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The authors present proofs of the results announced in their former paper [Russ. Acad. Sci., Dokl., Math. 46, No. 2, 279-281 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 3, 414-416 (1992; Zbl 0792.32009)]. Let \(\Omega \subset \mathbb{C}^ n\) be a domain of holomorphy, \(n \geq 2\), and let \(\G... | 1 |
The authors present proofs of the results announced in their former paper [Russ. Acad. Sci., Dokl., Math. 46, No. 2, 279-281 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 3, 414-416 (1992; Zbl 0792.32009)]. This paper is devoted to the well-posedness and long-time behavior of a stochastic Kirchho... | 0 |
Let \(Y\) be a smooth projective surface defined over an algebraically closed field of characteristic \(\neq 2\). A nodal curve of \(Y\) is a smooth rational curve \(N\) such that \(K_YN=0\). An even set of nodal curves is a set \(N_1,\dots N_k\) of disjoint nodal curves such that the divisor \(N_1+\cdots+N_k\) is divi... | 1 |
Let \(Y\) be a smooth projective surface defined over an algebraically closed field of characteristic \(\neq 2\). A nodal curve of \(Y\) is a smooth rational curve \(N\) such that \(K_YN=0\). An even set of nodal curves is a set \(N_1,\dots N_k\) of disjoint nodal curves such that the divisor \(N_1+\cdots+N_k\) is divi... | 0 |
The authors use the fixed point theorem of \textit{J. Brzdȩk} and \textit{K. Ciepliński} [Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 2, 377--390 (2018; Zbl 1399.39063)] to prove hyperstability results for the Jensen equation in the setting of 2-Banach spaces. The aim of this article is to prove a fixed point theorem in... | 1 |
The authors use the fixed point theorem of \textit{J. Brzdȩk} and \textit{K. Ciepliński} [Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 2, 377--390 (2018; Zbl 1399.39063)] to prove hyperstability results for the Jensen equation in the setting of 2-Banach spaces. Every chordal graph \( G\) admits a representation as the in... | 0 |
Soit \(v\) une solution de l'équation de Klein-Gordon quasilinéaire en dimension 1 d'espace
\[
\square v+v= F(v,\partial_t v,\partial v,\partial_t \partial_x v,\partial^2_xv)
\]
à données de Cauchy régulières à support compact, de taille \(\varepsilon\to 0\), où \(F\) est une non-linéarité \({\mathcal C}^\infty\), à ... | 1 |
Soit \(v\) une solution de l'équation de Klein-Gordon quasilinéaire en dimension 1 d'espace
\[
\square v+v= F(v,\partial_t v,\partial v,\partial_t \partial_x v,\partial^2_xv)
\]
à données de Cauchy régulières à support compact, de taille \(\varepsilon\to 0\), où \(F\) est une non-linéarité \({\mathcal C}^\infty\), à ... | 0 |
The author develops some of the foundations of the theory of relatively hyperbolic groups as originally formulated by \textit{M. Gromov} in Chapter 8.6 of his article entitled Hyperbolic groups, [Essays in group theory, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015)]. Here is proved the equivalence of tw... | 1 |
The author develops some of the foundations of the theory of relatively hyperbolic groups as originally formulated by \textit{M. Gromov} in Chapter 8.6 of his article entitled Hyperbolic groups, [Essays in group theory, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015)]. Here is proved the equivalence of tw... | 0 |
If f is an integrable function on the real line \({\mathbb{R}}\) with respect to the measure \(dx/(1+x^ 2)\) and H stands for the Hilbert transform, then [f,H] is an operator defined by
\[
[f,H]g(x)=H(fg)(x)-f(x)Hg(x)\quad (=\frac{1}{\pi}p.v.\int^{\infty}_{-\infty}\frac{f(y)-f(x)}{y- x}g(y)dy).
\]
The authors estab... | 1 |
If f is an integrable function on the real line \({\mathbb{R}}\) with respect to the measure \(dx/(1+x^ 2)\) and H stands for the Hilbert transform, then [f,H] is an operator defined by
\[
[f,H]g(x)=H(fg)(x)-f(x)Hg(x)\quad (=\frac{1}{\pi}p.v.\int^{\infty}_{-\infty}\frac{f(y)-f(x)}{y- x}g(y)dy).
