When the minimal length approach emerging from noncommutative Heisenberg algebra, generalized uncertainty principle (GUP), and thereby integrating gravitational fields to this fundamental theory of quantum mechanics (QM) is thoughtfully extended to Einstein field equations, the possible deformation of the metric tensor could be suggested. This is a complementary term combining the effects of QM and general relativity (GR) and comprising noncommutative algebra together with maximal spacelike four–acceleration. This deformation compiles with GR as curvature in relativistic eight–dimensional spacetime tangent bundle, generalization of Riemannian spacetime, is the recipe applied to derive the deformed metric tensor. This dictates how the affine connection on Riemannian manifold is straightforwardly deformed. We have discussed the symmetric property of deformed metric tensor and affine connection. Also, we have evaluated the dependence of a parallel transported tangent vector on the spacelike four–acceleration given in units of L, where L = rℏcG3 is a universal constant, c is speed of light, and ℏ is Planck constant, and G is Newton’s gravitational constant.

In the present paper we investigate the conservative conditions in Quadratic Gravity. It is shown explicitly that the Bianchi identities lead to the conservative condition of the left-hand-side of the (gravitational) field equation. Therefore, the total energy-momentum tensor is conservative in the bulk (like in General Relativity). However, in Quadratic Gravity it is possible to have singular hupersurfaces separating the bulk regions with different behavior of the matter energy-momentum tensor or different vacua. They require special consideration. We derived the conservative conditions on such singular hypersurfaces and demonstrated the very possibility of the matter creation. In the remaining part of the paper we considered some applications illustrating the obtained results.

It is already known that a simple nonlocal de Sitter gravity model, which we denote as dS gravity, contains an exact vacuum cosmological solution which mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of dS gravity motivated us to investigate how it works at lower than cosmic scale – galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild-de Sitter metric of the dS gravity model. To get exact solution, it is necessary to solve the corresponding nonlinear differential equation, what is a very complicated and difficult problem. What we obtained is a solution of linearized equation, which is related to space metric far from the massive body, where gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity dS in describing the effects in galactic dynamics that are usually attributed to dark matter. The solution has been tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements.

On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof.

This research focuses on exploring gravitational lensing of the wormhole in Einstein-bumblebee gravity with an antisymmetric tensor. The Gibbons and Werner technique based on the Gauss-Bonnet theorem is utilized to calculate the bending angle of light. The effects of non-plasma and plasma medium on the bending angles are investigated. Furthermore, we examine the deflection angle $\Tilde{\alpha}$ in relation to the impact parameter $\sigma$ and minimal radius $r_{0}$ in both non-plasma and plasma mediums. Our findings indicate that the deflection angle is positively correlated with $r_{0}$, meaning that larger values of $r_{0}$ result in larger deflection angles and smaller values of $r_{0}$ result in smaller deflection angles. On the other hand, the deflection angle $\Tilde{\alpha}$ is inversely related to the impact parameter $\sigma$.

Traditional discrimination techniques for Euler deconvolution use only the color spectrums of structural indexes, without considering the spatial distribution characteristics and inherent relationships among the Euler solutions to separate adjacent causative sources. In the present study, a new approach was developed for discriminating uncorrelated Euler solutions from coherent solutions based on the focusing levels indicated by the probability density distributions generated using multivariate kernel density estimations (KDE). A novel multiple coverage technique was proposed by using a series of different sized moving windows over gridded gravity data, which formed tight clusters of Euler solutions for different sized causative sources. The results of the probability density distributions were obtained using a 3-D KDE method for the Euler solution subsets {x, y, z} of synthetical models, and real data from a survey conducted in British Columbia (Canada) which had successfully established more credible and meaningful geological models when compared with three other subsets.

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let’s delve into the mathematical intricacies of these sequences. We’ve previously devised a mathematical approach for defining a “healthy” sequence (10.14218/GE.2023.00079). This sequence is characterized by having at most four distinct nucleotides (denoted as nt≤4). It serves as the generator of a group denoted as fp. The desired properties of this sequence are as follows: fp should be close to a free group of rank nt−1, it must be aperiodic, fp should not have isolated singularities within its SL2(C) character variety (specifically within the corresponding Groebner basis). Now, let’s explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S24. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI equation (10.3390/dynamics4010001). In certain cases, S24 degenerates, in the sense that two punctures collapse, resulting in a “wild” dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find applications in cancer research.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Ranked Set Sampling (RSS) is a useful technique for improving the estimator of population mean when the sampling units in a study can be easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skew distributions. It is shown that the gain in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal family of distributions.

Two extensions of the generalized double Lomax distribution are introduced - the spliced-scale generalized double Lomax distribution and the exponentiated generalized double Lomax distribution. Their properties are studied. Usefulness of the new distributions is shown by fitting them to stock returns datasets.

We consider a four-dimensional Riemannian manifold M with an additional structure S, whose fourth power is minus identity. In a local coordinate system the components of the metric g and the structure S form skew-circulant matrices. Both structures S and g are compatible, such that an isometry is induced in every tangent space of M. By a special identity for the curvature tensor, generated by the Riemannian connection of g, we determine classes of Einstein and almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some characteristic 2-planes in a tangent space of M. We consider a Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a K\"{a}hler manifold. We construct some examples of the considered manifolds on Lie groups.

Most popular machine learning algorithms like k-nearest neighbour, k-means, SVM uses a metric to identify the distance(or similarity) between data instances. It is clear that performances of these algorithm heavily depends on the metric being used. In absence of prior knowledge about data we can only use general purpose metrics like Euclidean distance, Cosine similarity or Manhattan distance etc, but these metric often fail to capture the correct behaviour of data which directly affects the performance of the learning algorithm. Solution to this problem is to tune the metric according to the data and the problem, manually deriving the metric for high dimensional data which is often difficult to even visualize is not only tedious but is extremely difficult. Which leads to put effort on \textit{metric learning} which satisfies the data geometry.Goal of metric learning algorithm is to learn a metric which assigns small distance to similar points and relatively large distance to dissimilar points.

