In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

$S$ = 1/2 Ising kagome antiferromagnets (KAFs) are rare in reality. In this work, we report the magnetic ground state and field-induced transitions of an antiferromagnet with a stacked geometry, Na$_5$Co$_{15.5}$Te$_6$O$_{36}$. Upon cooling, susceptibility measurement reveals three successive at $T_1$ 45.2 K, $T_2$ 35.4 $T_3 \sim$ 20 K. When field is applied along $c$ axis, strikingly anomalous...

Groundstate magnetism of the one-band Hubbard model on frustrated square lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$ hoppings are considered at half-filling revisited within mean field approximation. Two new magnetic phases detected intermediate strength $U$ relative strong frustration $t_2/t_1$, named double-stripe plaquette antiferromagnetic states, which metal...

We consider $$u(t,x)=(u_1(t,x),\cdots ,u_d(t,x))$$ the solution to a system of non-linear stochastic heat equations in spatial dimension one driven by d-dimensional space-time white noise. prove that, when $$d\le 3$$ , local time $$L(\xi ,t)$$ $$\{u(t,x)\,,\;t\in [0,T]\}$$ exists and $$L(\cdot ,t) $$ belongs a.s. Sobolev space H^{\alpha }({\mathbb {R}}^d)$$ for $$\alpha <\frac{4-d}{2}$$ $$d\ge ...

$S$ = 1/2 Ising kagome antiferromagnets (KAFs) are rare in reality. In this work, we report the magnetic ground state and field-induced transitions of an antiferromagnet with a stacked geometry, Na$_5$Co$_{15.5}$Te$_6$O$_{36}$. Upon cooling, susceptibility measurement reveals three successive at $T_1$ 45.2 K, $T_2$ 35.4 $T_3 \sim$ 20 K. When field is applied along $c$ axis, strikingly anomalous...

Let \(a,n \in \mathbb Z^+\), with \(a<n\) and \(\gcd (a,n)=1\). \(P_{a,n}\) denote the lattice parallelogram spanned by (1, 0) (a, n), that is, $$P_{a,n} = \left\{ t_1(1,0)+ t_2(a,n) \, : 0\le t_1,t_2 \le 1 \right\} , $$ and let $$V(a,n) \# \text { of visible points in interior } P_{a,n}.$$ In this paper we prove some elementary (and straightforward) results for V(a, n). The most ...