\]
The authors estab... | 0 |
The notion of directional structures was introduced by E. Deák in 1964. This paper is a sequel of [ibid. 15, 45-61 (1980; Zbl 0558.54024)], where the author applies the theory of directional structures to obtain an internal characterization of subspaces of a Euclidean space in terms of the existence of an open subbase ... | 1 |
The notion of directional structures was introduced by E. Deák in 1964. This paper is a sequel of [ibid. 15, 45-61 (1980; Zbl 0558.54024)], where the author applies the theory of directional structures to obtain an internal characterization of subspaces of a Euclidean space in terms of the existence of an open subbase ... | 0 |
The paper is concerned with the Hasse principle and weak approximation for the class of varieties satisfying the Diophantine equation
\[
P(t)={\mathbf N}_{K/k}(x_1,\dots,x_n)\neq 0, \tag{1}
\]
where \({\mathbf N}_{K/k}\) is a full norm form for an extension \(K/k\) of number fields and \(P(t)\) is a polynomial in... | 1 |
The paper is concerned with the Hasse principle and weak approximation for the class of varieties satisfying the Diophantine equation
\[
P(t)={\mathbf N}_{K/k}(x_1,\dots,x_n)\neq 0, \tag{1}
\]
where \({\mathbf N}_{K/k}\) is a full norm form for an extension \(K/k\) of number fields and \(P(t)\) is a polynomial in... | 0 |
The authors generalise their earlier results [Bull. Lond. Math. Soc. 40, No. 1, 129--138 (2008; Zbl 1171.32018)] on functions on curves to the case of maps between curves. Let \(F: (\mathcal{X},0)\to (\mathcal{Y},0)\) be a deformation of the map \(f: (X,0)\to (Y,0)\), such that \(X_t\setminus \{0\}\) and \(Y_t\setminus... | 1 |
The authors generalise their earlier results [Bull. Lond. Math. Soc. 40, No. 1, 129--138 (2008; Zbl 1171.32018)] on functions on curves to the case of maps between curves. Let \(F: (\mathcal{X},0)\to (\mathcal{Y},0)\) be a deformation of the map \(f: (X,0)\to (Y,0)\), such that \(X_t\setminus \{0\}\) and \(Y_t\setminus... | 0 |
Recall that a metric space \((X, d)\) is called ultrametric (or isosceles, or non-Archimedian) if \(d(x, z)\leq\max\{d(x, y),d(y, z)\}\) for all \(x,y,z\in X\). It was shown by \textit{B. Fichet} in [Classification and related methods of data analysis, Proc. 1st Conf. IFCS, Aachen/FRG 1987, 439--444 (1984; Zbl 0734.620... | 1 |
Recall that a metric space \((X, d)\) is called ultrametric (or isosceles, or non-Archimedian) if \(d(x, z)\leq\max\{d(x, y),d(y, z)\}\) for all \(x,y,z\in X\). It was shown by \textit{B. Fichet} in [Classification and related methods of data analysis, Proc. 1st Conf. IFCS, Aachen/FRG 1987, 439--444 (1984; Zbl 0734.620... | 0 |
The author gives a description of the space of projective unitary representations of the orbifold fundamental group of a compact holomorphic orbifold \(X\) of dimension 2 in terms of the moduli space of stable parabolic bundles over \(X\). This allows the author to compute the cohomology of the \(SU(2)\)-character vari... | 1 |
The author gives a description of the space of projective unitary representations of the orbifold fundamental group of a compact holomorphic orbifold \(X\) of dimension 2 in terms of the moduli space of stable parabolic bundles over \(X\). This allows the author to compute the cohomology of the \(SU(2)\)-character vari... | 0 |
In the moduli space \({\mathcal M}(\Sigma, d)\) of reduced curves in \(\mathbb{C}\mathbb{P}^2\) with given degree \(d\) and prescribed configuration of singularities, a couple of reduced curves \(C\) and \(C'\) is said to be a Zariski pair if \(C\) and \(C'\) have the same combinatoric and the pairs \((\mathbb{C}\mathb... | 1 |
In the moduli space \({\mathcal M}(\Sigma, d)\) of reduced curves in \(\mathbb{C}\mathbb{P}^2\) with given degree \(d\) and prescribed configuration of singularities, a couple of reduced curves \(C\) and \(C'\) is said to be a Zariski pair if \(C\) and \(C'\) have the same combinatoric and the pairs \((\mathbb{C}\mathb... | 0 |
Consider polynomials
\[
F(x_1,\dots, x_r)= \sum^{n_1}_{t_1= 0}\cdots \sum^{n_r}_{t_r= 0} \alpha(t_1,\dots, t_r) x^{t_1}_1\cdots x^{r_r}_r
\]
