Wormholes supported by chiral fields

We consider static, spherically symmetric solutions of general relativity with a non-linear sigma model (NSM) as a source, i.e., a set of scalar fields Φ = (Φ¹, …, Φ ⁿ ) (so-called chiral fields) parametrizing a target space with a metric h _ab (Φ). For NSM with zero potential V (Φ), it is shown that the space-time geometry is the same as with a single scalar field but depends on h _ab . If the matrix h _ab is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.     

t-norms induced by metrics on Boolean algebras

Let d _ν be the metric associated with a strictly positive submeasure ν on some Boolean algebra . If d _ν is bounded from above by 1, E _ν=1−d _ν is a (fuzzy) similarity relation on at least w.r.t. the Lstrok ukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms.In this paper, we show that under certain assumptions on and ν, we may associate with ν in a natural way a continuous t-norm w.r.t. which E _ν is a similarity relation and which, in a certain sense, is the weakest such t-norm. Up to isomorphism, every continuous t-norm arises in this way     

On particle creation and renormalization in a cosmological model with a Big Rip

An exact solution is obtained for a massive scalar field conformally coupled with the curvature in a cosmological model with the scale factor a(t) = a ₀/|t|, corresponding to background matter with the equation of state p = −5ε/3. An expression for the number density of created particles is obtained, and its behavior is studied as the model approached the instant of a Big Rip. Renormalization of the energy-momentum tensor is considered, and it is shown that back reaction of the quantum effects of a conformally coupled scalar field on the space-time metric can be neglected if the field mass is much smaller than the Planck mass and if the time left to the Big Rip is greater than the Planck time.     

Notes on wormhole existence in scalar-tensor and <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G _eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G _eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G _eff changes its sign.     

On the Topology and Geometry of Spaces of Affine Shapes

We define the space of affine shapes of k points in R ⁿ to be the topological quotient of (R ⁿ ) ^k modulo the natural action of the affine group of R ⁿ . These spaces arise naturally in many image-processing applications, and despite having poor separation properties, have some topological and geometric properties reminiscent of the more familiar Procrustes shape spaces Σ _n ^k in which one identifies configurations related by an orientation-preserving Euclidean similarity transformation. We examine the topology of the connected, non-Hausdorff spaces Sh _n ^k in detail. Each Sh _n ^k is a disjoint union of naturally ordered strata, each of which is homeomorphic in the relative topology to a Grassmannian, and we show how the strata are attached to each other. The top stratum carries a natural Riemannian metric, which we compute explicitly for k>n, expressing the metric purely in terms of “pre-shape” data, i.e. configurations of k points in R ⁿ .     

Spinor field with induced nonlinearity in Bianchi VI cosmology: Exact and numerical solutions

A self-consistent system of interacting spinor and scalar fields in Bianchi type VI (B-VI) cosmology is studied in the presence of a cosmological constant. Exact solutions to the spinor, scalar and gravitational field equations are obtained for some special choice of the spinor field nonlinearity. It is shown that introduction of Λ > 0, which is often used to model dark energy, results in a rapid growth of the universe, while Λ < 0 gives rise to an oscillatory or non-periodic mode of expansion. If the metric functions a and b are taken to be inverse to each other (ab = 1), we have a singularity-free universe independently of the sign of Λ.     

The completeness and applications of the formal system ℒ<Superscript>*</Superscript>

Since the formal deductive system ℒ^* was built up in 1997, in has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system ℒ^* is still an open problem. In this paper, the properties and structure ofR ₀ algebras are further studied, and it is shown that every tautology on theR ₀ interval [0,1] is also a tautology on anyR ₀ algebra. Furthermore, based on the particular structure of ℒ^*-Lindenbaum algebra, the completeness and strong completeness of the system ℒ^* are proved. Some applications of the system ℒ^* in fuzzy reasoning are also discussed, and the obtained results and examples show that the system ℒ^* is suprior to some other important fuzzy logic systems.     

Sugli zeri delle funzioni di bessel

In this paper we give some inequalities for the zerosc _ν,n of the cilinder functionJ _ν (x)cosα−Y _ν (x)sindα, 0≤α<π, for the zerosc′_ν,n ofC′_ν(x) and we make an application to negative zerosa _n ,b _n of Airy functions Ai(x), Bi(x) of first and second kind respectively. We also make a comparison between inequalities related to the first zeroj _ν,1 of the Bessel functionJ _ν (x) of first kind with ν>0 and other known inequalities. Some results are new, other not, but in this case they are derived in a simpler way than usual ones.