We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD.

Disk galaxies have a typical dimension of few tens of thousands of light years. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect is absent in modelling used to calculate rotation curves throughout the entire galaxy and its external gas. The considerable differences between Newtonian action at a distance predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that applying general relativity in a rigorous fashion without mindlessly neglecting retardation, one can explain the radial velocities of galactic matter without modifying gravity or adding unseen matter. Moreover, it was shown that dark matter effects as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. In the original main paper on the subject only one galaxy (M33) was analysed in detail. This was later amended somewhat with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain an excellent fit without postulating dark matter or modifying general relativity.

We hypothesis that large earthquakes generate Horndeski-like Gravitational Wave (GW). We find that such a Horndeski-like GW propagates with the speed of sound. The sound waves generated by an earthquake make a local and temporal change to the Earth’s diagravitational medium; therefore, they modify the GW speed in a standard, Alternative-Theory-of-Gravity (ATG) sense. The quantum of the Horndeski-like GW is a massless scalar quasiparticle and cannot exist outside of the propagation region of the P-field. The Horndeski-like GW may be detectable by future GW detectors with a sensitivity of 10−15 Hz^−1/2 in the region of 0.1–1 Hz.

This letter attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz’s and Berdichevsky’s plastic dislocation density tensor are equivalent with each other, but not with Kondo’s one. To fix the problem, we propose a modified version of Kondo’s plastic dislocation density tensor.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

In this outlet, I’ve devised the concept of relation amid two points where these points are coming up to make situation which in that the set of objects are greed to represent the story of how to be in whatever situations when these two points have the styles of being everywhere in the highlights of the concept which are coming from the merits of these points where are eligible to make capable situation to overcome every situation when they’re participant in the hugely diverse situations which mean too styles of graphs with have the name or the general results for the general situation as possible as are.

In cosmology, the cosmic curvature $K$ and the cosmological constant $\Lambda$ are two most important parameters, whose values have strong influence on the behavior of the universe. By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological model, we get the following results: (i) $K= 1$, namely, the global spatial structure of the universe should be a 3-dimensional sphere $S^3$. (ii) $0\le\Lambda < 10 ^ {-24} {\rm ly} ^ {-2}$, the cosmological constant should be zero or an infinitesimal. (iii) $a(t)>0$, the initial singularity of the universe is unreachable, and the evolution of universe should be cyclic in time. This means that the initial Big Bang is impossible at all. Since the matter components considered are quite complete and the proof is very elementary and strict, these logical conclusions should be quite reliable. Obviously, these conclusions will be much helpful to correct some popular misconceptions and bring great convenience to further research other problems in cosmology such as property of dark matter and dark energy.

Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at extremely large and small thresholds is explored with particular emphasis on the skew-normal copula. Our numerical studies reveal that, when the correlation or skewness parameters are around at the boundary values, some asymptotic tail approximations of the skew-normal copulas proposed in the literature are not suitable to compute the measure of tail asymmetry with practically extremal thresholds.

Document deskewing is a fundamental problem in document image processing. While existing methods have limitations, such as Hough Line Transformation that can deskew images upside down, and Deep Learning models that require huge amounts of human labour and computational resources and still fail to deskew while taking care of orientation, OCR-based methods also struggle to read text when it is tilted. In this paper, we propose a novel, simple, cost-effective deep learning method for fixing the skew and orientation of documents. Our approach reduces the search space for the machine learning model to predict whether an image is upside down or not, avoiding the huge search space of predicting an angle between 0 and 360. We finetuned a MobileNetV2 model, which was pre-trained on imagenet, using only 200 images and achieve good results. This method is useful for automation-based tasks, such as data extraction using OCR technology, and can greatly reduce manual labour.

The attitude dynamics and orbit dynamics of large rigid space structures are coupled with each other under gravity gradient, which may affect the stability of the large rigid space structures. In this paper, the gravity gradient stability of a large rigid space structure is studied under both small and large disturbances. Based on the rigid body dynamics and orbit dynamics, an accurate dynamic model without any linearization of the large rigid space structure is established via the natural coordinate formulation (NCF), which is able to describe the large overall motions of the structures. By using the generalized-α algorithm, the gravity gradient stability of the large rigid space structure is simulated and analyzed via various examples, including the influence of large disturbance angles, the positions at the stabilization and unstabilization regions. Finally, the relationship between spinning stability and gravity gradient stability is also investigated via a large spinning space structure.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides mathematical framework in which, as demonstrated in previous publications, the description of a physical system in curved spacetime and its description in flat spacetime with fields are equivalent. The description of a system with electromagnetic field based on Alena Tensor can be used to reconcile physical descriptions. 1) In curvilinear description, Einstein Field Equations were obtained with Cosmological Constant related to the invariant of the electromagnetic field tensor, which can be interpreted as negative pressure of vacuum, filled with electromagnetic field. 2) In classical description for flat spacetime, three densities of four-forces were obtained: electromagnetic, gravity, and the force responsible for the Abraham-Lorentz effect (radiation reaction force). Obtained connection of Einstein tensor with gravity and radiation reaction force, after transition to curvilinear description, excludes black hole singularities. There was obtained Lagrangian density and generalized canonical four-momentum, containing electromagnetic four-potential and a term responsible for other two forces. In this description charged particles cannot remain at complete rest and should have spin, their energy results from the existence of the energy of the magnetic moment and the density of this energy is part of the Poyting four-vector. The distribution of charged matter was expressed as polarization-magnetization stress-energy tensor, what may explain why gravity is invisible in QED. 3) In quantum picture, QED Lagrangian density simplification was obtained, and the Dirac, Schrödinger and Klein-Gordon equations may be considered as approximations of the obtained quantum solution. Farther use of Alena Tensor in unification applications was also discussed.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi–hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric, and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them to reach the center. However in the present case this behavior is affected by the parameter γ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the θ−r subspace. Possible relevance of these results in the explanation of extragalactic jets, is brought out. .