with \(\alpha(0,\dots, 0)= 0\), and write \(\alpha\) for the vector of coefficients. Then the singular integral under consideration is
\[
\int^\infty_{-\infty}\cdots \int^\inft... | 1 |
Consider polynomials
\[
F(x_1,\dots, x_r)= \sum^{n_1}_{t_1= 0}\cdots \sum^{n_r}_{t_r= 0} \alpha(t_1,\dots, t_r) x^{t_1}_1\cdots x^{r_r}_r
\]
with \(\alpha(0,\dots, 0)= 0\), and write \(\alpha\) for the vector of coefficients. Then the singular integral under consideration is
\[
\int^\infty_{-\infty}\cdots \int^\inft... | 0 |
Let \(E\) be a ring spectrum that satisfies the standard assumptions for the construction and convergence of the \(E\)-based Adams spectral sequence, i.e. the corresponding spectral sequence converges to \(\pi_*(X)\) for \(E\)-complete spectra \(X\). In the present article the authors show that in this spectral sequenc... | 1 |
Let \(E\) be a ring spectrum that satisfies the standard assumptions for the construction and convergence of the \(E\)-based Adams spectral sequence, i.e. the corresponding spectral sequence converges to \(\pi_*(X)\) for \(E\)-complete spectra \(X\). In the present article the authors show that in this spectral sequenc... | 0 |
A Riemannian manifold \((M,g)\) is \textit{semi-symmetric} if \(R\cdot R=0\) where the dot means that the curvature operator acts on \(R\) as a derivation. This was generalized by \textit{R. Deszcz} in [Bull. Soc. Math. Belg., Sér. A 44, No. 1, 1--34 (1992; Zbl 0808.53012)] to \(R\cdot R=L_R\bar Q(g,R)\) on the set \(U... | 1 |
A Riemannian manifold \((M,g)\) is \textit{semi-symmetric} if \(R\cdot R=0\) where the dot means that the curvature operator acts on \(R\) as a derivation. This was generalized by \textit{R. Deszcz} in [Bull. Soc. Math. Belg., Sér. A 44, No. 1, 1--34 (1992; Zbl 0808.53012)] to \(R\cdot R=L_R\bar Q(g,R)\) on the set \(U... | 0 |
With the aid of the energy method [\textit{Y. Guo}, Invent. Math. 153, 593--630 (2003; Zbl 1029.82034)] the author proves the existence of global classical solution near the global Maxwellian \(\mu=e^{-|v|^2}\) for the Boltzmann equation
\[
[\partial_t+v\cdot\nabla_x]F=Q[F,F], \quad F(0,x,v)=F_0(x,v)
\]
with respect... | 1 |
With the aid of the energy method [\textit{Y. Guo}, Invent. Math. 153, 593--630 (2003; Zbl 1029.82034)] the author proves the existence of global classical solution near the global Maxwellian \(\mu=e^{-|v|^2}\) for the Boltzmann equation
\[
[\partial_t+v\cdot\nabla_x]F=Q[F,F], \quad F(0,x,v)=F_0(x,v)
\]
with respect... | 0 |
Similar to the Euclidean 3-space, in the hyperbolic space \(\mathbb H^3\) of curvature \(-1\) for each \(H > 1\) there is a family \(\mathcal D_\tau\), \(\tau \in (-\infty, \tau_H]\), of \textit{Delaunay surfaces}, that is rotationally symmetric surfaces of constant mean curvature (CMC) equal to \(H\). For \(\tau \in (... | 1 |
Similar to the Euclidean 3-space, in the hyperbolic space \(\mathbb H^3\) of curvature \(-1\) for each \(H > 1\) there is a family \(\mathcal D_\tau\), \(\tau \in (-\infty, \tau_H]\), of \textit{Delaunay surfaces}, that is rotationally symmetric surfaces of constant mean curvature (CMC) equal to \(H\). For \(\tau \in (... | 0 |
In an earlier paper with the same title \textit{F. Colonius} and \textit{K. Kunisch} [J. Reine Angew. Math. 370, 1-29 (1986; Zbl 0584.34009)] have shown that the solutions to the output least squares problems of the parameter estimation in two point boundary value problems depend Hölder continuously on the observation ... | 1 |
In an earlier paper with the same title \textit{F. Colonius} and \textit{K. Kunisch} [J. Reine Angew. Math. 370, 1-29 (1986; Zbl 0584.34009)] have shown that the solutions to the output least squares problems of the parameter estimation in two point boundary value problems depend Hölder continuously on the observation ... | 0 |
Kamae and Mendès-France, A. Bertrand-Mathis, Bourgain and the reviewer have found connections between van der Corput's equidistribution theorem, difference sets, \(FC^+\)-sets (forcing continuity of positive measures) and Poincaré sets. Several of these results are systematized here and extended to means defined by dif... | 1 |
