We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH₀ and dc/dt = 1.8cH₀ with H₀ as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH₀. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G.

Many models have been proposed to explain the intergalactic redshift using different observational data and different criteria for the goodness-of-fit of a model to the data. The purpose of this paper is to examine several suggested models using the same supernovae Ia data and gamma-ray burst (GRB) data with the same goodness-of-fit criterion and weigh them against the standard $\text{Λ}$ CDM model. We have used the redshift – distance modulus ( $z-\mu$ ) data for 580 supernovae Ia with $0.015\le z\le 1.414$ to determine the parameters for each model, and then use these model parameter to see how each model fits the sole SNe Ia data at $z=1.914$ and the GRB data up to $z=8.1$ . For the goodness-of-fit criterion, we have used the chi-square probability determined from the weighted least square sum through non-linear regression fit to the data relative to the values predicted by each model. We find that the standard ΛCDM model gives the highest chi-square probability in all cases albeit with a rather small margin over the next best model - the recently introduced nonadiabatic Einstein de Sitter model. We have made ( $z-\mu$ ) projections up to $z=1096$ for the best four models. The best two models differ in $\mu$ only by 0.328 at $z=1096$ , a tiny fraction of the measurement errors that are in the high redshift datasets.

Analyses of the Hubble diagrams are presented for SN1a supernovae and gamma ray bursts in the redshift ranges z = 0.01–1.3 and 0.034–8.1, respectively. Data are presented on the typical z/μ scale and also on the less common yet increasingly sensitive photon flight time t/(z+1) scale. The primary conclusion is that on the basis of the presently accessible data in the redshift range z = 0.01–8.1, the slope of the Hubble diagram is, or is extremely close to, exponential.

Hubble diagrams are examined for SN1a supernovae in the redshift range z = 0.01–1.3 and for gamma ray bursts in the range z = 0.034–8.1. It is shown that in the low redshift range, the Hubble diagram shows an innate equivocality between the ΛCDM and the tired light model. This means that the strong agreement between the z/µ data, calculated with the parameters of the ΛCDM model, and the experimentally measured z/µ values cannot be considered as definite evidence for the expansion hypothesis. The exponential function , which is characteristic of the tired light redshift mechanism, fits the data with similarly high accuracy. Hence, on the premise of low redshift data, a decision for or against either model is completely arbitrary. The Hubble diagram for high redshift gamma ray bursts shows poor agreement with the ΛCDM model, but concurs with the exponential energy decay following from the tired light redshift hypothesis.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

The weighted K-nearest neighbors (WKNN) algorithm has been widely used in indoor fingerprint localization, which utilizes fingerprint distance (FD) of pairwise positions to discriminate the physical distance (PD) between them. However, due to the varied states of different wireless access points (APs), their contribution to FD discrimination capability varies. In our study, we analyzed several critical causes that affect APs’ contribution, including AP’s health state, the distance, and the direction between APs and position pairs. Inspired by these insights, a threshold was set for all sample RSS to eliminate the impact of abnormal APs on FD, and a correction quantity for each RSS was provided by the distance between APs and sample positions to reduce the strong signal influence on FD. Furthermore, a priority weight was designed by RSS differences (RSSD) to further optimize FD’s capability to discriminate PD. Integrating the above policies, a new indoor fingerprint localization technique is redefined, referred to FD’s discrimination capability improvement WKNN (FDDC-WKNN), which is suitable for indoor scenes with a large number of APs that are not uniformly managed. Our simulation results show that the correlation and consistency between FD and PD are well improved, with strong correlation increasing from 0 to 76% and high consistency increasing from 26% to 99%, which confirms that the proposed policies can greatly enhance FD’s discrimination capabilities to PD, and we also found that abnormal APs can cause significant impact on FDs’ discrimination Capability. Further, by implementing the FDDC-WKNN algorithm in experiments, we obtained the optimal K value in both the simulation scene and real library scene, under which the average localization errors have been reduced from 2.2732m to 1.2183m and from 3.4295m to 2.2068m, respectively. In addition, compared to not using the FDDC-WKNN, the cumulative distribution function (CDF) of the localization errors curve converged faster and the errors fluctuation is smaller, which demonstrate FDDC-WKNN having stronger robustness and more stable localization performance to the state of APs in indoor environments.

