Multiverse/Hyperverse Models: (4 + 1)-Dimensional Landscape (Black Saturns, Bousso-Hawking Nucleation, Gogberashvili Multiverses, Schwarzschild-De Sitter Nurseries) and a (3 + 1)-Dimensional Model for Dark Energy

We consider the Hyperverse as a collection of multiverses in a (4 + 1)-dimensional spacetime with gravitational constant G. Multiverses in our model are bouquets of thin shells (with synchronized intrinsic times). If gis the gravitational constant of a shell Sand εits thickness, then G~εg. The physical universe is supposed to be one of those thin shells inside the local bouquet called Local Multiverse. Other remarkable objects of the Hyperverse are supposed to be black holes, black lenses, black rings and (generalized) Black Saturns. In addition, Schwarzschild-de Sitter multiversal nurseries can be hidden inside those Black Saturns, leading to their Bousso-Hawking nucleation. It also suggests that black holes in our physical universe might harbor embedded (2 + 1)-dimensional multiverses. This is compatible with outstanding ideas and results of Bekenstein, Hawking-Vaz and Corda about “black holes as atoms” and the condensation of matter on “apparent horizons”. It allows us to formulate conjecture 12.1 about the origin of the Local Multiverse. As an alternative model, we examine spacetime warping of our universe by external universes. It gives data for the accelerated expansion and the cosmological constant Λ, which are in agreement with observation, thus opening a possibility for verification of the multiverse model.

Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

Diagnostic Performance and Inter-Observer Agreement of 4-Dimensional Computed Tomography Parathyroid Scans in Patients with Primary and Secondary Hyperparathyroidism

Background: 4D-CT has been used to localize the parathyroid adenomas and hyperplasia since 2006 as a second line study after TC-99 m MIBI and ultrasonography. However, multiple studies have shown that 4D-CT is a robust imaging method with high diagnostic accuracy, becoming increasingly popular among surgeons and radiologists. Purpose: To assess the diagnostic performance of 4D-CT scans to identify the pathologic gland(s), using pathology and intraoperative findings as gold standards. Methods: We analyzed patients with primary and secondary hyperparathyroidism who had intraoperative reports, pathology, parathyroid hormone levels, and preoperative 4D-CT. Histology, surgical findings, and decreased parathyroid hormone levels were used as gold standards. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), accuracy and 95% confidence interval were calculated. Fleiss’ kappa was used to assess the inter-observer agreement. Results: Sixty-seven patients were included. Sixty-two patients had a single adenoma, and five patients had a multiple gland disease (adenomas or hyperplasia). A total of 72 glands were proven to have parathyroid adenomas or hyperplasia. The sensitivity, specificity, PPV, NPV and accuracy are 85%, 97%, 96%, 87% and 91% for lateralization and 76%, 96%, 85%, 92% and 90% for quadrant localization, respectively in single-gland disease. The sensitivity, specificity, PPV, NPV and accuracy are 88%, 100%, 100%, 50% and 90% for lateralization and 71%, 100%, 100%, 60% and 80% for quadrant localization respectively in multiple-gland disease. Fleiss’ kappa value is 5.6 (moderate inter-observer agreement). Conclusion: 4D-CT is a robust method in the localization of hyperfunctioning parathyroid glands with high accuracy and at least moderate inter-observer agreement.

The Realization of 4-dimensional 3-Lie Algebras

In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.

Numerical Simulation of Flow Behavior in Basilar Bifurcation Aneurysms Based on 4-Dimensional Computed Tomography Angiography

Initiation, growth, and rupture of cerebral aneurysms are caused by hemodynamic factors. It is extensively accepted that the cerebral aneurysm wall is assumed to be rigid using computational fluid dynamics (CFD). Furthermore, fluid-structure interactions have been recently applied for simulation of an elastic cerebral aneurysm model. Herein, we examined cerebral aneurysm hemodynamics in a realistic moving boundary deformation model based on 4-dimensional computed tomographic angiography (4D-CTA) obtained by high time-resolution using numerical simulation. The aneurysm of the realistic moving deformation model based on 4D-CTA at each phase was constructed. The effect of small wall deformation on hemodynamic characteristics might be interested. So, four hemodynamic factors (wall shear stress, wall shear stress divergence, oscillatory shear index and residual residence time) were determined from the numerical simulation, and their behaviors were assessed in the basilar bifurcation aneurysm.