Kamae and Mendès-France, A. Bertrand-Mathis, Bourgain and the reviewer have found connections between van der Corput's equidistribution theorem, difference sets, \(FC^+\)-sets (forcing continuity of positive measures) and Poincaré sets. Several of these results are systematized here and extended to means defined by dif... | 0 |
Generalizing well known constructions in Riemannian geometry, the tangent bundle of a smooth manifold endowed with a Riemannian metric and a torsion free linear connection carries a natural almost Kähler structure, provided that the dual connection is torsion free, too. Continuing his earlier work, the author studies t... | 1 |
Generalizing well known constructions in Riemannian geometry, the tangent bundle of a smooth manifold endowed with a Riemannian metric and a torsion free linear connection carries a natural almost Kähler structure, provided that the dual connection is torsion free, too. Continuing his earlier work, the author studies t... | 0 |
The author continues topics from his former paper [Izv. Akad. Nauk Arm. SSR, 22, No.2, 193-199 (1987; Zbl 0624.30030)]. The paper under review deals with the following problem:
Given a domain \(D:=K(0,1)\setminus \cup^{\infty}_{j=1}\overline{K(z_ j,r_ j)}\), where \(K(a,z):=\{z\in {\mathbb{C}}: | z-a| <r\}\), and th... | 1 |
The author continues topics from his former paper [Izv. Akad. Nauk Arm. SSR, 22, No.2, 193-199 (1987; Zbl 0624.30030)]. The paper under review deals with the following problem:
Given a domain \(D:=K(0,1)\setminus \cup^{\infty}_{j=1}\overline{K(z_ j,r_ j)}\), where \(K(a,z):=\{z\in {\mathbb{C}}: | z-a| <r\}\), and th... | 0 |
The authors consider a regularization method for solving a Volterra integral equation of the first kind. After discretization of the integral equation the classical Tikhonov regularization procedure is applied to compute the solution of the linear system. A modification of the method of \textit{S. Alliney} and \textit{... | 1 |
The authors consider a regularization method for solving a Volterra integral equation of the first kind. After discretization of the integral equation the classical Tikhonov regularization procedure is applied to compute the solution of the linear system. A modification of the method of \textit{S. Alliney} and \textit{... | 0 |
\textit{R. Askey} [IMA Vol. Math. Appl. 18, 151--158 (1989; Zbl 0694.33006)] introduced the \(q^{-1}\) Hermite-polynomials which has infinitely many orthogonality measures. The author provides algorithms to construct these measures using the properties of the theta-functions. These measures depend on an arbitrary numbe... | 1 |
\textit{R. Askey} [IMA Vol. Math. Appl. 18, 151--158 (1989; Zbl 0694.33006)] introduced the \(q^{-1}\) Hermite-polynomials which has infinitely many orthogonality measures. The author provides algorithms to construct these measures using the properties of the theta-functions. These measures depend on an arbitrary numbe... | 0 |
The function field of the hyperelliptic curve \(X_D: \;y^2=D(x)\) is \(K=\mathbb{F}_q (x, \sqrt{D(x)})\) over the finite field \(\mathbb{F}_q \) with odd \(q\) elements. The author determines \(\widehat {r}_2(D)\), the 2-rank of the Jacobian \(J_D(\mathbb{F}_q)\), i.e. the divisor class group with divisors of degree ze... | 1 |
The function field of the hyperelliptic curve \(X_D: \;y^2=D(x)\) is \(K=\mathbb{F}_q (x, \sqrt{D(x)})\) over the finite field \(\mathbb{F}_q \) with odd \(q\) elements. The author determines \(\widehat {r}_2(D)\), the 2-rank of the Jacobian \(J_D(\mathbb{F}_q)\), i.e. the divisor class group with divisors of degree ze... | 0 |
Let \(R\) be a complete discrete valuation ring with finite residue field \({\mathbb F}_q\), and let \(r_n\) be the probability that a random monic polynomial over \(R\) of degree \(n\) splits into linear factors. The authors prove: (i) the recursion formula
\[
r_n = \sum_{| d| =n} \prod_{0\leq i \leq q-1} q^{-\binom... | 1 |
Let \(R\) be a complete discrete valuation ring with finite residue field \({\mathbb F}_q\), and let \(r_n\) be the probability that a random monic polynomial over \(R\) of degree \(n\) splits into linear factors. The authors prove: (i) the recursion formula
