The first geodetic VLBI experiment with the Bologna radio telescope

Summary The results of the first geodetic experiment with the Bologna VLBI radiotelescope are presented, giving a decimeter level determination of the radio telescope position.     

The shape of a planet in hydrostatic equilibrium. An application to the Earth

Summary A new technique for computing gravitational equilibrium surfaces (considering gravitational and rotational potential) as a function of depth is presented here for a hydrostatic planet,i.e. a planet where rigidity is neglected. This work was formerly approached by Clairaut, and more recently by Lanzano; in this paper a new technique is developed that solves the problem without making use of the Clairaut differential equation. It is possible to define the gravitational potential of a planet by dividing it intoN shells, each of constant density, with a greater accuracy than in previous works; we can compute the equilibrium surface of each shell with an iterative technique,i.e. by modifying the solution by little steps until the desired accuracy is obtained. In the case of the Earth the geoid is found to be flatter than this ideal surface (this had already been observed also by means of completely different methods, for example by investigating the precession of the Earth). A possible reason for such a discrepancy is that it is too great an approximation to consider the Earth's density as being a function only of the depth.

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Riassunto Si presenta in questo lavoro una tecnica di calcolo per le superfici di equilibrio gravitazionale (considerando sia il potenziale gravitazionale che quello di rotazione) alle varie profondità per un pianeta considerato fluido, cioè privo di rigidità. Il calcolo è stato già affrontato in passato da Clairaut e poi piú recentemente da Lanzano, ma in questo lavoro si sviluppa una tecnica nuova che non risolve numericamente l'equazione differenziale di Clairaut. Si definisce il potenziale gravitazionale di un pianeta pensato con un numeroN di gusci ognuno di densità costante, con una migliore precisione che nei lavori precedenti; si esegue il calcolo delle superfici di equilibrio con una tecnica iterativa, cioè che corregge la soluzione a piccoli passi fino alla precisione desiderata. Il risultato per il caso della Terra mostra che il geoide è piú schiacciato di questa superficie ideale (questo fatto era già stato osservato anche con metodi completamente diversi, ad esempio osservando la precessione della Terra). Una possobile spiegazione per tale discrepanza è che è troppo approssimativo considerare la densità della Terra dipendente solo dalla profondità.

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Резюме Предлагается новая техника дла рачета поверхности гравитационного равновесия (рассматривая гравитационный и ротационный потениалы) в зависимости от глубины для гидростатической планеты, те. пренебрегая упругостьй планеты. Аналогичная задача рассматривалась Клэро и недавно Ландзано, но в этой статье развивается новая техника, которая позволяет решить проблему без использования дифференциального уравнения Клэро. Гравитационный потенциал планеты определяется с большей точностью, чем в предыдущих работах, разбивая планету наN оболочек с постоянными плотностями. Затем мы можем вычислить равновесную поверхность каждой оболочки, используя метод итераций. В случае Земли получается, что геоид представляет более сплющенную форму, чем идеальная поверхность (этот результат отмечался ранее с помощью других методов, например, при исследовании прецессии Земли). Возможное объяснение этого различия, повидимому, связано с тем, что плотность Земли приближенно рассматривается как функция только глубины.

     

Splines approximation in the inversion of gravity profiles

Summary A series of polynomials over adjacent intervals with continuous derivatives at the end point (splines) are used to approximate two-dimensional mass distribution in the inversion of a gravity profile. This method, which may be easily applied to a density interface with finite extension, may be considered a first approach to the general problem of inversion.

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Riassunto Si descrive un metodo per l'inversione dei dati gravimetrici relativi ad una struttura bidimensionale che si basa sull'utilizzazione di una serie di splines cubiche. Questo approccio diretto consente di ottenere la descrizione approssimata della struttura, e quò quindi essere utilizzata come soluzione iniziale nel processo piú generale d'inversione.

