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Let $X$ be a complete, connected and finitely connected Alexandrov space without boundary of dimension two whose curvature is bounded below by a constant and admitting total curvature. Denote by $F_p$ the union of all rays in $X$ emanating from the point $p\in X$ and by $A(p)$ the set of the directions of ray...	1
Let $X$ be a complete, connected and finitely connected Alexandrov space without boundary of dimension two whose curvature is bounded below by a constant and admitting total curvature. Denote by $F_p$ the union of all rays in $X$ emanating from the point $p\in X$ and by $A(p)$ the set of the directions of ray...	0
The authors determine all integers $x$ such that $x^2-1$ has only prime factors smaller than 100. They write $x^2-dy^2=1$, and solve the Pell equation by first computing the regulator of the ring of integers of the corresponding quadratic field and then from the regulator obtaining a compact representation of the...	1
The authors determine all integers $x$ such that $x^2-1$ has only prime factors smaller than 100. They write $x^2-dy^2=1$, and solve the Pell equation by first computing the regulator of the ring of integers of the corresponding quadratic field and then from the regulator obtaining a compact representation of the...	0
Kripke semantics for predicate modal logic provides a translation of the formulas of this logic into classical predicate logic. Attempts to use this translation directly for automated deduction were hopeless: too many irrelevant clauses were generated. The author proposed earlier [Lect. Notes Comput. Sci. 310, 500-516 ...	1
Kripke semantics for predicate modal logic provides a translation of the formulas of this logic into classical predicate logic. Attempts to use this translation directly for automated deduction were hopeless: too many irrelevant clauses were generated. The author proposed earlier [Lect. Notes Comput. Sci. 310, 500-516 ...	0
Let ${\mathcal C}_n$ be a local quasi-analytic subring of the ring of germs of $C^\infty$ functions on $\mathbb R^n$ and let ${\mathcal C}=\{{\mathcal C}_n,\;n\in\mathbb N\}.$ Let us denote by $\hat{\cdot}:{\mathcal C}_n \rightarrow\mathbb R[[x_1,\dots,x_n]]$ the map which associates to each \(f\in{\mathcal C...	1
Let ${\mathcal C}_n$ be a local quasi-analytic subring of the ring of germs of $C^\infty$ functions on $\mathbb R^n$ and let ${\mathcal C}=\{{\mathcal C}_n,\;n\in\mathbb N\}.$ Let us denote by $\hat{\cdot}:{\mathcal C}_n \rightarrow\mathbb R[[x_1,\dots,x_n]]$ the map which associates to each \(f\in{\mathcal C...	0
In the paper under review the author discusses the thesis of \textit{B. Vitrac} (1993) mentioned in the title. Recently \textit{B. Vitrac} published a French translation of Euclid's Elements [Euklid. Les Eléments. Volume I. Livres I--IV: Géométrie plane. Traduits du texte grec de Heiberg et avec commentaires par Bernar...	1
In the paper under review the author discusses the thesis of \textit{B. Vitrac} (1993) mentioned in the title. Recently \textit{B. Vitrac} published a French translation of Euclid's Elements [Euklid. Les Eléments. Volume I. Livres I--IV: Géométrie plane. Traduits du texte grec de Heiberg et avec commentaires par Bernar...	0
This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let $\Omega \subset \mathbb{R}^n$ be an unbounded open set and let $X$ be the space of bounded and continuous functions on $\overline \Omega$. For $p \geq 0$, let $W_p (s) = (1 + \|s \|)^p$ an...	1
This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let $\Omega \subset \mathbb{R}^n$ be an unbounded open set and let $X$ be the space of bounded and continuous functions on $\overline \Omega$. For $p \geq 0$, let $W_p (s) = (1 + \|s \|)^p$ an...	0
The Gauss-Bonnet theorem expresses the Euler characteristic of a surface with geodesic boundary as $2\pi$ times the integral of the Gaussian curvature. Its extension to higher dimension due to Chern involves the Pfaffian polynomial in the curvature tensor. The Euler characteristic may be interpreted as the index of t...	1
The Gauss-Bonnet theorem expresses the Euler characteristic of a surface with geodesic boundary as $2\pi$ times the integral of the Gaussian curvature. Its extension to higher dimension due to Chern involves the Pfaffian polynomial in the curvature tensor. The Euler characteristic may be interpreted as the index of t...	0
The minimization method for a quadratic functional with linear constraints, which is proposed in this paper, generalizes the technique previously published by the first author (see [\textit{A. A. Tret'yakov}, Russ. J. Numer. Anal. Math. Model. 25, No. 3, 279--288 (2010; Zbl 1193.65102)]). The aim of the authors is to o...	1
The minimization method for a quadratic functional with linear constraints, which is proposed in this paper, generalizes the technique previously published by the first author (see [\textit{A. A. Tret'yakov}, Russ. J. Numer. Anal. Math. Model. 25, No. 3, 279--288 (2010; Zbl 1193.65102)]). The aim of the authors is to o...	0
The first author has revived the theory of corings [in Algebr. Represent. Theory 5, No. 4, 389-410 (2002; Zbl 1025.16017)]. One of the main aims was the development of a Galois theory for corings, providing a new and elegant approach to Hopf-Galois theory. In the final section of his paper, the first author mentioned t...	1
The first author has revived the theory of corings [in Algebr. Represent. Theory 5, No. 4, 389-410 (2002; Zbl 1025.16017)]. One of the main aims was the development of a Galois theory for corings, providing a new and elegant approach to Hopf-Galois theory. In the final section of his paper, the first author mentioned t...	0
The indicatory property was defined in [\textit{S. Watanabe} and \textit{F. Ikeda}, JP J. Geom. Topol. 4, No. 2, 141--146 (2004; Zbl 1065.53058)]. The paper studies basic properties of indicatory Riemannian spaces defined by tensor fields of type $(0,k)$, $k\in\{2,3,4\}$. In Finsler spaces, the indicatory tensors (...	1
The indicatory property was defined in [\textit{S. Watanabe} and \textit{F. Ikeda}, JP J. Geom. Topol. 4, No. 2, 141--146 (2004; Zbl 1065.53058)]. The paper studies basic properties of indicatory Riemannian spaces defined by tensor fields of type $(0,k)$, $k\in\{2,3,4\}$. Official trials were conducted of a number ...	0
In [\textit{L. Pirio} and \textit{J.-M. Trépreau}, Int. Math. Res. Not. 2015, No. 13, 4449--4504 (2015; Zbl 1406.32014)], it has been proved that for $r>1$, $n\geq 2$ and $d\geq (r+1)(n-1)+2$, a $d$-web of type $(r,n)$ with maximal rank is algebraizable in the classical sense, except maybe when $n\geq 3$ an...	1
In [\textit{L. Pirio} and \textit{J.-M. Trépreau}, Int. Math. Res. Not. 2015, No. 13, 4449--4504 (2015; Zbl 1406.32014)], it has been proved that for $r>1$, $n\geq 2$ and $d\geq (r+1)(n-1)+2$, a $d$-web of type $(r,n)$ with maximal rank is algebraizable in the classical sense, except maybe when $n\geq 3$ an...	0
The main results of the paper are concerned around \textit{J. Herzog}'s question [see ``Homological properties of the modules of differentials'', Colecao Atas Soc. Brasileira Mat. 14 (1981)]: Let P be a regular local ring containing the rationals, let I be an ideal, and set $R=P/I$. Then does the vanishing of the cot...	1
The main results of the paper are concerned around \textit{J. Herzog}'s question [see ``Homological properties of the modules of differentials'', Colecao Atas Soc. Brasileira Mat. 14 (1981)]: Let P be a regular local ring containing the rationals, let I be an ideal, and set $R=P/I$. Then does the vanishing of the cot...	0
This paper considers representations of the fundamental group $\Gamma_g$ of the closed surface of genus $g$ in $\text{PSL}(2,\mathbb{R})$. Each such representation has an associated Euler class. The authors show that the Euler class of a discrete representation (i.e., one whose image is a discrete subgroup of \(\...	1
