4,573 research outputs found
Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring
We introduce a concept of a fractional-derivatives series and prove that any
linear partial differential equation in two independent variables has a
fractional-derivatives series solution with coefficients from a differentially
closed field of zero characteristic. The obtained results are extended from a
single equation to -modules having infinite-dimensional space of solutions
(i. e. non-holonomic -modules). As applications we design algorithms for
treating first-order factors of a linear partial differential operator, in
particular for finding all (right or left) first-order factors
Public-key cryptography and invariant theory
Public-key cryptosystems are suggested based on invariants of groups. We give
also an overview of the known cryptosystems which involve groups.Comment: 10 pages, LaTe
Angular dependence of magnetoresistance and Fermi-surface shape in quasi-2D metals
The analytical and numerical study of the angular dependence of
magnetoresistance in layered quasi-two-dimensional (Q2D) metals is performed.
The harmonic expansion analytical formulas for the angular dependence of
Fermi-surface cross-section area in external magnetic field are obtained for
various typical crystal symmetries. The simple azimuth-angle dependence of the
Yamaji angles is derived for the elliptic in-plane Fermi surface. These
formulas correct some previous results and allow the simple and effective
interpretation of the magnetic quantum oscillations data in cuprate
high-temperature superconducting materials, in organic metals and other Q2D
metals. The relation between the angular dependence of magnetoresistance and of
Fermi-surface cross-section area is derived. The applicability region of all
results obtained and of some previous widely used analytical results is
investigated using the numerical calculations.Comment: 14 pages, 7 figure
Bounds on the number of connected components for tropical prevarieties
For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−
On non-abelian homomorphic public-key cryptosystems
An important problem of modern cryptography concerns secret public-key
computations in algebraic structures. We construct homomorphic cryptosystems
being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups
and H is finite. A letter of a message to be encrypted is an element h element
of H, while its encryption g element of G is such that f(g)=h. A homomorphic
cryptosystem allows one to perform computations (operating in a group G) with
encrypted information (without knowing the original message over H).
In this paper certain homomorphic cryptosystems are constructed for the first
time for non-abelian groups H (earlier, homomorphic cryptosystems were known
only in the Abelian case). In fact, we present such a system for any solvable
(fixed) group H.Comment: 15 pages, LaTe
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