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

Digital gait monitoring is increasingly used to assess locomotion and fall risk. The aim of this work is analyzing the changes in the foot-floor contact sequences of Parkinson’s Disease (PD) patients in the year following the implant for deep brain stimulation (DBS). During their best-ON condition, 30 PD patients underwent gait analysis at baseline (T0), at 3 months (T1), and 12 months (T2) after the DBS neurosurgery for bilateral high-frequency subthalamic nucleus stimulation. Thirty age-matched controls underwent gait analysis once. Each subject was equipped with bilateral foot-switches and a 5-minute walk was recorded, including both straight-line and turnings. The walking speed, turning time, stride time variability, percentage of atypical gait cycles, stance, swing, and double support duration were estimated. Overall, the gait performance of PD patients improved after DBS, as also confirmed by the decrease in the UPDRS-III score from 19.4±1.8 to 10.2±1.0 points (T0 vs. T2) (p < 0.001). In particular, the percentage change of atypical gait cycles of PD more affected side decreased at T1 (Straigh-line: -72%; Turnings: -43%) and at T2 (Straigh-line: -54%; Turnings: -20%). The percentage of atypical gait cycles proved an informative digital biomarker for quantifying PD gait changes after DBS, both in straight-line paths and turnings.

Maxwell's energy-momentum tensor cannot be used as is in Einstein's equation for general relativity in the presence of sources. In this case, its four-divergence is non-zero, whereas the tensors in the equation must have this characteristic. However, the sun emits streams of ionized particles, gases are present within galaxies, material transfers in the form of ionized plasma can occur in binary star systems, and so on. These charges cannot be neglected in the study of space-time in these regions. Here, we present a modified version of this tensor that eliminates this flaw, provided that the potentials satisfy the Lorenz gauge. The distribution of sources will also be analyzed in light of fluid mechanics, allowing us to account for its influence in terms of generated pressure.

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

Theoretical physics addresses the fundamental principles of nature and the mysteries of the universe. In the last century, the theory of relativity challenged people's understanding of time and space, while quantum mechanics revealed various forms of energy. However, the concept of gravity remains elusive. All matter in the universe is composed of energy that can be converted into other forms, yet it is always conserved. However, achieving a state of equilibrium, represented by the equal sign, can be challenging to achieve on both macro and quantum scales. A phenomenon that can transition from one state to infinity is called collision and is essential for understanding natural phenomena and physical processes throughout the universe. In the study of general relativity cannot be three-dimensional problems to gain mathematical inspiration, understand the application of new dimensions. Here, we elucidate the nature of gravity, which inspires the solution of the Riemann hypothesis. Our results show that the conduction mode of dimensional energy is defined by Euler's formula. And a special mode of collision is derived which translates into vibration.

In a recent paper, we have shown how gravity and information can be related. The relation is based on the thermodynamic extension of the gravitational system under consideration using the holographic principle. Using this idea, we were able to derive the Gullstrand-Painlevé (GP) metric. In this short paper, we re-derive the GP metric using information. However, we now extend the spacetime to 5D with the fifth dimension being time, that is, the (3+1)D spacetime is now promoted to (3+1+1)D spacetime. We also comment on the possible Braneworld interpretation of this model.

Galaxies are rather big physical systems having a typical size of tens of kilo parsecs. Thus any change at the center of the galaxy will affect the outskirts only tens of thousand of years afterwards. Retardation seems to be neglected in current calculations of rotational velocities in the far edges of the galaxy and its surrounding gas. The differences between the velocities predicted by Newtonian theory and observational derivations are accommodated by either assuming "dark matter" or by introducing modifications to the laws of gravity in which MOdified Newtonian Dynamics (MOND) is one of the typical examples, celebrating now forty years since its inception. We show that there are overlapping conditions for retardation corrections in the weak approximation to general relativity and the low acceleration conditions for MOND corrections. We will also show that MOND interpolation formula is useful for calculating retardation effects provided an appropriate interpolation function is chosen.

This study investigates the elastic buckling behaviour of skew Functionally Graded Material (FGM) thin plates featuring a circular opening. FGM materials, known for their unique property gradients, have gained prominence in structural engineering due to their mechanical performance and durability. Including a circular opening introduces a critical geometric consideration, influencing the structural stability and load-carrying capacity of FGM plates. The study examines the effects of the skew angle, plate’s aspect ratio, opening position, and size on the critical buckling load, normalized buckling load, and various buckling failure modes through computer modelling and finite element analysis. The results offer valuable insights into the interplay between material heterogeneity, geometric configuration, and structural stability. For instance, the critical buckling load increases by 29%, 82%, and 194% with the increment of skew angle from 0° to 30°, 45°, and 60°, respectively. Moreover, as the opening shifts from the plate’s edge closer to the center, the critical buckling load decreases by 26%. This research contributes to the advancement of understanding FGM thin plates’ behaviour under skew loading conditions, with implications for the design and optimization of innovative structures. The findings presented provide a foundation for further exploration of advanced composite materials and their applications in structural engineering.

In this article it is shown, first, that a change of basis in Minkowski space is equivalent to a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. Second, that such mixed bases can be interpreted as a measurement system used by local, flat observers whose direct distance measurements are restricted to an (n−1)-dimensional submanifold in an n-dimensional Euclidean space. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean space measures a Minkowski spacetime. This interpretation could be useful for theories in special relativity and related fields that rely on spacetime concepts, as it offers a more intuitive geometric understanding of the Minkowski metric.

