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We study black hole solutions in dilatonic Einstein-Gauss-Bonnet theory with a coupling constant α between the dilaton field and the Gauss-Bonnet term. In a previous study, we considered the black hole with the vanishing cosmological constant in this theory and constructed the hairy black hole solution with the negative α. In this study, we present black hole solutions numerically with various physical properties in anti-de Sitter spacetime. We describe the procedure for constructing the black hole solutions in detail. [ABSTRACT FROM AUTHOR]

The Generalised Space-Time Autoregressive Moving Average-Exogenous (GSTARMA-X) model has been implemented to model spatial time series where the observed values at each location depend not only on the past observed values at neighbouring locations, but also on past values of an exogenous variable at neighbouring locations. Since space time series models involve the value of an observed variable at multiple locations, any such model can be viewed as a vector time series model, which enables the usage of methods commonly utilised to analyse vector time series. In this paper, datasets following a GSTARMA-X (11,11)-(11,11) were generated and analysed by first identifying an appropriate vector ARMA-X (VARMA-X) model for the space-time model, then representing the VARMA-X model as a state-space model. Finally, the state-space model is analysed using the Kalman filter method. The datasets generated fall into either one of three categories: stationary and invertible data, non-invertible but stationary data, and nonstationary but invertible data. The Kalman filter performed significantly better for the nonstationary but invertible data than for any of the other categories, however the Kalman forecasting only performed moderately well for the stationary and invertible data and not so much for the other categories. [ABSTRACT FROM AUTHOR]

Motivated by recent developments in the search of a suitable cosmological model of the universe this paper attempts to find a model representing the early stages of the universe represented by spatially anisotropic space-time Geometry. In this regard exact solution of Einstein's Field equation under different conditions has been analyzed to discuss various aspects of the cosmological model under consideration. It has been observed that the graphical pattern of cosmological parameters satisfies its observational behavior. [ABSTRACT FROM AUTHOR]

This paper deals with a new set of exact solutions obtained by solving non-linear differential equations of Einstein field equation for anisotropic cosmological models representing Bianchi Type V space-time geometry. The active role of dynamical G and Λ with polynomial type growth of scale factor in terms of cosmic time in the expanding universe has been explored. The first section of this paper is devoted to finding non-causal cosmological solutions, whereas in the second section causal cosmological solutions have been obtained. In both sections, cosmological parameters satisfy the observational behavior of the universe. [ABSTRACT FROM AUTHOR]

We have demonstrated that the modified Geroch mass fits the requirements of a good quasi-local mass definition for two-spheres in Reisner-Nordström spacetime after performing some computations using the standard approach. We have also demonstrated that the Riemannian Penrose inequality may be established using the modified Geroch mass. [ABSTRACT FROM AUTHOR]

The Covid-19 pandemic that has occurred in the past two years is still the main topic, especially when this pandemic ends. The essence of the Covid-19 pandemic is the movement of people (as virus carriers) from one place to another. The move allows a location to be interconnected with other locations in the increase in Covid-19 cases. This linkage is a spatial relationship between locations. The same applies to the relationship between time. The main factor is the incubation period of the virus, which causes the increase in cases today to be influenced by cases in the past few days. The two correlations between spatial and time are combined to form the basis for space-time modeling. The model used is the Generalized Space-Time Autoregressive (GSTAR) model, limited to the order of 1:1. The uniqueness of this model is the presence of a weight matrix representing the spatial correlation. In this study, the weight matrix was modified using the Queen Contiguity Weight Matrix, which is based on neighbors directly adjacent or not between locations. The data used in this study is data on positive confirmed cases of Covid-19 per district in three provinces on the island of Java, namely Banten, DKI Jakarta (the state capital), and West Java. The total locations used are 41 districts/cities. The modeling step is to calculate the weight matrix, then estimate the parameters, and finally, the prediction for the following five periods (which is also the primary goal of this study). The results obtained predictive values for 41 districts/cities on June 12-16, 2022. [ABSTRACT FROM AUTHOR]