\[
r_n = \sum_{| d| =n} \prod_{0\leq i \leq q-1} q^{-\binom... | 0 |
A question of great interest is, as phrased in [\textit{V. Bangert} and \textit{P. Emmerich}, J. Differ. Geom. 94, No. 3, 367--385 (2013; Zbl 1278.53038)]: ``Suppose a complete Riemannian plane \(P\) satisfies the parallel axiom, i.e., for every geodesic \(c\) on \(P\) and every point \(p \in P\) not on \(c\)
there ex... | 1 |
A question of great interest is, as phrased in [\textit{V. Bangert} and \textit{P. Emmerich}, J. Differ. Geom. 94, No. 3, 367--385 (2013; Zbl 1278.53038)]: ``Suppose a complete Riemannian plane \(P\) satisfies the parallel axiom, i.e., for every geodesic \(c\) on \(P\) and every point \(p \in P\) not on \(c\)
there ex... | 0 |
The authors study on-line optimization for Markov control processes (MCPs) with finite states based on a single sample path [cf. \textit{X.-R. Cao} and \textit{H.-F. Chen}, IEEE Trans. Autom. Control 42, 1382-1393 (1997; Zbl 0889.93039)]. An on-line optimization algorithm for MCPs is proposed here based on the theory o... | 1 |
The authors study on-line optimization for Markov control processes (MCPs) with finite states based on a single sample path [cf. \textit{X.-R. Cao} and \textit{H.-F. Chen}, IEEE Trans. Autom. Control 42, 1382-1393 (1997; Zbl 0889.93039)]. An on-line optimization algorithm for MCPs is proposed here based on the theory o... | 0 |
This paper is concerned with Hopf algebras obtained by ``gauge'' transformations. Let \(A\) be a Hopf algebra, with comultiplication \(\Delta\), antipode \(\mathcal S\) and counit \(\varepsilon\). Let \(F\in A\otimes A\) be an invertible element satisfying \((\varepsilon \otimes 1) F = (1 \otimes \varepsilon) F = 1\). ... | 1 |
This paper is concerned with Hopf algebras obtained by ``gauge'' transformations. Let \(A\) be a Hopf algebra, with comultiplication \(\Delta\), antipode \(\mathcal S\) and counit \(\varepsilon\). Let \(F\in A\otimes A\) be an invertible element satisfying \((\varepsilon \otimes 1) F = (1 \otimes \varepsilon) F = 1\). ... | 0 |
The authors analyze the longtime behavior of solutions to the Keller-Segel-Stokes model
\[
\begin{aligned} n_{t}+u\cdot \nabla n & =\Delta (n^m) -\nabla\cdot(n\chi(c)\nabla c),\cr c_{t}+u\cdot \nabla c & =\Delta c- nf(c),\cr u_t+\nabla p & =\eta \Delta u-n\nabla \phi,\cr \nabla\cdot u & =0, \end{aligned}
\]
in a b... | 1 |
The authors analyze the longtime behavior of solutions to the Keller-Segel-Stokes model
\[
\begin{aligned} n_{t}+u\cdot \nabla n & =\Delta (n^m) -\nabla\cdot(n\chi(c)\nabla c),\cr c_{t}+u\cdot \nabla c & =\Delta c- nf(c),\cr u_t+\nabla p & =\eta \Delta u-n\nabla \phi,\cr \nabla\cdot u & =0, \end{aligned}
\]
in a b... | 0 |
The authors introduce almost compactness and near compactness in a smooth topological space [the third author, ibid. 48, No. 3, 371-375 (1992; Zbl 0783.54007)]\ and establish some of their simple properties. In 1986, \textit{R. Badard} introduced the concept of a smooth topological space. In this paper, we give some li... | 1 |
The authors introduce almost compactness and near compactness in a smooth topological space [the third author, ibid. 48, No. 3, 371-375 (1992; Zbl 0783.54007)]\ and establish some of their simple properties. The energy \(E(G)\) of a graph \(G\) is defined as the sum of the absolute values of its eigenvalues. A connecte... | 0 |
The relations \(\tilde {\mathcal L}\), \(\tilde {\mathcal R}\) are defined on a semigroup \(S\) with the set of idempotents \(E\) by \((\forall e \in E)(ae = a \Leftrightarrow be = b)\), \(a\tilde {\mathcal R}b\) iff \((\forall e \in E)(ea = a \Leftrightarrow eb = b)\), \(a,b \in S\). \(S\) is weakly abundant if each \... | 1 |
The relations \(\tilde {\mathcal L}\), \(\tilde {\mathcal R}\) are defined on a semigroup \(S\) with the set of idempotents \(E\) by \((\forall e \in E)(ae = a \Leftrightarrow be = b)\), \(a\tilde {\mathcal R}b\) iff \((\forall e \in E)(ea = a \Leftrightarrow eb = b)\), \(a,b \in S\). \(S\) is weakly abundant if each \... | 0 |
