested in the endemic fixed point as well as its asymptotic stability. Depending on the parameters which are estimated using the data from US Department of health and SIRS modelling with optimization, two Flip and Transcritical bifurcations appear. We illustrate their diagrams, as well as their bifurcation curves using the method of Carcasses \cite{carcasses1993determination,carcasses1995singularities} for the Flip bifurcation and by an implicit function deduced from such an equation for the Transcritical bifurcation. We use the scanning of the parametric plane to have a global view of the behavior of the model and to highlight the zones of stability of the existing singularities. A superposition of the bifurcation curves with the parametric plane can show the overlap of the curves with the boundaries of the stability domains, which confirms the smooth running of the simulation and its correspondence with the theory, we finish this article with constrained optimal control applied to infection rate and recruitment rate for an SIRS discrete epidemic model. Pontryagin's maximum principle is used to determine these optimal controls. Finally using COVID-19 data in the USA, we obtain results that demonstrate the effectiveness of the proposed control strategy to mitigate the spread of the pandemic.

For a long time, physicists always directly use mathematical tools to deal with physical problems, and few people pay attention to the difference between mathematical theory and physical theory. Just like the dilemma that physicists once faced when dealing with the problem of blackbody radiation function.By analyzing the difference between the theoretical basis of mathematics and the theoretical basis of physics, this paper draws the following conclusions: (1) The theoretical basis of mathematics and the theoretical basis of physics are different, so when we use mathematical tools for physics research, we need to be very careful. (2) Finiteness and discreteness should be the basis of the whole physical theory; This paper points out that it is not advisable to use infinite " " and infinitesimal "0" without restriction and demonstration in physics, as well as the continuity of functions, which will bring a lot of trouble to physical theory.At the same time, through the analysis of Banach-Tarski paradox and Bertrand paradox, this paper proposes that if we revise the basic assumptions of probability theory: assuming that "points" have quantized sizes, and "lines" also have quantized widths. After the correction, we can not only avoid the troubles caused by Bertrand paradox, but also make probability theory better for practical application.

Exisitng studies argue life chances are, in part, vertically reproduced. Such a statement is applicable to the Chinese contexts as, but not limited to, parental hukou status, to some extent, determines the life chances their children receive. In this essay, the author would like to introduce human capital theory (HCT) and educational signalling theory (EST), and assess how the applications of each of these two models can enrich the understanding of vertical reproduction of individuals’ social mobility opportunities. The author would also present the limitations of each of these two models when addressing relevant Chinese contexts.

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

The study of emission, propagation, and reflection of balls in Newtonian mechanics, employing the laws of conservation of momentum and energy when the mass of balls converges to zero, concludes that the kinematics of light is like that of massless balls. The kinematics of light explains why light speed is the constant in each inertial frame in which the light source and reflective mirror are at rest, why the laws of physics have the same form in each inertial frame, and why any experiment in an inertial frame cannot prove the motion of that the other inertial frame. The theory of special relativity misapplies symmetry observed in phenomena to two inertial frames; therefore, it duplicates a physics phenomenon from one inertial frame, considered stationary, into another. Moreover, Lorentz’s transformation offers light speed at the constant in the moving and opposite direction of the inertial frame but is variable in any other direction. Therefore, the theory of special relativity rejects itself with these unacceptable conclusions.

In the paper the experimental methodology for the single-crystal circular plate deformation measurement and subsequent procedure for mechanical properties quantitation are developed. The procedure is based on a new numerical-analytical solution of nonlinear boundary-value problem for finite deformations of a circular anisotropic plate. Using the developed method, a study of the deformation of single-crystal circular plates formed on the basis of a silicon-on-insulator structure was carried out. The values of residual stresses are determined and it is shown that the presence of these stresses increases the flexural rigidity of the plate in several times.

