We develop new theory from a broad case-study approach to explore a better understanding of what constitutes knowledge and its value as identifiable to human-machine teams. From past research, this trail of exploration will lead to these initial questions: What is the value of debate in the furtherance of knowledge? Will machines with AI be able to contribute to a debate if we humans cannot define it or determine its value sufficiently for a machine’s understanding, contribution, exploration and identification? Like humans, as teammates, machines must be able to determine with AI what constitutes the usable knowledge that contributes to a team’s success in the field (e.g., testing "knowledge" in the field, identifying new knowledge, using knowledge to develop innovation) or its failure (viz., trouble shooting; identifying weaknesses; discovering vulnerabilities, hiding by deception). It matters not whether a debate is public, private or unexpressed by an individual human or machine agent alone; we speculate in this exploration that the process advances the science of autonomous human-machine teams and assists in interpretable machine learning. We conclude with questions and a speculation: How does a human become aware or express its awareness of knowledge? Can a machine be as expressive as its human teammates? And how does a human-machine teammate become aware that its teammates possess sufficient knowledge to perform a task? We speculate that the structure of “knowledge," once found, is resistant to alternatives (i.e., it is ordered); that its functional utility is generalizable; and that its applications are multifaceted (akin to maximum entropy production). The complexity of the team is taken into consideration in our search for knowledge, which can also be used as an information metric.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

Prestressed concrete sleepers (or railroad ties) are principally designed in order to carry wheel loads from the rails to the ground of railway tracks. Their design takes into account static and dynamic loading conditions. In spite of the most common use of the prestressed concrete crossties in railway tracks, there have always been many demands from rail engineers to improve serviceability and functionality of concrete crossties. For example, signaling, fiber optic, equipment cables are often damaged either by ballast corners or by tamping machine. There has been a need to re-design concrete crosstie to cater cables internally so that they would not experience detrimental or harsh environments. Also, many concrete crossties need a retrofit for automatic train control device and similar signaling equipment. In contrast, the effects of holes and web openings on structural capacity of concrete crossties have not been thoroughly investigated. This paper accordingly highlights the effect of holes and web openings on the toughness and ductility of concrete crossties. The outcome of this research enables better decision making process for retrofiting prestressed concrete crossties with holes and web opening in practice.

The origins of the stellar mass neutron black holes and supermassive dark matter black holes without the singularities are reported based on the 4-D Euclidean space. The neutron black holes with the mass of m_BH = 5 – 15 m_sun are made by the 6-quark merged states (N_6q) of two neutrons with the mass (m(N_6q) = 10 m(n)) of 9.4 GeV/c² that gives the black hole mass gap of m_BH = 3 – 5 m_sun. Also, the supermassive black holes with the mass of m_SMBH = 10⁶ – 10¹¹ msun are made by the merged 3-D states (J(B1B2B3)₃ particles) of the dark matters. The supermassive black hole at the center of the Milky way galaxy has the mass of mSMBH = 4.1 10⁶ m_sun that is consistent with m_SMBH = 2.08 - 6.23 10⁶ m_sun calculated from the 3-D states (J(B1B2B3)₃ particles) of the dark matters with the mass of m(J) = 1.95 10¹⁵ eV/c². In other words, this supports the existence of the B1, B2 and B3 dark matters with the proposed masses. The first dark matter black hole (primary black hole) was created at the big bang. This first dark matter black hole decayed to the supermassive dark matter black holes through the secondary dark matter black holes that are explained by the merged states of the J(B1B2B3)₃ particles. The universe evolution is closely connected to the decaying process of the dark matter black holes since the big bang. The dark matter cloud states are proposed at the intermediate mass black hole range of m_IMBH = 10² – 10⁵ msun. This can explain why the dark matter black holes are not observed at the intermediate mass black hole range of m_IMBH = 10² – 10⁵ m_sun.

In this paper, we consider the formation of quantum black holes (QBHs) through a genuine quantum process. We treat particles at the Planck energy as QBHs. The Hawking temperature and entropy of QBHs are estimated. We also show that a QBH has a discrete energy spectrum. By analogy with supersymmetric theory, the mass of the superpartner of a QBH is estimated.

In classical General Relativity, White Holes (WH) refer to the time reverse Schwarzschild (SW) Black Hole (BH) solution of a point mass $M$ and gravitational radius $r_S=2GM$. The SW metric is static so that a time reverse WH solution simply corresponds to a violation of causality. The WH solution does not make any physical sense here. For a more physical model, such as the Lemaitre-Tolman-Bondi (LTB) metric with finite mass inside $r_S$, we show that both the expanding and collapsing solutions correspond to a BH and not to a WH.

The model of an oscillating universe proposed by A. Friedmann in 1922 dominated cosmology for a long time. R. Tolman put forward a thermodynamic argument against the cyclic cosmological model, believing that entropy should accumulate from cycle to cycle. J. Bekenstein and S. Hawking discovered a tremendous amount of entropy associated with black holes. This discovery led to the conclusion that the majority of the Universe's entropy is contained in black holes. N. Poplawski considers a Universe that oscillates within a black hole. This paper analyzes the relationship between the entropy of black holes and the oscillating Universe inside a large black hole. It is demonstrated that the entropy of a black hole can only be defined for an external observer. For an observer inside the black hole, its entropy is zero. This opens up the possibility of constructing a cyclic cosmology in which entropy and the size of the visible part of the Universe change strictly periodically. This does not violate the second law of thermodynamics because the continuous accumulation of entropy from cycle to cycle pertains to the surface of the big black hole, which is invisible to the internal observer.

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein-Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole's tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration's thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system's stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

This article develops duality principles and related convex dual formulations suitable for the local optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation.

This article develops a duality principle and a related convex dual formulation suitable for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a model in non-linear elasticity.