Finite-Size Scaling Analysis of a Three-Dimensional Blume-Capel Model in the Presence of External Magnetic Field

The Blume-Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent 5 is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range -0.1≤ h = H/J ≤0. The estimated value of the field critical exponent 5 is in good agreement with the universal value （δ = 5） in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.

The 5-dimensional model for electromagnetism and gravity

The generalization of Einstein’s special theory of relativity (SRT) is proposed. In this model, the possibility of unification of scalar gravity and electromagnetism into a single unified field is considered. Formally, the generalization of the SRT is that instead of (1+3)-dimensional Minkowski space the (1+4)-dimensional extension G is considered. As the fifth additional coordinate the interval S is used. This value is saved under the usual Lorentz transformations in Minkowski space M, but it changes when the transformations in the extended space G are used. We call this model the extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. If the rest mass of a particle does not change and the physical quantities do not depend on an additional variable S, then the electromagnetic and gravitational fields exist independently of each other. But if the rest mass is variable and there is a dependence on S, then these two fields are combined into a single unified field. In the extended space model a photon can have a nonzero mass and this mass can be either positive or negative. In this model the 5- vectors which components correspond to energy, pulse and mass of a particle are isotropic both for massive and massless particles. The rotations in the (1+4) dimensional extended space G can transform massive particles into massless and vice versa.

High-dimensional nonlinear variable separation solutions and novel wave excitations for the(4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.

Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.

A Model of Accelerated Expansion of the Universe Based on the Idea about a Hypothetical 4-Dimensial Substance with an Inverse Population of Energy Levels

Based on the idea of hypothetical 4-dimensial substance with an inverse population of energy levels, a model of accelerated expansion of the Universe has been developed, which describes Hubble diagrams with great accuracy for type Ia supernovae, quasars and gamma-ray burst sources at the Hubble parameter value of 67.7 km/s/Mpc, coinciding with the value obtained from analysis of inhomogeneities of relic radiation. Calculations at the Hubble parameter value of 73.5 km/s/Mpc, obtained using the ΛCDM model based on the analysis of data on type Ia supernovae and cepheids, differ markedly from the observed data. An explanation of the two values of the Hubble constant is proposed. It is shown that in this model, the magnitude of 13.8 billion years characterizes not the age of the Universe, but the time of propagation of light from those galaxes whose acceleration of removal has a minimal value. Based on the recently discovered curvature of the Universe, estimates are given of the lower limits of its size and lifetime, which turned out to be at least 270 billon years. The probability of transition from the excited state to the underlying energy levels of a hypothetical 4-dimensial substance, as well as the low of increasing energy density as a result of transitions to the underlying levels of this substance, is determined.

Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori,Ⅱ

We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni （2014） in an earlier paper.

Two-Dimensional Graphs Moving by Mean Curvature Flow

A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.

Four-Dimensional Toda Theories From Self-dual Yang-Mills Theory

Recently, much progress has been made toward the Hamiltonian reductions of the two-dimensional WZNW theory. The remarkable point is that such reductions give a unified description of many known and unforeknown two-dimensional integrable field theories, and that while using the WZNW field to parametrize the solutions of these integrable systems, the apparant singularities arising from the improper choices of coordinate systems can be removed.

Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0

In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean. We determine the α-and β(bp)-duals of the space εp r,s, and characterize the classes(ε_p^(r,s):M_u),(ε_p^(r,s):C_(bp)) and(ε_p^(r,s):L_q) of four dimensional matrix transformations, where 1 ≤q < ∞. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.

四维黑洞矢量粒子隧穿辐射

运用WKB近似和Hamilton-Jacobi方法从低维推广到四维黑洞时空中矢量粒子的隧穿辐射研究,结果表明矢量粒子与Dirac粒子及其他粒子的霍金温度是相同的.

Cosmological Duality in Four Time and Four Space Dimensions

We describe a duality transformation in a cosmological model of four time and four space dimensions ((4 + 4)-dimensions). In particular, we show that via the Fourier transform, at the level of the zero-point energy of quantum mechanics and the de Sitter space, a Gaussian distribution in four dimensions leads to a dual Gaussian distribution also in four dimensions, with duality transformation , in the standard deviation σ. Moreover, we show that as a consequence of such a duality in σ a duality of the cosmological constant Λ can be obtained. Finally, we comment on the possibility that both the oriented matroid theory as well as the surreal number theory are related to the formalism presented in this work.

Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

This paper intends to show how the fabled violation of Bell’s inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect. I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt. Designed to assess consequences of Einstein’s principle of local realism, the inequality pertains to a linear combination of four polarization products on the same pair of photons arising in a gedankenexperiment. My assessment displays that in this context, the summands of the relevant CHSH quantity s(λ) inhere four symmetric functional relations which have long been neglected in analytic considerations. Its expectation E[s(λ)] is not the sum of four “marginal” expectations from a joint distribution, as quantum theory explicitly avoids such a specification. Rather, I show that E[s(λ)] has four distinct representations as the sum of three expectations of polarization products plus the expectation of a fourth which is restricted to equal a function value determined by the other three. Analysis using Bruno de Finetti’s fundamental theorem of prevision (FTP) yields only a bound for E(s) within (1.1213,2] , surely not at all as is commonly understood. I exhibit slices of the 4-dimensional polytope of joint P++ probabilities actually motivated by quantum theory at the four stipulated angle settings, as it passes through 3-dimensional space. Bell’s inequality is satisfied everywhere within the convex hull of extreme distributions cohering with quantum theoretic specifications, even while in keeping with local realism. Aspect’s proposed “estimation” of E(s) near to is based on polarization products from different photon pairs that do not have embedded within them the functional relations inhering in the relevant gedankenexperiment. When one actively embeds the restrictions into Aspect’s estimation procedure, it yields an estimate of 1.7667, although this is not and cannot be definitive. While my analysis supports the subjectivist construction of probability as clarifying issues relevant to the interpretation of quantum theory, the error resolved herein is purely mathematical. It pertains to the reconsideration of Bell violation irrespective of one’s attitude toward the meaning of probability.

A New Version of Special Relativity Absorbed the Uncertainty Principle: Its Content as Well as Application and Experimental Test

Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this model, equations of the special relativity can be extended more perfectly, thereby achieving a unity of the special relativity and quantum mechanics in deeper level. New equations can not only interpret issues explained by old equations but also solve several important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV) is derived, to above 4 × 1019 eV UHECR protons the calculated |ξ| -30, although there is the LIV effect it is too weak to change the GZK cutoff, which is consistent with observations of HiRes and Auger;Also, a relation formula between the Hubble constant and several basic constants is derived, thus theoretically calculated H0 = 70.937 km·s-1·Mpc-1, which is well consistent with the final observation result of HST Key Project. In addition, an unusual effect predicted by new equations can be experimentally tested in the electron storage ring;a preliminary experiment result has hinted its signs of existence.

UNIFICATION AND APPLICATIONS OF MODERN OCEANIC/ATMOSPHERIC DATA ASSIMILATION ALGORITHMS

The key mathematics and applications of various modern atmospheric/oceanicdata assimilation methods including Optimal Interpolation (OI), 4-dimensional variational approach(4D-Var) and filters were systematically reviewed and classified. Based on the data assimilationphilosophy, i. e. , using model dynamics to extract the observational information, the commoncharacter of the problem, such as the probabilistic nature of the evolution of theatmospheric/oceanic system, noisy and irregularly spaced observations, and the advantages anddisadvantages of these data assimilation algorithms, were discussed. In the filtering framework, allmodern data assimilation algorithms were unified: OI/3D-Var is a stationary filter, 4D-Var is alinear (Kalman) filter and an ensemble of Kalman filters is able to construct a nonlinear filter.The nonlinear filter such as the Ensemble Kalman Filter (EN-KF), Ensemble Adjustment Kalman Filter(EAKF) and Ensemble Transformation Kalman Filter (ETKF) can, to some extent, account for thenon-Gaussian information of the prior distribution from the model. The flow-dependent covarianceestimated by an ensemble filter may be introduced to OI and 4D-Var to improve these traditionalalgorithms. In practice, the performance of algorithms may depend on the specific numerical modeland the choice of algorithm may depend on the specific problem. However, the unification ofalgorithms allows us to establish a unified test system to evaluate these algorithms, which providesmore insights into data assimilation philosophies and helps improve data assimilation techniques.