This paper considers representations of the fundamental group $\Gamma_g$ of the closed surface of genus $g$ in $\text{PSL}(2,\mathbb{R})$. Each such representation has an associated Euler class. The authors show that the Euler class of a discrete representation (i.e., one whose image is a discrete subgroup of \(\...	0
The authors study the stabilization of control systems modelled by an abstract retarded functional differential equation with infinite delay. The results reported in the paper extend those given by the first author in [Syst. Control Lett. 44, No. 1, 35--43 (2001; Zbl 0986.93057)] for the finite delay case. It is shown ...	1
The authors study the stabilization of control systems modelled by an abstract retarded functional differential equation with infinite delay. The results reported in the paper extend those given by the first author in [Syst. Control Lett. 44, No. 1, 35--43 (2001; Zbl 0986.93057)] for the finite delay case. It is shown ...	0
Let $X$ be a compact Kähler manifold of dimension $n$. By the Hodge decomposition theorem the $n$-th complex de Rham cohomology group $H^n(X,\mathbb{Z})\otimes\mathbb{C}$ of $X$ can be written as the direct sum $H^n(X,\mathbb{Z})\otimes\mathbb{C} =\sum_{p+q=n}H^{p,q}(X)$, where $H^{p,q}(X)$ denotes the co...	1
Let $X$ be a compact Kähler manifold of dimension $n$. By the Hodge decomposition theorem the $n$-th complex de Rham cohomology group $H^n(X,\mathbb{Z})\otimes\mathbb{C}$ of $X$ can be written as the direct sum $H^n(X,\mathbb{Z})\otimes\mathbb{C} =\sum_{p+q=n}H^{p,q}(X)$, where $H^{p,q}(X)$ denotes the co...	0
Let $f:X\rightarrow X$ be a map of a continuum (i.e., a compact, connected metric space) to itself. By $\Omega(f)$, the nonwandering points of $f$, we mean those $x\in X$ such that for any open neighborhood $U$ of $x$, there exists $y\in U$ and $n\in\mathbb N$ such that $f^n(y)\in U$. We call $x$ an...	1
Let $f:X\rightarrow X$ be a map of a continuum (i.e., a compact, connected metric space) to itself. By $\Omega(f)$, the nonwandering points of $f$, we mean those $x\in X$ such that for any open neighborhood $U$ of $x$, there exists $y\in U$ and $n\in\mathbb N$ such that $f^n(y)\in U$. We call $x$ an...	0
Actually considered is an IBV-problem for the linearized system of Navier-Stokes equations for a viscous compressible fluid in two state dimensions. The linearization is done around a steady state solution, the domain is a rectangle and its boundary is controlled. With a performance functional inspired from the article...	1
Actually considered is an IBV-problem for the linearized system of Navier-Stokes equations for a viscous compressible fluid in two state dimensions. The linearization is done around a steady state solution, the domain is a rectangle and its boundary is controlled. With a performance functional inspired from the article...	0
This is an attractive survey paper dealing with the problem how to discretize a manifold by selecting a large finite subset of its points. Natural candidates for such good point sets are point sets that minimize a certain energy functional. Suppose that the compact manifold $A$ is embedded in a Euclidean space. A mi...	1
This is an attractive survey paper dealing with the problem how to discretize a manifold by selecting a large finite subset of its points. Natural candidates for such good point sets are point sets that minimize a certain energy functional. Suppose that the compact manifold $A$ is embedded in a Euclidean space. A mi...	0
A Catalan triangulation of the Möbius band is an abstract simplicial complex that uses no interior vertices. The authors present a generating function for the number of triangulations with $n$ vertices analogous to that for Catalan triangulations of the disk [see, for example, \textit{D. D. Sleator}, \textit{R. E. Ta...	1
A Catalan triangulation of the Möbius band is an abstract simplicial complex that uses no interior vertices. The authors present a generating function for the number of triangulations with $n$ vertices analogous to that for Catalan triangulations of the disk [see, for example, \textit{D. D. Sleator}, \textit{R. E. Ta...	0
The type-II hidden symmetries are extra symmetries appearing when the number of variables in PDEq is reduced by a variable transformation found from a Lie symmetry of this PDE. The main of the goal of the article is to show that the provenance of the type II Lie point hidden symmetries found for differential equations ...	1
The type-II hidden symmetries are extra symmetries appearing when the number of variables in PDEq is reduced by a variable transformation found from a Lie symmetry of this PDE. The main of the goal of the article is to show that the provenance of the type II Lie point hidden symmetries found for differential equations ...	0
Authors' abstract: The Harnack inequality established in \textit{M. Röckner} and \textit{F.-Y. Wang} [J.~Funct.~Anal.~203, No. 1, 237--261 (2003; Zbl 1059.47051)] for generalized Mehler semigroup is improved and generalized. As applications, log-Harnack inequality, the strong Feller property, the hyper-bounded property...	1
Authors' abstract: The Harnack inequality established in \textit{M. Röckner} and \textit{F.-Y. Wang} [J.~Funct.~Anal.~203, No. 1, 237--261 (2003; Zbl 1059.47051)] for generalized Mehler semigroup is improved and generalized. As applications, log-Harnack inequality, the strong Feller property, the hyper-bounded property...	0
Let $F$ be an infinite field of characteristic not equal to $2$, $G$ an algebraic group over $F$, $V$ an algebraic $F$-representation (i.e. an algebraic group morphism $G\to\text{GL}_F(V)$), $F(V)$ the field of rational functions, and $F(V)^G$ the invariant field of $F(V)$ with respect to the natura...	1
Let $F$ be an infinite field of characteristic not equal to $2$, $G$ an algebraic group over $F$, $V$ an algebraic $F$-representation (i.e. an algebraic group morphism $G\to\text{GL}_F(V)$), $F(V)$ the field of rational functions, and $F(V)^G$ the invariant field of $F(V)$ with respect to the natura...	0
Let $G$ be a group, $A$ a $G$-graded ring. The author obtains necessary and sufficient conditions for the smash product $A \# G^*$ to be prime and simple, generalizing the results for finite $G$ obtained in [\textit{S. Montgomery} and \textit{D. S. Passman}, J. Algebra 115, 92-124 (1988; Zbl 0639.16002)]. Let...	1
Let $G$ be a group, $A$ a $G$-graded ring. The author obtains necessary and sufficient conditions for the smash product $A \# G^*$ to be prime and simple, generalizing the results for finite $G$ obtained in [\textit{S. Montgomery} and \textit{D. S. Passman}, J. Algebra 115, 92-124 (1988; Zbl 0639.16002)]. A r...	0
The author continues his work on the almost sure central limit theorem (ASCLT) [Studia Sci. Math. Hungar. 31, No. 1-3, 197-202 (1996)]. Firstly, he extends an ASCLT for a sequence of $\varphi$-mixing random variables to the $\rho$-mixing case, where $\varphi^{1/2} ()$ is replaced by $\rho ()$. Secondly, he gi...	1
The author continues his work on the almost sure central limit theorem (ASCLT) [Studia Sci. Math. Hungar. 31, No. 1-3, 197-202 (1996)]. Firstly, he extends an ASCLT for a sequence of $\varphi$-mixing random variables to the $\rho$-mixing case, where $\varphi^{1/2} ()$ is replaced by $\rho ()$. Secondly, he gi...	0
The object of study is the parabolic equation $\partial_t u-\nabla\cdot a(x,t,u,\nabla u)=b(x,t,u,\nabla u)$, where $a$ is assumed to be degenerately elliptic, with what is called ``$p $-growth'' with respect to the gradient variable at $0$ and $\infty$. It is proven that on balls, where a certain Wolff pote...	1
The object of study is the parabolic equation $\partial_t u-\nabla\cdot a(x,t,u,\nabla u)=b(x,t,u,\nabla u)$, where $a$ is assumed to be degenerately elliptic, with what is called ``$p $-growth'' with respect to the gradient variable at $0$ and $\infty$. It is proven that on balls, where a certain Wolff pote...	0