The study shows that the volumes and surfaces of $n$-balls, $n$-simplices, and $n$-orthoplices are holomorphic functions of $n$, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about $n$-balls reveal previously unknown properties of these geometric objects. In particular, for $0 < n < 1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing $n$-balls, and both their volumes and surfaces are smaller than those of inscribed $n$-balls. The surface of an $n$-simplex circumscribing unit diameter $n$-ball is spirally convergent to zero with real $n$ approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an $n$-orthoplex circumscribing unit diameter $n$-ball is spirally divergent with real $n$ approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, as its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about $n$-balls are proposed. symmetries of products and quotients of volumes in complex dimensions $n$ and $-n$ and of surfaces in complex dimensions $n$ and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between volumes and surfaces in dimensions $n = -1/2$ and $n = 1/2$.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

Black hole collision produce gravitational radiation which is generally thought in a quantum limit to be gravitons. The stretched horizon of a black hole contains quantum information, or a form of quantum hair, which in a coalescence of black holes participates in the generation of gravitons. This may be facilitated with a Bohr-like approach to black hole (BH) quantum physics with quasi-normal mode (QNM) approach to BH quantum mechanics. Quantum gravity and quantum hair on event horizons is excited to higher energy in BH coalescence. The near horizon condition for two BHs right before collision is a deformed AdS spacetime. These excited states of BH quantum hair then relax with the production of gravitons. This is then argued to define RT entropy given by quantum hair on the horizons. These qubits of information from a BH coalescence should then appear in gravitational wave (GW) data. This is a form of the standard AdS/CF T correspondence and the Ryu-Takayanagi (RT) formula [1]. The foundations of physics is proposed to be quantum information and a duality between spacetime observables and quantum fields.

Due to limitation of the binding energy of a self-gravitating matter, the radius of a body is at least twice larger than the Schwarzschild radius. The total energy is adsorbed at the body surface, giving rise of a size-dependent surface tension. Since the Hawking temperature appears to be the critical one, the black holes possess zero surface tension. Microscopic neutrino stars are also introduced.

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

This paper presents one of the approaches to solution of the problem of the repulsion origin in gravity. The approach is based on the property of compactness characteristic for a self-gravitating object in General Relativity. Here we understand compactness as estimation of the upper boundary for mass such an object in a static two--dimensional sphere. Repulsion originates when this boundary is violated. The main hypothesis is formulated in the form of the principle of maximal mass within a two-dimensional static sphere. It is demonstrated that the principle is true for Schwarzschild black holes on absorption of the matter in the process of accretion, both in the classical case and with due regard for quantum-gravitational corrections. The results have been extended to black holes with the Schwarzschild-de Sitter metric in the early Universe. The applicability of the principle suggested is analyzed for the early and for the present Universe.

The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It adresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.

We show how it is possible to define and study black holes of arbitrary shapes in the framework of Newtonian mechanics.

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

In this paper, we discuss the weak gravitational lensing in the context of stringy black holes. Initially, we examine the deflection angle of photon by charged stringy black hole. For this desire, we compute the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically balanced spacetime of stringy black hole. We also analyze the influence of plasma medium in the weak gravitational lensing for stringy black hole. Moreover, the graphical impact of coupling constant $\alpha$, impact parameter $b$ , black hole charge $Q$ on deflection angle by charged stringy black hole has been studied in plasma as well as non-plasma medium.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

Many manufacturing sectors require high surface finishing. After machining operations such as milling or drilling, undesirable burrs or insufficient edge finishing may be generated. For decades, many finishing processes have been handmade-basis; this fact is accentuated when dealing with complex geometries especially for high value-added parts. In recent years, it’s a tendency of trying to automate as far as possible this kind of processes, repeatability and time/money savings are main purposes. Based on that idea, the aim of this work is to check new tools and strategies for finishing aeronautical parts, especially critical engine parts made on Inconel 718, a very ductile nickel alloy. Automating edge finishing of chamfered holes is a complicated but really important goal. In this paper, flexible abrasive tools were used for this purpose. A complete study of different abrasive possibilities was carried out, mainly focusing on roughness analysis and final edge results obtained.

In this paper, we investigate the question of whether the generally accepted interpretation of the supermassive object in M87, investigated by EHT collaboration, is the only possible one. There are grounds for this, in particular, due to the detection of a magnetic field in its vicinity. For this purpose, the stability of self-gravitating objects is investigated based on the correct definition of the energy of gravitation in the framework of the bi-metric approach to the theory.

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.

Assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: a) the first Electroweak (EW) vacuum at $v_1\approx 246$ GeV—“true vacuum”, and b) the second Planck scale “false vacuum” at $v_2 \sim 10^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of the paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f(R)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog”—global monopole, that has been “swallowed” by the black-hole with mass core $M_{BH}\sim 10^{18}$ GeV and radius $\delta\sim 10^{-21}$ GeV$^{-1}$. Considering the results of the hedgehog lattice theory in the framework of the $SU(2)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs’ confinement phase ($T_c\sim 10^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU(2)$-triplet Higgs bosons) at the scale $\sim 10$ TeV. This theory predicts the stability of the EW-vacuum and the accuracy of the MPP.

Recently massless test scalar field perturbations of the holonomy corrected black holes [Z. Moreira et. al. Phys. Rev. D 107 (2023) 10, 104016] were studied in order to estimate quantum corrections to the quasinormal spectrum of a black hole. Here we study both the fundamental mode and overtones of scalar, electromagnetic and Dirac fields with the help of the Leaver method and higher order WKB formula with Pad\'e approximants. We observe that the overtones depend on the geometry near the event horizon, while the fundamental mode is localized near the peak of the potential barrier, what agrees with previous studies. We showed that unlike a massless field, the massive one possesses arbitrarily long lived modes. We also obtain the analytical eikonal formula for quasinormal modes and its extension beyond eikonal approximation as a series in powers of $1/\ell$, where $\ell$ is the multipole number.

