The Conservation of Energy Space-Time Metric for Space Outside Matter

By using experimentally determined measurements of potential energy together with the principle of conservation of energy and solving directly, the space-time geometry equation for space outside matter is obtained. That equation fits all the experimental observations that support the accepted Schwarzschild metric, yet predicts there isn’t a singularity at the Schwarzschild radius. The accepted Schwarzschild metric is the first approximation of the conservation of energy space-time metric. No observation yet made can distinguish between the predictions of the two metrics.

Robust Space-Time Adaptive Track-Before-Detect Algorithm Based on Persymmetry and Symmetric Spectrum

Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.

Curved Space-Time at the Planck Scale

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

Three Dimensional Space-Time Gravitational Metric, 3 Space + 3 Time Dimensions

We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional space-time, that is, three space dimensions and three time-dimensions, so some would call it six-dimensional. However, we have shown that collision-time and collision-length (space) are just two different sides of the same “coin” (space-time), so it is more intuitive to think of them as 3-dimensional space-time. In previous papers, we have not laid out a geometric coordinate system for our theory that also considers gravity, but we will do that here. We are pointing out that Einstein’s negative attitude towards relativistic mass can perhaps cause a weakness in the foundation of general relativity theory. When a relativistic mass is incorporated in the theory, this mass also seems to indicate one needs to move to three-dimensional space-time. Then, for example, our new theory matches fully up with all the properties of the Planck scale in relation to the mathematical properties of micro black holes, not only mathematically but also logically, something we demonstrate clearly that it is not the case of general relativity theory. Our new metric has many benefits as an alternative to the Schwarzschild metric and general relativity theory. It seems to be more consistent with the Planck units than the Schwarzschild metric. Most importantly, it seems to be fully consistent with a new quantum gravity theory that seems to unify gravity with quantum mechanics.

Coulomb Force, Charge, and Electric Properties under Collision Space-Time

We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.

On the Metric of Space-Time

Maxwell’s equations are obeyed in a one-parameter group of isotropic gravity-free flat space-times whose metric depends upon the value of the group parameter. An experimental determination of this value has been proposed. If it is zero, the metric is Minkowski’s. If it is non-zero, the metric is not Poincare invariant and local frequencies of electromagnetic waves change as they propagate. If the group parameter is positive, velocity-independent red-shifts develop and the group parameter play a role similar to that of Hubble’s constant in determining the relation of these red-shifts to propagation distance. In the resulting space-times, the velocity-dependence of red shifts is a function of propagation distance. If 2c times the group parameter and Hubble’s constant have approximately the same value, observed frequency shifts in radiation received from stellar sources can imply source velocities quite different from those implied in Minkowski space. Electromagnetic waves received from bodies in galactic Kepler orbits undergo frequency shifts which are indistinguishable from shifts currently attributed to dark matter and dark energy in Minkowski space, or to a non-Newtonian physics.

Rock Mass Quality Rating Based on the Multi-Criteria Grey Metric Space

Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality.

Principal Equatorial Null Geodesic Congruences in the Kerr Metric, and Their Quantum Propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.

Using Cross Entropy as a Performance Metric for Quantifying Uncertainty in DNN Image Classifiers: An Application to Classification of Lung Cancer on CT Images

Cross entropy is a measure in machine learning and deep learning that assesses the difference between predicted and actual probability distributions. In this study, we propose cross entropy as a performance evaluation metric for image classifier models and apply it to the CT image classification of lung cancer. A convolutional neural network is employed as the deep neural network (DNN) image classifier, with the residual network (ResNet) 50 chosen as the DNN archi-tecture. The image data used comprise a lung CT image set. Two classification models are built from datasets with varying amounts of data, and lung cancer is categorized into four classes using 10-fold cross-validation. Furthermore, we employ t-distributed stochastic neighbor embedding to visually explain the data distribution after classification. Experimental results demonstrate that cross en-tropy is a highly useful metric for evaluating the reliability of image classifier models. It is noted that for a more comprehensive evaluation of model perfor-mance, combining with other evaluation metrics is considered essential. .

Failure to Rescue as a Quality Metric in Congenital Heart Surgeries in a High-Complexity Service Provider Institution Located in a Middle-Income Country

Background:Failure to rescue has been an effective quality metric in congenital heart surgery.Conversely,mor-bidity and mortality depend greatly on non-modifiable individual factors and have a weak correlation with better-quality performance.We aim to measure the complications,mortality,and risk factors in pediatric patients undergoing congenital heart surgery in a high-complexity institution located in a middle-income country and compare it with other institutions that have conducted a similar study.Methods:A retrospective observational study was conducted in a high-complexity service provider institution,in Cali,Colombia.All pediatric patients undergoing any congenital heart surgery between 2019 and 2022 were included.The main outcomes evaluated in the study were complication,mortality,and failure to rescue rate.Univariate and multivariate logistic regression analysis was performed with mortality as the outcome variable.Results:We evaluated 308 congenital heart sur-geries.Regarding the outcomes,201(65%)complications occurred,23(7.5%)patients died,and the FTR of the entire cohort was 11.4%.The presence of a postoperative complication(OR 14.88,CI 3.06–268.37,p=0.009),age(OR 0.79,CI 0.57–0.96,p=0.068),and urgent/emergent surgery(OR 8.14,CI 2.97–28.66,p<0.001)were the most significant variables in predicting mortality.Conclusions:Failure to rescue is an effective and comparable quality measure in healthcare institutions and is the major contributor to postoperative mortality in congenital heart surgeries.Despite our higher mortality and complication rate,we obtained a comparable failure to rescue rate to high-income countries’health institutions.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.

A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

FLAT SUPERSYMMETRIC SPACE-TIME AND THE THEORY OF SUPER FIELDS

Flat supersymmetric space-time (x, θ) has been discussed under assumption that the Fermi variables are symplectic vectors only. We have abandoned the traditional assumption, that it must be the spinor representation of Lorentz group, which makes in the usual theory of supersymmetry.The even and odd generators of the ortho-symplectic group OS_p(414) have been calculated concretely in its dyads representation.New superfields, Lagrangian and the action integral, different from the usual theory, have been introduced in this flat case.

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

基于space-time的二叉树表示动态环境中的路径规划

研究具有空间和时间的三维动态环境下的机器人路径规划分析了四叉树表示二维空间的搜索算法,在此基础上,提出采space-time,用二叉树表示二维空间的方法时间信息中增加加速度利用二叉树遍历方法和算法设计一个在动态障碍物环境下进行路径规划的新算法并,,A*,,在足球机器人系统中进行仿真,实现了较好的路径规划。