Let (M, g) be a closed locally conformally flat Riemannian manifold of dimension $$n \ge 7$$ and positive Yamabe type. If $$h \in C^1(M)$$ $$\xi _0$$ is non-degenerate critical point the mass function we prove existence, for any $$ k 1$$ blowing-up solution $$u_\varepsilon $$\begin{aligned} \triangle _g u_\varepsilon +\big ( c_n S_g +\varepsilon h\big ) = ^{2^*-1} \end{aligned}$$ that blows up,...

In this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. The first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. They improve thecorresponding  conclusions in the literature.

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along crystalline $a$ axis on newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. our study, when is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\si...

We consider a 2D smectics model \begin{equation*} E_{\epsilon }\left( u\right) =\frac{1}{2}\int_\Omega \frac{1}{\varepsilon u_{z}-\frac{1% }{2}u_{x}^{2}\right) ^{2}+\varepsilon \left( u_{xx}\right) ^{2}dx\,dz. \end{equation*} For $\varepsilon _{n}\rightarrow 0$ and sequence $\left\{ u_{n}\right\} $ with bounded energies $E_{\varepsilon _{n}}\left(u_{n}\right) ,$ we prove compactness of $\{\part...

In this paper, we consider the problem of maximizing a monotone submodular function subject to knapsack constraint in streaming setting. such setting, elements arrive sequentially and at any point time, algorithm can store only small fraction that have arrived so far. For special case all unit sizes (i.e., cardinality-constraint case), one find $$(0.5-\varepsilon )$$ -approximate solution $$O(K...

Abstract A bipartite graph $H = \left (V_1, V_2; E \right )$ with $\lvert V_1\rvert + \lvert V_2\rvert n$ is semilinear if $V_i \subseteq \mathbb {R}^{d_i}$ for some $d_i$ and the edge relation consists of pairs points $(x_1, x_2) \in V_1 \times V_2$ satisfying a fixed Boolean combination s linear equalities inequalities in $d_1 d_2$ variables . We show that k , number edges $K_{k,k}$ -free H a...

For the Landau-de Gennes functional on 3D domains, $$\begin{aligned} I_\varepsilon (Q,\Omega ):=\int _{\Omega }\left\{ \frac{1}{2}|\nabla Q|^2+\frac{1}{\varepsilon ^2}\left( -\frac{a^2}{2}\mathrm {tr}(Q^2)-\frac{b^2}{3}\mathrm {tr}(Q^3)+\frac{c^2}{4}[\mathrm {tr}(Q^2)]^2 \right) \right\} \,dx, \end{aligned}$$ it is well-known that under suitable boundary conditions, global minimizer $$Q_\vareps...

We study the renormalisation of non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with interaction $\phi^2(i\phi)^\varepsilon$ using Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve Wetterich equation local potential approximation, both ultraviolet regime loop expansion. calculate scale-dependent effective its infrared limit. The is found ...