Integral atmospheric dispersion models are used widely for flammable hazard and its risk analysis. There is a widespread belief that flammable distances from these models are conservative when flammable ranges are calculated using the 0.5 lower flammability limits (LFL) concentration threshold. This is erroneous. This paper traces through the development of these models and the research that led to the Birch Guidance. It shows that the 0.5 LFL is a necessary factor to transform the results of dispersion models designed for environmental assessment to applications to flammable hazard assessment in quiescent conditions. Current applications do not take account of turbulence due to wind, large and small obstructions, etc. A set of simple guidance is given in the paper to manage flammable hazards based on results from atmospheric dispersion models, including topics for future research.

Based on historical facts, revisited from a present-day perspective, and on the documented opinions of the scientists involved in the discovery themselves, strong arguments are given in favor of a proposal to include prominent astronomer Vesto Slipher to the suggested addition of Georges Lemaître's name to Hubble's law on the expansion of the Universe, and thus eventually call it Hubble-Lemaître-Slipher's (HLS) law.

This paper aims at providing a multisource data analysis, including direct data collection, focussed on daily average distances covered with motorised mobility. Its results can be used as a basis for policies involving a shift towards new propulsions, electric motors or hybrid electric vehicles (HEV) for road vehicles. A number of variables influence the propensity of drivers to acquire or use electric traction, even the option of plug-in hybrid electric vehicles (PHEV). This paper addresses one of such variable: the compliancy of electric traction regarding both hybrid plug-in solutions and full-electric vehicles, in addition to the autonomy of batteries (range), with the daily travels by road vehicles, mainly by automobiles. We want to understand whether the constraints leading towards a greater independence from crude oil rather than constraints concerning emissions, mainly in urban contexts, might be compliant with the habitual daily trips of drivers. We also want to understand if these daily trips have varied much during recent years and the consequences they may have on operational costs of plug-in automobiles. We are well aware that the average distances do not represent the actual daily runs of vehicles; yet similar distributions of daily distances for different case studies indicate that a high percentage of trips respond to certain features. After introducing a general overview of road-motorised mobility in Italy, the paper compares data from other studies to provide an indication of average daily driving distances. This reveals how different recent analyses converge on a limited range of average road distances covered daily by Italians, which is compliant with ranges allowed by electric batteries, provided that their low energy density in comparison with that of oil-derived fuels do not imply a significant increase in vehicle mass. Subsequently, average distances in some EU Countries are taken from the literature, and the results are also compared with U.S. data. The study extends the analysis of trends on the use of automobiles and road-vehicles to the international context by also addressing average daily distances covered for freight transport in some EU Countries, thereby providing a further basis for comparison and for understanding whether the daily motorised mobility can be considered as a stable phenomenon. Finally, an analysis is provided of the economic operational advantages from using plug-in vehicles. The main aim of this paper is thereafter to investigate the average daily motorised mobility of single vehicles – so not an aggregated motorised mobility as collected by some statistics – by using private motorised vehicles in Italy, with related trends; thereafter, to compare these data with those obtained from other countries, making use of both existing research studies and directly collected data; the final aim is to understand both the compliance of daily activities based on the use of automobiles with the autonomy of batteries (range) and to calculate some economic outcomes.

We have shown that our varying physical constant model is consistent with the recently published variational approach wherein Einstein equations are modified to include the variation of the speed of light c, gravitational constant G and cosmological constant Λ using the Einstein-Hilbert action. The general constraint resulting from satisfying the local conservation laws and contracted Bianchi identities provides the freedom to choose the form of the variation of the constants as well as how their variations are related. When we choose dG/Gdt=3dc/cdt, ̇the same as in our quasi-phenomenological model, c=c₀ exp⁡(a^α-1), G=G₀ exp⁡[3(a^α-1)] and Λ=Λ₀ exp⁡[(a^-α-1)], where a is the scale factor and α=1.8, we are able to confirm the success of our the model in explaining three astrometric anomalies and the null results on the variation of G and the fine structure constant. We show that the model: (a) fits the supernovae 1a observational data better than the ΛCDM model; (b) determines the first peak in the power spectrum of the cosmic microwave background temperature anisotropies at multipole value of l=217.3; (c) calculates the age of the universe as 14.1 Gyr; and (d) finds the BAO acoustic scale to be 145.2 Mpc. These numbers are within less than 3% percent of the observed values and the values obtained by the ΛCDM model. Surprisingly we find that the dark-energy density is negative in a universe that has significant negative curvature and whose expansion is accelerating at a faster rate than predicted by the ΛCDM model.