A (2-dimensional) surface $M$ in the Lorentzian space $\mathbb{R}^n_1$ is called time-like if the induced scalar product on $TM$ is indefinite. The authors identify $\mathbb{R}^2$ with the ring $\mathbb{D}$ of double ($\equiv$ split complex) numbers $a+jb$, $j^2=1$, consider the standard embedding of \(...	1
A (2-dimensional) surface $M$ in the Lorentzian space $\mathbb{R}^n_1$ is called time-like if the induced scalar product on $TM$ is indefinite. The authors identify $\mathbb{R}^2$ with the ring $\mathbb{D}$ of double ($\equiv$ split complex) numbers $a+jb$, $j^2=1$, consider the standard embedding of \(...	0
The paper investigates a generalizations of Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions by introducing a notion of $c$-differential uniformity: Given a $p$-ary $(n, m)$-function $f : \mathbb{F}_p^n\rightarrow \mathbb{F}_p^m$, and $c\in\mathbb{F}_p^m$, the $c$-derivative of $f$ with...	1
The paper investigates a generalizations of Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions by introducing a notion of $c$-differential uniformity: Given a $p$-ary $(n, m)$-function $f : \mathbb{F}_p^n\rightarrow \mathbb{F}_p^m$, and $c\in\mathbb{F}_p^m$, the $c$-derivative of $f$ with...	0
A first result proved in this paper shows that for an arbitrary monic univariate complex polynomial whose coefficients are in $C^k(I)$ for some compact real interval $I$ there exist an integer $k\geq 1$ and a rational number $p > 1$, both depending only on the degree, such that any continuous choice of roots is...	1
A first result proved in this paper shows that for an arbitrary monic univariate complex polynomial whose coefficients are in $C^k(I)$ for some compact real interval $I$ there exist an integer $k\geq 1$ and a rational number $p > 1$, both depending only on the degree, such that any continuous choice of roots is...	0
Toth's ``Glimpses'' offer selected material that connect algebra and geometry (but also number-theoretic and topological topics), at a level that is meant to ``fill the gap between undergraduate and graduate mathematics studies''. The concept was to present this in a rather informal style in a discussion that goes far ...	1
Toth's ``Glimpses'' offer selected material that connect algebra and geometry (but also number-theoretic and topological topics), at a level that is meant to ``fill the gap between undergraduate and graduate mathematics studies''. The concept was to present this in a rather informal style in a discussion that goes far ...	0
The author gives a down-to-earth introduction to the theory of $p$-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the $U_p$-operator acting on $S_k(\Gamma_1(N_p))$ is bounded below ...	1
The author gives a down-to-earth introduction to the theory of $p$-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the $U_p$-operator acting on $S_k(\Gamma_1(N_p))$ is bounded below ...	0
The paper is a collection of results on real-valued Baire one functions, defined over an arbitrary topological space $X$. The main results, as it seems, are Theorems 5.4 and 5.6 which characterise $B_1$-embeddings ($B_1^*$-embeddings) in $X$, i.e., subspaces $Y\subset X$ that allow any (resp.\ bounded) Baire one functi...	1
The paper is a collection of results on real-valued Baire one functions, defined over an arbitrary topological space $X$. The main results, as it seems, are Theorems 5.4 and 5.6 which characterise $B_1$-embeddings ($B_1^*$-embeddings) in $X$, i.e., subspaces $Y\subset X$ that allow any (resp.\ bounded) Baire one functi...	0
The author presents a complete solution of the Jacobian problem for vector fields on the plane by proving the following theorem: Suppose that $v$ is a vector field in $\mathbb{R}^2$ such that $v(0)=0$, and suppose that $\text{div } v< 0$ and $J(v)> 0$ on the whole plane, where $J(v)$ is the Jacobian (that i...	1
The author presents a complete solution of the Jacobian problem for vector fields on the plane by proving the following theorem: Suppose that $v$ is a vector field in $\mathbb{R}^2$ such that $v(0)=0$, and suppose that $\text{div } v< 0$ and $J(v)> 0$ on the whole plane, where $J(v)$ is the Jacobian (that i...	0
The author comments on some of the results obtained by \textit{A. Barron}, \textit{L. Birgé} and \textit{P. Massard} [Probab. Theory Relat. Fields 113, No. 3, 301-413 (1999; see the preceding entry, Zbl 0946.62036)] via the results on sharp minimax estimation, where the squared integrated risk converges with optimal ra...	1
The author comments on some of the results obtained by \textit{A. Barron}, \textit{L. Birgé} and \textit{P. Massard} [Probab. Theory Relat. Fields 113, No. 3, 301-413 (1999; see the preceding entry, Zbl 0946.62036)] via the results on sharp minimax estimation, where the squared integrated risk converges with optimal ra...	0
Let $R$ denote a Noetherian ring, let $\mathfrak a \subset R$ be an ideal of $R$ and let $M$ be a finitely generated $R$-module. For an integer $i \geq 0$ let $H^i_{\mathfrak a}(M)$ denote the $i$-th local cohomology module of $M$ with respect to $\mathfrak a.$ The aim of this note is to show that t...	1
Let $R$ denote a Noetherian ring, let $\mathfrak a \subset R$ be an ideal of $R$ and let $M$ be a finitely generated $R$-module. For an integer $i \geq 0$ let $H^i_{\mathfrak a}(M)$ denote the $i$-th local cohomology module of $M$ with respect to $\mathfrak a.$ The aim of this note is to show that t...	0
A long-standing problem in the study of fuzzy logics is to understand and justify the motivation behind them. Two traditional approaches have tried to tackle this problem. A semantical approach aims to develop a framework for dealing with statements which are not necessarily fully true or fully false and modifies class...	1
A long-standing problem in the study of fuzzy logics is to understand and justify the motivation behind them. Two traditional approaches have tried to tackle this problem. A semantical approach aims to develop a framework for dealing with statements which are not necessarily fully true or fully false and modifies class...	0
The paper deals with two-level optimization problems. A function F(x,y) must be minimized with respect to x and subject to some constraints on x. The vector y, being a function of x, is the result of another minimization; minimize f(x,y), subject to some (combined) constraints on x and y. The problem can be viewed as a...	1
The paper deals with two-level optimization problems. A function F(x,y) must be minimized with respect to x and subject to some constraints on x. The vector y, being a function of x, is the result of another minimization; minimize f(x,y), subject to some (combined) constraints on x and y. The problem can be viewed as a...	0
There is a well-developed theory that examines the spectrum of the Laplace operator on manifolds. Less is known about the spectrum of the Laplace operator on forms. This paper uses Seiberg-Witten theory to derive an upper bound on the first eigenvalue of the Hodge Laplacian on co-exact $1$-forms on a wide class of \(...	1
There is a well-developed theory that examines the spectrum of the Laplace operator on manifolds. Less is known about the spectrum of the Laplace operator on forms. This paper uses Seiberg-Witten theory to derive an upper bound on the first eigenvalue of the Hodge Laplacian on co-exact $1$-forms on a wide class of \(...	0
The author considers the definable set $S$ [see \textit{L. van den Dries}, Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. 248. Cambridge: Cambridge Univ. Press (1998; Zbl 0953.03045)] and studies the scalar curvature measure on $S$ -- a generalization of the integral scalar...	1
