Initial Epoch Research Articles

Scalar field in the anisotropic universe

We discuss the primordial spectrum of a massless and minimally coupled scalar field, produced during the initial anisotropic epoch before the onset of inflation. We consider two models of the anisotropic cosmology, the (planar) Kasner-de Sitter solution (Bianchi I) and the Taub-NUT-de Sitter solution (Bianchi IX), where the 3-space geometry is initially anisotropic, followed by the de Sitter phase due to the presence of a positive cosmological constant. We discuss the behavior of a quantized, massless and minimally coupled scalar field in the anisotropic stage. This scalar field is not the inflaton and hence does not contribute to the background dynamics. We focus on the quantization procedure and evolution in the preinflationary anisotropic background. Also, in this paper for simplicity the metric perturbations are not taken into account. The initial condition is set by the requirement that the scalar field is initially in an adiabatic state. Usually, in a quantum harmonic oscillator system, an adiabatic process implies the one where the potential changes slowly enough compared to its size, and the time evolution can be obtained from the zeroth order WKB approximation. In our case, such a vacuum state exists only for limited solutions of the anisotropic universe, whose spacetime structure is regular in the initial times. In this paper, we call our adiabatic vacuum state the anisotropic vacuum. In the Kasner-de Sitter model, for one branch of planar solutions there is an anisotropic vacuum unless ${k}_{3}\ensuremath{\ne}0$, where ${k}_{3}$ is the comoving momentum along the third direction, while in the other branch there is no anisotropic vacuum state. In the first branch, for the moderate modes, ${k}_{3}\ensuremath{\sim}k$, where $k$ is the total comoving momentum, the scalar power spectrum has an oscillatory behavior and its direction dependence is suppressed. For the planar modes, ${k}_{3}\ensuremath{\ll}k$, in contrast, the direction dependence becomes more important, because of the amplification of the scalar amplitude during this interval of the violation of WKB approximation in the initial anisotropic stage. The qualitative behaviors in the Taub-NUT-de Sitter models are very similar to the case of the first branch of the planar Kasner-de Sitter model.

PERIOD VARIATIONS IN THE CLOSE BINARY BM UMa

We present the results of analysing of the light curve and O-C variations in the eclipsing sys- tem BM UMa, based on V-band observations which cover the period from JD 2454933 to 2454961 using two robotic remotely-controlled telescopes of Tzec Maun Observatory (USA) along with observations made with the RK-600 telescope of Odessa Astronomical Obser- vatory. The full light curve displays a total primary eclipse with a duration 0.06 of the period, or 24 min- utes, and a partial secondary eclipse, with both max- ima of equal magnitude. For our obesrvations, we determined the sta- tistically optimal values of the initial epoch of T0 = 2454944.2814 ± 0.0001 and orbital period of P =0 . d 271226 ± 0.000002. The depths of primary and secondary minima are nearly equal, 0. m 838 ± 0.006 and 0. m 748 ± 0.006, respectively. The physical pa- rameters of the system were calculated using the Wilson-Devinney code, appended with the Monte Carlo search algorithm. The result establishes BM UMa as a contact system (fillout factor 10.7%) with parameters: mass ratio 0.538 ± 0.001, inclination 86. ◦ 815 ± 0.005, and temperatures of components 4700 ± 20 K and 4510 ± 10 K. The more massive component is larger and cooler. The 72 archival and 11 newly-obtained times of light minimum cover the interval 1961-2010 and allowed us to exclude possible systematic period variations in BM UMa and to determine an initial epoch of HJD 2447927.382 and orbital period of P =0 . d 2712209 ± 0.0000006.

On Utilization of Solar Sails in Triangular Libration Point Missions in the Earth-Moon System

