On the equation of the pp-adic open string for the scalar tachyon field

We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the $p$-adic open string for the scalar tachyon field $p^{\frac12\partial^2_t}\Phi=\Phi^p$. We elicit the role of real zeros of the entire function $\Phi^p(z)$ and the behaviour of solutions $\Phi(t)$ in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if $p$ is even. We use the method of expanding the solution $\Phi$ and the function $\Phi^p$ in the Hermite polynomials and modified Hermite polynomials and establish a connection between the coefficients of these expansions (integral conservation laws). For $p=2$ we construct an infinite system of non-linear equations in the unknown Hermite coefficients and study its structure. We consider the 3-approximation. We indicate a connection between the problems stated and the non-linear boundary-value problem for the heat equation.Comment: AMSTeX, 26 page

Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes

An analytic understanding of the geodesic structure around non-Kerr spacetimes will result in a powerful tool that could make the mapping of spacetime around massive quiescent compact objects possible. To this end, I present an analytic closed form expression for the components of a the fourth order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is as yet unclear what subset of SAV spacetimes admit this solution. The solution is written in terms of an integral expression involving the metric functions and two specific Greens functions. A second integral expression has to vanish in order for the solution to be exact. In the event that the second integral does not vanish it is likely that the best fourth order approximation to the invariant has been found. This solution can be viewed as a generalized Carter constant providing an explicit expression for the fourth invariant, in addition to the energy, azimuthal angular momentum and rest mass, associated with geodesic motion in SAV spacetimes, be it exact or approximate. I further comment on the application of this result for the founding of a general algorithm for mapping the spacetime around compact objects using gravitational wave observatories.Comment: 5 Page

Nonlinear equations for p-adic open, closed, and open-closed strings

We investigate the structure of solutions of boundary value problems for a one-dimensional nonlinear system of pseudodifferential equations describing the dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar tachyon field using the method of successive approximations. For an open-closed string, we prove that the method converges for odd values of p of the form p=4n+1 under the condition that the solution for the closed string is known. For p=2, we discuss the questions of the existence and the nonexistence of solutions of boundary value problems and indicate the possibility of discontinuous solutions appearing.Comment: 16 pages, 3 figure

Urban occupations in a Siberian city (Tobolsk, 1897)

The article was submitted on 27.06.2016.Рассматривается профессиональная структура города Тобольска конца ХIX в. Сибирь была самым масштабным регионом Российской империи со слабо развитой сетью городов, большинство из которых выполняли роль опорных центров для административного управления огромной территорией. В наиболее освоенных и развитых в хозяйственном отношении западных и южных губерниях Сибири города становились не только административными, но и культурными, и экономическими их центрами. Вопрос представляется актуальным для понимания готовности сибирских губерний к тем общественным трансформациям, которые начались спустя два десятилетия после рассматриваемого периода. Особенностью исследования является использование персональных данных Первой всеобщей переписи населения Российской империи 1897 г. На уровне персоналий оно позволяет существенно расширить исследовательский диапазон, ранее ограниченный опубликованными агрегированными материалами. С их помощью дана характеристика занятости городского населения крупных сибирских городов, показана специфика занятости «военных», «аграрных» городов, а также губернских центров Западной и Восточной Сибири. Обработка данных переписи 1897 г. на индивидуальном уровне производилась с помощью базы данных «Население Тобольска в 1897 г.», включающей сведения о 92,5 % горожан, имевших самостоятельные занятия. Персональные данные позволили провести реконструкцию возрастной и гендерной структуры экономически активного населения губернского центра, выявить особенности занятости представителей разных сословных групп, специфику дополнительных занятий городского населения, определить влияние семьи на выбор сферы деятельности человека. Все сведения о занятиях населения городов Сибири, в том числе Тобольска, были закодированы с помощью Historical International Standard Classification of Occupations.The article studies the late 19th-century occupational structure of Tobolsk in the context of other major Siberian cities. Many urban centres were strongholds for governing this huge territory, and Tobolsk was a typical provincial capital in this regard. In the most economically developed Western and Southern Siberian provinces, cities were not only administrative hubs, but also cultural and economic centres. The authors look at how urban populations were distributed among different occupational groups and social classes, and what role gender and family relations played in terms of employment. This is important, as it may help understand whether Russia’s huge eastern provinces were ready for the transformations which started just two decades after the period whence the main source material of the article originates. The research is based on the first general census of the Russian Empire in 1897. The archives have not preserved primary census manuscripts as a unified collection: so far, only scattered manuscripts have emerged. Clearly, the use of the individual-level nominative census data found for Tobolsk considerably broadens the scope of the research, which was previously limited to aggregate data. The aggregate data provide an opportunity to characterise employment in Siberian cities more generally, demonstrating the occupational specificity of the ‘military’ and ‘agrarian’ cities as well as the provincial centres of Western and Eastern Siberia. The authors more closely analyse the nominative 1897 census data using the database ‘Tobolsk Population in 1897’, which contains information about 92.5 % of employed citizens. The individual-level data made it possible to reconstruct the age and gender structure of the economically active population of the provincial centre, to study the occupations of different estate groups, to look into specific features of secondary occupations, and to see the family’s influence on the choice of occupation. All the employment data on the Siberian urban population were coded according to the HISCO standard