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922. On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearityMin Zhao, Yueqiang Song, Dušan Repovš, 2024, original scientific article Abstract: In this article, we deal with the following $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: $ M\left([u]_{s,A}^{p}\right)(-\Delta)_{p, A}^{s} u+V(x)|u|^{p-2} u=\lambda\left(\int_\limits{\mathbb{R}^{N}} \frac{|u|^{p_{\mu, s}^{*}}}{|x-y|^{\mu}} \mathrm{d}y\right)|u|^{p_{\mu, s}^{*}-2} u+k|u|^{q-2}u,\ x \in \mathbb{R}^{N},$ where $0 < s < 1 < p$, $ps < N$, $p < q < 2p^{*}_{s,\mu}$, $0 < \mu < N$, $\lambda$ and $k$ are some positive parameters, $p^{*}_{s,\mu}=\frac{pN-p\frac{\mu}{2}}{N-ps}$ is the critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, and functions $V$, $M$ satisfy the suitable conditions. By proving the compactness results using the fractional version of concentration compactness principle, we establish the existence of nontrivial solutions to this problem.
Keywords: Hardy-Littlewood-Sobolev nonlinearity, Schrödinger-Kirchhoff equations, variational methods, electromagnetic fields
Published in DiRROS: 16.02.2024; Views: 294; Downloads: 109
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923. Nodal solutions for Neumann systems with gradient dependenceKamel Saoudi, Eadah Alzahrani, Dušan Repovš, 2024, original scientific article Abstract: We consider the following convective Neumann systems: $\begin{equation*}\left(\mathrm{S}\right)\qquad\left\{\begin{array}{ll}-\Delta_{p_1}u_1+\frac{|\nabla u_1|^{p_1}}{u_1+\delta_1}=f_1(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega,\\ -\Delta _{p_2}u_2+\frac{|\nabla u_2|^{p_2}}{u_2+\delta_2}=f_2(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega, \\ |\nabla u_1|^{p_1-2}\frac{\partial u_1}{\partial \eta }=0=|\nabla u_2|^{p_2-2}\frac{\partial u_2}{\partial \eta} \text{on}\;\partial\,\Omega,\end{array}\right.\end{equation*}$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ ($N\geq 2$) with a smooth boundary $\partial\,\Omega, \delta_1, \delta_2 > 0$ are small parameters, $\eta$ is the outward unit vector normal to $\partial\,\Omega, f_1, f_2: \Omega \times \mathbb{R}^2 \times \mathbb{R}^{2N} \rightarrow \mathbb{R}$ are Carathéodory functions that satisfy certain growth conditions, and $\Delta _{p_i}$ ($1< p_i < N,$ for $i=1,2$) are the $p$-Laplace operators $\Delta _{p_i}u_i=\mathrm{div}(|\nabla u_i|^{p_i-2}\nabla u_i)$, for $u_i \in W^{1,p_i}(\Omega).$ In order to prove the existence of solutions to such systems, we use a sub-supersolution method. We also obtain nodal solutions by constructing appropriate sub-solution and super-solution pairs. To the best of our knowledge, such systems have not been studied yet.
Keywords: Neumann elliptic systems, gradient dependence, subsolution method, supersolution method, nodal solutions
Published in DiRROS: 16.02.2024; Views: 280; Downloads: 105
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924. Quasi-copulas as linear combinations of copulasGregor Dolinar, Bojan Kuzma, Nik Stopar, 2024, original scientific article Abstract: We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernández-Sánchez, Quesada-Molina, and Úbeda-Flores who considered linear combinations of discrete copulas.
Keywords: quasi-copulas, copulas, linear combination, affine combination, Minkowski norm
Published in DiRROS: 16.02.2024; Views: 248; Downloads: 92
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926. Resolvability and convexity properties in the Sierpiński product of graphsMichael A. Henning, Sandi Klavžar, Ismael G. Yero, 2024, original scientific article Abstract: Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H$ associated with the vertices $g$ and $g'$ of $G$, respectively, of the form $(g,f(g'))(g',f(g))$. The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex.