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Резюме Последовательность полиномов на соседних интервалах с пепрерывными производными в конечной точке (?шпонки?) используется для аппроксимации массового распределения при инверсии профиля гравитации. Этот метод, который позволяет пепосредственно получить приближенное описание структуры, может рассматриваться как первый подход к общей проблеме инверсии.

     

High-statistics study of the low-energy cosmic-muons angular distribution: Results from MICRO

Summary We present results from MICRO, a muon telescope with good angular resolution, which has collected more than 31·10⁶ cosmic muons. Upper limits are given for the flux coming from point sources and for the periodic component from Cygnus X3.     

Paraconic pendulum: Proposal to detect the gravity screening effect during the full solar eclipse

Summary The possibility to detect Allais effect by the paraconic pendulum with the needle and ball suspension is considered. Foucalt force and friction force are estimated with the conclusion to use the ball suspension system for pendulum.     

Geodetic VLBI data analysis using VLBI3 software

Summary VLBI (Very Long Baseline Interferometry) geodetic data have been analysed. Baseline, lengths of several thousands kilometers and their time rates have been estimated from a subset of data, spanning three years, of the IRIS project and using VLBI3 software. A weighted-least-squares estimation has been carried out with thea priori standard deviations of the data modified to account for systematic biases due to mismodelling of the clocks and atmosphere. Comparisons with independent analysis show an agreement to the cm level or better both in baseline lengths and rates.     

Time series variation analysis with Fourier vector amplitudes

Summary A method is presented here to detect hidden trains of recurrences or periodicities in a time series ofN equispaced data. The complex amplitudes of the harmonic components of period τ of subseries of lengthT are computed along the series in a moving way with the fast Fourier transform. Then the progressive sums of the corresponding complex amplitudes or of their phases are plotted and compared with the analogous plots of a series of random data.

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Riassunto è qui presentato un metodo per rivelare treni di ricorrenze o periodicità nascosti in una serie di dati equispaziati. Le ampiezze complesse della comoonente armonica di periodo τ di ogni subserie di lunghezzaT>-τ sono calcolate lungo la serie nella maniera mobile per mezzo della trasformata veloce di Fourier. Il grafico della somma progressiva dei corrispondenti vettori delle ampiezze complesse o delle fasi è poi confrontato con quello ottenuto da una serie di dati casuali.

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Резюме В работе предлагается метод для определния ряда рекуррентных соотношений или периодичностей во временных последовательностяхN равнорасположенных данных. Подвижным образом с помошью быстрого преобразования Фурье вычисльются комплексные амплитуды дль гармонических компонент с периодом т для последователвности длиныT. Затем вычерчиваются графики прогрессивных сумм соответствуюших комплексных амплитуд или их фаэ. Полученные результаты сравниваются с аналогичным графиком для последователвности случайных данных.

     

Time vs. ensemble averages for nonstationary time series

We analyze whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)−x(t), e.g. x(t,T)=ln(p(t+T)/p(t)) in finance and economics, where p(t) is a price, and the assumption is that the increment is distributed independently of t. We apply Tchebychev’s Theorem to the construction of statistical ensembles, and then show that the convergence in probability condition is not satisfied when applied to time averages of functions of stationary increments. We further show that Tchebychev’s Theorem provides the basis for constructing approximate ensemble averages and densities from a single, historic time series where, as in FX markets, the series shows a definite ‘statistical periodicity’. The convergence condition is not satisfied strongly enough for densities and certain averages, but is well-satisfied by specific averages of direct interest. Rates of convergence cannot be established independently of specific models, however. Our analysis shows how to decide which empirical averages to avoid, and which ones to construct.     

Time series analysis of chaotic signals

The Box-Jenkins time series analysis is applied to obtain the amount of chaos for one-dimensional mappings and to characterize the non-chaotic part.     