The author considers the definable set $S$ [see \textit{L. van den Dries}, Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. 248. Cambridge: Cambridge Univ. Press (1998; Zbl 0953.03045)] and studies the scalar curvature measure on $S$ -- a generalization of the integral scalar...	0
The author studies the Keller-Segel-Navier-Stokes system \[\begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (n \nabla c) + \rho n - \mu n^2, & \quad (x,t) \in \Omega \times (0,\infty),\\ c_t + u \cdot \nabla c = \Delta c -c +n, & \quad (x,t) \in \Omega \times (0,\infty), \\ u_t + (u \cdot \nabla) u =...	1
The author studies the Keller-Segel-Navier-Stokes system \[\begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (n \nabla c) + \rho n - \mu n^2, & \quad (x,t) \in \Omega \times (0,\infty),\\ c_t + u \cdot \nabla c = \Delta c -c +n, & \quad (x,t) \in \Omega \times (0,\infty), \\ u_t + (u \cdot \nabla) u =...	0
This is a continuation of previous work by the authors on the theory of isomanifolds [Tsagas-Sourlas, Isomanifolds..., ibid. 12, No. 1, 1-65 (1995; see the paper above)]. In the present paper they study isomappings between isomanifolds and also introduce the notion of an isotensor field and isodistribution. The notion ...	1
This is a continuation of previous work by the authors on the theory of isomanifolds [Tsagas-Sourlas, Isomanifolds..., ibid. 12, No. 1, 1-65 (1995; see the paper above)]. In the present paper they study isomappings between isomanifolds and also introduce the notion of an isotensor field and isodistribution. Verf. bewei...	0
The semigroup $(P^t)_t$ of any one-dimensional diffusion in the general sense of Mandl satisfies the variation diminishing property: The sign changes of $\mu P^t$ decreases in $t$. The proof given by the reviewer [in: Markov processes and control theory. Math. Res. 54, 164-177 (1989; Zbl 0694.60072)], relies on a...	1
The semigroup $(P^t)_t$ of any one-dimensional diffusion in the general sense of Mandl satisfies the variation diminishing property: The sign changes of $\mu P^t$ decreases in $t$. The proof given by the reviewer [in: Markov processes and control theory. Math. Res. 54, 164-177 (1989; Zbl 0694.60072)], relies on a...	0
Let $\text{PG}(5,q)$ be the projective space of dimension $5$ over the finite field with $q$ elements. Let $\mathcal K$ be the Klein quadric of order $q$, i.e.\ the hyperbolic quadric contained in $\text{PG}(5,q)$. A $k$-cap of $\mathcal K$ is a set of $k$ points of $\mathcal K$ no three of which ar...	1
Let $\text{PG}(5,q)$ be the projective space of dimension $5$ over the finite field with $q$ elements. Let $\mathcal K$ be the Klein quadric of order $q$, i.e.\ the hyperbolic quadric contained in $\text{PG}(5,q)$. A $k$-cap of $\mathcal K$ is a set of $k$ points of $\mathcal K$ no three of which ar...	0
A generalized indefinite string is a triple $(L, \omega , v)$ where $L \in(0, \infty ]$, $\omega $ is a real distribution in $H_{\mathrm{loc}}^{-1} [0, L)$ and $v$ is a non-negative Borel measure on the interval $[0, L)$. Associated with this string is the differential equation \(-f''= z \omega f + z ^2 vf ...	1
A generalized indefinite string is a triple $(L, \omega , v)$ where $L \in(0, \infty ]$, $\omega $ is a real distribution in $H_{\mathrm{loc}}^{-1} [0, L)$ and $v$ is a non-negative Borel measure on the interval $[0, L)$. Associated with this string is the differential equation \(-f''= z \omega f + z ^2 vf ...	0
In the $n$-dimensional Euclidean space $\mathbb{R}^n$, let $K$ be a compact convex subset, and let $K_1$ be the Steiner symmetral of $K$ with respect to the hyperplane $e_1^{\perp}$, orthogonal to a unit vector $e_1\in\mathbb{R}^n$. Namely, $K_1$ is obtained by translating all the chords of $K$ in dir...	1
In the $n$-dimensional Euclidean space $\mathbb{R}^n$, let $K$ be a compact convex subset, and let $K_1$ be the Steiner symmetral of $K$ with respect to the hyperplane $e_1^{\perp}$, orthogonal to a unit vector $e_1\in\mathbb{R}^n$. Namely, $K_1$ is obtained by translating all the chords of $K$ in dir...	0
A conjecture of Deligne states that the special values of motivic $L$-functions may be expressed as algebraic numbers times certain periods. This expository article describes the situation for algebraic Hecke characters, that is cohomological automorphic representations of $\mathrm{GL}_1$. The first 5 sections syst...	1
A conjecture of Deligne states that the special values of motivic $L$-functions may be expressed as algebraic numbers times certain periods. This expository article describes the situation for algebraic Hecke characters, that is cohomological automorphic representations of $\mathrm{GL}_1$. The first 5 sections syst...	0
For $G$ a compact Lie group and $X$ a compact $G$-space, the Atiyah-Segal theorem (Theorem 1.1) identifies the topological $K$-theory of the Borel space $X_G=X\times_GE_G$ with the completion of the equivariant $K$-theory of $X$ with respect to the augmentation ideal, assuming a finiteness condition on th...	1
For $G$ a compact Lie group and $X$ a compact $G$-space, the Atiyah-Segal theorem (Theorem 1.1) identifies the topological $K$-theory of the Borel space $X_G=X\times_GE_G$ with the completion of the equivariant $K$-theory of $X$ with respect to the augmentation ideal, assuming a finiteness condition on th...	0
The paper under review regards singular holomorphic foliations $\mathcal F$ on the complex projective plane $\mathbb P^2$. Roughly speaking, the Baum-Bott map associates to a foliation the Baum-Bott indexes of its singularities. See also [\textit{A. Lins Neto} et al., Compos. Math. 142, No. 6, 1549--1586 (2006; Zbl...	1
The paper under review regards singular holomorphic foliations $\mathcal F$ on the complex projective plane $\mathbb P^2$. Roughly speaking, the Baum-Bott map associates to a foliation the Baum-Bott indexes of its singularities. See also [\textit{A. Lins Neto} et al., Compos. Math. 142, No. 6, 1549--1586 (2006; Zbl...	0
The authors make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition introduced in [\textit{G. Mastroeni}, in: Equilibrium problems and variational models, Nonconvex Optim. Appl. 6...	1
The authors make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition introduced in [\textit{G. Mastroeni}, in: Equilibrium problems and variational models, Nonconvex Optim. Appl. 6...	0
The main result of the book consist in (1) the identification and analysis of those categories of parallelism which are far beyond the ones typically associated with PROLOG (namely AND- and OR-parallelism), and (2) the derivation of MMLOP logic-based language suitable both for the specification of parallel problems and...	1
The main result of the book consist in (1) the identification and analysis of those categories of parallelism which are far beyond the ones typically associated with PROLOG (namely AND- and OR-parallelism), and (2) the derivation of MMLOP logic-based language suitable both for the specification of parallel problems and...	0
A lower bound for the Hausdorff dimension of the non-self-similar fractal $A_{F,T}$ generated by a certain family of constructions $F=(f_ 1,\dots,f_ p)$ (hyperbolic iterated function system) and a square matrix $T$ is found. The answer is given in terms of the lower bounds $r_ i$, $1\leq i\leq p$, of the Lips...	1
A lower bound for the Hausdorff dimension of the non-self-similar fractal $A_{F,T}$ generated by a certain family of constructions $F=(f_ 1,\dots,f_ p)$ (hyperbolic iterated function system) and a square matrix $T$ is found. The answer is given in terms of the lower bounds $r_ i$, $1\leq i\leq p$, of the Lips...	0

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Let \(X\) be a complete, connected and finitely connected Alexandrov space without boundary of dimension two whose curvature is bounded below by a constant and admitting total curvature. Denote by \(F_p\) the union of all rays in \(X\) emanating from the point \(p\in X\) and by \(A(p)\) the set of the directions of ray...	1
