It has been theorized that black holes are surrounded by firewalls, although there is not universal agreement concerning this. We first review basic concepts pertaining to Schwarzschild black holes and Hawking radiation. Then we discuss the anticipation of Hawking radiation—albeit from non-black holes—initially by R. C. Tolman and shortly thereafter with P. Ehrenfest. We compare evaporation into a vacuum at absolute zero (0 K) of black holes with that of non-black holes, and show that not only black holes but also non-black holes evaporate within a finite time. The times required for evaporation of black holes and non-black holes are compared. Next, we show that (i) if firewalls exist, they can originate via Hawking radiation at the minimum possible ruler distance (the Planck length) beyond the Schwarzschild horizon, where it has not suffered any gravitational redshift, or, alternatively, suffered maximal gravitational blueshift and (ii) the firewall temperature is on the order of the Planck temperature, independently of the mass and hence also of the Schwarzschild radius of a Schwarzschild black hole. We then explain the exponential nature of the gravitational frequency shift as a function of the gravitational potential. Next, we consider the firewall-mass problem, and provide an at least prima facie tentative resolution thereto based on: (i) the mass of a firewall being canceled by the negative gravitational mass = (negative gravitational energy)/c² accompanying its formation, (ii) the unchanged observations of a distant observer upon formation of a firewall, and (iii) Birkhoff's Theorem (actually first discovered by Jørg Tofte Jebsen). We then consider one aspect of thermodynamics in gravitational fields, showing that equilibrium relativistic gravitational temperature gradients cannot be exploited to violate the Second Law of Thermodynamics.

The structure and phenomena arising from charge transfer in cold field emission modus in a single closed carbon nanotube under cold field emission conditions were studied. By studying microphotographs in various microscopes - AFM, SEM, TEM it was found inhomogeneities in the form of two types of superlattices. The conductivity of the emitter section of a nanodiode circuit with an emitter made of an individual closed carbon nanotube (CNT) and arrays of closed CNTs was studied. High values of cold field emission were observed, as well as nonlinearity and anomalies of the current-voltage characteristic (I-V characteristics), which manifested themselves in the form of peaks at low and high current values. Peaks in the CVC have distinct areas of negative differential conductivity. It is argued, that the anomalously high currents in the I–V characteristics of cold field emission of electrons from a nanoemitter made of closed CNTs can be associated with a sharp increase in the density of electron states at energies near the van Hove singularity.

Because imbalanced power will cause the loss of the propulsion motor of the railway vehicle, and the increase in temperature will shorten the service life of the electric vehicle. Not only this, but also increase the cost of electricity and maintenance. In the past, the industry only focused on methods to improve power quality such as load capacity, relay setting, and harmonic resolution. Now, the consider of three-phase unbalance rate (TPUR) must be applied. I propose special transformers wiring (STW) to improve the three unbalance rates and provide different transformer wiring methods. According to the IEEE Committee, in the future, power companies will need to install balanced relay stations to improve three-phase unbalance rate. the internal regulations of Taipower must be less than 4.5% (voltage unbalance rate (NPSUR)of 2.5% and motor temperature rise of 12.5%). the derivation of the transformer "three-phase unbalance rate" model is the focus of the railway system. This research is based on the model derivation of different wiring methods to improve the hot problem caused by the three-phase imbalance and improve the service life of the train. And pointed out that Scott, Le-Blanc, Modified-Woodbridge three wiring methods can be applied to future railway system routes to improve the three-phase unbalance rate, in line with the IEEE standard of less than 2%.