Time series analysis of ozone data in Isfahan

Time series analysis used to investigate the stratospheric ozone formation and decomposition processes. Different time series methods are applied to detect the reason for extreme high ozone concentrations for each season. Data was convert into seasonal component and frequency domain, the latter has been evaluated by using the Fast Fourier Transform (FFT), spectral analysis. The power density spectrum estimated from the ozone data showed peaks at cycle duration of 22, 20, 36, 186, 365 and 40 days.According to seasonal component analysis most fluctuation was in 1999 and 2000, but the least fluctuation was in 2003. The best correlation between ozone and sun radiation was found in 2000. Other variables which are not available cause to this fluctuation in the 1999 and 2001. The trend of ozone is increasing in 1999 and is decreasing in other years.     

几周期余弦-高斯激光脉冲的时间重心

研究了几周期超短余弦-高斯脉冲的时间重心与绝对相位以及与余弦函数参量之间的关系．给出了几周期超短余弦-高斯脉冲时间重心的解析表达式和模拟图形．结果表明，余弦-高斯脉冲的时间重心随着绝对相位的变化而发生漂移，并且脉冲宽度对余弦-高斯脉冲时间重心的漂移量也有一定的影响．余弦函数的参量在一定取值范围内对余弦-高斯脉冲也有较大的影响，它可能导致几周期余弦-高斯脉冲的时间重心有较大的漂移．     

载波相位对超短脉冲时间重心的影响

以Gauss、Hyperbolic Secant、Lorentz三种脉冲为例,利用理论推导和数值模拟的方法研究了载波相位对超短脉冲时间重心的影响,并给出了三种脉冲的时间重心与载波相位的解析表达式和数值模拟的图形.研究结果表明:当脉冲包络的宽度短于一个光学振荡周期时,载波相位对超短脉冲的时间重心开始有较显著的影响.     

Numerical simulation of non-unitary gravity-induced localization

The localization of a quantum state is numerically exhibited in a non-unitary Newtonian model for gravity. It is shown that an unlocalized state of a ball of mass just above the expected threshold of 10¹¹ proton masses evolves into a mixed state with vanishing coherences above some localization lengths.     

Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.     

Time series of ac conductivities of terbium nitrate crystals at low temperatures

Time series of ac conductivities are measured at 2 kHz along three crystal directions in terbium nitrate crystal below 50 K. The anisotropy is found in the structure of the fluctuation observed in the time series of the conductivities. The bursts with non-periodic oscillations are found in only the measurements of the time series of the ac conductivities for one direction perpendicular to the c-axis (c2-axis). The anisotropy is seen in probability distribution functions and power spectral ones derived from the time series of the conductivities. The characteristic behaviors are found in the time series of the conductivity for the one crystal direction perpendicular to the c-axis. Asymmetric non-Gaussian line shape of the probability distribution function is seen for the c2-axis. Chaotic behavior is also found in the function of the correlation exponent to the embedding dimension derived from the time series of the conductivities.     

Time series analysis and long range correlations of Nordic spot electricity market data

The electricity system price of the Nord Pool spot market is analysed. Different time scale analysis tools are assessed with focus on the Hurst exponent and long range correlations. Daily and weekly periodicities of the spot market are identified. Even though space time separation plots suggest more stationary behaviour than other financial time series, we find large fluctuations of the spot price market which suggest time-dependent scaling parameters.     

Palatini formulation of modified gravity with squared scalar curvature

In this comment we indicate that in the Palatini formulation of R² gravity, there will be no gravity-driven inflation and under some particular assumptions there will be a mild power-law inflation a t².     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Spacetime structure of MOND with Tully-Fisher relation and Lorentz invariance violation

It is believed that the modification of Newtonian dynamics （MOND） is a possible alternative for dark matter hypothesis. Although Bekenstein＇s TeVeS supplies a relativistic version of MOND, one may still wish for a more concise covariant formulism of MOND. In this paper, within covariant geometrical framework, we present another version of MOND. We show the spacetime structure of MOND with properties of Tully-Fisher relation and Lorentz invariance violation.