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Lavoro eseguito nell'ambito del Gruppo Nazionale per l'Informatica Matematica del C.N.R.     

Greedy Algorithms for the Shortest Common Superstring That Are Asymptotically Optimal

There has recently been a resurgence of interest in the shortest common superstring problem due to its important applications in molecular biology (e.g., recombination of DNA) and data compression. The problem is NP-hard, but it has been known for some time that greedy algorithms work well for this problem. More precisely, it was proved in a recent sequence of papers that in the worst case a greedy algorithm produces a superstring that is at most β times (2≤β≤ 4 ) worse than optimal. We analyze the problem in a probabilistic framework, and consider the optimal total overlap O _n ^opt and the overlap O _n ^rg produced by various greedy algorithms. These turn out to be asymptotically equivalent. We show that with high probability , where n is the number of original strings and H is the entropy of the underlying alphabet. Our results hold under a condition that the lengths of all strings are not too short. Received November 1996; revised March 1997.     

A Better Constant-Factor Approximation for Selected-Internal Steiner Minimum Tree

The selected-internal Steiner minimum tree problem is a generalization of original Steiner minimum tree problem. Given a weighted complete graph G=(V,E) with weight function c, and two subsets R ^′ ⊊ R⊆V with |R−R ^′|≥2, selected-internal Steiner minimum tree problem is to find a minimum subtree T of G interconnecting R such that any leaf of T does not belong to R ^′. In this paper, suppose c is metric, we obtain a (1+ρ)-approximation algorithm for this problem, where ρ is the best-known approximation ratio for the Steiner minimum tree problem.     

Exact Algorithms for the Bottleneck Steiner Tree Problem

Given n points, called terminals, in the plane ℝ² and a positive integer k, the bottleneck Steiner tree problem is to find k Steiner points from ℝ² and a spanning tree on the n+k points that minimizes its longest edge length. Edge length is measured by an underlying distance function on ℝ², usually, the Euclidean or the L ₁ metric. This problem is known to be NP-hard. In this paper, we study this problem in the L _p metric for any 1≤p≤∞, and aim to find an exact algorithm which is efficient for small fixed k. We present the first fixed-parameter tractable algorithm running in f(k)⋅nlog ² n time for the L ₁ and the L _∞ metrics, and the first exact algorithm for the L _p metric for any fixed rational p with 1<p<∞ whose time complexity is f(k)⋅(n ^k +nlog n), where f(k) is a function dependent only on k. Note that prior to this paper there was no known exact algorithm even for the L ₂ metric.     

When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity ν _e has to depend on the invariants q = \frac12tr(S²)q = \frac{1}{2}\mathrm{tr}(S^{2}) and r = -\frac13tr(S³)r= -\frac{1}{3}\mathrm{tr}(S^{3}) of the (filtered) strain rate tensor S. The simplest model is then given by n_e = \frac32(D/p)² |r|/q\nu_{e} = \frac{3}{2}(\Delta/\pi)^{2} |r|/q. This model is successfully tested for a turbulent channel flow (Re  _τ =590).     

Finding the Schwarzschild metric from gravity’s Exterior and Interior Effacement algebra

In the author’s previous publications, a recursive linear algebraicmethod was introduced for obtaining (sans gravitational radiation) the full potential expansions for the gravitational metric field components and the Lagrangian for the general N-body system. Two apparent properties of gravity—Exterior Effacement and Interior Effacement—were defined and enforced to obtain the recursive algebra, especially for the motion-independent potential expansions of the general N-body situation. The linear algebraic equations of this method permit determination of the potential coefficients at any order n ^? of the expansions in terms of the lower order coefficients. To illustrate the capabilities of this algebraic method by enforcing exterior and interior effacement, and focusing on only a needed few potential series of the full motion-independent potential expansions, the complete exterior metric field for a single, spherically symmetric mass source is here obtained—the Schwarzschild metric field of general relativity (the Eddington PPN parameter γ = 1) as well as its generalization if the isotropic spatial metric potential’s linearized form is ?g _SS (γ, r) = 1 + 2γ Gm/c ² r +.... with γ ≠ 1 are obtained.     

