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Let H be a Hilbert space and let A be a simple symmetric operator in H with equal deficiency indices d := n±(A) < 1. We show that if, for all  in an open interval I  R, the dimension of defect subsp...
Nous démontrons l’intégralité des coefficients de Taylor de racines de séries de la forme q(z) := z exp(G(z)/F(z)), où F(z) et G(z) + log(z)F(z) sont des solutions particulières de certaines équations...
A unified analysis is presented for information transmission over Gaussian channels with memoryless nonlinear transceiver distortion, which encompasses various distortion models including transmit-sid...
In this survey we consider generalizations for Young and Cauchy–Bunyakowsky inequalities with applications.In section 2 it is noticed that in fact there two different Young inequalities (for two numbe...
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity.
We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of th...
We present a study of what may be called an intrinsic metric for a general regular Dirichlet form. For such forms we then prove a Rademacher type theorem.
Some problems of statistics can be reduced to extremal problems of minimiz-ing functionals of smooth functions defined on the cube [0, 1]m, m ≥ 2. In this paper, we study a class of extremal problems ...
For a domain D in Cz with smooth boundary and for a, b ∈ D, a 6= b, we have the circular (radial) slit mapping P(z)(Q(z)) on D such that P(z) − 1 z−a (Q(z) − 1 z−a ) is regular...
We observe that some special Itˆo diffusions are related to scattering properties of a Schr¨odinger operator on Rd, d  2. We introduce Feynman-Kac type formulae for these stochastic processes wh...
In this survey we consider main transmutation theory topics with many applications, including author’s own results. The topics covered are: transmutations for Sturm–Liouville operators, Vekua–Erdelyi...
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. W...
We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension n is two. As pointed out in [7] this case is more subtle than n = 3 or 4 due to the fact that the arguments of ...
Many problems in machine learning and statistics can be formulated as (generalized)eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding crit...
This paper presents a conception for computing gr¨obner basis. We convert some of gr¨obner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm.

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