In the real solar system, due to various perturbations, the triangular libration points of the earth-moon system are unstable. However, there are quasi-periodic orbits around them. These orbits show mild instability. Due to the instability, orbit control is necessary for the spacecrafts around these points. In the paper, solar sails were taken to fulfill the control. Numerical simulations were made in the earth-moon system. The results showed that taking the surface of the solar sail as the control parameter can achieve better results. Triangular Libration points in the earth-moon system have fixed configurations with the earth and the moon. This geometrical property is ideal for some space missions. For example, relay stations can be put around them. Spacecrafts can also be sent to these points for deep space observations. Along with the observations on earth, better observation data can be obtained. Besides this, these points are ideal potential candidates for space VLBI observations. In the restricted three-body problem of the earth-moon system, the mass ratio μ is smaller than Routh’s critical value μ1=0.03852…. They are linearly stable in the restricted three-body problem 1) . However, in the real solar system, various perturbations (mainly the gravitational perturbations from the sun) change their dynamical properties and these points are no longer stable anymore. Nevertheless, quasi-periodic orbits staying around them can be found. These orbits show mild instability. Due to their instability, orbit control is necessary for the spacecrafts moving on these orbits. Solar sails can produce long-lasting thrust and do not require any fuels. It’s an ideal choice for space missions. They were taken to fulfill the orbit control in this paper. The magnitude and direction of the thrust produced by the solar sail are coupled, and the force is always directed away from the sun. This is one shortcoming of the solar sails. Due to this property, instead of the tight control strategy, we took a loose one. This strategy needs a pre-determined nominal orbit. A quasi-periodic orbit around the triangular libration points was chosen as the nominal orbit. Two sets of different control variables were used. One set is the surface of the solar sail, and the other one is the normal direction angles of the solar sail. Numerical simulations were done in the earth-moon system. The results showed that taking the surface of the solar sail as the control variable is better. During the lifetime of the spacecraft, it may be shadowed from the sun by the earth or the moon. The solar sail is of no use when the spacecraft is in the shadow. In order to avoid the shadows, the initial epoch of the nominal orbit is carefully chosen. Since the inclination angle between the moon’s and the sun’s orbit planes is small, the z amplitude motion of the nominal orbit is chosen to be large to avoid the shadows too. For a short time mission, these steps can avoid the shadows. For a long time mission, the spacecraft will encounter the shadows anyway. At the end of the paper, a discussion of this case was made. For the shadows in the paper, cylindrical model was considered.

Long-Term Outcomes of Patients with Newly Diagnosed NK/T-Cell Lymphoma Treated by EPOCH Regimen.

Abstract 2689Poster Board II-665 Introduction:Extranodal NK/T-cell lymphoma (ENKL) is a distinct clinicopathological entity of non-Hodgkin's lymphoma, which is characterized by a highly aggressive clinical process and poor prognosis. There are no standard treatment strategies available now. The present study aimed to evaluate the treatment outcome and toxicity of EPOCH regimen for ENKL. Methods:From June 2003 to June 2008, 34 patients including 30 nasal ENKL (88.2%) and 4 extranasal ENKL (11.8%) received doxorubicin, vincristine, etoposide over 96 hours infusion with bolus cyclophosphamide and oral predinisone (EPOCH) combination as first-line treatment. By the Ann Arbor lymphoma Staging Classification, 29 patients (85.3%) had stage ±E-IIE disease and 5 patients (14.7%) had stage IIIE-‡WE disease. Median cycles of EPOCH regimen administered were 2.5 (range from 1 to 6 cycles). Additional involved field radiation therapy (IFRT) was administered to patients with localized regional disease after chemotherapy. Results:Among 34 patients, 33 were eligible for objective response evaluation. The response rate (RR) for the whole group was 60.6% (20/33) with complete remission (CR) rate of 45.5% (15/33). The RR of patients with nasal ENKL was 66.7% (20/30), the CR rate was 50% (15/30). Of the 4 patients with extranasal ENKL, only one achieved stable disease (SD), the other three had progressive disease (PD) during chemotherapy. After a median follow-up of 22 (2–68) months, the estimated overall 3-year overall survival rate (OS) was 52.2%. For patients with nasal ENKL, the estimated median survival time was not reached, the 3-year OS was 59.4%. For patients with extranasal ENKL, the estimated median survival time was only 7 months. For stage ±E-IIE patients with nasal ENKL who received initial EPOCH chemotherapy followed IFRT, the CR rate was 75.0%, and the 3-year survival rate was 75.0%. 102 cycles of chemotherapy were administered to 34 patients. Major adverse effect was myelosuppression. The incidence of grade III-‡W neutropenia was 30.9% and 60 cycles needed G-CSF support. Other toxicities were mild, no treatment-related mortality occurred. Conclusion:EPOCH regiment was effective on ENKL with acceptable toxlicity. EPOCH followed by IFRT yielded promising outcome for patients with localized nasal ENKL. However, patients with extranasal ENKL responded poorly, and more efficacious treatment strategies are urgently needed. Disclosures:No relevant conflicts of interest to declare.