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

In this work, we present some results related with the issue of the Loop Quantum Black Holes (LQBH) thermodynamics by the use of the tunneling radiation formalism. The information loss paradox is also discussed in this context, where we have considered the influence of back reaction effects.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

We propose a spectral filter based on Plastic Optical Fiber with micro-holes as a low-cost, robust, and highly reproducible spectral filter. The spectral filter is explored for two configurations: fiber extended in a straight line, and a fiber optic loop mirror scheme configuration. The transmission traces indicate a spectral blue shift of peak transmission, at 587 nm, 567 nm, 556 nm, and 536 nm for 0, 1, 2, and 3 holes in the fiber, respectively. The filter exhibits a bandpass period of approximately 120 nm. Additionally, we conducted a comparison of the transmission with holes separated by distances of 1 cm and 500 μm. The results demonstrate that the distance between holes does not alter the spectral transmission of the filter. In the case of the fiber loop mirror configuration, we observed that the bandpass can be adjusted, suggesting the presence of multimode interference. Exploring variations in the refractive index within the holes by filling them with glucose solutions at various concentrations, we determined that the filtering band and spectral shape remains unaltered, ensuring a stable and robust operation of our spectral filter.

Is it possible to quantify in General Relativity, GR, the entropy generated by supermassive black holes, BHs, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere?The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of BHs of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO), and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law (GSL) that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH.This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula.The entropy of the evaporation time of BHs proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the black hole.

The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.

Scoring targets in shooting sports is a crucial and time-consuming task that relies on manually counting bullet holes. This paper introduced an automatic score detection model using object detection techniques. The performance of seven models belonging to two different architectural setups was compared. Models like YOLOv8n, YOLOv8s, YOLOv8m, RetinaNet-50, and RetinaNet-101 are single-shot detectors, while Faster RCNN-50 and Faster RCNN-101 belong to the two-shot detectors category. The dataset was manually captured from the shooting range and expanded by generating more versatile data using Python code. Before the dataset was trained to develop models, it was resized (640x640) and augmented using Roboflow API. The trained models were then assessed on the test dataset, and their performance was compared using matrices like mAP50, mAP50-90, precision, and recall. The results showed that YOLOv8 models can detect multiple objects with good confidence scores. Among all, YOLOv8m performed the best with the highest mAP50 value of 96.7%, followed by the performance of YOLOv8s with the mAP50 value of 96.5%. It is suggested that if the system is to be implemented in a real-time environment, YOLOv8s is a better choice since it took significantly less inference time (2.3ms) than YOLOv8m (5.7ms) and yet generated the competitive mAP50.

This paper seeks to fill in the gaps of modern relativistic Cosmology by utilizing the total symmetry between space and time dimensions and re-interpreting the scale factor of the Universe as a gravitational potential generated by the mass/energy of the entire Universe as a whole. The gradient of this potential is along the cosmological time dimension through which the Universe is falling. This gradient gives us an arrow of time, we find explanations for why the Universe began expanding and why the expansion is accelerating without the need for a Cosmological Constant. In a finite time, the gradient will point in the opposite direction of time turning the expanding Universe into a collapsing one where it is shown that when placing the Schwarzschild metric in the dynamic Cosmological background, gravity becomes repulsive and things like would-be Black Holes become White Holes. The model naturally describes a Universe and an anti-Universe (consisting of antimatter) moving in opposite directions of time that collide at the end of collapse, annihilating and subsequently pair producing two new Universes as the cycle begins again. It is shown that the model's Hubble diagram fits the currently available supernova and quasar data. It is found that Dark Matter can perhaps be understood as ordinary matter that is not connected to us with null geodesics.

Thermodynamics and phase transitions of magnetic Anti-de Sitter black holes are studied. We consider an extended phase space thermodynamics with the cosmological constant being a thermodynamic pressure and the black hole mass is treated as a chemical enthalpy. The extended phase space thermodynamics of black holes mimics the behavior of the Van der Walls liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It is demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation take place. The Joule--Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of inversion temperature are found.

While the quantum realm seems hidden, it can also reach examples of infinite energy, especially when a part of space is roughly removed until it disappears, possibly forever. Since it follows that {\it Nothing } can enter a region where the space is missing, the quantum realm, as seen now in affine quantization, will automatically come to help everything else by creating colossal `quantum walls' that will ensure that everything stays out of all black holes. In this article, we show that the expanded quantum realm allows {\it Nothing} to ever fall into a black hole.

A bijective analysis is confirming, the expansion of universal space has never been directly observed, and this assumption is unproven thus far. The measurement of the gravitational redshift, which was confirmed using the Mossbauer experiment, proves only the gravitational redshift and nothing more because there is no causality between the gravitational redshift and hypothetical expansion. Thus, even if the universal space is assumed to expand, the gravitational redshift cannot be assumed to be proof of the expansion. In addition, the Doppler effect was never observed in an expanding space; thus, the claim that the cosmological redshift is partially caused by the Doppler effect, which is caused by the expansion of space, is an unproven assumption. Furthermore, the discovery of cosmic microwave background (CMB) radiation simply proves that the radiation is emitted by the entire universal space, but does not prove the existence of a recombination period. In evidence-based cosmology, every element in the model has a corresponding element in physical reality that is observed and measured. The evidence-based cosmology model is related to the real universe by a bijective function of set theory. Supermassive black holes in the centre of galaxies are rejuvenating systems of the universe. They rotate their local superfluid space which is the physical origin of galactic rotation curves.