In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

Since general relativity (GR) has already established that matter can simultaneously have two different values of mass depending on its context, we argue that the missing mass attributed to non-baryonic dark matter (DM) actually obtains because there are two different values of mass for the baryonic matter involved. The globally obtained "dynamical mass'' of baryonic matter can be understood as a small perturbation to a background spacetime metric even though it's much larger than the locally obtained "proper mass". Having successfully fit the SCP Union2.1 SN Ia data without accelerating expansion or a cosmological constant, we employ the same ansatz to compute dynamical mass from proper mass and explain galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (Planck 2015 data) without DM. We compare our fits to modified Newtonian dynamics (MOND), metric skew-tensor gravity (MSTG) and scalar-tensor-vector gravity (STVG) for each data set, respectively, since these modified gravity programs are known to generate good fits to these data. Overall, we find our fits to be comparable to those of MOND, MSTG and STVG. While this favorable comparison does not establish the validity of our proposition, it does provide confidence in using the fits to pursue an underlying action. Indeed, the functional form of our ansatz reveals an interesting structure in these fits.

It has been proven that in standard Einstein gravity, exotic matter (i.e. matter violating the point-wise and averaged weak and null energy conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field . Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods of minimizing the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity and in this review paper we first explore f(R) theories and then explore some wormhole solutions in f(R) theories including Lovelock gravity.

The notion of Golden structure was introduced 15 years ago by the present authors and know a constant interest by several geometers. Now, we propose a new generalization apart of that called metallic structure and considered also by the authors. By adding a compatible Riemannian metric we focus on the study of submanifolds in this setting.

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra sl(2,R) and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R42: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R⁴₂: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

Recent discoveries of potential ice particles and ice-cemented regolith on celestial bodies like the Moon and Mars have ushered in new opportunities for developing technologies to extract water, facilitating future space missions and activities on these celestial surfaces. This study delves into the potential for water extraction from regolith through an experiment designed to test water recuperation from regolith simulant under varying gravitational conditions. The resultant water vapor extracted from the regolith is re-condensed on a substrate surface and collected in liquid form. Three types of substrates, hydrophobic, hydrophilic, and grooved, are explored. The system’s functionality was assessed during a parabolic flight campaign simulating three distinct gravity levels: microgravity, lunar gravity, and Martian gravity. Our findings reveal that the hydrophobic surface demonstrates the highest efficiency due to drop-wise condensation, and lower gravity levels result in increased water condensation on the substrates. This experiment aims to provide insights into in-situ water recovery, which is pivotal for establishing economically-sustainable water supplies for future missions.

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

In actuarial practice, the modeling of total losses tied to a certain policy is a non-trivial task. Traditional parametric models to predict total losses have limitations due to complex distributional features such as extreme skewness, zero inflation, multi-modality, etc., and the lack of explicit solutions for log-normal convolution. In the recent literature, the application of the Dirichlet process mixture for insurance loss has been proposed to eliminate the risk of model misspecification biases; however, the effect of covariates as well as missing covariates in the modeling framework is rarely studied. In this article, we propose novel connections among covariate-dependent Dirichlet process mixture, log-normal convolution, and missing covariate imputation. Assuming an individual loss is log-normally distributed, we develop a log skew-normal Dirichlet process to approximate the log-normal sum. As a generative approach, our framework models the joint of outcome and covariates, which allows to impute missing covariates under the assumption of missingness at random. The performance is assessed by applying our model to several insurance datasets, and the empirical results demonstrate the benefit of our model compared to the existing actuarial models such as the Tweedie-based generalized linear model, generalized additive model, or multivariate adaptive regression spline.

In this article, we review some of the key results concerning the stress-energy-momentum tensor in general theory of relativty. First, we derive Einstein's field equation using analytic approach. Then, we discuss different properties of stress-energy-momentum tensor for physical and scalar fields.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

To extend the calculation power of tensor analysis, we introduce four new definition of tensor calculations. Some useful tensor identities have been proved. We demonstrate the application of the tensor identities in continuum mechanics: momentum conservation law and deformation superposition.

The holographic principle states that the information about the volume of space is stored on its boundary. Assuming this holds, we can explain the aspects of gravity. The spacetime needs to be extended to 5D to explain gravity in this context. This naturally explains the four classical tests of gravity namely the gravitational redshift, the perihelion precession, the bending of light, and the gravitational time delay. We also show a novel way in which the universe expands in an accelerated manner at late times without the need for any form of dark energy.

At present there is a renewed interest in theories of ”modified” gravity. Here, under a more drastic modification enforced by Galilei group, we obtain a completely new gravitational structure, and which exists in addition to the already available general relativity of today. Correlated with this, we show that in addition, there is a new ”modified” quantum mechanics, in as much as it exists as an independent and new ”pure” non-relativistic quantum me- chanics, and which has no relativistic counterpart. This is in addition to the present quantum mechanics, where the relativistic and non-relativistic structures are counterparts of each other. The above holds, firstly due to the correlation between Galilei group and quantum mechanics. These math- ematical conclusions are consolidated by the fact that there exists a physical Majorana interaction between each neutron- proton pairs in nuclei. Galilei invariance of Majorana exchange in Majorana interaction, shows that the mass here is of pure gravitational nature, and which is immune to the other three forces. This makes an amazing connection between the gravitational force and the quantum mechanics. This pure gravitational mass would man- ifest itself as dark matter of the universe. It is our new modified gravity that generates the dark matter.

Unsupervised metric learning has been generally studied as a byproduct of dimensionality reduction or manifold learning techniques. Manifold learning techniques like Diusion maps, Laplacian eigenmaps has a special property that embedded space is Euclidean. Although laplacian eigenmaps can provide us with some (dis)similarity information it does not provide with a metric which can further be used on out-of-sample data. On other hand supervised metric learning technique like ITML which can learn a metric needs labeled data for learning. In this work propose methods for incremental unsupervised metric learning. In rst approach Laplacian eigenmaps is used along with Information Theoretic Metric Learning(ITML) to form an unsupervised metric learning method. We rst project data into a low dimensional manifold using Laplacian eigenmaps, in embedded space we use euclidean distance to get an idea of similarity between points. If euclidean distance between points in embedded space is below a threshold t₁ value we consider them as similar points and if it is greater than a certain threshold t₂ we consider them as dissimilar points. Using this we collect a batch of similar and dissimilar points which are then used as a constraints for ITML algorithm and learn a metric. To prove this concept we have tested our approach on various UCI machine learning datasets. In second approach we propose Incremental Diusion Maps by updating SVD in a batch-wise manner.