Close-contact melting phenomena occur when a heated body is in contact with a solid phase-change material. Deter-mining the velocity at which the heat source melts through the solid is fundamental to investigate the process and extrapolate it to operating conditions that cannot be replicated by experiments. Available results in the literature consider a thermo-mechanical equilibrium in the contact film and thus derive a constant melting velocity. In this work we relax this assumption and present a transient contact melting model for a planar heat source. After solving for the heat equation in the solid phase with a space-time finite element approach, the transient heat flux around the heated body is used to compute the time-dependent melting velocity. With the latter we can update the computational domain via a mesh-update method, so that the displacement of the heat source is represented over time. To demonstrate the potential of our approach, we introduce a numerical example with a 2D test case. Afterwards, we show the evolving position of the heat source and we compare the transient melting velocity against the equilibrium estimate. A more complex time-dependent input power is then considered in view of realistic applications. [ABSTRACT FROM AUTHOR]

Time series is a group of observation values obtained at different points in time with the same time interval. In some empirical studies, time-series data often has its complexity. CPI data is time-series data, so it can be modeled using the time-series analysis method. Time series is a series of observations arranged sequentially according to time in a certain period of time-series data, current observations are related to previous observations. Time and location-related (spatiotemporal) modeling for CPI forecasting can be used. GSTAR stands for generalized space-time autoregressive. to improve prediction accuracy, Exogenous variables were added to the GSTAR model to transform it into the GSTARX model. Eid al-Fitr, Eid al-Adha, Christmas, and New Year, which are the results of calendar fluctuations, as well as increasing fuel prices, are exogenous variables included in GSTARX models for CPI forecasting. The case study in GSTARX modeling is applied to CPI forecasting for five cities in Java, namely Yogyakarta, Semarang, Tegal, Surakarta, and Purwokerto. The purpose of this study was to obtain a suitable GSTARX model for forecasting the CPI for 5 cities in Java. The best model for GSTAR and GSTARX is the normalized weight of cross-correlation with MSE 12.9% and RMSE 19.35% [ABSTRACT FROM AUTHOR]

West Kalimantan has the largest peat-land in Kalimantan sland after Central Kalimantan, which is 29.99%. Peat soils in West Kalimantan classified as low-maturity soils; therefore, it is still highly weathered. These could affect the infrastructure sector, especially in planting concrete piles for a building. The planted concrete stakes must reach a layer of soil/rock could be done by drilling, measuring log data, density data, or resistivity data. The data obtained requires considerable time, weather, cost, and energy factors. In addition, reaching a certain depth will take more time, effort, and cost as well. One way to make these factors more efficient is to perform predictive modeling for unmeasured/observable depths. In this article, stochastic modeling is carried out to predict the depth of soil/rock layers based on resistivity data in the West Kalimantan region and interpreted in the description of rock layers. The results obtained that the depth of the peat layer in Pontianak city is up to a depth of 4-5 meters measured from above sea level. This is number obtained from data estimation using the generalized space-time autoregressive (GSTAR) model with kernel Gaussian function. The random variable is represented by the resistivity value, while the time parameter index used is the depth of the soil layer. The results of the root mean square error (RMSE) obtained for locations 1, 2, and 3, respectively, are 12.87, 6.48, and 5.34. This RMSE value is relatively small based on the in-sample data used, it means the model is performing well. With the least-squares method, the parameter estimation is significant and stationary. However, in the residual test, an error is obtained which still has a time correlation. [ABSTRACT FROM AUTHOR]

Research on infectious diseases prediction has become a concern for many researches globally. This is realized because the outbreak of infectious diseases has a negative impact for on the quality of human life, including economic conditions. The aim of prediction of infectious diseases is to maximize preventive action so the large-scale outbreak of infectious diseases could be minimized. Although predicting the diseases is not an easy job, but with more data being collected and the progress of methods, this not impossible to do. In addition, some infectious diseases such as ARI (Acute Respiratory Infection) often occur in certain environmental conditions and certain time. So it has been realized that some occurrences of these diseases are seasonal and also cannot be separated from the condition of time and location. Therefore, in this study we create a model to predict a potential incidence of infectious diseases based on space-time condition using STARIMA (Seasonal Space-Time Autoregressive Moving Average). To evaluate the model we compare the MAE value of STARIMA dan SARIMA model. The result shows that STARIMA model can used to predict the incidence of infectious diseases better than SARIMA model with the MAE value of STARIMA are 28.10% for data testing, 19.34% data training. [ABSTRACT FROM AUTHOR]