State Transition Matrix Approximation Using a Generalized Averaging Method

This paper presents a method for approximating the state transition matrix for orbits around a primary body and subject to arbitrary perturbations. A generalized averaging method is employed to isolate the high- and low-frequency regions of the perturbation terms and to construct a functional form of the approximate state transition matrix composed only of elementary analytic functions. The resulting state transition matrix is expressed with a small number of constant parameter matrices and osculating orbit parameters at an initial epoch and is valid for tens of orbital revolutions without having to update the parameters. Numerical simulations show that this method is valid for arbitrary-eccentricity orbits with semimajor axes ranging from low Earth orbit up to around 10 Earth radii when applied to Earth orbits. This method has been developed for implementation onboard spacecraft for high-accuracy formation-flying missions. Furthermore, it is shown that the symplectic property, which is a fundamental mathematical structure of Hamiltonian systems, can be incorporated into the method. This not only reduces the number of parameters required for approximations, but also preserves the physically true structure of the state transition matrix and provides some important properties that are useful for practical onboard computation.

Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain

Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain

The randomized vacation policy for a batch arrival queue

This paper examines an M [ x ] / G / 1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p . This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters ( p ∗ , J ∗ ) at a minimum cost, and some numerical examples are presented for illustrative purpose.

Universal Generation of Statistical Self-Similarity: A Randomized Central Limit Theorem

A universal mechanism for the generation of statistical self-similarity-i.e., fractality in the context of random processes-is established. We consider a generic system which superimposes independent stochastic signals, producing a system output; all signals share a common statistical signal pattern, yet each signal has its own transmission parameters-amplitude, frequency, and initiation epoch. We characterize the class of parameter randomizations yielding statistically self-similar outputs in a universal fashion-i.e., for whatever signals fed into the system. Statistically self-similar outputs with finite variance further display (i) anomalous diffusion behavior-characterized by power-law temporal variance growth-and (ii) 1/f noise behavior-characterized by power-law power spectra. The mechanism presented is a "randomized central limit theorem" for fractal statistics of random processes.

Gridline methods for detection of object displacements and rigid body movements

Abstract If measurements are performed without artificial targets, deformation analysis cannot refer to the points on the objects defined at an initial or prior measurement epoch. This paper describes how an arrangement of virtual lines, so-called grid lines (GL), offers a solution. A total station, measuring distances without a reflector, or a theodolite measurement system can be used to make the measurements. The GLs should intersect the object to be measured, as far as possible, at right angles and they can be arranged in such a way that each of them runs through one of the object points chosen for the initial measurements. Subsequently deformations of the object can be described along the GLs. The general idea behind this method is to track the virtual lines with the optical axis of a theodolite, until it aims at the points where the GLs intersect the surface. Tracking starts where the GLs intersected the surface of the object during the last measurement epoch. However, if the surface moved this point will be no longer an intersection point and the optical axis hits the surface at another point. Consequently there will be a separation of these two points, and if the theodolite starts tracking the GL, a distance function is obtained. This can be used to determine the new intersection point of the GL if that line is tracked until the value of the distance function is zero. The following sections describe how this process can be iteratively controlled by algorithms for an one-dimensional search space. The algorithms are based on the binary-search-, so-called parabola-, and regula-falsi method. Simulations and practical tests are used to evaluate the different search algorithms. The accuracy of the intersection points and the number of necessary iteration steps, describing the speed of the algorithms, are used as quality assessment parameters. Both quality characteristics depend on the truncation criteria: a distance and a length of an interval.

Steady state analysis of a M<SUP align=right>x</SUP>/G/1 queue with two service modes and multiple vacations

This paper deals with a single server Poisson queue with state dependent service. The service is rendered with different service modes as singly or in bulk according to the queue length. The service starts only if at least one customer is waiting for service. The server switches over from single service to bulk service only at service initiation epoch according to the queue length. If the number of customers waiting for service is ξ (1 ≤ ξ < a), then the server serves one by one. At the service initiation epoch, if the number of waiting customers ξ is at least 'a' (a < b), then the service is rendered according to Neut's general bulk service rule. At the service completion epoch, if there are no customers in the queue, the server avails multiple vacations, until he finds at least one customer in the queue. The Probability Generating Function (PGF) of the queue size and performance measures are obtained. Numerical results are presented in order to illustrate the effectiveness of performance of the state dependent queue.