The aim of the study was to test the significance of the EPT index in the water quality assessment of three types of water bodies in hilly and mountainous region of Serbia. The aquatic macroinvertebrate community was dominated by the group of insects, of which 95 taxa represent the EPT group. We compared the obtained values of biological indices used for the assessment of water quality according to the national legislation with the overall status assessment represented by the ecological quality classes (EQC). The results of the Spearman correlation test showed a negative correlation of EQC with the EPT index, BMWP score, H', total number of taxa and number of sensitive taxa, while a positive correlation was observed for the values of SI and Tubificinae %. The values of EQC and biological indices were subjected to principal component analysis (PCA). The results showed that the parameters that contributed most to the differences were the EPT index, the BMWP score and the number of sensitive taxa. The results indicate that the EPT index is an excellent indicator of changes in water quality and an important tool for the ecological categorization of water bodies in mountain regions.

This paper aims the automatic ball balancers (ABBs) used in passive balancing devices for suppressing vibration of the eccentric rotor. The system model describes which equipped with a skew-mounted ABB with angular deviation. The dynamic equilibrium equations of the system are deduced from the perspective of three-dimensional (3D) dynamics. The results obtained are consistent with those derived from the Euler-Lagrange equations. It is exciting that the spatial dynamics method reveals the spatial geometric characteristic of dynamic balance positioning of the balls when the system is balanced with vibration suppression. The spatial property emerges the perpendicular line from each ball to the rotating spindle of the system must pass through the central axis of the orbit perpendicular to the ABB plane. This characteristic is a general rule that can be used to explain the phenomenon of the stable equilibrium positions of the balls in all previously studied cases.

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

In this article we first write a brief review of supersymmetric quantum mechanics and then we discuss the equivalence of two co-existing formalisms viz. tensor product formalism and partner hamiltonian formalism for 1-D SUSY Harmonic oscillator. Finally, we present a Mathematica code with which one can calculate the eigenstates of any 1-D SUSY partner Hamiltonian along with two illustrated examples of 1-D SUSY HO and 1-D SUSY infinite potential box.

Tuning tensor program generation involves navigating a vast search space to find optimal program transformations and measurements for a program on target hardware. The complexity of this process is further amplified by the exponential combinations of transformations, especially in heterogeneous environments. This research addresses these challenges by introducing a novel approach that learns the joint neural network and hardware features space, facilitating knowledge transfer to new, unseen target hardware. A comprehensive analysis is conducted on the existing state-of-the-art dataset, TenSet, including a thorough examination of test split strategies and the proposal of methodologies for dataset pruning. Leveraging an attention-inspired technique, we tailor the tuning of tensor programs to embed both neural network and hardware-specific features. Notably, our approach substantially reduces the dataset size by up to 53% compared to the baseline without compromising Pairwise Comparison Accuracy (PCA). Furthermore, our proposed methodology demonstrates competitive or improved mean inference times with only 25%40% of the baseline tuning time across various networks and target hardware. The attention-based tuner can effectively utilize schedules learned from previous hardware program measurements to optimize tensor program tuning on previously unseen hardware, achieving a top-5 accuracy exceeding 90%. This research introduces a significant advancement in auto-tuning tensor program generation, addressing the complexities associated with heterogeneous environments and showcasing promising results regarding efficiency and accuracy.

Control And Data Acquisition (SCADA) systems currently monitor and collect a huge among of data from all kind of processes. In practice, due to sensor failures or to communication errors, in the long-time running, some data may be lost. When it happens, given the nature of these failures, information is lost in bursts, that is, sets of consecutive samples, which besides can be very long. Data completion is a critical step, which must be done with the utmost rigour in order to not propagate errors in the rest of the processing chain stages. Some Big Data techniques do not work if the data series are incomplete, due to the loss of some data. When this occurs it is necessary to fill out the gaps of the historical data with a reliable data completion method. This paper presents an ad-hoc method to replenish the data lost by a SCADA system in case of long bursts. The data correspond to levels of drinking water tanks of a Water Network company that present patterns on a daily and a weekly scale. A method based on tensors is used to take advantage of the data structure. A specially designed \textit{tensorization} is employed to deal with bursts of missed data, applying a twice tensor decomposition and a signal continuity correction. Statistical tests are realized, which consist of apply the data reconstruction algorithms, by deliberately removing bursts of data in verified historical database servers, to be able to evaluate the real effectiveness of the tested methods. For this application, the presented approach outperforms the other techniques found in the literature.

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.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

The extremely high rotation of some SMBHs is the origin of their relativistic rotational energy that results in their relativistic mass. Relativistic mass creates their relativistic gravity which is a partial answer to the missing dark matter.

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

Video quality assessment (VQA) plays an important role in video applications for quality evaluation and resource allocation. It aims to evaluate the video quality consistent with the human perception. In this letter, a hierarchical gradient similarity based VQA metric is proposed inspired by the structure of the primate visual cortex, in which visual information is processed through sequential visual areas. These areas are modeled with the corresponding measures to evaluate the overall perceptual quality. Experimental results on the LIVE database show that the proposed VQA metric significantly outperforms the state-of-the-art VQA metrics.