By drilling periodic thru-holes in a suspended film, the phonon system can be modified. Being motivated by the BCS theory, the technique, so-called phonon engineering, was applied to a niobium sheet. The newly emergent high-T_c superconductivity, however, cannot be accounted for by the BCS theory. Rather, its exposed configuration, namely a square-lattice oxygen network, is reminiscent of the copper--oxygen plane in cuprate high-T_c superconductors. It turns out that its magnetic result is consistent with the principle of giant atom, which was developed by another heroes of superconductivity, Fritz London and John Slater, in the 1930s, several decades earlier than the propagation of BCS theory. The superconducting transition feature is discussed on the basis of a comprehensive theory of the giant atom---the theory of hole superconductivity.

It is proven that the Clapeyron-Mendeleev equation, originally discovered for gases with large entropy, describes the state of dark matter and energy due to enormous self-gravitation. It is shown that the dark matter exists as compact cold neutrino stars at positive temperature with size twice the Schwarzschild radius. In contrast, the dark energy is dark matter at temperature below the absolute zero, which is locked entirely in black holes, where the pressure is negative as required for the Universe intrinsic expansion. The derived dark phase diagram predicts negative critical temperatures for the Big Bang and the Big Rip of black holes.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and applying the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma as well as non-plasma medium.

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

The algorithm described in this paper inherits the concepts of layered fusion, insertion, and set from four convex hull-based heuristic algorithms. It summarizes relevant definitions and theorems, proposes valuable research hypotheses, combines grouping and insertion, and innovatively introduces the practice of "grouped insertion."

In this paper, a distributed algorithm is proposed to solve a consensus convex optimization problem. It is a Jacobi-proximal alternating direction method of multipliers with a damping parameter $\gamma$ in the iteration of multiplier. Compared with existing algorithms, it has the following nice properties: (1) The restriction on proximal matrix is relaxed substantively, thus alleviating the weight of the proximal term. Therefore, the algorithm has a faster convergence speed. (2) The convergence analysis of the algorithm is established for any damping parameter $\gamma\in(0,2]$, which is larger ones in the literature. In addition, some numerical experiments and an application to a logistic regression problem are provided to validate the effectiveness and the characteristics of the proposed algorithm.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

In this paper, we study the weak deflection angle using Gauss-Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner's approach, first we acquire the Gaussian optical curvature to use in Gauss-Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we look into the graphical behaviour of bending angles and greybody bounds at some specific values of multiple parameters as well as black holes charges. It is to be mention here that all the results for the electric and magnetic charged black holes solutions reduce into the Schwarzschild black hole solution in the absence of the black holes charges.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

Space-time evolution of our universe is explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (E = cDtDV), charges and energy density (|q| = r = cDt) and absolute time (ct) are newly defined based on the 4-D Euclidean space. The photon flat space with the constant energy density of r = cDt_q is proposed as the dark energy (DE). The dark energy is separated into the n DE and photon DE which create the new photon spaces with the constant energy density of r = cDt_q. The v DE is from the n pair production by the CPT symmetry and the photon DE is from the photon space pair production by the T symmetry. The vacuum energy crisis and Hubble’s constant puzzle are explained by the photon space with the n DE and photon DE. The big bang and inflation of the primary black hole is connected to the accelerated space expansion and big collapse of the photon space through the universe evolution. The big bang from the nothing is the pair production of the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry. Our universe is the matter universe with the negative charges of electric charge (EC), lepton charge (LC) and color charge (CC). This first universe is made of dark matter -, lepton -, and quark - primary black holes with the huge negative charges which cause the Coulomb repulsive forces much bigger than the gravitational forces. The huge Coulomb forces induce the inflation of the primary black holes, that decay to the super-massive black holes and particles.

This letter aims to show the connection between the sinc approximation for high-energy absorption cross section and the shadow radius of the spherically symmetric black hole. This connection can give a physical interpretation of the absorption cross section in the eikonal limit parameters. Moreover, the use of this alternative way, one can extract its shadow radius from the absorption cross section in high energy limits to gain more information about the black hole spacetime. Our results indicate that the increasing the value of the shadow radius of the black hole, exponentially increase the the absorption cross section of the black hole in high-energy limits which can be captured by the Event Horizon Telescope (EHT) collaboration.

Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems’ description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of utmost functional importance, allowing reversible transformations of cellular structures. The focus here is on the widespread occurrence of intracytoplasmic holes, that deeply modifies the topology of living cells and provides researchers with novel operational tools to investigate intracellular dynamics. We take as example the prokaryotic gas vesicles, i.e., intracellular cavities filled with gases spreading from the nearby medium. The mechanical and topological cellular properties dictated by intracytoplasmic holes are investigated, focusing on the physical constraints imposed by their very existence. For instance, the presence of gas vesicles breaks the cytoplasmic homogeneity, leading to inhomogeneity in functional activities and modifications in intracellular flows. Also, a topological approach to cytoplasmic holes suggests novel physiological roles for gas vesicles. For example, the gas vesicles’ ability to increase/decrease cellular volumes provides a mechanism that counteracts the detrimental effects of the surface/volume ratio. In conclusion, a structural/methodological approach based on the occurrence of holes testifies once again how the simple biophysical structure alone can dictate the function.

In this paper, we analyze the Hawking radiation phenomenon for types of Banados-Teitelboim-Zanelli-like (BTZ-like) black holes. For this purpose, using the Hamilton-Jacobi method, we consider semi-classical WKB approximation to calculate the tunneling probabilities of massive boson particles. For these particles, we use the equation of motion for the Glashow-Weinberg-Salam model. Using quantum tunneling process of charged massive bossons, we compute the corresponding Hawking temperatures. Furthermore, we discuss the effects of rotation parameter on tunneling probability and temperature.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-convex functions, GA, GG, GH-convex functions and HA, HG, HH-convex function are given. Applications for p, r-convex and LogExp functions are presented as well.

