Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In pa...

Abstract A well-known conjecture of Gilbreath, and independently Proth from the 1800s, states that if $$a_{0,n} = p_n$$ a 0 , n = p denotes n th prime number $$a_{i,n} |a_{i-1,n}-...

Let p n : C <mml:mo stretch...

In this paper, we are interested in studying the set $$\mathcal {A}_{\Vert \cdot \Vert }(X, Y)$$ of all norm-attaining operators T from X into Y satisfying following: given $$\varepsilon >0$$ , there exists $$\eta $$ such that if $$\Vert Tx\Vert > 1 - \eta then is $$x_0$$ x_0 x\Vert < \varepsilon and itself attains its norm at . We show every one functional on $$c_0$$ which belongs to }(c_0, \m...

Consider the generalized absolute value function defined by $$a(t) = \left| t \right|{t^{n - 1}},\,\,\,\,\,t \in \mathbb{R},n {\mathbb{N}_{\ge 1}}.$$ . Further, consider n-th order divided difference a[n]: ℝn+1 → ℂ and let 1 < p1, …, pn ∞ be such that $$\sum\nolimits_{l 1}^n {p_l^{- 1} $$ Let $${{\cal S}_{{p_l}}}$$ denote Schatten-von Neumann ideals S}_{1,\infty}}$$ weak trace class ideal. We s...

This is the third paper in a series which we develop machine learning (ML) moment closure models for radiative transfer equation. In our previous work (Huang et al. J Comput Phys 453:110941, 2022), proposed an approach to learn gradient of unclosed high order moment, performs much better than itself and conventional $$P_N$$ closure. However, while ML has accuracy, it not able guarantee hyperbol...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

Given two graphs G and H, the Ramsey number R(G, H) is minimum integer N such that any coloring of edges $$K_N$$ in red or blue yields a H. Let $$\chi (G)$$ be chromatic G, s(G) denote surplus cardinality color class taken over all proper colorings with colors. A connected graph called H-good if $$R(G,H)=(v(G)-1)(\chi (H)-1)+s(H)$$ . Chvátal (J. Graph Theory 1:93, 1977) showed tree $$K_m$$ -goo...

Abstract In this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g h , where is normalized, moderate growth, $$0&lt;h(n) \le h(n+1)$$ 0 &lt; h ( n ) ≤</m...