Abstract This paper consists of three parts: First, letting $b_1(z)$ , $b_2(z)$ $p_1(z)$ and $p_2(z)$ be nonzero polynomials such that have the same degree $k\geq 1$ distinct leading coefficients $1$ $\alpha$ respectively, we solve entire solutions Tumura–Clunie type differential equation $f^{n}+P(z,\,f)=b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}$ where $n\geq 2$ is an integer, $P(z,\,f)$ a polynomial i...

The bow-tie product is a newly named binary operation on graphs. In this article, we present some properties of the graphs, as well results both harmonic centrality and centralization path \(P_2\) with any \(P_m\), cycle \(C_m\), star \(S_m\), fan \(F_m\), wheel \(W_m\).

In two dimensional digital geometry, lattice points are 4-connected (resp. 8-connected) if their Euclidean distance is at most one \(\sqrt{2}\)). A set \(S \subset \mathbb {Z}^2\) for all pair of \(p_1, p_2\) in S there a path connecting \(p_1\) to \(p_2\) such that every edge consists points. The original definition convexity which states {Z}^d\) convex \(\mathrm {conv}(S) \cap {Z}^d= S\), whe...

In this paper, we classify the solution of following mixed-order conformally invariant system with coupled nonlinearity in $ \mathbb{R}^4 $: \begin{equation} \left\{ \begin{split} & -\Delta u(x) = u^{p_1}(x) e^{q_1v(x)}, \quad x\in \mathbb{R}^4, \\ (-\Delta)^2 v(x) u^{p_2}(x) e^{q_2v(x)}, \end{split} \right. \end{equation}\;\;\;\;\;\;(1) where 0\leq p_1 < 1 $, p_2 >0 q_1 > 0 q_2 \g...

We investigate the complexity of Boolean clone membership problem (CMP): given a set functions $F$ and function $f$, determine if $f$ is in generated by $F$, i.e., it can be expressed circuit with $F$-gates. Here, elements are as circuits or formulas over usual De Morgan basis. B\"ohler Schnoor (2007) proved that for any fixed coNP-complete, few exceptions where P. Vollmer (2009) incorrectly cl...

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential number correlation functions, $R_{2} \left( \Delta \eta, \varphi \right)$, transverse momentum $P_2 \right)$ charged particles produced in \PbPb\ collisions at the LHC centre-of-mass energy $\sqrt{s_{\rm NN}} =$ 2.76 TeV with UrQMD, AMPT EPOS models. Model predictions for $R_2$ $P_2$ functions are p...

We present an analysis of the subpulse drift in PSR J1750-3503, which is characterized by abrupt transitions direction. As pulsar does not exhibit other mode changes or clear nulling, it ideal candidate system for studying phenomenon direction change. For $\sim 80\%$ time subpulses are positive - from early to later longitudes while negative 20\%$. The separation single pulses with drift, $P_2=...

We show that if $$N \geq {\rm exp}({\rm exp} (k^{O(1)})))$$ , then any k-colouring of the primes are less than N contains a monochromatic solution to $$p_1 - p_2 = p_3 -1$$ .