ABSTRACT. The immunotherapies, as a modern therapeutic approach, get an attention because of theirs’ promise to treat a large number of different medical disorders. Immunomodulation effects of low titres (10 HA/ml) of NDV (Newcastle Disease Virus) ZG1999HDS or La Sota were tested on TLT (Human macrophage cell line) bound to PBMC (Peripheral Blood Mononuclear Cells). During the immunomodulation, the amount of NO, H2O2, lysozym and induced antibacterial activity against Gram - positive bacteria (Staphylococcus aureus, MRSA, Streptococcus pyogenes, Streptococcus agalactiae and Streptococcus mutants) and against Gram - negative bacteria (Escherichia coli, Pseudomonas aeruginosa, Proteus mirabilis and Acinetobacter baumanii) were analysed. In addition, the cytokine secretion, IL-1α, IL-2, IL-4, GM-CSF, TNF-α, IFN-α and IFN-α were evaluated. Firstly, the TLT cells are activated through the NDV ZG1999HDS or La Sota binding, followed by the NO “burst” and H2O2 and lysozyme level increase. Secondly, after the binding to the TLT cells and interaction with the PBMCs, the decrease of GM-CSF, and an increase of TNF – α and IFN – γ were found. Simultaneously, the decrease of pro – inflammatory cytokine IFN-α and the differentially increase of IL-1α, IL-2 and IL-4 were recorded. During the induction of the antibacterial response, against Gram - positive bacteria (Staphylococcus aureus, MRSA, Streptococcus pyogenes, Streptococcus agalactiae and Streptococcus mutants) the effect was one third higher with NDV ZG1999HDS compared to La Sota. Antibacterial response against Gram - negative bacteria (Escherichia coli, Pseudomonas aeruginosa, Proteus mirabilis and Acinetobacter baumanii) was not so clear. In general, NDV ZG1999HDS or La Sota activated TLT cells, further bound to PBMC; the ZG1999HDS is stronger immunomodulator than La Sota.

Chen, et al., compared two modified polyurethane-based wound dressings (PUE and PUESi), both intended for use in chronic wounds, with a negative control (gauze) and a positive control (PolyMem) via a series of preliminary in vitro and rodent model tests. Future studies may find that one or both of these two new dressings are beneficial. However, the results of this first study cannot be relied upon. Although they exhibited in-depth knowledge of manufacturing techniques, the study designers seem far less familiar with the science of wound healing and with PolyMem wound dressings. This helps explain the flaws in the methods that lead to many of their tests not being translatable to real-world settings. In addition, the interpretation of some of the test results is questionable.

We tested the possibility of using “adverse events count” (AEC) as a drug-risk indicator and side-effect severity indicator. Data from 3938 adverse event (AE) reports for COVID-19 vaccines (Comirnaty, Moderna, Vaxzevria, and Janssen) and 6869 AE reports for other medicines were collected from the Bulgarian Drug Agency database (01.01.2018–31.03.2022). AEC was modeled with zero-adjusted negative binomial (ZANBI) and zero-adjusted Poisson inverse Gaussian (ZAPIG) regression models, which account for zero absence and overdispersion. The models’ fit was checked with residual diagnostic plots and parametric correspondence to normality. Explanatory variables were: age, sex, sequence number (order of submission), severity of AE, and vaccine type. Average AEC was higher in severe vs. non-severe AE, and in females vs. males; it decreased with age and was lower in Comirnaty than other vaccines. Variability of AEC for COVID-19 data decreased with sequence number in severe AE and increased in non-severe AE. Full ZANBI models had greater sensitivity than parametric ZANBI or ZAPIG models. Results showed correlation between AEC and AE severity, suggesting AEC as a simple and reliable measure of drug-risk and side-effect severity for clinicians and regulators, especially for COVID-19 vaccines.

AI is extraordinarily useful technology but it is becoming increasingly powerful with rapidly growing capabilities to disrupt and harm human society. We call on international and national organizations and individuals to join forces in banning the development of superintelligent AI and introducing regulations to prevent and mitigate AI-caused harm.

Immune checkpoint receptors play a crucial role in steering tumor progression, prompting a focused investigation into the role of TIM3 in breast cancer. Analysis of TCGA BRCA data unveiled diverse correlations between TIM-3 expression and immune cell infiltration across subtypes. In our in-house cohort studied through IHC, significant changes in TIM3 expression with tumor grades were observed. Higher TIM3 expression correlated with increased disease-free survival in pan breast cancer, marking the first revelation of TIM3's positive role in pan BC prognosis. The study indicates that alluring TIM3 response, rather than suppression, may enhance breast cancer prognosis.