We review the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. As an example of practical worth, we consider the Drell-Yan process and discuss the gauge invariance of the corresponding hadron tensor. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in SU(3) gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

This article focuses on methods for designing heuristic models within the paradigm of systems theory and in the disciplinary context of intercultural communication. The main question arises from the striking observation that the common language is insufficient to develop knowledge about human communication, especially when many factors of complexity (such as ambiguity, paradoxes, or uncertainty) are involved in the composition of an abstract research object. This epistemological, theoretical, and methodological problematic is one of the main challenges to the scientificity of anthropological theories and concepts on culture. Moreover, these questions lie at the heart of research in intercultural communication. Authors and theorists in the complexity sciences have already stressed the need, in such case, to think in terms of models or semiotic representations, since these tools of thought can mediate much more effectively than unformalized language between the heterogeneous set of perceptions arising from the field of experience, on the one hand, and the philosophical principles that organize speculative thought, on the other. This sets the scene for a reflection on the need to master the theory of heuristic models when it comes to developing scientific knowledge in the field of intercultural communication. In this essay, my first aim is to make explicit the conditions likely to ensure the heuristic value of a model, while my second aim is to clarify the operational function and required level of abstraction of certain terms such as concepts, categories, headings, models, systems, or theories that are among the most commonly used by academics in their descriptive accounts or explanatory hypotheses. To achieve this second objective, I propose to create cognitive meta-categories to identify the three (nominal, cardinal or ordinal) roles of words in the reference grids we use to classify our ideas, and to specify how to use these meta-categories in the construction of our heuristic models. Alongside the theoretical presentation, examples of application are provided, almost all of which are drawn from my own research into the increased cultural vigilance of the majority population in Quebec since the reasonable accommodation crisis in this French-speaking province of Canada. The typology I propose will perhaps help to avoid the confusions regularly committed by authors who attribute only cosmetic functions to words that nevertheless have a highly heuristic value, and who forget to consider the logical leaps of their theoretical thinking in the construction of heuristic models.

Lipofuscin is indigestible garbage that accumulates in the autophagic vesicles and cytosol of post-mitotic cells with age. Drs. Brunk and Terman postulated that lipofuscin accumulation is the main or at least a major driving factor in aging. They even posited that the evolution of memory is the reason why we get lipofuscin at all, as stable synaptic connections must be maintained over time, meaning that the somas of neurons must also remain in the same locale. In other words, they cannot dilute out their garbage over time through cell division. Mechanistically, their position certainly makes sense given that rendering a large percentage of a post-mitotic cell’s lysosomes useless must almost certainly negatively affect that cell and the surrounding microenvironment. Here, I explore the possibility that the accumulation of lipofuscin may to some extent exacerbate every other kind of age-related damage. I do not think that lipofuscin removal will reverse/prevent all forms of aging, just the major component facing us currently. In this piece, I will review what is known about lipofuscin accumulation from evolutionary and mechanistic standpoints and discuss a method of removing it from single cells in vitro.

Reptilians or reptoids are staple characters of Hollywood cinema, science fiction literature, ufology and conspiracy theories. Despite its popularity, the reptoid has been dismissed by the scientific community as a figment of the imagination; born out of a speculation, paranoia and wanton anthropocentricism. In this paper, however, the Life Sequence Conjecture is advanced as a supportive framework for the notion of reptilian extraterrestrials. This paper is not an argument in support of the existence of extraterrestrials. Rather, it proposes that if extraterrestrials do exist, then a reptilian morphology is not untenable.

Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and energy, describe observational data more effectively, and formulate quantum gravity. In addition, despite the immense success of the quantum field theory, the framework requires renormalization techniques and breaks down at high energies. Recently, the Planck legacy 2018 release has confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level higher than 99%. This study considers the implied curvature of the early Universe as the curvature of “the background or 4D conformal bulk as a manifestation of vacuum energy” and distinguishes it from the localized curvature that is induced in the bulk by the presence of celestial objects that are regarded as ”4D relativistic cloud-worlds.” Analogously, because gravity appears to emerge owing to spacetime curvature and does not exhibit critical characteristics shared by other fields, it has been incorporated as the local curvature of the bulk affecting the embedded quantum fields that are regarded as propagating “4D relativistic quantum clouds.” To consider the effects of the bulk on embedded clouds, this paper presents interaction field equations in terms of brane-world modified gravity and the perspective of geometrization of the quantum mechanics wherein gravity is manifested by the curvature of 4D conformal bulk as an indicator of the field strength of vacuum energy on the embedded 4D relativistic clouds in addition to the boundary interactions, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic cloud-worlds over the conformal spacetime of the 4D bulk is presented, whereas the standard said theories can be recovered from the interaction field equations.