We show that perturbations of a scalar field in the background of the black hole obtained with the Starobinsky-Bel-Robinson Gravity is unstable unless the dimensionless coupling $\beta$ describing the compactification of M-theory is small enough. In the sector of stability quasinormal spectrum show peculiar behavior both in the frequency and time domains: the ringing consists of two stages where two different modes dominate. The WKB method does not reproduce part of the spectrum including the fundamental mode, which is responsible for the first stage of the ringing. Consequently, the correspondence between the eikonal quasinormal modes and null geodesics allows to reproduce only part of the eikonal spectrum. The frequencies are obtained with the help of three methods (Frobenius, WKB and time-domain integration) with excellent agreement among them.

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

In this paper, a method of direct spinning is proposed for direct spinning of heterogeneous spun wire-blown holes standard parts and the motherboard mounted on the spin board assemblies. The standardization of the spinneret hole was conducive to improving the machining accuracy and efficiency of the pores, and the spinneret holes could be replaced in time when a hole in the spinneret fails. Moreover; on the other hand, according to the needs of the process of spinning, the spinnerets with various cross-sections were combined and installed on the same motherboard for spinning, and the spinning obtained different bionic new functional products. Based on the results, a finite element model of the standard part of the spinneret hole was developed, and the spinnability of the combinable spinnable spinneret board was verified by simulating the melt flow in the spinneret channel through POLYFLOW software. Further, by the processing of the spinneret, the motherboard was installed into a combined spinneret, and the spinneret assembly was installed on the spinning machine for the experiments. Furthermore, the tow section was observed using a microscope, and the results showed the feasibility of the proposed method.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

Fastener holes are among the most common natural stress concentrators in metal structures. The life cycles of various structural elements, such as those in aircraft structures, automobiles, and rail-end bolt joints are limited by fatigue damage around the holes. An effective approach to delay the formation and growth of fatigue macrocracks is to introduce residual hoop compressive stresses around the holes. Two methods have become established in the prestressing of fastener holes in aircraft components: split sleeve and split mandrel, which implement one-sided processes. The common disadvantage of both methods is the complex procedure due to the need for high accuracy of the initial holes. This article presents a new modified split mandrel method providing the same tightness (interference fit) with a wide tolerance of the pre-drilled hole diameters reducing the number of technological cycle steps and production costs. То implement the new method, a functionally connected tool and a device with a hydraulic drive were developed. An extensive experimental study of 2024-T3 AA specimens was carried out to evaluate the effectiveness of the method under a high scattering of the pre-drilled holes. The new method provided a deep zone of residual hoop compressive stresses on both faces of the specimens after cold working and after hole final reaming. The removal of a plastically deformed layer around the hole of suitable thickness during the final reaming decreased the axial gradient of residual hoop stress distribution. Fatigue tests on a tensile pulsating cycle verified the effectiveness of the modified split mandrel method to significantly increase the fatigue life by 6.6 times based on cycle fatigue strength compared to the conventional case of machining the holes. The obtained S-N curves for three groups of samples with initial hole diameters of 8.0, 8.1, and 8.2 mm which were cold worked with the same tightness of 0.32 mm and final reamed, aligned well indicating that the new method can provide constant fatigue strength for a given stress amplitude.

Natural Fibre Reinforced Composites (NFRCs) represent a significant category of materials that has the capacity to contribute to the worldwide objectives of sustainability and environmental preservation. To maximise the potential of composite materials, it is essential to establish their high quality and cost-effective manufacture. While the basic production procedures for producing items based on NFRCs have reached a high level of development, more research efforts are needed to advance their secondary manufacturing processes, namely in the areas of machining and joining. The primary factor leading to the rejection of composite goods with holes is the damage generated during the drilling process. The present experimental study aims to examine the effectiveness of hole production during the moulding phase. A comparative analysis has been conducted to assess the mechanical characteristics of moulded and drilled holes in jute fibre reinforced epoxy composite. It was observed that the moulded holes exhibit superior performance compared to the drilled holes for jute/epoxy materials. Additionally, the load extension curves indicate that the moulded holes experience greater extension in comparison to the drilled holes.

In this work, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss-Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss-Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of NLED, plasma, and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-h-convex functions, GA, GG, GH-h-convex functions and HA, HG, HH-h-convex function are given.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

We considered the hypothesis that the sources of dark energy (DE) could be black holes (BHs) or more exotic objects, such as naked singularities or gravastars. We proposed a definition of the presence of DE in the Universe and a criterion for what can be considered the source of this dark energy. It is based on the idea of the accelerated expansion of the Universe, which requires antigravity caused by large negative pressure. A recently proposed hypothesis was examined that mass of BHs increases with time according to the same law as the volume of the part of the Universe containing it and the population of BHs can mimic DE. We demonstrate the reasons why it cannot be accepted, even if all the assumptions on which this hypothesis is based are considered true.

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from $f(Q)$'s field equations which prevents it from deriving spherically symmetric black hole solutions, the result is either $Q'=0$ or $f_{QQ}=0$. We derive static anti-de-Sitter black holes in $D$-dimensions using the cylindrical coordinate in the framework of the cubic form of $f(Q)$ gravity, where the coincident gauge condition is imposed \cite{Heisenberg:2023lru,Maurya:2023muz}. Within this study we are going to use the power-law ansatz which is the most viable according to observations where $f(Q)=Q+\frac{1}2\gamma Q^2+\frac{1}3\gamma Q^3-2\Lambda$, and the condition $D \geq 4$ is satisfied. Since these solutions lack a general relativity limit, they belong to a brand-new solution class, the characteristics of which are derived only from the non-metricity $Q$ modification. We investigate the singularities of the solutions by computing the values of different curvature and non-metricity invariants. We discover that the solutions indeed have a central singularity, but because of the f(Q) impact, it is softer than in the typical general relativity case. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.