The insuperable obstacle between gravity and quantum mechanics is their spacetimes. Introduction of a (quantum) quadratic form on a state Hilbert space and a (quantum) metric tensor in (3+1)D quantum spacetime solves the problem by providing a common spacetime for both gravity and quantum mechanics which helps further to develop an accurate and generalized form of quantum gravity, i.e., General Quantum Gravity. This formalism yields a (3+1)D pseudo-gravity first order quantum equation, which is technically more accurate than Schr\"odinger equation. A (quantum) Lorentz-like transformation is also possible to be developed in (3+1)D quantum spacetime. Instead of one common Einstein field equation to explain gravitational effects, this formalism yields two individual (quantum) Einstein field equations, namely, one for bosons and another for fermions. In this work, (quantum) metric tensor as well as quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar all are found to be the objects of quantization. Apparently, these quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar are also found to be multiplicatively renormalizable while all divergences of their higher orders vanish in (3+1)D quantum spacetime. Ultimately, General Quantum Gravity yields that: Quantum Mechanics and Theory of Special and General Relativity are inseparable and naturally inter-expressible for the (quantum) quadratic form and the (quantum) metric tensor in (3+1)D quantum spacetime.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

This study focuses on examining various approaches for Tensor Decompositions (TDs) and their potential applications in satellite imaging (SI) and deep learning (DL). The research highlights how these decompositions can contribute to the advancement of SI and DL, providing valuable insights for future utilization of TDs in research. It explores how these techniques contribute to the advancement of SI and DL methods, providing insights into their potential applications and suggesting future research directions. The study aims to enhance the use of TDs techniques to further advance research efforts in these fields. More importantly, the current investigation offers a thorough analysis of the potential advantages and reasons for employing TDs techniques in different domains, including satellite imaging and deep learning. The aim is to enhance research outcomes by utilizing TDs. The review also identifies unresolved issues and proposes future directions for further investigation in this field. Fundamentally, these proposed open problems will open new grounds to the research community to articulate, innovate, and provide more real-life applications to improve the current state of the art by delving into a wider vision for a higher-level performance of both satellite imaging (SI) and deep learning (DL). Looking at the bigger scenario, this also suggests that TDs could be potentially employed to revolutionize existing machine learning technologies as well as the current space AI industry.

Reconstructing a 3D model of a scene from a set of multiple views poses a significant challenge in the field of computer vision. The advent of NeRF has marked a major breakthrough in this domain. However, there is a need to extend the capabilities of the NeRF model to enable editing tasks such as relighting and deformation, as well as to enhance its training efficiency. Neural reflectance fields introduce the concept of the reflectance equation into the NeRF framework to achieve relighting of the NeRF model. We leverage the TensoRF approach, which incorporates tensor decomposition and employs multiple tensors to store features, to expedite the training process of the NeRF model. Our novel method, called StensorR, combines the reflectance equation and tensor decomposition within the radiation field model framework. Differing from previous approaches, we employ a single tensor to store scene features and render the surface color of our scene using a simplified reflectance equation. This approach accelerates model convergence and enables relighting of the NeRF model. Experimental results demonstrate that our method achieves a 50% faster convergence rate compared to existing relighting radiation field models, while successfully enabling relighting and improving the quality of synthesized images from new viewpoints.

The magnetic polarization tensor has a promising capability of determining the geometry and material properties of metallic samples. In this paper, a novel computation method is proposed to estimate the magnetic polarization tensors for the metallic samples using the boundary element method. In this method, the metallic sample is placed in a uniformly distributed magnetic field. Based on assumptions that the excitation frequency and/or the conductivity of the sample is very high, the metallic sample is regarded as a perfect electrical conductor (PEC). Therefore, the scattered field at a certain distance can be simulated. By utilising the boundary element method, the magnetic polarization tensor can be derived from the simulated scattered field. The theoretical calculation is presented and simulations and experiments have been carried out to validate the proposed method. The results from the simulation are matched with the analytical solution for the case of sphere samples. Moreover, there is a good agreement between the simulation results and the experimental results for the copper cylindrical samples.

Computing the rotation tensor is vital in the analysis of deformable bodies. This paper describes an explicit expression for the SO(3) rotation tensor R of the deformation gradient F, and successfully establishes an intrinsic relation between the exponential mapping Q = exp A and the deformation F. As an application, Truesdell's simple shear deformation is revisited.

The dislocation density tensors of thin elastic shells have been formulated explicitly in terms of the Riemann curvature tensor. The formulation reveals that the dislocation density of the shells is proportional to KA3=2, where K is the Gauss curvature and A is the determinant of metric tensor of the middle surface.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

For personalized recommender systems,matrix factorization and its variants have become mainstream in collaborative filtering.However,the dot product in matrix factorization does not satisfy the triangle inequality and therefore fails to capture fine-grained information. Metric learning-based models have been shown to be better at capturing fine-grained information than matrix factorization. Nevertheless,most of these models only focus on rating data and social information, which are not sufficient for dealing with the challenges of data sparsity. In this paper,we propose a metric learning-based social recommendation model called SRMC.SRMC exploits users' co-occurrence pattern to discover their potentially similar or dissimilar users with symmetric relationships and change their relative positions to achieve better recommendations.Experiments on three public datasets show that our model is more effective than the compared models.

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper we apply the formalism to derive the metric induced by a `static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized is space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

The study of Graviton as Goldstone bosons appeared in the 1960s, after Bjorken interacting idea of Electrodynamics. However, no recent advancement has been done in the field, because of very constraints as well as low-attractiveness of the theory. We do the non-metric tensor (covariant derivative of the metric tensor) case of Gravitation and eventually get SO(1,3) broken in the vacuum state of quantized field theory, then find the Graviton as Goldstone Boson. We, in final, see that Gravitons can have appearances in many modified (and extended) theories of Gravitation.

Imagination is more important than knowledge, but if intellect does not provide the needed logical structures, capacities for envisioning new possibilities are overly constrained. The sustainability problems we face today cannot be solved with the same kind of thinking that created them, but clarity on what counts as a new kind of thinking is sorely lacking. This article proposes methodical, model-based ways of heeding Bateson's warning about the negative consequences for the ecology of mind that follow from ignoring the contexts of relationships. Informed by S. L. Star's sense of boundary objects, a sequence of increasingly complex logical types distinguishes and interconnects qualitatively different kinds of thinking in ways that liberate imaginative new possibilities for life. The economy of thought instantiated at each level of complexity is only as meaningful, useful, beautiful, ethical, and efficient as the standards informing local adaptive improvisations. Standards mediating the general and specific, global and local, universally transcendent and embodied particulars enable meaningful negotiations, agreements, and communications. Attending to the differences between levels of discourse sets up new possibilities for creative and imaginative entrepreneurial approaches to viable, feasible, and desirable goals for measuring and managing sustainable development.