This review covers some of the central relationships between artificial intelligence, psychology, and economics through the lens of information theory, specifically focusing on formal models of decision-theory. In doing so we look at a particular approach that each field has adopted and how information theory has informed the development of the ideas of each field. A key theme is expected utility theory, its connection to information theory, and the Bayesian approach to decision-making and forms of (bounded) rationality. What emerges from this review is a broadly unified formal perspective derived from three very different starting points that reflect the unique principles of each field. Each of the three approaches reviewed can, in principle at least, be implemented in a computational model in such a way that, with sufficient computational power, they could be compared with human abilities in complex tasks. However, a central critique that can be applied to all three approaches was first put forward by Savage in {\it The Foundations of Statistics} and recently brought to the fore by the economist Binmore: Bayesian approaches to decision-making work in what Savage called `small worlds' but cannot work in `large worlds'. This point, in various different guises, is central to some of the current debates about the power of artificial intelligence and its relationship to human-like learning and decision-making. Recent work on artificial intelligence has gone some way to bridging this gap but significant questions still need to be answered in all three fields in order to make progress on these problems.

Graph theory plays significant role in every field of science as well as technology. Every situation can be articulated in terms of suitable graphs by using various approaches of graph theory. Considering the recent pandemic in the world and the precautions taken for prevention of the COVID 19, it is the most appropriate way to exercise the graph models with theoretical as well as practical aspects to control this epidemic. This paper defines the variable set, variable graphs and their types with respect to variable vertex sets and variable edge sets. Depending upon the nature of the pandemic, there are four types of Virus graphs. Virus graph I and III are not so perilous for all living beings. Although, Virus graphs II and IV are extremely hazardous for the harmony of the world. In view of different aspects for expand of pandemic, growth types of virus graphs are divided in 1-1, 1-P and 1-all growth types. The COVID19 initially was in Virus graph-I type, but presently it is in Virus graph-II types. We present the table involving the number of infected people after n days with respect to different values of P and growth rates with I0 = 100. Moreover, the country wise starting dates of stages of the virus graph-I and II are specified. The concept of cut sets is applicable for prevention of COVID19 and the whole world is using the same analogy.

In this short note, the described step-by-step derivations of the industrial energy demand function from the production function framework and provided researchers with two specifications. Then we applied these theoretical specifications to the time series data as empirical analysis. We concluded that theories should be considered at the beginning of the empirical analyses but the data also should be allowed to speak freely. Hence, the main suggestion of this short note is that it would be a better strategy to consider the combination of theory-driven and data-driven approaches in the empirical analyses.

Concept Knowledge (C-K) theory has been used in engineering and science-based research for more than a decade. Design of an Information Technology (IT) artefact is mostly pragmatic in nature. Design Science Research (DSR) methodology applied and studied in many Information Systems (IS) research. Many sub design decisions involved through the design of an IT artefact from a concept (idea) to a working prototype. A DSR artefact is based on a combination of decisions made during several sub-design stages. Artefacts are built based on the selection of elements in each sub-design space. Recording the design decisions on each sub-design space would be beneficial for future researchers. By knowing the design decisions on each sub-design space, researchers would be able to try different combinations of the design. C-K theory provides the ability to capture the design processes’ several sub-design spaces. In this paper, we discuss the DSR research methodology by looking at the stages proposed in the literature, and the application of C-K theory in an IT-based DSR. This paper also proposed a C-K theory-based protocol called Concept Tree for tracking and reporting artefact design steps. The application of C-K theory in DSR is exhibited using the implementation of the Concept Tree for a prototype design IT artefact.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances.

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized using the distinctions (`dits') of a partition (a pair of points distinguished by the partition). All the definitions of simple, joint, conditional, and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates (cohered together in the pure superposition state being measured) that are distinguished by the measurement (decohered in the post-measurement mixed state). Both the classical and quantum versions of logical entropy have simple interpretations as "two-draw" probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states.