The main aim of this work is to give some insights on various aspects of lower dimensional gravity via constructing the consistent cross-couplings that can be introduced in D = 2 spacetimes between a collection of BF models and a set of arbitrary matter fields. We work in a standard QFT ansatz related to space-time locality and other a priori requests on the interaction vertices and perform various cohomological computations based on the local BRST cohomology of the free model. These results are further translated at the level of the overall functional that governs the interacting BF-matter models, known as the deformed solution to the master equation, from which we deduce all the properties and features of the allowed couplings and their underlying gauge algebra. [ABSTRACT FROM AUTHOR]

The Tolman-Bondi-de Sitter metric is a solution to Einstein's field equation which describes the inhomogeneous gravitational collapse in an asymptotically de Sitter spacetime. This paper examines the modification of this metric with the presence of a function f(r, θ) on the radial term, which certainly makes this metric more general. We use Cartan's structure equations to calculate several important aspects namely Riemann tensor, Ricci tensor, Ricci scalar, and Einstein tensor. We analyze two general conditions that arise as a result of two main constraints after analyzing Einstein's field equations. Finally, we also analyze the conditions for the existence of the real singularity of this metric. [ABSTRACT FROM AUTHOR]

The Multivariate Generalized Space-Time Autoregressive (MGSTAR) model is a model that is used to forecast space-time data with several variables in several locations. MGSTAR model has been developed into hybrid MGSTAR-ANN model for non-linear cases and hybrid MGSTARX-RNN model for cases with calendar variation effect. The calendar variation effect is a non-metric exogenous variable. This study aims to propose the MGSTARX model for cases with metric exogenous variables. There are two steps of MGSTARX modeling. The first step is modeling the data that involve exogenous variables using two approaches, i.e., Time Series Regression (TSR) and Transfer Function (TF). Then, the residuals from the first step are modeled using MGSTAR. This study focused on a simulation study to evaluate the goodness of the MGSTARX model. The result shows that the MGSTARX model with the transfer function approach is more accurate and has the smallest RMSE for forecasting the data than the other model. In general, the MGSTARX model with an exogenous variable can improve the accuracy of forecasting. This result is in line with the results of the M5 Accuracy Competition. Further study is needed to expand the MGSTARX model for higher dimensions data and other patterns such as seasonal and non-linear. [ABSTRACT FROM AUTHOR]

Corona Virus Disease 2019 (COVID-19) is a new virus that can be contagious and its worst effects can lead to death. COVID-19 first appeared in Wuhan, China until it finally spread throughout the country, one of which is Indonesia. The spread of COVID-19 cases in Indonesia itself is quite rapid until finally the World Health Organization (WHO) designates COVID-19 cases as pandemics. Based on current conditions, this paper discuss about predict positive case data of COVID-19 at five locations in East Java (Malang City, Batu City, Pasuruan Regency, Malang Regency, Pasuruan City) using a space-time model namely Generalized Space-Time Autoregressive (GSTAR). Considering that COVID-19 is very easy to spread not only depending on the time but also the proximity between locations, the GSTAR method is good enough to be used to predict the assumption of parameters between heterogeneous locations. The estimation used is OLS with the location weight of cross-correlation normalization. The results of this study obtained the GSTAR(21)-OLS model is the best model to predict the number of positive cases of COVID-19 in.five locations in East Java by weighting the normalization of cross-correlation based on the smallest RMSE value in data out sample. Forecast results for the next 10 days of positive cases of COVID-19 in.all five locations show not very significant changes. [ABSTRACT FROM AUTHOR]

In this paper, we study several aspects of modified Hawking mass (MHM) for two-spheres in Schwarzschild and Reissner-Nordström spacetime. Our purpose is to find the MHM value and its critical points and monotonicity in Schwarzschild and Reissner-Nordström spacetime using conventional calculation methods. The calculations show that MHM is equal to M in Schwarzschild spacetime and is not greater than M in Reissner-Nordström spacetime. In addition, we also find that in Schwarzschild spacetime, MHM has a critical point and is monotone increasing. In contrast, in Reissner-Nordström spacetime, MHM has no critical point and is strictly increasing. These results are in line with our expectations. [ABSTRACT FROM AUTHOR]

