Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/ local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late

Freely falling 2-surfaces and the quasi-local energy

We derive an expression for effective gravitational mass for any closed spacelike 2-surface. This effective gravitational energy is defined directly through the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitive expectation that the gravitational mass should be determined by the motion of test body moving freely in gravitational field. We find that this effective gravitational mass has reasonable positive value for a small sphere in the non-vacuum space-times and can be negative for vacuum case. Further, this effective gravitational energy is compared with the quasi-local energy based on the $(2+2)$ formalism of the General Relativity. Although some gauge freedoms exist, analytic expressions of the quasi-local energy for vacuum cases are same as the effective gravitational mass. Especially, we see that the contribution from the cosmological constant is the same in general cases.Comment: 11 pages, no figures, REVTeX. Estimation of the effective mass of small spheres in non-vaccum spacetime and Schwarzschild spacetime are added. The negativity of the latter is discusse

Conserved charges for gravity with locally AdS asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let

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b→sγb \to s \gamma Decay in SU(2)L×SU(2)R×U(1)SU(2)_L \times SU(2)_R \times U(1) Extensions of the Standard Model

The rare radiative decay $b \to s \gamma$ is studied in $SU(2)_L \times SU(2)_R \times U(1)$ extensions of the Standard Model. Matching conditions for coefficients of operators appearing in the low energy effective Hamiltonian for this process are derived, and QCD corrections to these coefficients are analyzed. The $b \to s \gamma$ decay rate is then calculated and compared with the corresponding Standard Model result. We find that observable deviations from Standard Model predictions can occur in $SU(2)_L \times SU(2)_R \times U(1)$ theories for a reasonable range of parameter values.Comment: 17 pages with 5 figures not included but available upon request, CALT-68-1893, TUM-T31-52/9

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

Nuclear Clusters as a Probe for Expansion Flow in Heavy Ion Reactions at 10-15AGeV

A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters d,t and He are predicted for central Au(11.6AGeV)Au and Si(14.6AGeV)Si reactions in the framework of the RQMD transport approach. Transverse expansion leads to a strong shoulder-arm shape and different inverse slope parameters in the transverse spectra of nuclear clusters deviating markedly from thermal distributions. A clear ``bounce-off'' event shape is seen: the averaged transverse flow velocities in the reaction plane are for clusters larger than for protons. The cluster yields --particularly at low $p_t$ at midrapidities-- and the in-plane (anti)flow of clusters and pions change if suitably strong baryon potential interactions are included. This allows to study the transient pressure at high density via the event shape analysis of nucleons, nucleon clusters and other hadrons.Comment: 38 pages, 9 figures, LaTeX type, eps used, subm. to Phys. Rev.

Quantum Cosmology and Open Universes

Quantum creation of Universes with compact spacelike sections that have curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the flat and open cases, the superpotential of the Wheeler De Witt equation is significantly modified, and as a result the qualitative behaviour of a typical wavefunction differs from the traditional closed case. Using regularity arguments, it is shown that the only consistent state for the wavefunction is the Tunneling one. By computing the quantum probabilities for the curvature of the sections, it is shown that quantum cosmology actually favours that the Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$ e-foldings is predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.Comment: 11 pages, Revtex, 7 figures. Accepted for publication in PRD. New material and important corrections added in response to referee's repor

Genetic research: the role of citizens, public health and international stakeholders

Background: Genetic research has become an indispensable instrument for medical research, and the subjects involved have both divergent and convergent interests. Objective: The possibility of having more detailed genetic information undoubtedly offers benefits for the health of the subject, but could also pose risks and make the subject vulnerable to discrimination. Methods: The scientific community has viewed very favorably the public health utility of family history, in which data from a family whose members suffer from chronic pathologies is collected and filed, in order to develop a sort of “stratification of family risk.” Even though in the last decade the scientific and juridical literature has contributed greatly to the topic of biobanks, the perplexities that continue to surround this theme give the idea that current ethical protocols on research are inadequate. Results: Researchers, citizens, International stakeholders, mass media, Public Health and Governments play a key role in genetic research. It is obvious that the methods used for genetic research do not present intrinsic risks; they are much less dangerous than other activities of diagnosis and research. Before authorizing a research project, it is important to reflect on the responsibility and transparency of the studies to be conducted, and on the impact they may have on the interests of public health. Conclusion: We believe that the highest priority need is to develop a common language on the theme, as is the case in the sphere of clinical experimentation where rules of good clinical practice, albeit at times conflicting, have led to uniform convergences in the scientific world on the points to be actuated

Dyson summation without violating Ward identities and the Goldstone-boson equivalence theorem

In contrast to the conventional treatment of gauge theories, in the background-field method the Ward identities for connected Green functions are not violated by Dyson summation of self-energies in finite orders of perturbation theory. Thus, Dyson summation does not spoil gauge cancelations at high energies which are ruled by the Goldstone-boson equivalence theorem. Moreover, in the background-field method the precise formulation of the equivalence theorem in higher orders (including questions of renormalization) is simplified rendering actual calculations easier. Finally, the equivalence theorem is also formulated for the Standard Model with a non-linearly realized scalar sector and for the gauged non-linear $\sigma$-model.Comment: 26 pages, latex, complete ps-file available via anonymous ftp from ftp://ftp.physik.uni-wuerzburg.de/pub/preprint/1996/WUE-ITP-96-002.ps, reference added and some comments on Ref.[6] modifie