The redshifted 21 cm line signal is a powerful probe of the cosmic dawn and the epoch of reionisation. The global spectrum can potentially be detected with a single antenna and spectrometer. However, this measurement requires an extremely accurate calibration of the instrument to facilitate the separation of the 21 cm signal from the much brighter foregrounds and possible variations in the instrument response. Understanding how the measurement errors propagate in a realistic instrument system and affect system calibration is the focus of this work. We simulate a 21 cm global spectrum observation based on the noise wave calibration scheme. We focus on how measurement errors in reflection coefficients affect the noise temperature, and how typical errors impact on the recovery of the 21 cm signal, especially in the frequency domain. Results show that for our example set up, a typical VNA measurement error in the magnitude of the reflection coefficients of the antenna, receiver, open cable which are 0.001, 0.001, 0.002 (linear) respectively would result in a 200 mK deviation on the detected signal, and a typical measurement error of 0.48∘, 0.78∘, 0.15∘ in the respective phases would cause a 40 mK deviation. The VNA measurement error can greatly affect the result of a 21 cm global spectrum experiment using this calibration technique, and such a feature could be mistaken for or be combined with the 21 cm signal.

We consider a real scalar field in de Sitter background and compute its thermal propagators. We propose that in a dS/CFT context, non-trivial thermal effects as seen by an `out' observer can be encoded in the anomalous dimensions of the d=3 Ising model. One of these anomalous dimensions, the critical exponent eta, fixes completely a number of cosmological observables, which we compute.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces in a unified manner. Thus, each force must furnish a system with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is the fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties of the vacuum, thus they must be present in all systems of units. The upgraded Planck system $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe.

The wave-particle description of quantum mechanics is briefly reviewed to set an analogy between the quantum mechanics of particles and fields and quantum cosmology. It is shown that quantum cosmology can be seen as a quantum field theory developed in the space of three metrics (the metrics of the spatial sections of the spacetime), where the classical evolution of the universe corresponds to a definite trajectory and the quantum mechanics of matter fields emerges as the first order quantum correction. Like in a quantum field theory developed in an isotropic background, the universes are created in universe-antiuniverse pairs, which might provide us with an explanation for the matter-antimatter asymmetry observed in our universe without going beyond the standard model. Moreover, the states of the matter and the antimatter fields of the pair of universes are entangled and that makes that their initial states are in a non-vacuum state (presumably in a thermal state). That might open the possibility of looking for observable imprints of the creation of universes in pairs is the astronomical data.

When dealing with galactic dynamics, or more specifically, with galactic rotation curves, one basic assumption is always taken: the frame of reference relative to which the rotational velocities are given is assumed to be inertial. In other words, fictitious forces are assumed to vanish relative to the observational frame of a given galaxy. It might be interesting, however, to explore the outcomes of dropping that assumption; that is, to search for signatures of non-inertial behavior in the observed data. In this work, we show that the very discrepancy in galaxy rotation curves could be attributed to non-inertial effects. We derive a model for spiral galaxies that takes into account the possible influence of fictitious forces and find that the additional terms in the new model, due to fictitious forces, closely resemble dark halo profiles. Following this result, we apply the new model to a wide sample of galaxies, spanning a large range of luminosities and radii. It turns out that the new model accurately reproduces the structures of the rotation curves and provides very good fittings to the data.

Huge filaments with scales from several hundred megaparsecs to gigaparsecs are detected in the distribution of galaxies and clusters, quasars, gamma-bursters. The hypothesis on the nature of the huge filaments as regions of space-time deformation is proposed. An anisotropic deformation of the local region is described by the strain tensor, it depends on the velocities of matter. Galaxies get an extra velocity in the region, which leads to the formation of filamentary structures. The class of exact solution of the GR equations is constructed by introducing the special definition of the Christoffel symbols as function of the velocity of matter. With a definition of these symbols, the motion matter equation turns into identity. For the sake of simplicity, an ideal fluid is considered.

We explore the possibility of using the external regions of galaxy clusters to measure their mass accretion rate (MAR). The main goal is to provide a method to observationally investigate the growth of structures on the nonlinear scales of galaxy clusters. We derive the MAR by using the mass profile beyond the splashback radius, evaluating the mass of a spherical shell and the time it takes to fall in. The infall velocity of the shell is extracted from N-body simulations. The average MAR returned by our prescription in the redshift range z=[0, 2] is within 20-40% of the average MAR derived from the merger trees of dark matter haloes in the reference N-body simulations. Our result suggests that the external regions of galaxy clusters can be used to measure the mean MAR of a sample of clusters.