Consumer Price Index (CPI) is one of the important economic indicators that can provide information regarding the development of the price of goods or services paid by consumers. The rate of change CPI that occurs will reflect the purchasing power of the money people use to meet their daily needs. CPI data collected at several years and cities can be modeled using Generalized Space-Time Autoregressive (GSTAR). GSTAR model has two parameters, namely time series and spatial parameter. The GSTAR parameters values in each location have different values so that this model is more suitable for modeling in several different locations. Determination of spatial weights that indicate the data relationship between locations has an important issue in GSTAR. The purpose of this research is to obtain the best spatial weight of three compared spatial weights in GSTAR models namely normalized cross-correlation, uniform, and inverse distance. CPI data in seven cities in East Java from January 2014 until August 2021 are used in this research. The result shows that normalized cross correlation weight has the smallest value AIC and MSE, respectively 1155,72 and 0,582. This indicates that normalized cross-correlation is the best spatial weight for East Java CPI using GSTAR. [ABSTRACT FROM AUTHOR]

Regular features in plastic-strain macrolocalization are examined at the parabolic stage of strain hardening in the E110, E635 and Zircaloy-2 zirconium alloys. Instability of the plastic flow is observed, which is manifested as a periodic variation of space–time distributions of local strain as revealed by means of speckle interferometry. The data obtained are discussed within the framework of a synergetic model for the plastic flow evolution at the final stage. [ABSTRACT FROM AUTHOR]

The long-term challenges of our time objectively presuppose the response of our society to the need for the development of road transportation due to increasing mobility of modern civilizations. The philosophical outlook of the question implies the study of the spacetime paradigm. It is believed that in modern economic conditions, it is of paramount importance to reduce the time spent on overcoming distances, that is, to accelerate space. [ABSTRACT FROM AUTHOR]

We present new extended Strichartz estimates for the solutions to the heat equation with inhomogeneous nonlinearity in the mass-energy intercritical framework in space dimension d ≥ 1. As an application we show local and global well-posedness in the Strichartz space Lq((0,T); Lr(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the Sobolev space Hσ(ℝd)), with σ ∈ (0, 1]. [ABSTRACT FROM AUTHOR]

We investigate the internal structures of a Schwarzschild black hole by solving the Wheeler-DeWitt equation. The generic bounded wave function has a bouncing point around r ≃ M, where M is the black hole mass. Due to this quantum bouncing, there appears an ambiguity to define the arrow of time. If we introduce two arrows of time, one can then interpret that two classical spacetime is annihilated around the bouncing point. Finally, we provide a conceptual explanation based on the generalized uncertainty principle. [ABSTRACT FROM AUTHOR]

The issues of computation optimization for digital signal processing operations are considered when choosing the variant of their organization in the space-time environment. The implementation of such research is based on the obtained model description of computation organization, which allows us to synthesize a variety of their variants and perform the concurrent exploration of algorithms and architectures. Methods of computation optimization obtained as a result of analyzing parameters characterizing the above model description are discussed. Using these methods in the concurrent exploration of algorithms and architectures allows you to find the best variants for computation organization. [ABSTRACT FROM AUTHOR]

This paper presents a space-time radial basis function approximation of a hyperbolic optimal control problem of harvesting of age-structure population. The hyperbolic optimal control problem is transformed to nonlinear optimisation using semi-discretisation. Then the objective function is optimised by particle swarm optimisation methods. [ABSTRACT FROM AUTHOR]

A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary Lagrangian Eulerian type, which is suitable to work on fixed as well as on moving meshes. In our space-time formulation, by expressing the numerical solution in terms of piecewise space-time polynomials, an arbitrary high order of accuracy in time is achieved through a simple and efficient method of Picard iterations. For the dual mesh, the basis functions consist in the union of continuous piecewise polynomials on the two subtriangles within the quadrilaterals: this allows the construction of a quadrature-free scheme, resulting in a very efficient algorithm. Some numerical examples confirm that the proposed method outperform existing ones. [ABSTRACT FROM AUTHOR]

In this work we study the thermodynamic properties and phase transition of higher dimensional regular Bardeen black hole in AdS spacetime. The black hole thermodynamics is studied using Hawking temperature vs Bekenstein entropy (T - S) plot, which shows a critical behaviour. This is followed by the investigation of the phase transition by observing the divergence of specific heat. The critical behaviour of the blackhole is further analysed in detail via Ruppeiner geometry. The divergence behaviour similar to specific heat is found in Ruppeiner curvature scalar confirms a second order phase transition. [ABSTRACT FROM AUTHOR]