Let \(X\) be a complete, connected and finitely connected Alexandrov space without boundary of dimension two whose curvature is bounded below by a constant and admitting total curvature. Denote by \(F_p\) the union of all rays in \(X\) emanating from the point \(p\in X\) and by \(A(p)\) the set of the directions of ray...	0
The authors determine all integers \(x\) such that \(x^2-1\) has only prime factors smaller than 100. They write \(x^2-dy^2=1\), and solve the Pell equation by first computing the regulator of the ring of integers of the corresponding quadratic field and then from the regulator obtaining a compact representation of the...	1
The authors determine all integers \(x\) such that \(x^2-1\) has only prime factors smaller than 100. They write \(x^2-dy^2=1\), and solve the Pell equation by first computing the regulator of the ring of integers of the corresponding quadratic field and then from the regulator obtaining a compact representation of the...	0
Kripke semantics for predicate modal logic provides a translation of the formulas of this logic into classical predicate logic. Attempts to use this translation directly for automated deduction were hopeless: too many irrelevant clauses were generated. The author proposed earlier [Lect. Notes Comput. Sci. 310, 500-516 ...	1
Kripke semantics for predicate modal logic provides a translation of the formulas of this logic into classical predicate logic. Attempts to use this translation directly for automated deduction were hopeless: too many irrelevant clauses were generated. The author proposed earlier [Lect. Notes Comput. Sci. 310, 500-516 ...	0
Let \({\mathcal C}_n\) be a local quasi-analytic subring of the ring of germs of \(C^\infty\) functions on \(\mathbb R^n\) and let \({\mathcal C}=\{{\mathcal C}_n,\;n\in\mathbb N\}.\) Let us denote by \(\hat{\cdot}:{\mathcal C}_n \rightarrow\mathbb R[[x_1,\dots,x_n]]\) the map which associates to each \(f\in{\mathcal C...	1
Let \({\mathcal C}_n\) be a local quasi-analytic subring of the ring of germs of \(C^\infty\) functions on \(\mathbb R^n\) and let \({\mathcal C}=\{{\mathcal C}_n,\;n\in\mathbb N\}.\) Let us denote by \(\hat{\cdot}:{\mathcal C}_n \rightarrow\mathbb R[[x_1,\dots,x_n]]\) the map which associates to each \(f\in{\mathcal C...	0
In the paper under review the author discusses the thesis of \textit{B. Vitrac} (1993) mentioned in the title. Recently \textit{B. Vitrac} published a French translation of Euclid's Elements [Euklid. Les Eléments. Volume I. Livres I--IV: Géométrie plane. Traduits du texte grec de Heiberg et avec commentaires par Bernar...	1
In the paper under review the author discusses the thesis of \textit{B. Vitrac} (1993) mentioned in the title. Recently \textit{B. Vitrac} published a French translation of Euclid's Elements [Euklid. Les Eléments. Volume I. Livres I--IV: Géométrie plane. Traduits du texte grec de Heiberg et avec commentaires par Bernar...	0
This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let \(\Omega \subset \mathbb{R}^n\) be an unbounded open set and let \(X\) be the space of bounded and continuous functions on \(\overline \Omega\). For \(p \geq 0\), let \(W_p (s) = (1 + \|s \|)^p\) an...	1
This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let \(\Omega \subset \mathbb{R}^n\) be an unbounded open set and let \(X\) be the space of bounded and continuous functions on \(\overline \Omega\). For \(p \geq 0\), let \(W_p (s) = (1 + \|s \|)^p\) an...	0
The Gauss-Bonnet theorem expresses the Euler characteristic of a surface with geodesic boundary as \(2\pi\) times the integral of the Gaussian curvature. Its extension to higher dimension due to Chern involves the Pfaffian polynomial in the curvature tensor. The Euler characteristic may be interpreted as the index of t...	1
The Gauss-Bonnet theorem expresses the Euler characteristic of a surface with geodesic boundary as \(2\pi\) times the integral of the Gaussian curvature. Its extension to higher dimension due to Chern involves the Pfaffian polynomial in the curvature tensor. The Euler characteristic may be interpreted as the index of t...	0
The minimization method for a quadratic functional with linear constraints, which is proposed in this paper, generalizes the technique previously published by the first author (see [\textit{A. A. Tret'yakov}, Russ. J. Numer. Anal. Math. Model. 25, No. 3, 279--288 (2010; Zbl 1193.65102)]). The aim of the authors is to o...	1
The minimization method for a quadratic functional with linear constraints, which is proposed in this paper, generalizes the technique previously published by the first author (see [\textit{A. A. Tret'yakov}, Russ. J. Numer. Anal. Math. Model. 25, No. 3, 279--288 (2010; Zbl 1193.65102)]). The aim of the authors is to o...	0
The first author has revived the theory of corings [in Algebr. Represent. Theory 5, No. 4, 389-410 (2002; Zbl 1025.16017)]. One of the main aims was the development of a Galois theory for corings, providing a new and elegant approach to Hopf-Galois theory. In the final section of his paper, the first author mentioned t...	1
The first author has revived the theory of corings [in Algebr. Represent. Theory 5, No. 4, 389-410 (2002; Zbl 1025.16017)]. One of the main aims was the development of a Galois theory for corings, providing a new and elegant approach to Hopf-Galois theory. In the final section of his paper, the first author mentioned t...	0
The indicatory property was defined in [\textit{S. Watanabe} and \textit{F. Ikeda}, JP J. Geom. Topol. 4, No. 2, 141--146 (2004; Zbl 1065.53058)]. The paper studies basic properties of indicatory Riemannian spaces defined by tensor fields of type \((0,k)\), \(k\in\{2,3,4\}\). In Finsler spaces, the indicatory tensors (...	1
The indicatory property was defined in [\textit{S. Watanabe} and \textit{F. Ikeda}, JP J. Geom. Topol. 4, No. 2, 141--146 (2004; Zbl 1065.53058)]. The paper studies basic properties of indicatory Riemannian spaces defined by tensor fields of type \((0,k)\), \(k\in\{2,3,4\}\). Official trials were conducted of a number ...	0
In [\textit{L. Pirio} and \textit{J.-M. Trépreau}, Int. Math. Res. Not. 2015, No. 13, 4449--4504 (2015; Zbl 1406.32014)], it has been proved that for \(r>1\), \(n\geq 2\) and \(d\geq (r+1)(n-1)+2\), a \(d\)-web of type \((r,n)\) with maximal rank is algebraizable in the classical sense, except maybe when \(n\geq 3\) an...	1
In [\textit{L. Pirio} and \textit{J.-M. Trépreau}, Int. Math. Res. Not. 2015, No. 13, 4449--4504 (2015; Zbl 1406.32014)], it has been proved that for \(r>1\), \(n\geq 2\) and \(d\geq (r+1)(n-1)+2\), a \(d\)-web of type \((r,n)\) with maximal rank is algebraizable in the classical sense, except maybe when \(n\geq 3\) an...	0
The main results of the paper are concerned around \textit{J. Herzog}'s question [see ``Homological properties of the modules of differentials'', Colecao Atas Soc. Brasileira Mat. 14 (1981)]: Let P be a regular local ring containing the rationals, let I be an ideal, and set \(R=P/I\). Then does the vanishing of the cot...	1
The main results of the paper are concerned around \textit{J. Herzog}'s question [see ``Homological properties of the modules of differentials'', Colecao Atas Soc. Brasileira Mat. 14 (1981)]: Let P be a regular local ring containing the rationals, let I be an ideal, and set \(R=P/I\). Then does the vanishing of the cot...	0
This paper considers representations of the fundamental group \(\Gamma_g\) of the closed surface of genus \(g\) in \(\text{PSL}(2,\mathbb{R})\). Each such representation has an associated Euler class. The authors show that the Euler class of a discrete representation (i.e., one whose image is a discrete subgroup of \(\...	1