Consider a robot that is navigating in a space modeled by a graph, and that wants to know its current location. It can send a signal to determine how far it is from each landmark among a set of fixed landmarks. We study the problem of computing the minimum required number of landmarks, and where they should be placed so that the robot can always determine its location. Since the problem is an NP-complete problem, the robot's responses to the actions are slow. To accelerate this response, we can use the parallel version of this problem. In this work, we introduce a new parallel implementation for determining the metric dimension of a given graph. We run the proposed algorithm on a symmetric multi-processing (SMP) cluster using C programming language and the Message Passing Interface (MPI) library. Finally, we run our implementation on four categories of graphs (the tracks in which the robot moves): a cycle graph Cn, a path graph Pn, a triangular snake graph and a ladder graph Ln. Preliminary computational results indicate that the metric dimension problem is an NP-complete problem and prove the ability of the proposed algorithm to achieve a speedup of 6 for 8 processors.

The presented work offers a novel process scheme for valorizing historical Pb-Zn slag, which involves crushing, grinding, and then using separation techniques to concentrate valuable components (nonferrous metals). This methodology could have a significant impact on the global beneficiation of metallurgical slags since, in theory, it is significantly more simple, environmentally friendly, and cost-effective than standard pyrometallurgical or hydrometallurgical procedures. According to previous physicochemical and mineralogical studies, Pb-Zn slag from "Topilnica" Veles is a valuable secondary raw material. This inhomogeneous technogenic resource contains substantial amounts of nonferrous metals (Pb, Zn, Cu, and Ag). However, laboratory tests have indicated that the Pb-Zn slag contains a very uneven valuable metals amounts, ranging from several g/ton to several tens of g/ton. The main issue is that traditional metallurgical procedures for releasing beneficial elements are not commercially viable since the valuable elements are "trapped" within amorphous aluminosilicates or intergrowths of alloy grains and glassy phases. Gravity concentration (Wilfley 13 shaking table) and magnetic separation (Davis separator and disk separator) were used to obtain the final concentrate following comminution and grindability testing. The gravity concentration proved more effective. This streamlined approach of valorizing Pb-Zn slag can reduce the need for hazardous chemicals used in hydrometallurgical refinement operations, as well as the extremely high temperatures required for pyrometallurgical processing. This is the first investigation into the feasibility of this novel approach, which includes direct investigations of the Pb-Zn slag feed using these alternative technologies. After extracting the valuable metals, the amorphous aluminosilicate part of the Pb-Zn slag can be reapplied as an alternative raw material in the building sector, adding to the circularity of the suggested approach..

A viable radiation dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of F(R) in the modified theory of gravity, and the metric compatible F(T) together with the symmetric F(Q) in alternative teleparallel theories of gravity from different perspectives, primarily rendering emphasis on a viable FLRW radiation era. Inflation has also been studied for a particular choice of the scalar potential. The inflationary parameters are found to agree appreciably with the recently released observational data.

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity.

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.

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

The recently proposed and logically developed paradigm of deep genetical affinity of scientific terms "energy-entropy-information" harmonizes classical and quantum physics with general and special theories of relativity. For the first time in engineering practice, a complex vector-tensor-matrix description of gravitational, thermal and electromagnetic fields in ideal solid, liquid and gaseous media was performed analytically and without preliminary measurements. The basic set of fundamental quantum constants of the standard physical model has been computed with an extreme precision of 1/10^64, which is a natural limit arising due to elementary recursive arithmetic and elementary functional analysis in digital notation.

It is shown that Verlinde’s hypothetical concepts of entropic gravity can be successfully applied to the author’s previous work on the modification of the Newtonian gravity by Einstein’s Cosmological Constant. It allows a theoretical justification for Milgrom’s empirical acceleration constant, thereby revealing some fundamental differences with Verlinde’s conclusions.

We study a localization of gravity through the matching point between non-inertial frames and local inertial frames. This localization of gravity is done through defining relative gravitational red-shift. This lead to an emergence of a timeless state in a mathematically consistent way. In this timeless state of gravity, we find a geometric interpretation of the speed of light and mass. The experimental support of the timeless state is the quantum entanglement and internal symmetries that are independent of time. Therefore gravity would be responsible for measurements independent of time including quantum entanglement. Timeless state in that sense explain why do we have gravity/gauge correspondence. We conjecture that the universe emerged from a black hole with a global $SU(3)\times SU(2)\times U(1)$ symmetry on its event horizon that produces gauge fields Electromagnetism, weak and strong nuclear force through localization of this global symmetry. Through the localization in the gravity field, the timeless measurements such as spin will be correlated with the varying of timeless measurement which is relative gravitational red-shift. We present a gravitational or geometric interpretation of spin-0, spin-1, and spin-1/2 states. We present an interpretation of why do we measure matter rather than anti-matter. We found that the Higgs scalar field is represented by the gravitational red-shift at every point in the space around the black hole. We derive the numerical value of the cosmological constant that agrees with experimental observations.

The thesis proposes a argument that a mass point moving in a horizontal circle on the Earth’s surface can generate a radial centrifugal force of the Earth’s center of mass, thus realizing an unconventional anti-gravity path. Based on the author’s theory of absolute airspace and its reference system, and through the theoretical analysis of the difference in the distribution of gravitational acceleration at different latitudes caused by the rotation of the earth, and the centrifugal force of a mass point moving in a horizontal circle on the earth’s surface is analyzed, the validity of the argument is demonstrated. At the same time, the paper puts forward two possible basic principles, and makes theoretical analysis and demonstration. Conceive of the concrete experimental verification of principle two is proposed. Four technical schemes for anti-gravity ascent are proposed and basic analysis is made. On the premise of not fully considering the practical technical ability, it is theoretically proved that three of them have realistic operability and development potential. In theory, this paper opens up a different way of anti-gravity for human beings, which will bring new ideas and prospects for human beings to get rid of the bondage of gravity.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

Employing low tensor rank decompositions in image inpainting has attracted increasing attention. This paper exploits a novel tensor-augmentation schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed augmentation schemes enhance the low-rankness of an image under three tensor decompositions: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solve the image inpainting problem with three low-rank con-strained models which use the matrix rank, TT rank, and tubal rank as constrained priors re-spectively. The tensor tubal rank and tensor train multi-rank are developed from t-SVD and TT decomposition respectively. We exploit efficient ADMM algorithms for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and supe-rior to numerous close methods.

