How massless are massless fields in AdSdAdS_d

Massless fields of generic Young symmetry type in $AdS_d$ space are analyzed. It is demonstrated that in contrast to massless fields in Minkowski space whose physical degrees of freedom transform in irreps of $o(d-2)$ algebra, $AdS$ massless mixed symmetry fields reduce to a number of irreps of $o(d-2)$ algebra. From the field theory perspective this means that not every massless field in flat space admits a deformation to $AdS_d$ with the same number of degrees of freedom, because it is impossible to keep all of the flat space gauge symmetries unbroken in the AdS space. An equivalent statement is that, generic irreducible AdS massless fields reduce to certain reducible sets of massless fields in the flat limit. A conjecture on the general pattern of the flat space limit of a general $AdS_d$ massless field is made. The example of the three-cell ``hook'' Young diagram is discussed in detail. In particular, it is shown that only a combination of the three-cell flat-space field with a graviton-like field admits a smooth deformation to $AdS_d$.Comment: 23 pages, LaTeX, a few typos correcte

Higher Spin Conformal Currents in Minkowski Space

Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.Comment: LaTeX, 10 pages. Corrected typo

Deformed Oscillator Algebras and Higher-Spin Gauge Interactions of Matter Fields in 2+1 Dimensions

We formulate a non-linear system of equations which describe higher-spin gauge interactions of massive matter fields in 2+1 dimensional space-time and explain some properties of the deformed oscillator algebra which underlies this formulation. In particular we show that the parameter of mass $M$ of matter fields is related to the deformation parameter in this algebra.Comment: LaTex, 12 pages, no figures; Invited talk at the International Seminar Supersymmetry and Quantum Field Theory dedicated to the memory of Dmitrij V. Volkov; Kharkov, January 1997; to appear in the proceeding

M. M. Bakhtin as a University Professor

This article presents M. M. Bakhtin as a University professor through his own views of on the nature of university teaching: lecturing, seminars and colloquia, engaging students in debates and reflexive analysis of literary texts, “scientific thinking”, and working with bibliography. As a Chair of Russian and Foreign Literature department of the Mordovian National Pedagogical Institute (later the Mordovia State University), for a quarter of a century, Bakhtin was promoting teaching approaches that would support students’ informed, independent, analytical and reflexive learning. According to the minutes from different department meetings at his university, over the years, Bakhtin struggled to define and improve his own guidance and teaching in the Literature studies and the overall work of his department. His three pedagogical goals for a literary lecture were: 1) Communication of certain information on a given topic - establishing the level of students’ familiarity with the topic; 2) Fostering students’ scientific thinking; and 3) Fostering students’ aesthetic perception and taste. Some of his former students emphasized his erudition, pedagogic skill, and ability to stimulate his students’ imagination and reflective thinking

M. M. Bakhtin as a University Professor

This article presents M. M. Bakhtin as a University professor through his own views of on the nature of university teaching: lecturing, seminars and colloquia, engaging students in debates and reflexive analysis of literary texts, “scientific thinking”, and working with bibliography. As a Chair of Russian and Foreign Literature department of the Mordovian National Pedagogical Institute (later the Mordovia State University), for a quarter of a century, Bakhtin was promoting teaching approaches that would support students’ informed, independent, analytical and reflexive learning. According to the minutes from different department meetings at his university, over the years, Bakhtin struggled to define and improve his own guidance and teaching in the Literature studies and the overall work of his department. His three pedagogical goals for a literary lecture were: 1) Communication of certain information on a given topic - establishing the level of students’ familiarity with the topic; 2) Fostering students’ scientific thinking; and 3) Fostering students’ aesthetic perception and taste. Some of his former students emphasized his erudition, pedagogic skill, and ability to stimulate his students’ imagination and reflective thinking

Explicit Solution to the N-Body Calogero Problem

We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form \half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}], by constructing annihilation and creation operators of the form $a_i^\mp =\frac 1 {\sqrt 2} (x _i \pm i\hat{p}_i )$, where $\hat{p}_i$ is a modified momentum operator obeying %!!!!!!! Heisenberg-type commutation relations with $x_i$, involving explicitly permutation operators. On the other hand, $D_j =i\,\hat{p}_j$ can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed.Comment: 6 p., latex, USITP-92-

Mathematical description of matter exchange between water components and adsorbing surface of filter medium of water purification units

The article presents the theory of mass transfer processes between water polluting components and the adsorbing surface of filter medium of water purification units