This paper considers representations of the fundamental group \(\Gamma_g\) of the closed surface of genus \(g\) in \(\text{PSL}(2,\mathbb{R})\). Each such representation has an associated Euler class. The authors show that the Euler class of a discrete representation (i.e., one whose image is a discrete subgroup of \(\...	0
The authors study the stabilization of control systems modelled by an abstract retarded functional differential equation with infinite delay. The results reported in the paper extend those given by the first author in [Syst. Control Lett. 44, No. 1, 35--43 (2001; Zbl 0986.93057)] for the finite delay case. It is shown ...	1
The authors study the stabilization of control systems modelled by an abstract retarded functional differential equation with infinite delay. The results reported in the paper extend those given by the first author in [Syst. Control Lett. 44, No. 1, 35--43 (2001; Zbl 0986.93057)] for the finite delay case. It is shown ...	0
Let \(X\) be a compact Kähler manifold of dimension \(n\). By the Hodge decomposition theorem the \(n\)-th complex de Rham cohomology group \(H^n(X,\mathbb{Z})\otimes\mathbb{C}\) of \(X\) can be written as the direct sum \(H^n(X,\mathbb{Z})\otimes\mathbb{C} =\sum_{p+q=n}H^{p,q}(X)\), where \(H^{p,q}(X)\) denotes the co...	1
Let \(X\) be a compact Kähler manifold of dimension \(n\). By the Hodge decomposition theorem the \(n\)-th complex de Rham cohomology group \(H^n(X,\mathbb{Z})\otimes\mathbb{C}\) of \(X\) can be written as the direct sum \(H^n(X,\mathbb{Z})\otimes\mathbb{C} =\sum_{p+q=n}H^{p,q}(X)\), where \(H^{p,q}(X)\) denotes the co...	0
Let \(f:X\rightarrow X\) be a map of a continuum (i.e., a compact, connected metric space) to itself. By \(\Omega(f)\), the nonwandering points of \(f\), we mean those \(x\in X\) such that for any open neighborhood \(U\) of \(x\), there exists \(y\in U\) and \(n\in\mathbb N\) such that \(f^n(y)\in U\). We call \(x\) an...	1
Let \(f:X\rightarrow X\) be a map of a continuum (i.e., a compact, connected metric space) to itself. By \(\Omega(f)\), the nonwandering points of \(f\), we mean those \(x\in X\) such that for any open neighborhood \(U\) of \(x\), there exists \(y\in U\) and \(n\in\mathbb N\) such that \(f^n(y)\in U\). We call \(x\) an...	0
Actually considered is an IBV-problem for the linearized system of Navier-Stokes equations for a viscous compressible fluid in two state dimensions. The linearization is done around a steady state solution, the domain is a rectangle and its boundary is controlled. With a performance functional inspired from the article...	1
Actually considered is an IBV-problem for the linearized system of Navier-Stokes equations for a viscous compressible fluid in two state dimensions. The linearization is done around a steady state solution, the domain is a rectangle and its boundary is controlled. With a performance functional inspired from the article...	0
This is an attractive survey paper dealing with the problem how to discretize a manifold by selecting a large finite subset of its points. Natural candidates for such good point sets are point sets that minimize a certain energy functional. Suppose that the compact manifold \(A\) is embedded in a Euclidean space. A mi...	1
This is an attractive survey paper dealing with the problem how to discretize a manifold by selecting a large finite subset of its points. Natural candidates for such good point sets are point sets that minimize a certain energy functional. Suppose that the compact manifold \(A\) is embedded in a Euclidean space. A mi...	0
A Catalan triangulation of the Möbius band is an abstract simplicial complex that uses no interior vertices. The authors present a generating function for the number of triangulations with \(n\) vertices analogous to that for Catalan triangulations of the disk [see, for example, \textit{D. D. Sleator}, \textit{R. E. Ta...	1
A Catalan triangulation of the Möbius band is an abstract simplicial complex that uses no interior vertices. The authors present a generating function for the number of triangulations with \(n\) vertices analogous to that for Catalan triangulations of the disk [see, for example, \textit{D. D. Sleator}, \textit{R. E. Ta...	0
The type-II hidden symmetries are extra symmetries appearing when the number of variables in PDEq is reduced by a variable transformation found from a Lie symmetry of this PDE. The main of the goal of the article is to show that the provenance of the type II Lie point hidden symmetries found for differential equations ...	1
The type-II hidden symmetries are extra symmetries appearing when the number of variables in PDEq is reduced by a variable transformation found from a Lie symmetry of this PDE. The main of the goal of the article is to show that the provenance of the type II Lie point hidden symmetries found for differential equations ...	0
Authors' abstract: The Harnack inequality established in \textit{M. Röckner} and \textit{F.-Y. Wang} [J.~Funct.~Anal.~203, No. 1, 237--261 (2003; Zbl 1059.47051)] for generalized Mehler semigroup is improved and generalized. As applications, log-Harnack inequality, the strong Feller property, the hyper-bounded property...	1
Authors' abstract: The Harnack inequality established in \textit{M. Röckner} and \textit{F.-Y. Wang} [J.~Funct.~Anal.~203, No. 1, 237--261 (2003; Zbl 1059.47051)] for generalized Mehler semigroup is improved and generalized. As applications, log-Harnack inequality, the strong Feller property, the hyper-bounded property...	0
Let \(F\) be an infinite field of characteristic not equal to \(2\), \(G\) an algebraic group over \(F\), \(V\) an algebraic \(F\)-representation (i.e. an algebraic group morphism \(G\to\text{GL}_F(V)\)), \(F(V)\) the field of rational functions, and \(F(V)^G\) the invariant field of \(F(V)\) with respect to the natura...	1
Let \(F\) be an infinite field of characteristic not equal to \(2\), \(G\) an algebraic group over \(F\), \(V\) an algebraic \(F\)-representation (i.e. an algebraic group morphism \(G\to\text{GL}_F(V)\)), \(F(V)\) the field of rational functions, and \(F(V)^G\) the invariant field of \(F(V)\) with respect to the natura...	0
Let \(G\) be a group, \(A\) a \(G\)-graded ring. The author obtains necessary and sufficient conditions for the smash product \(A \# G^*\) to be prime and simple, generalizing the results for finite \(G\) obtained in [\textit{S. Montgomery} and \textit{D. S. Passman}, J. Algebra 115, 92-124 (1988; Zbl 0639.16002)]. Let...	1
Let \(G\) be a group, \(A\) a \(G\)-graded ring. The author obtains necessary and sufficient conditions for the smash product \(A \# G^*\) to be prime and simple, generalizing the results for finite \(G\) obtained in [\textit{S. Montgomery} and \textit{D. S. Passman}, J. Algebra 115, 92-124 (1988; Zbl 0639.16002)]. A r...	0
The author continues his work on the almost sure central limit theorem (ASCLT) [Studia Sci. Math. Hungar. 31, No. 1-3, 197-202 (1996)]. Firstly, he extends an ASCLT for a sequence of \(\varphi\)-mixing random variables to the \(\rho\)-mixing case, where \(\varphi^{1/2} ()\) is replaced by \(\rho ()\). Secondly, he gi...	1
The author continues his work on the almost sure central limit theorem (ASCLT) [Studia Sci. Math. Hungar. 31, No. 1-3, 197-202 (1996)]. Firstly, he extends an ASCLT for a sequence of \(\varphi\)-mixing random variables to the \(\rho\)-mixing case, where \(\varphi^{1/2} ()\) is replaced by \(\rho ()\). Secondly, he gi...	0
The object of study is the parabolic equation \(\partial_t u-\nabla\cdot a(x,t,u,\nabla u)=b(x,t,u,\nabla u)\), where \(a\) is assumed to be degenerately elliptic, with what is called ``\(p \)-growth'' with respect to the gradient variable at \(0\) and \(\infty\). It is proven that on balls, where a certain Wolff pote...	1
The object of study is the parabolic equation \(\partial_t u-\nabla\cdot a(x,t,u,\nabla u)=b(x,t,u,\nabla u)\), where \(a\) is assumed to be degenerately elliptic, with what is called ``\(p \)-growth'' with respect to the gradient variable at \(0\) and \(\infty\). It is proven that on balls, where a certain Wolff pote...	0