The Casimir effect can either work over very short distances or at very low temperatures. At the cosmic scale, we naturally deal with long distances, but at the same time, we encounter extraordinarily low temperatures, namely the CMB (Cosmic Microwave Background) tem- perature. Recently, there has been increased interest in the Casimir effect and its implications in cosmology. Here, we briefly demonstrate that the luminosity and radiation pressure of the CMB is mathematical identical to a theoretical Casimir effect within the Hubble sphere, or actually our solution seems to be valid for any Schwarzschild black hole. The Casimir effect forevery Schwarzschild black hole is identical. This also include the Hubble sphere if we treat it as a Schwarzschild black hole that is related to increased interest in black hole cosmology.

It is desirable to upgrade previous evolutionary theories, which have remained incomplete and controversial for decades. Here we employ the concept of carbon-based entities (CBEs), which include methane, amino acids, proteins, organisms, and other entities containing relatively many carbon atoms. We deduce the driving force, mechanisms, steps, modes, tempos of CBE evolution, through integration of biology, physics, and chemistry using logics for complex issues. We hence establish the Carbon-Based Evolutionary Theory (CBET). The CBET suggests that evolution is the increase in hierarchy, diversity, fitness of CBEs under natural selection and driven by thermodynamics due to the chemical effect of the thermodynamic features of the Earth on CBEs. It provides better explanations for life origin, macroevolution events, natural selection, sympatric speciation, and evolution tempos than previous evolutionary theories. It reveals the evolutionary basis of multiple important social notions, including diversity, collaboration, altruism, obeying rules, and proper increase in freedom. It refutes some wrong notions in thermodynamics, including negative entropy (negentropy) and that biological order is equal to thermodynamic order, which have misled many people. The CBET is supported by its deduction and application. It could be a rare bridge linking laws of thermodynamics, evolution of life, and development of human society, and could have great significance in various sciences.

This paper describes an entropy equation that can be used for measuring energy. It originated from measuring economy in AI models, where the assumption would be that any organic system makes use of energy efficiency to form its structures. Looking at clustering and cohesion resulted in the equation E = (mean * variance). It was apparent however, that it was a very generic type of equation and it could be adjusted so that distance represents mean. This new version was applied to the domain of physics and the universe, when the equation can support the idea that work is done through the energy released by the 'change' in entropy. A comparison with Einstein's relativity equation is made and also the audacious suggestion that a black hole has only potential energy inside, which converts to kinetic energy after a Big Bang, for example. From that suggestion, a universal theory about state change can be made.

We demonstrate that multiple well-known metrics, such as the Schwarzschild metric and the extremal solution of the Reissner-Nordstr ̈om metric, can be expressed in what we will call thermodynamic form. These formulations appear to be valid for all Rs = ct growing black holes and, therefore, also within the framework of Rh = ct growing black hole cosmology. However, the metrics can also be applied to non-black hole gravitational objects as long as one calculates the CMB and Hawking temperature of the hypothetical black hole from the gravitational mass.

A regional organisation (RO) is a group of states that, through the formation of mutual relation-ships, work together for shared regional goals such as economic growth, social welfare, security, and democracy. The Association of South East Asian Nations (ASEAN) is one such organisation, of interest because of its operative paradoxes. However, current theory to study ROs is both fragmented across the field of study, and inadequate. Taking ROs to be complex adaptive systems, diagnosing ROs requires theory that can to explore their hidden aspects. The metacybernetics framework enables the creation of a critical realism configurative a-priori inquiry approach to theory building, the configurations providing coordinative schemas able to respond to predefined complex modelling needs. To analyse ROs using metacybernetics, we offer a derivative schema, Cultural Agency Theory (CAT). Currently this is limited to exploring modes of information acquisition processes through cognitive style, and until now has had no inherent mechanism to explore social relationships as is required to explore ROs. To enable CAT to explore such relationships, we configure the Tönnies social organisation paradigm for CAT. Mindset Agency Theory (MAT) is a specific elaboration of CAT, and creates an empirical setting for the set of formative traits that de-fine an RO character. A related derivative of CAT is that of Multiple Identity Theory (MIT) which enables organisational pathologies to be explored in terms of identity conflicts. Thes multifaceted paradigm provides a relatively simple approach to the RO diagnosis, in particular in terms of stability/coherence. This paper is in two parts. In this part 1, the CAT theory will be further developed through the joint configuration of Tönnies social organisation paradigm allowing its pathologies to be diagnosed. In part 2 of the paper, the theory will be applied to ASEAN and the diagnosis will show that it is an inherently incoherent organisation

This article examines the application of Keynesian theory in economic geography, focusing on regional development and reducing inequalities. The objective is to highlight the relevance and benefits of applying Keynesian principles in addressing spatial economic challenges. The novelty lies in examining the intersection of Keynesian economics and geography, which offers insights into regional planning, infrastructure development, and cluster formation. The results show how policymakers and researchers can use Keynesian theory to promote balanced growth and improve living standards. The keywords for this article are Keynesian theory, economic geography, regional development, disparities, and policy interventions.