In general, a superconductor has zero resistance, although it requires significant refrigeration or high pressures with high manufacturing costs, which prevents it into practical applications. In other words, solving these issues implies main superconducting researches. To solve these problems, this paper describes a new type of superconductivity, which is independent for temperatures and which operates without pressures. The principles of the presented system are as follows:First a voltage source, a current source and a load are connected in series. Then, the voltage of the voltage source is adjusted to balance the voltage of the load. Under this condition, the balance of the two voltages provides a zero voltage between the taps of the current source and the generated current from the voltage source becomes zero because of the internal infinite resistance of the current source. As a result, the electric powers generated by the two sources are zero, and therefore, the load cannot generate Joule heating because of energy conservation. However, the current from the current source (not the voltage source) is not zero; therefore, we can predict that the resistance of the load must be zero. As a theory, we derived a new electric field and transient attractive force, which result in a very short coherence of an electron pair because there is not the Coulomb repulsive force due to the existence of the above transient attractive force. Note that both the forces are derived by the Poisson equation, which implies that they cannot be compatible. Therefore, the pair combination energy from spins becomes extremely strong, which is not destroyed by the normal heat energy. Moreover, every center-of-mass motion of electron pair results in the Bose-Einstein condensation and the macroscopic wave function, which produces the London equation (i.e., the Meissner effect). Moreover, by introducing the equivalent circuit, this paper conducted numerical calculations. As a result, we could derive numerically zero resistance and responses for additional static magnetic fields as a discharged current, which implies the Meissner effect. Note that this paper has prepared Appendix section, which provides a guide to reproduce actual experiments and preliminary experimental results. These results in the Appendix indicate the zero resistances and Meissner effects.

Abstract: Discussed is an expansion of SRT to fourth-order of space-time including any velocities and possible negative kinetic energies by real rest mass in analogy of the model amplitude of enforced damped oscillation. This paper serves an introduction to developed SRT including superluminar translating velocities without tachyons or imaginary restmass. Focused is on those parts, which develop the elaborated lorentz-transformations. Discussed are the problems of this theory.

There are unsolved problems related to inflation, gravity, dark matter, dark energy, missing antimatter, and the birth of the universe. Some of them can be better answered by assuming the existence of aether and hypoatoms. Both were created during the inflation in the very early universe. While aether forms vacuum, hypoatoms, composed of both matter and antimatter and believed to be neutrinos, form all observable matter. In vacuum, aether exists between the particle-antiparticle dark matter form and the dark energy form in a dynamic equilibrium: A + A-bar = gamma + gamma. The same reaction stabilizes hypoatoms and generates a 3-dimensional sink flow of aether that causes gravity. Based on the hypoatom structure, the singularity does not exist inside a black hole; the core of the black hole is a hypoatom star or neutrino star. By gaining enough mass, ca. 3 X 10²² M_sun, to exceed neutrino degeneracy pressure, the black hole collapses or annihilates into the singularity, thus turning itself into a white hole or a Big Bang. The universe is anisotropic. Its center, or where the Big Bang happened, is at 0.66^+0.03_-0.01 times the radius of the observable universe at Galactic coordinates (l, b) = (286⁺¹⁰_-10, -43⁺⁷_-6). If we look from the Local Group to the center of the universe, the universe is rotating clockwise.

Background: Cervical cancer prevention in regions with limited access to screening and HPV vaccination necessitates innovative approaches. This study explored the potential of a test-and-treat strategy using mRNA HPV tests to impact cervical cancer prevention in a high-prevalence HIV population. Methods: A cervical screening study was conducted at three South African hospitals involving 710 under-screened, non-pregnant women (25 to 65 years) without known cervical diseases. Cytology, HPV testing, colposcopy, and biopsies were performed concurrently. Histopathologists determined final histological diagnoses based on biopsy and LLETZ histology. mRNA-HPV-genotyping for 3 (16, 18, 45) to 8 (16, 18, 31, 33, 35, 45, 52, 58) high-risk types was performed on leftover liquid-based cytology material. The preventive potential of the test-and-treat approach was estimated based on published data, reporting the causative HPV types in cervical cancer tissue from South African women. Treatment was provided as needed. Results: HPV positivity rate more than doubled from 3-type (15.2%; 95% CI: 12.6-17.8) to 8-type mRNA (31.5%; 95% CI: 28.8-34.9) combinations, significantly higher among HIV-positive women. CIN3+ prevalence among HIV-positive women (26.4%) was double that of HIV-negative women (12.9%) (p<0.01). The 6-type combination showed the best balance of sensitivity, specificity and treatment group size, and effectiveness to prevent cervical cancer. A 4-type combination (16, 18, 35, 45) could potentially prevent 77.6% (95% CI: 71.2-84.0) of cervical cancer burden by treating 20% and detecting 41.1% of CIN3 cases in the study group. Similarly, a 6-type combination (16, 18, 31, 33, 35, 45), treating 25% and including 62% of CIN3 cases, might prevent 85% of cervical cancer cases (95% CI: 79.6-90.6) among HIV-positive and negative women. Conclusion: Employing mRNA HPV tests within a test-and-treat approach holds huge promise for targeted cervical cancer prevention in under-screened populations. Testing for mRNA of the 6 highest-risk HPV types in this population and treating them all is projected to effectively prevent progression from CIN3 to invasive cervical cancer while reducing overtreatment in resource-constrained settings.

