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- ArtykułOtwarty dostępAsymptotic analysis for confluent hypergeometric function in two variables given by double integral(Wydawnictwa AGH, 2024) Haraoka, YoshishigeWe study an integrable connection with irregular singularities along a normally crossing divisor. The connection is obtained from an integrable connection of regular singular type by a confluence, and has irregular singularities along $x=\infty$ and $y=\infty$. Solutions are expressed by a double integral of Euler type with resonances among the exponents in the integrand. We specify twisted cycles that give main asymptotic behaviors in sectorial domains around $(\infty,\infty)$. Then we obtain linear relations among the twisted cycles, and get an explicit expression of the Stokes multiplier. The methods to derive the asymptotic behaviors for double integrals and to get linear relations among twisted cycles in resonant case, which we developed in this paper, seem to be new.We study an integrable connection with irregular singularities along a normally crossing divisor. The connection is obtained from an integrable connection of regular singular type by a confluence, and has irregular singularities along $x=\infty$ and $y=\infty$. Solutions are expressed by a double integral of Euler type with resonances among the exponents in the integrand. We specify twisted cycles that give main asymptotic behaviors in sectorial domains around $(\infty,\infty)$. Then we obtain linear relations among the twisted cycles, and get an explicit expression of the Stokes multiplier. The methods to derive the asymptotic behaviors for double integrals and to get linear relations among twisted cycles in resonant case, which we developed in this paper, seem to be new.
- ArtykułOtwarty dostępCesàro summability of Taylor series in higher order weighted Dirichlet-type spaces(Wydawnictwa AGH, 2024) Ghara, Soumitra; Gupta, Rajeev; Reza, Md. RamizFor a positive integer $m$ and a finite non-negative Borel measure $\mu$ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces $\mathcal H_{\mu, m}$. We show that if $\alpha\gt\frac{1}{2}$, then for any $f$ in $\mathcal H_{\mu, m}$ the sequence of generalized Ces?ro sums $\{\sigma_n^{\alpha}[f]\}$ converges to $f$. We further show that if $\alpha=\frac{1}{2}$ then for the Dirac delta measure supported at any point on the unit circle, the previous statement breaks down for every positive integer $m$.
- ArtykułOtwarty dostępDegenerate singular parabolic problems with natural growth(Wydawnictwa AGH, 2024) El Ouardy, Mounim; El Hadfi, Youssef; Sbai, AbdelaazizIn this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term $\$ \begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{|\nabla u|^{p}}{u^{\gamma}}=f & \text{ in } Q,\\ u(x,t)=0 & \text{ on } \Gamma, \\ u(x,t=0)=u_{0}(x) & \text{ in } \Omega, \end{cases} \$$ where $\Omega$ is a bounded open subset of $\mathbb{R}^{N}$, $N\gt 2$, $Q$ is the cylinder $\Omega \times (0,T)$, $T\gt 0$, $\Gamma$ the lateral surface $\partial \Omega \times (0,T)$, $2\leq p\lt N$, $a(x,t)$ and $b(x,t)$ are positive measurable bounded functions, $q\geq 0$, $0\leq\gamma\lt 1$, and $f$ non-negative function belongs to the Lebesgue space $L^{m}(Q)$ with $m\gt 1$, and $u_{0}\in L^{\infty}(\Omega)$ such that $\$\forall\omega\subset\subset\Omega\, \exists D_{\omega}\gt 0:\, u_{0}\geq D_{\omega}\text{ in }\omega.\$$ More precisely, we study the interaction between the term $u^{q}$ $(q>0)$ and the singular lower order term $d(x,t)|\nabla u|^{p}u^{-\gamma}$ $(0\lt\gamma\lt 1)$ in order to get a solution to the above problem. The regularizing effect of the term $u^q$ on the regularity of the solution and its gradient is also analyzed.
- ArtykułOtwarty dostępFinitely additive functions in measure theory and applications(Wydawnictwa AGH, 2024) Alpay, Daniel; Jorgensen, PalleIn this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory, in particular, to the study of $\mu$-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures $\mu$ , and to adjoints of composition operators.