Virtual learning is intended to overcome the problem of the separation of space and time between students and instructors through computer media. Students can obtain learning materials that have been designed in available learning packages. Practicum is a form of scientific evidence of what has been learned. Algorithm and Programming subjects study an algorithm by applying it in the form of Pascal programming. Technology users are used for hybrid learning, through constructive learning through creative, collaborative and reflective virtual compositions. This research applied a learning method approach and verified the usefulness of the initial prototype that was built to support it. The researchers proposed to combine conventional practical lectures and distributed user interfaces to increase the skills of students to follow constructive learning processes. Then, the need to manage challenges that are carried out to collaborate with a distributed approach is also discussed. [ABSTRACT FROM AUTHOR]

This research is stressed at time and space characteristics (centre of gravity movements) in female pole vault. Kinetic parameters were gained by two-dimension analyser Consport Motion Analysis System (CMAS). There are involved 19 female pole vault jumpers with sport performance 380 - 483 cm, divided on 2 different groups; higher and lower level from the point of sport performance. We found that in time parameters reached better results high performance level jumpers in phases hanging and lifting. It is coursed by better transmission on pole after take-off and by better work on the pole. As for the centre of gravity the jumpers of higher performance reached higher growth in all phases. The most significant difference can be seen in phase of lifting. Comparison of time and space characteristics enable to show the way for technique improvement in female pole-vault. [ABSTRACT FROM AUTHOR]

In the multi rope diamond beaded rope saw sawing process the vibration characteristics play a key role insofar for reliability and processing quality. The dynamic model of diamond beaded rope was established by using Hamilton's principle. The influences of the parameters, such as the tension force of diamond beaded rope, its position in diamond beaded rope, on the vibration characteristics of diamond beaded rope were studied and the effectiveness of the designed control scheme is verified by numerical simulation analysis. The results show that the Vibration displacement deformation of diamond beads rope present a fluctuating phenomenon, which is mainly due to the impact force produced by diamond beads in time and space is time-varying, and the maximum lateral vibration deformation of the first beaded rope decreased from 9.198mm to 4.6755mm, the vibration deformation of the first beaded rope decreases by 31.438% on average, and the maximum deformation of the transverse vibration of the beaded rope in the third segment is also reduced, the average amplitude was reduced by 15.89%. [ABSTRACT FROM AUTHOR]

In this paper, B-Spline Alternating Group Explicit (BSPAGE) iterative method is proposed to solve one dimensional diffusion equation which is the heat conduction equation. The Alternating Group Explicit (AGE) iterative method is derived from the cubic B-Spline collocation technique called BSPAGE iterative method. We only consider the stationary case with odd number of points with even number of interval for both time and space dimension. The comparison will be made based on AGE iterative method, Spline Alternating Group Explicit (SPAGE) iterative method, BSPAGE iterative method and the exact solution. BSPAGE is more accurate and converges faster than AGE and SPAGE. [ABSTRACT FROM AUTHOR]

In this study, we examine cylindrically symmetric domain wall distributions in the context of unimodular f(R) gravity. We use unimodular and static cylindrically symmetric spacetime. Field equations and their solutions for the spacetime and the matter are considered. It is shown that unimodular f(R) gravity allows to static cylindrically symmetric spacetime geometry independent from domain wall tension. Other properties of the model are also discussed. [ABSTRACT FROM AUTHOR]

The paper presents the creation of a general mathematical model of a two-step optimization problem which finds the most-safer route of an electric-bicycle cyclist. The first step is a multi-criteria problem which finds the average risk in the different segments which forms the complete route. To solve the problem, a scalarization method is used (also known as weighted sum method). In the second step, the safer route is found by applying a network optimization model. To find the solution a method for dynamic optimization is applied (Bellman's Principle). The generation of data is based on the a priori known information as well as on information which is periodic and stochastic in the time and space. [ABSTRACT FROM AUTHOR]

The paper presents the creation of a general mathematical model of a two-step optimization problem which finds the most energy efficient route where the battery and the electric engine of an electric-bicycle are used to minimum. In the first step, a multi-criteria problem is solved which finds the most efficient mode of operation of the battery and the engine in every segment part of the complete route. To solve this task a scalarization method is used (also known as weighted sum method). In the second step, a common most efficient route is found by applying a network optimization model. To find the solution a method of dynamic optimization is used - Bellman's Principle. The major part of the paper is dedicated to the mathematical models, the approaches and the demonstration of the models’ workability. For this reason, the generation of data is based on the a priori known information as well as on information which is periodic and stochastic in the time and space. [ABSTRACT FROM AUTHOR]