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.

In an $m$-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player $k$ in an $m$-person symmetric game is $k$-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the $m$-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

In this work, we discuss a newly proposed scalar-tensor theory in Minkowski spacetime. The basic frame in Minkowski spacetime is obtained. Consider a charged particle in the electromagnetic field, we make an attempt to connect this theory with conventional quantum theory. Two specific models are chosen to calculate values of the time delay.

This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

Radio bursts provide important diagnostics of energetic phenomena of the Sun. In particular, bursts in decimetric and metric wavelengths probe the physical conditions and the energy release processes in the low corona as well as their association with heliospheric phenomena. The advent of spectral radio data with high time and high frequency resolution has provided a wealth of information on phenomena of short duration and narrow bandwidth. Of particular value are spectral data combined with imaging observations at specific frequencies. In this work we briefly review the results of a series of observations comprised from high-sensitivity, low-noise dynamic spectra obtained with the acousto-optic analyzer (SAO) of the ARTEMIS-IV/JLS solar radiospectrograph, in conjunction with high time-resolution images from the Nançay Radioheliograph (NRH). Our studies include fine structures embedded in type IV burst continua (mostly narrow-band "spikes" and intermediate drift "fiber" bursts) and spike-like structures detected near the front of type-II bursts. The implications of the observational results to theoretical models are discussed.

We describe a recently developed approach to quantify welfare loss in animals, the Cumulative Pain metric. It combines the two most relevant dimensions of negative affective experiences: intensity and duration. The metric enables estimating the time individuals spend in negative affective states of a physical or psychological nature (operationally referred to simply as ‘pain’) of different intensities as the result of one or more challenges (e.g., diseases, injuries, deprivations). A new notation protocol (the Pain-Track) is used in which the duration of the experience is represented along the horizontal axis and intensity is represented by four categories in the vertical axis. Pain experiences are partitioned into temporal segments, where hypotheses for the experienced duration and intensity are proposed based on existing welfare indicators (e.g., neurophysiological, behavioral, anatomical, evolutionary). This structure forces transparency about assumptions and uncertainties, highlights knowledge gaps, and enables estimates to be continuously adjusted. Because the Cumulative Pain metric is based on parameters with a broadly common biological meaning, it provides the much needed interoperability among assessments of animal welfare. It enables comparing the impact of practices and living conditions, policies and interventions, and the calculation of welfare footprints of animal-sourced products using a universal measurement unit.

The Lorentz boost and rapidity for a radially falling frame are derived for the Schwarzschild metric in Kruskal-Szekeres coordinates. It is found through this analysis that the spacetime is radially length contracted toward the metric source in the falling frame as a result of the Lorentz boosting relative to the rest frame (which is shown to be consistent with the rest frame). When the falling frame reaches the event horizon, the Lorentz boost goes to infinity, causing the falling frame to become light-like, but trapped at the horizon. It is shown that in the falling frame at the horizon, the density of the source goes to infinity as a result of the length contraction.

Our research is in the tangent space of a point on a 4-dimensional Riemannian manifold. Besides the positive definite metric, the manifold is endowed with a tensor structure of type (1,1), whose fourth power is minus the identity. Both structures are compatible and they define an indefinite metric on the manifold. With the help of the indefinite metric we determine a circle in different 2-planes in the tangent space on the manifold, we also calculate the length and area of the circle. On a smooth closed curve such as a circle, we define a vector force field. Further, we obtain the circulation done by the vector force field along the curve, as well as the flux of the curl of this vector force field across the curve. Finally, we find a relation between these two values, which is an analogue of the well known Green’s formula in the Euclidean space.

In this article we estimate the level of Control of Corruption for 193 countries in the period 2011-2020 using data from the ESG World Bank Database. Various econometric techniques are applied i.e.: Panel Data with Random Effects, Panel Data with Fixed Effects, Pooled OLS, WLS. Results show that “Control of Corruption” is positively associated, among others, to “Government Effectiveness” and “Political Stability and Absence of Violence/Terrorism”, while it is negatively associated among others to “Agriculture, Forestry, and Fishing Value Added as Percentage of GDP” and “GHG Net Emissions/Removals by LUCF”. A cluster analysis implemented with the k-Means algorithm optimized with the Elbow Method shows four clusters. A confrontation among eight Machine Learning algorithms is proposed for the prediction of Control of Corruption. Polynomial Regression is the best predictor for the training data. The level of Control of Corruption is expected to growth by 10.36% on average.

In the following article, the value of the "Knowledge Intensive Services Exports in Europe" in 36 European countries is estimated. The data were analyzed through a set of econometric models or: Poled OLS, Dynamic Panel, Panel Data with Fixed Effects, Panel Data with Random Effects, WLS. The results show that “Knowledge Intensive Services Exports” is negatively associated, among others, with "Buyer Sophistication", "Government Procurement of Advanced Technology Products", and positively associated with the following variables i.e. "Innovation Index", "Sales Impacts" and "Total Entrepreneurial Activity". Then a clusterization with k-Means algorithm was made with the Elbow method. The results show the presence of 3 clusters. A network analysis was later built and 4 complex network structures and three structures with simplified networks were detected. To predict the future trend of the variable, a comparison was made with eight different machine learning algorithms. The results show that prediction with Augmented Data-AD is more efficient than prediction with Original Data-AD with a reduction of the mean of statistical errors equal to 55,94%.