Examining Initial Sleep Onset in Primary Insomnia: A Case-Control Study Using 4-Second Epochs

To explore the sleep onset process in primary insomnia patients, new rules for scoring 4-second epochs were implemented to score sleep and artifacts during initial sleep onset. Conventional scorings in 20-second and 60-second epochs were also obtained. The start of the initial 60-second epoch of stage 1 was used to define "time zero" (t0). Sleep onset periods from 11 patients and 11 individually age- and sex-matched controls spanned from 5 minutes before t0 through 29 minutes after t0. Using the new rules, the periods were scored blind to group assignment. This t0 time-referenced the data analysis to one plausible midpoint in the sleep onset process. In parallel, latencies were time-referenced from good night time. Reliability in scoring sleep and artifacts was adequate (kappa = 0.68 & 0.63, respectively, p <0.001). Group differences in sleep latencies were marginal in 60-second and 20-second scoring but significant with a definition of 4-second sleep latency. Patients had more 4-second epochs scored as awake (Mantel-Haenszel chi2 = 271, d.f. = 1, p <0.001) and containing artifact (M-H chi2 = 143, p <0.001). Patients took longer to achieve 30 continuous 4-second epochs of NREM sleep (Breslow chi2 = 4.03, d.f. = 1, p = 0.045) after t0. Patients accumulated sleep more slowly with all 3 scoring rules after t0. A slower rate of accumulating sleep after t0 was detected only with the 4-second scoring (p = 0.047). Evidence was present for momentary state-switching instabilities in the patients during the initial sleep onset process. Using rules for scoring small epochs may reveal such instabilities more readily than traditional scoring methods.

An Autopolyploidy-Based Genetic Algorithm for Enhanced Evolution of Linear Polyfractal Arrays

There has been considerable recent interest in techniques for the optimization of large-N antenna arrays. Unfortunately, the successful development of such techniques has been hindered by the large number of independent parameters that must be optimized and the complexity of the calculations needed for the electromagnetic evaluation of large-N arrays. One promising new design methodology for large-N arrays which has recently been introduced is based on properties of a subset of fractal-random arrays called polyfractal arrays. Polyfractal arrays have many embedded self-similar structures, thereby allowing very large and seemingly complex array layouts to be described with only a small set of independent parameters. In addition, by effectively utilizing the self-similarity of polyfractal arrays, a considerable reduction can be achieved in the amount of time required to evaluate the radiation patterns of large-N arrays. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm (GA) technique to evolve optimal polyfractal array layouts. The most unique aspect of this optimization technique is a new autopolyploidy-based chromosome expansion that maximizes the efficiency of the GAs. Simple polyfractal geometries are used in the initial stage or first epoch of the optimization because the number of independent parameters is small and the computation times are relatively fast. After the optimization converges for the first epoch, more complicated descriptions of these polyfractal arrays are introduced to provide additional independent parameters for the optimizer as it progresses through later epochs of evolution. This process has been shown to be very effective in creating optimized large-N arrays, the largest example considered here being a 1616-element linear array with a -24.30-dB sidelobe level and a 0.056deg half-power beamwidth

Dwarf spheroidal satellites: are they of tidal origin?

The Milky Way and Andromeda must have formed through an initial epoch of sub-structure merging. As a result of fundamental physical conservation laws tidal-dwarf galaxies (TDGs) have likely been produced. Here we show that such TDGs appear, after a Hubble-time of dynamical evolution in the host dark-matter halo, as objects that resemble known dSph satellite galaxies. We discuss the possibility that some of the Milky Way's satellites may be of tidal origin.

Gravitational collapse from smooth initial data with vanishing radial pressure

We study here the spherical gravitational collapse assuming initial data to be necessarily smooth, as motivated by requirements based on physical reasonableness. A tangential pressure model is constructed and analysed in order to understand the final fate of collapse explicitly in terms of the density and pressure parameters at the initial epoch from which the collapse develops. It is seen that both black holes and naked singularities are produced as collapse end states even when the initial data are smooth. We show that the outcome is decided entirely in terms of the initial data, as given by density, pressure and velocity profiles at the initial epoch, from which the collapse evolves.