The paper proposes a theoretical study that investigates the quantum effects on the gravity of black holes. The study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation. The research calculates the mass density distribution of quantum black holes, specifically in the case of central symmetry. The gravity of the quantum black hole shows contributions coming from the quantum potential energy, which is also sensitive to the presence of the background of gravitational noise. The additional energy, stored in the quantum potential fluctuations and constituting a form of dark energy, leads to a repulsive gravity in the weak gravity limit. This repulsive gravity overcomes the attractive classical Newtonian force at large distances of order of the intergalactic length.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikove-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.

A Micro holes in a diamond are presented by using a homemade femtosecond (fs) Yb:KGW laser. An fs laser source was used emitting pulse duration of 230 fs at 1030 nm wavelength, whereas the spot size amounted to 8.9 μm. Parameters like pulse energy, and pulse number were varied over a wide range in order to evaluate their influence both on the micro hole geometry like hole diameter, circularity, taper angle, and on the drilling quality. Hourglass-shaped micro holes whose diameters decrease and increase again after a certain depth have important applications. The results demonstrate the feasibility of extending the drilling of an hourglass-shaped hole in a diamond sample, which has similar diameters at the hole entrance (92 μm) and exit (95 μm), but a much smaller diameter (28 μm) at a certain waist section inside the hole.

In this work, we examine the deflection angle of black hole in effective loop quantum gravity in non-plasma medium via the geometrical technique of Gibbons and Werner in weak field limits. For this, we attain the optical metric and calculate the Gaussian optical curvature and then we apply the Gauss-Bonnet theorem. We also study the influence of the plasma and dark matter mediums on the deflection angle. Further, we obtain the deflection angle by using Keeton and Petters method. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the bending angle and bounds on the greybody factor. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduces to the Schwarzschild black hole solutions when dimensionless non-negative parameter $A_{\lambda}=0$.

In this paper we establish several Hermite-Hadamard type integral inequalities for trigonometrically rho-convex functions. Applications for special means are provided as well.

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

This study describes all the properties of high T_c cuprates by introducing rotating holes that are created by angular momentum conservations on a 2D CuO₂ surface, and which have a different mass from that of a normal hole because of the magnetic field energy induced by the rotation. This new particle called a macroscopic Boson describes the doping dependences of pseudo-gap temperature and the transition temperature at which an anomaly metal phase appears and describes the origin of the pseudo-gap. Furthermore, this study introduces a new model to handle many-body interactions, which results in a new statistic equation. This statistic equation describing many-body interactions accurately explains why high T_c cuprates have significantly high critical temperatures. Moreover a partition function of macroscopic Bosons describes all the properties of anomaly metal phase, which sufficiently agree with experiments, using the result from our previous study [1] that analytically describes the doping dependence of T_c. By introducing a macroscopic Boson and the new statistical model for many-body interactions, this study uncovered the mystery of high T_c cuprates, which have been a challenge for many researchers. An important point is that, in this study, pure analytical calculations are consistently conducted, which agree with experimental data well (i.e., they do not use numerical calculations or fitting methods but use many actual physical constants).

A parallel between defense powers of sovereign nations and effective immunity that guards health is relevant to demonstrate vulnerability of immune system under external forces (vaccines, drugs). History demonstrated that sovereignty (power within) of small nations often threatened or destroyed by military might of powerful nations (power without) who use false-flags and propaganda for motives that are financial-control-driven. Similarly, we propose that body’s complex immune neuroplasticity (power within, adaptive, horizontal) is stretched-thin and weakened by the external forces, particularly by vaccination of the unborn/newborn or immune-compromised individuals. Validity of genomics (innate, perpendicular) as origins of ‘hereditary’ diseases (eg, allergies, diabetes, cancers) that for a century dominated research and treatment is also challenged. In conclusion, we propose that the pressure/power from within creates life with potential to sustain health, while the pressure/power from without, weaken and destroy life.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.

We have developed circular defects in 2-dimensional photonic crystal lasers that allow current injection for interconnected optical communications. However, when cleaving the sample to measure the output light, the output light intensity changes due to the cleaving position. In a previous study, we discovered through simulation that this effect could be eliminated and that a higher optical output might be obtained by applying a convex edge structure. In this paper, we develop the fabrication technology for this structure, fabricate samples, and measure the output light experimentally. Room-temperature continuous-wave laser oscillations using this structure are observed. The laser threshold is similar to well-lasing samples with normal cleavage edge faces. We are assured that these results contribute to future work such as accurate manufacturing and improving the end-face configuration to obtain higher outputs.

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. [J. Optim. Theory Appl. 2023, 196, 1036–1055.] and Yu et al. [Mathematics, 2023, 11, 2000] provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

In the framework of a multiplicative metric space. We have discuss some Properties of convex structures in pseudo multiplicative metric space and have applied these properties toiobtain alfixed point results in complete pseudo. It would be interesting to prove some further results in such metric spaces with completeness property.