Forest recreation can be successfully conducted for the purpose of psychological relaxation, as has been proven in previous scientific studies. During the winter in many countries, when snow cover occurs frequently, forest recreation (walking, relaxation, photography, etc.) is common. Nevertheless, whether forest therapy conducted in a forest environment with a snow cover will also have a positive effect on psychological indicators remains unknown. Furthermore, male subjects frequently participate in forest therapy experiments, whereas females are rarely involved. Thus, in this study, the effectuality of forest recreation during winter and with snow cover was tested on 32 young females. For these reasons, the experiment involved 15-minute periods of relaxation in a forest environment or in an urban environment, in addition to a pre-test under indoor conditions. Four psychological questionnaires (POMS, PANAS, ROS, SVS) were administered to participants before and after interventions. Results showed that participants’ levels of negative mood, as measured by different aspects of the POMS questionnaire (tension-anxiety, anger-hostility, depression-dejection, confusion, fatigue), decreased after exposure to the forest environment. In contrast, both tension-anxiety and anger-hostility increased in the urban environment. The indicator of negative affect from the PANAS questionnaire also increased after exposure to the urban environment, whereas the indicator of positive affect based on PANAS was higher in the forest environment than in the urban environment. Restorativeness and subjective vitality exhibited higher values after exposure to the forest environment in comparison to those from the control and pre-test. The changes in these indicators demonstrates that forest recreation in the snow during winter can significantly increase psychological relaxation in young females, as well as showing that recreation can be successfully conducted under these winter conditions.

This research paper explores the framework of Extended Classical Mechanics, with a focus on the Equivalence Principle, Mass, and Gravitational Dynamics. Volume 1 of this study re-examines the classical equivalence principle, which maintains the equivalence of inertial mass and gravitational mass (also referred to as gravitating mass) and extends this concept to incorporate new findings related to both illuminating (baryonic) matter and dark matter. The paper provides a comprehensive analysis of Matter Mass (Mᴍ) and Gravitating Mass (Mɢ) and their roles within the extended framework. It introduces the concept of Apparent Mass (Mᵃᵖᵖ), a negative mass component that influences Effective Mass (Mᵉᶠᶠ), in alignment with the research by A.D. Chernin et al. on dark energy and the structure of the Coma Cluster of Galaxies. Additionally, the paper reinterprets Newton's Law of Universal Gravitation by integrating Apparent Mass, leading to a revised understanding of gravitational potential. The study demonstrates how the interaction between Matter Mass and Negative Apparent Mass contributes to a redefined concept of Gravitating Mass. These extensions enhance classical mechanics by incorporating modern scientific insights, including the gravitational effects of dark matter and the alignment of Apparent Mass with the negative effective mass of dark energy.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

Hidradenitis suppurativa and Langerhans cell histiocytosis are rare disorders that can reveal similar clinical manifestations, making differential diagnosis difficult. A definitive diagnosis requires biopsy and histological confirmation in suspicious cases. The complex pathophysiology of these diseases has still not been understood, therefore the treatment is still a challenge for physicians. It is seen with predilection in the intertriginous areas of the body, predominantly in the axillary region, rarely requiring a surgical procedure. However perineal, perianal, and gluteal HS usually necessitates some form of surgical treatment. Langerhans cell histiocytosis (histiocytosis X) is a very rare systemic disease manifested by clonal cell proliferation of histiocytic-dendritic nature, with pseudonodular manifestation that deeply infiltrates the hypodermis and ulcerates the epidermis on the surface. Langerhans cells are dendritic, antigen-presenting cells localized in the suprabasal regions of the squamous epithelium of the skin and mucous membranes, which help regulate the immune system. In this report, we present our experience with extensive gluteal, perineal, and perianal hidradenitis suppurativa and Langerhans cell histiocytosis cases, including our treatment methods and outcomes.