In this work we study the following problem, from a computational point of view: If three points are selected in the unit square at random, what is the probability that the triangle obtained is obtuse, acute or right? We provide two convergent strategies: the frst derived from the ideas introduced in [2] and the second built on the combinatorics theory. The combined use of these two methods allows us to address the random triangle theory from a new perspective and, we hope, to work out a general method of dealing with some classes of computational problems.

We establish a Gröbner-Shirshov bases theory for trialgebras and show that every ideal of a free trialgebra has a unique reduced Gröbner-Shirshov basis. As applications, we give a method for the construction of normal forms of elements of an arbitrary trisemigroup, in particular, A.V. Zhuchok’s (2019) normal forms of the free commutative trisemigroups are rediscovered and some normal forms of the free abelian trisemigroups are first constructed. Moreover, the Gelfand-Kirillov dimension of finitely generated free commutative trialgebra and free abelian trialgebra are calculated respectively.

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a calamitic counterion-only system in proximity of a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic-isotropic wetting phase with a Donnan potential difference.

The scalar field of space-time film is considered as unified fundamental field. The field model under consideration is the space-time generalization of the model for a two-dimensional thin film. The force and metrical interactions between solitons are considered. These interactions correspond to the electromagnetic and gravitational interactions respectively. The metrical interaction and its correspondence to the gravitational one are considered in detail. The practical applications of this approach are discussed.

This paper introduces a theory for the evolution of corporates in which the growth and sustainability strategies are developed simultaneously. Since the introduction of corporate sustainability, it has been an extra cost for risk mitigation and making ‘compensating’ positive impact. The world has reached a tipping point of volatility, mainly due to climate change but also by emergence of COVID-19, so that the applicability of existing corporate structures is under question and these poses high risk to the existence of our planet. On the other hand, the technology cost for sustainable investment has reached a parity in comparison with non-sustainable alternatives. Therefore, our proposed Organic Grow Theory introduces a step-by-step approach so that corporates can grow and be profitable without compromising the ability of future generations to meet their needs. It is concluded that, a new structure for corporate, called Founcorp, would be needed to direct corporates to evolve being a responsible legal entity.

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

Sleep is still considered a mystery, despite intense scientific investigation. Here we present the first complete biological theory of sleep. The role of sleep is to restore the optimal homeostatic state, which is essential for tissue performance and health. Non-rapid eye movement sleep (NREMS) restores cortical and most other brain neurons, via relaxed global activity managed by thalamocortical circuits. The role of REM sleep is to restore acetylcholine (ACh) neurons, which support focused responses and hence cannot participate in global oscillations. Sleep enhances learning and memory via state restoration and ACh-affected paths. NREMS induces a lack of consciousness because global synchronous activity prevents focused responses, which are essential for consciousness. Dreams result from focused neural firing during sharp-wave ripples and REMS, and have a sense of reality because they involve the same neurons representing focused perceptual responses during wake. Anesthetics utilize a variety of mechanisms that prevent focused responses.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

The implementation of graphene-based electronics requires fabrication processes able to cover large device areas since exfoliation method is not compatible with industrial applications. Chemical vapor deposition of large-area graphene represents a suitable solution having the important drawback of producing polycrystalline graphene with formation of grain boundaries, which are responsible for limitation of the device performance. With these motivations, we formulate a theoretical model of graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the particle transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach and represents per se an important enrichment of the scattering theory of graphene. Moreover, the outcomes of the theory can contribute in understanding and limiting detrimental effects of graphene grain boundaries also providing a benchmark for more elaborated techniques.

Several specific types of ordinary and generalized separation axioms of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized separation axioms of a generalized topological space is reported herein as a starting point for more generalized classes.