The abstract Cauchy problem for the space-time fractional evolution equation is considered, which contains the Caputo time-derivative of order β ∈ (0, 1) and the operator −Aα, α ∈ (0, 1), where −A generates a strongly continuous one-parameter semigroup on a Banach space. The analyticity of the solution operator is studied by applying subordination principles for space- and time-fractional evolution equations and taking into account the asymptotic behavior of the subordination kernels, expressed in terms of Lévy extremal stable densities and Mainardi function. [ABSTRACT FROM AUTHOR]

We consider a deformed version of four-dimensional de Sitter spacetime. The setup consist of two (antipodal) disconnected Rindler observers, each one with an S4 topology. We show that the two observers have an entanglement entropy, in the low energy sector, given by a quarter of the area of a pair minimal surfaces, that corresponds to the set of fixed points of an ℤq orbifold. The result matches with the Gibbons–Hawking entropy when we restrict the ℤq action to a single Rindler wedge. [ABSTRACT FROM AUTHOR]

Our universe has full of mysteries. The universe is actually an encoded form of information. The universe is a universal language expressing itself. The misery is that the mysteries cannot be easily decoded to understand the laws governing the behavior of the universe. Some parameters are explicit in the universe and they can decode the whole universe. For example, space and time can be treated as the necessary conditions of the universe while mass and energy can be regarded as the sufficient conditions of the universe. All we need to find how to relate all four parameters. This paper will discuss that we can transform any of the four conditions into the rest of the other conditions. The speed is a parameter that relates space with time. The Einstein’s mass – energy equivalence condition can help in the transformation. I will show a space – time – mass – energy matrix can be regarded as mathematical formulation of the transformation. [ABSTRACT FROM AUTHOR]

The method of phase space reconstruction by the time characteristics of biomedical signals is described. It is shown that the Poincaré plot contains useful information related to the presence of nonlinear components in the process under study. The method of analyzing a sequence of ECG cardiocycles is proposed in order to diagnose several types of arrhythmias. During experiments on a sample of real ECG signals, it was established, that the Poincaré mapping allows one to obtain additional information on the dynamics of the behavior of the time series and, due to this, it is more efficient to solve the problems of classifying states in health and pathology. [ABSTRACT FROM AUTHOR]

In this paper, Extended B-Spline Alternating Group Explicit (ExtBSPAGE) iterative method is proposed to solve one-dimensional diffusion equation which is the heat conduction equation. The Alternating Group Explicit (AGE) iterative method is derived from the cubic Extended B-Spline collocation technique. We only consider the stationary case with odd number of points with even number of interval for both time and space dimension. The comparison will be made based on AGE, Cubic B-Spline Alternating Group Explicit (BSPAGE), ExtBSPAGE iterative method and the exact solution. [ABSTRACT FROM AUTHOR]

The article deals with a novel genre of the virtual discourse – a letter to the future. Openness, non-linearity, hypertextuality, polydiscoursive and rhizomatic nature of virtual discourse allow Internet users to overcome time and space limitations and dissipate their personality into “Present Me” and “Future Me”. Positioning himself in different spatio-temporal data, a writer constructs a dialogue between them. The most effective tools for dialogization of the narrative are question-answer unities. The functions of questions “here and now” when “Present Me” exteriorizes his inner speech in the letter are self-reflective, self-regulative and emotive. Request for information, i.e., truly interrogative function will be realized in future, when “Future Me” will loop the communication chain. [ABSTRACT FROM AUTHOR]

The split-step modified cubic B-splines collocation (SSM3BC) method is constructed by combining the split-step approach with the modified cubic B-splines collocation method for the two-dimensional (2D) nonlinear Schrödinger (NLS) equation. Numerical tests are carried out, and the SSM3BC schemes are efficient both for the one-dimensional (1D) and 2D NLS equations. It is also numerically verified that the proposed 1D and 2D schemes are second-order convergence both in time and space. [ABSTRACT FROM AUTHOR]

We compute the vacuum polarization energies for a couple of soliton models in one space and one time dimensions. These solitons are mappings that connect different degenerate vacua. From the considered sample solitons we conjecture that the vacuum polarization contribution to the total energy leads to instabilities whenever degenerate vacua with different curvatures in field space are accessible to the soliton. [ABSTRACT FROM AUTHOR]