Background: Nodal peripheral T-cell lymphomas (nPTCLs) encompass a heterogeneous group of mature and aggressive lymphoid malignancies, including peripheral T-cell lymphoma, not otherwise specified (PTCL/NOS), angioimmunoblastic T-cell lymphoma (AITL) and anaplastic large cell lymphoma (ALCL) ALK-positive and ALK-negative. Their differential diagnosis and prognosis are an issue in the clinical practice. Accurate biomarkers to refine the different subtypes of nPTCLs and to stratify their prognosis are essential to improve their treatment approach. The aim of this study was to test the prognostic impact of GATA3 gene expression, and its capability to discriminate the different subtypes of nPTCLs. Patients and Methods: From 2000 to 2017, 80 patients with nPTCLs were eligible for GATA3 gene expression analysis that was assessed retrospectively by quantitative real time PCR (qRT-PCR) of neoplastic biopsies in Formalin-Fixed Paraffin-Embedded samples (FFPE). Results: Median age was 49 years old (IqR 34-59), 43/80 (53.7%) were male. Median follow-up was 1.72 years. Of them, 36.3% were classified as PTCL/NOS, 31.2% ALK-negative ALCL, 21.2% ALK-positive ALCL and 11.3% AITL. The majority of cases had advanced stage (III/IV). Two-year estimated overall survival (OS) and progression-free survival (PFS) were 52.2% and 39.5%, respectively. The median GATA3 gene expression level was 0.49% (range 0 – 7.07) in all cohort, it was 0.11% for ALK-positive ALCL, 0.46% for ALK-negative ALCL, 0.86% for PTCL/NOS and 0.67% for AITL. The difference of GATA3 gene expression among distinct variants of nPTCLs was statistically significant (p < 0.001). GATA3 gene expression levels ≥ 0.71% discriminate PTCL/NOS from ALK-negative ALCL and AITL with sensitivity of 62% and specificity of 80.3%. GATA3 gene expression levels ≥ median was associated with poor 2-year OS for PTCL/NOS (46.7% x 21.4%, p=0.04) and for ALK-negative ALCL (85.7% x 54.5%, p=0.04). Conclusion: Despite the relative small and heterogeneous group of patients with nPTCLs, GATA3 gene overexpression may be an important biomarker associated with poor prognosis in PTCL/NOS and ALK-negative ALCL. Moreover it may also discriminate different subtypes of nPTCLs. Further studies with larger series of patients should confirm our findings.

Abstract: A prevalence boundary (PB) marks the point in prevalence where the false omission rate, RFO=FN/(TN+FN), exceeds the tolerance limit for missed diagnoses. Objectives were to mathematically analyze rapid antigen test (RAgT) performance, determine why PBs are breeched, and evaluate the merits of testing three times over five days, now required by the US Food and Drug Administration for asymptomatic persons. Equations were derived to compare test performance patterns, calculate PBs, and perform recursive computations. An independent July 2023 FDA-university-commercial evaluation of RAgTs provided performance data used in theoretical calculations. Tiered sensitivity/specificity comprise: Tier-1) 90%, 95%; Tier-2) 95%, 97.5%; and Tier-3) 100%, ≥99%, respectively. Repeating a T2 test improves the PB from 44.6% to 95.2% (RFO 5%). In the FDA-university-commercial evaluation, RAgTs generated sensitivity of 34.4%, which improved to 55.3% when repeated, then 68.5% with the third test. With RFO=5%, PBs were 7.37/10.46/14.22%, respectively. PB analysis suggests RAgTs should achieve clinically proven sensitivity of 91.0-91.4%. When prevalence exceeds PBs, missed diagnoses can perpetuate virus transmission. Repeating low-sensitivity RAgTs delays diagnosis. In homes, high-risk settings, and hotspots, PB breaches may prolong contagion, defeat mitigation, facilitate new variants, and transform outbreaks into endemic disease. Molecular diagnostics can help avoid these potential vicious cycles

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, charge-less, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, , are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two variable models, where, , is Newton’s constant, and, , increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/ zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.