- ArtykułOtwarty dostępGeometric properties of the lattice of polynomials with integer coefficients(Wydawnictwa AGH, 2024) Lipnicki, Artur; Śmietański, Marek J.This paper is related to the classic but still being examined issue of approximation of functions by polynomials with integer coefficients. Let $r$, $n$ be positive integers with $n \ge 6r$. Let $\boldsymbol{P}_n \cap \boldsymbol{M}_r$ be the space of polynomials of degree at most $n$ on $[0,1]$ with integer coefficients such that $P^{(k)}(0)/k!$ and $P^{(k)}(1)/k!$ are integers for $k=0,\dots,r-1$ and let $\boldsymbol{P}_n^\mathbb{Z} \cap \boldsymbol{M}_r$ be the additive group of polynomials with integer coefficients. We explore the problem of estimating the minimal distance of elements of $\boldsymbol{P}_n^\mathbb{Z} \cap \boldsymbol{M}_r$ from $\boldsymbol{P}_n \cap \boldsymbol{M}_r$ in $L_2(0,1)$. We give rather precise quantitative estimations for successive minima of $\boldsymbol{P}_n^\mathbb{Z}$ in certain specific cases. At the end, we study properties of the shortest polynomials in some hyperplane in $\boldsymbol{P}_n \cap \boldsymbol{M}_r$.
- ArtykułOtwarty dostępGraphs whose vertex set can be partitioned into a total dominating set and an independent dominating set(Wydawnictwa AGH, 2024) Haynes, Teresa W.; Henning, Michael A.A graph $G$ whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield infinite families of graphs that are not TI-graphs. We study regular graphs that are TI-graphs. Among other results, we prove that all toroidal graphs are TI-graphs.
- ArtykułOtwarty dostępJan Stochel, a stellar mathematician(Wydawnictwa AGH, 2024) Chavan, Sameer; Curto, Raúl; Jabłoński, Zenon Jan; Jung, Il Bong; Putinar, MihaiThe occasion for this survey article was the 70th birthday of Jan Stochel, professor at Jagiellonian University, former head of the Chair of Functional Analysis and a prominent member of the Kraków school of operator theory. In the course of his mathematical career, he has dealt, among other things, with various aspects of functional analysis, single and multivariable operator theory, the theory of moments, the theory of orthogonal polynomials, the theory of reproducing kernel Hilbert spaces, and mathematical aspects of quantum mechanics.
- ArtykułOtwarty dostępA note on the general moment problem(Wydawnictwa AGH, 2024) El Azhar, Hamza; Hanine, Abdelouahab; Zerouali, El HassanIn this note we show that given an indeterminate Hamburger moment sequence, it is possible to perturb the first moment in such way that the obtained sequence remains an indeterminate Hamburger moment sequence. As a consequence we prove that every sequence of real numbers is a moment sequence for a signed discrete measure supported in $\mathbb{R}_{+}$.
- ArtykułOtwarty dostępOn the Möbius invariant principal functions of Pincus(Wydawnictwa AGH, 2024) Ghosh, Sagar; Misra, GadadharIn this semi-expository short note, we prove that the only homogeneous pure hyponormal operator $T$ with $\operatorname{rank} (T^*T-TT^*) =1$, modulo unitary equivalence, is the unilateral shift.
- ArtykułOtwarty dostępOn the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data(Wydawnictwa AGH, 2024) Taourirte, Laila; Charkaoui, Abderrahim; Alaa, Nour EddineWe analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and $L^1$ data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder's topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.
- CzasopismoOpuscula MathematicaAGH University Press (2005-)
ISSN: 1232-9274 e-ISSN: 2300-6919 - Rocznik czasopismaOpuscula MathematicaVol. 29 (2009)
- Numer czasopismaOpuscula Mathematica2009 - Vol. 29 - No. 1
- Numer czasopismaOpuscula Mathematica2009 - Vol. 29 - No. 3
- Numer czasopismaOpuscula Mathematica2009 - Vol. 29 - No. 4
- Numer czasopismaOpuscula Mathematica2009 - Vol. 29 - No. 2
- Numer czasopismaOpuscula Mathematica2008 - Vol. 28 - No. 1
- Numer czasopismaOpuscula Mathematica2008 - Vol. 28 - No. 4
- Numer czasopismaOpuscula Mathematica2008 - Vol. 28 - No. 3
- Rocznik czasopismaOpuscula MathematicaVol. 28 (2008)