In this paper we review the problem of numerically solving the relativistic Euler gas dynamic equations, comparing results obtained from Riemann free methods and Approximate Riemann Solvers, namely the FORCE and TVD-SLIC methods in the former case and the Flux Vector Splitting and HLL methods in the latter. The test cases of the weak and strong blast waves are considered in rectangular Minkowski, spherical Minkowski and Schwarzschild space-times. Results for each numerical method are reported and compared. [ABSTRACT FROM AUTHOR]

Orbital torus is a spatial figure formed by an elliptical orbit of a small body in a coordinate system rotating around a central body. The conception of orbital tori was introduced by the author about 35 years ago choosing high-apogee orbits of artificial Earth satellites (AES) to study near-Earth space. In this paper, is investigated the evolution of orbital tori in space and time under the influence of external gravitational perturbations. These studies based on qualitative perturbation theory methods developed in the Lidov-Kozai theory (TLK). At the same time, to study the evolution of orbital tori, numerical integration of orbits carried out taking into account various perturbing factors, and TLK used to understand the essence and description of the character of the evolution of orbits and orbital tori. As an illustration of these studies, the evolution of near-Earth orbital tori under the influence of external gravitational perturbations from the Moon and the Sun is used. It shown that the Moon has a more effective influence on the evolution of orbits and orbital tori than the Sun, and the precession of the Moon’s orbit changes the character of the evolution of orbits and orbital tori. [ABSTRACT FROM AUTHOR]

This work explores the correlations of modern physics and the (Orthodox Christian) theology, through the analysis of space and light. In modern physics, the space we think we occupy is nothing but constant repulsion of point-like particles. "Space" tends to concepts such as separation - demarcation, distance - range, space - dimension. While light with bosonic nature tends to gather and unite instead of separate, it "lives" out of time and space instead of decay and isolation. On the other hand, Theology teaches that selfishness is what separates us, separate will that holds us in distance, sin that depart us from our original destination. The proposition: co-space, co-fit, co-placement (forgiveness, “sin-horesi” in Greek) and love that is union, coupling, and leads to salvation (hold in one unit, “sotiria” in Greek), which tends to keep man as one unit through reunion with the Creator. In this sense, the characteristics of light in physics described above are correlated. [ABSTRACT FROM AUTHOR]

Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the classical approximation. Matching picture for the observable algebra as the corresponding representation of the group C∗-algebra, describes the full dynamical pictures equally successfully. Extension of the scheme to a Lorentz covariant setting and beyond will also be addressed. The formulation of quantum mechanics allows the theory to be seen in a new picture in line with the notion of a noncommutative spacetime. [ABSTRACT FROM AUTHOR]

We present the unification of Theories of Physics (TPs) with real or infinite Universal Speed, such as Newtonian Physics (NPs) and Einstein Relativity Theory (ERT). This is achieved, by using isometric Euclidean Closed Linear Transformations of Complex Spacetime (ECLSTTs) endowed with the corresponding Metrics and the Generalized Real Boost (GRB), which maintain the formalism of ERT. We also produce generalized Maxwell equations, covariant under the ECLSTTs and GRB. Thus, we obtain results, which contain the fundamental parameter ξI= sqrt(-gI11/gI00) of TPs, where gI=diag(gI00, gI11, gI11, gI11) is the spacetime metric of the Relativistic Inertial Observers (RIOs). We then pass to General Relativity, defining the 1st Generalized Schwarzschild metric (1GSM), in accordance with Einstein field equations for any TPs. We compute the corresponding Lagrangian, equations of motion, precession of planets‟ orbits etc. The experimental data of our Solar system, produce a valid value of ξI. Besides the unification of TPs give us the capability of modifying objects of one TPs (such as NPs with ξI=0) in order to be used in another TPs (such as ERT with ξI=1). Thus the 2nd Generalized Schwarzschild Metric (2GSM) allows us to transform the metric-gravitation of Modified Newtonian Dynamics (MOND) to the corresponding of ERT. This explains the rotation curves in galaxies and solar systems, eliminating Dark Matter. Finally we pass to Microcosmos, combining GRB with Quantum-Mechanics. Thus we obtain valid value of ξI on Earth, by using the energies of fine structure peaks of the atomic hydrogen spectrum. [ABSTRACT FROM AUTHOR]