Über die Nullstellen der ersten Ableitung von Besselfunktionen

Zusammenfassung Die Arbeit liefert einen Beitrag zur derLense'schen Vermutung über die Bewegung der Doppelnullstellen der AbleitungI′ _ν (z) der Besselfunktionen bei ver?nderlichem negativen ν.

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Summary This paper gives a contribution to the hypothesis ofLense regarding the movements of the second order zeros of the derivativesI′ _ν (z) of Bessel functions for every negativ variable ν.

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Mit 3 Textabbildungen

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HerrnJ. Lense zum 75. Geburtstag gewidmet.     

The smooth metric in the class of plane figures with piecewise-convex and concave boundary. PART II

Conclusion To summarize, we can state that, in the present paper, the new metric ρ⁽¹⁾ has been constructed in a rather wide class of plane figures. This metric is a topologically majorant continuation of the metric of the space of continuously differentiable functions. Such metrics are called smooth. It is clear that in the smooth metric ρ⁽¹⁾ the proximity of figures from the classS implies the proximity of their perimeters. Note that there are many other examples of metrization of spaces of plane figures. In [3], a metric ρ₃ is introduced that generalizes the Hausdorff metric and takes into account the behavior of the boundaries of figures, but it is not smooth. One can easily convince oneself by the following example. Part 1 was published in Cybernetics and Systems Analysis, No. 1, 1999. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 111–120, March–April, 1999.     

On Generalization Performance and Non-Convex Optimization of Extended <Emphasis Type="Italic">ν</Emphasis>-Support Vector Machine

The ν-support vector classification (ν-SVC) algorithm was shown to work well and provide intuitive interpretations, e.g., the parameter ν roughly specifies the fraction of support vectors. Although ν corresponds to a fraction, it cannot take the entire range between 0 and 1 in its original form. This problem was settled by a non-convex extension of ν-SVC and the extended method was experimentally shown to generalize better than original ν-SVC. However, its good generalization performance and convergence properties of the optimization algorithm have not been studied yet. In this paper, we provide new theoretical insights into these issues and propose a novel ν-SVC algorithm that has guaranteed generalization performance and convergence properties.

Bianchi-I cosmologies with magnetic and spinor fields

We consider Bianchi type I cosmologies with unidirectional magnetic and electric fields as well as a global spinor field ϕ(t) containing a nonlinearity in the form s ⁿ , where s = ϕ and n = const (the special case n = 1 corresponds to a Dirac massive field). The structure of the stress-energy tensor of the spinor field is shown to be the same as that of a perfect fluid with the equation of state p = wρ with the parameter w = n − 1. The Dirac massive spinor field and nonlinear fields with n < 4/3 are shown to be able to provide late-time isotropization. Talk given at the International Conference RUSGRAV-13, June 23–28, 2008, PFUR, Moscow.     

Optimal input sets for time minimality in quantized control systems

Limited capacity of communication channels has brought to the attention of many researchers the analysis of control systems subject to a quantized input set. In some fundamental cases such systems can be reduced to quantized control system of type x⁺=x+u, where the u takes values in a set of 2m+1 integer numbers, symmetric with respect to 0. In this paper we consider these types of systems and analyse the reachable set after K steps. Our aim is to find a set of m input values such that the reachable set after K steps contains an interval of integers [−N, . . . , N] with N as large as possible. For m=2,3 and 4, we completely solve the problem and characterize the metric associated to this quantized control system.     

Correlation between the gradients of the quadratic functional and its clipped prototype

Applicability of clipping of quadratic functional E = −0.5x ⁺ Tx + Bx in the minimization problem is considered (here x is the configurational vector and B ∈ R ^N is real valued vector). The probability that the gradient of this functional and the gradient of clipped functional ɛ = −0.5x ⁺ τx + bx are collinear is shown to be very high (the matrix τ is obtained by clipping of original matrix T: τ_ij = sgnT _ij ). It allows the conclusion that minimization of functional ɛ implies minimization of functional E. We can therefore replace the laborious process of minimizing functional E by the minimization of its clipped prototype ɛ. Use of the clipped functional allows sixteen-times reduction of the computation time and computer memory usage.