Keywords: Sierpiński product of graphs, metric dimension, trees, convex subgraph
Published in DiRROS: 16.02.2024; Views: 263; Downloads: 115
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927. Tumor vaccinesMojca Frank Bertoncelj, Alojz Ihan, 2006, review article Abstract: Tumor vaccines have several potential advantages over standard anticancer regirrcents. They represent highly specific anticancer therapy. Inducing tumor-specific memory T-lymphocytes, they have potential for long-lived antitumor effects. However, clinical trials, in which cancer patients were vaccinated with tccmor aaccines, have been so far mainly disappointing. There are many reasons for the inefficiency of tumor vaccines. Most cancer antigens are normal self-molecules to which imrrtune tolerance exists. That is why the population of tumor-specific lymphocytes is represented by a small number of low-affinity T-lymphocytes that induce weak antitumor immune response. Simultaneously, tumors evolve many mechanisms to actively evade immune system,what makes them poorly immunogenic or even tolerogenic. Novel irrtmunotherapeutic strategies are directed toward breaking immune tolerance to tumor antigens, enhancing immunogenicity of tumor vaccines and overcoming mechanisms of tumor escape. There are several approaches, unfortunately, all of them still far away from an ideal tumor vaccine that would reject a tumor. Difficulties in the activation of antitumor immune response by tumor vaccines have led to the development of alternative immunotherapeutic strategies that directly focus on effector mechanisms of immune system (adoptive tumor-specific T-lymphocyte transfer and tumor specific monoclonal antibodies).
Published in DiRROS: 15.02.2024; Views: 214; Downloads: 59
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928. Electrochemotherapy of tumoursGregor Serša, Maja Čemažar, Damijan Miklavčič, Zvonimir Rudolf, 2006, review article Abstract: Electroehemotherapy consists of chemotherapy followed by local application of electrie pulses to the tumour to increase drug delivery into cells. Drug uptake can be inereased by electroporation for only those drugs whose transport through the plasma membrane is impeded. Among many drugs that have been tested so far, only bleomycin and cisplatin found their way from preclinical testing to clinical trials. In vitro studies demonstrated several fold inerease of their cytotoxicity after electroporation of cells. In vivo, electroporation of tumours after local or systemic administration of either ofthe drugs, i.e. electrochemotherapy, proved to be an effective antitumour treatment. In preclinical studies on several tumour models, electrochemotherapy either with bleomycin or cisplatin was elaborated and parameters for effective local tumour control were determined. In veterinary medicine, electrochemotherapy also proved to be effective in the treatment of primary tumours in cats, dogs and horses. In human clinical studies, electrochemotherapy was performed on the patients with progressive disease andaccessible tumour nodules of different malignancies. All clinical studies demonstrated that electrochemotherapy is an effective treatment for local tumour control in cancer patients.
Published in DiRROS: 15.02.2024; Views: 236; Downloads: 67
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930. The role of p38 MAP kinase in cancer cell apoptosisMetka Lenassi, Ana Plemenitaš, 2006, review article Abstract: Background. Cellular behaviour in response to many extracellular stimuli is mediated through MAP kinase signalling pathways. p38 MAP kinase that is represented in mammals by four isoforms (p38alfa, p38beta, p38gama and p38delta) is one of the four main subgroups of MAP kinases. Recent studies show that p38 activation is necessary for cancer cell death initiated by variety of anti-cancer agents. This finding connected cancer therapies previously considered to be mechanistically unrelated and raised the possibility of developing anti-cancer agents that lack the side effects causedby events upstream of p38 MAPK Many of the details of p38 induced apoptosis still need to be elucidated. Since most of the past studies rely only on the cell culture models, all the results have to be verified using in vivo models. Also very little is known about the role of p38 mediated apoptosis on non-neoplastic cells in response to anti-cancer agents. Conclusion. Although p38 activation of cancer cell apoptosis is a very complexprocess, recent studies indicate a good starting point for new strategies that would increase the efficiency and decrease the toxicity of proven therapies.
Published in DiRROS: 15.02.2024; Views: 202; Downloads: 44
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