We present a detailed analysis of the thermodynamics of black holes in flat spacetime with Eddington inspired Born-Infeld theory of gravity. The thermodynamic properties are obtained through the surface gravity method that is well known in black hole mechanics. We analyse the stability of the black holes configuration through the property of its specific heat. It is found that electrically charged black holes in EiBI gravity are unstable, and this may be related to the thermodynamic instability of flat spacetime itself. [ABSTRACT FROM AUTHOR]

The self-similar crystallization is described by the scaling relation between the space (ξ) and time (t) variables: ξ/√t. In this paper, we discuss this process with a mushy layer and consider some power dependencies for the parabolic growth rate constant, solid fraction and solute concentration. [ABSTRACT FROM AUTHOR]

In this paper, we present the main ideas of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metrics (ECLTCSCMs), which unify Theories of Physics (TPs), such as Newtonian physics (NPs) etc, keeping Einstein Relativity Theory's (ERT's) formalism. Thus, we may obtain physical results, which contain a Fundamental Parameter (ωI), depending on the spacetime metrics of the Relativistic Inertial Observers (RIOs) of each specific TPs. This unification give us the capability of modifying objects of one TPs (like NPs) in order to be used in another TPs (like ERT). For example, we begin from the metric-gravitation of Modified Newtonian Dynamics (MOND) and we obtain a new metric-gravitation which is in accordance with ERT. This application to Megacosmos, explains the rotation curves in galaxies and solar systems, eliminating Dark Matter. Besides, the specific value ωI=±i gives Vossos transformation (VT) endowed with Lorentz metric of complex spacetime and invariant spacetime interval (or equivalently invariant speed of light in vacuum), producing the theory of Euclidean Complex Relativistic Mechanics (ECRMs) which is associated with ERT. Applying the aforementioned theory to Microcosmos, we calculate the position of the fine structure peaks of the atomic hydrogen spectrum. The result is better not only than this extracted using P. Dirac theory, but also than that of L. H. Thomas method. [ABSTRACT FROM AUTHOR]

To deal with the variation and correlation structure of accident data along with recognized covariate effects, we develop a spatio-temporal model for multivariate accident count data. Based on the multivariate Poisson lognormal model, we introduce linear combinations of random impulses to capture spatial correlation. For temporal effects, the lagged observations are added to this model. Model estimation is carried out using Markov Chain Monte Carlo methods. Simulated data sets are used in assessing the performance of this model. An advantage of this new model is that it not only copes with three sources of variations; time, space and multivariate data variations, but also provides information on time and space dependency. The model is also capable of providing an improvement in the accuracy of count data modelling. [ABSTRACT FROM AUTHOR]

We summarize some applications of big bang nucleosythesis (BBN) and the cosmic microwave background (CMB) to constrain the first moments of the creation of matter in the universe. We review the basic elements of BBN and how it constraints physics of the radiation-dominated epoch. In particular, how the existence of higher dimensions impacts the cosmic expansion through the projection of curvature from the higher dimension in the "dark radiation" term. We summarize current constraints from BBN and the CMB on this brane-world dark radiation term. At the same time, the existence of extra dimensions during the earlier inflation impacts the tensor to scalar ratio and the running spectral index as measured in the CMB. We summarize how the constraints on inflation shift when embedded in higher dimensions. Finally, one expects that the universe was born out of a complicated multiverse landscape near the Planck time. In these moments the energy scale of superstrings was obtainable during the early moments of chaotic inflation. We summarize the quest for cosmological evidence of the birth of space-time out of the string theory landscape. We will explore the possibility that a superstring excitations may have made itself known via a coupling to the field of inflation. This may have left an imprint of "dips" in the power spectrum of temperature fluctuations in the cosmic microwave background. The identification of this particle as a superstring is possible because there may be evidence for different oscillator states of the same superstring that appear on different scales on the sky. It will be shown that from this imprint one can deduce the mass, number of oscillations, and coupling constant for the superstring. Although the evidence is marginal, this may constitute the first observation of a superstring in Nature. [ABSTRACT FROM AUTHOR]

The nonlinear partial differential equations have an important role in real life problems. To obtain the exact solutions of the nonlinear partial differential equations, a number of approximate methods are known in the literature. In this work, a time-space modulated nonlinearities of coupled Schrödinger equations are considered. We provide a large class of Jacobi-elliptic solutions via the auxiliary equation method with sixth order nonlinearity and the Chebyshev approximation. [ABSTRACT FROM AUTHOR]