Let \(M\) be a closed orientable 3-manifold with a Heegaard splitting \(M=V \cup_F W\), and \(S\) a separating \(2\)-sphere \(S\) embedded in \(M\). We call \(S\) a Haken sphere if it intersects the splitting surface \(F\) only in an essential circle \(C\) in \(F\). Suppose genus\((F)=2\) and \(M\) is not prime. It is ... | 1 |
Let \(M\) be a closed orientable 3-manifold with a Heegaard splitting \(M=V \cup_F W\), and \(S\) a separating \(2\)-sphere \(S\) embedded in \(M\). We call \(S\) a Haken sphere if it intersects the splitting surface \(F\) only in an essential circle \(C\) in \(F\). Suppose genus\((F)=2\) and \(M\) is not prime. It is ... | 0 |
\textit{T. Høholdt, J. van Lint} and \textit{R. Pellikaan} [V.S. Pless and W.C. Huffman (Eds), Handbook of Coding Theory, 1, 871--961 (1998; Zbl 0922.94015)] introduced the notions of order and weight functions over an algebra \(R\) defined over a finite field \(F_q\)\, to give a setting which can be used for the const... | 1 |
\textit{T. Høholdt, J. van Lint} and \textit{R. Pellikaan} [V.S. Pless and W.C. Huffman (Eds), Handbook of Coding Theory, 1, 871--961 (1998; Zbl 0922.94015)] introduced the notions of order and weight functions over an algebra \(R\) defined over a finite field \(F_q\)\, to give a setting which can be used for the const... | 0 |
Let \(\{X_{\mathbf j}; {\mathbf j}\in \mathbb{N}^d\}\), \(d>1\), be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space \(\mathbb{H}\) and \(\xi_{\mathbf n}\), \({\mathbf n}\in \mathbb{N}^d,\) be the summation processes based on the collection of sets \([0,t_1]\times\cdot... | 1 |
Let \(\{X_{\mathbf j}; {\mathbf j}\in \mathbb{N}^d\}\), \(d>1\), be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space \(\mathbb{H}\) and \(\xi_{\mathbf n}\), \({\mathbf n}\in \mathbb{N}^d,\) be the summation processes based on the collection of sets \([0,t_1]\times\cdot... | 0 |
The paper studies two kinds of optimal Hermitian backward perturbations for the Hermitian eigenvalue problem which are obtained from different orthogonal decompositions of computed eigenvectors. It is shown that small residuals and almost orthogonality of the computed eigenvectors does not necessarily imply the smallne... | 1 |
The paper studies two kinds of optimal Hermitian backward perturbations for the Hermitian eigenvalue problem which are obtained from different orthogonal decompositions of computed eigenvectors. It is shown that small residuals and almost orthogonality of the computed eigenvectors does not necessarily imply the smallne... | 0 |
Let \(\lambda \in [ 0,1]\) and \(\mu >0\). The proximal average of the lower semicontinuous proper convex functions \(f_{0},f_{1}:\mathbb{R}^{d}\to]-\infty ,+\infty ]\) was defined by \textit{H. H. Bauschke, E. Matoušková} and \textit{S. Reich} [Nonlinear Anal., Theory Methods Appl., Ser. A 56, No. 5, 715--738 (2004; Z... | 1 |
Let \(\lambda \in [ 0,1]\) and \(\mu >0\). The proximal average of the lower semicontinuous proper convex functions \(f_{0},f_{1}:\mathbb{R}^{d}\to]-\infty ,+\infty ]\) was defined by \textit{H. H. Bauschke, E. Matoušková} and \textit{S. Reich} [Nonlinear Anal., Theory Methods Appl., Ser. A 56, No. 5, 715--738 (2004; Z... | 0 |
A theorem on isomorphisms of graphs of lattices (dealing with proper cells) which was proved by the reviewer [Czech. Math. J. 35(110), 188-200 (1985; Zbl 0575.06004)] is generalized in the present paper for the case of isomorphisms of graphs of directed sets. For a long time, graph isomorphisms of distributive, modular... | 1 |
A theorem on isomorphisms of graphs of lattices (dealing with proper cells) which was proved by the reviewer [Czech. Math. J. 35(110), 188-200 (1985; Zbl 0575.06004)] is generalized in the present paper for the case of isomorphisms of graphs of directed sets. Separable continuous images of ordered bicompacta are studie... | 0 |
The author [``Double implementation in Nash and strong Nash equilibria'', Soc. Choice Welfare 14, 439-447 (1997; Zbl 0881.90012)], considered a decision making problem where there is a set of options and a finite number of agents with preferences defined over the set of options, and obtained a necessary and sufficient ... | 1 |
