Estimation of Probability Densities of the Absolute Value and Argument of Complex Random Variables

We particularize criteria proposed by one of the authors for estimating the probability densities of a random vector of size N to the case of even N. For the presentation convenience in this case, two-dimensional vectors are treated as complex random variables and the probability densities of their absolute values and arguments are estimated. The estimation algorithms are synthesized on the basis of the obtained criteria under conditions of both presence and absence of complete a priori information on the sample statistic. A number of examples are given to prove that the obtained algorithms are optimal in the statistical sense. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 616–627, July 2005.     

Color-dependent conductance of graphene with adatoms

We study ballistic transport properties of graphene with a low concentration of vacancies or adatoms. The conductance of graphene doped to the Dirac point is found to depend on the relative distribution of impurities among different sites of the honeycomb lattice labeled in general by six colors. The conductivity is shown to be sensitive to the crystal orientation if adatom sites have a preferred color. Our theory is confirmed by numerical simulations using recursive Green's functions with no adjustable parameters.     

Effect of coherence and polarization on resolution of optical imaging system

The effect of coherence properties of illumination on image resolution, well known in a scalar case, is studied for the case of vector electromagnetic illumination. Using an example of vector Gaussian Schell-model illumination, we analyze the dependence of optical system resolution on the transverse correlation lengths of the orthogonal field components and on the ratio of the powers of these components, each taken separately.     

The Linear-Array Conjecture in Communication Complexity Is False

linear array network consists of k+1 processors with links only between and (0≤i<k). It is required to compute some boolean function f(x,y) in this network, where initially x is stored at and y is stored at . Let be the (total) number of bits that must be exchanged to compute f in worst case. Clearly, , where D(f) is the standard two-party communication complexity of f. Tiwari proved that for almost all functions and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an infinite family of functions for which is essentially at most . Our construction also leads to progress on another major problem in this area: It is easy to bound the two-party communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are such bounds? We exhibit certain functions, for which the (two-party) communication complexity is twice as large as the best lower bound obtainable this way. Received: March 1, 1996     

Tools for Assigning Resonance Structures in Collisions of Few-Body Quantum Systems

The complex dilated Mittag-Leffler, the T-matrix, and the Siegert pseudostate methods are briefly reviewed. Their respective strengths and weaknesses and some recent results are discussed. Permanent address: V. Fock Institute of Physics, St. Petersburg State University, St. Petersburg, 198504 Russia Permanent address: Department of Mathematical and Computational Physics, St. Petersburg State University, St. Petersburg, Russia Permanent address: Department of Physics, University of South Africa, P.O. Box 392, Pretoria, South Africa     

Strong Direct Magnetic Coupling in a Dinuclear CoII Tetrazine Radical Single‐Molecule Magnet

The ligand‐centered radical complex [(CoTPMA)₂‐μ‐bmtz^.?](O₃SCF₃)₃ ? CH₃CN (bmtz=3,6‐bis(2′‐pyrimidyl)‐1,2,4,5‐tetrazine, TPMA=tris‐(2‐pyridylmethyl)amine) has been synthesized from the neutral bmtz precursor. Single‐crystal X‐ray diffraction studies have confirmed the presence of the ligand‐centered radical. The Co^II complex exhibits slow paramagnetic relaxation in an applied DC field with a barrier to spin reversal of 39 K. This behavior is a result of strong antiferromagnetic metal–radical coupling combined with positive axial and strong rhombic anisotropic contributions from the Co^II ions.     

��-Homogeneity of Borel sets

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set C a sum of a countable number of pairwise disjoint h-homogeneous subspaces that are closed in X? It follows that every Borel set ${X \subset {\bf R}^n}$ can be partitioned into countably many h-homogeneous subspaces that are G _?? -sets in X.     

Multichannel detection of signals and estimation of signal parameters in non-Gaussian clutter

Multichannel asymptotically optimal signal detectors and signal parameter meters are synthesized in non-Gaussian clutter. The estimates of the detection and measurement efficiency of synthesized structures are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1044–1056, August, 1996.     

Maps of Borel sets

Questions concerning the structure of Borel sets were raised in special cases by Luzin, Aleksandrov, and Uryson as the problems of distinguishing the sets with certain homogeneous properties in Borel classes and determining the number of such pairwise nonhomemorphic sets. The universal homogeneity, i.e., the property to contain an everywhere closed copy of any Borel set of the same or smaller class, was considered by L.V. Keldysh. She called the sets of classes Π _α ⁰ , α > 2, of first category in themselves that possess this homogeneity property canonical and proved their uniqueness. Thus she revealed the central role of the universality property when describing homeomorphic Borel sets. These investigations led her to the problem of universality of Borel sets and to the problem of finding conditions under which there exists an open map between Borel sets. In this paper, such conditions are presented and similar questions are considered for closed, compact-covering, harmonious, and other stable maps.