<abstract><p>The zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by ^0R_{\alpha}(G) is the sum items (d_{v})^{\alpha} over all vertices v\in V_G where \alpha a pertinently chosen real number. In this paper, we obtain sharp upper and lower bounds on ^0R_{\alpha} trees with given domination number \gamma for \alpha\in(-\infty, 0)\cup(1, \infty) \alpha\in(0, 1) r...

We investigate the nonnegative solutions to nonlinear integral inequality $u \ge I_{\alpha}\ast\big((I_\beta \ast u^p)u^q\big)$ a.e. in $\mathbb{R}^N$, where $\alpha, \beta\in (0,N)$, $p, q>0$ and $I_\alpha$, $I_\beta$ denote Riesz potentials of order $\alpha$ $\beta$ respectively. Our approach relies on a nonlocal positivity principle which allows us derive optimal ranges for parameters $\alph...

<abstract><p>Let $ A(G) and D(G) be the adjacency matrix degree diagonal of a graph G $, respectively. For any real number \alpha \in[0, 1] Nikiforov defined A_{\alpha} $-matrix as A_{\alpha}(G) = D(G)+(1-\alpha)A(G) $. Let S_k(A_{\alpha}(G)) sum k largest eigenvalues In this paper, some bounds on are obtained, which not only extends results signless Laplacian matrix, but it also gi...

Lowest energy spectrum of the $^{12}$C nucleus is analyzed in 3$\alpha$ cluster model with a deep $\alpha\alpha$-potential Buck, Friedrich and Wheatley Pauli forbidden states $S$ $D$ waves. The direct orthogonalization method applied for elimination 3$\alpha$-Pauli states. effects possible first order quantum phase transition are shown lowest $^{12}$C($0_1^+)$ $^{12}$C($2_1^+)$ from weakly boun...

We study structures of the $0^+$ states $^{13}_\Lambda$C within framework $\alpha+\alpha+\alpha+\Lambda$ four-body orthogonality condition model with Gaussian expansion method. obtain five and compare them low-lying four $^{12}$C. find that $0_1^+$, $0_2^+$ $0_4^+$ correspond to $^{12}$C, respectively. also both $0_3^+$ $0_5^+$ have analogous nature state where additional $\Lambda$ particle cou...

The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = \alpha J_1$ second neighbors. supports both gapless quantum phases nondegenerate ground states gapped $\Delta(\alpha) doubly degenerate states. Exact thermodynamics limited to $\alpha 0$, the linear Heisenberg antiferromagnet (HAF). diagonalization of small systems at f...

Alpha-thalassemia (α-thal) is probably the most prevalent monogenic condition in the world. Deletions are the most common types of mutations in α-thal, followed by point mutations and small insertion/deletion. In the context of national screening program for prevention of thalassemia and hemoglobinopathies in Iran, α-thal carriers have come to more attention. Therefore, the fr...