2,164 research outputs found
Positivstellensatz and flat functionals on path *-algebras
We consider the class of non-commutative *-algebras which are path algebras
of doubles of quivers with the natural involutions. We study the problem of
extending positive truncated functionals on such *-algebras. An analog of the
solution of the truncated Hamburger moment problem by Curto and Fialkow for
path *-algebras is presented and non-commutative positivstellensatz is proved.
We aslo present an analog of the flat extension theorem of Curto and Fialkow
for this class of algebras.Comment: corrected typo
Reduction Operators of Linear Second-Order Parabolic Equations
The reduction operators, i.e., the operators of nonclassical (conditional)
symmetry, of (1+1)-dimensional second order linear parabolic partial
differential equations and all the possible reductions of these equations to
ordinary differential ones are exhaustively described. This problem proves to
be equivalent, in some sense, to solving the initial equations. The ``no-go''
result is extended to the investigation of point transformations (admissible
transformations, equivalence transformations, Lie symmetries) and Lie
reductions of the determining equations for the nonclassical symmetries.
Transformations linearizing the determining equations are obtained in the
general case and under different additional constraints. A nontrivial example
illustrating applications of reduction operators to finding exact solutions of
equations from the class under consideration is presented. An observed
connection between reduction operators and Darboux transformations is
discussed.Comment: 31 pages, minor misprints are correcte
Conservation laws and normal forms of evolution equations
We study local conservation laws for evolution equations in two independent
variables. In particular, we present normal forms for the equations admitting
one or two low-order conservation laws. Examples include Harry Dym equation,
Korteweg-de-Vries-type equations, and Schwarzian KdV equation. It is also shown
that for linear evolution equations all their conservation laws are (modulo
trivial conserved vectors) at most quadratic in the dependent variable and its
derivatives.Comment: 16 page
PHASE DYNAMICS OF PHYTOCOENOSIS ON THE DAMPED WASTE HEAPS OF NOVOVOLYN MINING AREA
Nineteen non-recultivated waste heaps are found on the territory of the Novovolyn mining
area (Lviv-Volyn coal basin), three of which are damping. The total area of disturbed lands is 116.7
hectares. An important role for optimization of disturbed objects is played by natural colonization
by vegetation, since it indicates the state of the rocks the waste heaps are made of. Studying of
phytocoenoses, which are formed during self-establishment, gives an opportunity to estimate the
formed groups, considering their place and role in the vegetation cover of the region and predict
their further development
THE IMPACT OF COAL WASTE HEAPS ON THE ENVIRONMENT OF SOKAL DISTRICT OF LVIV REGION
The environmental situation in Sokal district is one of the most complicated in Lviv region,
which is caused by man-made environmental impact of mining, coal preparation and chemical
industries. Most of the territory is occupied by coal waste heaps
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