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

Theoretical approaches to calculate pKa values for Brønsted acids is a challenging task that, most of the time, involves sophisticated and time-consuming methods. Therefore, heuristic approaches are efficient and appealing methodologies to approximate these values. Herein, by considering the electrostatic potential on acidic hydrogen atoms in a similar fashion that a σ–hole is defined, we calculated the maximum surface potential, V_S,max, and used it as a descriptor to correlate it with experimental acidity constants. These values were calculated using the CPCM implicit solvent model (water) with six different methods: five density functionals and the Møller–Plesset second order perturbation theory. Six different basis sets were combined with each method in order to benchmark a total of thirty-six levels of theory. Overall, 1080 calculations were performed and found to correlate with experimental data. The ωB97X-D/6-31+G(d,p) level of theory stands as the best one for consistently reproduce the reported pKa values.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Maxwell's fish eye has been known to be a perfect lens in optics. In this letter, using the Gibbons-Werner method, namely Gauss-Bonnet theorem on optical geometry of black hole, we extend the calculation of the weak gravitational lensing within the Maxwell's fisheye as a perfect lensing in medium composed of an isotropic refractive index that near-field information can be obtained from far-field distances. Moreover, these results provide an excellent tool to observe compact massive object by weak gravitational lensing within the dark matter medium and to understand the nature of the dark matter that may effect the gravitational waves. Moreover, we show that Gauss-Bonnet theorem is a global effect and this method can be used as a new tool on any optical geometry of compact objects in dark matter medium.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

Communities in semi-arid lands use sand dams to enhance access water during the dry seasons. However, there is limited information on the quality of water derived from these sand dams, especially in degraded lands where storm surface runoff poses contamination risk. Thus, this study aimed at assessing the spatial-temporal variations in water quality of sand dams in Chepareria, West Pokot County in Kenya. Water samples were collected from scooping holes across18 purposefully selected sand dams. Results obtained showed significant differences in water quality based on sand-dams age and location of scooping holes, but the magnitude of these differences differed with specific properties. For instance, in recently constructed sand dams (< 1 year), scooping holes near the sand dam wall had lower pH values (8.5) than holes scooped a distance from the sand dam wall (9.2). For total dissolved solutes and microbial properties, sand dam age had the greatest impact than the location of scooping holes. For example, water obtained from < 1 year old sand dams had significantly higher TDS with an average value of 100.3 mg L-1. The thermotolerant coliforms (TTC) exceeded the maximum allowable levels recommended by World Health Organization. Thus, water obtained from these sand dams should be treated before consumption. Finally, sand dams meant for domestic water harvesting should be protected. Shallow wells with appropriate aprons for effective protection against contamination should be installed to enhance abstraction of safe water from sand dams.

A single tree topology is a commonly employed topology for wireless sensor networks (WSN) to connect sensors to one or more remote gateways. However, its many-to-one traffic routing pattern imposes heavy burden on downstream nodes, as the same routes are repeatedly used for packet transfer, from one or more upstream branches. The challenge is how to choose the most optimal routing paths that minimizes energy consumption across the entire network. This paper proposes a proactive energy awareness-based many-to-one traffic routing scheme to alleviate the above said problem referred to as Energy Balance-Based Energy Hole Alleviation in tree topology (EBEHA-T). This protocol combines updated status of variations in energy consumption pattern around sink-hole zones and distribution of joint nodes among the trees. With this approach, EBEHA-T proactively prevents sink-hole formation instead of just a reactive response after they have occurred. Performance evaluation of EBEHA-T against benchmark method RaSMaLai shows increased energy saving across the entire network and a marked improvement in energy consumption balance in energy-hole zones. This precludes energy hole formation and the consequent network partitioning, leading to improved network lifetime beyond that of the RasMaLai. OMNET++ network simulation software has been used for the evaluation.

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

Positive invariant set is an important concept of dynamic systems. The purpose of this paper is to study the sufficient and necessary conditions that the set of ellipsoids and the Lorenz cone are positive invariant sets of discrete time systems. By means of nonlinear programming and induced norm, the problem of positive invariance is formulated as an optimization problem, and the equivalent dual form optimization is also presented using the dual optimization method. Our results provide more alternative methods for determining the positive invariance of quadratic form convex sets from the point of view of optimization and dual optimization. The effectiveness of this method is demonstrated by numerical examples.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

Near-infrared (NIR) photodetectors (PDs) have attracted much attention in noninvasive medical diagnosis and treatment. Especially, the self-filtered NIR PDs are highly demandable for tremendous biomedical application due to their strong ability in wavelength discrimination. In this work, we designed and then fabricated a Si micro-holes array/Graphene (Si MHA/Gr) van der Waals (vdW) Schottky NIR photodiode by using PbS quantum dots (QDs) coating. The device exhibits a unique self-filtered NIR response with a responsivity of 0.7 A/W at -1 V and a response time of 61 μs, which are higher than that without PbS QDs coating and even most of previous Si/Gr Schottky photodiodes. The light trapping of the Si MHA and the PbS QDs coating can be attributed to the high responsivity of the vdW photodiode. Furthermore, the presented NIR photodiode can also be integrated in photoplethysmography (PPG) for real-time heart-rate (HR) monitoring. The extracted HR is in great accord with the value measured with the patient monitor by analyzing the Fourier transform of the stable and reliable fingertip PPG waveform, suggesting its potential for practical applications.

In the last decades the primordial black holes ({\bf pbhs}) have attracted much attention of cosmologists and astrophysicists. This is associated with origination of such black holes in the early Universe as a result of a gravitational collapse of the high-density matter, making them natural ''detectors'' of the processes involved. In inflationary cosmology of particular importance are {\bf pbhs} originated during the pre-inflationary period. And, since they are small and generated at the energies close to the Planck energies, for them we should take into consideration the quantum-gravitational corrections ({\bf qgcs}). In turn, these corrections change (shift) the inflationary parameters. The paper presents a study of the above-mentioned shifts with regard to these corrections for different scenarios. It is shown that probabilities of occurrence of the {\bf pbhs} under study with due regard for the given {\bf qgcs} are rising as compared to the semiclassical consideration. Besides, high-energy deformations of Friedmann Equations created on the basis of these corrections have been derived for different patterns. Conclusion contains the general remarks concerning the above-mentioned {\bf qgcs} for cosmological parameters and perturbations due to inflation; the steps for their investigation are outlined and the key problems of such a study are formulated.

