On a subtle point of sum rules calculations: toy model

We consider a two-point correlator in massless $\phi^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules technique with a simple "resonance + continuum" model of the spectrum allows to predict parameters of the "resonance" very accurately in the sense that all necessary criteria of stability are perfectly satisfied.Comment: LaTeX fil

A lower limit on the dark particle mass from dSphs

We use dwarf spheroidal galaxies as a tool to attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making cored dark halo fits to the line of sight velocity dispersions as a function of projected radius (taken from Walker et al. 2007) for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt velocity anisotropy profiles, but find that no benefit is gained over constant velocity anisotropy. In contrast to previous attempts, we do not assume any relation between the stellar velocity dispersions and the dark matter ones, but instead we solve directly for the sterile neutrino velocity dispersion at all radii by using the equation of state for a partially degenerate neutrino gas (which ensures hydrostatic equilibrium of the sterile neutrino halo). This yields a 1:1 relation between the sterile neutrino density and velocity dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn limit at all radii. By varying the sterile neutrino particle mass, we locate the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn limit is not exceeded at any radius (in particular at the centre). We find sizeable differences between the ranges of feasible sterile neutrino particle mass for each dwarf, but interestingly there exists a small range 270-280eV which is consistent with all dSphs at the 1-$\sigma$ level.Comment: 13 pages, 2 figures, 1 tabl

IMPROVING THE ACCURACY DIGITAL ACQUISITION AND DEMODULATION OF OFDM SIGNALS WITH KNOWN PARAMETERS

Дано краткое описание особенностей OFDM сигналов, определяющих перечень возможных идентификационных признаков. Усовершенствован корреляционный метод оценки основных параметров сигналов, основанный на цикличной префиксной структуре сигнала, за счет привязки начал интервалов ортогональности к эталонной сетке частот. Моделированием показана возможность помехоустойчивой демодуляции сигналов на основе решения систем линейных алгебраических уравнений (СЛАУ).Дано коротке описання особливостей OFDM сигналів, які визначають перелік можливих ідентифікаційних ознак. Удосконалено кореляційний метод оцінки основних параметрів сигналів, заснований на циклічній префіксній структурі сигналу, за рахунок прив’язки начал інтервалів ортогональності до еталонної сітки частот. Моделюванням показана можливість завадостійкої демодуляції сигналів шляхом рішення систем лінійних алгебраїчних рівнянь (СЛАР).A brief description of the features of OFDM signals, determine a list of possible signs of identity. Improved correlation method for estimating key parameters pas signals, based on the cyclic prefix signal structure by binding began intervals orthogonal to the reference frequency grid. The simulation showed possibility of interference-signal demodulation based on solving systems of linear algebra equations (SLAE)

A DIGITAL CROSS-CORRELATION METHOD OF ANALYSIS OF PARAMETERS OF OFDM SIGNALS IS IN THE SYSTEMS OF THE AUTOMATIC RADIO MONITORING

Дано краткое описание частотно-временных особенностей OFDM сигналов, определяющих перечень возможных идентификационных признаков. Предложен корреляционный метод оценки основных параметров сложных сигналов в условиях априорной неопределенности, основанный на цикличной префиксной структуре комбинированного сигнала в пределах интервала модуляции и осуществляемый по данным цифровых выборок минимального качества. Предложены этапы обработки и пути их реализации. Показаны преимущества предложенного метода по сравнению с традиционными методами спектрального анализа структуры сигналов.Наданий короткий опис частотно-часових особливостей OFDM сигналів, якій дозволяє визначити перелік можливих ідентифікаційних ознак. Запропонований кореляційний метод оцінки основних параметрів складних сигналів в умовах апріорної невизначеності, заснований на циклічній префіксній структурі комбінованого сигналу в межах інтервалу модуляції, якій здійснюється за даними цифрових вибірок мінімальної якості. Для визначення списку робочих ортогональних частот запропонований метод лінійної алгебри, що забезпечує підвищену точність оцінок при мінімумі обчислювальних витрат. Показані переваги запропонованого методу в порівнянні з традиційними методами спектрального аналізу структури сигналів.Short description of frequency-temporal features of OFDM of signals, determining the list of possible identification signs is given. The cross-correlation method of estimation of basic parameters of difficult signals is offered in the conditions of a priori vagueness, based on the cyclic prefix structure of the combined signal within the limits of interval of mo dulation and carried out from data of digital selections of minimum quality. For determination of list of workings orthogonal sub bearings frequencies the method of linear algebra, providing enhanceable exactness of estimations at a min imum of calculable expenses, is offered. Advantages of the offered method are rotined as compared to the traditional methods of spectral structure of signals

"Non-cold" dark matter at small scales: A general approach

Structure formation at small cosmological scales provides an important frontier for dark matter (DM) research. Scenarios with small DM particle masses, large momenta or hidden interactions tend to suppress the gravitational clustering at small scales. The details of this suppression depend on the DM particle nature, allowing for a direct link between DM models and astrophysical observations. However, most of the astrophysical constraints obtained so far refer to a very specific shape of the power suppression, corresponding to thermal warm dark matter (WDM), i.e., candidates with a Fermi-Dirac or Bose-Einstein momentum distribution. In this work we introduce a new analytical fitting formula for the power spectrum, which is simple yet flexible enough to reproduce the clustering signal of large classes of non-thermal DM models, which are not at all adequately described by the oversimplified notion of WDM . We show that the formula is able to fully cover the parameter space of sterile neutrinos (whether resonantly produced or from particle decay), mixed cold and warm models, fuzzy dark matter, as well as other models suggested by effective theory of structure formation (ETHOS). Based on this fitting formula, we perform a large suite of N-body simulations and we extract important nonlinear statistics, such as the matter power spectrum and the halo mass function. Finally, we present first preliminary astrophysical constraints, based on linear theory, from both the number of Milky Way satellites and the Lyman-\uce\ub1 forest. This paper is a first step towards a general and comprehensive modeling of small-scale departures from the standard cold DM model