The author [``Double implementation in Nash and strong Nash equilibria'', Soc. Choice Welfare 14, 439-447 (1997; Zbl 0881.90012)], considered a decision making problem where there is a set of options and a finite number of agents with preferences defined over the set of options, and obtained a necessary and sufficient ... | 0 |
In a previous paper with the same title [Number Theory, Ulm/FRG 1987, Lect. Notes Math. 1380, 120--136 (1989; Zbl 0674.10032)], the mean value
\[
I=\sum_{r=1}^R \int_0^V \biggl| \sum_M^{M'} d(m) g(m,v,y_r) e(f(m,v,y_r))\biggr|^2 \,dv
\]
was estimated. Here \(d(m)\) is the divisor function, the functions \(f\) and... | 1 |
In a previous paper with the same title [Number Theory, Ulm/FRG 1987, Lect. Notes Math. 1380, 120--136 (1989; Zbl 0674.10032)], the mean value
\[
I=\sum_{r=1}^R \int_0^V \biggl| \sum_M^{M'} d(m) g(m,v,y_r) e(f(m,v,y_r))\biggr|^2 \,dv
\]
was estimated. Here \(d(m)\) is the divisor function, the functions \(f\) and... | 0 |
For a given matrix polynomial \(P(\lambda )=\sum _{i=0}^mA_i\lambda ^i\), where the \(A_i\) are \(n\times n\) complex matrices, and for a given complex number \(\mu\) and integer \(\kappa \geq 2\), the authors determine the distance (suitably defined) from \(P(\lambda )\) to the set of matrix polynomials having \(\mu\)... | 1 |
For a given matrix polynomial \(P(\lambda )=\sum _{i=0}^mA_i\lambda ^i\), where the \(A_i\) are \(n\times n\) complex matrices, and for a given complex number \(\mu\) and integer \(\kappa \geq 2\), the authors determine the distance (suitably defined) from \(P(\lambda )\) to the set of matrix polynomials having \(\mu\)... | 0 |
A fundamental theorem (Wolfe's theorem) in geometric integration theory states that the space of flat \(m\)-forms, endowed with the flat norm, is isometric to the space of flat \(m\)-cochains. In the paper under review the authors generalize such a theorem to the setting of Sobolev differential forms and Sobolev cochai... | 1 |
A fundamental theorem (Wolfe's theorem) in geometric integration theory states that the space of flat \(m\)-forms, endowed with the flat norm, is isometric to the space of flat \(m\)-cochains. In the paper under review the authors generalize such a theorem to the setting of Sobolev differential forms and Sobolev cochai... | 0 |
Let L be an ample line bundle on a complex projective smooth surface X. The spannedness and the very ampleness properties of the pluriadjoint bundles \((K_ X\otimes L)^{\otimes t}\), \(t\geq 2\), are investigated by using Reider's theorem [\textit{I. Reider}, Ann. Math., II. Ser. 127, No.2, 309-316 (1988; Zbl 0663.1401... | 1 |
Let L be an ample line bundle on a complex projective smooth surface X. The spannedness and the very ampleness properties of the pluriadjoint bundles \((K_ X\otimes L)^{\otimes t}\), \(t\geq 2\), are investigated by using Reider's theorem [\textit{I. Reider}, Ann. Math., II. Ser. 127, No.2, 309-316 (1988; Zbl 0663.1401... | 0 |
In complete fuzzy metric spaces the author gives a fixed point theorem of Banach type, extending a result of \textit{V. Gregori} and \textit{A. Sapena} [Fuzzy Sets Syst. 125, No. 2, 245--252 (2002; Zbl 0995.54046)]. The authors have attempted to extend the Banach fixed point theorem to fuzzy contractive mappings on dif... | 1 |
In complete fuzzy metric spaces the author gives a fixed point theorem of Banach type, extending a result of \textit{V. Gregori} and \textit{A. Sapena} [Fuzzy Sets Syst. 125, No. 2, 245--252 (2002; Zbl 0995.54046)]. This chapter presents the main concepts of morphological image processing. Mathematical morphology has a... | 0 |
In this interesting paper a bilevel programming problem is considered. The lower level problem is a one-parametric optimization problem. The concepts of optimistic and pessimistic strategies are introduced according to the assumptions on the reactions of the follower in front of the actions of the leader. The paper is ... | 1 |
In this interesting paper a bilevel programming problem is considered. The lower level problem is a one-parametric optimization problem. The concepts of optimistic and pessimistic strategies are introduced according to the assumptions on the reactions of the follower in front of the actions of the leader. The paper is ... | 0 |
