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 ...

In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and a kind of convergence space V. A V is called semi-order (in short space), if there exist an W operator T from into W. way, say that with respect to \(\{W, T\}\). net \(\{x_\alpha \}\subseteq V\) said be \({\{W,T\}}\)-order convergent \(x\in write \(x_\alpha \xrightarrow {\{W, T\}}x\)), wheneve...

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 ...

Abstract The anisotropic microstructure of white matter is reflected in various MRI contrasts. Transverse relaxation rates can be probed as a function fibre-orientation with respect to the main magnetic field, while diffusion properties are an encoding gradient. While latter easy obtain by varying orientation gradient, field fixed, obtaining former requires re-orienting head. In this work we de...

Digital signature schemes in general and representative collective digital schemes, particular, are often built based on the difficulty of discrete logarithm problem finite field, elliptic curve, factor analysis, finding roots modulo large primes or a combination difficult problems mentioned above. In this paper, we use new problem, which is to find with root ground field GF(p) build but chosen...

Our aim is the development and analysis of numerical schemes for approximately solving backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two levels, i.e., $u(T_1)$ $u(T_2)$, we simultaneously recover initial data $u(0)$ $u_t(0)$ hence solution $u(t)$ all $t > 0$. First, existence, uniqueness, Lipschitz stab...