A (2-dimensional) surface \(M\) in the Lorentzian space \(\mathbb{R}^n_1\) is called time-like if the induced scalar product on \(TM\) is indefinite. The authors identify \(\mathbb{R}^2\) with the ring \(\mathbb{D}\) of double (\(\equiv\) split complex) numbers \(a+jb\), \(j^2=1\), consider the standard embedding of \(...	1
A (2-dimensional) surface \(M\) in the Lorentzian space \(\mathbb{R}^n_1\) is called time-like if the induced scalar product on \(TM\) is indefinite. The authors identify \(\mathbb{R}^2\) with the ring \(\mathbb{D}\) of double (\(\equiv\) split complex) numbers \(a+jb\), \(j^2=1\), consider the standard embedding of \(...	0
The paper investigates a generalizations of Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions by introducing a notion of \(c\)-differential uniformity: Given a \(p\)-ary \((n, m)\)-function \(f : \mathbb{F}_p^n\rightarrow \mathbb{F}_p^m\), and \(c\in\mathbb{F}_p^m\), the \(c\)-derivative of \(f\) with...	1
The paper investigates a generalizations of Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions by introducing a notion of \(c\)-differential uniformity: Given a \(p\)-ary \((n, m)\)-function \(f : \mathbb{F}_p^n\rightarrow \mathbb{F}_p^m\), and \(c\in\mathbb{F}_p^m\), the \(c\)-derivative of \(f\) with...	0
A first result proved in this paper shows that for an arbitrary monic univariate complex polynomial whose coefficients are in \(C^k(I)\) for some compact real interval \(I\) there exist an integer \(k\geq 1\) and a rational number \(p > 1\), both depending only on the degree, such that any continuous choice of roots is...	1
A first result proved in this paper shows that for an arbitrary monic univariate complex polynomial whose coefficients are in \(C^k(I)\) for some compact real interval \(I\) there exist an integer \(k\geq 1\) and a rational number \(p > 1\), both depending only on the degree, such that any continuous choice of roots is...	0
Toth's ``Glimpses'' offer selected material that connect algebra and geometry (but also number-theoretic and topological topics), at a level that is meant to ``fill the gap between undergraduate and graduate mathematics studies''. The concept was to present this in a rather informal style in a discussion that goes far ...	1
Toth's ``Glimpses'' offer selected material that connect algebra and geometry (but also number-theoretic and topological topics), at a level that is meant to ``fill the gap between undergraduate and graduate mathematics studies''. The concept was to present this in a rather informal style in a discussion that goes far ...	0
The author gives a down-to-earth introduction to the theory of \(p\)-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the \(U_p\)-operator acting on \(S_k(\Gamma_1(N_p))\) is bounded below ...	1
The author gives a down-to-earth introduction to the theory of \(p\)-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the \(U_p\)-operator acting on \(S_k(\Gamma_1(N_p))\) is bounded below ...	0
The paper is a collection of results on real-valued Baire one functions, defined over an arbitrary topological space $X$. The main results, as it seems, are Theorems 5.4 and 5.6 which characterise $B_1$-embeddings ($B_1^*$-embeddings) in $X$, i.e., subspaces $Y\subset X$ that allow any (resp.\ bounded) Baire one functi...	1
The paper is a collection of results on real-valued Baire one functions, defined over an arbitrary topological space $X$. The main results, as it seems, are Theorems 5.4 and 5.6 which characterise $B_1$-embeddings ($B_1^*$-embeddings) in $X$, i.e., subspaces $Y\subset X$ that allow any (resp.\ bounded) Baire one functi...	0
The author presents a complete solution of the Jacobian problem for vector fields on the plane by proving the following theorem: Suppose that \(v\) is a vector field in \(\mathbb{R}^2\) such that \(v(0)=0\), and suppose that \(\text{div } v< 0\) and \(J(v)> 0\) on the whole plane, where \(J(v)\) is the Jacobian (that i...	1
The author presents a complete solution of the Jacobian problem for vector fields on the plane by proving the following theorem: Suppose that \(v\) is a vector field in \(\mathbb{R}^2\) such that \(v(0)=0\), and suppose that \(\text{div } v< 0\) and \(J(v)> 0\) on the whole plane, where \(J(v)\) is the Jacobian (that i...	0
The author comments on some of the results obtained by \textit{A. Barron}, \textit{L. Birgé} and \textit{P. Massard} [Probab. Theory Relat. Fields 113, No. 3, 301-413 (1999; see the preceding entry, Zbl 0946.62036)] via the results on sharp minimax estimation, where the squared integrated risk converges with optimal ra...	1
The author comments on some of the results obtained by \textit{A. Barron}, \textit{L. Birgé} and \textit{P. Massard} [Probab. Theory Relat. Fields 113, No. 3, 301-413 (1999; see the preceding entry, Zbl 0946.62036)] via the results on sharp minimax estimation, where the squared integrated risk converges with optimal ra...	0
Let \(R\) denote a Noetherian ring, let \(\mathfrak a \subset R\) be an ideal of \(R\) and let \(M\) be a finitely generated \(R\)-module. For an integer \(i \geq 0\) let \(H^i_{\mathfrak a}(M)\) denote the \(i\)-th local cohomology module of \(M\) with respect to \(\mathfrak a.\) The aim of this note is to show that t...	1
Let \(R\) denote a Noetherian ring, let \(\mathfrak a \subset R\) be an ideal of \(R\) and let \(M\) be a finitely generated \(R\)-module. For an integer \(i \geq 0\) let \(H^i_{\mathfrak a}(M)\) denote the \(i\)-th local cohomology module of \(M\) with respect to \(\mathfrak a.\) The aim of this note is to show that t...	0
A long-standing problem in the study of fuzzy logics is to understand and justify the motivation behind them. Two traditional approaches have tried to tackle this problem. A semantical approach aims to develop a framework for dealing with statements which are not necessarily fully true or fully false and modifies class...	1
A long-standing problem in the study of fuzzy logics is to understand and justify the motivation behind them. Two traditional approaches have tried to tackle this problem. A semantical approach aims to develop a framework for dealing with statements which are not necessarily fully true or fully false and modifies class...	0
The paper deals with two-level optimization problems. A function F(x,y) must be minimized with respect to x and subject to some constraints on x. The vector y, being a function of x, is the result of another minimization; minimize f(x,y), subject to some (combined) constraints on x and y. The problem can be viewed as a...	1
The paper deals with two-level optimization problems. A function F(x,y) must be minimized with respect to x and subject to some constraints on x. The vector y, being a function of x, is the result of another minimization; minimize f(x,y), subject to some (combined) constraints on x and y. The problem can be viewed as a...	0
There is a well-developed theory that examines the spectrum of the Laplace operator on manifolds. Less is known about the spectrum of the Laplace operator on forms. This paper uses Seiberg-Witten theory to derive an upper bound on the first eigenvalue of the Hodge Laplacian on co-exact \(1\)-forms on a wide class of \(...	1
There is a well-developed theory that examines the spectrum of the Laplace operator on manifolds. Less is known about the spectrum of the Laplace operator on forms. This paper uses Seiberg-Witten theory to derive an upper bound on the first eigenvalue of the Hodge Laplacian on co-exact \(1\)-forms on a wide class of \(...	0
The author considers the definable set \(S\) [see \textit{L. van den Dries}, Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. 248. Cambridge: Cambridge Univ. Press (1998; Zbl 0953.03045)] and studies the scalar curvature measure on \(S\) -- a generalization of the integral scalar...	1