In 1984, the reviewer gave a sharp upper bound for the sum \(g(T_n)\) of the distances between all ordered pairs of vertices in a strong tournament \(T_n\) of order \(n\) (see J. Graph Theory 8, 1-21 (1984; Zbl 0552.05048)). The result is strengthened by introducing the score \(s\) of some removable vertex \(v\) (i.e. ... | 1 |
In 1984, the reviewer gave a sharp upper bound for the sum \(g(T_n)\) of the distances between all ordered pairs of vertices in a strong tournament \(T_n\) of order \(n\) (see J. Graph Theory 8, 1-21 (1984; Zbl 0552.05048)). The result is strengthened by introducing the score \(s\) of some removable vertex \(v\) (i.e. ... | 0 |
These lectures give an overview of the properties of Artin and elliptic \(L\)-functions. The underlying thesis of the lectures is that ``the connection between random matrices and \(L\)-functions is rooted ''in the so-called Sato-Tate laws''. In the case of Artin \(L\)-functions the author's description culminates in t... | 1 |
These lectures give an overview of the properties of Artin and elliptic \(L\)-functions. The underlying thesis of the lectures is that ``the connection between random matrices and \(L\)-functions is rooted ''in the so-called Sato-Tate laws''. In the case of Artin \(L\)-functions the author's description culminates in t... | 0 |
[For Part I, see Zbl 1013.46003 above.]
This is the second part of the book dedicated to set-theoretic formalisms that allow us to use actual infinitely large and actual infinitesimal quantities. Applications of infinitesimal methods in topology, measure theory, optimization, and harmonic analysis are studied in deta... | 1 |
[For Part I, see Zbl 1013.46003 above.]
This is the second part of the book dedicated to set-theoretic formalisms that allow us to use actual infinitely large and actual infinitesimal quantities. Applications of infinitesimal methods in topology, measure theory, optimization, and harmonic analysis are studied in deta... | 0 |
The main goal of the paper is to recover the gradient of the scalar conductivity defined on a bounded open set in \(\mathbb{R}^d\) from the Dirichlet to Neumann map from the \(p\)-Laplace equation. Given a bounded open set \(\Omega\in \mathbb{R}^d\) and a bounded conductivity \(\gamma>0\) on \(\overline{\Omega}\) consi... | 1 |
The main goal of the paper is to recover the gradient of the scalar conductivity defined on a bounded open set in \(\mathbb{R}^d\) from the Dirichlet to Neumann map from the \(p\)-Laplace equation. Given a bounded open set \(\Omega\in \mathbb{R}^d\) and a bounded conductivity \(\gamma>0\) on \(\overline{\Omega}\) consi... | 0 |
The article deals with variational methods for grid generation and construction of spatial mappings with prescribed properties. Such mappings are applied in many areas, examples of which are delivered in the text. The spatial mappings are treated with respect to the best-maximum principle, which allows to formulate an ... | 1 |
The article deals with variational methods for grid generation and construction of spatial mappings with prescribed properties. Such mappings are applied in many areas, examples of which are delivered in the text. The spatial mappings are treated with respect to the best-maximum principle, which allows to formulate an ... | 0 |
Solutions \(u \in H^1(\mathbb{R}^N)\) of the nonlinear Schrödinger equation
\[
-\Delta u + V(|y|)u = u^p, u>0\tag{1}
\]
are constructed when \(1<p<\frac{N+2}{N-2}\), \(N \ge 3\), and the radial potential \(V\) is positive, bounded and \[ V(|y|) =V_0 + \frac{a}{|y|^m} + O\left(\frac{1}{|y|^{m+\sigma}}\right) \text{ as ... | 1 |
Solutions \(u \in H^1(\mathbb{R}^N)\) of the nonlinear Schrödinger equation
\[
-\Delta u + V(|y|)u = u^p, u>0\tag{1}
\]
are constructed when \(1<p<\frac{N+2}{N-2}\), \(N \ge 3\), and the radial potential \(V\) is positive, bounded and \[ V(|y|) =V_0 + \frac{a}{|y|^m} + O\left(\frac{1}{|y|^{m+\sigma}}\right) \text{ as ... | 0 |
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