This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is developed as an application to a Ginzburg-Landau type system in superconductivity in the absence of a magnetic field. In the first sections, we develop new general dual convex variational formulations, more specifically, dual formulations with a large region of convexity around the critical points which are suitable for the non-convex optimization for a large class of models in physics and engineering. Finally, in the last section we present some numerical results concerning the generalized method of lines applied to a Ginzburg-Landau type equation.

The existence of the hole on a plate affects the calculation of eddy current problems. Consequently, the accuracy for the prediction of the material properties decreases if the effect of the hole is not taken into account. In this paper, a novel analytical method based on the modified integration range is proposed which can address the presence of the hole. Due to the presence of the hole, the conventional Dodd-Deeds analytical solution cannot be used to calculate the inductance change. Therefore, a revised upper integration limit is introduced to replace the original limit -- ∞ when using the co-axially air-core electromagnetic sensor. With the presence of the hole, the magnitude of the received signal reduces, and the peak frequency feature changes. The analytical method is validated by measured and numerical simulation results. It is found that the upper limit is related to the radius of the open hole. With the new technique, the thickness of sample plates with holes can be estimated based on the peak frequency feature.

The black hole information paradox is one of the most puzzling paradoxes in physics. Black holes trap everything that falls into them, while their mass may leak away through purely thermal Hawking radiation. When a black hole vanishes, all the information locked inside, if any, is just lost, thus challenging the principles of quantum mechanics. However, some information does have a way to escape from inside the black hole, that is, through gravitational waves. Here, a concise extension of this notion is introduced. When a black hole swallows something, whether it is a smaller black hole or an atom, the system emits gravitational waves carrying the information about the “food”. Although most of the signals are too weak to be detected, the information encoded within them will persist in the universe. This speculation provides an explanation for a large part, if not all, of the supposed “information loss” in black holes, and thus reconciles the predictions of general relativity and quantum mechanics.

In this paper, we argue that one can calculate the weak deflection angle in the background of Einstein-Maxwell-Dilaton-Axion black hole using the Gauss-Bonnet theorem. To support this, the optical geometry of the black hole with the Gibbons-Werner method are used to obtain the deflection angle of light in the weak field limits. Moreover, we investigate the effect of a plasma medium on deflection of light for a given black hole. Because of dilaton and axion are one of the candidate of the dark matter, it can give us a hint on observation of dark matter which is supported the black hole. Hence we demonstrate the observational viability via showing the effect of the dark matter on the weak deflection angle.

This is an introduction to a new concept of quantum gravity that seamlessly merges General Relativity to the Standard Model. Based upon a novel patent-pending magnetic confinement method that was designed to emulate how our sun confines and rotates charged particles about a singularity; this confinement method uses a collective of off-centered confinement coils that are directed to curve rotating charged particles about a singularity in a way that allows charged particles to relatively accelerate from geodesic deviation. With this confinement method, the subtle Relative Accelerated Energy (RAE) from deviating charged particles has the capability to be focused and exponentially increased relative to the mass-energy of a closed system; which allows for a simple pathway to understand how black holes operate at their singularities. While in the pursuit of proving that this novel method of confinement mimics how our sun operates; I was also able to develop a logical explanation of how our sun reverses its magnetic poles and cycles using the core principles of Michael Faraday. If this concept of quantum gravity is correct, there is a simple explanation for the additional observed gravitational force about the galaxies that are said to obtain dark matter. In short, this theory of quantum gravity has the potential to fully discredit the existence of theorized dark matter with a simple experiment.

This research paper presents a new test based on a novel approach for identifying clustered graphical passwords within the Passpoints scenario. Graphical authentication methods serve as a viable alternative to the conventional alphanumeric password-based authentication method, which is susceptible to known weaknesses arising from user-generated passwords of this nature. The test proposed in this study is based on estimating the distributions of the perimeter of the convex hull. This perimeter is calculated based on the points users select as passwords within an image measuring 1920 × 1080 pixels. The test is formulated once the optimal theoretical distributions that fit the data are identified. Evaluating the proposed test’s effectiveness involves estimating type I and II errors. In this study, we compare the effectiveness and efficiency of the proposed test with existing tests from the literature that can detect this type of pattern in Passpoints graphic passwords. Our findings indicate that the new test demonstrates a significant improvement in effectiveness compared to previously published tests. Furthermore, the joint application of the two tests also shows improvement. Depending on the significance level determined by the user or system, the enhancement results in a higher detection rate of clustered passwords, ranging from 0.1% to 8% compared to the most effective previous methods. This improvement leads to a decrease in the estimated probability of committing a type II error. In terms of efficiency, the proposed test outperforms several previous tests; however, it falls short of being the most efficient. It can be concluded that the newly developed test demonstrates the highest effectiveness and the second-highest efficiency level compared to other tests available in the existing literature for the same purpose.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

The paper focuses on the application of a multilevel, integrative and territorial approach to the protection of cultural heritage through planning instruments in Serbia. It points out the problems of the sectoral approach and discusses international recommendations that can be integrated into the planning methodology. The case study is the area of Djerdap National Park, which has an already established international and national importance. The research suggests that the cultural heritage in the area, with the exception of the Roman limes, is still recognized at the level of individual localities. The study emphasizes the importance of aligning all levels of governance to safeguard the whole spatial entity rather than focusing solely on its particular areas. The interna-tional and national importance of the planning area contributes to the strengthening of awareness of heritage and its institutional protection. However, the vitality of the area, which is key to its sustainable development, comes from the local level. Planning documents contribute to the inte-gration of local values and local communities into development programs and projects.