The author considers the definable set \(S\) [see \textit{L. van den Dries}, Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. 248. Cambridge: Cambridge Univ. Press (1998; Zbl 0953.03045)] and studies the scalar curvature measure on \(S\) -- a generalization of the integral scalar...	0
The author studies the Keller-Segel-Navier-Stokes system \[\begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (n \nabla c) + \rho n - \mu n^2, & \quad (x,t) \in \Omega \times (0,\infty),\\ c_t + u \cdot \nabla c = \Delta c -c +n, & \quad (x,t) \in \Omega \times (0,\infty), \\ u_t + (u \cdot \nabla) u =...	1
The author studies the Keller-Segel-Navier-Stokes system \[\begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (n \nabla c) + \rho n - \mu n^2, & \quad (x,t) \in \Omega \times (0,\infty),\\ c_t + u \cdot \nabla c = \Delta c -c +n, & \quad (x,t) \in \Omega \times (0,\infty), \\ u_t + (u \cdot \nabla) u =...	0
This is a continuation of previous work by the authors on the theory of isomanifolds [Tsagas-Sourlas, Isomanifolds..., ibid. 12, No. 1, 1-65 (1995; see the paper above)]. In the present paper they study isomappings between isomanifolds and also introduce the notion of an isotensor field and isodistribution. The notion ...	1
This is a continuation of previous work by the authors on the theory of isomanifolds [Tsagas-Sourlas, Isomanifolds..., ibid. 12, No. 1, 1-65 (1995; see the paper above)]. In the present paper they study isomappings between isomanifolds and also introduce the notion of an isotensor field and isodistribution. Verf. bewei...	0
The semigroup \((P^t)_t\) of any one-dimensional diffusion in the general sense of Mandl satisfies the variation diminishing property: The sign changes of \(\mu P^t\) decreases in \(t\). The proof given by the reviewer [in: Markov processes and control theory. Math. Res. 54, 164-177 (1989; Zbl 0694.60072)], relies on a...	1
The semigroup \((P^t)_t\) of any one-dimensional diffusion in the general sense of Mandl satisfies the variation diminishing property: The sign changes of \(\mu P^t\) decreases in \(t\). The proof given by the reviewer [in: Markov processes and control theory. Math. Res. 54, 164-177 (1989; Zbl 0694.60072)], relies on a...	0
Let \(\text{PG}(5,q)\) be the projective space of dimension \(5\) over the finite field with \(q\) elements. Let \(\mathcal K\) be the Klein quadric of order \(q\), i.e.\ the hyperbolic quadric contained in \(\text{PG}(5,q)\). A \(k\)-cap of \(\mathcal K\) is a set of \(k\) points of \(\mathcal K\) no three of which ar...	1
Let \(\text{PG}(5,q)\) be the projective space of dimension \(5\) over the finite field with \(q\) elements. Let \(\mathcal K\) be the Klein quadric of order \(q\), i.e.\ the hyperbolic quadric contained in \(\text{PG}(5,q)\). A \(k\)-cap of \(\mathcal K\) is a set of \(k\) points of \(\mathcal K\) no three of which ar...	0
A generalized indefinite string is a triple \((L, \omega , v)\) where \(L \in(0, \infty ]\), \(\omega \) is a real distribution in \(H_{\mathrm{loc}}^{-1} [0, L)\) and \(v\) is a non-negative Borel measure on the interval \([0, L)\). Associated with this string is the differential equation \(-f''= z \omega f + z ^2 vf ...	1
A generalized indefinite string is a triple \((L, \omega , v)\) where \(L \in(0, \infty ]\), \(\omega \) is a real distribution in \(H_{\mathrm{loc}}^{-1} [0, L)\) and \(v\) is a non-negative Borel measure on the interval \([0, L)\). Associated with this string is the differential equation \(-f''= z \omega f + z ^2 vf ...	0
In the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\), let \(K\) be a compact convex subset, and let \(K_1\) be the Steiner symmetral of \(K\) with respect to the hyperplane \(e_1^{\perp}\), orthogonal to a unit vector \(e_1\in\mathbb{R}^n\). Namely, \(K_1\) is obtained by translating all the chords of \(K\) in dir...	1
In the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\), let \(K\) be a compact convex subset, and let \(K_1\) be the Steiner symmetral of \(K\) with respect to the hyperplane \(e_1^{\perp}\), orthogonal to a unit vector \(e_1\in\mathbb{R}^n\). Namely, \(K_1\) is obtained by translating all the chords of \(K\) in dir...	0
A conjecture of Deligne states that the special values of motivic \(L\)-functions may be expressed as algebraic numbers times certain periods. This expository article describes the situation for algebraic Hecke characters, that is cohomological automorphic representations of \(\mathrm{GL}_1\). The first 5 sections syst...	1
A conjecture of Deligne states that the special values of motivic \(L\)-functions may be expressed as algebraic numbers times certain periods. This expository article describes the situation for algebraic Hecke characters, that is cohomological automorphic representations of \(\mathrm{GL}_1\). The first 5 sections syst...	0
For \(G\) a compact Lie group and \(X\) a compact \(G\)-space, the Atiyah-Segal theorem (Theorem 1.1) identifies the topological \(K\)-theory of the Borel space \(X_G=X\times_GE_G\) with the completion of the equivariant \(K\)-theory of \(X\) with respect to the augmentation ideal, assuming a finiteness condition on th...	1
For \(G\) a compact Lie group and \(X\) a compact \(G\)-space, the Atiyah-Segal theorem (Theorem 1.1) identifies the topological \(K\)-theory of the Borel space \(X_G=X\times_GE_G\) with the completion of the equivariant \(K\)-theory of \(X\) with respect to the augmentation ideal, assuming a finiteness condition on th...	0
The paper under review regards singular holomorphic foliations \(\mathcal F\) on the complex projective plane \(\mathbb P^2\). Roughly speaking, the Baum-Bott map associates to a foliation the Baum-Bott indexes of its singularities. See also [\textit{A. Lins Neto} et al., Compos. Math. 142, No. 6, 1549--1586 (2006; Zbl...	1
The paper under review regards singular holomorphic foliations \(\mathcal F\) on the complex projective plane \(\mathbb P^2\). Roughly speaking, the Baum-Bott map associates to a foliation the Baum-Bott indexes of its singularities. See also [\textit{A. Lins Neto} et al., Compos. Math. 142, No. 6, 1549--1586 (2006; Zbl...	0
The authors make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition introduced in [\textit{G. Mastroeni}, in: Equilibrium problems and variational models, Nonconvex Optim. Appl. 6...	1
The authors make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition introduced in [\textit{G. Mastroeni}, in: Equilibrium problems and variational models, Nonconvex Optim. Appl. 6...	0
The main result of the book consist in (1) the identification and analysis of those categories of parallelism which are far beyond the ones typically associated with PROLOG (namely AND- and OR-parallelism), and (2) the derivation of MMLOP logic-based language suitable both for the specification of parallel problems and...	1
The main result of the book consist in (1) the identification and analysis of those categories of parallelism which are far beyond the ones typically associated with PROLOG (namely AND- and OR-parallelism), and (2) the derivation of MMLOP logic-based language suitable both for the specification of parallel problems and...	0
A lower bound for the Hausdorff dimension of the non-self-similar fractal \(A_{F,T}\) generated by a certain family of constructions \(F=(f_ 1,\dots,f_ p)\) (hyperbolic iterated function system) and a square matrix \(T\) is found. The answer is given in terms of the lower bounds \(r_ i\), \(1\leq i\leq p\), of the Lips...	1
A lower bound for the Hausdorff dimension of the non-self-similar fractal \(A_{F,T}\) generated by a certain family of constructions \(F=(f_ 1,\dots,f_ p)\) (hyperbolic iterated function system) and a square matrix \(T\) is found. The answer is given in terms of the lower bounds \(r_ i\), \(1\leq i\leq p\), of the Lips...	0