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In this paper, we construct fast discrete transforms of wavelet type with an arbitrary number of zero moments for nonuniform grids. We obtain explicit formulas for the parameters defining the wavelet transform. [ABSTRACT FROM AUTHOR]

In the present paper, we classify the finite subgroups $G\backslash subset\backslash operatorname\{GL\}\_4(\backslash Bbb\; C)$ such that the quotient $\backslash Bbb\; C^4$ by the action $G$ has only isolated terminal Gorenstein singularities. [ABSTRACT FROM AUTHOR]

We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval [ a, b] ⊂ (−1, 1). The condition is stated in terms of the second differences of the interpolated function and uses its values only at the interpolation nodes. Some well-known criteria for uniform convergence are obtained as a consequence of our result. [ABSTRACT FROM AUTHOR]

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved. [ABSTRACT FROM AUTHOR]

We study the problem of the attractors of the boundary-value problem $u\_t=\backslash sqrt\; \backslash varepsilon\; (D\_0\; +\; \backslash sqrt\; \backslash varepsilon\; D\_1)\backslash Delta\; u\; +\; (A\_0\; +\; \backslash varepsilon\; A\_1)u\; +\; F(u),\backslash qquad\; u\_x|\_\{x=0,\backslash ,\backslash ,\; x=l\_1\}\; =\; u\_y|\_\{y=0,\backslash ,\backslash ,\; y=l\_2\}=0,$ where $0\; \backslash le\; \backslash varepsilon\; \backslash ll\; \backslash nomathbreak\; 1$, $u\backslash in\; \backslash Bbb\{R\}^N$, $N\backslash ge\; \backslash nomathbreak\; 3$, ~$\backslash Delta$ is the Laplace operator, and $-D\_0$ is the Hurwitz matrix. For such a boundary-value problem, under certain assumptions, we establish the existence of any finite fixed number of stable cycles, provided that $\backslash varepsilon\; >\; \backslash nomathbreak\; 0$ is chosen appropriately small. In other words, it is shown that this boundary-value problem involves the buffer phenomenon. [ABSTRACT FROM AUTHOR]

It is shown that, except for several explicitly described cases, two hyperbolic tube domains in $\backslash CC^2$ are biholomorphically equivalent if and only if they are affinely equivalent. [ABSTRACT FROM AUTHOR]

For $N=\; 2^s$, in the space of complex-valued $N$-periodic functions of an integer argument, we construct $s$ orthogonal bases such that the elements of the $r$th basis, where $r\backslash in\backslash \; 1,\backslash dots,s\backslash$, take $2^r$ values of uniformly distributed on the unit circle in the complex plane. [ABSTRACT FROM AUTHOR]

We classify purely log-terminal blow-ups of index $1$ of three-dimensional terminal singularities. [ABSTRACT FROM AUTHOR]

We obtain necessary and sufficient conditions for the Lipschitzian invertibility of the differential mapping $d/dt-\; \backslash nomathbreak\; f$, where $f\backslash :\{\backslash Bbb\; R\}\backslash to\{\backslash Bbb\; R\}$ is a continuous mapping, in the spaces $L\_p(\{\backslash Bbb\; R\},\{\backslash Bbb\; R\})$, $1\backslash le\; p\backslash le\; \backslash nomathbreak\; \backslash infty$. [ABSTRACT FROM AUTHOR]