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state p = kρ. It is shown that given regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black-hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells and the dynamical evolutions as allowed by the Einstein equations. This clarifies the role that equation of state and initial data play in determining the final fate of gravitational collapse.

The evolution of baryon density fluctuations in multicomponent cosmological simulations

We critically examine how the evolution of the matter density field in cosmological simulations is affected by details of setting up initial conditions. We show that it is non-trivial to realize an initial distribution of matter in N-body/hydrodynamic simulations so that the baryon and dark matter density fluctuations and their velocities evolve consistently as theoretically predicted. We perform a set of cosmological simulations and use them to distinguish and verify an appropriate method for generating initial conditions. We show that a straightforward way of applying the Zel'dovich approximation to each component using distinct transfer functions results in an incorrect growth of density fluctuations and that it is necessary to correct velocities at the initial epoch. The unperturbed uniform particle distribution must be also generated appropriately to avoid tight coupling of the baryonic and dark matter components. We recommend using independent ‘glass’ particle distributions, using distinct transfer functions for baryons and dark matter, and taking into account the difference in the velocity fields at the initialization epoch. The proposed method will be useful for studies of the evolution of the intergalactic medium and the formation of the first cosmological objects using numerical simulations.

Constraining the cosmic star formation rate with the MeV backgroung

The Cosmic Gamma-ray Background (CGB) in the MeV regime has been measured with COMPTEL and SMM. The origin of the CGB in this energy regime is believed to be dominated by gamma-rays from Type Ia supernovae. We calculate the CGB spectrum within the framework of FRW cosmology as a function of the cosmic star formation rate, SFR(z). Several estimates of the SFR(z) have been reported since the pioneering work of Madau et al. Here we discuss observational constraints on SFR(z) derived from models of the CGB. In particular, we consider the SFR obtained from Gamma-Ray Burst observations, which increases dramatically with redshift beyond z ~ 1 in contrast to most estimates which saturate or show a mild increase with redshift. Gamma-ray bursts may be the most powerful tracers of star formation in the early universe and thus provide signposts of the initial epoch of element synthesis. The star formation rate implied by GRB statistics results in a gamma-ray background that matches the observations more closely than that inferred from other tracers of star formation. This may provide some support for the GRB/SFR-paradigm, which in turn promises a powerful diagnostic of star formation, and thus cosmic chemical evolution, from the era of Population III stars to the present.

Rigorous transformation of variance-covariance matrices of GPS-derived coordinates and velocities

With the advances in the field of GPS positioning and the global densification of perma- nent GPS tracking stations, it is now possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity transformations between frames are available, but also their rates, all given at some epoch tk. This paper introduces rigorous matrix equations to esti- mate variance-covariance matrices for transformed coordinates at any epoch t based on a stochastic model that takes into consideration all a priori in- formation of the parameters involved at epoch tk, and the coordinates and velocities at the reference frame initial epoch t0. The results of this investiga- tion suggest that in order to attain maximum accu- racy, the agencies determining the 14-parameter transformations between reference frames should also publish their full variance-covariance matrix.

HST Observations of 3 More Old LMC Clusters

We present color-magnitude diagrams (CMDs) based on HST F555W (“V”) and F814W (“I”) observations of three old LMC clusters: NGC 2210, NGC 1786, and Reticulum. The fiducial derived from the CMD of NGC 2257, another LMC cluster, provided a good fit to the data for the new clusters. Because NGC 2257 has a similar metallicity ([Fe/H]∼ −1.8) to NGC 2210, NGC 1786, and Reticulum, the agreement between the CMDs of all four clusters indicates that they have the same age. This preliminary analysis suggests that any age differences are smaller than 2 Gyr. These new results mean that there are now 11 old LMC clusters with similar ages. An initial epoch of star cluster formation therefore happened in a short period over a large volume of space, a volume much larger than is now covered by the present-day optical LMC.

Stability of the GJ 876 Planetary System

The newly discovered planetary system of the GJ 876 is stabilized by a 2:1 mean-motion resonance. We carried out numerical simulations of the GJ 876 planetary system for several sets of initial epochs, and investigated their stability, since this planetary system is very sensitive to an initial epoch because of a large difference between the osculating elements and the mean elements.